I. A Theoretical Investigation of the Charge Transfer Process in Alkali-Atom Alkali-Ion Collisions. II. Ab Initio Effective Potentials for Use in Molecular Calculations

Citation

Melius, Carl Frederick (1973) I. A Theoretical Investigation of the Charge Transfer Process in Alkali-Atom Alkali-Ion Collisions. II. Ab Initio Effective Potentials for Use in Molecular Calculations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/8YKN-Z171. https://resolver.caltech.edu/CaltechTHESIS:11202009-152551437

Abstract

PART I. The charge transfer processes occurring in collisions of alkali atoms with alkali ions have been studied theoretically using the molecular wavefunction approach. In Part A, we discuss the coupling process between electronic states as exemplified in collisions of Li + Na^+ and Na + Li^+. We find that the total transition process can be decomposed into a succession of simple two-state transition processes. The Σ-Σ two-state process can be described by a three-step process involving a coupling region, an uncoupled phase changing region, and a decoupling region. On the other hand, in the molecular wavefunction formulation, the Σ- II two-state transition involves a continuous coupling process. The resulting transition probabilities for Σ-II coupling differs from Σ- Σ coupling leading to different cross sections. In Part B, the molecular wavefunction approach is used to calculate the charge transfer cross sections of alkali-atoms and alkali-ions involving Li, Na, and K. PART II. We have investigated the method of effective potentials in replacing the core electrons in molecular calculations. The effective potential method has been formulated in a way which will simplify computations while preserving ab initio quality results. The effective potential is expressed in an analytic form which represents the actual ab initio non-local potential (as defined by the matrix elements for a given basis set). Furthermore, this analytic form permits efficient computations of the effective potential integrals by incorporating the properties of Gaussian basis functions. To minimize the number of basis functions required in the molecular calculations, we define a new ab initio effective potential derived from a modified IMF orbital whose core character has been removed. The effective potential method as formulated becomes a very strong but reliable tool in attempting calculations on very large molecules.

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