A theory of self-consistent electron pairs. Computational methods and preliminary applications

Abstract

The recently developed theory of self‐consistent electron pairs (SCEP) is an iterative method of obtaining correlated wavefunctions. In its variational form, it is equivalent to a configuration interaction (CI) treatment including all single and double substitutions from a reference determinant. The computational application of the theory has been fully implemented and tested for a variety of chemical systems. Some theoretical refinements which resulted from these tests are presented. The chemical systems selected for this first SCEP study of molecular electronic structure test most of the anticipated difficulties in using the theory and include H₂, LiH, BeH⁺, BH, Be₂, CH₂, H₂O, H₂CO, and HCCH. Some of the potential advantages of SCEP relative to conventional CI appear to be computational efficiency, variationally additive pair correlation energies, and the capability to treat systems nearly as large as can be studied with one‐configuration self‐consistent‐field (SCF) theory. The method’s efficiency results largely from the avoidance of an explicit integrals transformation or construction and diagonalization of a large CI matrix. Because SCEP theory is formulated using Hartree–Fock‐like operators, with the same dimensionality as the Fock operator, large basis sets are handled nearly as easily as with SCF calculations. One of the largest calculations reported here involved 42 contracted Gaussian functions and accounts for ∼88% of the valence shell correlation energy of singlet methylene. The equivalent CI wavefunction would include 2926 symmetry‐adapted configurations. For the water molecule, an even more extensive SCEP treatment (equivalent to 4631 ¹A₁ configurations) is reported.