Investigations of Spin-Eigenfunction Correlated Wavefunctions

Citation

Bobrowicz, Frank Wilhelm (1974) Investigations of Spin-Eigenfunction Correlated Wavefunctions. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/2XSV-1F12. https://resolver.caltech.edu/CaltechETD:etd-09272005-143127

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Part I Generalized Valence-Bond descriptions for the low-lying [...], [...], and [...] states of CH are presented. These wavefunctions are found to behave properly at all internuclear distances, giving a clear and consistent physical picture of formation of these molecules from their constituent atoms. Part II A procedure for calculating Spin-Eigenfunction Configuration Interaction matrices utilizing the U matrices which form the irreducible representations of [...] is presented. In addition, an improved determinant method is summarized. By combining both of these U-matrix and Determinant methods, it has been possible to formulate a practical and yet highly efficient procedure for generating such CI matrices. Part III Even for relatively simple Hartree-Fock (HF) or Perfect-Pairing Generalized Valence-Bond (PPGVB) many-electron wavefunctions, self-consistent calculations can be prohibitively expensive for, many chemically interesting systems. Considerable effort has been devoted toward developing highly efficient computational techniques for solving for such wavefunctions. The results of this research, as embodied in the GVBTWO program, have made such calculations on relatively large systems a practical reality. Part IV The Generalized Valence-Bond (GVB) wavefunction has had considerable success in describing chemical reactions and molecular structure. Unfortunately, this method can only be applied to systems involving a few electrons. The Perfect-Pairing approximation to GVB (PPGVB) greatly simplifies the situation and is found to adequately describe the low-lying states of many molecules. However, in describing chemical reactions the restrictions of PPGVB are quite serious. The Strongly Orthogonal approximation (SOGVB) described here overcomes this problem by allowing the orbitals to recouple while still retaining the simplifying orbital restrictions of PPGVB. This intermediate method correctly describes many chemical reactions and is practical for treating relatively large systems.

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