Molecular symmetry in methods for electron correlation

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Abstract
This paper is concerned with a procedure to obtain molecular integrals from symmetry unique integrals over atomic orbitals, a step found in many methods dealing with electron correlation in the context of the linear combination of atomic orbitals (LCAO) approach. This ‘‘symmetrization’’ procedure incorporated in the four-index transformation is based on symmetry coupling of the molecular orbitals to create charge distributions followed by an inverse transformation. The method involves the use of Clebsch–Gordan coefficients and works for all point groups, including those with complex representations. It is currently implemented in the hondo8 computer program. The relationship between this approach and other previously proposed approaches is shown. A formal expression of Pitzer’s equal contribution theorem is provided. Timing data related to the computer implementation of the proposed procedure is analyzed.