Multiconfigurational perturbation theory

Many-body and Rayleigh-Schrodinger perturbation theories have traditionally been applied to a single determinant Hartree-Fock reference wave function. These perturbative approaches are both physically appealing and computationally efficient means of describing correlation effects. However, the success of these perturbation theories at low-order is grounded in the assumption that the Hartree-Fock wave function is a good zeroth-order description of the system. The Hartree-Fock wave function is known to be insufficient for both dissociation processes and for systems requiring more general spin couplings. A large effort has been devoted towards devising and variationally optimizing multiconfigurational wave functions which can properly describe bond dissociation and general spin couplings. Although these multiconfigurational wave functions can properly describe the overall shape of potential surfaces, they are generally insufficient for quantitatively predicting spectroscopic observables. The direct method of improving the multiconfigurational wave functions is to diagonalize the full Hamiltonian in a larger space of configurations generated from the set of reference configurations. Such diagonalization approaches have been shown to give accurate observables at a relatively high computational cost. Unfortunately, such a direct approach is computationally demanding. This thesis develops a Rayleigh-Schrodinger perturbation theory applicable to multiconfigurational wave functions. This perturbation theory effectively approximates the direct diagonalization approach by constructing, for a chosen reference space, an appropriate zeroth-order Hamiltonian and associated perturbative potential. The simplified nature of the zeroth-order Hamiltonian leads to higher computational efficiency relative to direct diagonalization thus allowing for the correlation of larger systems. Most importantly, the convergence of the perturbation series is far superior to the traditional Hartree-Fock based perturbation theories when the Hartree-Fock reference is an inadequate zeroth-order approximation. This multiconfigurational perturbation theory is applied up to third-order to the determination of the potential surfaces of molecules with single and multiple bonds. In addition, the determination of energy differences between different molecular and atomic electronic states is studied. The use of a multiconfigurational reference wave function is shown to be essential in many cases for obtaining physically meaningful low-order corrections to the reference space