diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..e43b0f9 --- /dev/null +++ b/.gitignore @@ -0,0 +1 @@ +.DS_Store diff --git a/Project#01/README.md b/Project#01/README.md index fa0e147..b6a1d47 100644 --- a/Project#01/README.md +++ b/Project#01/README.md @@ -1,10 +1,7 @@ -# TODO: -- [ ] Add embedded equations -- [ ] Add hints and solutions for each step -- [ x ] Add input/output links for test cases - # Molecular-Geometry-Analysis -The purpose of this project is to introduce you to fundamental C-language (or C++) programming techniques in the context of a scientific problem, viz. the calculation of the internal coordinates (bond lengths, bond angles, dihedral angles), moments of inertia, and rotational constants of a polyatomic molecule. A concise set of instructions for this project may be found [here](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2301/project1-instructions.pdf). +The purpose of this project is to introduce you to fundamental C-language (or C++) programming techniques in the context of a scientific problem, viz. the calculation of the internal coordinates (bond lengths, bond angles, dihedral angles), moments of inertia, and rotational constants of a polyatomic molecule. A concise set of instructions for this project may be found [here](./project1-instructions.pdf). + +We thank Dr. Yukio Yamaguchi of the University of Georgia for the original version of this project. ## Step 1: Read the Coordinate Data from Input The input to the program is the set of Cartesian coordinates of the atoms (in bohr) and their associated atomic numbers. A sample molecule (acetaldehyde) to use as input to the program is: @@ -18,133 +15,116 @@ The input to the program is the set of Cartesian coordinates of the atoms (in bo 1 -1.007295466862 -1.669971842687 -0.705916966833 1 -1.007295466862 1.669971842687 -0.705916966833 -The first line above is the number of atoms (an integer), while the remaining lines contain the z-values and x-, y-, and z-coordinates of each atom (one integer followed by three double-precision floating-point numbers). This [input file](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2301/input/acetaldehyde.dat) ("acetaldehyde.dat") along with a few other test cases can be found in this repository in the [input directory](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2301/input). +The first line above is the number of atoms (an integer), while the remaining lines contain the z-values and x-, y-, and z-coordinates of each atom (one integer followed by three double-precision floating-point numbers). This [input file](./input/acetaldehyde.dat) ("acetaldehyde.dat") along with a few other test cases can be found in this repository in the [input directory](./input). After downloading the file to your computer (to a file called “geom.dat”, for example), you must open the file, read the data from each line into appropriate variables, and finally close the file. -- Hint #1: Opening and closing the file stream -- Hint #2: Reading the number of atoms -- Hint #3: Storing the z-values and the coordinates -- Solution +- [Hint #1](./hints/hint1-1.md): Opening and closing the file stream +- [Hint #2](./hints/hint1-2.md): Reading the number of atoms +- [Hint #3](./hints/hint1-3.md): Storing the z-values and the coordinates +- [Solution](./hints/step1-solution.md) ## Step 2: Bond Lengths Calculate the interatomic distances using the expression: -``` -EQUATION -``` + where x, y, and z are Cartesian coordinates and i and j denote atomic indices. -- Hint 1: Memory allocation -- Hint 2: Loop structure -- Hint 3: Printing the results -- Hint 4: Extending the Molecule class -- Solution +- [Hint 1](./hints/hint2-1.md): Memory allocation +- [Hint 2](./hints/hint2-2.md): Loop structure +- [Hint 3](./hints/hint2-3.md): Printing the results +- [Hint 4](./hints/hint2-4.md): Extending the Molecule class +- [Solution](./hints/step2-solution.md) ## Step 3: Bond Angles Calculate all possible bond angles. For example, the angle, φijk, between atoms i-j-k, where j is the central atom is given by: -``` -EQUATION -``` + -where the e⃗ij are unit vectors between the atoms, e.g., +where the eij are unit vectors between the atoms, e.g., -``` -EQUATION -``` + -- Hint 1: Memory allocation for the unit vectors -- Hint 2: Avoiding a divide-by-zero -- Hint 3: Memory allocation for the bond angles -- Hint 4: Smart printing -- Hint 5: Trigonometric functions -- Solution +- [Hint 1](./hints/hint3-1.md): Memory allocation for the unit vectors +- [Hint 2](./hints/hint3-2.md): Avoiding a divide-by-zero +- [Hint 3](./hints/hint3-3.md): Memory allocation for the bond angles +- [Hint 4](./hints/hint3-4.md): Smart printing +- [Hint 5](./hints/hint3-5.md): Trigonometric functions +- [Solution](./hints/step3-solution.md) ## Step 4: Out-of-Plane Angles Calculate all possible out-of-plane angles. For example, the angle θijkl for atom i out of the plane containing atoms j-k-l (with k as the central atom, connected to i) is given by: -``` -EQUATION -``` + -- Hint 1: Memory allocation? -- Hint 2: Cross products -- Hint 3: Numerical precision -- Hint 4: Smarter printing -- Solution +- [Hint 1](./hints/hint4-1.md): Memory allocation? +- [Hint 2](./hints/hint4-2.md): Cross products +- [Hint 3](./hints/hint4-3.md): Numerical precision +- [Hint 4](./hints/hint4-4.md): Smarter printing +- [Solution](./hints/step4-solution.md) ## Step 5: Torsion/Dihedral Angles Calculate all possible torsional angles. For example, the torsional angle τijkl for the atom connectivity i-j-k-l is given by: -``` -EQUATION -``` + Can you also determine the sign of the torsional angle? -- Hint 1: Memory allocation? -- Hint 2: Numerical precision -- Hint 3: Smart printing -- Hint 4: Sign -- Solution +- [Hint 1](./hints/hint5-1.md): Memory allocation? +- [Hint 2](./hints/hint5-2.md): Numerical precision +- [Hint 3](./hints/hint5-3.md): Smart printing +- [Hint 4](./hints/hint5-4.md): Sign +- [Solution](./hints/step5-solution.md) ## Step 6: Center-of-Mass Translation Find the center of mass of the molecule: -``` -EQUATION -``` + where mi is the mass of atom i and the summation runs over all atoms in the molecule. Translate the input coordinates of the molecule to the center-of-mass. -- Hint 1: Atomic masses -- Hint 2: Translating between atomic number and atomic mass -- Solution +- [Hint 1](./hints/hint6-1.md): Atomic masses +- [Hint 2](./hints/hint6-2.md): Translating between atomic number and atomic mass +- [Solution](./hints/step6-solution.md) ## Step 7: Principal Moments of Inertia Calculate elements of the [moment of inertia tensor](http://en.wikipedia.org/wiki/Moment_of_inertia_tensor). Diagonal: -``` -EQUATION -``` -Off-diagonal: -``` -EQUATION -``` + + +Off-diagonal (add a negative sign): + + Diagonalize the inertia tensor to obtain the principal moments of inertia: -``` -EQUATION -``` + + Report the moments of inertia in amu bohr2, amu Å2, and g cm2. Based on the relative values of the principal moments, determine the [molecular rotor type](http://en.wikipedia.org/wiki/Rotational_spectroscopy): linear, oblate, prolate, asymmetric. -- Hint 1: Diagonalization of a 3×3 matrix -- Hint 2: Physical constants -- Solution +- [Hint 1](./hints/hint7-1.md): Diagonalization of a 3×3 matrix +- [Hint 2](./hints/hint7-2.md): Physical constants +- [Solution](./hints/step7-solution.md) ## Step 8: Rotational Constants Compute the rotational constants in cm-1 and MHz: -``` -EQUATION -``` + -- Solution +- [Solution](./hints/step8-solution.md) ## Test Cases -- Acetaldehyde: [input coordinates](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2301/input/acetaldehyde.dat) | [output](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2301/output/acetaldehyde_out.txt) -- Benzene: [input coordinates](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2301/input/benzene.dat) | [output](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2301/output/benzene_out.txt) -- Allene: [input coordinates](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2301/input/allene.dat) | [output](https://github.com/CrawfordGroup/ProgrammingProjects/blob/master/Project%2301/output/allene_out.txt) +- Acetaldehyde: [input coordinates](./input/acetaldehyde.dat) | [output](./output/acetaldehyde_out.txt) +- Benzene: [input coordinates](./input/benzene.dat) | [output](./output/benzene_out.txt) +- Allene: [input coordinates](./input/allene.dat) | [output](./output/allene_out.txt) ## References E.B. Wilson, J.C. Decius, and P.C. 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file mode 100644 index 0000000..7ae4d3b --- /dev/null +++ b/Project#01/hints/hint1-1.md @@ -0,0 +1,20 @@ +To open a file named "geom.dat", you need a file stream object: + +```c++ +#include +#include +#include + +... + +int main() +{ + ifstream input("geom.dat"); + + ... + + input.close(); + + return 0; +} +``` diff --git a/Project#01/hints/hint1-2.md b/Project#01/hints/hint1-2.md new file mode 100644 index 0000000..7fa15f6 --- /dev/null +++ b/Project#01/hints/hint1-2.md @@ -0,0 +1,21 @@ +Use the ">>" operator to read the data from the file: + +```c++ +#include +#include +#include + +... + +int main() +{ + ifstream input("geom.dat"); + + int natom; + input >> natom; + + input.close(); + + return 0; +} +``` diff --git a/Project#01/hints/hint1-3.md b/Project#01/hints/hint1-3.md new file mode 100644 index 0000000..ecd2d17 --- /dev/null +++ b/Project#01/hints/hint1-3.md @@ -0,0 +1,20 @@ +It may be convenient to use arrays to store the z-values and Cartesian coordinates of the atoms: +```c++ +int zval[50]; +double x[50], y[50], z[50]; +``` + +A more elegant solution is to allocate the memory dynamically for each array once you know the number of atoms: +```c++ +int natom; +input >> natom; + +int *zval = new int[natom]; +double *x = new double[natom]; +double *y = new double[natom]; +double *z = new double[natom]; + +delete[] zval; delete[] x; delete[] y; delete[] z; +``` + +Don't forget to delete[] the memory after you're finished! diff --git a/Project#01/hints/hint2-1.md b/Project#01/hints/hint2-1.md new file mode 100644 index 0000000..68bb23c --- /dev/null +++ b/Project#01/hints/hint2-1.md @@ -0,0 +1,18 @@ +If we choose to store the matrix of bond distances, we need to allocate the necessary memory, either as a static two-dimensional array: +```c++ +double R[50][50]; +``` + +or via dynamic allocation using the [Molecule class](https://github.com/CrawfordGroup/ProgrammingProjects/wiki/Classes-and-Objects): +```c++ +double **R = new double* [mol.natom]; +for(int i=0; i < mol.natom; i++) + R[i] = new double[mol.natom]; +``` + +Don't forget to delete[] the memory at the end of the program: +```c++ +for(int i=0; i < mol.natom; i++) + delete[] R[i]; +delete[] R; +``` diff --git a/Project#01/hints/hint2-2.md b/Project#01/hints/hint2-2.md new file mode 100644 index 0000000..49dc043 --- /dev/null +++ b/Project#01/hints/hint2-2.md @@ -0,0 +1,15 @@ +To build the distance matrix, we need a loop for each index: +```c++ + ... + #include + ... + + for(int i=0; i < mol.natom; i++) { + for(int j=0; j < mol.natom; j++) { + R[i][j] = sqrt( (mol.geom[i][0]-mol.geom[j][0])*(mol.geom[i][0]-mol.geom[j][0]) + + (mol.geom[i][1]-mol.geom[j][1])*(mol.geom[i][1]-mol.geom[j][1]) + + (mol.geom[i][2]-mol.geom[j][2])*(mol.geom[i][2]-mol.geom[j][2]) ); + } + } +``` +Note also that the `sqrt()` function is part of the C math library; thus we need the `#include ` directive. diff --git a/Project#01/hints/hint2-3.md b/Project#01/hints/hint2-3.md new file mode 100644 index 0000000..30bbb93 --- /dev/null +++ b/Project#01/hints/hint2-3.md @@ -0,0 +1,7 @@ +To print the interatomic distance matrix, we could just run through its unique values: +```c++ + for(int i=0; i < mol.natom; i++) + for(int j=0; j < i; j++) + printf("%d %d %8.5f\n", i, j, R[i][j]); +``` +Note the conditional on the index `j` which keeps the code form printing redundant information. diff --git a/Project#01/hints/hint2-4.md b/Project#01/hints/hint2-4.md new file mode 100644 index 0000000..b7c4f47 --- /dev/null +++ b/Project#01/hints/hint2-4.md @@ -0,0 +1,11 @@ +Now that we've written some code to compute bond distances, we can extend the Molecule class a bit more to define our `bond()` function: +```c++ +double Molecule::bond(int a, int b) +{ + return sqrt( (geom[a][0]-geom[b][0])*(geom[a][0]-geom[b][0]) + + (geom[a][1]-geom[b][1])*(geom[a][1]-geom[b][1]) + + (geom[a][2]-geom[b][2])*(geom[a][2]-geom[b][2]) ); +} +``` + +Note that since `bond()` is a member function of the Molecule class, we can access the geom array with just `geom` rather than `mol.geom` diff --git a/Project#01/hints/hint3-1.md b/Project#01/hints/hint3-1.md new file mode 100644 index 0000000..8bc992a --- /dev/null +++ b/Project#01/hints/hint3-1.md @@ -0,0 +1,18 @@ +Each unit vector points from one atom to another, hence each Cartesian component should be treated as a matrix, much like the interatomic distance matrix. For now, let's store the unit vectors in memory, but later we'll write a function to recompute them as needed: +```c++ + double **ex = new double* [mol.natom]; + double **ey = new double* [mol.natom]; + double **ez = new double* [mol.natom]; + for(int i=0; i < mol.natom; i++) { + ex[i] = new double[mol.natom]; + ey[i] = new double[mol.natom]; + ez[i] = new double[mol.natom]; + } +``` +And don't forget to delete[] them at the end: +```c++ + for(int i=0; i < mol.natom; i++) { + delete[] ex[i]; delete[] ey[i]; delete[] ez[i]; + } + delete[] ex; delete[] ey; delete[] ez; +``` diff --git a/Project#01/hints/hint3-2.md b/Project#01/hints/hint3-2.md new file mode 100644 index 0000000..731dda4 --- /dev/null +++ b/Project#01/hints/hint3-2.md @@ -0,0 +1,10 @@ +Be careful about the diagonal elements of the unit vector matrices because of the division by the bond distance between atoms i and j. You should restrict the loops to skip those elements involving a divide-by-zero condition! +```c++ + for(i=0; i < mol.natom; i++) { + for(j=0; j < i; j++) { + ex[i][j] = ex[j][i] = -(x[i] - x[j])/R[i][j]; + ey[i][j] = ey[j][i] = -(y[i] - y[j])/R[i][j]; + ez[i][j] = ez[j][i] = -(z[i] - z[j])/R[i][j]; + } + } +``` diff --git a/Project#01/hints/hint3-3.md b/Project#01/hints/hint3-3.md new file mode 100644 index 0000000..f6f19ee --- /dev/null +++ b/Project#01/hints/hint3-3.md @@ -0,0 +1,10 @@ +If you choose to store the bond angles for later use (not absolutely necessary, as we'll see), you need a three-dimensional array: +```c++ + double ***phi = new double** [mol.natom]; + for(int i=0; i < mol.natom; i++) { + phi[i] = new double* [mol.natom]; + for(int j=0; j < mol.natom; j++) { + phi[i][j] = new double[mol.natom]; + } + } +``` diff --git a/Project#01/hints/hint3-4.md b/Project#01/hints/hint3-4.md new file mode 100644 index 0000000..766d3a9 --- /dev/null +++ b/Project#01/hints/hint3-4.md @@ -0,0 +1,22 @@ +If you print the angle between every possible combination of three atoms, you'll get lots of zeroes and angles between atoms that are far apart. To print mainly interesting angles, use if-else blocks to enforce these restrictions: +```c++ +if(i!=j && i!=k && j!=k) { } /* Skip coincidences */ +``` + +and +```c++ +if(i < j && j < k && R[i][j] < 4.0 && R[j][k] < 4.0) { } /* Skip atoms far apart (specifically with bond distances > 4.0 bohr) */ +``` + +Alternatively, you can limit the loop structure and just filter out the bond distances: +```c++ +for(int i=0; i < mol.natom; i++) { + for(int j=0; j < i; j++) { + for(int k=0; k < j; k++) { + if(R[i][j] < 4.0 && R[j][k] < 4.0) { + ... + } + } + } +} +``` diff --git a/Project#01/hints/hint3-5.md b/Project#01/hints/hint3-5.md new file mode 100644 index 0000000..c7f19d9 --- /dev/null +++ b/Project#01/hints/hint3-5.md @@ -0,0 +1 @@ +To compute the final bond angle, you must use the `acos()` function (arccos), which, like the `sqrt()` function, is part of the [C math library](http://en.wikipedia.org/wiki/Math.h). diff --git a/Project#01/hints/hint4-1.md b/Project#01/hints/hint4-1.md new file mode 100644 index 0000000..e1f85cd --- /dev/null +++ b/Project#01/hints/hint4-1.md @@ -0,0 +1 @@ +Note that, unlike the interatomic distance matrix and the three-dimensional bond angle array, the out-of-plane angles are not needed later in the program. Hence, there is no need to allocate any memory to store these angles. Simply print them one at a time. diff --git a/Project#01/hints/hint4-2.md b/Project#01/hints/hint4-2.md new file mode 100644 index 0000000..0cd31f4 --- /dev/null +++ b/Project#01/hints/hint4-2.md @@ -0,0 +1,10 @@ +A cross product between two vectors is another vector. Therefore, to store the cross product needed to compute a given out-of-plane angle, you need to store the x, y, and z components of the resulting vector, which you then use to compute a dot product with yet another vector. It is convenient to assign separate variables for each part of this calculation: +```c++ +ejkl_x = (ey[k][j] * ez[k][l] - ez[k][j] * ey[k][l]); +ejkl_y = (ez[k][j] * ex[k][l] - ex[k][j] * ez[k][l]); +ejkl_z = (ex[k][j] * ey[k][l] - ey[k][j] * ex[k][l]); + +exx = ejkl_x * ex[k][i]; +eyy = ejkl_y * ey[k][i]; +ezz = ejkl_z * ez[k][i]; +``` diff --git a/Project#01/hints/hint4-3.md b/Project#01/hints/hint4-3.md new file mode 100644 index 0000000..ab6b32b --- /dev/null +++ b/Project#01/hints/hint4-3.md @@ -0,0 +1,8 @@ +The final out-of-plane angle is computed using the `asin()` function. Note that since sine yields values between -1 and +1, the `asin()` function can only take arguments between -1.0 and +1.0. However, numerical precision in the calculation of the cross- and dot-products earlier in the calculation can yield results slightly outside this domain. Hence, you should test the argument of `asin()` before you call it: +```c++ + theta = (exx + eyy + ezz)/sin(phi[j][k][l]); + + if(theta < -1.0) theta = asin(-1.0); + else if(theta > 1.0) theta = asin(1.0); + else theta = asin(theta); +``` diff --git a/Project#01/hints/hint4-4.md b/Project#01/hints/hint4-4.md new file mode 100644 index 0000000..6aebb96 --- /dev/null +++ b/Project#01/hints/hint4-4.md @@ -0,0 +1,8 @@ +Just as for the bond angle code, we need to exclude ijkl combinations involving coincidences among the indices as well as distant atom pairs: +```c++ + if(i!=j && i!=k && i!=l && j!=k && j!=l && k!=l) { } /* Skip coincidences */ +``` +and +```c++ + if(R[i][k] < 4.0 && R[k][j] < 4.0 && R[k][l] < 4.0) { } /* Skip distant atom pairs */ +``` diff --git a/Project#01/hints/hint5-1.md b/Project#01/hints/hint5-1.md new file mode 100644 index 0000000..32e48c3 --- /dev/null +++ b/Project#01/hints/hint5-1.md @@ -0,0 +1 @@ +Just as for the out-of-plane angles, there is no need to store the torsional angles after they are printed, so no special memory allocation procedure is needed for this step. diff --git a/Project#01/hints/hint5-2.md b/Project#01/hints/hint5-2.md new file mode 100644 index 0000000..4a4ffb9 --- /dev/null +++ b/Project#01/hints/hint5-2.md @@ -0,0 +1 @@ +Just as for `asin()` in the out-of-plane angle calculation, you should check the argument to `acos()` to make sure it lies between -1.0 and +1.0. diff --git a/Project#01/hints/hint5-3.md b/Project#01/hints/hint5-3.md new file mode 100644 index 0000000..0613c4a --- /dev/null +++ b/Project#01/hints/hint5-3.md @@ -0,0 +1 @@ +To print only the unique dihedral angles, it is straightforward in this case to limit the loop structure over i, j, k, and l to keep j < i, k < j, and l < k. Also, one should limit the printing only to atom pairs that are close together. diff --git a/Project#01/hints/hint5-4.md b/Project#01/hints/hint5-4.md new file mode 100644 index 0000000..43f3dd5 --- /dev/null +++ b/Project#01/hints/hint5-4.md @@ -0,0 +1 @@ +The sign of a torsional/dihedral angle among atoms **_i-j-k-l_** is positive (negative) if the vector along **_k-l_** lies to the right (left) of the plane formed by **_i-j-k_** when the plane is viewed along the **_j-k_** vector. diff --git a/Project#01/hints/hint6-1.md b/Project#01/hints/hint6-1.md new file mode 100644 index 0000000..27f9698 --- /dev/null +++ b/Project#01/hints/hint6-1.md @@ -0,0 +1 @@ +An excellent source for atomic masses and other physical constants is the [National Institute of Standard and Technology (NIST) website](http://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=&ascii=html&isotype=some). diff --git a/Project#01/hints/hint6-2.md b/Project#01/hints/hint6-2.md new file mode 100644 index 0000000..aea0a42 --- /dev/null +++ b/Project#01/hints/hint6-2.md @@ -0,0 +1,10 @@ +An elegant way to translate between the atomic number (z-value) of a given atom and its mass is to prepare a static array of the masses of the most abundant isotope of each element. I suggest preparing a header file containing a [global array](https://github.com/CrawfordGroup/ProgrammingProjects/wiki/Variable-Scope-and-Reference-Types#global-variables), e.g.: +```c++ + double masses[] = { + 0.0000000, + 1.007825, + 4.002603, + 6.015123, + ...}; +``` +Note that, for example, `masses[1] = 1.007825`, which is the correct atomic mass for a hydrogen atom. diff --git a/Project#01/hints/hint7-1.md b/Project#01/hints/hint7-1.md new file mode 100644 index 0000000..4aa7771 --- /dev/null +++ b/Project#01/hints/hint7-1.md @@ -0,0 +1,45 @@ +Here are two approaches for the [diagonalization](http://en.wikipedia.org/wiki/Diagonalizable_matrix) of the moment of inertia tensor: + +## Secular Determinant +Since the moment of inertia tensor is only a 3x3 matrix, a brute-force approach via the secular determinant is feasible: + + + +This leads to a cubic equation in λ, which one can solve directly. Have fun with that. + +## More General Algorithms +"Canned" algorithms are definitely the way to go for general matrix diagonalization. Most such algorithms are based on a two-step procedure: + - Reduction of the matrix to a tridiagonal form using the [Householder](http://en.wikipedia.org/wiki/Householder's_method) or Givens approaches. + - Diagonalization of the tridiagonal structure, either by solving its secular determinant or by other methods, e.g. [QR or QL decompositions](http://en.wikipedia.org/wiki/QR_decomposition). + +A convenient canned library for a wide range of linear algebraic operations is the [Eigen package](http://eigen.tuxfamily.org). This is a template-only library that provides a very clean interface for manipulating a large number of matrix types. You can either download and install the library from the [official website](http://eigen.tuxfamily.org) or just grab the [gzipped tarfile from here](../eigen.tar.gz). Unpack the library in the same directory as your source code, and you're ready to get started. + +To use the library to diagonalize your moment inertia tensor, follow these steps: + +- Add the following lines to your main source file below the inclusion of other headers: +```c++ +#include "Eigen/Dense" +#include "Eigen/Eigenvalues" +#include "Eigen/Core" + +typedef Eigen::Matrix Matrix; +``` +This code defines a new type called a `Matrix` that may be dynamically allocated and contains only doubles. +- Allocate your moment of inertia tensor by a line of code like: +```c++ +Matrix I(3,3); +``` +- Access or assign individual elements of the Matrix using parenthetical notation rather than brackets, e.g.: +```c++ +I(0,0) = 2.0; +``` +- The Eigen package makes it easy to examine your matrix using cout: +```c++ +cout << I << endl; +``` +- After you have built the moment of inertia tensor, you may compute its eigenvalues and eigenvectors as follows: +```c++ + Eigen::SelfAdjointEigenSolver solver(I); + Matrix evecs = solver.eigenvectors(); + Matrix evals = solver.eigenvalues(); +``` diff --git a/Project#01/hints/hint7-2.md b/Project#01/hints/hint7-2.md new file mode 100644 index 0000000..5a9a10c --- /dev/null +++ b/Project#01/hints/hint7-2.md @@ -0,0 +1 @@ +Lots of useful and precise physical constants are available at the [National Institute of Standards and Technology website](http://physics.nist.gov/cuu/Constants/index.html?/codata86.html). diff --git a/Project#01/hints/step1-solution.md b/Project#01/hints/step1-solution.md new file mode 100644 index 0000000..9a1ffe4 --- /dev/null +++ b/Project#01/hints/step1-solution.md @@ -0,0 +1,60 @@ +```c++ +#include +#include +#include +#include + +using namespace std; + +int main() +{ + ifstream input("geom.dat"); + + int natom; + input >> natom; + + int *zval = new int[natom]; + double *x = new double[natom]; + double *y = new double[natom]; + double *z = new double[natom]; + + for(int i=0; i < natom; i++) + input >> zval[i] >> x[i] >> y[i] >> z[i]; + + input.close(); + + cout << "Number of atoms: " << natom << endl; + cout << "Input Cartesian coordinates:\n"; + for(int i=0; i < natom; i++) + printf("%d %20.12f %20.12f %20.12f\n", (int) zval[i], x[i], y[i], z[i]); + + delete[] zval; + delete[] x; delete[] y; delete[] z; + + return 0; +} +``` + +An even more elegant solution would be to couple the above to the [Molecule class](https://github.com/CrawfordGroup/ProgrammingProjects/wiki/Classes-and-Objects) we defined earlier in the Fundamentals section: +```c++ +#include "molecule.h" +#include +#include +#include +#include + +using namespace std; + +int main() +{ + Molecule mol("geom.dat", 0); + + cout << "Number of atoms: " << mol.natom << endl; + cout << "Input Cartesian coordinates:\n"; + mol.print_geom(); + + return 0; +} +``` + + diff --git a/Project#01/hints/step2-solution.md b/Project#01/hints/step2-solution.md new file mode 100644 index 0000000..bc24c9e --- /dev/null +++ b/Project#01/hints/step2-solution.md @@ -0,0 +1,63 @@ +Here we use the Molecule class we've been working on so far, and thanks to the new "bond()" function, we don't need to worry about storing the distances in a matrix: + +```c++ +#include "molecule.h" +#include +#include +#include +#include +#include + +using namespace std; + +int main() +{ + Molecule mol("geom.dat", 0); + + cout << "Number of atoms: " << mol.natom << endl; + cout << "Input Cartesian coordinates:\n"; + mol.print_geom(); + + cout << "Interatomic distances (bohr):\n"; + for(int i=0; i < mol.natom; i++) + for(int j=0; j < i; j++) + printf("%d %d %8.5f\n", i, j, mol.bond(i,j)); + + return 0; +} +``` + +The output from the above program for the acetaldehyde test case is: +``` +Number of atoms: 7 +Input Cartesian coordinates: +6 0.000000000000 0.000000000000 0.000000000000 +6 0.000000000000 0.000000000000 2.845112131228 +8 1.899115961744 0.000000000000 4.139062527233 +1 -1.894048308506 0.000000000000 3.747688672216 +1 1.942500819960 0.000000000000 -0.701145981971 +1 -1.007295466862 -1.669971842687 -0.705916966833 +1 -1.007295466862 1.669971842687 -0.705916966833 +Interatomic distances (bohr): +1 0 2.84511 +2 0 4.55395 +2 1 2.29803 +3 0 4.19912 +3 1 2.09811 +3 2 3.81330 +4 0 2.06517 +4 1 4.04342 +4 2 4.84040 +4 3 5.87463 +5 0 2.07407 +5 1 4.05133 +5 2 5.89151 +5 3 4.83836 +5 4 3.38971 +6 0 2.07407 +6 1 4.05133 +6 2 5.89151 +6 3 4.83836 +6 4 3.38971 +6 5 3.33994 +``` diff --git a/Project#01/hints/step3-solution.md b/Project#01/hints/step3-solution.md new file mode 100644 index 0000000..8de6c2d --- /dev/null +++ b/Project#01/hints/step3-solution.md @@ -0,0 +1,128 @@ +Here again we've extended the Molecule class to compute the bond angles without storing them. This also required the addition of a new function to compute the Cartesian unit vectors on the fly, whose declaration we add to the member functions of molecule.h: +```c++ +#include + +using namespace std; + +class Molecule +{ + public: + int natom; + int charge; + int *zvals; + double **geom; + string point_group; + + void print_geom(); + void rotate(double phi); + void translate(double x, double y, double z); + double bond(int atom1, int atom2); + double angle(int atom1, int atom2, int atom3); + double torsion(int atom1, int atom2, int atom3, int atom4); + double unit(int cart, int atom1, int atom2); + + Molecule(const char *filename, int q); + ~Molecule(); +}; +``` + +Now the two new functions added to molecule.cc: +```c++ +// Returns the value of the unit vector between atoms a and b +// in the cart direction (cart=0=x, cart=1=y, cart=2=z) +double Molecule::unit(int cart, int a, int b) +{ + return -(geom[a][cart]-geom[b][cart])/bond(a,b); +} + +// Returns the angle between atoms a, b, and c in radians +double Molecule::angle(int a, int b, int c) +{ + return acos(unit(0,b,a) * unit(0,b,c) + unit(1,b,a) * unit(1,b,c) + unit(2,b,a) * unit(2,b,c)); +} +``` + +And finally, the code that makes use of the above: + +```c++ +#include "molecule.h" +#include +#include +#include +#include +#include + +using namespace std; + +int main() +{ + Molecule mol("geom.dat", 0); + + cout << "Number of atoms: " << mol.natom << endl; + cout << "Input Cartesian coordinates:\n"; + mol.print_geom(); + + cout << "Interatomic distances (bohr):\n"; + for(int i=0; i < mol.natom; i++) + for(int j=0; j < i; j++) + printf("%d %d %8.5f\n", i, j, mol.bond(i,j)); + + cout << "\nBond angles:\n"; + for(int i=0; i < mol.natom; i++) { + for(int j=0; j < i; j++) { + for(int k=0; k < j; k++) { + if(mol.bond(i,j) < 4.0 && mol.bond(j,k) < 4.0) + printf("%2d-%2d-%2d %10.6f\n", i, j, k, mol.angle(i,j,k)*(180.0/acos(-1.0))); + } + } + } + + return 0; +} +``` +Note that the value of π is obtained with machine precision using `acos(-1.0)`. + +The above code produces the following output for the acetaldehyde test case: + +``` +Number of atoms: 7 +Input Cartesian coordinates: +6 0.000000000000 0.000000000000 0.000000000000 +6 0.000000000000 0.000000000000 2.845112131228 +8 1.899115961744 0.000000000000 4.139062527233 +1 -1.894048308506 0.000000000000 3.747688672216 +1 1.942500819960 0.000000000000 -0.701145981971 +1 -1.007295466862 -1.669971842687 -0.705916966833 +1 -1.007295466862 1.669971842687 -0.705916966833 +Interatomic distances (bohr): +1 0 2.84511 +2 0 4.55395 +2 1 2.29803 +3 0 4.19912 +3 1 2.09811 +3 2 3.81330 +4 0 2.06517 +4 1 4.04342 +4 2 4.84040 +4 3 5.87463 +5 0 2.07407 +5 1 4.05133 +5 2 5.89151 +5 3 4.83836 +5 4 3.38971 +6 0 2.07407 +6 1 4.05133 +6 2 5.89151 +6 3 4.83836 +6 4 3.38971 +6 5 3.33994 + +Bond angles: + 2- 1- 0 124.268308 + 3- 1- 0 115.479341 + 3- 2- 1 28.377448 + 5- 4- 0 35.109529 + 6- 4- 0 35.109529 + 6- 5- 0 36.373677 + 6- 5- 4 60.484476 +``` diff --git a/Project#01/hints/step4-solution.md b/Project#01/hints/step4-solution.md new file mode 100644 index 0000000..5c3ae48 --- /dev/null +++ b/Project#01/hints/step4-solution.md @@ -0,0 +1,174 @@ +We've added a new function to the Molecule class for computing the out-of-plane angles. Here's the new molecule.h: + +```c++ +#include + +using namespace std; + +class Molecule +{ + public: + int natom; + int charge; + int *zvals; + double **geom; + string point_group; + + void print_geom(); + void rotate(double phi); + void translate(double x, double y, double z); + double bond(int atom1, int atom2); + double angle(int atom1, int atom2, int atom3); + double torsion(int atom1, int atom2, int atom3, int atom4); + double oop(int atom1, int atom2, int atom3, int atom4); + double unit(int cart, int atom1, int atom2); + + Molecule(const char *filename, int q); + ~Molecule(); +}; +``` + +Here's the new `oop()` function for molecule.cc: + +```c++ +double Molecule::oop(int a, int b, int c, int d) +{ + double ebcd_x = (unit(1,c,b) * unit(2,c,d) - unit(2,c,b) * unit(1,c,d)); + double ebcd_y = (unit(2,c,b) * unit(0,c,d) - unit(0,c,b) * unit(2,c,d)); + double ebcd_z = (unit(0,c,b) * unit(1,c,d) - unit(1,c,b) * unit(0,c,d)); + + double exx = ebcd_x * unit(0,c,a); + double eyy = ebcd_y * unit(1,c,a); + double ezz = ebcd_z * unit(2,c,a); + + double theta = (exx + eyy + ezz)/sin(angle(b,c,d)); + + if(theta < -1.0) theta = asin(-1.0); + else if(theta > 1.0) theta = asin(1.0); + else theta = asin(theta); + + return theta; +} +``` + +And finally the new code that makes use of the class: + +```c++ +#include "molecule.h" +#include +#include +#include +#include +#include + +using namespace std; + +int main() +{ + Molecule mol("geom.dat", 0); + + cout << "Number of atoms: " << mol.natom << endl; + cout << "Input Cartesian coordinates:\n"; + mol.print_geom(); + + cout << "Interatomic distances (bohr):\n"; + for(int i=0; i < mol.natom; i++) + for(int j=0; j < i; j++) + printf("%d %d %8.5f\n", i, j, mol.bond(i,j)); + + cout << "\nBond angles:\n"; + for(int i=0; i < mol.natom; i++) { + for(int j=0; j < i; j++) { + for(int k=0; k < j; k++) { + if(mol.bond(i,j) < 4.0 && mol.bond(j,k) < 4.0) + printf("%2d-%2d-%2d %10.6f\n", i, j, k, mol.angle(i,j,k)*(180.0/acos(-1.0))); + } + } + } + + cout << "\nOut-of-Plane angles:\n"; + for(int i=0; i < mol.natom; i++) { + for(int k=0; k < mol.natom; k++) { + for(int j=0; j < mol.natom; j++) { + for(int l=0; l < j; l++) { + if(i!=j && i!=k && i!=l && j!=k && k!=l && mol.bond(i,k) < 4.0 && mol.bond(k,j) < 4.0 && mol.bond(k,l) < 4.0) + printf("%2d-%2d-%2d-%2d %10.6f\n", i, j, k, l, mol.oop(i,j,k,l)*(180.0/acos(-1.0))); + } + } + } + } + + return 0; +} +``` + +The above code produces the following output for the acetaldehyde test case: + +``` +Number of atoms: 7 +Input Cartesian coordinates: +6 0.000000000000 0.000000000000 0.000000000000 +6 0.000000000000 0.000000000000 2.845112131228 +8 1.899115961744 0.000000000000 4.139062527233 +1 -1.894048308506 0.000000000000 3.747688672216 +1 1.942500819960 0.000000000000 -0.701145981971 +1 -1.007295466862 -1.669971842687 -0.705916966833 +1 -1.007295466862 1.669971842687 -0.705916966833 +Interatomic distances (bohr): +1 0 2.84511 +2 0 4.55395 +2 1 2.29803 +3 0 4.19912 +3 1 2.09811 +3 2 3.81330 +4 0 2.06517 +4 1 4.04342 +4 2 4.84040 +4 3 5.87463 +5 0 2.07407 +5 1 4.05133 +5 2 5.89151 +5 3 4.83836 +5 4 3.38971 +6 0 2.07407 +6 1 4.05133 +6 2 5.89151 +6 3 4.83836 +6 4 3.38971 +6 5 3.33994 + +Bond angles: + 2- 1- 0 124.268308 + 3- 1- 0 115.479341 + 3- 2- 1 28.377448 + 5- 4- 0 35.109529 + 6- 4- 0 35.109529 + 6- 5- 0 36.373677 + 6- 5- 4 60.484476 + +Out-of-plane angles: + 0- 3- 1- 2 -0.000000 + 0- 6- 4- 5 19.939726 + 0- 6- 5- 4 -19.850523 + 0- 5- 6- 4 19.850523 + 1- 5- 0- 4 53.678778 + 1- 6- 0- 4 -53.678778 + 1- 6- 0- 5 54.977064 + 2- 3- 1- 0 0.000000 + 3- 2- 1- 0 -0.000000 + 4- 5- 0- 1 -53.651534 + 4- 6- 0- 1 53.651534 + 4- 6- 0- 5 -54.869992 + 4- 6- 5- 0 29.885677 + 4- 5- 6- 0 -29.885677 + 5- 4- 0- 1 53.626323 + 5- 6- 0- 1 -56.277112 + 5- 6- 0- 4 56.194621 + 5- 6- 4- 0 -30.558964 + 5- 4- 6- 0 31.064344 + 6- 4- 0- 1 -53.626323 + 6- 5- 0- 1 56.277112 + 6- 5- 0- 4 -56.194621 + 6- 5- 4- 0 30.558964 + 6- 4- 5- 0 -31.064344 +``` diff --git a/Project#01/hints/step5-solution.md b/Project#01/hints/step5-solution.md new file mode 100644 index 0000000..7c437d3 --- /dev/null +++ b/Project#01/hints/step5-solution.md @@ -0,0 +1,177 @@ +Now we've added a new member function to the Molecule class: +```c++ +// Computes the angle between planes a-b-c and b-c-d +double Molecule::torsion(int a, int b, int c, int d) +{ + double eabc_x = (unit(1,b,a)*unit(2,b,c) - unit(2,b,a)*unit(1,b,c)); + double eabc_y = (unit(2,b,a)*unit(0,b,c) - unit(0,b,a)*unit(2,b,c)); + double eabc_z = (unit(0,b,a)*unit(1,b,c) - unit(1,b,a)*unit(0,b,c)); + + double ebcd_x = (unit(1,c,b)*unit(2,c,d) - unit(2,c,b)*unit(1,c,d)); + double ebcd_y = (unit(2,c,b)*unit(0,c,d) - unit(0,c,b)*unit(2,c,d)); + double ebcd_z = (unit(0,c,b)*unit(1,c,d) - unit(1,c,b)*unit(0,c,d)); + + double exx = eabc_x * ebcd_x; + double eyy = eabc_y * ebcd_y; + double ezz = eabc_z * ebcd_z; + + double tau = (exx + eyy + ezz)/(sin(angle(a,b,c)) * sin(angle(b,c,d))); + + if(tau < -1.0) tau = acos(-1.0); + else if(tau > 1.0) tau = acos(1.0); + else tau = acos(tau); + + // Compute the sign of the torsion + double cross_x = eabc_y * ebcd_z - eabc_z * ebcd_y; + double cross_y = eabc_z * ebcd_x - eabc_x * ebcd_z; + double cross_z = eabc_x * ebcd_y - eabc_y * ebcd_x; + double norm = cross_x*cross_x + cross_y*cross_y + cross_z*cross_z; + cross_x /= norm; + cross_y /= norm; + cross_z /= norm; + double sign = 1.0; + double dot = cross_x*unit(0,b,c)+cross_y*unit(1,b,c)+cross_z*unit(2,b,c); + if(dot < 0.0) sign = -1.0; + + return tau*sign; +} +``` + +And we use the new function in the code as follows: + +```c++ +#include +#include +#include +#include +#include +#include "molecule.h" + +using namespace std; + +int main() +{ + Molecule mol("geom.dat", 0); + + cout << "Number of atoms: " << mol.natom << endl; + cout << "Input Cartesian coordinates:\n"; + mol.print_geom(); + + cout << "Interatomic distances (bohr):\n"; + for(int i=0; i < mol.natom; i++) + for(int j=0; j < i; j++) + printf("%d %d %8.5f\n", i, j, mol.bond(i,j)); + + cout << "\nBond angles:\n"; + for(int i=0; i < mol.natom; i++) { + for(int j=0; j < i; j++) { + for(int k=0; k < j; k++) { + if(mol.bond(i,j) < 4.0 && mol.bond(j,k) < 4.0) + printf("%2d-%2d-%2d %10.6f\n", i, j, k, mol.angle(i,j,k)*(180.0/acos(-1.0))); + } + } + } + + cout << "\nOut-of-Plane angles:\n"; + for(int i=0; i < mol.natom; i++) { + for(int k=0; k < mol.natom; k++) { + for(int j=0; j < mol.natom; j++) { + for(int l=0; l < j; l++) { + if(i!