Improved Quantum Theory of Many-Electron Systems. V. The Spin-Coupling Optimized GI Method

Abstract

The previously developed GI methods have an arbitrary aspect since they are based on a particular representation of the symmetric group. Here we remove this arbitrariness by optimizing the representation, that is, optimizing the spin‐coupling scheme simultaneously with the optimization of the orbitals. The resulting wavefunctions, called the spin‐coupling optimized GI or SOGI wavefunctions, have all of the general properties of GI wavefunctions including the independent particle interpretation and are found as the solutions to a set of coupled differential equations which differ from the GI equations only in that the equations are constructed from a different representation of the symmetric group. We have applied this method to the ground state and some excited states of Li, to the ground states of Be⁺ and B⁺⁺ and to the ground state of LiH. In each of these cases, we found that the SOGI wavefunction was only slightly different from the G1 wavefunction and led to very similar energies and other spatial properties. For the spin density at the nucleus, however, SOGI led to much better results. In order to illustrate the effects of spatial symmetry on the SOGI orbitals, we examined the lowest ${}^1{B}_{\text{1g}}$ , ${}^3{A}_{\text{2g}}$ , and ${}^3{E}_u$ states of square H₄ and the ${}^2{\Sigma }_u^{+}$ state of linear symmetrical H₃. We find that in three of these cases optimization of the spin representation is crucial to providing an adequate description of the state. To investigate how the SOGI method would describe chemical reactions, the SOGI wavefunctions were computed for several other nuclear configurations of the H₃ system along the reaction path. These calculations showed that the spin coupling changed significantly during the reaction H₂ + H⇆H + H₂ and that the variation of the SOGI orbitals provides a clear description of the changes in bonding which occur during this reaction.