Hartree Fock (HF) forms the starting point of most of the established methodologies for ab initio computational Quantum Chemistry, by defining such notions as orbitals, excitation energies, and excitation level. Generalized Valence Bond (GVB) wave functions offer a conceptually straightforward and instructive, as well as quantitatively superior, generalization of Hartree Fock. Instead of a 'Fermi Sphere'-like decomposition of phase space into purely conventional doubly-occupied, and unoccupied 'orbitals', GVB wave functions consist of well defined electron 'pairs'. This thesis derives a general post-GVB Methodology, and makes specific recommendations for constructing very broadly applicable wave functions. Code has been devised which implements a unique 'contraction scheme' available within the GVB framework, for compactifying correlated many body wave functions and the general matrix elements required for their calculation. Test calculations have been performed to measure the near equilibrium energy surface of single and multiple bonds, on singlet coupled and open shell molecules. Bond dissociation energies have also been computed. In all cases, the new approach leads to new levels of efficiency for approximating highly correlated wave functions, using small calculations chosen by simple criteria, whose physical basis is discussed. On large molecules, the savings over standard alternatives are up to many orders of magnitude. For bond breaking, the improvement over the Hartree Fock based approaches is significantly greater than for calculations near equilibrium. Using a localized rather than symmetry representation of the one electron degrees of freedom plays a central role in the identification of a small number of dominant many electron degrees of freedom. Other localization techniques already exist. These, as well as pseudospectral approaches to integrals over orbitals, should be used in conjunction with the new methodology of this work. Significant advances remain to be implemented in all these areas in order to achieve an ultimately routine approach to quantum chemistry, which is the clear and proper goal.
Thesis (Ph.D. in Physics and Astronomy) -- University of Pennsylvania, 1998. Source: Dissertation Abstracts International, Volume: 59-07, Section: B, page: 3525. Supervisors: Richard P. Messmer; P. Langacker.