=j && i!=k && i!=l && j!=k && k!=l && mol.bond(i,k) < 4.0 && mol.bond(k,j) < 4.0 && mol.bond(k,l) < 4.0) + printf("%2d-%2d-%2d-%2d %10.6f\n", i, j, k, l, mol.oop(i,j,k,l)*(180.0/acos(-1.0))); + } + } + } + } + + cout << "\nTorsional angles:\n\n"; + for(int i=0; i < mol.natom; i++) { + for(int j=0; j < i; j++) { + for(int k=0; k < j; k++) { + for(int l=0; l < k; l++) { + if(mol.bond(i,j) < 4.0 && mol.bond(j,k) < 4.0 && mol.bond(k,l) < 4.0) + printf("%2d-%2d-%2d-%2d %10.6f\n", i, j, k, l, mol.torsion(i,j,k,l)*(180.0/acos(-1.0))); + } + } + } + } + + return 0; +} +``` + +The above code produces the following output when applied to the acetaldehyde test case: + +``` +Number of atoms: 7 +Input Cartesian coordinates: +6 0.000000000000 0.000000000000 0.000000000000 +6 0.000000000000 0.000000000000 2.845112131228 +8 1.899115961744 0.000000000000 4.139062527233 +1 -1.894048308506 0.000000000000 3.747688672216 +1 1.942500819960 0.000000000000 -0.701145981971 +1 -1.007295466862 -1.669971842687 -0.705916966833 +1 -1.007295466862 1.669971842687 -0.705916966833 +Interatomic distances (bohr): +1 0 2.84511 +2 0 4.55395 +2 1 2.29803 +3 0 4.19912 +3 1 2.09811 +3 2 3.81330 +4 0 2.06517 +4 1 4.04342 +4 2 4.84040 +4 3 5.87463 +5 0 2.07407 +5 1 4.05133 +5 2 5.89151 +5 3 4.83836 +5 4 3.38971 +6 0 2.07407 +6 1 4.05133 +6 2 5.89151 +6 3 4.83836 +6 4 3.38971 +6 5 3.33994 + +Bond angles: + 0- 1- 2 124.268308 + 0- 1- 3 115.479341 + 0- 4- 5 35.109529 + 0- 4- 6 35.109529 + 0- 5- 6 36.373677 + 1- 2- 3 28.377448 + 4- 5- 6 60.484476 + +Out-of-plane angles: + 0- 3- 1- 2 -0.000000 + 0- 6- 4- 5 19.939726 + 0- 6- 5- 4 -19.850523 + 0- 5- 6- 4 19.850523 + 1- 5- 0- 4 53.678778 + 1- 6- 0- 4 -53.678778 + 1- 6- 0- 5 54.977064 + 2- 3- 1- 0 0.000000 + 3- 2- 1- 0 -0.000000 + 4- 5- 0- 1 -53.651534 + 4- 6- 0- 1 53.651534 + 4- 6- 0- 5 -54.869992 + 4- 6- 5- 0 29.885677 + 4- 5- 6- 0 -29.885677 + 5- 4- 0- 1 53.626323 + 5- 6- 0- 1 -56.277112 + 5- 6- 0- 4 56.194621 + 5- 6- 4- 0 -30.558964 + 5- 4- 6- 0 31.064344 + 6- 4- 0- 1 -53.626323 + 6- 5- 0- 1 56.277112 + 6- 5- 0- 4 -56.194621 + 6- 5- 4- 0 30.558964 + 6- 4- 5- 0 -31.064344 + +Torsional angles: + + 3- 2- 1- 0 180.000000 + 6- 5- 4- 0 36.366799 +``` diff --git a/Project#01/hints/step6-solution.md b/Project#01/hints/step6-solution.md new file mode 100644 index 0000000..4ea9d7e --- /dev/null +++ b/Project#01/hints/step6-solution.md @@ -0,0 +1,163 @@ +Note that the header file, `masses.h` is not provided. See the [Hint](./hint6-2.md) to learn how to construct it. Also note that we've made convenient use of our `translate()` member function for the Molecule class. + +```c++ +#include "molecule.h" +#include "masses.h" + +#include +#include +#include +#include +#include + +using namespace std; + +int main() +{ + Molecule mol("geom.dat", 0); + + cout << "Number of atoms: " << mol.natom << endl; + cout << "Input Cartesian coordinates:\n"; + mol.print_geom(); + + cout << "Interatomic distances (bohr):\n"; + for(int i=0; i < mol.natom; i++) + for(int j=0; j < i; j++) + printf("%d %d %8.5f\n", i, j, mol.bond(i,j)); + + cout << "\nBond angles:\n"; + for(int i=0; i < mol.natom; i++) { + for(int j=0; j < i; j++) { + for(int k=0; k < j; k++) { + if(mol.bond(i,j) < 4.0 && mol.bond(j,k) < 4.0) + printf("%2d-%2d-%2d %10.6f\n", i, j, k, mol.angle(i,j,k)*(180.0/acos(-1.0))); + } + } + } + + cout << "\nOut-of-Plane angles:\n"; + for(int i=0; i < mol.natom; i++) { + for(int k=0; k < mol.natom; k++) { + for(int j=0; j < mol.natom; j++) { + for(int l=0; l < j; l++) { + if(i!=j && i!=k && i!=l && j!=k && k!=l && mol.bond(i,k) < 4.0 && mol.bond(k,j) < 4.0 && mol.bond(k,l) < 4.0) + printf("%2d-%2d-%2d-%2d %10.6f\n", i, j, k, l, mol.oop(i,j,k,l)*(180.0/acos(-1.0))); + } + } + } + } + + cout << "\nTorsional angles:\n\n"; + for(int i=0; i < mol.natom; i++) { + for(int j=0; j < i; j++) { + for(int k=0; k < j; k++) { + for(int l=0; l < k; l++) { + if(mol.bond(i,j) < 4.0 && mol.bond(j,k) < 4.0 && mol.bond(k,l) < 4.0) + printf("%2d-%2d-%2d-%2d %10.6f\n", i, j, k, l, mol.torsion(i,j,k,l)*(180.0/acos(-1.0))); + } + } + } + } + + /* find the center of mass (COM) */ + double M = 0.0; + for(int i=0; i < mol.atom; i++) M += an2masses[(int) mol.zvals[i]]; + + double xcm=0.0; + double ycm=0.0; + double zcm=0.0; + double mi; + for(int i=0; i < mol.atom; i++) { + mi = an2masses[(int) mol.zvals[i]]; + xcm += mi * mol.geom[i][0]; + ycm += mi * mol.geom[i][1]; + zcm += mi * mol.geom[i][2]; + } + xcm /= M; + ycm /= M; + zcm /= M; + printf("\nMolecular center of mass: %12.8f %12.8f %12.8f\n", xcm, ycm, zcm); + + mol.translate(-xcm, -ycm, -zcm); + + return 0; +} +``` + +The above code produces the following output when applied to the acetaldehyde test case: + +``` +Number of atoms: 7 +Input Cartesian coordinates: +6 0.000000000000 0.000000000000 0.000000000000 +6 0.000000000000 0.000000000000 2.845112131228 +8 1.899115961744 0.000000000000 4.139062527233 +1 -1.894048308506 0.000000000000 3.747688672216 +1 1.942500819960 0.000000000000 -0.701145981971 +1 -1.007295466862 -1.669971842687 -0.705916966833 +1 -1.007295466862 1.669971842687 -0.705916966833 +Interatomic distances (bohr): +1 0 2.84511 +2 0 4.55395 +2 1 2.29803 +3 0 4.19912 +3 1 2.09811 +3 2 3.81330 +4 0 2.06517 +4 1 4.04342 +4 2 4.84040 +4 3 5.87463 +5 0 2.07407 +5 1 4.05133 +5 2 5.89151 +5 3 4.83836 +5 4 3.38971 +6 0 2.07407 +6 1 4.05133 +6 2 5.89151 +6 3 4.83836 +6 4 3.38971 +6 5 3.33994 + +Bond angles: + 0- 1- 2 124.268308 + 0- 1- 3 115.479341 + 0- 4- 5 35.109529 + 0- 4- 6 35.109529 + 0- 5- 6 36.373677 + 1- 2- 3 28.377448 + 4- 5- 6 60.484476 + +Out-of-plane angles: + 0- 3- 1- 2 -0.000000 + 0- 6- 4- 5 19.939726 + 0- 6- 5- 4 -19.850523 + 0- 5- 6- 4 19.850523 + 1- 5- 0- 4 53.678778 + 1- 6- 0- 4 -53.678778 + 1- 6- 0- 5 54.977064 + 2- 3- 1- 0 0.000000 + 3- 2- 1- 0 -0.000000 + 4- 5- 0- 1 -53.651534 + 4- 6- 0- 1 53.651534 + 4- 6- 0- 5 -54.869992 + 4- 6- 5- 0 29.885677 + 4- 5- 6- 0 -29.885677 + 5- 4- 0- 1 53.626323 + 5- 6- 0- 1 -56.277112 + 5- 6- 0- 4 56.194621 + 5- 6- 4- 0 -30.558964 + 5- 4- 6- 0 31.064344 + 6- 4- 0- 1 -53.626323 + 6- 5- 0- 1 56.277112 + 6- 5- 0- 4 -56.194621 + 6- 5- 4- 0 30.558964 + 6- 4- 5- 0 -31.064344 + +Torsional angles: + + 3- 2- 1- 0 180.000000 + 6- 5- 4- 0 36.366799 + +Molecular center of mass: 0.64494926 0.00000000 2.31663792 +``` diff --git a/Project#01/hints/step7-solution.md b/Project#01/hints/step7-solution.md new file mode 100644 index 0000000..babca70 --- /dev/null +++ b/Project#01/hints/step7-solution.md @@ -0,0 +1,232 @@ +Note that this is only the code for the `main()` function. The Eigen package, which provides the Matrix class and associated diagonalization capabilities is described in a [hint](./hint7-1.md). + +```c++ +#include "molecule.h" +#include "masses.h" + +#include +#include +#include +#include +#include + +#include "Eigen/Dense" +#include "Eigen/Eigenvalues" +#include "Eigen/Core" + +typedef Eigen::Matrix Matrix; +typedef Eigen::Matrix Vector; + +using namespace std; + +int main() +{ + Molecule mol("geom.dat", 0); + + cout << "Number of atoms: " << mol.natom << endl; + cout << "Input Cartesian coordinates:\n"; + mol.print_geom(); + + cout << "Interatomic distances (bohr):\n"; + for(int i=0; i < mol.natom; i++) + for(int j=0; j < i; j++) + printf("%d %d %8.5f\n", i, j, mol.bond(i,j)); + + cout << "\nBond angles:\n"; + for(int i=0; i < mol.natom; i++) { + for(int j=0; j < i; j++) { + for(int k=0; k < j; k++) { + if(mol.bond(i,j) < 4.0 && mol.bond(j,k) < 4.0) + printf("%2d-%2d-%2d %10.6f\n", i, j, k, mol.angle(i,j,k)*(180.0/acos(-1.0))); + } + } + } + + cout << "\nOut-of-Plane angles:\n"; + for(int i=0; i < mol.natom; i++) { + for(int k=0; k < mol.natom; k++) { + for(int j=0; j < mol.natom; j++) { + for(int l=0; l < j; l++) { + if(i!=j && i!=k && i!=l && j!=k && k!=l && mol.bond(i,k) < 4.0 && mol.bond(k,j) < 4.0 && mol.bond(k,l) < 4.0) + printf("%2d-%2d-%2d-%2d %10.6f\n", i, j, k, l, mol.oop(i,j,k,l)*(180.0/acos(-1.0))); + } + } + } + } + + cout << "\nTorsional angles:\n\n"; + for(int i=0; i < mol.natom; i++) { + for(int j=0; j < i; j++) { + for(int k=0; k < j; k++) { + for(int l=0; l < k; l++) { + if(mol.bond(i,j) < 4.0 && mol.bond(j,k) < 4.0 && mol.bond(k,l) < 4.0) + printf("%2d-%2d-%2d-%2d %10.6f\n", i, j, k, l, mol.torsion(i,j,k,l)*(180.0/acos(-1.0))); + } + } + } + } + + /* find the center of mass (COM) */ + double M = 0.0; + for(int i=0; i < natom; i++) M += an2masses[(int) mol.zvals[i]]; + + double xcm=0.0; + double ycm=0.0; + double zcm=0.0; + double mi; + for(int i=0; i < natom; i++) { + mi = an2masses[(int) mol.zvals[i]]; + xcm += mi * mol.geom[i][0]; + ycm += mi * mol.geom[i][1]; + zcm += mi * mol.geom[i][2]; + } + xcm /= M; + ycm /= M; + zcm /= M; + printf("\nMolecular center of mass: %12.8f %12.8f %12.8f\n", xcm, ycm, zcm); + + mol.translate(-xcm, -ycm, -zcm); + + Matrix I(3,3); + + for(int i=0; i < mol.natom; i++) { + mi = masses[(int) mol.zvals[i]]; + I(0,0) += mi * (mol.geom[i][1]*mol.geom[i][1] + mol.geom[i][2]*mol.geom[i][2]); + I(1,1) += mi * (mol.geom[i][0]*mol.geom[i][0] + mol.geom[i][2]*mol.geom[i][2]); + I(2,2) += mi * (mol.geom[i][0]*mol.geom[i][0] + mol.geom[i][1]*mol.geom[i][1]); + I(0,1) -= mi * mol.geom[i][0]*mol.geom[i][1]; + I(0,2) -= mi * mol.geom[i][0]*mol.geom[i][2]; + I(1,2) -= mi * mol.geom[i][1]*mol.geom[i][2]; + } + + I(1,0) = I(0,1); + I(2,0) = I(0,2); + I(2,1) = I(1,2); + + cout << "\nMoment of inertia tensor (amu bohr^2):\n"; + cout << I << endl; + + // find the principal moments + Eigen::SelfAdjointEigenSolver solver(I); + Matrix evecs = solver.eigenvectors(); + Matrix evals = solver.eigenvalues(); + + cout << "\nPrincipal moments of inertia (amu * bohr^2):\n"; + cout << evals << endl; + + double conv = 0.529177249 * 0.529177249; + cout << "\nPrincipal moments of inertia (amu * AA^2):\n"; + cout << evals * conv << endl; + + conv = 1.6605402E-24 * 0.529177249E-8 * 0.529177249E-8; + cout << "\nPrincipal moments of inertia (g * cm^2):\n"; + cout << evals * conv << endl; + + // classify the rotor + if(mol.natom == 2) cout << "\nMolecule is diatomic.\n"; + else if(evals(0) < 1e-4) cout << "\nMolecule is linear.\n"; + else if((fabs(evals(0) - evals(1)) < 1e-4) && (fabs(evals(1) - evals(2)) < 1e-4)) + cout << "\nMolecule is a spherical top.\n"; + else if((fabs(evals(0) - evals(1)) < 1e-4) && (fabs(evals(1) - evals(2)) > 1e-4)) + cout << "\nMolecule is an oblate symmetric top.\n"; + else if((fabs(evals(0) - evals(1)) > 1e-4) && (fabs(evals(1) - evals(2)) < 1e-4)) + cout << "\nMolecule is a prolate symmetric top.\n"; + else cout << "\nMolecule is an asymmetric top.\n"; + + return 0; +} +``` + +The above code produces the following output for the acetaldehyde test case: + +``` +Number of atoms: 7 +Input Cartesian coordinates: +6 0.000000000000 0.000000000000 0.000000000000 +6 0.000000000000 0.000000000000 2.845112131228 +8 1.899115961744 0.000000000000 4.139062527233 +1 -1.894048308506 0.000000000000 3.747688672216 +1 1.942500819960 0.000000000000 -0.701145981971 +1 -1.007295466862 -1.669971842687 -0.705916966833 +1 -1.007295466862 1.669971842687 -0.705916966833 +Interatomic distances (bohr): +1 0 2.84511 +2 0 4.55395 +2 1 2.29803 +3 0 4.19912 +3 1 2.09811 +3 2 3.81330 +4 0 2.06517 +4 1 4.04342 +4 2 4.84040 +4 3 5.87463 +5 0 2.07407 +5 1 4.05133 +5 2 5.89151 +5 3 4.83836 +5 4 3.38971 +6 0 2.07407 +6 1 4.05133 +6 2 5.89151 +6 3 4.83836 +6 4 3.38971 +6 5 3.33994 + +Bond angles: + 0- 1- 2 124.268308 + 0- 1- 3 115.479341 + 0- 4- 5 35.109529 + 0- 4- 6 35.109529 + 0- 5- 6 36.373677 + 1- 2- 3 28.377448 + 4- 5- 6 60.484476 + +Out-of-plane angles: + 0- 3- 1- 2 -0.000000 + 0- 6- 4- 5 19.939726 + 0- 6- 5- 4 -19.850523 + 0- 5- 6- 4 19.850523 + 1- 5- 0- 4 53.678778 + 1- 6- 0- 4 -53.678778 + 1- 6- 0- 5 54.977064 + 2- 3- 1- 0 0.000000 + 3- 2- 1- 0 -0.000000 + 4- 5- 0- 1 -53.651534 + 4- 6- 0- 1 53.651534 + 4- 6- 0- 5 -54.869992 + 4- 6- 5- 0 29.885677 + 4- 5- 6- 0 -29.885677 + 5- 4- 0- 1 53.626323 + 5- 6- 0- 1 -56.277112 + 5- 6- 0- 4 56.194621 + 5- 6- 4- 0 -30.558964 + 5- 4- 6- 0 31.064344 + 6- 4- 0- 1 -53.626323 + 6- 5- 0- 1 56.277112 + 6- 5- 0- 4 -56.194621 + 6- 5- 4- 0 30.558964 + 6- 4- 5- 0 -31.064344 + +Torsional angles: + + 3- 2- 1- 0 180.000000 + 6- 5- 4- 0 36.366799 + +Molecular center of mass: 0.64494926 0.00000000 2.31663792 + +Moment of inertia tensor (amu bohr^2): + 156.154091561645 0.000000000000 -52.855584120568 + 0.000000000000 199.371126996236 0.000000000000 + -52.855584120568 0.000000000000 54.459548882464 + +Principal moments of inertia (amu * bohr^2): + 31.964078 178.649562 199.371127 + +Principal moments of inertia (amu * AA^2): + 8.950855 50.026980 55.829610 + +Principal moments of inertia (g * cm^2): + 1.486325e-39 8.307181e-39 9.270731e-39 + +Molecule is an asymmetric top. +``` diff --git a/Project#01/hints/step8-solution.md b/Project#01/hints/step8-solution.md new file mode 100644 index 0000000..f85cabf --- /dev/null +++ b/Project#01/hints/step8-solution.md @@ -0,0 +1,252 @@ +Note that this is only the code for the `main()` function. The Eigen package, which provides the Matrix class and associated diagonalization capabilities is described in a [hint](./hint7-1.md). + +```c++ +#include "molecule.h" +#include "masses.h" + +#include +#include +#include +#include +#include + +#include "Eigen/Dense" +#include "Eigen/Eigenvalues" +#include "Eigen/Core" + +typedef Eigen::Matrix Matrix; +typedef Eigen::Matrix Vector; + +using namespace std; + +int main() +{ + Molecule mol("geom.dat", 0); + + cout << "Number of atoms: " << mol.natom << endl; + cout << "Input Cartesian coordinates:\n"; + mol.print_geom(); + + cout << "Interatomic distances (bohr):\n"; + for(int i=0; i < mol.natom; i++) + for(int j=0; j < i; j++) + printf("%d %d %8.5f\n", i, j, mol.bond(i,j)); + + cout << "\nBond angles:\n"; + for(int i=0; i < mol.natom; i++) { + for(int j=0; j < i; j++) { + for(int k=0; k < j; k++) { + if(mol.bond(i,j) < 4.0 && mol.bond(j,k) < 4.0) + printf("%2d-%2d-%2d %10.6f\n", i, j, k, mol.angle(i,j,k)*(180.0/acos(-1.0))); + } + } + } + + cout << "\nOut-of-Plane angles:\n"; + for(int i=0; i < mol.natom; i++) { + for(int k=0; k < mol.natom; k++) { + for(int j=0; j < mol.natom; j++) { + for(int l=0; l < j; l++) { + if(i!=j && i!=k && i!=l && j!=k && k!=l && mol.bond(i,k) < 4.0 && mol.bond(k,j) < 4.0 && mol.bond(k,l) < 4.0) + printf("%2d-%2d-%2d-%2d %10.6f\n", i, j, k, l, mol.oop(i,j,k,l)*(180.0/acos(-1.0))); + } + } + } + } + + cout << "\nTorsional angles:\n\n"; + for(int i=0; i < mol.natom; i++) { + for(int j=0; j < i; j++) { + for(int k=0; k < j; k++) { + for(int l=0; l < k; l++) { + if(mol.bond(i,j) < 4.0 && mol.bond(j,k) < 4.0 && mol.bond(k,l) < 4.0) + printf("%2d-%2d-%2d-%2d %10.6f\n", i, j, k, l, mol.torsion(i,j,k,l)*(180.0/acos(-1.0))); + } + } + } + } + + /* find the center of mass (COM) */ + double M = 0.0; + for(int i=0; i < natom; i++) M += an2masses[(int) mol.zvals[i]]; + + double xcm=0.0; + double ycm=0.0; + double zcm=0.0; + double mi; + for(int i=0; i < natom; i++) { + mi = an2masses[(int) mol.zvals[i]]; + xcm += mi * mol.geom[i][0]; + ycm += mi * mol.geom[i][1]; + zcm += mi * mol.geom[i][2]; + } + xcm /= M; + ycm /= M; + zcm /= M; + printf("\nMolecular center of mass: %12.8f %12.8f %12.8f\n", xcm, ycm, zcm); + + mol.translate(-xcm, -ycm, -zcm); + + Matrix I(3,3); + + for(int i=0; i < mol.natom; i++) { + mi = masses[(int) mol.zvals[i]]; + I(0,0) += mi * (mol.geom[i][1]*mol.geom[i][1] + mol.geom[i][2]*mol.geom[i][2]); + I(1,1) += mi * (mol.geom[i][0]*mol.geom[i][0] + mol.geom[i][2]*mol.geom[i][2]); + I(2,2) += mi * (mol.geom[i][0]*mol.geom[i][0] + mol.geom[i][1]*mol.geom[i][1]); + I(0,1) -= mi * mol.geom[i][0]*mol.geom[i][1]; + I(0,2) -= mi * mol.geom[i][0]*mol.geom[i][2]; + I(1,2) -= mi * mol.geom[i][1]*mol.geom[i][2]; + } + + I(1,0) = I(0,1); + I(2,0) = I(0,2); + I(2,1) = I(1,2); + + cout << "\nMoment of inertia tensor (amu bohr^2):\n"; + cout << I << endl; + + // find the principal moments + Eigen::SelfAdjointEigenSolver solver(I); + Matrix evecs = solver.eigenvectors(); + Matrix evals = solver.eigenvalues(); + + cout << "\nPrincipal moments of inertia (amu * bohr^2):\n"; + cout << evals << endl; + + double conv = 0.529177249 * 0.529177249; + cout << "\nPrincipal moments of inertia (amu * AA^2):\n"; + cout << evals * conv << endl; + + conv = 1.6605402E-24 * 0.529177249E-8 * 0.529177249E-8; + cout << "\nPrincipal moments of inertia (g * cm^2):\n"; + cout << evals * conv << endl; + + // classify the rotor + if(mol.natom == 2) cout << "\nMolecule is diatomic.\n"; + else if(evals(0) < 1e-4) cout << "\nMolecule is linear.\n"; + else if((fabs(evals(0) - evals(1)) < 1e-4) && (fabs(evals(1) - evals(2)) < 1e-4)) + cout << "\nMolecule is a spherical top.\n"; + else if((fabs(evals(0) - evals(1)) < 1e-4) && (fabs(evals(1) - evals(2)) > 1e-4)) + cout << "\nMolecule is an oblate symmetric top.\n"; + else if((fabs(evals(0) - evals(1)) > 1e-4) && (fabs(evals(1) - evals(2)) < 1e-4)) + cout << "\nMolecule is a prolate symmetric top.\n"; + else cout << "\nMolecule is an asymmetric top.\n"; + + // compute the rotational constants + double _pi = acos(-1.0); + conv = 6.6260755E-34/(8.0 * _pi * _pi); + conv /= 1.6605402E-27 * 0.529177249E-10 * 0.529177249E-10; + conv *= 1e-6; + cout << "\nRotational constants (MHz):\n"; + cout << "\tA = " << conv/evals(0) << "\t B = " << conv/evals(1) << "\t C = " << conv/evals(2) << endl; + + conv = 6.6260755E-34/(8.0 * _pi * _pi); + conv /= 1.6605402E-27 * 0.529177249E-10 * 0.529177249E-10; + conv /= 2.99792458E10; + cout << "\nRotational constants (cm-1):\n"; + cout << "\tA = " << conv/evals(0) << "\t B = " << conv/evals(1) << "\t C = " << conv/evals(2) << endl; + + return 0; +} +``` + +The above code produces the following output for the acetaldehyde test case: + +``` +Number of atoms: 7 +Input Cartesian coordinates: +6 0.000000000000 0.000000000000 0.000000000000 +6 0.000000000000 0.000000000000 2.845112131228 +8 1.899115961744 0.000000000000 4.139062527233 +1 -1.894048308506 0.000000000000 3.747688672216 +1 1.942500819960 0.000000000000 -0.701145981971 +1 -1.007295466862 -1.669971842687 -0.705916966833 +1 -1.007295466862 1.669971842687 -0.705916966833 +Interatomic distances (bohr): +1 0 2.84511 +2 0 4.55395 +2 1 2.29803 +3 0 4.19912 +3 1 2.09811 +3 2 3.81330 +4 0 2.06517 +4 1 4.04342 +4 2 4.84040 +4 3 5.87463 +5 0 2.07407 +5 1 4.05133 +5 2 5.89151 +5 3 4.83836 +5 4 3.38971 +6 0 2.07407 +6 1 4.05133 +6 2 5.89151 +6 3 4.83836 +6 4 3.38971 +6 5 3.33994 + +Bond angles: + 0- 1- 2 124.268308 + 0- 1- 3 115.479341 + 0- 4- 5 35.109529 + 0- 4- 6 35.109529 + 0- 5- 6 36.373677 + 1- 2- 3 28.377448 + 4- 5- 6 60.484476 + +Out-of-plane angles: + 0- 3- 1- 2 -0.000000 + 0- 6- 4- 5 19.939726 + 0- 6- 5- 4 -19.850523 + 0- 5- 6- 4 19.850523 + 1- 5- 0- 4 53.678778 + 1- 6- 0- 4 -53.678778 + 1- 6- 0- 5 54.977064 + 2- 3- 1- 0 0.000000 + 3- 2- 1- 0 -0.000000 + 4- 5- 0- 1 -53.651534 + 4- 6- 0- 1 53.651534 + 4- 6- 0- 5 -54.869992 + 4- 6- 5- 0 29.885677 + 4- 5- 6- 0 -29.885677 + 5- 4- 0- 1 53.626323 + 5- 6- 0- 1 -56.277112 + 5- 6- 0- 4 56.194621 + 5- 6- 4- 0 -30.558964 + 5- 4- 6- 0 31.064344 + 6- 4- 0- 1 -53.626323 + 6- 5- 0- 1 56.277112 + 6- 5- 0- 4 -56.194621 + 6- 5- 4- 0 30.558964 + 6- 4- 5- 0 -31.064344 + +Torsional angles: + + 3- 2- 1- 0 180.000000 + 6- 5- 4- 0 36.366799 + +Molecular center of mass: 0.64494926 0.00000000 2.31663792 + +Moment of inertia tensor (amu bohr^2): + 156.154091561645 0.000000000000 -52.855584120568 + 0.000000000000 199.371126996236 0.000000000000 + -52.855584120568 0.000000000000 54.459548882464 + +Principal moments of inertia (amu * bohr^2): + 31.964078 178.649562 199.371127 + +Principal moments of inertia (amu * AA^2): + 8.950855 50.026980 55.829610 + +Principal moments of inertia (g * cm^2): + 1.486325e-39 8.307181e-39 9.270731e-39 + +Molecule is an asymmetric top. + +Rotational constants (MHz): + A = 56461.542 B = 10102.130 C = 9052.169 + +Rotational constants (cm-1): + A = 1.8834 B = 0.3370 C = 0.3019 +``` diff --git a/Project#01/output/acetaldehyde_out.txt b/Project#01/output/acetaldehyde_out.txt index 73e224a..8ef02f9 100644 --- a/Project#01/output/acetaldehyde_out.txt +++ b/Project#01/output/acetaldehyde_out.txt @@ -1,4 +1,3 @@ -``` Number of atoms: 7 Input Cartesian coordinates: 6 0.000000000000 0.000000000000 0.000000000000 @@ -78,9 +77,9 @@ Moment of inertia tensor: 1 2 3 - 1 156.1540916 0.0000000 52.8555841 + 1 156.1540916 0.0000000 -52.8555841 2 0.0000000 199.3711270 0.0000000 - 3 52.8555841 0.0000000 54.4595489 + 3 -52.8555841 0.0000000 54.4595489 Principal moments of inertia (amu * bohr^2): 31.964078 178.649562 199.371127 @@ -98,4 +97,3 @@ Rotational constants (MHz): Rotational constants (cm-1): A = 1.8834 B = 0.3370 C = 0.3019 - ``` diff --git a/Project#01/output/allene_out.txt b/Project#01/output/allene_out.txt index 8318e2d..9787cdd 100644 --- a/Project#01/output/allene_out.txt +++ b/Project#01/output/allene_out.txt @@ -1,4 +1,3 @@ -``` Number of atoms: 7 Input Cartesian coordinates: 6 0.000000000000 0.000000000000 1.889725988579 @@ -153,4 +152,3 @@ Rotational constants (MHz): Rotational constants (cm-1): A = 5.5756 B = 0.2855 C = 0.2855 - ``` diff --git a/Project#01/output/benzene_out.txt b/Project#01/output/benzene_out.txt index fdc0c7f..0313cb5 100644 --- a/Project#01/output/benzene_out.txt +++ b/Project#01/output/benzene_out.txt @@ -1,4 +1,3 @@ -``` Number of atoms: 12 Input Cartesian coordinates: 6 0.000000000000 0.000000000000 0.000000000000 @@ -150,4 +149,3 @@ Rotational constants (MHz): Rotational constants (cm-1): A = 0.1932 B = 0.1932 C = 0.0966 - ``` diff --git a/Project#02/README.md b/Project#02/README.md index 325299b..758b491 100644 --- a/Project#02/README.md +++ b/Project#02/README.md @@ -1 +1,72 @@ # Project #2: Harmonic Vibrational Analysis + +The purpose of this project is to extend your fundamental C-language programming techniques through a normal coordinate/harmonic vibrational frequency calculation. The theoretical background and a concise set of instructions for this project may be found [here](./project2-instructions.pdf) + +We thank Dr. Yukio Yamaguchi of the University of Georgia for the original version of this project. + +## Step 1: Read the Coordinate Data + +The coordinate data are given in a format identical to that for [Project #1](../Project%2301). The test case +for the remainder of this project is the water molecule, optimized at the SCF/DZP level of theory. You can find the coordinates (in bohr) in the input directory. + +## Step 2: Read the Cartesian Hessian Data + +The primary input data for the harmonic vibrational calculation is the Hessian matrix, +which consists of second derivatives of the energy with respect to atomic positions. + + + +The Hessian matrix (in units of Eh/a02) can be downloaded [here](./input/h2o_hessian.txt) for the H2O test case. +The first integer in the file is the number of atoms (which you should compare to the corresponding value from the geometry file as a test of consistency), +while the remaining values have the following format: + + + + * [Hint 1](./hints/hint1.md): Reading the Hessian + +## Step 3: Mass-Weight the Hessian Matrix + +Divide each element of the Hessian matrix by the product of square-roots of the masses of the atoms associated with the given coordinates: + + + +where mi represents the mass of the atom corresponding to atom *i*. Use atomic mass units (amu) for the masses, just as +for [Project #1](../Project%2301). + + * [Hint 2](./hints/hint2.md): Solution + +## Step 4: Diagonalize the Mass-Weighted Hessian Matrix + +Compute the eigenvalues of the mass-weighted Hessian: + + + +You should consider using the same canned diagonalization function +you used in [Project #1](../Project%2301). + + * [Hint 3](./hints/hint3.md): Solution + +## Step 5: Compute the Harmonic Vibrational Frequencies + +The vibrational frequencies are proportional to the squareroot of the eigenvalues of the mass-weighted Hessian: + + + +The most common units to use for vibrational frequencies is cm-1. + + * [Hint 4](./hints/hint4.md): Solution + +## Reference +E.B. Willson, J.C. Decius, and P.C. Cross, __Molecular Vibrations__, McGraw-Hill, 1955. + +## Test Cases + + * Water: [Coordinates](./input/h2o_geom.txt) + | [Hessian](./input/h2o_hessian.txt) + | [Output](./output/h2o_vib_out.txt) (see the note at the bottom of [Hint 4](./hints/hint4.md)) + * Benzene: [Coordinates](./input/benzene_geom.txt) + | [Hessian](./input/benzene_hessian.txt) + | [Output](./output/benzene_vib_out.txt) + * 3-chloro-1-butene: [Coordinates](./input/3c1b_geom.txt) + | [Hessian](./input/3c1b_hessian.txt) + | [Output](./output/3c1b_vib_out.txt) diff --git a/Project#02/figures/.DS_Store b/Project#02/figures/.DS_Store new file mode 100644 index 0000000..cbaa184 Binary files /dev/null and b/Project#02/figures/.DS_Store differ diff --git a/Project#02/figures/diag-mass-weighted-hessian.png b/Project#02/figures/diag-mass-weighted-hessian.png new file mode 100644 index 0000000..93fe9f1 Binary files /dev/null and b/Project#02/figures/diag-mass-weighted-hessian.png differ diff --git a/Project#02/figures/hessian-file-format.png b/Project#02/figures/hessian-file-format.png new file mode 100644 index 0000000..29736b9 Binary files /dev/null and b/Project#02/figures/hessian-file-format.png differ diff --git a/Project#02/figures/hessian.png b/Project#02/figures/hessian.png new file mode 100644 index 0000000..769a566 Binary files /dev/null and b/Project#02/figures/hessian.png differ diff --git a/Project#02/figures/mass-weighted-hessian.png b/Project#02/figures/mass-weighted-hessian.png new file mode 100644 index 0000000..5f5e3b4 Binary files /dev/null and b/Project#02/figures/mass-weighted-hessian.png differ diff --git a/Project#02/figures/vib-freq.png b/Project#02/figures/vib-freq.png new file mode 100644 index 0000000..1d4617d Binary files /dev/null and b/Project#02/figures/vib-freq.png differ diff --git a/Project#02/hints/hint1.md b/Project#02/hints/hint1.md new file mode 100644 index 0000000..d37ff1e --- /dev/null +++ b/Project#02/hints/hint1.md @@ -0,0 +1,17 @@ +The Hessian stored in memory should be a square matrix, while the format of the input file is rectangular. Understanding the translation between the two takes a bit of thinking. Here's a partial code block that works for this purpose: +```c++ + ... + FILE *hessian; + int natom; + ... + + double **H = new double* [natom*3]; + for(int i=0; i < natom*3; i++) + H[i] = new double[natom*3]; + + for(int i=0; i < natom*3; i++) { + for(int j=0; j < natom; j++) { + fscanf(hessian, "%lf %lf %lf", &H[i][3*j], &H[i][3*j+1], &H[i][3*j+2]); + } + } +``` diff --git a/Project#02/hints/hint2.md b/Project#02/hints/hint2.md new file mode 100644 index 0000000..0da3f0a --- /dev/null +++ b/Project#02/hints/hint2.md @@ -0,0 +1,14 @@ +For the H2O test case, the 9×9 mass-weighted Hessian is: +``` + 1 2 3 4 5 6 7 8 9 + + 1 0.0057996 0.0000000 0.0000000 -0.0115523 0.0000000 0.0000000 -0.0115523 0.0000000 0.0000000 + 2 0.0000000 0.0198271 0.0000000 0.0000000 -0.0394937 0.0199304 0.0000000 -0.0394937 -0.0199304 + 3 0.0000000 0.0000000 0.0175112 0.0000000 0.0086617 -0.0348807 0.0000000 -0.0086617 -0.0348807 + 4 -0.0115523 0.0000000 0.0000000 0.0510672 0.0000000 0.0000000 -0.0050452 0.0000000 0.0000000 + 5 0.0000000 -0.0394937 0.0086617 0.0000000 0.1716643 -0.0569527 0.0000000 -0.0143291 0.0224462 + 6 0.0000000 0.0199304 -0.0348807 0.0000000 -0.0569527 0.1258526 0.0000000 -0.0224462 0.0131055 + 7 -0.0115523 0.0000000 0.0000000 -0.0050452 0.0000000 0.0000000 0.0510672 0.0000000 0.0000000 + 8 0.0000000 -0.0394937 -0.0086617 0.0000000 -0.0143291 -0.0224462 0.0000000 0.1716643 0.0569527 + 9 0.0000000 -0.0199304 -0.0348807 0.0000000 0.0224462 0.0131055 0.0000000 0.0569527 0.1258526 +``` diff --git a/Project#02/hints/hint3.md b/Project#02/hints/hint3.md new file mode 100644 index 0000000..7440aa9 --- /dev/null +++ b/Project#02/hints/hint3.md @@ -0,0 +1,12 @@ +The eigenvalues of the mass-weighted Hessian for the H2O test case (in atomic units) are: +``` + 8 0.2351542439 + 7 0.2107113210 + 6 0.1317512832 + 5 0.0561123974 + 4 0.0547551476 + 3 0.0518216614 + 2 0.0000000000 + 1 0.0000000000 + 0 0.0000000000 +``` diff --git a/Project#02/hints/hint4.md b/Project#02/hints/hint4.md new file mode 100644 index 0000000..ff7a389 --- /dev/null +++ b/Project#02/hints/hint4.md @@ -0,0 +1,13 @@ +The harmonic vibrational frequencies for the H2O test case (in cm-1) are: +``` + 8 2492.7600 + 7 2359.6522 + 6 1865.8704 + 5 1217.6808 + 4 1202.8640 + 3 1170.1990 + 2 0.0210 + 1 0.0000 + 0 0.0000 +``` +Note that there are only three zero frequencies in this case when there should be six. This is because the structure used in the computation is not a stationary point on the potential energy surface, and thus the three “rotational frequencies” are non-zero. diff --git a/Project#02/input/3c1b_geom.txt b/Project#02/input/3c1b_geom.txt new file mode 100644 index 0000000..5807948 --- /dev/null +++ b/Project#02/input/3c1b_geom.txt @@ -0,0 +1,13 @@ +12 + 6.0000000000 0.1690059610 3.1233433100 -0.3345553720 + 6.0000000000 -0.0386421959 0.4206229820 0.7520430680 + 6.0000000000 2.0569045600 -1.3758742600 -0.1486055380 + 6.0000000000 4.4719971000 -0.8585641720 -0.0315570842 + 1.0000000000 5.1968623000 0.9074367080 0.6974099730 + 1.0000000000 -1.3822808500 4.2799539600 0.3473315670 + 1.0000000000 5.8762121500 -2.2019961400 -0.6625964520 + 1.0000000000 1.4102155500 -3.1763622600 -0.8785797820 + 1.0000000000 -0.0505049904 0.5084677190 2.8179601800 + 1.0000000000 0.1191743850 3.0814658800 -2.3848397600 + 1.0000000000 1.9378539900 3.9710910300 0.2692445360 + 17.0000000000 -3.1213603000 -0.8957190610 -0.0958753352 diff --git a/Project#02/input/3c1b_hessian.txt b/Project#02/input/3c1b_hessian.txt new file mode 100644 index 0000000..d76214b --- /dev/null +++ b/Project#02/input/3c1b_hessian.txt @@ -0,0 +1,433 @@ + 12 + 0.8657865370 -0.0193723516 0.0037285582 + -0.1034653110 -0.0053915536 0.0064806574 + 0.0050877830 0.0279025738 -0.0110306541 + 0.0005287523 0.0008541335 0.0007205621 + -0.0000862171 0.0012219208 -0.0003643629 + -0.3029817730 0.1651959170 0.0995176887 + 0.0004078340 -0.0007663121 0.0006018250 + -0.0033086411 0.0018706724 0.0007392440 + 0.0025531857 0.0005286025 0.0008474632 + -0.0801500486 0.0005477647 -0.0099269319 + -0.3656960040 -0.1360388530 -0.0986442324 + -0.0186760972 -0.0365525139 0.0073301829 + -0.0193723516 0.7176364980 0.0541480410 + -0.0103690602 -0.2733669880 0.0732951671 + 0.0060738987 -0.0239076217 0.0066234440 + -0.0026717780 0.0001841977 0.0003721110 + -0.0000341409 -0.0004986819 0.0004856351 + 0.1668362290 -0.1945676090 -0.0748221434 + 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0.000000000000 0.000000000000 -0.134503695264 +1.00000000000 0.000000000000 -1.684916670000 1.067335684736 +1.00000000000 0.000000000000 1.684916670000 1.067335684736 diff --git a/Project#02/input/h2o_hessian.txt b/Project#02/input/h2o_hessian.txt new file mode 100644 index 0000000..bbfb967 --- /dev/null +++ b/Project#02/input/h2o_hessian.txt @@ -0,0 +1,28 @@ + 3 + 0.0927643390 0.0000000000 0.0000000000 + -0.0463821695 0.0000000000 0.0000000000 + -0.0463821695 0.0000000000 0.0000000000 + 0.0000000000 0.3171327134 0.0000000000 + 0.0000000000 -0.1585663567 0.0800202030 + 0.0000000000 -0.1585663567 -0.0800202030 + 0.0000000000 0.0000000000 0.2800907293 + 0.0000000000 0.0347765865 -0.1400453646 + 0.0000000000 -0.0347765865 -0.1400453646 + -0.0463821695 0.0000000000 0.0000000000 + 0.0514668232 0.0000000000 0.0000000000 + -0.0050846537 0.0000000000 0.0000000000 + 0.0000000000 -0.1585663567 0.0347765865 + 0.0000000000 0.1730075524 -0.0573983947 + 0.0000000000 -0.0144411957 0.0226218083 + 0.0000000000 0.0800202030 -0.1400453646 + 0.0000000000 -0.0573983947 0.1268373488 + 0.0000000000 -0.0226218083 0.0132080159 + -0.0463821695 0.0000000000 0.0000000000 + -0.0050846537 0.0000000000 0.0000000000 + 0.0514668232 0.0000000000 0.0000000000 + 0.0000000000 -0.1585663567 -0.0347765865 + 0.0000000000 -0.0144411957 -0.0226218083 + 0.0000000000 0.1730075524 0.0573983947 + 0.0000000000 -0.0800202030 -0.1400453646 + 0.0000000000 0.0226218083 0.0132080159 + 0.0000000000 0.0573983947 0.1268373488 diff --git a/Project#02/output/3c1b_vib_out.txt b/Project#02/output/3c1b_vib_out.txt new file mode 100644 index 0000000..7280401 --- /dev/null +++ b/Project#02/output/3c1b_vib_out.txt @@ -0,0 +1,76 @@ + +Hessian eigenvalues (hartree/amu-bohr^2): + 35 0.5504194388 + 34 0.5372530704 + 33 0.5351184811 + 32 0.5255730312 + 31 0.5062966607 + 30 0.4992575932 + 29 0.4845191221 + 28 0.1594678267 + 27 0.1246207278 + 26 0.1240628138 + 25 0.1124389759 + 24 0.1102183592 + 23 0.0940432225 + 22 0.0897847299 + 21 0.0836000497 + 20 0.0690595364 + 19 0.0640720123 + 18 0.0595822760 + 17 0.0569922250 + 16 0.0512084824 + 15 0.0498908695 + 14 0.0410337099 + 13 0.0283830220 + 12 0.0213722484 + 11 0.0088837125 + 10 0.0065288923 + 9 0.0046443780 + 8 0.0028070052 + 7 0.0022837821 + 6 0.0000001155 + 5 0.0000000871 + 4 0.0000000051 + 3 0.0000000000 + 2 0.0000000000 + 1 0.0000000000 + 0 -0.0004144295 + +Harmonic vibrational frequencies (cm^-1): + 35 3813.7387 + 34 3767.8491 + 33 3760.3566 + 32 3726.6670 + 31 3657.6874 + 30 3632.1719 + 29 3578.1580 + 28 2052.7714 + 27 1814.6764 + 26 1810.6098 + 25 1723.7032 + 24 1706.5972 + 23 1576.4050 + 22 1540.2999 + 21 1486.3029 + 20 1350.8772 + 19 1301.1826 + 18 1254.7656 + 17 1227.1901 + 16 1163.2552 + 15 1148.1922 + 14 1041.2966 + 13 866.0309 + 12 751.5003 + 11 484.5084 + 10 415.3592 + 9 350.3223 + 8 272.3489 + 7 245.6583 + 6 1.7468 + 5 1.5170 + 4 0.3667 + 3 0.0305 + 2 0.0290 + 1 0.0099 + 0 104.6476i diff --git a/Project#02/output/benzene_vib_out.txt b/Project#02/output/benzene_vib_out.txt new file mode 100644 index 0000000..de0cdc3 --- /dev/null +++ b/Project#02/output/benzene_vib_out.txt @@ -0,0 +1,76 @@ + +Hessian eigenvalues (hartree/amu-bohr^2): + 35 0.5314353702 + 34 0.5283614298 + 33 0.5283614298 + 32 0.5244972742 + 31 0.5244972740 + 30 0.5193180123 + 29 0.1413237674 + 28 0.1413237674 + 27 0.1189063721 + 26 0.1189063720 + 25 0.0963092312 + 24 0.0717564425 + 23 0.0711678923 + 22 0.0711678923 + 21 0.0568687601 + 20 0.0568687601 + 19 0.0558373314 + 18 0.0536488003 + 17 0.0536488003 + 16 0.0520195118 + 15 0.0506351705 + 14 0.0504228694 + 13 0.0407588957 + 12 0.0407588957 + 11 0.0267799115 + 10 0.0248951024 + 9 0.0185522334 + 8 0.0185522334 + 7 0.0086494099 + 6 0.0086494099 + 5 0.0000000170 + 4 0.0000000169 + 3 0.0000000169 + 2 0.0000000000 + 1 -0.0000000000 + 0 -0.0000000000 + +Harmonic vibrational frequencies (cm^-1): + 35 3747.3933 + 34 3736.5397 + 33 3736.5397 + 32 3722.8511 + 31 3722.8511 + 30 3704.4245 + 29 1932.4651 + 28 1932.4651 + 27 1772.5832 + 26 1772.5831 + 25 1595.2840 + 24 1377.0018 + 23 1371.3430 + 22 1371.3430 + 21 1225.8602 + 20 1225.8602 + 19 1214.6926 + 18 1190.6498 + 17 1190.6498 + 16 1172.4307 + 15 1156.7252 + 14 1154.2977 + 13 1037.8038 + 12 1037.8038 + 11 841.2181 + 10 811.0750 + 9 700.1678 + 8 700.1678 + 7 478.0764 + 6 478.0764 + 5 0.6694 + 4 0.6683 + 3 0.6683 + 2 0.0247 + 1 0.0116i + 0 0.0165i diff --git a/Project#02/output/h2o_vib_out.txt b/Project#02/output/h2o_vib_out.txt new file mode 100644 index 0000000..f491413 --- /dev/null +++ b/Project#02/output/h2o_vib_out.txt @@ -0,0 +1,22 @@ + +Hessian eigenvalues (hartree/amu-bohr^2): + 8 0.2351542439 + 7 0.2107113210 + 6 0.1317512832 + 5 0.0561123974 + 4 0.0547551476 + 3 0.0518216614 + 2 0.0000000000 + 1 0.0000000000 + 0 0.0000000000 + +Harmonic vibrational frequencies (cm^-1): + 8 2492.7600 + 7 2359.6522 + 6 1865.8704 + 5 1217.6808 + 4 1202.8640 + 3 1170.1990 + 2 0.0210 + 1 0.0000 + 0 0.0000 diff --git a/Project#02/project2-instructions.pdf b/Project#02/project2-instructions.pdf new file mode 100644 index 0000000..c09d512 Binary files /dev/null and b/Project#02/project2-instructions.pdf differ diff --git a/Project#03/README.md b/Project#03/README.md index 8a38fe4..f0ff162 100644 --- a/Project#03/README.md +++ b/Project#03/README.md @@ -1 +1,226 @@ # Project #3: The Hartree-Fock self-consistent field (SCF) procedure + +The purpose of this project is to provide a deeper understanding of Hartree-Fock theory by +demonstrating a simple implementation of the self-consistent-field method. +The theoretical background can be found in Ch. 3 of the text by Szabo and Ostlund or in the +[nice set of on-line notes](http://vergil.chemistry.gatech.edu/notes/hf-intro/hf-intro.html) written by David Sherrill. +A concise set of instructions for this project may be found [here](./project3-instructions.pdf). + +We thank Dr. Yukio Yamaguchi of the University of Georgia for the original version of this project. + +The test case used in the following discussion is for a water molecule with a bond-length of 1.1 Å +and a bond angle of 104.0o with an STO-3G basis set. The input to the project consists of the +[nuclear repulsion energy](./input/h2o/STO-3G/enuc.dat) + and pre-computed sets of one- and two-electron integrals: +[overlap integrals](./input/h2o/STO-3G/s.dat), +[kinetic-energy integrals](./input/h2o/STO-3G/t.dat), +[nuclear-attraction integrals](./input/h2o/STO-3G/v.dat), +[electron-electron repulsion integrals](./input/h2o/STO-3G/eri.dat). + + +## Step 1: Nuclear Repulsion Energy + +Read the nuclear repulsion energy from the [enuc.dat](./input/h2o/STO-3G/enuc.dat) + +## Step 2: One-Electron Integrals + +Read the AO-basis [overlap](./input/h2o/STO-3G/s.dat) + + + +[kinetic-energy](./input/h2o/STO-3G/t.dat) + + + +[nuclear-attraction integrals](./input/h2o/STO-3G/v.dat) + + + +and store them in appropriately constructed matrices. Then form the "core Hamiltonian": + + + +Note that the one-electron integrals provided include only the *permutationally unique* integrals, but you should store the full matrices for convenience. +Note also that the AO indices on the integrals in the files start with "1" rather than "0". + + * [Hint 1](./hints/hint2-1.md): Core Hamiltonian + +## Step #3: Two-Electron Integrals + +Read the two-electron repulsion integrals from the +[eri.dat](./input/h2o/STO-3G/eri.dat) +file. +The integrals in this file are provided in Mulliken notation over real AO basis functions: + + + +Hence, the integrals obey the eight-fold permutational symmetry relationships: + + + +and only the permutationally unique integrals are provided in the file, with the restriction that, for each integral, the following relationships hold: + + + +where + + + +Note that the two-electron integrals may be stored efficiently in a one-dimensional array and the above relationship used to map between given +μ, ν, λ, and σ indices and a "compound index" defined as: + + + + * [Hint 1](./hints/hint3-1.md): Compound indices + * [Hint 2](./hints/hint3-2.md): Pre-Computed Lookup Arrays + * [Hint 3](./hints/hint3-3.md): Reading the two-electron integrals + + +## Step 4: Build the Orthogonalization Matrix + +Diagonalize the overlap matrix: + + + +where LS is the matrix of eigenvectors (columns) and ΛS is the diagonal matrix of corresponding eigenvalues. + +Build the symmetric orthogonalization matrix using: + + + +where the tilde denotes the matrix transpose. + + * [Hint 1](./hints/hint4-1.md): S-1/2 Matrix + + +## Step 5: Build the Initial Guess Density + +Form an initial (guess) Fock matrix in the orthonormal AO basis using the core Hamiltonian as a guess: + + + +Diagonalize the Fock matrix: + + + +Note that the ε0 matrix contains the initial orbital energies. + +Transform the eigenvectors into the original (non-orthogonal) AO basis: + + + +Build the density matrix using the occupied MOs: + + + +where *m* indexes the columns of the coefficient matrices, and the summation includes only the occupied spatial MOs. + + * [Hint 1](./hints/hint5-1.md): Transformed Fock matrix + * [Hint 2](./hints/hint5-2.md): Initial MO Coefficients + * [Hint 3](./hints/hint5-3.md): Initial Density Matrix + +## Step 6: Compute the Inital SCF Energy + +The SCF electronic energy may be computed using the density matrix as: + + + +The total energy is the sum of the electronic energy and the nuclear repulsion energy: + + + +where *0* denotes the initial SCF energy. + + * [Hint 1](./hints/hint6-1.md): Initial Electronic Energy + +## Step #7: Compute the New Fock Matrix + +Start the SCF iterative procedure by building a new Fock matrix using the previous iteration's density as: + + + +where the double-summation runs over all the AOs and *i-1* denotes the density for the last iteration. + + * [Hint 1](./hints/hint7-1.md): New Fock Matrix + * [Hint 2](./hints/hint7-2.md): Fock-Build Code + +## Step #8: Build the New Density Matrix + +Form the new density matrix following the same procedure as in Step #5 above: + +Orthogonalize: + + + +Diagonalize: + + + +Back-transform: + + + +Compute the density: + + + +where *i* denotes the current iteration density. + +## Step #9: Compute the New SCF Energy + +Compute the new SCF energy as before: + + + +where *i* denotes the SCF energy for the *i*th iteration. + +## Step #10: Test for Convergence +Test both the energy and the density for convergence: + + + +If the difference in consecutive SCF energy and the root-mean-squared difference in consecutive densities do not fall below the prescribed thresholds, return to Step #7 and continue from there. + + * [Hint 1](./hints/hint10-1.md): Energies for Each Iteration + +## Additional Concepts +### The MO-Basis Fock Matrix +At convergence, the canonical Hartree-Fock MOs are, by definition, eigenfunctions of the Fock operator, viz. + + + +If we multiply on the left by an arbitrary MO and integrate, we obtain: + + + +In other words, the Fock matrix should be diagonal in the MO basis, with the orbital energies as its diagonal elements. We can demonstrate this explicitly using the AO-basis Fock matrix by first re-writing the above expression using the LCAO-MO coefficients: + + + +Use the above equation to transform the Fock matrix from the AO basis to the MO basis and demonstrate that it is indeed diagonal (to within the convergence limits of the SCF iterative procedure). + +### One-Electron Properties +As discussed in detail in Ch. 3 of the text by Szabo and Ostlund, the calculation of one-electron properties requires density matrix and the relevant property integrals. The electronic contribution to the electric-dipole moment may be computed using, + + + +where the vector notation implies three sets of dipole-moment integrals -- one for each Cartesian component of the dipole operator. + +Two points to note: + - In order to compute the total dipole moment, you must include the nuclear contribution, which requires the atomic numbers and Cartesian coordinates of the nuclei, in addition to the above. + - The factor 2 appearing above arises because the definition of the density used in this project differs from that used in Szabo & Ostlund. + +The test cases provided below include the structural information dipole integrals needed to compute the dipole moment. + +### Population Analysis/Atomic Charges +A Mulliken population analysis (also described in Szabo & Ostlund, Ch. 3) requires the overlap integrals and the electron density, in addition to information about the number of basis functions centered on each atom. The charge on atom *A* may be computed as: + + + +where the summation is limited to only those basis functions centered on atom *A*. + +## Test Cases + * STO-3G Water: [Geometry](./input/h2o/STO-3G/geom.dat) | [Enuc](./input/h2o/STO-3G/enuc.dat) | [S](./input/h2o/STO-3G/s.dat) | [T](./input/h2o/STO-3G/t.dat) | [V](./input/h2o/STO-3G/v.dat) | [ERI](./input/h2o/STO-3G/eri.dat) | [Mu_X](./input/h2o/STO-3G/mux.dat) | [Mu_Y](./input/h2o/STO-3G/muy.dat) | [Mu_Z](./input/h2o/STO-3G/muz.dat) | [output](./output/h2o/STO-3G/output.txt) + * DZ Water: [Geometry](./input/h2o/DZ/geom.dat) | [Enuc](./input/h2o/DZ/enuc.dat) | [S](./input/h2o/DZ/s.dat) | [T](./input/h2o/DZ/t.dat) | [V](./input/h2o/DZ/v.dat) | [ERI](./input/h2o/DZ/eri.dat) | [Mu_X](./input/h2o/DZ/mux.dat) | [Mu_Y](./input/h2o/DZ/muy.dat) | [Mu_Z](./input/h2o/DZ/muz.dat) | [output](./output/h2o/DZ/output.txt) + * DZP Water: [Geometry](./input/h2o/DZP/geom.dat) | [Enuc](./input/h2o/DZP/enuc.dat) | [S](./input/h2o/DZP/s.dat) | [T](./input/h2o/DZP/t.dat) | [V](./input/h2o/DZP/v.dat) | [ERI](./input/h2o/DZP/eri.dat) | [Mu_X](./input/h2o/DZP/mux.dat) | [Mu_Y](./input/h2o/DZP/muy.dat) | [Mu_Z](./input/h2o/DZP/muz.dat) | [output](./output/h2o/DZP/output.txt) + * STO-3G Methane: [Geometry](./input/ch4/STO-3G/geom.dat) | [Enuc](./input/ch4/STO-3G/enuc.dat) | [S](./input/ch4/STO-3G/s.dat) | [T](./input/ch4/STO-3G/t.dat) | [V](./input/ch4/STO-3G/v.dat) | [ERI](./input/ch4/STO-3G/eri.dat) | [Mu_X](./input/ch4/STO-3G/mux.dat) | [Mu_Y](./input/ch4/STO-3G/muy.dat) | [Mu_Z](./input/ch4/STO-3G/muz.dat) | [output](./output/ch4/STO-3G/output.txt) diff --git a/Project#03/figures/atomic-charge.png b/Project#03/figures/atomic-charge.png new file mode 100644 index 0000000..4442851 Binary files /dev/null and b/Project#03/figures/atomic-charge.png differ diff --git a/Project#03/figures/back-transform-coeff.png b/Project#03/figures/back-transform-coeff.png new file mode 100644 index 0000000..f5cfdce Binary files /dev/null and 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0000000..a48f076 Binary files /dev/null and b/Project#03/figures/permutational-symmetry.png differ diff --git a/Project#03/figures/symm-orthog-matrix.png b/Project#03/figures/symm-orthog-matrix.png new file mode 100644 index 0000000..7a9051a Binary files /dev/null and b/Project#03/figures/symm-orthog-matrix.png differ diff --git a/Project#03/figures/symmetric-integral-matrix.png b/Project#03/figures/symmetric-integral-matrix.png new file mode 100644 index 0000000..eebcc2a Binary files /dev/null and b/Project#03/figures/symmetric-integral-matrix.png differ diff --git a/Project#03/figures/transform-coeff.png b/Project#03/figures/transform-coeff.png new file mode 100644 index 0000000..12dfbb0 Binary files /dev/null and b/Project#03/figures/transform-coeff.png differ diff --git a/Project#03/hints/hint10-1.md b/Project#03/hints/hint10-1.md new file mode 100644 index 0000000..422bdcf --- /dev/null +++ b/Project#03/hints/hint10-1.md @@ -0,0 +1,40 @@ +The iteration-by-iteration electronic and total energies for the H2O test case are as follows: + +``` + Iter E(elec) E(tot) Delta(E) RMS(D) + 00 -125.842077437699 -117.839710375888 + 01 -78.286583284740 -70.284216222929 47.555494152959 1.826673084479 + 02 -84.048316253435 -76.045949191625 -5.761732968696 0.479570364860 + 03 -82.716965960855 -74.714598899044 1.331350292581 0.086831688906 + 04 -82.987140757002 -74.984773695191 -0.270174796147 0.031026136359 + 05 -82.938133187513 -74.935766125703 0.049007569488 0.010799283179 + 06 -82.946271078699 -74.943904016889 -0.008137891186 0.005254826831 + 07 -82.944486784914 -74.942119723104 0.001784293785 0.002438579642 + 08 -82.944617252243 -74.942250190433 -0.000130467329 0.001177279531 + 09 -82.944503500703 -74.942136438892 0.000113751541 0.000564543180 + 10 -82.944478930626 -74.942111868815 0.000024570077 0.000272204992 + 11 -82.944461627684 -74.942094565874 0.000017302941 0.000131180309 + 12 -82.944454198375 -74.942087136564 0.000007429310 0.000063275666 + 13 -82.944450445051 -74.942083383241 0.000003753324 0.000030522547 + 14 -82.944448661686 -74.942081599875 0.000001783365 0.000014725847 + 15 -82.944447795931 -74.942080734120 0.000000865755 0.000007104836 + 16 -82.944447379016 -74.942080317206 0.000000416914 0.000003428026 + 17 -82.944447177685 -74.942080115875 0.000000201331 0.000001654014 + 18 -82.944447080565 -74.942080018755 0.000000097120 0.000000798065 + 19 -82.944447033699 -74.942079971888 0.000000046867 0.000000385069 + 20 -82.944447011086 -74.942079949276 0.000000022613 0.000000185798 + 21 -82.944447000175 -74.942079938365 0.000000010911 0.000000089648 + 22 -82.944446994911 -74.942079933100 0.000000005264 0.000000043256 + 23 -82.944446992371 -74.942079930560 0.000000002540 0.000000020871 + 24 -82.944446991145 -74.942079929334 0.000000001226 0.000000010070 + 25 -82.944446990554 -74.942079928743 0.000000000591 0.000000004859 + 26 -82.944446990268 -74.942079928458 0.000000000285 0.000000002345 + 27 -82.944446990130 -74.942079928320 0.000000000138 0.000000001131 + 28 -82.944446990064 -74.942079928254 0.000000000066 0.000000000546 + 29 -82.944446990032 -74.942079928222 0.000000000032 0.000000000263 + 30 -82.944446990016 -74.942079928206 0.000000000016 0.000000000127 + 31 -82.944446990009 -74.942079928199 0.000000000007 0.000000000061 + 32 -82.944446990005 -74.942079928195 0.000000000004 0.000000000030 + 33 -82.944446990004 -74.942079928193 0.000000000002 0.000000000014 + 34 -82.944446990003 -74.942079928192 0.000000000001 0.000000000007 +``` diff --git a/Project#03/hints/hint2-1.md b/Project#03/hints/hint2-1.md new file mode 100644 index 0000000..b5217e6 --- /dev/null +++ b/Project#03/hints/hint2-1.md @@ -0,0 +1,12 @@ +The core Hamiltonian for the H2O test case is: +``` + 1 2 3 4 5 6 7 + + 1 -32.5773954 -7.5788328 0.0000000 -0.0144738 0.0000000 -1.2401023 -1.2401023 + 2 -7.5788328 -9.2009433 0.0000000 -0.1768902 0.0000000 -2.9067098 -2.9067098 + 3 0.0000000 0.0000000 -7.4588193 0.0000000 0.0000000 -1.6751501 1.6751501 + 4 -0.0144738 -0.1768902 0.0000000 -7.4153118 0.0000000 -1.3568683 -1.3568683 + 5 0.0000000 0.0000000 0.0000000 0.0000000 -7.3471449 0.0000000 0.0000000 + 6 -1.2401023 -2.9067098 -1.6751501 -1.3568683 0.0000000 -4.5401711 -1.0711459 + 7 -1.2401023 -2.9067098 1.6751501 -1.3568683 0.0000000 -1.0711459 -4.5401711 +``` diff --git a/Project#03/hints/hint3-1.md b/Project#03/hints/hint3-1.md new file mode 100644 index 0000000..1446996 --- /dev/null +++ b/Project#03/hints/hint3-1.md @@ -0,0 +1,35 @@ +## Symettric Matrices +How do we conveniently store the elements of the four-dimensional two-electron integral array in a one-dimensional array? Consider the lower triangle of an *n x n* symmetric matrix: + + + +The total number of elements in the lower triangle is *M = n(n+1)/2*. We could store these in a one-dimensional array by ordering them from top-to-bottom, left-to-right: + + + +How do we translate row (*i*) and column (*j*) indices of the matrix to the position in the linear array (*ij*)? + + + +Here's a code block to calculate the compound index using a standard [if-then-else conditional](https://github.com/CrawfordGroup/ProgrammingProjects/wiki/Control-Statements): +```c++ + int i, j, ij; + ... + if(i>j) ij = i*(i+1)/2 + j; + else ij = j*(j+1)/2 + i; +``` +Here's an equivalent piece of code that requires fewer keystrokes: +```c++ + int i, j, ij; + ... + ij = i>j ? i*(i+1)/2 + j : j*(j+1)/2 + i; +``` + +## Four-Dimensional Arrays +The eight-fold permutational symmetry of the two-electron repulsion integrals can be viewed similarly. The Mulliken-notation integrals are symmetric to permutations of the bra indices or of the ket indices. Hence, we can view the integral list as a symmetric "super-matrix" of the form: + + + +Thus, just as for the two-dimensional case above, we only need to store the lower triangle of this matrix, and a one-dimensional array of length *M(M+1)/2* will do the trick. Given four AO indices, *i*, *j*, *k*, and *l* corresponding to the integral, (ij|kl), we can translate these into compound row (*ij*) and column (*kl*) indices using the expression above, as well as the final compound index: + + diff --git a/Project#03/hints/hint3-2.md b/Project#03/hints/hint3-2.md new file mode 100644 index 0000000..77b74c5 --- /dev/null +++ b/Project#03/hints/hint3-2.md @@ -0,0 +1,20 @@ +If you've written your program so that the two-electron integrals are stored in a one-dimensional array, you may have recognized that your program spends quite a bit of its time calculating compound indices. Is there a way to speed up this process? Sure! Pre-compute the indices instead. Look again at the structure of a symmetric matrix, with the elements of the lower triangle numbered top-to-bottom/left-to-right: + + + +We calculate these above values from the raw row and column indices, *i* and *j*, respectively using: + + + +The expensive part of the above expression is the repeated evaluation of the *i(i+1)/2* and *j(j+1)/2* parts (which correspond to the first column of numbers in the above matrix). However, if we were to build an integer array (named `ioff`, for example) to store these values, then we could simplify the task to use array look-ups instead: +```c++ +ij = (i>j) ? ioff[i] + j : ioff[j] + i; +``` + +We can build the ioff array using a recursion: +```c++ +ioff[0] = 0; +for(int i=1; i < BIGNUM; i++) + ioff[i] = ioff[i-1] + i; +``` +where `BIGNUM` is some large number exceeding the maximum row/column dimension we expect to use in our calculations. diff --git a/Project#03/hints/hint3-3.md b/Project#03/hints/hint3-3.md new file mode 100644 index 0000000..87a6f2b --- /dev/null +++ b/Project#03/hints/hint3-3.md @@ -0,0 +1,43 @@ +Previously the [Hessian](../../Project%2302/hints/hint1.md) ([Project #2](../../Project%2302/)) and the one-electron quantities so far in [Project 3](../../Project%2303) have been provided in an order that makes reading them in using a loop structure trivial. + +```c++ + ... + + FILE *input; + int a, b; + double **S; + + ... + + input = fopen("s.dat", "r"); + for(int i=0; i < nao; i++) { + for(int j=0; j <= i; j++) { + fscanf(hessian, "%d %d %lf", &a, &b, &S[i][j]); + S[j][i] = S[i][j]; + } + } + fclose(input); +``` + +However the two-electron integrals are not provided in this convenient ordering, you could go through the file and attempt to reorder them so that a loop structure works, or you could put the previously ignored index information you're reading with your fscanf to good use. This prevents the use of hard-wired loops that assume a specific ordering of the data, and it also prevents having to calculate how many elements are in the file to be read. + +```c++ + ... + + FILE *input; + int i, j, k, l; + double val; + double **TEI; + + ... + + input = fopen("eri.dat", "r"); + while(fscanf(input, "%d %d %d %d %lf", &i, &j, &k, &l, &val) != EOF) { + + ... + + TEI[ijkl] = val; + } + fclose(input); +``` +The `EOF` above is the [end-of-file](http://en.wikipedia.org/wiki/End-of-file) condition, so `!= EOF` means the above while loop scans the file until it reaches the end. diff --git a/Project#03/hints/hint4-1.md b/Project#03/hints/hint4-1.md new file mode 100644 index 0000000..73ae91c --- /dev/null +++ b/Project#03/hints/hint4-1.md @@ -0,0 +1,12 @@ +The S-1/2 matrix for the H2O test case is: +``` + 1 2 3 4 5 6 7 + + 1 1.0236346 -0.1368547 -0.0000000 -0.0074873 -0.0000000 0.0190279 0.0190279 + 2 -0.1368547 1.1578632 0.0000000 0.0721601 0.0000000 -0.2223326 -0.2223326 + 3 -0.0000000 0.0000000 1.0733148 0.0000000 -0.0000000 -0.1757583 0.1757583 + 4 -0.0074873 0.0721601 0.0000000 1.0383050 0.0000000 -0.1184626 -0.1184626 + 5 -0.0000000 0.0000000 -0.0000000 0.0000000 1.0000000 -0.0000000 -0.0000000 + 6 0.0190279 -0.2223326 -0.1757583 -0.1184626 -0.0000000 1.1297234 -0.0625975 + 7 0.0190279 -0.2223326 0.1757583 -0.1184626 -0.0000000 -0.0625975 1.1297234 +``` diff --git a/Project#03/hints/hint5-1.md b/Project#03/hints/hint5-1.md new file mode 100644 index 0000000..7bd2dea --- /dev/null +++ b/Project#03/hints/hint5-1.md @@ -0,0 +1,13 @@ +The initial Fock matrix in the orthogonal AO basis for the H2O test case is: + +``` + 1 2 3 4 5 6 7 + + 1 -32.2545866 -2.7914909 -0.0000000 0.0086110 0.0000000 -0.1812967 -0.1812967 + 2 -2.7914909 -8.2368891 -0.0000000 -0.2282926 0.0000000 -0.3857987 -0.3857987 + 3 -0.0000000 -0.0000000 -7.5428890 -0.0000000 0.0000000 -0.1132121 0.1132121 + 4 0.0086110 -0.2282926 -0.0000000 -7.4570295 -0.0000000 -0.1102196 -0.1102196 + 5 0.0000000 0.0000000 0.0000000 -0.0000000 -7.3471449 0.0000000 0.0000000 + 6 -0.1812967 -0.3857987 -0.1132121 -0.1102196 0.0000000 -4.0329547 -0.0446466 + 7 -0.1812967 -0.3857987 0.1132121 -0.1102196 0.0000000 -0.0446466 -4.0329547 +``` diff --git a/Project#03/hints/hint5-2.md b/Project#03/hints/hint5-2.md new file mode 100644 index 0000000..e1be5eb --- /dev/null +++ b/Project#03/hints/hint5-2.md @@ -0,0 +1,13 @@ +The initial MO coefficient matrix for the H2O test case is: + +``` + 1 2 3 4 5 6 7 + + 1 -1.0015436 0.2336245 0.0000000 0.0856842 0.0000000 -0.0482226 -0.0000000 + 2 0.0071893 -1.0579388 -0.0000000 -0.3601105 -0.0000000 0.4631213 0.0000000 + 3 -0.0000000 -0.0000000 1.0610702 0.0000000 -0.0000000 -0.0000000 0.2965071 + 4 0.0002671 -0.4272843 -0.0000000 0.9399425 0.0000000 0.2129401 0.0000000 + 5 0.0000000 0.0000000 -0.0000000 0.0000000 -1.0000000 -0.0000000 -0.0000000 + 6 -0.0018213 0.1492533 -0.1377210 -0.0378579 0.0000000 -0.7807003 -0.8501403 + 7 -0.0018213 0.1492533 0.1377210 -0.0378579 -0.0000000 -0.7807003 0.8501403 +``` diff --git a/Project#03/hints/hint5-3.md b/Project#03/hints/hint5-3.md new file mode 100644 index 0000000..cdab244 --- /dev/null +++ b/Project#03/hints/hint5-3.md @@ -0,0 +1,13 @@ +The initial density matrix for the H2O test case is: + +``` + 1 2 3 4 5 6 7 + + 1 1.0650117 -0.2852166 -0.0000000 -0.0195534 -0.0000000 0.0334496 0.0334496 + 2 -0.2852166 1.2489657 0.0000000 0.1135594 0.0000000 -0.1442809 -0.1442809 + 3 -0.0000000 0.0000000 1.1258701 -0.0000000 -0.0000000 -0.1461317 0.1461317 + 4 -0.0195534 0.1135594 -0.0000000 1.0660638 0.0000000 -0.0993583 -0.0993583 + 5 -0.0000000 0.0000000 -0.0000000 0.0000000 1.0000000 -0.0000000 -0.0000000 + 6 0.0334496 -0.1442809 -0.1461317 -0.0993583 -0.0000000 0.0426802 0.0047460 + 7 0.0334496 -0.1442809 0.1461317 -0.0993583 -0.0000000 0.0047460 0.0426802 +``` diff --git a/Project#03/hints/hint6-1.md b/Project#03/hints/hint6-1.md new file mode 100644 index 0000000..b0d9ebf --- /dev/null +++ b/Project#03/hints/hint6-1.md @@ -0,0 +1 @@ +The initial Hartree-Fock electronic energy for the H2O test case is -125.842077437699 Hartrees. diff --git a/Project#03/hints/hint7-1.md b/Project#03/hints/hint7-1.md new file mode 100644 index 0000000..e0e2226 --- /dev/null +++ b/Project#03/hints/hint7-1.md @@ -0,0 +1,13 @@ +The first-iteration Fock matrix in the AO basis for the H2O test case is: + +``` + 1 2 3 4 5 6 7 + + 1 -18.8132695 -4.8726875 -0.0000000 -0.0115290 0.0000000 -0.8067323 -0.8067323 + 2 -4.8726875 -1.7909029 -0.0000000 -0.1808692 0.0000000 -0.5790557 -0.5790557 + 3 -0.0000000 -0.0000000 0.1939644 0.0000000 0.0000000 -0.1708886 0.1708886 + 4 -0.0115290 -0.1808692 0.0000000 0.2391247 0.0000000 -0.1828683 -0.1828683 + 5 0.0000000 0.0000000 0.0000000 0.0000000 0.3091071 0.0000000 0.0000000 + 6 -0.8067323 -0.5790557 -0.1708886 -0.1828683 0.0000000 -0.1450338 -0.1846675 + 7 -0.8067323 -0.5790557 0.1708886 -0.1828683 0.0000000 -0.1846675 -0.1450338 +``` diff --git a/Project#03/hints/hint7-2.md b/Project#03/hints/hint7-2.md new file mode 100644 index 0000000..0e502aa --- /dev/null +++ b/Project#03/hints/hint7-2.md @@ -0,0 +1,22 @@ +The following code illustrates the basic algorithm for building the Fock matrix (F) using the core Hamiltonian matrix (H), the density matrix (D), and the two-electron integrals stored in a one-dimensional array (TEI): +```c++ +for(int i=0; i < nao; i++) + for(int j=0; j < nao; j++) { + F[i][j] = H[i][j]; + for(int k=0; k < nao; k++) + for(int l=0; l < nao; l++) { + ij = INDEX(i,j); + kl = INDEX(k,l); + ijkl = INDEX(ij,kl); + ik = INDEX(i,k); + jl = INDEX(j,l); + ikjl = INDEX(ik,jl); + + F[i][j] += D[k][l] * (2.0 * TEI[ijkl] - TEI[ikjl]); + } + } +``` +The `INDEX` function is most easily defined as a macro using the `ioff` array explained in [an earlier hint](./hint3-2.md), e.g.: +```c++ +#define INDEX(i,j) (i>j) ? (ioff[i]+j) : (ioff[j]+i) +``` diff --git a/Project#03/input/ch4/STO-3G/enuc.dat b/Project#03/input/ch4/STO-3G/enuc.dat new file mode 100644 index 0000000..feb8199 --- /dev/null +++ b/Project#03/input/ch4/STO-3G/enuc.dat @@ -0,0 +1 @@ + 13.497304462036480 diff --git a/Project#03/input/ch4/STO-3G/eri.dat b/Project#03/input/ch4/STO-3G/eri.dat new file mode 100644 index 0000000..b1c1a16 --- /dev/null +++ b/Project#03/input/ch4/STO-3G/eri.dat @@ -0,0 +1,912 @@ + 1 1 1 1 3.541948297688456 + 2 1 1 1 0.576921328341946 + 2 2 1 1 0.854681772892244 + 2 1 2 1 0.111888125975301 + 2 2 2 1 0.205283870818581 + 2 2 2 2 0.624708798510611 + 3 3 1 1 0.852436095451127 + 4 4 1 1 0.852436095451127 + 5 5 1 1 0.852436095451127 + 3 1 3 1 0.020296465970775 + 4 1 4 1 0.020296465970775 + 5 1 5 1 0.020296465970775 + 3 3 2 1 0.205335088917950 + 4 4 2 1 0.205335088917950 + 5 5 2 1 0.205335088917950 + 3 2 3 1 0.030857749607787 + 4 2 4 1 0.030857749607787 + 5 2 5 1 0.030857749607787 + 3 3 2 2 0.624568373997849 + 4 4 2 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0.023364154750318 + 9 9 8 6 0.055912476950067 + 9 8 9 6 0.012847889010515 + 9 9 8 7 0.055912476950067 + 9 8 9 7 0.012847889010515 + 9 9 8 8 0.296353939081570 + 9 8 9 8 0.015770501299918 + 9 9 9 1 0.031703797879678 + 9 9 9 2 0.304981529941436 + 9 9 9 3 -0.206879432071914 + 9 9 9 4 -0.206879432071914 + 9 9 9 5 0.206879432071914 + 9 9 9 6 0.085276746780538 + 9 9 9 7 0.085276746780538 + 9 9 9 8 0.085276746780538 + 9 9 9 9 0.774605895725855 diff --git a/Project#03/input/ch4/STO-3G/geom.dat b/Project#03/input/ch4/STO-3G/geom.dat new file mode 100644 index 0000000..9c536a9 --- /dev/null +++ b/Project#03/input/ch4/STO-3G/geom.dat @@ -0,0 +1,6 @@ +5 +6.000000000000 -0.000000000000 0.000000000000 0.000000000000 +1.000000000000 1.183771681898 -1.183771681898 -1.183771681898 +1.000000000000 1.183771681898 1.183771681898 1.183771681898 +1.000000000000 -1.183771681898 1.183771681898 -1.183771681898 +1.000000000000 -1.183771681898 -1.183771681898 1.183771681898 diff --git a/Project#03/input/ch4/STO-3G/input.dat b/Project#03/input/ch4/STO-3G/input.dat new file mode 100644 index 0000000..6dfb483 --- /dev/null +++ b/Project#03/input/ch4/STO-3G/input.dat @@ -0,0 +1,43 @@ +psi: ( + label = "CH4 SCF Test Case" + wfn = scf + jobtype = oeprop + reference = rhf + basis = "STO-3G" + units = angstrom + subgroup = c1 + delete_tei = false + delete_oei = false + zmat = ( + C + H 1 r + H 1 r 2 td + H 1 r 2 td 3 d + H 1 r 2 td 4 d + ) + zvars = ( + r 1.085 + td 109.47122063449069136958 + d 120.0 + ) +) + +basis: ( + carbon: "STO-3G" = + ( (S ( 71.61683730 0.15432900) + ( 13.04509630 0.53532810) + ( 3.53051220 0.44463450) ) + (S ( 2.94124940 -0.09996720) + ( 0.68348310 0.39951280) + ( 0.22228990 0.70011550) ) + (P ( 2.94124940 0.15591630) + ( 0.68348310 0.60768370) + ( 0.22228990 0.39195740) ) + ) + + hydrogen: "STO-3G"= + ( (S ( 3.42525090 0.15432890) + ( 0.62391370 0.53532810) + ( 0.16885540 0.44463450) ) + ) +) diff --git a/Project#03/input/ch4/STO-3G/mux.dat 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1.1 2 104.0)) +) diff --git a/Project#03/input/h2o/DZ/mux.dat b/Project#03/input/h2o/DZ/mux.dat new file mode 100644 index 0000000..900a852 --- /dev/null +++ b/Project#03/input/h2o/DZ/mux.dat @@ -0,0 +1,105 @@ + 1 1 -0.000000000000000 + 2 1 -0.000000000000000 + 2 2 -0.000000000000000 + 3 1 -0.000000000000000 + 3 2 -0.000000000000000 + 3 3 -0.000000000000000 + 4 1 -0.000000000000000 + 4 2 -0.000000000000000 + 4 3 -0.000000000000000 + 4 4 -0.000000000000000 + 5 1 -0.065756994029223 + 5 2 -0.076390812514647 + 5 3 -0.495548317796719 + 5 4 -0.578524588047388 + 5 5 -0.000000000000000 + 6 1 0.000000000000000 + 6 2 0.000000000000000 + 6 3 0.000000000000000 + 6 4 -0.000000000000000 + 6 5 0.000000000000000 + 6 6 -0.000000000000000 + 7 1 -0.000000000000000 + 7 2 -0.000000000000000 + 7 3 -0.000000000000000 + 7 4 0.000000000000000 + 7 5 0.000000000000000 + 7 6 0.000000000000000 + 7 7 -0.000000000000000 + 8 1 -0.010743922716727 + 8 2 -0.007518663156056 + 8 3 -0.274494236174552 + 8 4 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b/Project#03/input/h2o/DZP/input.dat new file mode 100644 index 0000000..8cf45b4 --- /dev/null +++ b/Project#03/input/h2o/DZP/input.dat @@ -0,0 +1,13 @@ +psi: ( + label = "H2O SCF Test Case" + memory = (10.0 MB) + wfn = scf + jobtype = oeprop + delete_tei = false + delete_oei = false + reference = rhf + puream = false + basis = "DZP" + subgroup = c1 + zmat = ((o) (h 1 1.1) (h 1 1.1 2 104.0)) +) diff --git a/Project#03/input/h2o/DZP/mux.dat b/Project#03/input/h2o/DZP/mux.dat new file mode 100644 index 0000000..9eeb14c --- /dev/null +++ b/Project#03/input/h2o/DZP/mux.dat @@ -0,0 +1,351 @@ + 1 1 -0.000000000000000 + 2 1 -0.000000000000000 + 2 2 -0.000000000000000 + 3 1 -0.000000000000000 + 3 2 -0.000000000000000 + 3 3 -0.000000000000000 + 4 1 -0.000000000000000 + 4 2 -0.000000000000000 + 4 3 -0.000000000000000 + 4 4 -0.000000000000000 + 5 1 -0.065756994029223 + 5 2 -0.076390812514647 + 5 3 -0.495548317796719 + 5 4 -0.578524588047388 + 5 5 -0.000000000000000 + 6 1 0.000000000000000 + 6 2 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0.470723326368778 + 7 1 7 1 0.003683107960076 + 7 7 2 1 0.111191806911617 + 7 2 7 1 0.012121617421746 + 7 7 2 2 0.454660662254829 + 7 2 7 2 0.103816561020432 + 7 7 3 1 -0.008115429695629 + 7 7 4 1 0.006340468574121 + 7 3 7 1 -0.007487641649768 + 7 4 7 1 0.005849986797397 + 7 7 3 2 -0.088850240147481 + 7 7 4 2 0.069417415538897 + 7 3 7 2 -0.079876222072782 + 7 4 7 2 0.062406144205123 + 7 7 3 3 0.469762103528713 + 7 7 4 3 -0.025791716791396 + 7 7 4 4 0.456900909053721 + 7 7 5 5 0.436750211441671 + 7 3 7 3 0.075103217640351 + 7 4 7 3 -0.047460399285077 + 7 4 7 4 0.051436804504574 + 7 5 7 5 0.014356676714874 + 7 7 6 1 0.017890930404213 + 7 6 7 1 0.004091767456984 + 7 7 6 2 0.151924586584762 + 7 6 7 2 0.038415486590652 + 7 7 6 3 0.073615422819083 + 7 7 6 4 0.096752175289782 + 7 6 7 3 -0.025685197500691 + 7 6 7 4 0.025974451190177 + 7 7 6 6 0.302537910673863 + 7 6 7 6 0.017861326916860 + 7 7 7 1 0.018641085379951 + 7 7 7 2 0.235420950941441 + 7 7 7 3 -0.206690042488560 + 7 7 7 4 0.161483959338374 + 7 7 7 6 0.091353706761488 + 7 7 7 7 0.774605943919898 diff --git a/Project#03/input/h2o/STO-3G/geom.dat b/Project#03/input/h2o/STO-3G/geom.dat new file mode 100644 index 0000000..99b165d --- /dev/null +++ b/Project#03/input/h2o/STO-3G/geom.dat @@ -0,0 +1,4 @@ +3 +8.000000000000 0.000000000000 -0.143225816552 0.000000000000 +1.000000000000 1.638036840407 1.136548822547 -0.000000000000 +1.000000000000 -1.638036840407 1.136548822547 -0.000000000000 diff --git a/Project#03/input/h2o/STO-3G/input.dat b/Project#03/input/h2o/STO-3G/input.dat new file mode 100644 index 0000000..f8c5067 --- /dev/null +++ b/Project#03/input/h2o/STO-3G/input.dat @@ -0,0 +1,12 @@ +psi: ( + label = "H2O SCF Test Case" + memory = (10.0 MB) + wfn = scf + jobtype = oeprop + delete_tei = false + delete_oei = false + reference = rhf + basis = "STO-3G" + subgroup = c1 + zmat = ((o) (h 1 1.1) (h 1 1.1 2 104.0)) +) diff --git a/Project#03/input/h2o/STO-3G/mux.dat b/Project#03/input/h2o/STO-3G/mux.dat new file mode 100644 index 0000000..c5d92c5 --- /dev/null +++ b/Project#03/input/h2o/STO-3G/mux.dat @@ -0,0 +1,28 @@ + 1 1 -0.000000000000000 + 2 1 -0.000000000000000 + 2 2 -0.000000000000000 + 3 1 -0.050791929587912 + 3 2 -0.641172844324925 + 3 3 -0.000000000000000 + 4 1 0.000000000000000 + 4 2 0.000000000000000 + 4 3 0.000000000000000 + 4 4 -0.000000000000000 + 5 1 0.000000000000000 + 5 2 -0.000000000000000 + 5 3 -0.000000000000000 + 5 4 0.000000000000000 + 5 5 -0.000000000000000 + 6 1 -0.002229654052248 + 6 2 -0.262742503532769 + 6 3 -0.437630646182039 + 6 4 -0.147399448800486 + 6 5 0.000000000000000 + 6 6 -1.638036840407314 + 7 1 0.002229654052248 + 7 2 0.262742503532769 + 7 3 -0.437630646182039 + 7 4 0.147399448800486 + 7 5 -0.000000000000000 + 7 6 0.000000000000000 + 7 7 1.638036840407314 diff --git a/Project#03/input/h2o/STO-3G/muy.dat b/Project#03/input/h2o/STO-3G/muy.dat new file mode 100644 index 0000000..1efcbad --- /dev/null +++ b/Project#03/input/h2o/STO-3G/muy.dat @@ -0,0 +1,28 @@ + 1 1 0.143225816551918 + 2 1 0.033902114587819 + 2 2 0.143225816551918 + 3 1 -0.000000000000000 + 3 2 0.000000000000000 + 3 3 0.143225816551918 + 4 1 -0.050791929587912 + 4 2 -0.641172844324925 + 4 3 -0.000000000000000 + 4 4 0.143225816551918 + 5 1 -0.000000000000000 + 5 2 0.000000000000000 + 5 3 0.000000000000000 + 5 4 -0.000000000000000 + 5 5 0.143225816551918 + 6 1 0.003758676726377 + 6 2 -0.149971890752635 + 6 3 -0.108952162150434 + 6 4 -0.334090713364948 + 6 5 0.000000000000000 + 6 6 -1.136548822546795 + 7 1 0.003758676726377 + 7 2 -0.149971890752635 + 7 3 0.108952162150434 + 7 4 -0.334090713364948 + 7 5 0.000000000000000 + 7 6 -0.206578984758302 + 7 7 -1.136548822546794 diff --git a/Project#03/input/h2o/STO-3G/muz.dat b/Project#03/input/h2o/STO-3G/muz.dat new file mode 100644 index 0000000..35dfd9f --- /dev/null +++ b/Project#03/input/h2o/STO-3G/muz.dat @@ -0,0 +1,28 @@ + 1 1 -0.000000000000000 + 2 1 -0.000000000000000 + 2 2 -0.000000000000000 + 3 1 0.000000000000000 + 3 2 -0.000000000000000 + 3 3 -0.000000000000000 + 4 1 0.000000000000000 + 4 2 0.000000000000000 + 4 3 0.000000000000000 + 4 4 -0.000000000000000 + 5 1 -0.050791929587912 + 5 2 -0.641172844324925 + 5 3 -0.000000000000000 + 5 4 0.000000000000000 + 5 5 -0.000000000000000 + 6 1 -0.000000000000000 + 6 2 0.000000000000000 + 6 3 0.000000000000000 + 6 4 0.000000000000000 + 6 5 -0.248967955099984 + 6 6 0.000000000000000 + 7 1 -0.000000000000000 + 7 2 0.000000000000000 + 7 3 -0.000000000000000 + 7 4 0.000000000000000 + 7 5 -0.248967955099984 + 7 6 0.000000000000000 + 7 7 0.000000000000000 diff --git a/Project#03/input/h2o/STO-3G/s.dat b/Project#03/input/h2o/STO-3G/s.dat new file mode 100644 index 0000000..9b764da --- /dev/null +++ b/Project#03/input/h2o/STO-3G/s.dat @@ -0,0 +1,28 @@ + 1 1 1.000000000000000 + 2 1 0.236703936510848 + 2 2 1.000000000000000 + 3 1 -0.000000000000000 + 3 2 0.000000000000000 + 3 3 1.000000000000000 + 4 1 -0.000000000000000 + 4 2 -0.000000000000000 + 4 3 -0.000000000000000 + 4 4 1.000000000000000 + 5 1 -0.000000000000000 + 5 2 0.000000000000000 + 5 3 0.000000000000000 + 5 4 -0.000000000000000 + 5 5 1.000000000000000 + 6 1 0.038405599785757 + 6 2 0.386138840478249 + 6 3 0.268438243716457 + 6 4 0.209726941420375 + 6 5 -0.000000000000000 + 6 6 1.000000000000000 + 7 1 0.038405599785757 + 7 2 0.386138840478250 + 7 3 -0.268438243716457 + 7 4 0.209726941420375 + 7 5 -0.000000000000000 + 7 6 0.181759886298063 + 7 7 1.000000000000000 diff --git a/Project#03/input/h2o/STO-3G/t.dat b/Project#03/input/h2o/STO-3G/t.dat new file mode 100644 index 0000000..8927c33 --- /dev/null +++ b/Project#03/input/h2o/STO-3G/t.dat @@ -0,0 +1,28 @@ + 1 1 29.003199945539588 + 2 1 -0.168010939316492 + 2 2 0.808127954930347 + 3 1 0.000000000000000 + 3 2 0.000000000000000 + 3 3 2.528731198194763 + 4 1 0.000000000000000 + 4 2 -0.000000000000000 + 4 3 -0.000000000000000 + 4 4 2.528731198194763 + 5 1 -0.000000000000000 + 5 2 0.000000000000000 + 5 3 0.000000000000000 + 5 4 -0.000000000000000 + 5 5 2.528731198194763 + 6 1 -0.008416383544591 + 6 2 0.070517372751001 + 6 3 0.147090913304052 + 6 4 0.114920016354202 + 6 5 -0.000000000000000 + 6 6 0.760031883566609 + 7 1 -0.008416383544591 + 7 2 0.070517372751002 + 7 3 -0.147090913304052 + 7 4 0.114920016354202 + 7 5 -0.000000000000000 + 7 6 -0.003979868621841 + 7 7 0.760031883566609 diff --git a/Project#03/input/h2o/STO-3G/v.dat b/Project#03/input/h2o/STO-3G/v.dat new file mode 100644 index 0000000..d5b7411 --- /dev/null +++ b/Project#03/input/h2o/STO-3G/v.dat @@ -0,0 +1,28 @@ + 1 1 -61.580595358149914 + 2 1 -7.410821877330996 + 2 2 -10.009071226859687 + 3 1 0.000000000000000 + 3 2 0.000000000000000 + 3 3 -9.987550507419133 + 4 1 -0.014473835903318 + 4 2 -0.176890246723779 + 4 3 0.000000000000000 + 4 4 -9.944042952440439 + 5 1 0.000000000000000 + 5 2 0.000000000000000 + 5 3 -0.000000000000000 + 5 4 0.000000000000000 + 5 5 -9.875876065926128 + 6 1 -1.231685872788711 + 6 2 -2.977227202971528 + 6 3 -1.822241058022723 + 6 4 -1.471788274313766 + 6 5 0.000000000000000 + 6 6 -5.300202953839792 + 7 1 -1.231685872788712 + 7 2 -2.977227202971529 + 7 3 1.822241058022724 + 7 4 -1.471788274313766 + 7 5 0.000000000000001 + 7 6 -1.067166014696110 + 7 7 -5.300202953839793 diff --git a/Project#03/output/ch4/STO-3G/output.txt b/Project#03/output/ch4/STO-3G/output.txt new file mode 100644 index 0000000..933d4ef --- /dev/null +++ b/Project#03/output/ch4/STO-3G/output.txt @@ -0,0 +1,187 @@ + +Nuclear repulsion energy = 13.4973044620 + + Overlap Integrals: + + 1 2 3 4 5 6 7 8 9 + + 1 1.0000000 0.2483624 0.0000000 -0.0000000 0.0000000 0.0630068 0.0630068 0.0630068 0.0630068 + 2 0.2483624 1.0000000 0.0000000 0.0000000 0.0000000 0.4936348 0.4936348 0.4936348 0.4936348 + 3 0.0000000 0.0000000 1.0000000 0.0000000 0.0000000 0.2707690 0.2707690 -0.2707690 -0.2707690 + 4 -0.0000000 0.0000000 0.0000000 1.0000000 0.0000000 -0.2707690 0.2707690 0.2707690 -0.2707690 + 5 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 -0.2707690 0.2707690 -0.2707690 0.2707690 + 6 0.0630068 0.4936348 0.2707690 -0.2707690 -0.2707690 1.0000000 0.1714170 0.1714170 0.1714170 + 7 0.0630068 0.4936348 0.2707690 0.2707690 0.2707690 0.1714170 1.0000000 0.1714170 0.1714170 + 8 0.0630068 0.4936348 -0.2707690 0.2707690 -0.2707690 0.1714170 0.1714170 1.0000000 0.1714170 + 9 0.0630068 0.4936348 -0.2707690 -0.2707690 0.2707690 0.1714170 0.1714170 0.1714170 1.0000000 + + Kinetic-Energy Integrals: + + 1 2 3 4 5 6 7 8 9 + + 1 15.8911236 -0.0858899 -0.0000000 0.0000000 -0.0000000 -0.0103444 -0.0103444 -0.0103444 -0.0103444 + 2 -0.0858899 0.4722500 0.0000000 0.0000000 -0.0000000 0.1085007 0.1085007 0.1085007 0.1085007 + 3 -0.0000000 0.0000000 1.4777281 0.0000000 0.0000000 0.1525711 0.1525711 -0.1525711 -0.1525711 + 4 0.0000000 0.0000000 0.0000000 1.4777281 0.0000000 -0.1525711 0.1525711 0.1525711 -0.1525711 + 5 -0.0000000 -0.0000000 0.0000000 0.0000000 1.4777281 -0.1525711 0.1525711 -0.1525711 0.1525711 + 6 -0.0103444 0.1085007 0.1525711 -0.1525711 -0.1525711 0.7600318 -0.0053080 -0.0053080 -0.0053080 + 7 -0.0103444 0.1085007 0.1525711 0.1525711 0.1525711 -0.0053080 0.7600318 -0.0053080 -0.0053080 + 8 -0.0103444 0.1085007 -0.1525711 0.1525711 -0.1525711 -0.0053080 -0.0053080 0.7600318 -0.0053080 + 9 -0.0103444 0.1085007 -0.1525711 -0.1525711 0.1525711 -0.0053080 -0.0053080 -0.0053080 0.7600318 + + Nuclear Attraction Integrals: + + 1 2 3 4 5 6 7 8 9 + + 1 -35.6036270 -4.6767553 0.0000000 -0.0000000 0.0000000 -1.2077110 -1.2077110 -1.2077110 -1.2077110 + 2 -4.6767553 -7.0845291 -0.0000000 0.0000000 0.0000000 -2.9815402 -2.9815402 -2.9815402 -2.9815402 + 3 0.0000000 -0.0000000 -7.0427086 -0.0000000 -0.0000000 -1.5116937 -1.5116937 1.5116937 1.5116937 + 4 -0.0000000 0.0000000 -0.0000000 -7.0427086 0.0000000 1.5116937 -1.5116937 -1.5116937 1.5116937 + 5 0.0000000 0.0000000 -0.0000000 0.0000000 -7.0427086 1.5116937 -1.5116937 1.5116937 -1.5116937 + 6 -1.2077110 -2.9815402 -1.5116937 1.5116937 1.5116937 -4.9835182 -0.9341422 -0.9341422 -0.9341422 + 7 -1.2077110 -2.9815402 -1.5116937 -1.5116937 -1.5116937 -0.9341422 -4.9835182 -0.9341422 -0.9341422 + 8 -1.2077110 -2.9815402 1.5116937 -1.5116937 1.5116937 -0.9341422 -0.9341422 -4.9835182 -0.9341422 + 9 -1.2077110 -2.9815402 1.5116937 1.5116937 -1.5116937 -0.9341422 -0.9341422 -0.9341422 -4.9835182 + + Core Hamiltonian: + + 1 2 3 4 5 6 7 8 9 + + 1 -19.7125033 -4.7626451 0.0000000 0.0000000 0.0000000 -1.2180554 -1.2180554 -1.2180554 -1.2180554 + 2 -4.7626451 -6.6122791 0.0000000 0.0000000 0.0000000 -2.8730395 -2.8730395 -2.8730395 -2.8730395 + 3 0.0000000 0.0000000 -5.5649805 0.0000000 0.0000000 -1.3591225 -1.3591225 1.3591225 1.3591225 + 4 0.0000000 0.0000000 0.0000000 -5.5649805 0.0000000 1.3591225 -1.3591225 -1.3591225 1.3591225 + 5 0.0000000 0.0000000 0.0000000 0.0000000 -5.5649805 1.3591225 -1.3591225 1.3591225 -1.3591225 + 6 -1.2180554 -2.8730395 -1.3591225 1.3591225 1.3591225 -4.2234865 -0.9394502 -0.9394502 -0.9394502 + 7 -1.2180554 -2.8730395 -1.3591225 -1.3591225 -1.3591225 -0.9394502 -4.2234865 -0.9394502 -0.9394502 + 8 -1.2180554 -2.8730395 1.3591225 -1.3591225 1.3591225 -0.9394502 -0.9394502 -4.2234865 -0.9394502 + 9 -1.2180554 -2.8730395 1.3591225 1.3591225 -1.3591225 -0.9394502 -0.9394502 -0.9394502 -4.2234865 + + S^-1/2 Matrix: + + 1 2 3 4 5 6 7 8 9 + + 1 1.0299976 -0.1813138 0.0000000 0.0000000 0.0000000 0.0261560 0.0261560 0.0261560 0.0261560 + 2 -0.1813138 1.5904476 0.0000000 0.0000000 -0.0000000 -0.3473780 -0.3473780 -0.3473780 -0.3473780 + 3 0.0000000 0.0000000 1.1753346 -0.0000000 0.0000000 -0.2039715 -0.2039715 0.2039715 0.2039715 + 4 0.0000000 0.0000000 -0.0000000 1.1753346 0.0000000 0.2039715 -0.2039715 -0.2039715 0.2039715 + 5 0.0000000 -0.0000000 0.0000000 0.0000000 1.1753346 0.2039715 -0.2039715 0.2039715 -0.2039715 + 6 0.0261560 -0.3473780 -0.2039715 0.2039715 0.2039715 1.2764126 -0.0280511 -0.0280511 -0.0280511 + 7 0.0261560 -0.3473780 -0.2039715 -0.2039715 -0.2039715 -0.0280511 1.2764126 -0.0280511 -0.0280511 + 8 0.0261560 -0.3473780 0.2039715 -0.2039715 0.2039715 -0.0280511 -0.0280511 1.2764126 -0.0280511 + 9 0.0261560 -0.3473780 0.2039715 0.2039715 -0.2039715 -0.0280511 -0.0280511 -0.0280511 1.2764126 + + Initial F' Matrix: + + 1 2 3 4 5 6 7 8 9 + + 1 -19.5241878 -1.5499726 -0.0000000 -0.0000000 -0.0000000 -0.2141242 -0.2141242 -0.2141242 -0.2141242 + 2 -1.5499726 -5.9413680 -0.0000000 -0.0000000 -0.0000000 -0.3620641 -0.3620641 -0.3620641 -0.3620641 + 3 -0.0000000 -0.0000000 -5.6274166 0.0000000 -0.0000000 -0.1020488 -0.1020488 0.1020488 0.1020488 + 4 -0.0000000 -0.0000000 0.0000000 -5.6274166 -0.0000000 0.1020488 -0.1020488 -0.1020488 0.1020488 + 5 -0.0000000 -0.0000000 -0.0000000 -0.0000000 -5.6274166 0.1020488 -0.1020488 0.1020488 -0.1020488 + 6 -0.2141242 -0.3620641 -0.1020488 0.1020488 0.1020488 -3.6394349 -0.0181358 -0.0181358 -0.0181358 + 7 -0.2141242 -0.3620641 -0.1020488 -0.1020488 -0.1020488 -0.0181358 -3.6394349 -0.0181358 -0.0181358 + 8 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0.0705174 0.1470909 0.1149200 -0.0000000 0.7600319 -0.0039799 + 7 -0.0084164 0.0705174 -0.1470909 0.1149200 -0.0000000 -0.0039799 0.7600319 + + Nuclear Attraction Integrals: + + 1 2 3 4 5 6 7 + + 1 -61.5805954 -7.4108219 0.0000000 -0.0144738 0.0000000 -1.2316859 -1.2316859 + 2 -7.4108219 -10.0090712 0.0000000 -0.1768902 0.0000000 -2.9772272 -2.9772272 + 3 0.0000000 0.0000000 -9.9875505 0.0000000 -0.0000000 -1.8222411 1.8222411 + 4 -0.0144738 -0.1768902 0.0000000 -9.9440430 0.0000000 -1.4717883 -1.4717883 + 5 0.0000000 0.0000000 -0.0000000 0.0000000 -9.8758761 0.0000000 0.0000000 + 6 -1.2316859 -2.9772272 -1.8222411 -1.4717883 0.0000000 -5.3002030 -1.0671660 + 7 -1.2316859 -2.9772272 1.8222411 -1.4717883 0.0000000 -1.0671660 -5.3002030 + + Core Hamiltonian: + + 1 2 3 4 5 6 7 + + 1 -32.5773954 -7.5788328 0.0000000 -0.0144738 0.0000000 -1.2401023 -1.2401023 + 2 -7.5788328 -9.2009433 0.0000000 -0.1768902 0.0000000 -2.9067098 -2.9067098 + 3 0.0000000 0.0000000 -7.4588193 0.0000000 0.0000000 -1.6751501 1.6751501 + 4 -0.0144738 -0.1768902 0.0000000 -7.4153118 0.0000000 -1.3568683 -1.3568683 + 5 0.0000000 0.0000000 0.0000000 0.0000000 -7.3471449 0.0000000 0.0000000 + 6 -1.2401023 -2.9067098 -1.6751501 -1.3568683 0.0000000 -4.5401711 -1.0711459 + 7 -1.2401023 -2.9067098 1.6751501 -1.3568683 0.0000000 -1.0711459 -4.5401711 + + S^-1/2 Matrix: + + 1 2 3 4 5 6 7 + + 1 1.0236346 -0.1368547 -0.0000000 -0.0074873 -0.0000000 0.0190279 0.0190279 + 2 -0.1368547 1.1578632 0.0000000 0.0721601 0.0000000 -0.2223326 -0.2223326 + 3 -0.0000000 0.0000000 1.0733148 0.0000000 -0.0000000 -0.1757583 0.1757583 + 4 -0.0074873 0.0721601 0.0000000 1.0383050 0.0000000 -0.1184626 -0.1184626 + 5 -0.0000000 0.0000000 -0.0000000 0.0000000 1.0000000 -0.0000000 -0.0000000 + 6 0.0190279 -0.2223326 -0.1757583 -0.1184626 -0.0000000 1.1297234 -0.0625975 + 7 0.0190279 -0.2223326 0.1757583 -0.1184626 -0.0000000 -0.0625975 1.1297234 + + Initial F' Matrix: + + 1 2 3 4 5 6 7 + + 1 -32.2545866 -2.7914909 -0.0000000 0.0086110 0.0000000 -0.1812967 -0.1812967 + 2 -2.7914909 -8.2368891 -0.0000000 -0.2282926 0.0000000 -0.3857987 -0.3857987 + 3 -0.0000000 -0.0000000 -7.5428890 -0.0000000 0.0000000 -0.1132121 0.1132121 + 4 0.0086110 -0.2282926 -0.0000000 -7.4570295 -0.0000000 -0.1102196 -0.1102196 + 5 0.0000000 0.0000000 0.0000000 -0.0000000 -7.3471449 0.0000000 0.0000000 + 6 -0.1812967 -0.3857987 -0.1132121 -0.1102196 0.0000000 -4.0329547 -0.0446466 + 7 -0.1812967 -0.3857987 0.1132121 -0.1102196 0.0000000 -0.0446466 -4.0329547 + + Initial C Matrix: + + 1 2 3 4 5 6 7 + + 1 -1.0015436 0.2336245 0.0000000 0.0856842 0.0000000 -0.0482226 -0.0000000 + 2 0.0071893 -1.0579388 -0.0000000 -0.3601105 -0.0000000 0.4631213 0.0000000 + 3 -0.0000000 -0.0000000 1.0610702 0.0000000 -0.0000000 -0.0000000 0.2965071 + 4 0.0002671 -0.4272843 -0.0000000 0.9399425 0.0000000 0.2129401 0.0000000 + 5 0.0000000 0.0000000 -0.0000000 0.0000000 -1.0000000 -0.0000000 -0.0000000 + 6 -0.0018213 0.1492533 -0.1377210 -0.0378579 0.0000000 -0.7807003 -0.8501403 + 7 -0.0018213 0.1492533 0.1377210 -0.0378579 -0.0000000 -0.7807003 0.8501403 + + Initial Density Matrix: + + 1 2 3 4 5 6 7 + + 1 1.0650117 -0.2852166 -0.0000000 -0.0195534 -0.0000000 0.0334496 0.0334496 + 2 -0.2852166 1.2489657 0.0000000 0.1135594 0.0000000 -0.1442809 -0.1442809 + 3 -0.0000000 0.0000000 1.1258701 -0.0000000 -0.0000000 -0.1461317 0.1461317 + 4 -0.0195534 0.1135594 -0.0000000 1.0660638 0.0000000 -0.0993583 -0.0993583 + 5 -0.0000000 0.0000000 -0.0000000 0.0000000 1.0000000 -0.0000000 -0.0000000 + 6 0.0334496 -0.1442809 -0.1461317 -0.0993583 -0.0000000 0.0426802 0.0047460 + 7 0.0334496 -0.1442809 0.1461317 -0.0993583 -0.0000000 0.0047460 0.0426802 + + + Iter E(elec) E(tot) Delta(E) RMS(D) + 00 -125.842077437699 -117.839710375888 + + Fock Matrix: + + 1 2 3 4 5 6 7 + + 1 -18.8132695 -4.8726875 -0.0000000 -0.0115290 0.0000000 -0.8067323 -0.8067323 + 2 -4.8726875 -1.7909029 -0.0000000 -0.1808692 0.0000000 -0.5790557 -0.5790557 + 3 -0.0000000 -0.0000000 0.1939644 0.0000000 0.0000000 -0.1708886 0.1708886 + 4 -0.0115290 -0.1808692 0.0000000 0.2391247 0.0000000 -0.1828683 -0.1828683 + 5 0.0000000 0.0000000 0.0000000 0.0000000 0.3091071 0.0000000 0.0000000 + 6 -0.8067323 -0.5790557 -0.1708886 -0.1828683 0.0000000 -0.1450338 -0.1846675 + 7 -0.8067323 -0.5790557 0.1708886 -0.1828683 0.0000000 -0.1846675 -0.1450338 + 01 -78.286583284740 -70.284216222929 47.555494152959 1.826673084479 + 02 -84.048316253435 -76.045949191625 -5.761732968696 0.479570364860 + 03 -82.716965960855 -74.714598899044 1.331350292581 0.086831688906 + 04 -82.987140757002 -74.984773695191 -0.270174796147 0.031026136359 + 05 -82.938133187513 -74.935766125703 0.049007569488 0.010799283179 + 06 -82.946271078699 -74.943904016889 -0.008137891186 0.005254826831 + 07 -82.944486784914 -74.942119723104 0.001784293785 0.002438579642 + 08 -82.944617252243 -74.942250190433 -0.000130467329 0.001177279531 + 09 -82.944503500703 -74.942136438892 0.000113751541 0.000564543180 + 10 -82.944478930626 -74.942111868815 0.000024570077 0.000272204992 + 11 -82.944461627684 -74.942094565874 0.000017302941 0.000131180309 + 12 -82.944454198375 -74.942087136564 0.000007429310 0.000063275666 + 13 -82.944450445051 -74.942083383241 0.000003753324 0.000030522547 + 14 -82.944448661686 -74.942081599875 0.000001783365 0.000014725847 + 15 -82.944447795931 -74.942080734120 0.000000865755 0.000007104836 + 16 -82.944447379016 -74.942080317206 0.000000416914 0.000003428026 + 17 -82.944447177685 -74.942080115875 0.000000201331 0.000001654014 + 18 -82.944447080565 -74.942080018755 0.000000097120 0.000000798065 + 19 -82.944447033699 -74.942079971888 0.000000046867 0.000000385069 + 20 -82.944447011086 -74.942079949276 0.000000022613 0.000000185798 + 21 -82.944447000175 -74.942079938365 0.000000010911 0.000000089648 + 22 -82.944446994911 -74.942079933100 0.000000005264 0.000000043256 + 23 -82.944446992371 -74.942079930560 0.000000002540 0.000000020871 + 24 -82.944446991145 -74.942079929334 0.000000001226 0.000000010070 + 25 -82.944446990554 -74.942079928743 0.000000000591 0.000000004859 + 26 -82.944446990268 -74.942079928458 0.000000000285 0.000000002345 + 27 -82.944446990130 -74.942079928320 0.000000000138 0.000000001131 + 28 -82.944446990064 -74.942079928254 0.000000000066 0.000000000546 + 29 -82.944446990032 -74.942079928222 0.000000000032 0.000000000263 + 30 -82.944446990016 -74.942079928206 0.000000000016 0.000000000127 + 31 -82.944446990009 -74.942079928199 0.000000000007 0.000000000061 + 32 -82.944446990005 -74.942079928195 0.000000000004 0.000000000030 + 33 -82.944446990004 -74.942079928193 0.000000000002 0.000000000014 + 34 -82.944446990003 -74.942079928192 0.000000000001 0.000000000007 + + 1 2 3 4 5 6 7 + + 1 -0.0000000 -0.0000000 -0.0507919 0.0000000 0.0000000 -0.0022297 0.0022297 + 2 -0.0000000 -0.0000000 -0.6411728 0.0000000 -0.0000000 -0.2627425 0.2627425 + 3 -0.0507919 -0.6411728 -0.0000000 0.0000000 -0.0000000 -0.4376306 -0.4376306 + 4 0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 -0.1473994 0.1473994 + 5 0.0000000 -0.0000000 -0.0000000 0.0000000 -0.0000000 0.0000000 -0.0000000 + 6 -0.0022297 -0.2627425 -0.4376306 -0.1473994 0.0000000 -1.6380368 0.0000000 + 7 0.0022297 0.2627425 -0.4376306 0.1473994 -0.0000000 0.0000000 1.6380368 + + 1 2 3 4 5 6 7 + + 1 1.0548737 -0.2327977 -0.0000000 0.0526229 -0.0000000 -0.0081506 -0.0081506 + 2 -0.2327977 1.0151108 0.0000000 -0.2823000 0.0000000 -0.0305395 -0.0305395 + 3 -0.0000000 0.0000000 0.3687949 -0.0000000 -0.0000000 0.2750987 -0.2750987 + 4 0.0526229 -0.2823000 -0.0000000 0.5660419 0.0000000 0.2586150 0.2586150 + 5 -0.0000000 0.0000000 -0.0000000 0.0000000 1.0000000 -0.0000000 -0.0000000 + 6 -0.0081506 -0.0305395 0.2750987 0.2586150 -0.0000000 0.3345267 -0.0758872 + 7 -0.0081506 -0.0305395 -0.2750987 0.2586150 -0.0000000 -0.0758872 0.3345267 + +Mu-X = 0.000000000000 +Mu-Y = 0.603521296525 +Mu-Z = -0.000000000000 +Total dipole moment (au) = 0.603521296525 + +Charge on atom 0: -0.253146052405 +Charge on atom 1: 0.126573026202 +Charge on atom 2: 0.126573026202 diff --git a/Project#03/project3-instructions.pdf b/Project#03/project3-instructions.pdf new file mode 100644 index 0000000..ee6cc41 Binary files /dev/null and b/Project#03/project3-instructions.pdf differ diff --git a/Project#04/README.md b/Project#04/README.md index d0308e0..fabf300 100644 --- a/Project#04/README.md +++ b/Project#04/README.md @@ -1 +1,57 @@ # Project #4: The second-order Moller-Plesset perturbation (MP2) energy +Unlike the Hartree-Fock energy, correlation energies like the MP2 energy are usually expressed in terms of MO-basis quantities (integrals, MO energies). +The most expensive part of the calculation is the transformation of the two-electron integrals from the AO to the MO basis representation. +The purpose of this project is to understand this transformation and fundamental techniques for its efficient implementation. +The theoretical background and a concise set of instructions for this project may be found [here](./project4-instructions.pdf). + +## Step #1: Read the Two-Electron Integrals +The Mulliken-ordered integrals are defined as: + + + +Concise instructions for this step can be found in [Project #3](../Project%2303). + +## Step #2: Obtain the MO Coefficients and MO Energies +Use the values you computed in the Hartree-Fock program of [Project #3](../Project%2303). +## Step #3: Transform the Two-Electron Integrals to the MO Basis +### The Noddy Algorithm + +The most straightforward expression of the AO/MO integral transformation is + + + +This approach is easy to implement (hence the word "[noddy](http://www.hackerslang.com/noddy.html)" above), but is expensive due to its N8 computational order. Nevertheless, you should start with this algorithm to get your code working, and run timings (use the UNIX "time" command) for the test cases below to get an idea of its computational cost. + + * [Hint 1](./hints/hint1.md): Noddy transformation code +### The Smarter Algorithm + +Notice that none of the *C* coefficients in the above expression have any indices in common. Thus, the summation could be rearranged such that: + + + +This means that each summation within brackets could be carried out separately, +starting from the innermost summation over σ, if we store the results at each step. This reduces the N8 algorithm above to four N5 steps. + +Be careful about the permutational symmetry of the integrals and intermediates at each step: +while the AO-basis integrals have eight-fold permutational symmetry, the partially transformed integrals have much less symmetry. + +After you have the noddy algorithm working and timed, modify it to use this smarter algorithm and time the test cases again. Enjoy! + + * [Hint 2](./hints/hint2.md): Smarter transformation code + +## Step #4: Compute the MP2 Energy + + + +where *i* and *j* denote doubly-occupied orbitals and *a* and *b* unoccupied orbitals, and the denominator involves the MO energies. + + * [Hint 3](./hints/hint3.md): Occupied versus unoccupied orbitals + +## Test Cases +The input structures, integrals, etc. for these examples are found in the [input directory](./input). + +* STO-3G Water | [output](./output/h2o/STO-3G/output.txt) +* DZ Water | [output](./output/h2o/DZ/output.txt) +* DZP Water | [output](./output/h2o/DZP/output.txt) +* STO-3G Methane | [output](./output/ch4/STO-3G/output.txt) + diff --git a/Project#04/figures/eri.png b/Project#04/figures/eri.png new file mode 100644 index 0000000..b1d8f52 Binary files /dev/null and b/Project#04/figures/eri.png differ diff --git a/Project#04/figures/mp2-energy.png b/Project#04/figures/mp2-energy.png new file mode 100644 index 0000000..1003c08 Binary files /dev/null and b/Project#04/figures/mp2-energy.png differ diff --git a/Project#04/figures/noddy-transform.png b/Project#04/figures/noddy-transform.png new file mode 100644 index 0000000..ecf954c Binary files /dev/null and b/Project#04/figures/noddy-transform.png differ diff --git a/Project#04/figures/smart-transform.png b/Project#04/figures/smart-transform.png new file mode 100644 index 0000000..4432a91 Binary files /dev/null and b/Project#04/figures/smart-transform.png differ diff --git a/Project#04/hints/hint1.md b/Project#04/hints/hint1.md new file mode 100644 index 0000000..01221e1 --- /dev/null +++ b/Project#04/hints/hint1.md @@ -0,0 +1,37 @@ +Here's a code block that demonstrates how to carry out the AO to MO two-electron integral transformation using a single N8 step. Note that the original AO- and transformed MO-basis integrals are stored in a one-dimensional array taking full advantage of their eight-fold permutational symmetry, as described in [Project #3](../../Project%2303). + +Note how the loop structure in the MO-indices (*i*, *j*, *k*, and *l*) automatically takes into account the permutational symmetry of the fully transformed integrals. + +```c++ + #define INDEX(i,j) ((i>j) ? (((i)*((i)+1)/2)+(j)) : (((j)*((j)+1)/2)+(i))) + ... + double *TEI_AO, *TEI_MO; + int i, j, k, l, ijkl; + int p, q, r, s, pq, rs, pqrs; + ... + + for(i=0,ijkl=0; i < nao; i++) { + for(j=0; j <= i; j++) { + for(k=0; k <= i; k++) { + for(l=0; l <= (i==k ? j : k); l++,ijkl++) { + + for(p=0; p < nao; p++) { + for(q=0; q < nao; q++) { + pq = INDEX(p,q); + for(r=0; r < nao; r++) { + for(s=0; s < nao; s++) { + rs = INDEX(r,s); + pqrs = INDEX(pq,rs); + + TEI_MO[ijkl] += C[p][i] * C[q][j] * C[r][k] * C[s][l] * TEI_AO[pqrs]; + + } + } + } + } + + } + } + } + } +``` diff --git a/Project#04/hints/hint2.md b/Project#04/hints/hint2.md new file mode 100644 index 0000000..79a46dd --- /dev/null +++ b/Project#04/hints/hint2.md @@ -0,0 +1,59 @@ +Here's a code block that demonstrates how to carry out the AO to MO two-electron integral transformation using four N5 steps. Note that the original AO- and transformed MO-basis integrals are stored in a one-dimensional array taking advantage of their eight-fold permutational symmetry, as described in [Project #3](../../Project%2303). However, the half-transformed integrals, which lack bra-ket permutational symmetry, are stored in a two-dimensional array. + +A number of convenient functions [`mmult()`, `init_matrix()`, etc.] used in this code block can be found in the [diag.cc](http://sirius.chem.vt.edu/~crawdad/programming/diag.cc) discussed in [Project #1](../../Project%2301). + +```c++ + #define INDEX(i,j) ((i>j) ? (((i)*((i)+1)/2)+(j)) : (((j)*((j)+1)/2)+(i))) + ... + double **X, **Y, **TMP, *TEI; + int i, j, k, l, ij, kl, ijkl, klij; + + ... + X = init_matrix(nao, nao); + Y = init_matrix(nao, nao); + + TMP = init_matrix((nao*(nao+1)/2),(nao*(nao+1)/2)); + for(i=0,ij=0; i < nao; i++) + for(j=0; j <= i; j++,ij++) { + for(k=0,kl=0; k < nao; k++) + for(l=0; l <= k; l++,kl++) { + ijkl = INDEX(ij,kl); + X[k][l] = X[l][k] = TEI[ijkl]; + } + zero_matrix(Y, nao, nao); + mmult(C, 1, X, 0, Y, nao, nao, nao); + zero_matrix(X, nao, nao); + mmult(Y, 0, C, 0, X, nao, nao, nao); + for(k=0, kl=0; k < nao; k++) + for(l=0; l <= k; l++, kl++) + TMP[kl][ij] = X[k][l]; + } + + zero_array(TEI, (nao*(nao+1)/2)*((nao*(nao+1)/2)+1)/2); + + for(k=0,kl=0; k < nao; k++) + for(l=0; l <= k; l++,kl++) { + zero_matrix(X, nao, nao); + zero_matrix(Y, nao, nao); + for(i=0,ij=0; i < nao; i++) + for(j=0; j <=i; j++,ij++) + X[i][j] = X[j][i] = TMP[kl][ij]; + zero_matrix(Y, nao, nao); + mmult(C, 1, X, 0, Y, nao, nao, nao); + zero_matrix(X, nao, nao); + mmult(Y, 0, C, 0, X, nao, nao, nao); + for(i=0, ij=0; i < nao; i++) + for(j=0; j <= i; j++,ij++) { + klij = INDEX(kl,ij); + TEI[klij] = X[i][j]; + } + } + + ... + + free_matrix(X, nao); + free_matrix(Y, nao); + free_matrix(TMP, (nao*(nao+1)/2)); + +``` + diff --git a/Project#04/hints/hint3.md b/Project#04/hints/hint3.md new file mode 100644 index 0000000..d6ae3ab --- /dev/null +++ b/Project#04/hints/hint3.md @@ -0,0 +1,20 @@ +The following code block illustrates a simple-minded MP2 energy calculation with the two-electron integrals stored in a one-dimensional array. The molecular orbitals are assumed to be ordered with all doubly-occupied orbitals first, followed by the unoccupied/virtual orbitals. Notice the difference in limits of the loops over *i* and *a*: + +```c++ + Emp2 = 0.0; + for(i=0; i < ndocc; i++) { + for(a=ndocc; a < nao; a++) { + ia = INDEX(i,a); + for(j=0; j < ndocc; j++) { + ja = INDEX(j,a); + for(b=ndocc; b < nao; b++) { + jb = INDEX(j,b); + ib = INDEX(i,b); + iajb = INDEX(ia,jb); + ibja = INDEX(ib,ja); + Emp2 += TEI[iajb] * (2 * TEI[iajb] - TEI[ibja])/(eps[i] + eps[j] - eps[a] - eps[b]); + } + } + } + } +``` diff --git a/Project#04/input/ch4/STO-3G/enuc.dat b/Project#04/input/ch4/STO-3G/enuc.dat new file mode 100644 index 0000000..feb8199 --- /dev/null +++ b/Project#04/input/ch4/STO-3G/enuc.dat @@ -0,0 +1 @@ + 13.497304462036480 diff --git a/Project#04/input/ch4/STO-3G/eri.dat b/Project#04/input/ch4/STO-3G/eri.dat new file mode 100644 index 0000000..b1c1a16 --- /dev/null +++ b/Project#04/input/ch4/STO-3G/eri.dat @@ -0,0 +1,912 @@ + 1 1 1 1 3.541948297688456 + 2 1 1 1 0.576921328341946 + 2 2 1 1 0.854681772892244 + 2 1 2 1 0.111888125975301 + 2 2 2 1 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--- /dev/null +++ b/Project#04/input/ch4/STO-3G/geom.dat @@ -0,0 +1,6 @@ +5 +6.000000000000 -0.000000000000 0.000000000000 0.000000000000 +1.000000000000 1.183771681898 -1.183771681898 -1.183771681898 +1.000000000000 1.183771681898 1.183771681898 1.183771681898 +1.000000000000 -1.183771681898 1.183771681898 -1.183771681898 +1.000000000000 -1.183771681898 -1.183771681898 1.183771681898 diff --git a/Project#04/input/ch4/STO-3G/input.dat b/Project#04/input/ch4/STO-3G/input.dat new file mode 100644 index 0000000..6dfb483 --- /dev/null +++ b/Project#04/input/ch4/STO-3G/input.dat @@ -0,0 +1,43 @@ +psi: ( + label = "CH4 SCF Test Case" + wfn = scf + jobtype = oeprop + reference = rhf + basis = "STO-3G" + units = angstrom + subgroup = c1 + delete_tei = false + delete_oei = false + zmat = ( + C + H 1 r + H 1 r 2 td + H 1 r 2 td 3 d + H 1 r 2 td 4 d + ) + zvars = ( + r 1.085 + td 109.47122063449069136958 + d 120.0 + ) +) + +basis: ( + carbon: "STO-3G" = + ( (S ( 71.61683730 0.15432900) + ( 13.04509630 0.53532810) + ( 3.53051220 0.44463450) ) + (S ( 2.94124940 -0.09996720) + ( 0.68348310 0.39951280) + ( 0.22228990 0.70011550) ) + (P ( 2.94124940 0.15591630) + ( 0.68348310 0.60768370) + ( 0.22228990 0.39195740) ) + ) + + hydrogen: "STO-3G"= + ( (S ( 3.42525090 0.15432890) + ( 0.62391370 0.53532810) + ( 0.16885540 0.44463450) ) + ) +) diff --git a/Project#04/input/ch4/STO-3G/mux.dat b/Project#04/input/ch4/STO-3G/mux.dat new file mode 100644 index 0000000..9dca8dd --- /dev/null +++ b/Project#04/input/ch4/STO-3G/mux.dat @@ -0,0 +1,45 @@ + 1 1 0.000000000000000 + 2 1 0.000000000000000 + 2 2 0.000000000000000 + 3 1 -0.071855488532817 + 3 2 -0.838743574800986 + 3 3 0.000000000000000 + 4 1 -0.000000000000000 + 4 2 0.000000000000000 + 4 3 -0.000000000000000 + 4 4 0.000000000000000 + 5 1 0.000000000000000 + 5 2 0.000000000000000 + 5 3 -0.000000000000000 + 5 4 0.000000000000000 + 5 5 0.000000000000000 + 6 1 -0.004780775261548 + 6 2 -0.306592476518555 + 6 3 -0.519567036508228 + 6 4 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9 0.159113527052961 + 14 14 13 11 0.009951274752134 + 14 13 14 11 0.038116382020967 + 14 14 13 12 0.081327533137207 + 14 13 14 12 0.121960603517987 + 14 14 13 13 0.612387322002054 + 14 13 14 13 0.360965402209413 + 14 14 14 1 0.024716026818688 + 14 14 14 2 0.029089756857835 + 14 14 14 3 0.150191104167012 + 14 14 14 4 0.272357832855963 + 14 14 14 5 -0.097701806167297 + 14 14 14 6 0.076333016842254 + 14 14 14 8 -0.238596838405760 + 14 14 14 9 0.186412280376366 + 14 14 14 11 0.053008269605208 + 14 14 14 12 0.157953012201836 + 14 14 14 13 0.390201782129369 + 14 14 14 14 0.475528488258028 diff --git a/Project#04/input/h2o/DZ/geom.dat b/Project#04/input/h2o/DZ/geom.dat new file mode 100644 index 0000000..99b165d --- /dev/null +++ b/Project#04/input/h2o/DZ/geom.dat @@ -0,0 +1,4 @@ +3 +8.000000000000 0.000000000000 -0.143225816552 0.000000000000 +1.000000000000 1.638036840407 1.136548822547 -0.000000000000 +1.000000000000 -1.638036840407 1.136548822547 -0.000000000000 diff --git a/Project#04/input/h2o/DZ/input.dat b/Project#04/input/h2o/DZ/input.dat new file mode 100644 index 0000000..c9eeb62 --- /dev/null +++ b/Project#04/input/h2o/DZ/input.dat @@ -0,0 +1,12 @@ +psi: ( + label = "H2O SCF Test Case" + memory = (10.0 MB) + wfn = scf + jobtype = oeprop + delete_tei = false + delete_oei = false + reference = rhf + basis = "DZ" + subgroup = c1 + zmat = ((o) (h 1 1.1) (h 1 1.1 2 104.0)) +) diff --git a/Project#04/input/h2o/DZ/mux.dat b/Project#04/input/h2o/DZ/mux.dat new file mode 100644 index 0000000..900a852 --- /dev/null +++ b/Project#04/input/h2o/DZ/mux.dat @@ -0,0 +1,105 @@ + 1 1 -0.000000000000000 + 2 1 -0.000000000000000 + 2 2 -0.000000000000000 + 3 1 -0.000000000000000 + 3 2 -0.000000000000000 + 3 3 -0.000000000000000 + 4 1 -0.000000000000000 + 4 2 -0.000000000000000 + 4 3 -0.000000000000000 + 4 4 -0.000000000000000 + 5 1 -0.065756994029223 + 5 2 -0.076390812514647 + 5 3 -0.495548317796719 + 5 4 -0.578524588047388 + 5 5 -0.000000000000000 + 6 1 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a/Project#04/input/h2o/DZ/s.dat b/Project#04/input/h2o/DZ/s.dat new file mode 100644 index 0000000..80cc184 --- /dev/null +++ b/Project#04/input/h2o/DZ/s.dat @@ -0,0 +1,105 @@ + 1 1 1.000000000000000 + 2 1 0.838055657090899 + 2 2 1.000000000000000 + 3 1 0.339351358965910 + 3 2 0.432187282413285 + 3 3 1.000000000000000 + 4 1 0.160966484410815 + 4 2 0.194384266485776 + 4 3 0.776448695132864 + 4 4 1.000000000000000 + 5 1 0.000000000000000 + 5 2 -0.000000000000000 + 5 3 0.000000000000000 + 5 4 0.000000000000000 + 5 5 1.000000000000000 + 6 1 -0.000000000000000 + 6 2 -0.000000000000000 + 6 3 -0.000000000000000 + 6 4 0.000000000000000 + 6 5 0.000000000000000 + 6 6 1.000000000000000 + 7 1 0.000000000000000 + 7 2 0.000000000000000 + 7 3 0.000000000000000 + 7 4 -0.000000000000000 + 7 5 -0.000000000000000 + 7 6 0.000000000000000 + 7 7 1.000000000000000 + 8 1 0.000000000000000 + 8 2 0.000000000000000 + 8 3 0.000000000000000 + 8 4 0.000000000000000 + 8 5 0.505998479748195 + 8 6 0.000000000000000 + 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b/Project#04/input/h2o/DZP/input.dat new file mode 100644 index 0000000..8cf45b4 --- /dev/null +++ b/Project#04/input/h2o/DZP/input.dat @@ -0,0 +1,13 @@ +psi: ( + label = "H2O SCF Test Case" + memory = (10.0 MB) + wfn = scf + jobtype = oeprop + delete_tei = false + delete_oei = false + reference = rhf + puream = false + basis = "DZP" + subgroup = c1 + zmat = ((o) (h 1 1.1) (h 1 1.1 2 104.0)) +) diff --git a/Project#04/input/h2o/DZP/mux.dat b/Project#04/input/h2o/DZP/mux.dat new file mode 100644 index 0000000..9eeb14c --- /dev/null +++ b/Project#04/input/h2o/DZP/mux.dat @@ -0,0 +1,351 @@ + 1 1 -0.000000000000000 + 2 1 -0.000000000000000 + 2 2 -0.000000000000000 + 3 1 -0.000000000000000 + 3 2 -0.000000000000000 + 3 3 -0.000000000000000 + 4 1 -0.000000000000000 + 4 2 -0.000000000000000 + 4 3 -0.000000000000000 + 4 4 -0.000000000000000 + 5 1 -0.065756994029223 + 5 2 -0.076390812514647 + 5 3 -0.495548317796719 + 5 4 -0.578524588047388 + 5 5 -0.000000000000000 + 6 1 0.000000000000000 + 6 2 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0.470723326368778 + 7 1 7 1 0.003683107960076 + 7 7 2 1 0.111191806911617 + 7 2 7 1 0.012121617421746 + 7 7 2 2 0.454660662254829 + 7 2 7 2 0.103816561020432 + 7 7 3 1 -0.008115429695629 + 7 7 4 1 0.006340468574121 + 7 3 7 1 -0.007487641649768 + 7 4 7 1 0.005849986797397 + 7 7 3 2 -0.088850240147481 + 7 7 4 2 0.069417415538897 + 7 3 7 2 -0.079876222072782 + 7 4 7 2 0.062406144205123 + 7 7 3 3 0.469762103528713 + 7 7 4 3 -0.025791716791396 + 7 7 4 4 0.456900909053721 + 7 7 5 5 0.436750211441671 + 7 3 7 3 0.075103217640351 + 7 4 7 3 -0.047460399285077 + 7 4 7 4 0.051436804504574 + 7 5 7 5 0.014356676714874 + 7 7 6 1 0.017890930404213 + 7 6 7 1 0.004091767456984 + 7 7 6 2 0.151924586584762 + 7 6 7 2 0.038415486590652 + 7 7 6 3 0.073615422819083 + 7 7 6 4 0.096752175289782 + 7 6 7 3 -0.025685197500691 + 7 6 7 4 0.025974451190177 + 7 7 6 6 0.302537910673863 + 7 6 7 6 0.017861326916860 + 7 7 7 1 0.018641085379951 + 7 7 7 2 0.235420950941441 + 7 7 7 3 -0.206690042488560 + 7 7 7 4 0.161483959338374 + 7 7 7 6 0.091353706761488 + 7 7 7 7 0.774605943919898 diff --git a/Project#04/input/h2o/STO-3G/geom.dat b/Project#04/input/h2o/STO-3G/geom.dat new file mode 100644 index 0000000..99b165d --- /dev/null +++ b/Project#04/input/h2o/STO-3G/geom.dat @@ -0,0 +1,4 @@ +3 +8.000000000000 0.000000000000 -0.143225816552 0.000000000000 +1.000000000000 1.638036840407 1.136548822547 -0.000000000000 +1.000000000000 -1.638036840407 1.136548822547 -0.000000000000 diff --git a/Project#04/input/h2o/STO-3G/input.dat b/Project#04/input/h2o/STO-3G/input.dat new file mode 100644 index 0000000..f8c5067 --- /dev/null +++ b/Project#04/input/h2o/STO-3G/input.dat @@ -0,0 +1,12 @@ +psi: ( + label = "H2O SCF Test Case" + memory = (10.0 MB) + wfn = scf + jobtype = oeprop + delete_tei = false + delete_oei = false + reference = rhf + basis = "STO-3G" + subgroup = c1 + zmat = ((o) (h 1 1.1) (h 1 1.1 2 104.0)) +) diff --git a/Project#04/input/h2o/STO-3G/mux.dat b/Project#04/input/h2o/STO-3G/mux.dat new file mode 100644 index 0000000..c5d92c5 --- /dev/null +++ b/Project#04/input/h2o/STO-3G/mux.dat @@ -0,0 +1,28 @@ + 1 1 -0.000000000000000 + 2 1 -0.000000000000000 + 2 2 -0.000000000000000 + 3 1 -0.050791929587912 + 3 2 -0.641172844324925 + 3 3 -0.000000000000000 + 4 1 0.000000000000000 + 4 2 0.000000000000000 + 4 3 0.000000000000000 + 4 4 -0.000000000000000 + 5 1 0.000000000000000 + 5 2 -0.000000000000000 + 5 3 -0.000000000000000 + 5 4 0.000000000000000 + 5 5 -0.000000000000000 + 6 1 -0.002229654052248 + 6 2 -0.262742503532769 + 6 3 -0.437630646182039 + 6 4 -0.147399448800486 + 6 5 0.000000000000000 + 6 6 -1.638036840407314 + 7 1 0.002229654052248 + 7 2 0.262742503532769 + 7 3 -0.437630646182039 + 7 4 0.147399448800486 + 7 5 -0.000000000000000 + 7 6 0.000000000000000 + 7 7 1.638036840407314 diff --git a/Project#04/input/h2o/STO-3G/muy.dat b/Project#04/input/h2o/STO-3G/muy.dat new file mode 100644 index 0000000..1efcbad --- /dev/null +++ b/Project#04/input/h2o/STO-3G/muy.dat @@ -0,0 +1,28 @@ + 1 1 0.143225816551918 + 2 1 0.033902114587819 + 2 2 0.143225816551918 + 3 1 -0.000000000000000 + 3 2 0.000000000000000 + 3 3 0.143225816551918 + 4 1 -0.050791929587912 + 4 2 -0.641172844324925 + 4 3 -0.000000000000000 + 4 4 0.143225816551918 + 5 1 -0.000000000000000 + 5 2 0.000000000000000 + 5 3 0.000000000000000 + 5 4 -0.000000000000000 + 5 5 0.143225816551918 + 6 1 0.003758676726377 + 6 2 -0.149971890752635 + 6 3 -0.108952162150434 + 6 4 -0.334090713364948 + 6 5 0.000000000000000 + 6 6 -1.136548822546795 + 7 1 0.003758676726377 + 7 2 -0.149971890752635 + 7 3 0.108952162150434 + 7 4 -0.334090713364948 + 7 5 0.000000000000000 + 7 6 -0.206578984758302 + 7 7 -1.136548822546794 diff --git a/Project#04/input/h2o/STO-3G/muz.dat b/Project#04/input/h2o/STO-3G/muz.dat new file mode 100644 index 0000000..35dfd9f --- /dev/null +++ b/Project#04/input/h2o/STO-3G/muz.dat @@ -0,0 +1,28 @@ + 1 1 -0.000000000000000 + 2 1 -0.000000000000000 + 2 2 -0.000000000000000 + 3 1 0.000000000000000 + 3 2 -0.000000000000000 + 3 3 -0.000000000000000 + 4 1 0.000000000000000 + 4 2 0.000000000000000 + 4 3 0.000000000000000 + 4 4 -0.000000000000000 + 5 1 -0.050791929587912 + 5 2 -0.641172844324925 + 5 3 -0.000000000000000 + 5 4 0.000000000000000 + 5 5 -0.000000000000000 + 6 1 -0.000000000000000 + 6 2 0.000000000000000 + 6 3 0.000000000000000 + 6 4 0.000000000000000 + 6 5 -0.248967955099984 + 6 6 0.000000000000000 + 7 1 -0.000000000000000 + 7 2 0.000000000000000 + 7 3 -0.000000000000000 + 7 4 0.000000000000000 + 7 5 -0.248967955099984 + 7 6 0.000000000000000 + 7 7 0.000000000000000 diff --git a/Project#04/input/h2o/STO-3G/s.dat b/Project#04/input/h2o/STO-3G/s.dat new file mode 100644 index 0000000..9b764da --- /dev/null +++ b/Project#04/input/h2o/STO-3G/s.dat @@ -0,0 +1,28 @@ + 1 1 1.000000000000000 + 2 1 0.236703936510848 + 2 2 1.000000000000000 + 3 1 -0.000000000000000 + 3 2 0.000000000000000 + 3 3 1.000000000000000 + 4 1 -0.000000000000000 + 4 2 -0.000000000000000 + 4 3 -0.000000000000000 + 4 4 1.000000000000000 + 5 1 -0.000000000000000 + 5 2 0.000000000000000 + 5 3 0.000000000000000 + 5 4 -0.000000000000000 + 5 5 1.000000000000000 + 6 1 0.038405599785757 + 6 2 0.386138840478249 + 6 3 0.268438243716457 + 6 4 0.209726941420375 + 6 5 -0.000000000000000 + 6 6 1.000000000000000 + 7 1 0.038405599785757 + 7 2 0.386138840478250 + 7 3 -0.268438243716457 + 7 4 0.209726941420375 + 7 5 -0.000000000000000 + 7 6 0.181759886298063 + 7 7 1.000000000000000 diff --git a/Project#04/input/h2o/STO-3G/t.dat b/Project#04/input/h2o/STO-3G/t.dat new file mode 100644 index 0000000..8927c33 --- /dev/null +++ b/Project#04/input/h2o/STO-3G/t.dat @@ -0,0 +1,28 @@ + 1 1 29.003199945539588 + 2 1 -0.168010939316492 + 2 2 0.808127954930347 + 3 1 0.000000000000000 + 3 2 0.000000000000000 + 3 3 2.528731198194763 + 4 1 0.000000000000000 + 4 2 -0.000000000000000 + 4 3 -0.000000000000000 + 4 4 2.528731198194763 + 5 1 -0.000000000000000 + 5 2 0.000000000000000 + 5 3 0.000000000000000 + 5 4 -0.000000000000000 + 5 5 2.528731198194763 + 6 1 -0.008416383544591 + 6 2 0.070517372751001 + 6 3 0.147090913304052 + 6 4 0.114920016354202 + 6 5 -0.000000000000000 + 6 6 0.760031883566609 + 7 1 -0.008416383544591 + 7 2 0.070517372751002 + 7 3 -0.147090913304052 + 7 4 0.114920016354202 + 7 5 -0.000000000000000 + 7 6 -0.003979868621841 + 7 7 0.760031883566609 diff --git a/Project#04/input/h2o/STO-3G/v.dat b/Project#04/input/h2o/STO-3G/v.dat new file mode 100644 index 0000000..d5b7411 --- /dev/null +++ b/Project#04/input/h2o/STO-3G/v.dat @@ -0,0 +1,28 @@ + 1 1 -61.580595358149914 + 2 1 -7.410821877330996 + 2 2 -10.009071226859687 + 3 1 0.000000000000000 + 3 2 0.000000000000000 + 3 3 -9.987550507419133 + 4 1 -0.014473835903318 + 4 2 -0.176890246723779 + 4 3 0.000000000000000 + 4 4 -9.944042952440439 + 5 1 0.000000000000000 + 5 2 0.000000000000000 + 5 3 -0.000000000000000 + 5 4 0.000000000000000 + 5 5 -9.875876065926128 + 6 1 -1.231685872788711 + 6 2 -2.977227202971528 + 6 3 -1.822241058022723 + 6 4 -1.471788274313766 + 6 5 0.000000000000000 + 6 6 -5.300202953839792 + 7 1 -1.231685872788712 + 7 2 -2.977227202971529 + 7 3 1.822241058022724 + 7 4 -1.471788274313766 + 7 5 0.000000000000001 + 7 6 -1.067166014696110 + 7 7 -5.300202953839793 diff --git a/Project#04/output/ch4/STO-3G/output.txt b/Project#04/output/ch4/STO-3G/output.txt new file mode 100644 index 0000000..50d24d1 --- /dev/null +++ b/Project#04/output/ch4/STO-3G/output.txt @@ -0,0 +1,3 @@ +Escf = -39.726850324347 +Emp2 = -0.056046676165 +Etot = -39.782897000512 diff --git a/Project#04/output/h2o/DZ/output.txt b/Project#04/output/h2o/DZ/output.txt new file mode 100644 index 0000000..caa92c7 --- /dev/null +++ b/Project#04/output/h2o/DZ/output.txt @@ -0,0 +1,3 @@ +Escf = -75.977878975377 +Emp2 = -0.152709879075 +Etot = -76.130588854452 diff --git a/Project#04/output/h2o/DZP/output.txt b/Project#04/output/h2o/DZP/output.txt new file mode 100644 index 0000000..d3e27b9 --- /dev/null +++ b/Project#04/output/h2o/DZP/output.txt @@ -0,0 +1,3 @@ +Escf = -76.008821792901 +Emp2 = -0.222519233815 +Etot = -76.231341026716 diff --git a/Project#04/output/h2o/STO-3G/output.txt b/Project#04/output/h2o/STO-3G/output.txt new file mode 100644 index 0000000..28f6056 --- /dev/null +++ b/Project#04/output/h2o/STO-3G/output.txt @@ -0,0 +1,3 @@ +Escf = -74.942079928192 +Emp2 = -0.049149636120 +Etot = -74.991229564312 diff --git a/Project#04/project4-instructions.pdf b/Project#04/project4-instructions.pdf new file mode 100644 index 0000000..6a8da0b Binary files /dev/null and b/Project#04/project4-instructions.pdf differ diff --git a/Project#05/README.md b/Project#05/README.md index 0876ea9..d4ee632 100644 --- a/Project#05/README.md +++ b/Project#05/README.md @@ -1 +1,52 @@ # Project #5: The coupled cluster singles and doubles (CCSD) energy +The coupled cluster model provides a higher level of accuracy beyond the MP2 approach. The purpose of this project is to understand the fundamental aspects of the calculation of the CCSD wave function and corresponding energy. A good reference article (with correct, factored equations!) is [J.F. Stanton, J. Gauss, J.D. Watts, and R.J. Bartlett, J. Chem. Phys. volume 94, pp. 4334-4345 (1991)]( http://sirius.chem.vt.edu/wiki/lib/exe/fetch.php?media=crawdad:programming:jcp_94_4334_1991.pdf). +## Step #1: Preparing the Spin-Orbital Basis Integrals +Each term in the equations given in the above paper by Stanton et al. depends on the T1 or T2 +amplitudes as well as Fock-matrix elements and antisymmetrized, Dirac-notation two-electron integrals, all given in the molecular spin-orbital basis +(as opposed to the spatial-orbital basis used in the earlier [MP2 Project](../Project%2304). +Thus, the transformation of the AO-basis integrals into the spatial-MO basis must also include their translation into the spin-orbital basis: + + + +Thus, if you know the ordering of the orbitals (e.g. all occupied orbitals before virtual orbitals, perhaps alternating between alpha and beta spins), it is straightforward to carry out the integration over the spin components (the σ's) in the above expression. Thus, each spatial-orbital MO-basis two-electron integral translates to 16 possible spin-orbital integrals, only four of which are non-zero. + +Don't forget that you must also create the spin-orbital Fock matrix: + + + +Suggestion: For simplicity, store the two-electron integrals in a four-dimensional array. This will greatly facilitate debugging of the complicated CCSD equations. + + * [Hint 1](./hints/hint1.md): Sample spatial- to spin-orbital translation code. + +## Step #2: Build the Initial-Guess Cluster Amplitudes +For Hartree-Fock reference determinants, the most common initial guess for the cluster amplitudes are the Moller-Plesset first-order perturbed wave function: + + + +Note that if you have constructed the Fock matrix, two-electron integrals, and initial-guess amplitudes correctly at this point, +you should be able to compute the MP2 correlation energy using the simple spin-orbital expression and get identical results to those from [Project #4](../Project%2304): + + + +## Step #3: Calculate the CC Intermediates +Use the spin-orbital Eqs. 3-13 from Stanton's paper to build the two-index (F) and four-index (W) intermediates, as well as the effective doubles (labelled with the Greek letter τ). + +## Step #4: Compute the Updated Cluster Amplitudes +Use Eqs. 1 and 2 from Stanton's paper to compute the updated T1 and T2 cluster amplitudes. + +## Step #5: Check for Convergence and Iterate +Calculate the current CC correlation energy: + + + +Compare energies and cluster amplitudes (using RMS differences) between iterations to check for convergence to some specified cutoff. +If convergence is reached, you're done; if not, return to Step #3 and continue. + +## Test Cases +The input structures, integrals, etc. for these examples are found in the +[input directory](./input). + +* STO-3G Water | [output](./output/h2o/STO-3G/output.txt) +* DZ Water | [output](./output/h2o/DZ/output.txt) +* DZP Water | [output](./output/h2o/DZP/output.txt) +* STO-3G Methane | [output](./output/ch4/STO-3G/output.txt) diff --git a/Project#05/figures/cc-correlation-energy.png b/Project#05/figures/cc-correlation-energy.png new file mode 100644 index 0000000..0be10b2 Binary files /dev/null and b/Project#05/figures/cc-correlation-energy.png differ diff --git a/Project#05/figures/init-t-amps.png b/Project#05/figures/init-t-amps.png new file mode 100644 index 0000000..9d8e797 Binary files /dev/null and b/Project#05/figures/init-t-amps.png differ diff --git a/Project#05/figures/mp2-energy.png b/Project#05/figures/mp2-energy.png new file mode 100644 index 0000000..cae007a Binary files /dev/null and b/Project#05/figures/mp2-energy.png differ diff --git a/Project#05/figures/spin-orbital-eri.png b/Project#05/figures/spin-orbital-eri.png new file mode 100644 index 0000000..71b5501 Binary files /dev/null and b/Project#05/figures/spin-orbital-eri.png differ diff --git a/Project#05/figures/spin-orbital-fock.png b/Project#05/figures/spin-orbital-fock.png new file mode 100644 index 0000000..69e8771 Binary files /dev/null and b/Project#05/figures/spin-orbital-fock.png differ diff --git a/Project#05/hints/hint1.md b/Project#05/hints/hint1.md new file mode 100644 index 0000000..6483590 --- /dev/null +++ b/Project#05/hints/hint1.md @@ -0,0 +1,19 @@ +This block of code takes the one-dimensional array of MO-basis spatial-orbital two-electron integrals we've been using thus far and translates it to a four-dimensional array of antisymmetrized integrals over spin-orbitals. Note that alpha and beta spin functions alternate here, with even-numbered orbitals corresponding to alpha, and odd-numbered to beta. The variable `nmo` is the number of spin orbitals, and the `INDEX` function is the same as that [used before](../../Project%2303/hints/hint7-2.md). + +```c++ + /* Translate integrals to spin-orbital basis */ + for(p=0; p < nmo; p++) + for(q=0; q < nmo; q++) + for(r=0; r < nmo; r++) + for(s=0; s < nmo; s++) { + pr = INDEX(p/2,r/2); + qs = INDEX(q/2,s/2); + prqs = INDEX(pr,qs); + value1 = TEI[prqs] * (p%2 == r%2) * (q%2 == s%2); + ps = INDEX(p/2,s/2); + qr = INDEX(q/2,r/2); + psqr = INDEX(ps,qr); + value2 = TEI[psqr] * (p%2 == s%2) * (q%2 == r%2); + ints[p][q][r][s] = value1 - value2; + } +``` diff --git a/Project#05/input/ch4/STO-3G/enuc.dat b/Project#05/input/ch4/STO-3G/enuc.dat new file mode 100644 index 0000000..feb8199 --- /dev/null +++ b/Project#05/input/ch4/STO-3G/enuc.dat @@ -0,0 +1 @@ + 13.497304462036480 diff --git a/Project#05/input/ch4/STO-3G/eri.dat b/Project#05/input/ch4/STO-3G/eri.dat new file mode 100644 index 0000000..b1c1a16 --- /dev/null +++ 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0.085276746780538 + 9 9 9 9 0.774605895725855 diff --git a/Project#05/input/ch4/STO-3G/geom.dat b/Project#05/input/ch4/STO-3G/geom.dat new file mode 100644 index 0000000..9c536a9 --- /dev/null +++ b/Project#05/input/ch4/STO-3G/geom.dat @@ -0,0 +1,6 @@ +5 +6.000000000000 -0.000000000000 0.000000000000 0.000000000000 +1.000000000000 1.183771681898 -1.183771681898 -1.183771681898 +1.000000000000 1.183771681898 1.183771681898 1.183771681898 +1.000000000000 -1.183771681898 1.183771681898 -1.183771681898 +1.000000000000 -1.183771681898 -1.183771681898 1.183771681898 diff --git a/Project#05/input/ch4/STO-3G/input.dat b/Project#05/input/ch4/STO-3G/input.dat new file mode 100644 index 0000000..6dfb483 --- /dev/null +++ b/Project#05/input/ch4/STO-3G/input.dat @@ -0,0 +1,43 @@ +psi: ( + label = "CH4 SCF Test Case" + wfn = scf + jobtype = oeprop + reference = rhf + basis = "STO-3G" + units = angstrom + subgroup = c1 + delete_tei = false + delete_oei = false + zmat = ( + C + H 1 r + H 1 r 2 td + H 1 r 2 td 3 d + H 1 r 2 td 4 d + ) + zvars = ( + r 1.085 + td 109.47122063449069136958 + d 120.0 + ) +) + +basis: ( + carbon: "STO-3G" = + ( (S ( 71.61683730 0.15432900) + ( 13.04509630 0.53532810) + ( 3.53051220 0.44463450) ) + (S ( 2.94124940 -0.09996720) + ( 0.68348310 0.39951280) + ( 0.22228990 0.70011550) ) + (P ( 2.94124940 0.15591630) + ( 0.68348310 0.60768370) + ( 0.22228990 0.39195740) ) + ) + + hydrogen: "STO-3G"= + ( (S ( 3.42525090 0.15432890) + ( 0.62391370 0.53532810) + ( 0.16885540 0.44463450) ) + ) +) diff --git a/Project#05/input/ch4/STO-3G/mux.dat b/Project#05/input/ch4/STO-3G/mux.dat new file mode 100644 index 0000000..9dca8dd --- /dev/null +++ b/Project#05/input/ch4/STO-3G/mux.dat @@ -0,0 +1,45 @@ + 1 1 0.000000000000000 + 2 1 0.000000000000000 + 2 2 0.000000000000000 + 3 1 -0.071855488532817 + 3 2 -0.838743574800986 + 3 3 0.000000000000000 + 4 1 -0.000000000000000 + 4 2 0.000000000000000 + 4 3 -0.000000000000000 + 4 4 0.000000000000000 + 5 1 0.000000000000000 + 5 2 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b/Project#05/input/ch4/STO-3G/muy.dat @@ -0,0 +1,45 @@ + 1 1 -0.000000000000000 + 2 1 -0.000000000000000 + 2 2 -0.000000000000000 + 3 1 -0.000000000000000 + 3 2 0.000000000000000 + 3 3 -0.000000000000000 + 4 1 -0.071855488532817 + 4 2 -0.838743574800986 + 4 3 0.000000000000000 + 4 4 -0.000000000000000 + 5 1 -0.000000000000000 + 5 2 -0.000000000000000 + 5 3 0.000000000000000 + 5 4 -0.000000000000000 + 5 5 -0.000000000000000 + 6 1 0.004780775261548 + 6 2 0.306592476518555 + 6 3 0.163831354490276 + 6 4 -0.519567036508228 + 6 5 -0.163831354490276 + 6 6 1.183771681897730 + 7 1 -0.004780775261548 + 7 2 -0.306592476518555 + 7 3 -0.163831354490276 + 7 4 -0.519567036508228 + 7 5 -0.163831354490276 + 7 6 -0.000000000000000 + 7 7 -1.183771681897730 + 8 1 -0.004780775261548 + 8 2 -0.306592476518555 + 8 3 0.163831354490276 + 8 4 -0.519567036508228 + 8 5 0.163831354490276 + 8 6 -0.000000000000000 + 8 7 -0.202918556316052 + 8 8 -1.183771681897730 + 9 1 0.004780775261548 + 9 2 0.306592476518555 + 9 3 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0.000000000000 -0.143225816552 0.000000000000 +1.000000000000 1.638036840407 1.136548822547 -0.000000000000 +1.000000000000 -1.638036840407 1.136548822547 -0.000000000000 diff --git a/Project#05/input/h2o/DZ/input.dat b/Project#05/input/h2o/DZ/input.dat new file mode 100644 index 0000000..c9eeb62 --- /dev/null +++ b/Project#05/input/h2o/DZ/input.dat @@ -0,0 +1,12 @@ +psi: ( + label = "H2O SCF Test Case" + memory = (10.0 MB) + wfn = scf + jobtype = oeprop + delete_tei = false + delete_oei = false + reference = rhf + basis = "DZ" + subgroup = c1 + zmat = ((o) (h 1 1.1) (h 1 1.1 2 104.0)) +) diff --git a/Project#05/input/h2o/DZ/mux.dat b/Project#05/input/h2o/DZ/mux.dat new file mode 100644 index 0000000..900a852 --- /dev/null +++ b/Project#05/input/h2o/DZ/mux.dat @@ -0,0 +1,105 @@ + 1 1 -0.000000000000000 + 2 1 -0.000000000000000 + 2 2 -0.000000000000000 + 3 1 -0.000000000000000 + 3 2 -0.000000000000000 + 3 3 -0.000000000000000 + 4 1 -0.000000000000000 + 4 2 -0.000000000000000 + 4 3 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a/Project#05/input/h2o/DZ/t.dat b/Project#05/input/h2o/DZ/t.dat new file mode 100644 index 0000000..53902be --- /dev/null +++ b/Project#05/input/h2o/DZ/t.dat @@ -0,0 +1,105 @@ + 1 1 52.614894976915927 + 2 1 15.661014804629346 + 2 2 14.298299999999999 + 3 1 0.833950187178430 + 3 2 1.109154871321247 + 3 3 1.409700000000000 + 4 1 0.130741042908871 + 4 2 0.161153767635618 + 4 3 0.508839754794995 + 4 4 0.426900000000000 + 5 1 -0.000000000000000 + 5 2 -0.000000000000000 + 5 3 0.000000000000000 + 5 4 0.000000000000000 + 5 5 3.634977567017164 + 6 1 0.000000000000000 + 6 2 -0.000000000000000 + 6 3 -0.000000000000000 + 6 4 0.000000000000000 + 6 5 0.000000000000000 + 6 6 3.634977567017164 + 7 1 -0.000000000000000 + 7 2 -0.000000000000000 + 7 3 0.000000000000000 + 7 4 -0.000000000000000 + 7 5 -0.000000000000000 + 7 6 0.000000000000000 + 7 7 3.634977567017164 + 8 1 0.000000000000000 + 8 2 -0.000000000000000 + 8 3 0.000000000000000 + 8 4 0.000000000000000 + 8 5 0.432293973533708 + 8 6 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a/Project#05/input/h2o/DZP/geom.dat b/Project#05/input/h2o/DZP/geom.dat new file mode 100644 index 0000000..99b165d --- /dev/null +++ b/Project#05/input/h2o/DZP/geom.dat @@ -0,0 +1,4 @@ +3 +8.000000000000 0.000000000000 -0.143225816552 0.000000000000 +1.000000000000 1.638036840407 1.136548822547 -0.000000000000 +1.000000000000 -1.638036840407 1.136548822547 -0.000000000000 diff --git a/Project#05/input/h2o/DZP/input.dat b/Project#05/input/h2o/DZP/input.dat new file mode 100644 index 0000000..8cf45b4 --- /dev/null +++ b/Project#05/input/h2o/DZP/input.dat @@ -0,0 +1,13 @@ +psi: ( + label = "H2O SCF Test Case" + memory = (10.0 MB) + wfn = scf + jobtype = oeprop + delete_tei = false + delete_oei = false + reference = rhf + puream = false + basis = "DZP" + subgroup = c1 + zmat = ((o) (h 1 1.1) (h 1 1.1 2 104.0)) +) diff --git a/Project#05/input/h2o/DZP/mux.dat b/Project#05/input/h2o/DZP/mux.dat new file mode 100644 index 0000000..9eeb14c --- /dev/null +++ b/Project#05/input/h2o/DZP/mux.dat 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-0.013099738777752 + 7 3 6 4 -0.025320151118325 + 7 4 6 3 0.025320151118325 + 7 4 6 4 0.038857871090576 + 7 5 6 5 0.011033892047394 + 7 6 6 1 0.004091767456984 + 7 1 6 6 0.017890930404213 + 7 6 6 2 0.038415486590652 + 7 2 6 6 0.151924586584762 + 7 6 6 3 0.025685197500691 + 7 6 6 4 0.025974451190177 + 7 3 6 6 -0.073615422819083 + 7 4 6 6 0.096752175289782 + 7 6 6 6 0.091353706761488 + 7 7 1 1 0.470723326368778 + 7 1 7 1 0.003683107960076 + 7 7 2 1 0.111191806911617 + 7 2 7 1 0.012121617421746 + 7 7 2 2 0.454660662254829 + 7 2 7 2 0.103816561020432 + 7 7 3 1 -0.008115429695629 + 7 7 4 1 0.006340468574121 + 7 3 7 1 -0.007487641649768 + 7 4 7 1 0.005849986797397 + 7 7 3 2 -0.088850240147481 + 7 7 4 2 0.069417415538897 + 7 3 7 2 -0.079876222072782 + 7 4 7 2 0.062406144205123 + 7 7 3 3 0.469762103528713 + 7 7 4 3 -0.025791716791396 + 7 7 4 4 0.456900909053721 + 7 7 5 5 0.436750211441671 + 7 3 7 3 0.075103217640351 + 7 4 7 3 -0.047460399285077 + 7 4 7 4 0.051436804504574 + 7 5 7 5 0.014356676714874 + 7 7 6 1 0.017890930404213 + 7 6 7 1 0.004091767456984 + 7 7 6 2 0.151924586584762 + 7 6 7 2 0.038415486590652 + 7 7 6 3 0.073615422819083 + 7 7 6 4 0.096752175289782 + 7 6 7 3 -0.025685197500691 + 7 6 7 4 0.025974451190177 + 7 7 6 6 0.302537910673863 + 7 6 7 6 0.017861326916860 + 7 7 7 1 0.018641085379951 + 7 7 7 2 0.235420950941441 + 7 7 7 3 -0.206690042488560 + 7 7 7 4 0.161483959338374 + 7 7 7 6 0.091353706761488 + 7 7 7 7 0.774605943919898 diff --git a/Project#05/input/h2o/STO-3G/geom.dat b/Project#05/input/h2o/STO-3G/geom.dat new file mode 100644 index 0000000..99b165d --- /dev/null +++ b/Project#05/input/h2o/STO-3G/geom.dat @@ -0,0 +1,4 @@ +3 +8.000000000000 0.000000000000 -0.143225816552 0.000000000000 +1.000000000000 1.638036840407 1.136548822547 -0.000000000000 +1.000000000000 -1.638036840407 1.136548822547 -0.000000000000 diff --git a/Project#05/input/h2o/STO-3G/input.dat b/Project#05/input/h2o/STO-3G/input.dat new file mode 100644 index 0000000..f8c5067 --- /dev/null +++ b/Project#05/input/h2o/STO-3G/input.dat @@ -0,0 +1,12 @@ +psi: ( + label = "H2O SCF Test Case" + memory = (10.0 MB) + wfn = scf + jobtype = oeprop + delete_tei = false + delete_oei = false + reference = rhf + basis = "STO-3G" + subgroup = c1 + zmat = ((o) (h 1 1.1) (h 1 1.1 2 104.0)) +) diff --git a/Project#05/input/h2o/STO-3G/mux.dat b/Project#05/input/h2o/STO-3G/mux.dat new file mode 100644 index 0000000..c5d92c5 --- /dev/null +++ b/Project#05/input/h2o/STO-3G/mux.dat @@ -0,0 +1,28 @@ + 1 1 -0.000000000000000 + 2 1 -0.000000000000000 + 2 2 -0.000000000000000 + 3 1 -0.050791929587912 + 3 2 -0.641172844324925 + 3 3 -0.000000000000000 + 4 1 0.000000000000000 + 4 2 0.000000000000000 + 4 3 0.000000000000000 + 4 4 -0.000000000000000 + 5 1 0.000000000000000 + 5 2 -0.000000000000000 + 5 3 -0.000000000000000 + 5 4 0.000000000000000 + 5 5 -0.000000000000000 + 6 1 -0.002229654052248 + 6 2 -0.262742503532769 + 6 3 -0.437630646182039 + 6 4 -0.147399448800486 + 6 5 0.000000000000000 + 6 6 -1.638036840407314 + 7 1 0.002229654052248 + 7 2 0.262742503532769 + 7 3 -0.437630646182039 + 7 4 0.147399448800486 + 7 5 -0.000000000000000 + 7 6 0.000000000000000 + 7 7 1.638036840407314 diff --git a/Project#05/input/h2o/STO-3G/muy.dat b/Project#05/input/h2o/STO-3G/muy.dat new file mode 100644 index 0000000..1efcbad --- /dev/null +++ b/Project#05/input/h2o/STO-3G/muy.dat @@ -0,0 +1,28 @@ + 1 1 0.143225816551918 + 2 1 0.033902114587819 + 2 2 0.143225816551918 + 3 1 -0.000000000000000 + 3 2 0.000000000000000 + 3 3 0.143225816551918 + 4 1 -0.050791929587912 + 4 2 -0.641172844324925 + 4 3 -0.000000000000000 + 4 4 0.143225816551918 + 5 1 -0.000000000000000 + 5 2 0.000000000000000 + 5 3 0.000000000000000 + 5 4 -0.000000000000000 + 5 5 0.143225816551918 + 6 1 0.003758676726377 + 6 2 -0.149971890752635 + 6 3 -0.108952162150434 + 6 4 -0.334090713364948 + 6 5 0.000000000000000 + 6 6 -1.136548822546795 + 7 1 0.003758676726377 + 7 2 -0.149971890752635 + 7 3 0.108952162150434 + 7 4 -0.334090713364948 + 7 5 0.000000000000000 + 7 6 -0.206578984758302 + 7 7 -1.136548822546794 diff --git a/Project#05/input/h2o/STO-3G/muz.dat b/Project#05/input/h2o/STO-3G/muz.dat new file mode 100644 index 0000000..35dfd9f --- /dev/null +++ b/Project#05/input/h2o/STO-3G/muz.dat @@ -0,0 +1,28 @@ + 1 1 -0.000000000000000 + 2 1 -0.000000000000000 + 2 2 -0.000000000000000 + 3 1 0.000000000000000 + 3 2 -0.000000000000000 + 3 3 -0.000000000000000 + 4 1 0.000000000000000 + 4 2 0.000000000000000 + 4 3 0.000000000000000 + 4 4 -0.000000000000000 + 5 1 -0.050791929587912 + 5 2 -0.641172844324925 + 5 3 -0.000000000000000 + 5 4 0.000000000000000 + 5 5 -0.000000000000000 + 6 1 -0.000000000000000 + 6 2 0.000000000000000 + 6 3 0.000000000000000 + 6 4 0.000000000000000 + 6 5 -0.248967955099984 + 6 6 0.000000000000000 + 7 1 -0.000000000000000 + 7 2 0.000000000000000 + 7 3 -0.000000000000000 + 7 4 0.000000000000000 + 7 5 -0.248967955099984 + 7 6 0.000000000000000 + 7 7 0.000000000000000 diff --git a/Project#05/input/h2o/STO-3G/s.dat b/Project#05/input/h2o/STO-3G/s.dat new file mode 100644 index 0000000..9b764da --- /dev/null +++ b/Project#05/input/h2o/STO-3G/s.dat @@ -0,0 +1,28 @@ + 1 1 1.000000000000000 + 2 1 0.236703936510848 + 2 2 1.000000000000000 + 3 1 -0.000000000000000 + 3 2 0.000000000000000 + 3 3 1.000000000000000 + 4 1 -0.000000000000000 + 4 2 -0.000000000000000 + 4 3 -0.000000000000000 + 4 4 1.000000000000000 + 5 1 -0.000000000000000 + 5 2 0.000000000000000 + 5 3 0.000000000000000 + 5 4 -0.000000000000000 + 5 5 1.000000000000000 + 6 1 0.038405599785757 + 6 2 0.386138840478249 + 6 3 0.268438243716457 + 6 4 0.209726941420375 + 6 5 -0.000000000000000 + 6 6 1.000000000000000 + 7 1 0.038405599785757 + 7 2 0.386138840478250 + 7 3 -0.268438243716457 + 7 4 0.209726941420375 + 7 5 -0.000000000000000 + 7 6 0.181759886298063 + 7 7 1.000000000000000 diff --git a/Project#05/input/h2o/STO-3G/t.dat b/Project#05/input/h2o/STO-3G/t.dat new file mode 100644 index 0000000..8927c33 --- /dev/null +++ b/Project#05/input/h2o/STO-3G/t.dat @@ -0,0 +1,28 @@ + 1 1 29.003199945539588 + 2 1 -0.168010939316492 + 2 2 0.808127954930347 + 3 1 0.000000000000000 + 3 2 0.000000000000000 + 3 3 2.528731198194763 + 4 1 0.000000000000000 + 4 2 -0.000000000000000 + 4 3 -0.000000000000000 + 4 4 2.528731198194763 + 5 1 -0.000000000000000 + 5 2 0.000000000000000 + 5 3 0.000000000000000 + 5 4 -0.000000000000000 + 5 5 2.528731198194763 + 6 1 -0.008416383544591 + 6 2 0.070517372751001 + 6 3 0.147090913304052 + 6 4 0.114920016354202 + 6 5 -0.000000000000000 + 6 6 0.760031883566609 + 7 1 -0.008416383544591 + 7 2 0.070517372751002 + 7 3 -0.147090913304052 + 7 4 0.114920016354202 + 7 5 -0.000000000000000 + 7 6 -0.003979868621841 + 7 7 0.760031883566609 diff --git a/Project#05/input/h2o/STO-3G/v.dat b/Project#05/input/h2o/STO-3G/v.dat new file mode 100644 index 0000000..d5b7411 --- /dev/null +++ b/Project#05/input/h2o/STO-3G/v.dat @@ -0,0 +1,28 @@ + 1 1 -61.580595358149914 + 2 1 -7.410821877330996 + 2 2 -10.009071226859687 + 3 1 0.000000000000000 + 3 2 0.000000000000000 + 3 3 -9.987550507419133 + 4 1 -0.014473835903318 + 4 2 -0.176890246723779 + 4 3 0.000000000000000 + 4 4 -9.944042952440439 + 5 1 0.000000000000000 + 5 2 0.000000000000000 + 5 3 -0.000000000000000 + 5 4 0.000000000000000 + 5 5 -9.875876065926128 + 6 1 -1.231685872788711 + 6 2 -2.977227202971528 + 6 3 -1.822241058022723 + 6 4 -1.471788274313766 + 6 5 0.000000000000000 + 6 6 -5.300202953839792 + 7 1 -1.231685872788712 + 7 2 -2.977227202971529 + 7 3 1.822241058022724 + 7 4 -1.471788274313766 + 7 5 0.000000000000001 + 7 6 -1.067166014696110 + 7 7 -5.300202953839793 diff --git a/Project#05/output/ch4/STO-3G/output.txt b/Project#05/output/ch4/STO-3G/output.txt new file mode 100644 index 0000000..ea1c2a2 --- /dev/null +++ b/Project#05/output/ch4/STO-3G/output.txt @@ -0,0 +1,37 @@ +Escf = -39.726850324347 +Emp2 = -0.056046676165 +Etot = -39.782897000512 +iter = 1 Ecc = -0.070745263263 +iter = 2 Ecc = -0.075483796521 +iter = 3 Ecc = -0.077200328167 +iter = 4 Ecc = -0.077865987703 +iter = 5 Ecc = -0.078135369924 +iter = 6 Ecc = -0.078247914883 +iter = 7 Ecc = -0.078296205328 +iter = 8 Ecc = -0.078317411865 +iter = 9 Ecc = -0.078326913387 +iter = 10 Ecc = -0.078331243411 +iter = 11 Ecc = -0.078333244509 +iter = 12 Ecc = -0.078334179793 +iter = 13 Ecc = -0.078334620840 +iter = 14 Ecc = -0.078334830264 +iter = 15 Ecc = -0.078334930235 +iter = 16 Ecc = -0.078334978150 +iter = 17 Ecc = -0.078335001185 +iter = 18 Ecc = -0.078335012284 +iter = 19 Ecc = -0.078335017641 +iter = 20 Ecc = -0.078335020230 +iter = 21 Ecc = -0.078335021483 +iter = 22 Ecc = -0.078335022089 +iter = 23 Ecc = -0.078335022383 +iter = 24 Ecc = -0.078335022525 +iter = 25 Ecc = -0.078335022594 +iter = 26 Ecc = -0.078335022627 +iter = 27 Ecc = -0.078335022643 +iter = 28 Ecc = -0.078335022651 +iter = 29 Ecc = -0.078335022655 +iter = 30 Ecc = -0.078335022657 +iter = 31 Ecc = -0.078335022658 +CC iterations converged +Ecc = -0.078335022658 +Etot = -39.805185347005 diff --git a/Project#05/output/h2o/DZ/output.txt b/Project#05/output/h2o/DZ/output.txt new file mode 100644 index 0000000..3105ecd --- /dev/null +++ b/Project#05/output/h2o/DZ/output.txt @@ -0,0 +1,44 @@ +Escf = -75.977878975377 +Emp2 = -0.152709879075 +Etot = -76.130588854452 +iter = 1 Ecc = -0.153219621639 +iter = 2 Ecc = -0.157583607713 +iter = 3 Ecc = -0.158780675351 +iter = 4 Ecc = -0.159372391348 +iter = 5 Ecc = -0.159624912154 +iter = 6 Ecc = -0.159744546198 +iter = 7 Ecc = -0.159800894442 +iter = 8 Ecc = -0.159828278264 +iter = 9 Ecc = -0.159841746027 +iter = 10 Ecc = -0.159848484750 +iter = 11 Ecc = -0.159851902014 +iter = 12 Ecc = -0.159853658806 +iter = 13 Ecc = -0.159854573327 +iter = 14 Ecc = -0.159855055123 +iter = 15 Ecc = -0.159855311795 +iter = 16 Ecc = -0.159855449966 +iter = 17 Ecc = -0.159855525065 +iter = 18 Ecc = -0.159855566244 +iter = 19 Ecc = -0.159855589005 +iter = 20 Ecc = -0.159855601678 +iter = 21 Ecc = -0.159855608780 +iter = 22 Ecc = -0.159855612784 +iter = 23 Ecc = -0.159855615052 +iter = 24 Ecc = -0.159855616344 +iter = 25 Ecc = -0.159855617082 +iter = 26 Ecc = -0.159855617505 +iter = 27 Ecc = -0.159855617749 +iter = 28 Ecc = -0.159855617890 +iter = 29 Ecc = -0.159855617971 +iter = 30 Ecc = -0.159855618018 +iter = 31 Ecc = -0.159855618046 +iter = 32 Ecc = -0.159855618062 +iter = 33 Ecc = -0.159855618071 +iter = 34 Ecc = -0.159855618077 +iter = 35 Ecc = -0.159855618080 +iter = 36 Ecc = -0.159855618082 +iter = 37 Ecc = -0.159855618083 +iter = 38 Ecc = -0.159855618083 +CC iterations converged +Ecc = -0.159855618083 +Etot = -76.137734593460 diff --git a/Project#05/output/h2o/DZP/output.txt b/Project#05/output/h2o/DZP/output.txt new file mode 100644 index 0000000..0eb9c42 --- /dev/null +++ b/Project#05/output/h2o/DZP/output.txt @@ -0,0 +1,44 @@ +Escf = -76.008821792901 +Emp2 = -0.222519233815 +Etot = -76.231341026716 +iter = 1 Ecc = -0.224897568695 +iter = 2 Ecc = -0.229765989813 +iter = 3 Ecc = -0.230690952187 +iter = 4 Ecc = -0.231206877752 +iter = 5 Ecc = -0.231397181303 +iter = 6 Ecc = -0.231490655906 +iter = 7 Ecc = -0.231532173950 +iter = 8 Ecc = -0.231552454278 +iter = 9 Ecc = -0.231562184987 +iter = 10 Ecc = -0.231567038587 +iter = 11 Ecc = -0.231569475351 +iter = 12 Ecc = -0.231570726044 +iter = 13 Ecc = -0.231571376449 +iter = 14 Ecc = -0.231571720404 +iter = 15 Ecc = -0.231571904849 +iter = 16 Ecc = -0.231572005163 +iter = 17 Ecc = -0.231572060412 +iter = 18 Ecc = -0.231572091200 +iter = 19 Ecc = -0.231572108536 +iter = 20 Ecc = -0.231572118390 +iter = 21 Ecc = -0.231572124037 +iter = 22 Ecc = -0.231572127296 +iter = 23 Ecc = -0.231572129188 +iter = 24 Ecc = -0.231572130292 +iter = 25 Ecc = -0.231572130940 +iter = 26 Ecc = -0.231572131321 +iter = 27 Ecc = -0.231572131546 +iter = 28 Ecc = -0.231572131679 +iter = 29 Ecc = -0.231572131758 +iter = 30 Ecc = -0.231572131805 +iter = 31 Ecc = -0.231572131833 +iter = 32 Ecc = -0.231572131849 +iter = 33 Ecc = -0.231572131859 +iter = 34 Ecc = -0.231572131865 +iter = 35 Ecc = -0.231572131869 +iter = 36 Ecc = -0.231572131871 +iter = 37 Ecc = -0.231572131872 +iter = 38 Ecc = -0.231572131873 +CC iterations converged +Ecc = -0.231572131873 +Etot = -76.240393924774 diff --git a/Project#05/output/h2o/STO-3G/output.txt b/Project#05/output/h2o/STO-3G/output.txt new file mode 100644 index 0000000..83bc8e4 --- /dev/null +++ b/Project#05/output/h2o/STO-3G/output.txt @@ -0,0 +1,44 @@ +Escf = -74.942079928192 +Emp2 = -0.049149636120 +Etot = -74.991229564312 +iter = 1 Ecc = -0.062758205955 +iter = 2 Ecc = -0.067396582597 +iter = 3 Ecc = -0.069224536410 +iter = 4 Ecc = -0.070007757556 +iter = 5 Ecc = -0.070360041902 +iter = 6 Ecc = -0.070523820218 +iter = 7 Ecc = -0.070602032617 +iter = 8 Ecc = -0.070640293027 +iter = 9 Ecc = -0.070659428829 +iter = 10 Ecc = -0.070669194426 +iter = 11 Ecc = -0.070674268048 +iter = 12 Ecc = -0.070676944995 +iter = 13 Ecc = -0.070678375859 +iter = 14 Ecc = -0.070679148887 +iter = 15 Ecc = -0.070679570139 +iter = 16 Ecc = -0.070679801279 +iter = 17 Ecc = -0.070679928796 +iter = 18 Ecc = -0.070679999445 +iter = 19 Ecc = -0.070680038717 +iter = 20 Ecc = -0.070680060604 +iter = 21 Ecc = -0.070680072825 +iter = 22 Ecc = -0.070680079661 +iter = 23 Ecc = -0.070680083488 +iter = 24 Ecc = -0.070680085633 +iter = 25 Ecc = -0.070680086836 +iter = 26 Ecc = -0.070680087511 +iter = 27 Ecc = -0.070680087891 +iter = 28 Ecc = -0.070680088103 +iter = 29 Ecc = -0.070680088223 +iter = 30 Ecc = -0.070680088290 +iter = 31 Ecc = -0.070680088328 +iter = 32 Ecc = -0.070680088349 +iter = 33 Ecc = -0.070680088361 +iter = 34 Ecc = -0.070680088368 +iter = 35 Ecc = -0.070680088372 +iter = 36 Ecc = -0.070680088374 +iter = 37 Ecc = -0.070680088375 +iter = 38 Ecc = -0.070680088376 +CC iterations converged +Ecc = -0.070680088376 +Etot = -75.012760016568 diff --git a/Project#06/README.md b/Project#06/README.md index 562c490..effecf3 100644 --- a/Project#06/README.md +++ b/Project#06/README.md @@ -1 +1,84 @@ -# Project #6: A perturbative triples correction to CCSD [CCSD(T)] +# Project #6: A perturbative triples correction to CCSD: CCSD(T) + +The CCSD(T) method is often referred to as the "gold standard" of quantum chemistry for its high accuracy and reliability. The purpose of this project is to illustrate the fundamental aspects of an efficient implementation of the (T) energy correction. This project builds upon the results of +[Project #5](../Project%2305). + +The spin-orbital expression for the (T) correction, using the same notation as in +[Project #5](../Project%2305), is: + + + +where + + + +the "disconnected" triples are defined as + + + +and the "connected" triples as + + + +The three-index permutation operator is defined by its action on an algebraic function as + + + +The total energy is + + + +## Algorithm #1: Full Storage of Triples + +The most straightforward approach to evaluation of the (T) energy correction is to compute and store explicitly the connected and disconnected triples and plug them into the energy expression above. Store the triples amplitudes as six-dimensional arrays over occupied and virtual spin orbitals. + +## Algorithm #2: Avoided Storage of Triples + +Note that each T3 amplitude depends on all the T1 and T2 amplitudes, **not** on other triples. This suggests that the calculation of the T3 amplitudes appearing in the energy expression could proceed one amplitude at a time: + +``` + Loop over i + Loop over j + Loop over k + Loop over a + Loop over b + Loop over c + + Compute connected and disconnected T3 amplitudes for current i,j,k,a,b,c combination + + Calculate contribution of these T3 amplitudes to the (T) energy + + End c loop + End b loop + End a loop + End k loop + End j loop + End i loop +``` + +This algorithm reduces the storage (memory and disk) requirements of the (T) correction **considerably**. One can conceive of other approaches as well, including calculations of batches of T3 amplitudes (rather than one at a time) to improve floating-point performance. For example: + +``` + Loop over i + Loop over j + Loop over k + + Compute all T3 amplitudes (all a,b,c combinations) for current i,j,k + + Calculation contribution of these T3 amplitudes to the (T) energy + + End k loop + End j loop + End i loop +``` + +This approach requires more storage [O(v3)] than the one-at-a-time approach, but can be considerably faster for modern high-performance computers. A good discussion of the most efficient algorithm can be found in A. P. Rendell, T. J. Lee, A. Komornicki, //Chem. Phys. Lett.