Generalized quantum defect methods in quantum chemistry

Abstract

The reaction matrix of multichannel quantum defect theory, K, gives a complete picture of the electronic structure and the electron - nuclear dynamics for a molecule. The reaction matrix can be used to examine both bound states and free electron scattering properties of molecular systems, which are characterized by a Rydberg/scattering electron incident on an ionic-core. An ab initio computation of the reaction matrix for fixed molecular geometries is a substantive but important theoretical effort. In this thesis, a generalized quantum defect method is presented for determining the reaction matrix in a form which minimizes its energy dependence. This reaction matrix method is applied to the Rydberg electronic structure of Calcium monofluoride. The spectroscopic quantum defects for the ... states of CaF are computed using an effective one-electron calculation. Good agreement with the experimental values is obtained. The E-symmetry eigenquantum defects obtained from the CaF reaction matrix are found to have an energy dependence characteristic of a resonance. The analysis shows that the main features of the energy-dependent structure in the eigenphases are a consequence of a broad shape resonance in the 2E+ Rydberg series.

(cont.) This short-lived resonance is spread over the entire 2E+ Rydberg series and extends well into the ionization continuum. The effect of the shape resonance is manifested as a global "scarring" of the Rydberg spectrum, which is distinct from the more familiar local level-perturbations. This effect has been unnoticed in previous analyses. The quantum chemical foundation of the quantum defect method is established by a many-electron generalization of the reaction matrix calculation. Test results that validate the many-electron theory are presented for the quantum defects of the lsagnpo, E+ Rydberg series of the hydrogen molecule. It is possible that the reaction matrix calculations on CaF and H2 can pave the way for a novel type of quantum chemistry that aims to calculate the electronic structure over the entire bound-state region, as opposed to the current methods that focus on state by state calculations.