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General method for symmetry orbitals and tensors in electronic structure calculations

The symmetry orbital tensor (SOT) method, which makes full use of symmetries in all point groups and can be applied to the self‐consistent field (SCF) and post‐SCF calculations, is introduced. The principal feature of this method is the definition of the symmetry orbitals (SOs). Any element in a molecular point group will transform one SO to another equivalent SO or simply to itself, and no mixture among SOs exists. Thus, although the SOs for non‐Abelian point groups may adapt to reducible representations, their transformation properties are much simpler than in conventional treatments. This article also presents a general scheme to generate SOs for all point groups. The direct products of N SOs form an Nth‐rank SOT group, and each matrix element between SOTs is the product of a physical factor and a geometric factor. Compared with the canonical molecular orbitals, the use of SOs can noticeably reduce the computation efforts by decreasing the number of integrals needed in the SCF calculations or the number of configurations needed in the configuration interaction (CI) calculations. The SOT‐SCF and SOT‐CI approaches are formulated and a preliminary SOT‐SCF program is written. Pilot calculations demonstrate the value of the SOT approach, at least at the closed‐shell Hartree–Fock level. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 305–321, 1999