// **178**, 462-470 (1991). + +## Test Cases +The input structures, integrals, etc. for these examples may be found in the [input](./input) +directory, the CCSD Energies can be found in [Project #5](../Project%2305). + +* STO-3G Water | [Output](./output/h2o/STO-3G/output.txt) +* DZ Water | [Output](./output/h2o/DZ/output.txt) +* DZP Water | [Output](./output/h2o/DZP/output.txt) +* STO-3G Methane | [Output](./output/ch4/STO-3G/output.txt) diff --git a/Project#06/figures/D.png b/Project#06/figures/D.png new file mode 100644 index 0000000..b2dd664 Binary files /dev/null and b/Project#06/figures/D.png differ diff --git a/Project#06/figures/connected-triples.png b/Project#06/figures/connected-triples.png new file mode 100644 index 0000000..a8ca008 Binary files /dev/null and b/Project#06/figures/connected-triples.png differ diff --git a/Project#06/figures/disconnected-triples.png b/Project#06/figures/disconnected-triples.png new file mode 100644 index 0000000..6e421ef Binary files /dev/null and b/Project#06/figures/disconnected-triples.png differ diff --git a/Project#06/figures/t-correction.png b/Project#06/figures/t-correction.png new file mode 100644 index 0000000..1461dd7 Binary files /dev/null and b/Project#06/figures/t-correction.png differ diff --git a/Project#06/figures/three-index-permutation.png b/Project#06/figures/three-index-permutation.png new file mode 100644 index 0000000..e922a5d Binary files /dev/null and b/Project#06/figures/three-index-permutation.png differ diff --git a/Project#06/figures/total-energy.png b/Project#06/figures/total-energy.png new file mode 100644 index 0000000..3aab6c0 Binary files /dev/null and b/Project#06/figures/total-energy.png differ diff --git a/Project#06/input/ch4/STO-3G/enuc.dat b/Project#06/input/ch4/STO-3G/enuc.dat new file mode 100644 index 0000000..feb8199 --- /dev/null +++ b/Project#06/input/ch4/STO-3G/enuc.dat @@ -0,0 +1 @@ + 13.497304462036480 diff --git a/Project#06/input/ch4/STO-3G/eri.dat 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0.206879432071914 + 9 9 9 6 0.085276746780538 + 9 9 9 7 0.085276746780538 + 9 9 9 8 0.085276746780538 + 9 9 9 9 0.774605895725855 diff --git a/Project#06/input/ch4/STO-3G/geom.dat b/Project#06/input/ch4/STO-3G/geom.dat new file mode 100644 index 0000000..9c536a9 --- /dev/null +++ b/Project#06/input/ch4/STO-3G/geom.dat @@ -0,0 +1,6 @@ +5 +6.000000000000 -0.000000000000 0.000000000000 0.000000000000 +1.000000000000 1.183771681898 -1.183771681898 -1.183771681898 +1.000000000000 1.183771681898 1.183771681898 1.183771681898 +1.000000000000 -1.183771681898 1.183771681898 -1.183771681898 +1.000000000000 -1.183771681898 -1.183771681898 1.183771681898 diff --git a/Project#06/input/ch4/STO-3G/input.dat b/Project#06/input/ch4/STO-3G/input.dat new file mode 100644 index 0000000..6dfb483 --- /dev/null +++ b/Project#06/input/ch4/STO-3G/input.dat @@ -0,0 +1,43 @@ +psi: ( + label = "CH4 SCF Test Case" + wfn = scf + jobtype = oeprop + reference = rhf + basis = "STO-3G" + units = angstrom + subgroup = c1 + delete_tei = false + delete_oei = false + zmat = ( + C + H 1 r + H 1 r 2 td + H 1 r 2 td 3 d + H 1 r 2 td 4 d + ) + zvars = ( + r 1.085 + td 109.47122063449069136958 + d 120.0 + ) +) + +basis: ( + carbon: "STO-3G" = + ( (S ( 71.61683730 0.15432900) + ( 13.04509630 0.53532810) + ( 3.53051220 0.44463450) ) + (S ( 2.94124940 -0.09996720) + ( 0.68348310 0.39951280) + ( 0.22228990 0.70011550) ) + (P ( 2.94124940 0.15591630) + ( 0.68348310 0.60768370) + ( 0.22228990 0.39195740) ) + ) + + hydrogen: "STO-3G"= + ( (S ( 3.42525090 0.15432890) + ( 0.62391370 0.53532810) + ( 0.16885540 0.44463450) ) + ) +) diff --git a/Project#06/input/ch4/STO-3G/mux.dat b/Project#06/input/ch4/STO-3G/mux.dat new file mode 100644 index 0000000..9dca8dd --- /dev/null +++ b/Project#06/input/ch4/STO-3G/mux.dat @@ -0,0 +1,45 @@ + 1 1 0.000000000000000 + 2 1 0.000000000000000 + 2 2 0.000000000000000 + 3 1 -0.071855488532817 + 3 2 -0.838743574800986 + 3 3 0.000000000000000 + 4 1 -0.000000000000000 + 4 2 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100644 index 0000000..99b165d --- /dev/null +++ b/Project#06/input/h2o/DZ/geom.dat @@ -0,0 +1,4 @@ +3 +8.000000000000 0.000000000000 -0.143225816552 0.000000000000 +1.000000000000 1.638036840407 1.136548822547 -0.000000000000 +1.000000000000 -1.638036840407 1.136548822547 -0.000000000000 diff --git a/Project#06/input/h2o/DZ/input.dat b/Project#06/input/h2o/DZ/input.dat new file mode 100644 index 0000000..c9eeb62 --- /dev/null +++ b/Project#06/input/h2o/DZ/input.dat @@ -0,0 +1,12 @@ +psi: ( + label = "H2O SCF Test Case" + memory = (10.0 MB) + wfn = scf + jobtype = oeprop + delete_tei = false + delete_oei = false + reference = rhf + basis = "DZ" + subgroup = c1 + zmat = ((o) (h 1 1.1) (h 1 1.1 2 104.0)) +) diff --git a/Project#06/input/h2o/DZ/mux.dat b/Project#06/input/h2o/DZ/mux.dat new file mode 100644 index 0000000..900a852 --- /dev/null +++ b/Project#06/input/h2o/DZ/mux.dat @@ -0,0 +1,105 @@ + 1 1 -0.000000000000000 + 2 1 -0.000000000000000 + 2 2 -0.000000000000000 + 3 1 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b/Project#06/input/h2o/DZP/input.dat new file mode 100644 index 0000000..8cf45b4 --- /dev/null +++ b/Project#06/input/h2o/DZP/input.dat @@ -0,0 +1,13 @@ +psi: ( + label = "H2O SCF Test Case" + memory = (10.0 MB) + wfn = scf + jobtype = oeprop + delete_tei = false + delete_oei = false + reference = rhf + puream = false + basis = "DZP" + subgroup = c1 + zmat = ((o) (h 1 1.1) (h 1 1.1 2 104.0)) +) diff --git a/Project#06/input/h2o/DZP/mux.dat b/Project#06/input/h2o/DZP/mux.dat new file mode 100644 index 0000000..9eeb14c --- /dev/null +++ b/Project#06/input/h2o/DZP/mux.dat @@ -0,0 +1,351 @@ + 1 1 -0.000000000000000 + 2 1 -0.000000000000000 + 2 2 -0.000000000000000 + 3 1 -0.000000000000000 + 3 2 -0.000000000000000 + 3 3 -0.000000000000000 + 4 1 -0.000000000000000 + 4 2 -0.000000000000000 + 4 3 -0.000000000000000 + 4 4 -0.000000000000000 + 5 1 -0.065756994029223 + 5 2 -0.076390812514647 + 5 3 -0.495548317796719 + 5 4 -0.578524588047388 + 5 5 -0.000000000000000 + 6 1 0.000000000000000 + 6 2 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0.161483959338374 + 7 7 7 6 0.091353706761488 + 7 7 7 7 0.774605943919898 diff --git a/Project#06/input/h2o/STO-3G/geom.dat b/Project#06/input/h2o/STO-3G/geom.dat new file mode 100644 index 0000000..99b165d --- /dev/null +++ b/Project#06/input/h2o/STO-3G/geom.dat @@ -0,0 +1,4 @@ +3 +8.000000000000 0.000000000000 -0.143225816552 0.000000000000 +1.000000000000 1.638036840407 1.136548822547 -0.000000000000 +1.000000000000 -1.638036840407 1.136548822547 -0.000000000000 diff --git a/Project#06/input/h2o/STO-3G/input.dat b/Project#06/input/h2o/STO-3G/input.dat new file mode 100644 index 0000000..f8c5067 --- /dev/null +++ b/Project#06/input/h2o/STO-3G/input.dat @@ -0,0 +1,12 @@ +psi: ( + label = "H2O SCF Test Case" + memory = (10.0 MB) + wfn = scf + jobtype = oeprop + delete_tei = false + delete_oei = false + reference = rhf + basis = "STO-3G" + subgroup = c1 + zmat = ((o) (h 1 1.1) (h 1 1.1 2 104.0)) +) diff --git a/Project#06/input/h2o/STO-3G/mux.dat b/Project#06/input/h2o/STO-3G/mux.dat new file mode 100644 index 0000000..c5d92c5 --- /dev/null +++ b/Project#06/input/h2o/STO-3G/mux.dat @@ -0,0 +1,28 @@ + 1 1 -0.000000000000000 + 2 1 -0.000000000000000 + 2 2 -0.000000000000000 + 3 1 -0.050791929587912 + 3 2 -0.641172844324925 + 3 3 -0.000000000000000 + 4 1 0.000000000000000 + 4 2 0.000000000000000 + 4 3 0.000000000000000 + 4 4 -0.000000000000000 + 5 1 0.000000000000000 + 5 2 -0.000000000000000 + 5 3 -0.000000000000000 + 5 4 0.000000000000000 + 5 5 -0.000000000000000 + 6 1 -0.002229654052248 + 6 2 -0.262742503532769 + 6 3 -0.437630646182039 + 6 4 -0.147399448800486 + 6 5 0.000000000000000 + 6 6 -1.638036840407314 + 7 1 0.002229654052248 + 7 2 0.262742503532769 + 7 3 -0.437630646182039 + 7 4 0.147399448800486 + 7 5 -0.000000000000000 + 7 6 0.000000000000000 + 7 7 1.638036840407314 diff --git a/Project#06/input/h2o/STO-3G/muy.dat b/Project#06/input/h2o/STO-3G/muy.dat new file mode 100644 index 0000000..1efcbad --- /dev/null +++ b/Project#06/input/h2o/STO-3G/muy.dat @@ -0,0 +1,28 @@ + 1 1 0.143225816551918 + 2 1 0.033902114587819 + 2 2 0.143225816551918 + 3 1 -0.000000000000000 + 3 2 0.000000000000000 + 3 3 0.143225816551918 + 4 1 -0.050791929587912 + 4 2 -0.641172844324925 + 4 3 -0.000000000000000 + 4 4 0.143225816551918 + 5 1 -0.000000000000000 + 5 2 0.000000000000000 + 5 3 0.000000000000000 + 5 4 -0.000000000000000 + 5 5 0.143225816551918 + 6 1 0.003758676726377 + 6 2 -0.149971890752635 + 6 3 -0.108952162150434 + 6 4 -0.334090713364948 + 6 5 0.000000000000000 + 6 6 -1.136548822546795 + 7 1 0.003758676726377 + 7 2 -0.149971890752635 + 7 3 0.108952162150434 + 7 4 -0.334090713364948 + 7 5 0.000000000000000 + 7 6 -0.206578984758302 + 7 7 -1.136548822546794 diff --git a/Project#06/input/h2o/STO-3G/muz.dat b/Project#06/input/h2o/STO-3G/muz.dat new file mode 100644 index 0000000..35dfd9f --- /dev/null +++ b/Project#06/input/h2o/STO-3G/muz.dat @@ -0,0 +1,28 @@ + 1 1 -0.000000000000000 + 2 1 -0.000000000000000 + 2 2 -0.000000000000000 + 3 1 0.000000000000000 + 3 2 -0.000000000000000 + 3 3 -0.000000000000000 + 4 1 0.000000000000000 + 4 2 0.000000000000000 + 4 3 0.000000000000000 + 4 4 -0.000000000000000 + 5 1 -0.050791929587912 + 5 2 -0.641172844324925 + 5 3 -0.000000000000000 + 5 4 0.000000000000000 + 5 5 -0.000000000000000 + 6 1 -0.000000000000000 + 6 2 0.000000000000000 + 6 3 0.000000000000000 + 6 4 0.000000000000000 + 6 5 -0.248967955099984 + 6 6 0.000000000000000 + 7 1 -0.000000000000000 + 7 2 0.000000000000000 + 7 3 -0.000000000000000 + 7 4 0.000000000000000 + 7 5 -0.248967955099984 + 7 6 0.000000000000000 + 7 7 0.000000000000000 diff --git a/Project#06/input/h2o/STO-3G/s.dat b/Project#06/input/h2o/STO-3G/s.dat new file mode 100644 index 0000000..9b764da --- /dev/null +++ b/Project#06/input/h2o/STO-3G/s.dat @@ -0,0 +1,28 @@ + 1 1 1.000000000000000 + 2 1 0.236703936510848 + 2 2 1.000000000000000 + 3 1 -0.000000000000000 + 3 2 0.000000000000000 + 3 3 1.000000000000000 + 4 1 -0.000000000000000 + 4 2 -0.000000000000000 + 4 3 -0.000000000000000 + 4 4 1.000000000000000 + 5 1 -0.000000000000000 + 5 2 0.000000000000000 + 5 3 0.000000000000000 + 5 4 -0.000000000000000 + 5 5 1.000000000000000 + 6 1 0.038405599785757 + 6 2 0.386138840478249 + 6 3 0.268438243716457 + 6 4 0.209726941420375 + 6 5 -0.000000000000000 + 6 6 1.000000000000000 + 7 1 0.038405599785757 + 7 2 0.386138840478250 + 7 3 -0.268438243716457 + 7 4 0.209726941420375 + 7 5 -0.000000000000000 + 7 6 0.181759886298063 + 7 7 1.000000000000000 diff --git a/Project#06/input/h2o/STO-3G/t.dat b/Project#06/input/h2o/STO-3G/t.dat new file mode 100644 index 0000000..8927c33 --- /dev/null +++ b/Project#06/input/h2o/STO-3G/t.dat @@ -0,0 +1,28 @@ + 1 1 29.003199945539588 + 2 1 -0.168010939316492 + 2 2 0.808127954930347 + 3 1 0.000000000000000 + 3 2 0.000000000000000 + 3 3 2.528731198194763 + 4 1 0.000000000000000 + 4 2 -0.000000000000000 + 4 3 -0.000000000000000 + 4 4 2.528731198194763 + 5 1 -0.000000000000000 + 5 2 0.000000000000000 + 5 3 0.000000000000000 + 5 4 -0.000000000000000 + 5 5 2.528731198194763 + 6 1 -0.008416383544591 + 6 2 0.070517372751001 + 6 3 0.147090913304052 + 6 4 0.114920016354202 + 6 5 -0.000000000000000 + 6 6 0.760031883566609 + 7 1 -0.008416383544591 + 7 2 0.070517372751002 + 7 3 -0.147090913304052 + 7 4 0.114920016354202 + 7 5 -0.000000000000000 + 7 6 -0.003979868621841 + 7 7 0.760031883566609 diff --git a/Project#06/input/h2o/STO-3G/v.dat b/Project#06/input/h2o/STO-3G/v.dat new file mode 100644 index 0000000..d5b7411 --- /dev/null +++ b/Project#06/input/h2o/STO-3G/v.dat @@ -0,0 +1,28 @@ + 1 1 -61.580595358149914 + 2 1 -7.410821877330996 + 2 2 -10.009071226859687 + 3 1 0.000000000000000 + 3 2 0.000000000000000 + 3 3 -9.987550507419133 + 4 1 -0.014473835903318 + 4 2 -0.176890246723779 + 4 3 0.000000000000000 + 4 4 -9.944042952440439 + 5 1 0.000000000000000 + 5 2 0.000000000000000 + 5 3 -0.000000000000000 + 5 4 0.000000000000000 + 5 5 -9.875876065926128 + 6 1 -1.231685872788711 + 6 2 -2.977227202971528 + 6 3 -1.822241058022723 + 6 4 -1.471788274313766 + 6 5 0.000000000000000 + 6 6 -5.300202953839792 + 7 1 -1.231685872788712 + 7 2 -2.977227202971529 + 7 3 1.822241058022724 + 7 4 -1.471788274313766 + 7 5 0.000000000000001 + 7 6 -1.067166014696110 + 7 7 -5.300202953839793 diff --git a/Project#06/output/ch4/STO-3G/output.txt b/Project#06/output/ch4/STO-3G/output.txt new file mode 100644 index 0000000..8dc637b --- /dev/null +++ b/Project#06/output/ch4/STO-3G/output.txt @@ -0,0 +1,4 @@ +ESCF = -39.726850324347 +ECCSD = -0.078335022658 +E(T) = -0.000136278738 +ECCSD(T) = -39.805321625743 diff --git a/Project#06/output/h2o/DZ/output.txt b/Project#06/output/h2o/DZ/output.txt new file mode 100644 index 0000000..deba668 --- /dev/null +++ b/Project#06/output/h2o/DZ/output.txt @@ -0,0 +1,4 @@ +ESCF = -75.977878975377 +ECCSD = -0.159855618083 +E(T) = -0.001538065776 +ECCSD(T) = -76.139272659236 diff --git a/Project#06/output/h2o/DZP/output.txt b/Project#06/output/h2o/DZP/output.txt new file mode 100644 index 0000000..debb2e6 --- /dev/null +++ b/Project#06/output/h2o/DZP/output.txt @@ -0,0 +1,4 @@ +ESCF = -76.008821792901 +ECCSD = -0.231572131873 +E(T) = -0.003855328165 +ECCSD(T) = -76.244249252939 diff --git a/Project#06/output/h2o/STO-3G/output.txt b/Project#06/output/h2o/STO-3G/output.txt new file mode 100644 index 0000000..8ac0995 --- /dev/null +++ b/Project#06/output/h2o/STO-3G/output.txt @@ -0,0 +1,4 @@ +ESCF = -74.942079928192 +ECCSD = -0.070680088376 +E(T) = -0.000099877272 +ECCSD(T) = -75.012859893840 diff --git a/Project#08/README.md b/Project#08/README.md index 16e69b5..dc85873 100644 --- a/Project#08/README.md +++ b/Project#08/README.md @@ -1 +1,139 @@ # Project #8: DIIS extrapolation for the SCF procedure + +The convergence of the self-consistent field (SCF) algorithm presented in [Project #3](../Project%2303) is rather slow. +Even the STO-3G H2O example requires more than 20 iterations to converge the RMS density difference to a relatively loose threshold of 10-8. +One of the most effective methods for speeding up such iterative sequences is the +"Direct Inversion in the Iterative Subspace (DIIS)" approach, which was +[presented by Pulay](http://sirius.chem.vt.edu/wiki/lib/exe/fetch.php?media=crawdad:programming:sdoc8328.pdf) +in the 1980's. The essential idea of the DIIS approach is as follows: +if the current guess at the wave function/density matrix/Fock matrix is sufficiently close to the final (converged) result, +a new guess may be constructed as a simple linear combination of the previous few iterates, +where the coefficients of such an extrapolation are determined from Lagrangian minimization procedure. + +The purpose of this programming project is to implement the Pulay DIIS procedure within the SCF algorithm from +[Project #3](../Project%2303). + +## Working Equations + +Given a series of Fock matrices, Fi (expressed in the AO basis set), a new approximation to the converged solution may be written as + + + +by requiring that the corresponding extrapolated "error" matrix + + + +is approximately the zero matrix in a least-squares sense. The error matrix for each iteration is given by + + + +where Di is the AO-basis density matrix used to construct +Fi, and S is the AO-basis overlap matrix. Minimization of e' under the constraint that + + + +leads to the following system of linear equations for the ci: + + + +where lambda is a Lagrangian multiplier and the elements Bij are computed as dot products of error matrices: + + + +## Step #1: Compute the Error Matrix in Each Iteration + +Compute the error matrix for the current iteration using the matrix equation for ei given above. +Note that the density matrix you use must be the same one used to construct the corresponding Fock matrix. +If you print the error matrix in each iteration, you should be able to note that it gradually falls to zero as the SCF procedure converges. + +## Step #2: Build the B Matrix and Solve the Linear Equations + +After you have computed at least two error matrices, it is possible to begin the DIIS extrapolation procedure. +Compute the B matrix above for all of the current error matrices. +(Note that the matrix is symmetric, so one need only compute the lower triangle to get the entire matrix). + +Next, use a standard linear-equation solver (such as the DGESV function in the LAPACK library, +to which PSI4 has an interface named C_DGESV) to compute the ci coefficients. +(NB: If you use the LAPACK solver, or any LAPACK or BLAS function for that matter, you must use matrices allocated as contiguous memory, +as discussed in [Project #7](../Project%2307)). + +## Step #3: Compute the New Fock Matrix + +Build a new Fock matrix using the equation for F' above and continue with the SCF procedure as usual. +This implies that one must store all of the Fock matrices corresponding to each of the error matrices used in constructing the B matrix above. +Note: + + * Do **not** use the extrapolated Fock matrix to compute error matrices for subsequent DIIS steps. + * Keep only a relatively small number of error matrices; six to eight are reasonable for closed-shell SCF calculations. When the chosen number of error + matrices is exceeded delete the oldest error matrix. + +Once the procedure is complete and working correctly, you should notice a considerable reduction in the number of SCF cycles required to achieve convergence. +For example, for the STO-3G/H2O test case from [Project #3](../Project%2303), +the simple SCF algorithm converges to 10-12 in the density in 39 iterations: +``` + Iter E(elec) E(tot) Delta(E) RMS(D) + 00 -125.842077437699 -117.839710375888 + 01 -78.286583284740 -70.284216222929 47.555494152959 7.026491112304 + 02 -84.048316253435 -76.045949191625 -5.761732968695 1.586429080972 + 03 -82.716965960855 -74.714598899044 1.331350292581 0.329292871345 + 04 -82.987140757002 -74.984773695191 -0.270174796147 0.120465253222 + 05 -82.938133187513 -74.935766125703 0.049007569488 0.043060496803 + 06 -82.946271078699 -74.943904016889 -0.008137891186 0.020309423061 + 07 -82.944486784914 -74.942119723104 0.001784293785 0.009137578496 + 08 -82.944617252243 -74.942250190433 -0.000130467329 0.004460301971 + 09 -82.944503500703 -74.942136438892 0.000113751541 0.002127028935 + 10 -82.944478930626 -74.942111868815 0.000024570077 0.001026790950 + 11 -82.944461627685 -74.942094565874 0.000017302941 0.000494443064 + 12 -82.944454198375 -74.942087136565 0.000007429310 0.000238548591 + 13 -82.944450445051 -74.942083383241 0.000003753324 0.000115056300 + 14 -82.944448661686 -74.942081599876 0.000001783365 0.000055511004 + 15 -82.944447795931 -74.942080734120 0.000000865755 0.000026782106 + 16 -82.944447379017 -74.942080317206 0.000000416914 0.000012922161 + 17 -82.944447177685 -74.942080115875 0.000000201331 0.000006234890 + 18 -82.944447080565 -74.942080018755 0.000000097120 0.000003008344 + 19 -82.944447033699 -74.942079971889 0.000000046867 0.000001451536 + 20 -82.944447011086 -74.942079949276 0.000000022613 0.000000700372 + 21 -82.944447000175 -74.942079938365 0.000000010911 0.000000337933 + 22 -82.944446994911 -74.942079933100 0.000000005265 0.000000163055 + 23 -82.944446992371 -74.942079930560 0.000000002540 0.000000078675 + 24 -82.944446991145 -74.942079929335 0.000000001226 0.000000037961 + 25 -82.944446990554 -74.942079928743 0.000000000591 0.000000018316 + 26 -82.944446990268 -74.942079928458 0.000000000285 0.000000008838 + 27 -82.944446990131 -74.942079928320 0.000000000138 0.000000004264 + 28 -82.944446990064 -74.942079928254 0.000000000066 0.000000002058 + 29 -82.944446990032 -74.942079928222 0.000000000032 0.000000000993 + 30 -82.944446990017 -74.942079928206 0.000000000016 0.000000000479 + 31 -82.944446990009 -74.942079928199 0.000000000007 0.000000000231 + 32 -82.944446990005 -74.942079928195 0.000000000004 0.000000000112 + 33 -82.944446990004 -74.942079928193 0.000000000002 0.000000000054 + 34 -82.944446990003 -74.942079928193 0.000000000001 0.000000000026 + 35 -82.944446990002 -74.942079928192 0.000000000000 0.000000000013 + 36 -82.944446990002 -74.942079928192 0.000000000000 0.000000000006 + 37 -82.944446990002 -74.942079928192 0.000000000000 0.000000000003 + 38 -82.944446990002 -74.942079928192 0.000000000000 0.000000000001 + 39 -82.944446990002 -74.942079928192 0.000000000000 0.000000000001 +``` + +With DIIS extrapolation using six error matrices, this is reduced to only ten iterations: + +``` + Iter E(elec) E(tot) Delta(E) RMS(D) + 00 -125.842077437699 -117.839710375888 + 01 -78.286583284740 -70.284216222929 47.555494152959 7.026491112304 + 02 -82.579039780737 -74.576672718926 -4.292456495997 1.366619501600 + 03 -83.108076865885 -75.105709804074 -0.529037085148 0.349635242477 + 04 -82.957022995474 -74.954655933663 0.151053870411 0.082112373912 + 05 -82.941311458592 -74.938944396782 0.015711536881 0.045048744784 + 06 -82.944472996531 -74.942105934721 -0.003161537939 0.001798803069 + 07 -82.944447027029 -74.942079965219 0.000025969502 0.000003764196 + 08 -82.944446990675 -74.942079928865 0.000000036354 0.000000202704 + 09 -82.944446990002 -74.942079928192 0.000000000673 0.000000001127 + 10 -82.944446990002 -74.942079928192 0.000000000000 0.000000000000 +``` + +## References + + * P. Pulay, "Convergence Acceleration of Iterative Sequences. The Case of the SCF Iteration", *Chem. Phys. Lett.* **73**, 393-398 (1980). + * P. Pulay, "Improved SCF Convergence Acceleration", *J. Comp. Chem.* **3**, 556-560 (1982). + * T. P. Hamilton and P. Pulay, "Direct Inversion in the Iterative Subspace (DIIS) Optimization of Open-Shell, Excited-State, + and Small Multiconfiguration SCF Wave functions", *J. Chem. Phys.* **84**, 5728-5734 (1986). diff --git a/Project#08/figures/Bij.png b/Project#08/figures/Bij.png new file mode 100644 index 0000000..e8e0a7b Binary files /dev/null and b/Project#08/figures/Bij.png differ diff --git a/Project#08/figures/constraint.png b/Project#08/figures/constraint.png new file mode 100644 index 0000000..72230eb Binary files /dev/null and b/Project#08/figures/constraint.png differ diff --git a/Project#08/figures/error-matrix.png b/Project#08/figures/error-matrix.png new file mode 100644 index 0000000..3d70a7b Binary files /dev/null and b/Project#08/figures/error-matrix.png differ diff --git a/Project#08/figures/iter-error-matrix.png b/Project#08/figures/iter-error-matrix.png new file mode 100644 index 0000000..f29a1df Binary files /dev/null and b/Project#08/figures/iter-error-matrix.png differ diff --git a/Project#08/figures/new-approx-fock.png b/Project#08/figures/new-approx-fock.png new file mode 100644 index 0000000..abd7c12 Binary files /dev/null and b/Project#08/figures/new-approx-fock.png differ diff --git a/Project#08/figures/sys-lin-eqn-ci.png b/Project#08/figures/sys-lin-eqn-ci.png new file mode 100644 index 0000000..9bdf555 Binary files /dev/null and b/Project#08/figures/sys-lin-eqn-ci.png differ diff --git a/Project#09/README.md b/Project#09/README.md index a90efde..1a01dbd 100644 --- a/Project#09/README.md +++ b/Project#09/README.md @@ -1 +1,200 @@ # Project #9: Using symmetry in the SCF procedure + +The use of point-group symmetry in quantum chemical calculations can lead to exceptionally efficient programs, +both in terms of their memory/disk usage and their computing times. If a molecule has even one element of symmetry, +for example, this can reduce the number of wave function parameters that must be stored by up to a factor of two (the order of the point group) +and the computing effort by up to a factor of four (the square of the order of the point group). +Most quantum chemical programs can take advantage of Abelian symmetry -- more accurately, +D2h and its subgroups -- which means that higher symmetry structures can yield up to a factor of 64 reduction in the computational costs. + +The purpose of this project is to take advantage of basic point-group symmetry in an SCF calculation. +While the most efficient programs will store only the symmetry-allowed sets of two-electron integrals, +for the purposes of this project we'll deal only with the one-electron (two-index) components. + +## Background + +The vanishing integral rule of point-group theory may be stated as follows for Abelian groups: + + + +where ΓX denotes the irreducible representation (irrep) of entity X. +That is, unless the direct product of the irreps of the functions or operators in the integrand contains the totally symmetric irrep, the integral must be zero. + +The vanishing integral rule of group theory may be readily applied to the various integrals and wave-function parameters in the SCF procedure +if the AO-basis functions over which the they are evaluated have been properly symmetrized +[i.e. used to form symmetry-adapted linear combinations, normally referred to as symmetry orbitals (SOs)]. + +For example, consider the H2O test case with the STO-3G basis set as given in [Project #3](../Project%2303). The AO +([contracted Gaussian](http://sirius.chem.vt.edu/wiki/lib/exe/fetch.php?media=basis_sets.pdf)) basis functions +on the oxygen atom consist of 1s, 2s, 2px, 2py, and 2pz orbitals, +which those for each hydrogen atom consist of only the 1s, giving a total of seven AOs. +If we take oxygen to be the first atom and ignore the C2v point group symmetry of the molecule, +the resulting overlap integral matrix looks like: + +``` + 1 2 3 4 5 6 7 + + 1 1.0000000 0.2367039 -0.0000000 -0.0000000 -0.0000000 0.0384056 0.0384056 + 2 0.2367039 1.0000000 0.0000000 -0.0000000 0.0000000 0.3861388 0.3861388 + 3 -0.0000000 0.0000000 1.0000000 -0.0000000 0.0000000 0.2684382 -0.2684382 + 4 -0.0000000 -0.0000000 -0.0000000 1.0000000 -0.0000000 0.2097269 0.2097269 + 5 -0.0000000 0.0000000 0.0000000 -0.0000000 1.0000000 -0.0000000 -0.0000000 + 6 0.0384056 0.3861388 0.2684382 0.2097269 -0.0000000 1.0000000 0.1817599 + 7 0.0384056 0.3861388 -0.2684382 0.2097269 -0.0000000 0.1817599 1.0000000 +``` +The first five row/column indices correspond to the basis functions on the oxygen (in the order listed above), +while rows/columns six and seven correspond to the basis functions on each hydrogen. +Thus, the 1-2 element is the overlap integral between the 1s and 2s orbitals on the oxygen, +while element 3-7 is the overlap integral between the oxygen 2px orbital and the second hydrogen 1s orbital. + +Points to note about this matrix: + - The 1s and 2s orbitals on oxygen are not orthogonal to one another, but both are orthogonal to all three p-type orbitals. + This occurs because, in Cartesian Gaussian basis sets, + orthogonality is generally obtained only between functions of different angular momenta on the same atomic center. + - The 1s orbitals on the hydrogens have the same overlap integral (to within a sign) + with all the orbitals on the oxygen because they are symmetry equivalent. + However, the 1s orbitals alone do not transform as irreps of the C2v point group. + - The hydrogen 1s orbitals are orthogonal to the 2pz orbital on the oxygen (cf. elements 5-6 and 5-7). + This is because the water molecule was arbitrarily oriented in the xy-plane to compute the above integrals; + thus the 2pz orbital is perpendicular to the molecular plane containing the hydrogen 1s orbitals. + +What happens if we turn on symmetry, i.e. take linear combinations of the AO to obtain SOs? +If we orient the molecule oriented in the yz-plane, so that the z-axis corresponds to the C2 rotation axis, +we find that the AOs transform as the following irreps: + +| SO | Irrep | +|------|--------| +| O 1s | A1 | +| O 2s | A1 | +| O 2px | B1 | +| O 2py | B2 | +| O 2pz | A1 | +| H1 1s + H2 1s | A1 | +| H1 1s - H2 1s | B2 | + +Thus, after symmetrization, there are four A1 SOs, one B1 SO, and two B2 SOs. +(The STO-3G basis set contains no A2 orbitals. One must include at least d-type functions on the oxygen and/or +p-type functions on the hydrogens to obtain A2 orbitals.) Note that a normalization factor of 1/sqrt(2) should be included for the H 1s SOs above. + +In the SO basis, the overlap integral matrix becomes: +``` + 1 2 3 4 5 6 7 + + 1 1.0000000 0.2367039 -0.0000000 0.0543137 0.0000000 0.0000000 0.0000000 + 2 0.2367039 1.0000000 -0.0000000 0.5460828 0.0000000 0.0000000 0.0000000 + 3 -0.0000000 -0.0000000 1.0000000 0.2965987 0.0000000 0.0000000 0.0000000 + 4 0.0543137 0.5460828 0.2965987 1.1817599 0.0000000 0.0000000 0.0000000 + 5 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 0.0000000 0.0000000 + 6 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 0.3796290 + 7 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.3796290 0.8182401 +``` + +Points to note about this matrix: + - The matrix now has a block-diagonal structure, with 4x4, 1x1, and 2x2 sub-matrices, corresponding to the A1, B1, and B2 irreps, + respectively. All off-diagonal blocks correspond to overlaps between SOs of different irreps, which must be zero according to the vanishing integral rule. + - There is only one B1 SO (the O 2px orbital), and it is normalized. + - The oxygen 1s and 2s orbitals are still orthogonal to the oxygen 2pz because they are functions of different angular momentum on the same atomic center. + - The same block-diagonal structure will appear for the kinetic-energy (T), one-electron potential-energy (V), and core Hamiltonian (H) integrals. + +## Obtaining Symmetry Information from PSI + +The PSI checkpoint file contains a great deal of useful symmetry information. To convert your SCF program to make use of symmetry, two key pieces of information are: + * The number of irreps in the molecular point group. Use the `chkpt_rd_nirreps()` function to retrieve this integer. + * The number of SOs per irrep, available as an integer array from the `chkpt_rd_sopi()` function. + +## Storing One-Electron Integrals with Symmetry + +The block-diagonal structure above implies that one need only store and use the sub-matrices of the integrals rather than the full matrix. +One way of doing this is to store the one-electron integrals as an array of smaller matrices, +the size of which is dictated by the number of SOs per irrep. For example, here's a code snippet that will extract the one-electron integrals +from the appropriate file (as was done in [Project #7](../Project%2307) ), +but stores them in an array of matrices: + +```c++ + int ntri, nirreps; + double *scratch; + double ***S; + ... + ntri = nso*(nso+1)/2; + scratch = init_array(ntri); + ... + symm_offset = init_int_array(nirreps); + for(h=1; h < nirreps; h++) symm_offset[h] = symm_offset[h-1] + sopi[h-1]; + ... + /* overlap integrals */ + S = (double ***) malloc(nirreps*sizeof(double **)); + stat = iwl_rdone(PSIF_OEI, PSIF_SO_S, scratch, ntri, 0, 0, outfile); + for(h=0; h < nirreps; h++) { + S[h] = block_matrix(sopi[h], sopi[h]); + for(i=0; i < sopi[h]; i++) + for(j=0; j <= i; j++) { + ij = INDEX(i+symm_offset[h],j+symm_offset[h]); + S[h][i][j] = S[h][j][i] = scratch[ij]; + } + } +``` + +Notice how S is now a `double ***` -- i.e. an array of matrices. This code uses the same `INDEX()` function found in +[Project #3](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2303), +and the sopi array is the integer array of SOs per irrep obtained using the `chkpt_rd_sopi()` function. +The `symm_offset` array is useful for converting between relative orbital indices and absolute orbital indices. +(For example, orbital 0 in the B2 irrep block corresponds to orbital 5 +in the full list of orbitals; the first number is the relative index, the second is the absolute index.) + +## Multiplication of Matrices with Symmetry + +If we store the integral, MO coefficient, density, and Fock matrices in the block-diagonal structure described above, +we may compute matrix products of these quantities separately for each diagonal block. For example, the matrix product may be written as: + + + +where *h* denotes a particular irrep of the point group and Ch denotes the *h*-th irrep subblock of the full matrix C. +(The notation of the large plus with a circle around it indicates a direct sum.) + +## Occupied Orbitals and the Density Matrix + +The calculation of the density matrix requires information about the number of occupied orbitals: + + + +In a calculation without symmetry, one need only know the number of electrons (equivalently, the atomic numbers of the atoms and the overall molecular charge) +to evaluate this expression. However, if the density and MO coefficient matrices are stored in symmetry-blocked form, +as above, one needs to know the number of occupied MOs in each irrep. + +For the case of the C2v water molecule, which has two σ O-H bonds, two oxygen lone pairs, +and one oxygen core orbital, the orbital occupations are not difficult to determine, given the above information about the number of SOs in each irrep. +Since the MOs are constructed as linear combinations of the SOs, and only SOs of the same irrep can combine, we may rationalize the occupied orbitals of +H2O as follows: + +| Occupied MO | Irrep | Description | +|---------------|----------|-------------| +| O 1s | A1 | Oxygen Core | +| O 2s + (H1 1s + H2 1s) | A1 | Symmetric Combination of O-H σ Bonds | +| O 2pz | A1 | In-Plane Oxygen Lone Pair | +| O 2px | B1 | Out-of-Plane Oxygen Lone Pair | +| O 2py + (H1 1s - H2 1s) | B2 | Antisymmetric Combination of O-H σ Bonds | + +Thus, for the water molecule, there are 3 A1, 1 B1, and 1 B2 occupied orbitals. + +Determining the occupations automatically is sometimes a difficult task, especially for molecules with unusual bonding patterns. +Many SCF programs will simply take the core Hamiltonian matrix (often used as the initial guess for the Fock matrix), +diagonalize it (in the othogonal AO basis) in each irrep block, and identify the lowest eigenvalues in each irrep as occupied. +However, this approach often fails for many molecules (especially those with open shells) because of near-degeneracies +that may not be adequately described by the simple core Hamiltonian. Thus, some programs will make use of more +sophisticated guesses at the Fock matrix, e.g. Hueckel orbitals or other (semi)empirical forms. + +## Building the Fock Matrix + +The only portion of the SCF procedure involving two-electron integrals is the Fock-matrix build: + + + +where the notation used in [Project #3](../Project%2303) is retained above. +If the Fock matrix and density matrix are stored in a symmetry-blocked manner similar to the overlap matrix above, +then one may limit the corresponding loops only to the symmetry-allowed combinations, e.g. the irreps of μ and +ν must match for Fμν to be non-zero and the irreps of λ +and σ must match for Dλσ to be non-zero. +Note, however, that, because of the symmetries in the two-electron integrals, +the irrep of λ and σ do not necessarily have to match that of μ and ν. + + * [Hint](./hints/hint1.md): Fock-Build Code diff --git a/Project#09/figures/density-matrix.png b/Project#09/figures/density-matrix.png new file mode 100644 index 0000000..7a81c07 Binary files /dev/null and b/Project#09/figures/density-matrix.png differ diff --git a/Project#09/figures/fock-build.png b/Project#09/figures/fock-build.png new file mode 100644 index 0000000..90eb475 Binary files /dev/null and b/Project#09/figures/fock-build.png differ diff --git a/Project#09/figures/matrix-product.png b/Project#09/figures/matrix-product.png new file mode 100644 index 0000000..aaa4ff7 Binary files /dev/null and b/Project#09/figures/matrix-product.png differ diff --git a/Project#09/figures/point-group-rule.png b/Project#09/figures/point-group-rule.png new file mode 100644 index 0000000..a4ae26b Binary files /dev/null and b/Project#09/figures/point-group-rule.png differ diff --git a/Project#09/hints/hint1.md b/Project#09/hints/hint1.md new file mode 100644 index 0000000..670bf7d --- /dev/null +++ b/Project#09/hints/hint1.md @@ -0,0 +1,28 @@ +```c++ + for(h=0; h < nirreps; h++) { + for(i=0; i < sopi[h]; i++) { + I = symm_offset[h] + i; + for(j=0; j < sopi[h]; j++) { + J = symm_offset[h] + j; + F[h][i][j] = H[h][i][j]; + + for(g=0; g < nirreps; g++) { + for(k=0; k < sopi[g]; k++) { + K = symm_offset[g] + k; + for(l=0; l < sopi[g]; l++) { + L = symm_offset[g] + l; + + ij = INDEX(I,J); kl = INDEX(K,L); + ijkl = INDEX(ij,kl); + ik = INDEX(I,K); jl = INDEX(J,L); + ikjl = INDEX(ik,jl); + + F[h][i][j] += D[g][k][l] * (2.0 * TEI[ijkl] - TEI[ikjl]); + } + } + + } + } + } + } +``` diff --git a/Project#10/README.md b/Project#10/README.md index 1ff3479..48e85fe 100644 --- a/Project#10/README.md +++ b/Project#10/README.md @@ -1 +1,119 @@ # Project #10: DIIS extrapolation for solving the CC amplitude equations +In an earlier project, we examined how DIIS ("direct inversion in the iterative +subspace") can reduce substantially the number of iterations required to converge the +self-consistent field. In this project, we examine how DIIS can similarly speed +convergence in the CC amplitude equations. This approach was first used by Scuseria, +Lee, and Schaefer in 1986 ["Accelerating the conference of the coupled-cluster +approach. The use of the DIIS method", *Chem. Phys. Lett.