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where <html>Γ<sub>X</sub></html> denotes the irreducible representation (irrep) of entity X.
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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.
@@ -146,7 +146,7 @@ in the full list of orbitals; the first number is the relative index, the second
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If we store the integral, MO coefficient, density, and Fock matrices in the block-diagonal structure described above,
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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 <b><i>C</i></b><sub>h</sub> denotes the *h*-th irrep subblock of the full matrix <b><i>C</i></b>.
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(The notation of the large plus with a circle around it indicates a direct sum.)
@@ -155,7 +155,7 @@ where *h* denotes a particular irrep of the point group and <b><i>C</i></b><sub>
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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)
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to evaluate this expression. However, if the density and MO coefficient matrices are stored in symmetry-blocked form,
@@ -187,7 +187,7 @@ sophisticated guesses at the Fock matrix, e.g. Hueckel orbitals or other (semi)e
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The only portion of the SCF procedure involving two-electron integrals is the Fock-matrix build:
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