* **130**, 236 (1986)]. + +## Error Vectors +The DIIS approach requires a well-defined "error vector", a quantity that approaches +zero as the equations converge. In the SCF procedure, we use the atomic-orbital +representation of the occupied-virtual block of the Fock matrix. In the CC method, we +could choose the difference between successive sets of cluster amplitudes: + + + +where Ti represents a vector containing all the cluster amplitudes for the *i*-th iteration. + +There are three important points to note about this choice of error vector: + * Defining the error vectors as differences between successive sets of amplitudes + implies that one cannot begin the DIIS extrapolation until at least three + iterations are complete. + * Just as in the SCF DIIS procedure, error vectors should only be computed using + non-extrapolated sets of cluster amplitudes. + * The set of cluster amplitudes can require substantial memory for larger + molecules; hence, the choice of the number of error vectors used in the CC DIIS + procedure is potentially dependent on the available storage (disk and memory). + +## Extrapolation +Given the above definition of the error vectors, the set of linear equations to be solved is the same as that for the SCF DIIS procedure: + + + +where λ is a Lagrangian multiplier and the elements Bij are computed as dot products of error matrices: + + + +A new set of cluster amplitudes is then obtained as a linear combinations of older amplitudes using the coefficients from the linear equations above: + + + +Again: The extrapolated cluster amplitudes should be used only in the CC amplitude equations, not to compute subsequent error vectors. + +## Results +Once the procedure is working, you should observe a considerable reduction in the +number of iterations required to converge the CC amplitude equations to a given +tolerance. For example, without DIIS extrapolation, the STO-3G H2O test +case from [Project #5](../Project%2305) converges in 38 iterations to a +precision of 10-12: + +``` +iter = 1 Ecc = -0.062758205955 +iter = 2 Ecc = -0.067396582597 +iter = 3 Ecc = -0.069224536410 +iter = 4 Ecc = -0.070007757556 +iter = 5 Ecc = -0.070360041902 +iter = 6 Ecc = -0.070523820218 +iter = 7 Ecc = -0.070602032617 +iter = 8 Ecc = -0.070640293027 +iter = 9 Ecc = -0.070659428829 +iter = 10 Ecc = -0.070669194426 +iter = 11 Ecc = -0.070674268048 +iter = 12 Ecc = -0.070676944995 +iter = 13 Ecc = -0.070678375859 +iter = 14 Ecc = -0.070679148887 +iter = 15 Ecc = -0.070679570139 +iter = 16 Ecc = -0.070679801279 +iter = 17 Ecc = -0.070679928796 +iter = 18 Ecc = -0.070679999445 +iter = 19 Ecc = -0.070680038717 +iter = 20 Ecc = -0.070680060604 +iter = 21 Ecc = -0.070680072825 +iter = 22 Ecc = -0.070680079661 +iter = 23 Ecc = -0.070680083488 +iter = 24 Ecc = -0.070680085633 +iter = 25 Ecc = -0.070680086836 +iter = 26 Ecc = -0.070680087511 +iter = 27 Ecc = -0.070680087891 +iter = 28 Ecc = -0.070680088103 +iter = 29 Ecc = -0.070680088223 +iter = 30 Ecc = -0.070680088290 +iter = 31 Ecc = -0.070680088328 +iter = 32 Ecc = -0.070680088349 +iter = 33 Ecc = -0.070680088361 +iter = 34 Ecc = -0.070680088368 +iter = 35 Ecc = -0.070680088372 +iter = 36 Ecc = -0.070680088374 +iter = 37 Ecc = -0.070680088375 +iter = 38 Ecc = -0.070680088376 +``` + +The DIIS extrapolation with eight error vectors reduces the number of iterations to just 16: + +``` +iter = 1 Ecc = -0.062758205955 +iter = 2 Ecc = -0.067396582597 +iter = 3 Ecc = -0.070325967097 +iter = 4 Ecc = -0.070642541851 +iter = 5 Ecc = -0.070681441999 +iter = 6 Ecc = -0.070679216733 +iter = 7 Ecc = -0.070680252965 +iter = 8 Ecc = -0.070680084062 +iter = 9 Ecc = -0.070680084577 +iter = 10 Ecc = -0.070680089084 +iter = 11 Ecc = -0.070680088015 +iter = 12 Ecc = -0.070680088239 +iter = 13 Ecc = -0.070680088359 +iter = 14 Ecc = -0.070680088381 +iter = 15 Ecc = -0.070680088377 +iter = 16 Ecc = -0.070680088376 +``` + + +## Additional Reading + * G.E. Scuseria, T.J. Lee, and H.F. Schaefer, "Accelerating the conference of the + coupled-cluster approach. The use of the DIIS method", *Chem. Phys. Lett.* + **130**, 236 (1986). + * G.D. Purvis and R.J. Bartlett, "The reduced linear equation method in coupled + cluster theory", *J. Chem. Phys.* **75**, 1284 (1981). diff --git a/Project#10/figures/Bij.png b/Project#10/figures/Bij.png new file mode 100644 index 0000000..e8e0a7b Binary files /dev/null and b/Project#10/figures/Bij.png differ diff --git a/Project#10/figures/error-vector.png b/Project#10/figures/error-vector.png new file mode 100644 index 0000000..2c54b20 Binary files /dev/null and b/Project#10/figures/error-vector.png differ diff --git a/Project#10/figures/new-t-amps.png b/Project#10/figures/new-t-amps.png new file mode 100644 index 0000000..8782089 Binary files /dev/null and b/Project#10/figures/new-t-amps.png differ diff --git a/Project#10/figures/sys-lin-eqn-ci.png b/Project#10/figures/sys-lin-eqn-ci.png new file mode 100644 index 0000000..9bdf555 Binary files /dev/null and b/Project#10/figures/sys-lin-eqn-ci.png differ diff --git a/Project#11/README.md b/Project#11/README.md index 658d3b1..944698a 100644 --- a/Project#11/README.md +++ b/Project#11/README.md @@ -1 +1,147 @@ # Project #11: An “out of core” SCF procedure +By far the greatest memory hog in the SCF procedure is the storage of the +two-electron repulsion integrals. In earlier SCF programming projects, we have +chosen to read these integrals from a file on disk and store them in a +one-dimensional array. However, even if we take full advantage of the inherent +eight-fold permutational symmetry of the Mulliken-notation integrals, we +encounter a memory bottleneck even for relatively small basis sets. The table +below summarizes the required size of the one-dimensional integral array for +different basis sets for a water molecule (ignoring spatial symmetry): + +| Basis Set | # Basis Functions | Memory (MB) | +|-------------|---------------------|---------------| +| STO-3G | 7 | 0.003248 | +| cc-pVDZ | 24 | 0.3612 | +| aug-cc-pVDZ | 41 | 2.969 | +| cc-pVTZ | 58 | 11.72 | +| aug-cc-pVTZ | 92 | 73.22 | +| cc-pVQZ | 115 | 118.0 | +| aug-cc-pVQZ | 172 | 885.5 | +| cc-pV5Z | 201 | 1649 | +| aug-cc-pV5Z | 287 | 6832 | + +Thus, even a relatively small number of basis functions outstrips the typical +physical memory available on workstations or supercomputer nodes. + +The purpose of this project is to consider and implement an "out-of-core" SCF +algorithm, that is, an approach that minimizes the core-memory requirements of +the program by reading the two-electron repulsion integrals from disk in +batches when only they are needed (An alternative approach is the so-called +"direct" SCF, in which the two-electron integrals are re-computed in each SCF +iteration rather than stored on disk) + +## The Fock Matrix Build + +At the heart of the SCF procedure is the expensive Fock-matrix term: + + + +where we use *i*, *j*, *k*, and *l* to denote AO-basis indices. As described +in [Project #3](../Project%2303), a simple algorithm for evaluating this matrix is: + +```cpp +for(i=0; i < nao; i++) + for(j=0; j < nao; j++) { + F[i][j] = H[i][j]; + for(k=0; k < nao; k++) + for(l=0; l < nao; l++) { + ij = INDEX(i,j); + kl = INDEX(k,l); + ijkl = INDEX(ij,kl); + ik = INDEX(i,k); + jl = INDEX(j,l); + ikjl = INDEX(ik,jl); + + F[i][j] += D[k][l] * (2.0 * TEI[ijkl] - TEI[ikjl]); + } + } +``` + +This algorithm hinges on the fact that all the two-electron integrals are +immediately available in the TEI array (which takes advantage of permutational +symmetry). In [Project #7](../Project%2307) you made use of the following code, +which reads the integrals into the TEI array in batches (sometimes referred to +in PSI as "buffers"): + +```cpp + iwl_buf_init(&InBuf, PSIF_SO_TEI, 1e-14, 1, 0); + do { + iwl_buf_fetch(&InBuf); + lblptr = InBuf.labels; + valptr = InBuf.values; + lastbuf = InBuf.lastbuf; + for(idx=4*InBuf.idx; InBuf.idx < InBuf.inbuf; InBuf.idx++) { + i = abs((int) lblptr[idx++]); + j = (int) lblptr[idx++]; + k = (int) lblptr[idx++]; + l = (int) lblptr[idx++]; + ij = INDEX(i,j); + kl = INDEX(k,l); + ijkl = INDEX(ij,kl); + TEI[ijkl] = (double) valptr[InBuf.idx]; + } + } while (!lastbuf); + iwl_buf_close(&InBuf, 1); +``` + +The basic idea behind an out-of-core Fock-build code is to read the +two-electron integrals in batches and make use of each batch immediately before +moving to the next batch. Thus, the above code would be moved into the SCF +iterative procedure and modified appropriately to compute the contribution of +each individual integral to the Fock matrix: + +```cpp + iwl_buf_init(&InBuf, PSIF_SO_TEI, 1e-14, 1, 0); + do { + iwl_buf_fetch(&InBuf); + lblptr = InBuf.labels; + valptr = InBuf.values; + lastbuf = InBuf.lastbuf; + for(idx=4*InBuf.idx; InBuf.idx < InBuf.inbuf; InBuf.idx++) { + i = abs((int) lblptr[idx++]); + j = (int) lblptr[idx++]; + k = (int) lblptr[idx++]; + l = (int) lblptr[idx++]; + + integral = (double) valptr[InBuf.idx]; + + /* Compute the contribution of this integral to the Fock matrix */ + + } + } while (!lastbuf); + iwl_buf_close(&InBuf, 1); +``` + +Thus a given integral, (ij|kl), would contribute to at least two Fock matrix elements as: + + + +and + + + +## Handling Permutational Symmetry + +The most difficult aspect of the out-of-core algorithm is the fact that file contains only the permutationally unique integrals, +*(ij|kl)*, such that: + + + +where + + + +Thus, when determining the contribution of a given integral to various elements +of the Fock matrix, one must consider all possible unique permutations of the +indices, *i*, *j*, *k*, and *l*. Note, however, that coincidences among the +indices can limit the number of possibilities. For example, if one encountered +the integral *(22|11)*, it would contribute to a total of four Fock +matrix elements, viz. + + + +All such cases must be included in the algorithm to obtain a correct Fock matrix. + +## Additional Reading + * J. Almlof, K. Faegri, and K. Korsell, "Principles for a Direct SCF Approach to LCAO-MO *Ab Initio* Calculations," *J. Comp. Chem.* **3**, 385-399 (1982). + diff --git a/Project#11/figures/compound-indices.png b/Project#11/figures/compound-indices.png new file mode 100644 index 0000000..714c307 Binary files /dev/null and b/Project#11/figures/compound-indices.png differ diff --git a/Project#11/figures/fock-contribution-1.png b/Project#11/figures/fock-contribution-1.png new file mode 100644 index 0000000..4e7a2a2 Binary files /dev/null and b/Project#11/figures/fock-contribution-1.png differ diff --git a/Project#11/figures/fock-contribution-2.png b/Project#11/figures/fock-contribution-2.png new file mode 100644 index 0000000..5c69e70 Binary files /dev/null and b/Project#11/figures/fock-contribution-2.png differ diff --git a/Project#11/figures/fock-contribution-3.png b/Project#11/figures/fock-contribution-3.png new file mode 100644 index 0000000..3234c8a Binary files /dev/null and b/Project#11/figures/fock-contribution-3.png differ diff --git a/Project#11/figures/fock-matrix.png b/Project#11/figures/fock-matrix.png new file mode 100644 index 0000000..82afe61 Binary files /dev/null and b/Project#11/figures/fock-matrix.png differ diff --git a/Project#11/figures/index-restrictions.png b/Project#11/figures/index-restrictions.png new file mode 100644 index 0000000..d9cfed7 Binary files /dev/null and b/Project#11/figures/index-restrictions.png differ diff --git a/Project#12/README.md b/Project#12/README.md index f078c13..c0e76cd 100644 --- a/Project#12/README.md +++ b/Project#12/README.md @@ -1 +1,221 @@ # Project #12: Excited Electronic States: CIS and TDHF/RPA + +The simplest *ab initio* methods for describing excited electronic states are +based on Hartree-Fock theory, namely configuration interaction singles (CIS) +and time-dependent Hartree-Fock (TDHF), which is also known as the random-phase +approximation (RPA). The purpose of this project is to develop simple +implementations of these two methods and to understand the basic differences +between them. This project assumes you have completed at least the +[CCSD programming project](../Project%2305). + +You can read more about these methods in +[J.B. Foresman, M. Head-Gordon, J.A. Pople, and M.J. Frisch, J. Phys. Chem. 96, 135-141 (1992)](http://pubs.acs.org/doi/pdf/10.1021/j100180a030) (CIS) +and [P. Jørgensen and J. Simons, "Second-Quantization Based Methods in Quantum Chemistry", Academic Press, New York, 1981.](http://addison.vt.edu/record=b1305858~S1) (RPA) + +## Configuration Interaction Singles (CIS) + +The fundamental idea behind CIS is the representation of the excited-state wave +functions as linear combinations of singly excited determinants relative to the +Hartree-Fock reference wave function, *viz.* + + + +where *m* identifies the various excited states, and we will use *i* and *j* +(*a* and *b*) to denote occupied (unoccupied) spin-orbitals. Inserting this +into the Schrödinger equation and left-projecting onto a +particular singly excited determinant gives + + + +If we recognize that we have one of these equations for every combination of +*i* and *a* spin-orbitals, then this equation may be viewed as a matrix +eigenvalue problem: + + + +To solve this equation, we need an expression for the matrix elements in terms +of things we already know, i.e. Fock matrix elements and two-electron +integrals. This can be done using either algebraic or diagrammatic techniques +to obtain (in the spin-orbital notation of previous projects): + + + +Our task is then relatively simple: Build the Hamiltonian matrix (expressed in +the basis of all singly excited determinants) using the above expression and +diagonalize it. Note that the CIS Hamiltonian matrix is symmetric (check for +yourself by swapping *i/a* and *j/b*), with dimensions of the number of +occupied orbitals times the number of unoccupied orbitals. For our +STO-3G/H2O test case, with its ten occupied and four unoccupied +spin-orbitals, the matrix will be 40 x 40. + + * [Hint](./hints/hint1.md): CIS Hamiltonian for STO-3G H2O + +Make sure you can compute the correct CIS excitation energies for each of the +four test cases provided at the end of the page. Before you move on to the +next section, can you explain the degeneracies appearing in the +excitation-energy list? + +## Spin Adaptation of CIS + +If you carefully examine the list of eigenvalues you computed above, you will +notice a pattern: some of the eigenvalues are unique (i.e., they occur only +once), while others appear in groups of three. The former correspond to +spin-singlet excited states and the latter to spin-triplets, and all are +eigenfunctions of the S2 and Sz operators by virtue of +the fact that the spin-restricted Hartree-Fock reference wave function is such +an eigenfunction (by design, of course) and that the single-excitation +operators must yield identical amplitudes (to within a sign) for both +α- and β-spin excitations. + +Consider the structure of the singlet and triplet determinantal wave functions +from a simple two-electron/two-orbital example (such as the *1s 2s* excited +state configuration of the He atom). One can easily show that the four +possible determinants arising from this configuration, + + + +are components of one singlet and one triplet in the following combinations: + + + + + +where the superscript is the spin multiplicity (*2S+1*) and the subscript is +the *MS* value of the wave function. So, if we wanted to compute +only the eigenvalues and eigenfunctions corresponding spin singlets in our CIS +calculation, we could introduce the restriction on our CIS coefficients that α +and β excitations involving the same spatial orbitals +must be identical (including the sign). Similarly, if we wanted only triplets, +we could require that the α and β excitations +have the same magnitude but opposite signs. + +Let's begin with the singlets. Starting from the spin-orbital eigenvalue +expression and the equation for the CIS Hamiltonian matrix elements in the +previous section, we may write a spin-factored equation for the α +coefficients as + + + +Note that the mix-spin cases (where *j=*α and +*b=*β or *vice versa*) do not contribute since the Fock +matrix elements and two-electron integrals must all give zero. If we then +carry out spin integration on the integrals in the above expression and assume +that the α and β CI coefficients are +identical for the same spatial orbitals, i.e., + + + +we obtain the spatial orbital expression + + + +The part in brackets above is an expression for the spatial-orbital CIS +Hamiltonian, spin-adapted for singlet excited states, and diagonalization of +this matrix will yield only the singlet eigenvalues you obtained from your +spin-orbital matrix earlier. + + * [Hint](./hints/hint2.md): Spin-adapted CIS singlet Hamiltonian for STO-3G H2O + +How about the triplets? We use exactly the same spin-factorization, but +instead require + + + +This yields a slightly simpler Hamiltonian: + + + +which, upon diagonalization, will yield only the triplet eigenvalues (but each only occurring once) from your earlier diagonalziation. + +Why should we worry about spin adaptation? Because the dimension of the +spatial-orbital Hamiltonian matrix is **half** that of the spin-orbital +Hamiltonian, which is a factor of **four** savings in the storage of the matrix +and a factor of **eight** in the diagonalization. For large basis sets and/or +large molecules, this is a considerable computational savings and essential for +production-level codes. + +Make sure you can implement the spin-adapted CIS approach entirely in spatial +orbitals and obtain the correct excitation energies so that you can take +advantage of this greater efficiency available in this formulation. (NB: For +the CH4 test case below, you still get groups of three excitation +energies in the spin-adapted formulation. Do you understand why this +degeneracy arises?) + +## Time-Dependent Hartree Fock (TDHF)/The Random Phase Approximation (RPA) + +The TDHF/RPA approach is closely related to CIS in that only singles are +involved in the wave function expansion, except that both excitation and +"de-excitation" operators are involved. (It is probably better to view the +TDHF/RPA wave function expansion in terms of orbital rotations instead of +Slater determinants, but that's a discussion for another day.) The TDHF/RPA +eigenvalue equations take the form + + + +The definition of the ***A*** matrix is just the CIS matrix itself, *viz.* + + + +while **X** and **Y** are the parameters of single excitations and +de-excitations, respectively, and the ***B*** matrix is simply + + + +Thus, the row/column dimension of the TDHF/RPA Hamiltonian is twice that of the +CIS Hamiltonian, and the matrix is non-symmetric (so you must be careful about +the diagonalization function you choose). Do you obtain twice as many +excitation energies? + + * [Hint](./hints/hint3.md): TDHF/RPA Hamiltonian for STO-3G H2O + +## A Better Approach to Solving the TDHF/RPA Eigenvalue Equations + +Instead of solving the full-dimensional TDHF/RPA equations, which, as noted +above, is twice the size of the CIS problem (and thus four times the +Hamiltonian storage cost), one can rearrange the eigenvalue equations. First +write eigenvalue equation two separate equations, each in terms of the +submatrices **A** and **B**: + + + +and + + + +Now take +/- combinations of these equations to obtain + + + +and + + + +Solve for ***(X+Y)*** in the second equation: + + + +Insert this result into the first equation, rearrange a bit, and finally +obtain: + + + +This is an eigenvalue equation of the same dimension as the CIS eigenvalue +equation (number of occupied orbitals times number of unoccupied orbitals), +where the eigenvalue is the square of the excitation energy and the eigenvector +is ***X-Y*** . + +Make sure you can get the same set of excitation energies using the +full-dimensional TDHF/RPA approach above, as well as this reduced-dimension +approach, for all four test cases below. + +## Test Cases +The input structures, integrals, etc. for these examples may be found in the +[input directory](./input). + +| Test Case | CIS | RPA (Method 1) | RPA (Method 2) | +|-----------|-----|----------------|----------------| +| STO-3G Water | [output](./output/h2o/STO-3G/output_cis.txt) | [output](./output/h2o/STO-3G/output_rpa1.txt) | [output](./output/h2o/STO-3G/output_rpa2.txt) | +| DZ Water | [output](./output/h2o/DZ/output_cis.txt) | [output](./output/h2o/DZ/output_rpa1.txt) | [output](./output/h2o/DZ/output_rpa2.txt) | +| DZP Water | [output](./output/h2o/DZP/output_cis.txt) | [output](./output/h2o/DZP/output_rpa1.txt) | [output](./output/h2o/DZP/output_rpa2.txt) | +| STO-3G Methane | [output](./output/ch4/STO-3G/output_cis.txt) | [output](./output/ch4/STO-3G/output_rpa1.txt) | [output](./output/ch4/STO-3G/output_rpa2.txt) | + diff --git a/Project#12/figures/A-matrix.png b/Project#12/figures/A-matrix.png new file mode 100644 index 0000000..12867fa Binary files /dev/null and b/Project#12/figures/A-matrix.png differ diff --git a/Project#12/figures/B-matrix.png b/Project#12/figures/B-matrix.png new file mode 100644 index 0000000..9201e19 Binary 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new file mode 100644 index 0000000..f6576a2 Binary files /dev/null and b/Project#12/figures/spatial-orbital-expression.png differ diff --git a/Project#12/figures/spin-factored-eqn.png b/Project#12/figures/spin-factored-eqn.png new file mode 100644 index 0000000..f0167ff Binary files /dev/null and b/Project#12/figures/spin-factored-eqn.png differ diff --git a/Project#12/figures/tdhf-eqn.png b/Project#12/figures/tdhf-eqn.png new file mode 100644 index 0000000..318b921 Binary files /dev/null and b/Project#12/figures/tdhf-eqn.png differ diff --git a/Project#12/figures/triplet-combinations.png b/Project#12/figures/triplet-combinations.png new file mode 100644 index 0000000..e533875 Binary files /dev/null and b/Project#12/figures/triplet-combinations.png differ diff --git a/Project#12/hints/hint1.md b/Project#12/hints/hint1.md new file mode 100644 index 0000000..a05b2d7 --- /dev/null +++ b/Project#12/hints/hint1.md @@ -0,0 +1,174 @@ +Here is the CIS matrix for the same H2O STO-3G test case we've been using throughout these projects. Note that the row/column ordering follows *i* and *a* combinations with *a* as the faster-running index (i.e., *a* indexes the inner loop). Thus the first row/column corresponds to *i=0* and *a=0* and the second row/column to *i=0* and *a=1*. Notice that the matrix is diagonally dominant --- that is, the largest element on any row/column combination is the diagonal entry --- and that all the diagonal elements are positive. +``` + 1 2 3 4 5 6 7 8 9 10 + + 1 19.9847006 0.0000000 0.0000000 0.0000000 0.0000000 0.0261967 0.0000000 -0.0000000 0.0172405 0.0000000 + 2 0.0000000 19.9585039 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0074145 + 3 0.0000000 0.0000000 20.0308559 0.0000000 0.0000000 -0.0000000 0.0000000 0.0195218 0.0000000 0.0000000 + 4 0.0000000 0.0000000 0.0000000 20.0113341 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 + 5 0.0000000 0.0000000 0.0000000 0.0000000 19.9585039 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 + 6 0.0261967 0.0000000 -0.0000000 0.0000000 0.0000000 19.9847006 0.0000000 0.0000000 0.0098259 0.0000000 + 7 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 20.0113341 0.0000000 0.0000000 0.0000000 + 8 -0.0000000 0.0000000 0.0195218 0.0000000 0.0000000 0.0000000 0.0000000 20.0308559 0.0000000 0.0000000 + 9 0.0172405 0.0000000 0.0000000 0.0000000 0.0000000 0.0098259 0.0000000 0.0000000 1.1883321 0.0000000 + 10 0.0000000 0.0074145 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 1.0931793 + 11 0.0000000 0.0000000 0.0280239 0.0000000 0.0000000 0.0000000 0.0000000 0.0191033 0.0000000 0.0000000 + 12 0.0000000 -0.0000000 0.0000000 0.0089205 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 + 13 0.0000000 0.0000000 0.0000000 0.0000000 0.0074145 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 + 14 0.0098259 0.0000000 0.0000000 0.0000000 0.0000000 0.0172405 0.0000000 0.0000000 0.0951527 0.0000000 + 15 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 0.0089205 0.0000000 0.0000000 0.0000000 + 16 0.0000000 0.0000000 0.0191033 0.0000000 0.0000000 0.0000000 0.0000000 0.0280239 -0.0000000 0.0000000 + 17 -0.0000000 0.0000000 -0.0046225 0.0000000 0.0000000 -0.0000000 0.0000000 0.0030386 0.0000000 0.0000000 + 18 0.0000000 -0.0000000 0.0000000 -0.0076611 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 + 19 -0.0134310 0.0000000 -0.0000000 0.0000000 0.0000000 -0.0057699 0.0000000 0.0000000 -0.0178319 0.0000000 + 20 0.0000000 -0.0076611 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.0867137 + 21 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 -0.0076611 0.0000000 0.0000000 0.0000000 + 22 -0.0000000 0.0000000 0.0030386 0.0000000 0.0000000 -0.0000000 0.0000000 -0.0046225 0.0000000 0.0000000 + 23 0.0000000 0.0000000 0.0000000 0.0000000 -0.0076611 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 + 24 -0.0057699 0.0000000 0.0000000 0.0000000 0.0000000 -0.0134310 0.0000000 -0.0000000 0.0688817 0.0000000 + 25 0.0197793 0.0000000 -0.0000000 0.0000000 0.0000000 0.0017709 0.0000000 0.0000000 -0.0117148 0.0000000 + 26 0.0000000 0.0180084 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0485372 + 27 0.0000000 0.0000000 0.0149879 0.0000000 0.0000000 0.0000000 0.0000000 0.0112477 0.0000000 0.0000000 + 28 0.0000000 -0.0000000 0.0000000 0.0037402 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 + 29 0.0000000 0.0000000 0.0000000 0.0000000 0.0180084 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 + 30 0.0017709 0.0000000 0.0000000 0.0000000 0.0000000 0.0197793 0.0000000 -0.0000000 -0.0602520 0.0000000 + 31 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 0.0037402 0.0000000 0.0000000 0.0000000 + 32 0.0000000 0.0000000 0.0112477 0.0000000 0.0000000 0.0000000 0.0000000 0.0149879 0.0000000 0.0000000 + 33 -0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 -0.0000000 0.0000000 0.0000000 + 34 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 + 35 0.0000000 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 + 36 0.0000000 0.0000000 0.0000000 -0.0000000 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0.0000000 -0.0178319 0.0000000 0.0000000 0.0000000 0.0000000 0.1594489 0.0000000 + 25 0.0000000 0.0000000 0.0000000 -0.0602520 0.0000000 0.0000000 -0.0000000 0.0000000 -0.0383679 0.0000000 + 26 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0615255 + 27 -0.0011401 0.0000000 0.0000000 0.0000000 0.0000000 0.0171886 0.0073884 0.0000000 -0.0000000 0.0000000 + 28 0.0000000 -0.0183287 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0615255 0.0000000 -0.0000000 + 29 0.0000000 0.0000000 0.0485372 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 + 30 0.0000000 0.0000000 0.0000000 -0.0117148 0.0000000 0.0000000 -0.0000000 0.0000000 -0.0998933 0.0000000 + 31 0.0000000 0.0000000 -0.0000000 0.0000000 -0.0183287 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 + 32 0.0171886 0.0000000 0.0000000 0.0000000 0.0000000 -0.0011401 -0.0541371 0.0000000 0.0000000 0.0000000 + 33 0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 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0.0180084 0.0000000 -0.0000000 0.0000000 0.0000000 + 3 0.0000000 0.0030386 0.0000000 0.0000000 -0.0000000 0.0000000 0.0149879 0.0000000 0.0000000 0.0000000 + 4 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 0.0037402 0.0000000 0.0000000 + 5 -0.0000000 0.0000000 -0.0076611 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0180084 0.0000000 + 6 0.0000000 -0.0000000 0.0000000 -0.0134310 0.0017709 0.0000000 0.0000000 0.0000000 0.0000000 0.0197793 + 7 -0.0076611 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 + 8 0.0000000 -0.0046225 0.0000000 -0.0000000 0.0000000 0.0000000 0.0112477 0.0000000 0.0000000 -0.0000000 + 9 0.0000000 0.0000000 0.0000000 0.0688817 -0.0117148 0.0000000 0.0000000 0.0000000 0.0000000 -0.0602520 + 10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0485372 0.0000000 -0.0000000 0.0000000 0.0000000 + 11 0.0000000 0.0302565 0.0000000 -0.0000000 0.0000000 0.0000000 -0.0011401 0.0000000 0.0000000 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0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 + 19 0.0000000 0.0000000 -0.0000000 0.0000000 -0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 -0.0000000 + 20 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 + 21 0.0615255 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 + 22 0.0000000 0.0073884 -0.0000000 0.0000000 -0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 0.0000000 + 23 -0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 + 24 0.0000000 -0.0000000 -0.0000000 0.0000000 -0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 -0.0000000 + 25 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 + 26 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 + 27 0.0000000 0.0709527 -0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 + 28 0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 + 29 -0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 + 30 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 + 31 0.4442931 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 + 32 0.0000000 0.5152458 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 0.0000000 + 33 0.0000000 0.0000000 0.3218586 0.0000000 0.0000000 0.0000000 0.0000000 0.0346031 0.0000000 -0.0000000 + 34 0.0000000 0.0000000 0.0000000 0.2872555 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 + 35 0.0000000 0.0000000 0.0000000 0.0000000 0.3910304 0.0000000 0.0000000 -0.0000000 0.0000000 0.0250414 + 36 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.3659890 0.0000000 0.0000000 0.0000000 0.0000000 + 37 -0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.2872555 0.0000000 0.0000000 0.0000000 + 38 0.0000000 -0.0000000 0.0346031 0.0000000 -0.0000000 0.0000000 0.0000000 0.3218586 0.0000000 0.0000000 + 39 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.3659890 0.0000000 + 40 0.0000000 0.0000000 -0.0000000 0.0000000 0.0250414 0.0000000 0.0000000 0.0000000 0.0000000 0.3910304 +``` diff --git a/Project#12/hints/hint2.md b/Project#12/hints/hint2.md new file mode 100644 index 0000000..10c5901 --- /dev/null +++ b/Project#12/hints/hint2.md @@ -0,0 +1,16 @@ +Here is the CIS spin-adapted singlet matrix for the H2O STO-3G test case. Note that the row/column ordering follows *i* and *a* combinations with *a* as the faster-running index (i.e., *a* indexes the inner loop). Thus the first row/column corresponds to *i=0* and *a=0* and the second row/column to *i=0* and *a=1*. Notice that the matrix is diagonally dominant --- that is, the largest element on any row/column combination is the diagonal entry --- and that all the diagonal elements are positive. +``` + 1 2 3 4 5 6 7 8 9 10 + + 1 20.0108972 0.0000000 0.0270664 0.0000000 -0.0000000 -0.0192010 0.0215503 0.0000000 -0.0000000 0.0000000 + 2 0.0000000 20.0503777 0.0000000 0.0471272 -0.0015840 -0.0000000 -0.0000000 0.0262356 0.0000000 -0.0000000 + 3 0.0270664 0.0000000 1.2834848 -0.0000000 0.0000000 0.0510498 -0.0719668 0.0000000 -0.0000000 -0.0000000 + 4 0.0000000 0.0471272 -0.0000000 1.3244734 -0.0262007 0.0000000 0.0000000 0.0160485 0.0000000 0.0000000 + 5 -0.0000000 -0.0015840 0.0000000 -0.0262007 0.6257548 0.0000000 -0.0000000 -0.0467487 -0.0000000 -0.0000000 + 6 -0.0192010 -0.0000000 0.0510498 0.0000000 0.0000000 0.8716646 -0.1382612 -0.0000000 -0.0000000 -0.0000000 + 7 0.0215503 -0.0000000 -0.0719668 0.0000000 -0.0000000 -0.1382612 0.5614679 0.0000000 0.0000000 0.0000000 + 8 0.0000000 0.0262356 0.0000000 0.0160485 -0.0467487 -0.0000000 0.0000000 0.5861985 0.0000000 0.0000000 + 9 -0.0000000 0.0000000 -0.0000000 0.0000000 -0.0000000 -0.0000000 0.0000000 0.0000000 0.3564618 0.0000000 + 10 0.0000000 -0.0000000 -0.0000000 0.0000000 -0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 0.4160717 + +``` diff --git a/Project#12/hints/hint3.md b/Project#12/hints/hint3.md new file mode 100644 index 0000000..13b0e43 --- /dev/null +++ b/Project#12/hints/hint3.md @@ -0,0 +1,666 @@ +Here is the TDHF/RPA version of the H2O STO-3G Hamitlonian. The row/column ordering is the same as for CIS above, but there two blocks of *i/a* pairs, one for each of the ***A*** and ***B*** submatrices. This matrix is also diagonally dominant, but not all the diagonal elements are positive. +``` + 1 2 3 4 5 6 7 8 9 10 + + 1 19.9847006 0.0000000 0.0000000 0.0000000 0.0000000 0.0261967 0.0000000 -0.0000000 0.0172405 0.0000000 + 2 0.0000000 19.9585039 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0074145 + 3 0.0000000 0.0000000 20.0308559 0.0000000 0.0000000 -0.0000000 0.0000000 0.0195218 0.0000000 0.0000000 + 4 0.0000000 0.0000000 0.0000000 20.0113341 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 + 5 0.0000000 0.0000000 0.0000000 0.0000000 19.9585039 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 + 6 0.0261967 0.0000000 -0.0000000 0.0000000 0.0000000 19.9847006 0.0000000 0.0000000 0.0098259 0.0000000 + 7 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 20.0113341 0.0000000 0.0000000 0.0000000 + 8 -0.0000000 0.0000000 0.0195218 0.0000000 0.0000000 0.0000000 0.0000000 20.0308559 0.0000000 0.0000000 + 9 0.0172405 0.0000000 0.0000000 0.0000000 0.0000000 0.0098259 0.0000000 0.0000000 1.1883321 0.0000000 + 10 0.0000000 0.0074145 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 1.0931793 + 11 0.0000000 0.0000000 0.0280239 0.0000000 0.0000000 0.0000000 0.0000000 0.0191033 0.0000000 0.0000000 + 12 0.0000000 -0.0000000 0.0000000 0.0089205 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 + 13 0.0000000 0.0000000 0.0000000 0.0000000 0.0074145 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 + 14 0.0098259 0.0000000 0.0000000 0.0000000 0.0000000 0.0172405 0.0000000 0.0000000 0.0951527 0.0000000 + 15 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 0.0089205 0.0000000 0.0000000 0.0000000 + 16 0.0000000 0.0000000 0.0191033 0.0000000 0.0000000 0.0000000 0.0000000 0.0280239 -0.0000000 0.0000000 + 17 -0.0000000 0.0000000 -0.0046225 0.0000000 0.0000000 -0.0000000 0.0000000 0.0030386 0.0000000 0.0000000 + 18 0.0000000 -0.0000000 0.0000000 -0.0076611 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 + 19 -0.0134310 0.0000000 -0.0000000 0.0000000 0.0000000 -0.0057699 0.0000000 0.0000000 -0.0178319 0.0000000 + 20 0.0000000 -0.0076611 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.0867137 + 21 0.0000000 0.0000000 0.0000000 0.0000000 -0.0000000 0.0000000 -0.0076611 0.0000000 0.0000000 0.0000000 + 22 -0.0000000 0.0000000 0.0030386 0.0000000 0.0000000 -0.0000000 0.0000000 -0.0046225 0.0000000 0.0000000 + 23 0.0000000 0.0000000 0.0000000 0.0000000 -0.0076611 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 + 24 -0.0057699 0.0000000 0.0000000 0.0000000 0.0000000 -0.0134310 0.0000000 -0.0000000 0.0688817 0.0000000 + 25 0.0197793 0.0000000 -0.0000000 0.0000000 0.0000000 0.0017709 0.0000000 0.0000000 -0.0117148 0.0000000 + 26 0.0000000 0.0180084 0.0000000 -0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0485372 + 27 0.0000000 0.0000000 0.0149879 0.0000000 0.0000000 0.0000000 0.0000000 0.0112477 0.0000000 0.0000000 + 28 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0.012847889010515 + 9 9 8 8 0.296353939081570 + 9 8 9 8 0.015770501299918 + 9 9 9 1 0.031703797879678 + 9 9 9 2 0.304981529941436 + 9 9 9 3 -0.206879432071914 + 9 9 9 4 -0.206879432071914 + 9 9 9 5 0.206879432071914 + 9 9 9 6 0.085276746780538 + 9 9 9 7 0.085276746780538 + 9 9 9 8 0.085276746780538 + 9 9 9 9 0.774605895725855 diff --git a/Project#12/input/ch4/STO-3G/geom.dat b/Project#12/input/ch4/STO-3G/geom.dat new file mode 100644 index 0000000..9c536a9 --- /dev/null +++ b/Project#12/input/ch4/STO-3G/geom.dat @@ -0,0 +1,6 @@ +5 +6.000000000000 -0.000000000000 0.000000000000 0.000000000000 +1.000000000000 1.183771681898 -1.183771681898 -1.183771681898 +1.000000000000 1.183771681898 1.183771681898 1.183771681898 +1.000000000000 -1.183771681898 1.183771681898 -1.183771681898 +1.000000000000 -1.183771681898 -1.183771681898 1.183771681898 diff --git a/Project#12/input/ch4/STO-3G/input.dat b/Project#12/input/ch4/STO-3G/input.dat new file mode 100644 index 0000000..6dfb483 --- /dev/null +++ b/Project#12/input/ch4/STO-3G/input.dat @@ -0,0 +1,43 @@ +psi: ( + label = "CH4 SCF Test Case" + wfn = scf + jobtype = oeprop + reference = rhf + basis = "STO-3G" + units = angstrom + subgroup = c1 + delete_tei = false + delete_oei = false + zmat = ( + C + H 1 r + H 1 r 2 td + H 1 r 2 td 3 d + H 1 r 2 td 4 d + ) + zvars = ( + r 1.085 + td 109.47122063449069136958 + d 120.0 + ) +) + +basis: ( + carbon: "STO-3G" = + ( (S ( 71.61683730 0.15432900) + ( 13.04509630 0.53532810) + ( 3.53051220 0.44463450) ) + (S ( 2.94124940 -0.09996720) + ( 0.68348310 0.39951280) + ( 0.22228990 0.70011550) ) + (P ( 2.94124940 0.15591630) + ( 0.68348310 0.60768370) + ( 0.22228990 0.39195740) ) + ) + + hydrogen: "STO-3G"= + ( (S ( 3.42525090 0.15432890) + ( 0.62391370 0.53532810) + ( 0.16885540 0.44463450) ) + ) +) diff --git a/Project#12/input/ch4/STO-3G/mux.dat b/Project#12/input/ch4/STO-3G/mux.dat new file mode 100644 index 0000000..9dca8dd --- /dev/null +++ b/Project#12/input/ch4/STO-3G/mux.dat @@ -0,0 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0.163831354490276 + 9 6 0.000000000000000 + 9 7 0.000000000000000 + 9 8 0.202918556316052 + 9 9 1.183771681897731 diff --git a/Project#12/input/ch4/STO-3G/muy.dat b/Project#12/input/ch4/STO-3G/muy.dat new file mode 100644 index 0000000..3b70d58 --- /dev/null +++ b/Project#12/input/ch4/STO-3G/muy.dat @@ -0,0 +1,45 @@ + 1 1 -0.000000000000000 + 2 1 -0.000000000000000 + 2 2 -0.000000000000000 + 3 1 -0.000000000000000 + 3 2 0.000000000000000 + 3 3 -0.000000000000000 + 4 1 -0.071855488532817 + 4 2 -0.838743574800986 + 4 3 0.000000000000000 + 4 4 -0.000000000000000 + 5 1 -0.000000000000000 + 5 2 -0.000000000000000 + 5 3 0.000000000000000 + 5 4 -0.000000000000000 + 5 5 -0.000000000000000 + 6 1 0.004780775261548 + 6 2 0.306592476518555 + 6 3 0.163831354490276 + 6 4 -0.519567036508228 + 6 5 -0.163831354490276 + 6 6 1.183771681897730 + 7 1 -0.004780775261548 + 7 2 -0.306592476518555 + 7 3 -0.163831354490276 + 7 4 -0.519567036508228 + 7 5 -0.163831354490276 + 7 6 -0.000000000000000 + 7 7 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14 12 0.157953012201836 + 14 14 14 13 0.390201782129369 + 14 14 14 14 0.475528488258028 diff --git a/Project#12/input/h2o/DZ/geom.dat b/Project#12/input/h2o/DZ/geom.dat new file mode 100644 index 0000000..99b165d --- /dev/null +++ b/Project#12/input/h2o/DZ/geom.dat @@ -0,0 +1,4 @@ +3 +8.000000000000 0.000000000000 -0.143225816552 0.000000000000 +1.000000000000 1.638036840407 1.136548822547 -0.000000000000 +1.000000000000 -1.638036840407 1.136548822547 -0.000000000000 diff --git a/Project#12/input/h2o/DZ/input.dat b/Project#12/input/h2o/DZ/input.dat new file mode 100644 index 0000000..c9eeb62 --- /dev/null +++ b/Project#12/input/h2o/DZ/input.dat @@ -0,0 +1,12 @@ +psi: ( + label = "H2O SCF Test Case" + memory = (10.0 MB) + wfn = scf + jobtype = oeprop + delete_tei = false + delete_oei = false + reference = rhf + basis = "DZ" + subgroup = c1 + zmat = ((o) (h 1 1.1) (h 1 1.1 2 104.0)) +) diff --git a/Project#12/input/h2o/DZ/mux.dat b/Project#12/input/h2o/DZ/mux.dat new file mode 100644 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0.161483959338374 + 7 7 7 6 0.091353706761488 + 7 7 7 7 0.774605943919898 diff --git a/Project#12/input/h2o/STO-3G/geom.dat b/Project#12/input/h2o/STO-3G/geom.dat new file mode 100644 index 0000000..99b165d --- /dev/null +++ b/Project#12/input/h2o/STO-3G/geom.dat @@ -0,0 +1,4 @@ +3 +8.000000000000 0.000000000000 -0.143225816552 0.000000000000 +1.000000000000 1.638036840407 1.136548822547 -0.000000000000 +1.000000000000 -1.638036840407 1.136548822547 -0.000000000000 diff --git a/Project#12/input/h2o/STO-3G/input.dat b/Project#12/input/h2o/STO-3G/input.dat new file mode 100644 index 0000000..f8c5067 --- /dev/null +++ b/Project#12/input/h2o/STO-3G/input.dat @@ -0,0 +1,12 @@ +psi: ( + label = "H2O SCF Test Case" + memory = (10.0 MB) + wfn = scf + jobtype = oeprop + delete_tei = false + delete_oei = false + reference = rhf + basis = "STO-3G" + subgroup = c1 + zmat = ((o) (h 1 1.1) (h 1 1.1 2 104.0)) +) diff --git a/Project#12/input/h2o/STO-3G/mux.dat b/Project#12/input/h2o/STO-3G/mux.dat 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-1.822241058022723 + 6 4 -1.471788274313766 + 6 5 0.000000000000000 + 6 6 -5.300202953839792 + 7 1 -1.231685872788712 + 7 2 -2.977227202971529 + 7 3 1.822241058022724 + 7 4 -1.471788274313766 + 7 5 0.000000000000001 + 7 6 -1.067166014696110 + 7 7 -5.300202953839793 diff --git a/Project#12/output/ch4/STO-3G/output_cis.txt b/Project#12/output/ch4/STO-3G/output_cis.txt new file mode 100644 index 0000000..f3c7774 --- /dev/null +++ b/Project#12/output/ch4/STO-3G/output_cis.txt @@ -0,0 +1,83 @@ +CIS Excitation Energies: + # Hartree eV +-- -------------------- -------------------- + 0 0.6020603967 16.3826654551 + 1 0.6020603967 16.3826654551 + 2 0.6020603967 16.3826654551 + 3 0.6546366260 17.8133172292 + 4 0.6546366260 17.8133172292 + 5 0.6546366260 17.8133172292 + 6 0.6546366260 17.8133172292 + 7 0.6546366260 17.8133172292 + 8 0.6546366260 17.8133172292 + 9 0.6546366260 17.8133172292 +10 0.6546366260 17.8133172292 +11 0.6546366260 17.8133172292 +12 0.7925534416 21.5661717003 +13 0.7925534416 21.5661717003 +14 0.7925534416 21.5661717003 +15 0.7925534416 21.5661717003 +16 0.7925534416 21.5661717003 +17 0.7925534416 21.5661717003 +18 0.8104989266 22.0544862905 +19 0.8104989266 22.0544862905 +20 0.8104989266 22.0544862905 +21 0.8104989266 22.0544862905 +22 0.8104989266 22.0544862905 +23 0.8104989266 22.0544862905 +24 0.8104989266 22.0544862905 +25 0.8104989266 22.0544862905 +26 0.8104989266 22.0544862905 +27 0.8170915540 22.2338782755 +28 0.8170915540 22.2338782755 +29 0.8170915540 22.2338782755 +30 0.8360459590 22.7496465909 +31 0.8360459590 22.7496465909 +32 0.8486146550 23.0916533779 +33 0.8486146550 23.0916533779 +34 0.8486146550 23.0916533779 +35 0.8486146550 23.0916533779 +36 0.8486146550 23.0916533779 +37 0.8486146550 23.0916533779 +38 0.8486146550 23.0916533779 +39 0.8486146550 23.0916533779 +40 0.8486146550 23.0916533779 +41 0.8913704032 24.2550800412 +42 0.8913704032 24.2550800412 +43 0.8913704032 24.2550800412 +44 0.9136371036 24.8609792263 +45 0.9136371036 24.8609792263 +46 0.9136371036 24.8609792263 +47 1.0550274759 28.7083526472 +48 1.1630382205 31.6474330168 +49 1.1630382205 31.6474330168 +50 1.1630382205 31.6474330168 +51 1.1630382205 31.6474330168 +52 1.1630382205 31.6474330168 +53 1.1630382205 31.6474330168 +54 1.1630382205 31.6474330168 +55 1.1630382205 31.6474330168 +56 1.1630382205 31.6474330168 +57 1.2328669461 33.5475424711 +58 1.2328669461 33.5475424711 +59 1.2328669461 33.5475424711 +60 1.2450464833 33.8789598567 +61 1.2450464833 33.8789598567 +62 1.2450464833 33.8789598567 +63 1.3671423280 37.2013098866 +64 11.0153873178 299.7397043034 +65 11.0153873178 299.7397043034 +66 11.0153873178 299.7397043034 +67 11.0153873178 299.7397043034 +68 11.0153873178 299.7397043034 +69 11.0153873178 299.7397043034 +70 11.0153873178 299.7397043034 +71 11.0153873178 299.7397043034 +72 11.0153873178 299.7397043034 +73 11.0571105649 300.8750355807 +74 11.0571105649 300.8750355807 +75 11.0571105649 300.8750355807 +76 11.0919527271 301.8231256577 +77 11.0919527271 301.8231256577 +78 11.0919527271 301.8231256577 +79 11.1922772144 304.5530552801 diff --git a/Project#12/output/ch4/STO-3G/output_rpa1.txt b/Project#12/output/ch4/STO-3G/output_rpa1.txt new file mode 100644 index 0000000..1280a2e --- /dev/null +++ b/Project#12/output/ch4/STO-3G/output_rpa1.txt @@ -0,0 +1,163 @@ +RPA Excitation Energies: + # Hartree eV +-- -------------------- -------------------- + 0 -11.1920443899 -304.5467198931 + 1 -11.0918058048 -301.8191277536 + 2 -11.0918058048 -301.8191277536 + 3 -11.0918058048 -301.8191277536 + 4 -11.0570161273 -300.8724658402 + 5 -11.0570161273 -300.8724658402 + 6 -11.0570161273 -300.8724658402 + 7 -11.0153437688 -299.7385192922 + 8 -11.0153437688 -299.7385192922 + 9 -11.0153437688 -299.7385192922 +10 -11.0153437688 -299.7385192922 +11 -11.0153437688 -299.7385192922 +12 -11.0153437688 -299.7385192922 +13 -11.0153437688 -299.7385192922 +14 -11.0153437688 -299.7385192922 +15 -11.0153437688 -299.7385192922 +16 -1.3413754999 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-17.3892624692 +77 -0.5656719613 -15.3924997386 +78 -0.5656719613 -15.3924997386 +79 -0.5656719613 -15.3924997386 +80 0.5656719613 15.3924997386 +81 0.5656719613 15.3924997386 +82 0.5656719613 15.3924997386 +83 0.6390526798 17.3892624692 +84 0.6390526798 17.3892624692 +85 0.6390526798 17.3892624692 +86 0.6390526798 17.3892624692 +87 0.6390526798 17.3892624692 +88 0.6390526798 17.3892624692 +89 0.6390526798 17.3892624692 +90 0.6390526798 17.3892624692 +91 0.6390526798 17.3892624692 +92 0.7914475213 21.5360785018 +93 0.7914475213 21.5360785018 +94 0.7914475213 21.5360785018 +95 0.7914475213 21.5360785018 +96 0.7914475213 21.5360785018 +97 0.7914475213 21.5360785018 +98 0.8103245505 22.0497413444 +99 0.8103245505 22.0497413444 +100 0.8103245505 22.0497413444 +101 0.8103245505 22.0497413444 +102 0.8103245505 22.0497413444 +103 0.8103245505 22.0497413444 +104 0.8103245505 22.0497413444 +105 0.8103245505 22.0497413444 +106 0.8103245505 22.0497413444 +107 0.8167562952 22.2247555485 +108 0.8167562952 22.2247555485 +109 0.8167562952 22.2247555485 +110 0.8360443539 22.7496029142 +111 0.8360443539 22.7496029142 +112 0.8454699509 23.0060828334 +113 0.8454699509 23.0060828334 +114 0.8454699509 23.0060828334 +115 0.8454699509 23.0060828334 +116 0.8454699509 23.0060828334 +117 0.8454699509 23.0060828334 +118 0.8454699509 23.0060828334 +119 0.8454699509 23.0060828334 +120 0.8454699509 23.0060828334 +121 0.8859617574 24.1079053817 +122 0.8859617574 24.1079053817 +123 0.8859617574 24.1079053817 +124 0.9131485984 24.8476865100 +125 0.9131485984 24.8476865100 +126 0.9131485984 24.8476865100 +127 1.0250451839 27.8925044984 +128 1.1611159110 31.5951250540 +129 1.1611159110 31.5951250540 +130 1.1611159110 31.5951250540 +131 1.1611159110 31.5951250540 +132 1.1611159110 31.5951250540 +133 1.1611159110 31.5951250540 +134 1.1611159110 31.5951250540 +135 1.1611159110 31.5951250540 +136 1.1611159110 31.5951250540 +137 1.2319714851 33.5231760824 +138 1.2319714851 33.5231760824 +139 1.2319714851 33.5231760824 +140 1.2436343096 33.8405331976 +141 1.2436343096 33.8405331976 +142 1.2436343096 33.8405331976 +143 1.3413754999 36.5001687275 +144 11.0153437688 299.7385192922 +145 11.0153437688 299.7385192922 +146 11.0153437688 299.7385192922 +147 11.0153437688 299.7385192922 +148 11.0153437688 299.7385192922 +149 11.0153437688 299.7385192922 +150 11.0153437688 299.7385192922 +151 11.0153437688 299.7385192922 +152 11.0153437688 299.7385192922 +153 11.0570161273 300.8724658402 +154 11.0570161273 300.8724658402 +155 11.0570161273 300.8724658402 +156 11.0918058048 301.8191277536 +157 11.0918058048 301.8191277536 +158 11.0918058048 301.8191277536 +159 11.1920443899 304.5467198931 diff --git a/Project#12/output/ch4/STO-3G/output_rpa2.txt b/Project#12/output/ch4/STO-3G/output_rpa2.txt new file mode 100644 index 0000000..a4d4ada --- /dev/null +++ b/Project#12/output/ch4/STO-3G/output_rpa2.txt @@ -0,0 +1,83 @@ +RPA Excitation Energies: + # Hartree eV +-- -------------------- -------------------- + 0 0.5656719613 15.3924997386 + 1 0.5656719613 15.3924997386 + 2 0.5656719613 15.3924997386 + 3 0.6390526798 17.3892624692 + 4 0.6390526798 17.3892624692 + 5 0.6390526798 17.3892624692 + 6 0.6390526798 17.3892624692 + 7 0.6390526798 17.3892624692 + 8 0.6390526798 17.3892624692 + 9 0.6390526798 17.3892624692 +10 0.6390526798 17.3892624692 +11 0.6390526798 17.3892624692 +12 0.7914475213 21.5360785018 +13 0.7914475213 21.5360785018 +14 0.7914475213 21.5360785018 +15 0.7914475213 21.5360785018 +16 0.7914475213 21.5360785018 +17 0.7914475213 21.5360785018 +18 0.8103245505 22.0497413444 +19 0.8103245505 22.0497413444 +20 0.8103245505 22.0497413444 +21 0.8103245505 22.0497413444 +22 0.8103245505 22.0497413444 +23 0.8103245505 22.0497413444 +24 0.8103245505 22.0497413444 +25 0.8103245505 22.0497413444 +26 0.8103245505 22.0497413444 +27 0.8167562952 22.2247555485 +28 0.8167562952 22.2247555485 +29 0.8167562952 22.2247555485 +30 0.8360443539 22.7496029142 +31 0.8360443539 22.7496029142 +32 0.8454699509 23.0060828334 +33 0.8454699509 23.0060828334 +34 0.8454699509 23.0060828334 +35 0.8454699509 23.0060828334 +36 0.8454699509 23.0060828334 +37 0.8454699509 23.0060828334 +38 0.8454699509 23.0060828334 +39 0.8454699509 23.0060828334 +40 0.8454699509 23.0060828334 +41 0.8859617574 24.1079053817 +42 0.8859617574 24.1079053817 +43 0.8859617574 24.1079053817 +44 0.9131485984 24.8476865100 +45 0.9131485984 24.8476865100 +46 0.9131485984 24.8476865100 +47 1.0250451839 27.8925044984 +48 1.1611159110 31.5951250540 +49 1.1611159110 31.5951250540 +50 1.1611159110 31.5951250540 +51 1.1611159110 31.5951250540 +52 1.1611159110 31.5951250540 +53 1.1611159110 31.5951250540 +54 1.1611159110 31.5951250540 +55 1.1611159110 31.5951250540 +56 1.1611159110 31.5951250540 +57 1.2319714851 33.5231760824 +58 1.2319714851 33.5231760824 +59 1.2319714851 33.5231760824 +60 1.2436343096 33.8405331976 +61 1.2436343096 33.8405331976 +62 1.2436343096 33.8405331976 +63 1.3413754999 36.5001687275 +64 11.0153437688 299.7385192922 +65 11.0153437688 299.7385192922 +66 11.0153437688 299.7385192922 +67 11.0153437688 299.7385192922 +68 11.0153437688 299.7385192922 +69 11.0153437688 299.7385192922 +70 11.0153437688 299.7385192922 +71 11.0153437688 299.7385192922 +72 11.0153437688 299.7385192922 +73 11.0570161273 300.8724658402 +74 11.0570161273 300.8724658402 +75 11.0570161273 300.8724658402 +76 11.0918058048 301.8191277536 +77 11.0918058048 301.8191277536 +78 11.0918058048 301.8191277536 +79 11.1920443899 304.5467198931 diff --git a/Project#12/output/h2o/DZ/output_cis.txt b/Project#12/output/h2o/DZ/output_cis.txt new file mode 100644 index 0000000..9be5a85 --- /dev/null +++ b/Project#12/output/h2o/DZ/output_cis.txt @@ -0,0 +1,183 @@ +CIS Excitation Energies: + # Hartree eV +-- -------------------- -------------------- + 0 0.2521733734 6.8618896640 + 1 0.2521733734 6.8618896640 + 2 0.2521733734 6.8618896640 + 3 0.2929742879 7.9721233473 + 4 0.2951406202 8.0310714157 + 5 0.2951406202 8.0310714157 + 6 0.2951406202 8.0310714157 + 7 0.3175855602 8.6418206778 + 8 0.3175855602 8.6418206778 + 9 0.3175855602 8.6418206778 +10 0.3372543633 9.1770284804 +11 0.3372543633 9.1770284804 +12 0.3372543633 9.1770284804 +13 0.3466019985 9.4313869817 +14 0.3844210667 10.4604816447 +15 0.4129756328 11.2374799430 +16 0.4129756328 11.2374799430 +17 0.4129756328 11.2374799430 +18 0.4382472054 11.9251447065 +19 0.4482402900 12.1970665300 +20 0.4482402900 12.1970665300 +21 0.4482402900 12.1970665300 +22 0.4912333948 13.3669519050 +23 0.6128418167 16.6760386748 +24 0.7609972870 20.7074971761 +25 0.7609972870 20.7074971761 +26 0.7609972870 20.7074971761 +27 0.8535911371 23.2270684304 +28 0.8535911371 23.2270684304 +29 0.8535911371 23.2270684304 +30 0.8889605749 24.1895062030 +31 0.8889605749 24.1895062030 +32 0.8889605749 24.1895062030 +33 0.8997293379 24.4825350145 +34 0.9172227314 24.9585477444 +35 0.9172227314 24.9585477444 +36 0.9172227314 24.9585477444 +37 0.9196035320 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1673.1808389998 diff --git a/Project#12/output/h2o/DZ/output_rpa2.txt b/Project#12/output/h2o/DZ/output_rpa2.txt new file mode 100644 index 0000000..6453e50 --- /dev/null +++ b/Project#12/output/h2o/DZ/output_rpa2.txt @@ -0,0 +1,183 @@ +RPA Excitation Energies: + # Hartree eV +-- -------------------- -------------------- + 0 0.2458308730 6.6893038844 + 1 0.2458308730 6.6893038844 + 2 0.2458308730 6.6893038844 + 3 0.2637567614 7.1770852349 + 4 0.2637567614 7.1770852349 + 5 0.2637567614 7.1770852349 + 6 0.2896457262 7.8815498545 + 7 0.3073528488 8.3633783674 + 8 0.3073528488 8.3633783674 + 9 0.3073528488 8.3633783674 +10 0.3111679098 8.4671899948 +11 0.3111679098 8.4671899948 +12 0.3111679098 8.4671899948 +13 0.3427717403 9.3271618244 +14 0.3800739542 10.3421923684 +15 0.4070382580 11.0759180378 +16 0.4070382580 11.0759180378 +17 0.4070382580 11.0759180378 +18 0.4284475765 11.6584870029 +19 0.4284475765 11.6584870029 +20 0.4284475765 11.6584870029 +21 0.4334070450 11.7934391018 +22 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59.3835794777 1615.8865811678 +177 59.3835794777 1615.8865811678 +178 59.3835794777 1615.8865811678 +179 61.4891345044 1673.1808389998 diff --git a/Project#12/output/h2o/DZP/output_cis.txt b/Project#12/output/h2o/DZP/output_cis.txt new file mode 100644 index 0000000..44f19b4 --- /dev/null +++ b/Project#12/output/h2o/DZP/output_cis.txt @@ -0,0 +1,423 @@ +CIS Excitation Energies: + # Hartree eV +-- -------------------- -------------------- + 0 0.2601682546 7.0794383768 + 1 0.2601682546 7.0794383768 + 2 0.2601682546 7.0794383768 + 3 0.3020421301 8.2188684011 + 4 0.3092671403 8.4154681536 + 5 0.3092671403 8.4154681536 + 6 0.3092671403 8.4154681536 + 7 0.3238098671 8.8111902928 + 8 0.3238098671 8.8111902928 + 9 0.3238098671 8.8111902928 +10 0.3472643886 9.4494112790 +11 0.3472643886 9.4494112790 +12 0.3472643886 9.4494112790 +13 0.3531481926 9.6095154696 +14 0.4001562179 10.8886508445 +15 0.4237213482 11.5298816071 +16 0.4237213482 11.5298816071 +17 0.4237213482 11.5298816071 +18 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44.8089454816 1219.2962155003 +404 44.9078495791 1221.9874948960 +405 44.9078495791 1221.9874948960 +406 44.9078495791 1221.9874948960 +407 44.9537204970 1223.2356884434 +408 45.1158712438 1227.6479724155 +409 45.1158712438 1227.6479724155 +410 45.1158712438 1227.6479724155 +411 45.1351492485 1228.1725461998 +412 45.5549141549 1239.5947690680 +413 45.5549141549 1239.5947690680 +414 45.5549141549 1239.5947690680 +415 45.6745123915 1242.8491566847 +416 61.5010549224 1673.5052054925 +417 61.5010549224 1673.5052054925 +418 61.5010549224 1673.5052054925 +419 63.4733960911 1727.1745810345 diff --git a/Project#12/output/h2o/STO-3G/output_cis.txt b/Project#12/output/h2o/STO-3G/output_cis.txt new file mode 100644 index 0000000..c4a8b36 --- /dev/null +++ b/Project#12/output/h2o/STO-3G/output_cis.txt @@ -0,0 +1,43 @@ +CIS Excitation Energies: + # Hartree eV +-- -------------------- -------------------- + 0 0.2872554996 7.8165094000 + 1 0.2872554996 7.8165094000 + 2 0.2872554996 7.8165094000 + 3 0.3444249963 9.3721485742 + 4 0.3444249963 9.3721485742 + 5 0.3444249963 9.3721485742 + 6 0.3564617587 9.6996809147 + 7 0.3659889948 9.9589265386 + 8 0.3659889948 9.9589265386 + 9 0.3659889948 9.9589265386 +10 0.3945137992 10.7351149906 +11 0.3945137992 10.7351149906 +12 0.3945137992 10.7351149906 +13 0.4160717386 11.3217280788 +14 0.5056282877 13.7586513356 +15 0.5142899971 13.9943451123 +16 0.5142899971 13.9943451123 +17 0.5142899971 13.9943451123 +18 0.5551918860 15.1073264088 +19 0.5630557635 15.3213103815 +20 0.5630557635 15.3213103815 +21 0.5630557635 15.3213103815 +22 0.6553184485 17.8318703012 +23 0.9101216891 24.7653212808 +24 1.1087709658 30.1707667495 +25 1.1087709658 30.1707667495 +26 1.1087709658 30.1707667495 +27 1.2000961331 32.6558158774 +28 1.2000961331 32.6558158774 +29 1.2000961331 32.6558158774 +30 1.3007851948 35.3956659366 +31 1.3257620652 36.0753115562 +32 19.9585264123 543.0914622058 +33 19.9585264123 543.0914622058 +34 19.9585264123 543.0914622058 +35 20.0109794203 544.5187610062 +36 20.0113420895 544.5286295981 +37 20.0113420895 544.5286295981 +38 20.0113420895 544.5286295981 +39 20.0505319444 545.5950247379 diff --git a/Project#12/output/h2o/STO-3G/output_rpa1.txt b/Project#12/output/h2o/STO-3G/output_rpa1.txt new file mode 100644 index 0000000..321fd22 --- /dev/null +++ b/Project#12/output/h2o/STO-3G/output_rpa1.txt @@ -0,0 +1,83 @@ +RPA Excitation Energies: + # Hartree eV +-- -------------------- -------------------- + 0 -20.0504919449 -545.5939363129 + 1 -20.0113074586 -544.5276872551 + 2 -20.0113074586 -544.5276872551 + 3 -20.0113074586 -544.5276872551 + 4 -20.0109471551 -544.5178830377 + 5 -19.9585040647 -543.0908541050 + 6 -19.9585040647 -543.0908541050 + 7 -19.9585040647 -543.0908541050 + 8 -1.3237421886 -36.0203486946 + 9 -1.2832053178 -34.9172999015 +10 -1.1957870714 -32.5385620002 +11 -1.1957870714 -32.5385620002 +12 -1.1957870714 -32.5385620002 +13 -1.1038187957 -30.0360132492 +14 -1.1038187957 -30.0360132492 +15 -1.1038187957 -30.0360132492 +16 -0.8734253708 -23.7667777637 +17 -0.6502707118 -17.6945163383 +18 -0.5513718846 -15.0033803508 +19 -0.5460719086 -14.8591627038 +20 -0.5460719086 -14.8591627038 +21 -0.5460719086 -14.8591627038 +22 -0.5106610509 -13.8955978550 +23 -0.5106610509 -13.8955978550 +24 -0.5106610509 -13.8955978550 +25 -0.5001011401 -13.6082521222 +26 -0.4153174946 -11.3012043465 +27 -0.3651313107 -9.9355880949 +28 -0.3651313107 -9.9355880949 +29 -0.3651313107 -9.9355880949 +30 -0.3547782530 -9.6538710427 +31 -0.3526266606 -9.5953240628 +32 -0.3526266606 -9.5953240628 +33 -0.3526266606 -9.5953240628 +34 -0.2997434467 -8.1563189292 +35 -0.2997434467 -8.1563189292 +36 -0.2997434467 -8.1563189292 +37 -0.2851637170 -7.7595899029 +38 -0.2851637170 -7.7595899029 +39 -0.2851637170 -7.7595899029 +40 0.2851637170 7.7595899029 +41 0.2851637170 7.7595899029 +42 0.2851637170 7.7595899029 +43 0.2997434467 8.1563189292 +44 0.2997434467 8.1563189292 +45 0.2997434467 8.1563189292 +46 0.3526266606 9.5953240628 +47 0.3526266606 9.5953240628 +48 0.3526266606 9.5953240628 +49 0.3547782530 9.6538710427 +50 0.3651313107 9.9355880949 +51 0.3651313107 9.9355880949 +52 0.3651313107 9.9355880949 +53 0.4153174946 11.3012043465 +54 0.5001011401 13.6082521222 +55 0.5106610509 13.8955978550 +56 0.5106610509 13.8955978550 +57 0.5106610509 13.8955978550 +58 0.5460719086 14.8591627038 +59 0.5460719086 14.8591627038 +60 0.5460719086 14.8591627038 +61 0.5513718846 15.0033803508 +62 0.6502707118 17.6945163383 +63 0.8734253708 23.7667777637 +64 1.1038187957 30.0360132492 +65 1.1038187957 30.0360132492 +66 1.1038187957 30.0360132492 +67 1.1957870714 32.5385620002 +68 1.1957870714 32.5385620002 +69 1.1957870714 32.5385620002 +70 1.2832053178 34.9172999015 +71 1.3237421886 36.0203486946 +72 19.9585040647 543.0908541050 +73 19.9585040647 543.0908541050 +74 19.9585040647 543.0908541050 +75 20.0109471551 544.5178830377 +76 20.0113074586 544.5276872551 +77 20.0113074586 544.5276872551 +78 20.0113074586 544.5276872551 +79 20.0504919449 545.5939363129 diff --git a/Project#12/output/h2o/STO-3G/output_rpa2.txt b/Project#12/output/h2o/STO-3G/output_rpa2.txt new file mode 100644 index 0000000..8385a9c --- /dev/null +++ b/Project#12/output/h2o/STO-3G/output_rpa2.txt @@ -0,0 +1,43 @@ +RPA Excitation Energies: + # Hartree eV +-- -------------------- -------------------- + 0 0.2851637170 7.7595899029 + 1 0.2851637170 7.7595899029 + 2 0.2851637170 7.7595899029 + 3 0.2997434467 8.1563189292 + 4 0.2997434467 8.1563189292 + 5 0.2997434467 8.1563189292 + 6 0.3526266606 9.5953240628 + 7 0.3526266606 9.5953240628 + 8 0.3526266606 9.5953240628 + 9 0.3547782530 9.6538710427 +10 0.3651313107 9.9355880949 +11 0.3651313107 9.9355880949 +12 0.3651313107 9.9355880949 +13 0.4153174946 11.3012043465 +14 0.5001011401 13.6082521222 +15 0.5106610509 13.8955978550 +16 0.5106610509 13.8955978550 +17 0.5106610509 13.8955978550 +18 0.5460719086 14.8591627038 +19 0.5460719086 14.8591627038 +20 0.5460719086 14.8591627038 +21 0.5513718846 15.0033803508 +22 0.6502707118 17.6945163383 +23 0.8734253708 23.7667777637 +24 1.1038187957 30.0360132492 +25 1.1038187957 30.0360132492 +26 1.1038187957 30.0360132492 +27 1.1957870714 32.5385620002 +28 1.1957870714 32.5385620002 +29 1.1957870714 32.5385620002 +30 1.2832053178 34.9172999015 +31 1.3237421886 36.0203486946 +32 19.9585040647 543.0908541050 +33 19.9585040647 543.0908541050 +34 19.9585040647 543.0908541050 +35 20.0109471551 544.5178830377 +36 20.0113074586 544.5276872551 +37 20.0113074586 544.5276872551 +38 20.0113074586 544.5276872551 +39 20.0504919449 545.5939363129 diff --git a/Project#13/README.md b/Project#13/README.md index 4bff667..54d22da 100644 --- a/Project#13/README.md +++ b/Project#13/README.md @@ -1 +1,113 @@ # Project #13: The Davidson-Liu Algorithm: CIS + +A common problem in quantum chemistry is the need to compute a few eigenvalues +of a very large matrix -- far too large to store entirely in core memory. In +1975, Ernest Davidson published a robust algorithm[1](#f1) +to solve this problem, and it has been used in electronic structure +software packages ever since. A few years later, Bowen Liu extended the +algorithm to allow computation of several eigenvalues simultaneously rather +than one at a time[2](#f2). The +purpose of this project is to illustrate the use of what is now called the +Davidson-Liu algorithm in the context of a +[CIS computation](../Project%2312). + +## The Basic Algorithm + +This is an outline of the essential aspects of the Davidson-Liu algorithm. +There are many ways to tweak the approach to improve its rate of convergence or +efficiency, and for details I recommend David Sherrill's excellent CI review +article[3](#f3), from which also we take our notation below. + +## Step #1: Select Guess Vectors + +Compute a set of *L* orthonormal guess eigenvectors, {***b***i} --- +at least one for every desired root. A simple choice is a set of unit vectors, +or one can taken them from another level of theory or perhaps the eigenvectors +from a well-chosen subspace of the full determinantal space. + +## Step #2: Build and Diagonalize the Subspace Hamiltonian + +Compute a representation of the Hamiltonian within the space of guess vectors, + + + +and then diagonalize this so-called "subspace Hamiltonian", + + + +where *M* is the number of roots of interest. The current estimate of each of +the *M* eigenvectors we want is a linear combination of the guess vectors, +with the αk subspace eigenvectors providing the +coefficients, *viz.* + + + +The dimension of ***G*** is typically very small (perhaps a dozen times the +number of guess vectors, *L*), so one can used a standard diagonalization +package (such as DSYEV in LAPACK) for this task. Note that the most expensive +part of the Davidson-Liu algorithm is the computation of σ, +the products of the Hamiltonian matrix with the guess vectors. In some of the +largest CI calculations, the Hamiltonian cannot even be stored on disk and its +elements must be computed "on the fly" during the computation of each +σ. + +## Step #3: Build the Correction Vectors + +Build a set of "correction vectors", + + + +where the "residual" vectors are defined as + + + +and *N* is the dimension of the Hamiltonian (i.e. the number of determinants). +The inverse appearing in the definition of the correction vectors is commonly +referred to as the "preconditioner". Notice that the residual vectors are so +named because they would be zero if the guess vectors, ***b***i, +were the true eigenvectors. Thus, convergence of the algorithm is checked at +this point, based on the norms of the residual vectors (one for each desired +root) and the change in the corresponding eigenvalue between each iteration. +## Step #4: Orthonormalize the Correction Vectors + +Normalize each correction vector, fδk, +then orthogonalize it against the existing set of guesses, **b**i, +using the [Schmidt Orthogonalization procedure](http://en.wikipedia.org/wiki/Gram–Schmidt_process), +for example. If the orthonormalized correction vector has a norm larger than some chosen threshold (e.g. 10-3), +include it in the set of guess vectors. If not, discard it. (Thus, the dimension of the guess space, *L*, gradually increases in each iteration.) + +Return to step #2 and continue. + +## CIS Sigma Equation + +We will focus on the spin-adapted singlet formulation of CIS, +for which the σ = H c equation was given in +[Project 12](../Project%2312): + + + +## Unit Guess Vectors + +What should we choose for guess vectors? As noted above, the simplest choice +is probably a set of unit vectors, one for each eigenvalue you want. But in +what position of the vector should we put the 1? For a hint, look at the +structure of the [spin-adapted singlet CIS Hamiltonian](../Project%2312/hints/hint2.md) +for the H2O STO-3G test case and note that it is +strongly diagonally dominant. Thus, if the diagonal elements are reasonable +approximations to the true eigenvalues, and we want to compute only the lowest +*M* eigenvalues, then our guess unit vectors should have a 1 in the position +corresponding to the row/column of the smallest elements of the Hamiltonian. + +## Subspace Collapse + +If the number of guess vectors grows to be too large, we may need to reduce its +dimension to something more manageable before continuing the Davidson-Liu +algorithm. A typical choice is to collapse to the current best set of guesses +using the equation given above for the current final eigenvectors: + + + +#### References + - 1: E.R. Davidson, "The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices," *J. Comput. Phys.* **17**, 87 (1975). [(return to text)](#r1) + - 2: B.Liu, "The simultaneous expansion method for the iterative solution of several of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices," Technical Report LBL-8158, Lawrence Berkeley Laboratory, University of California, Berkeley, 1978. [(return to text)](#r2) + - 3: C.D. Sherrill, "The Configuration Interaction Method: Advances in Highly Correlated Approaches," *Adv. Quantum Chem.* **34**, 143 (1998). [(return to text)](#r3) diff --git a/Project#13/figures/coefficients.png b/Project#13/figures/coefficients.png new file mode 100644 index 0000000..09b91cf Binary files /dev/null and b/Project#13/figures/coefficients.png differ diff --git a/Project#13/figures/correction-vectors.png b/Project#13/figures/correction-vectors.png new file mode 100644 index 0000000..229b957 Binary files /dev/null and b/Project#13/figures/correction-vectors.png differ diff --git a/Project#13/figures/diag-subspace-hamiltonian.png b/Project#13/figures/diag-subspace-hamiltonian.png new file mode 100644 index 0000000..41fc305 Binary files /dev/null and b/Project#13/figures/diag-subspace-hamiltonian.png differ diff --git a/Project#13/figures/final-eigenvectors.png b/Project#13/figures/final-eigenvectors.png new file mode 100644 index 0000000..936621f Binary files /dev/null and b/Project#13/figures/final-eigenvectors.png differ diff --git a/Project#13/figures/guess-vector-hamiltonian.png b/Project#13/figures/guess-vector-hamiltonian.png new file mode 100644 index 0000000..a4add57 Binary files /dev/null and b/Project#13/figures/guess-vector-hamiltonian.png differ diff --git a/Project#13/figures/residual-vectors.png b/Project#13/figures/residual-vectors.png new file mode 100644 index 0000000..1438091 Binary files /dev/null and b/Project#13/figures/residual-vectors.png differ diff --git a/Project#13/figures/spin-adapted-cis-eqn.png b/Project#13/figures/spin-adapted-cis-eqn.png new file mode 100644 index 0000000..726668b Binary files /dev/null and b/Project#13/figures/spin-adapted-cis-eqn.png differ diff --git a/README.md b/README.md index 4d5140b..d2ad75d 100644 --- a/README.md +++ b/README.md @@ -1,12 +1,3 @@ -# Underdevelopment - -###TODO: - - [ x ] add links for fundamentals - - [ ] add links for programming projects - - [ ] add project inputs - - [ ] add project readme's - - [ ] expand git intro - # C++ Programming Tutorial in Chemistry This tutorial is intended to touch on many, but certainly not all, of the fundamentals of C++ programming with an emphasis on quantum chemistry. Although I hope this section will get you started, it is not a substitute for a more complete reference manual. For more C++ language details, you may find the standard text by Josuttis [buy it](http://www.amazon.com/C-Standard-Library-Tutorial-Reference/dp/0201379260) useful or, for VT users, get it [on-line from the campus library](http://proquest.safaribooksonline.com/0201379260) or a decent on-line tutorial such as [this one](http://www.cplusplus.com/doc/tutorial/) or [this one](http://www.cprogramming.com/tutorial.html). @@ -33,10 +24,10 @@ git clone git@github.com:CrawfordGroup/ProgrammingProjects.git ``` Now you should see a directory called `ProgrammingProjects` inside you will find all of the files that you can see on github. -# The Fundamentals (Updated: 29 August 2014) +# The Fundamentals - [An Initial Example](https://github.com/CrawfordGroup/ProgrammingProjects/wiki/An-Initial-Example) - [What is a "Compilation"](https://github.com/CrawfordGroup/ProgrammingProjects/wiki/What-is-a-%22Compilation%22%3F) - - [Code Comments](https://github.com/CrawfordGroup/ProgrammingProjects/wiki/Comments) + - [Code Comments](https://github.com/CrawfordGroup/ProgrammingProjects/wiki/Code-Comments) - [Data Types and Variables](https://github.com/CrawfordGroup/ProgrammingProjects/wiki/Data-Types-and-Variables) - [Operators](https://github.com/CrawfordGroup/ProgrammingProjects/wiki/Operators) - [Control Statements](https://github.com/CrawfordGroup/ProgrammingProjects/wiki/Control-Statements) @@ -63,3 +54,11 @@ Now you should see a directory called `ProgrammingProjects` inside you will find - [Project #13](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2313): the Davidson-Liu Algorithm: CIS - [Project #14](https://github.com/CrawfordGroup/ProgrammingProjects/tree/master/Project%2314): Excited Electronic States: EOM-CCSD (*In Preparation*) +# Possible Future Projects + - Some Future Projects + - SCF Analytic Energy Gradients + - MP2 Analytic Energy Gradients + - Integral-direct SCF + - Response properties: Hartree-Fock dipole-polarizabilities + - Response properties: CCSD dipole-polarizabilities + - Local MP2