Studies of atomic and molecular processes and properties in the random phase approximation

Citation

Martin, Patrick H. S. (1975) Studies of atomic and molecular processes and properties in the random phase approximation. Master's thesis, California Institute of Technology. doi:10.7907/FASY-ZM58. https://resolver.caltech.edu/CaltechTHESIS:04212010-085207566

Abstract

Part I - Dipole Properties of Atoms and Molecules in the Random Phase Approximation: A random phase approximation (RPA) calculation and a direct sum over states is used to calculate second-order optical properties and van der Waals coefficients. A basis set expansion technique is used and no continuum-like functions are included in the basis. However, unlike other methods we do not force the basis functions to satisfy any sum-rule constraints but rather the formalism (RPA) is such that the Thomas Reiche-Kuhn sum rule is satisfied exactly. Central attention is paid to the dynamic polarizability from which most of the other properties are derived. Application is made to helium and molecular hydrogen. In addition to the polarizability and van der Waals coefficients, results are given for the molecular anisotropy of H_2, Rayleigh scattering cross sections and Verdet constants as a function of frequency. Agreement with experiment and other theories is good. Other energy weighted sum-rules are calculated and compare very well with previous estimates. The practicality of our method suggests its applications to larger molecular systems and other properties. Part II - Photoionization Cross Sections for H_2 in the Random Phase Approximation with a Square-Integrable Basis: Total photoionization cross sections for H_2 are calculated in the Random Phase Approximation (RPA) through a numerical analytic continuation procedure applied to the polarizability for complex valuesof the frequency. The representation of the polarizability that is required is obtained from a discrete set of excitation energies and oscillator strengths that satisfies the Thomas-Reich-Kuhn sum rule exactly and other energy-weighted sum rules approximately. The fact that the excitation spectrum is obtained through a solution of the RPA equations with no continuum functions added to the basis makes the method well suited for general molecular photoionization calculations. The results are compared with experiment and good agreement is found. Part III - Oscillator Strengths for the X^1∑^+ - A^1π System in CH^+ from the Equations of Motion Method: The equations of motion method is used to study the X^1∑^+ - A^1π system in CH^+. In a computationally simple scheme, these calculations, which were done in modest sized basis sets, provide transition moments and oscillator strengths that agree well with the best CI calculations to date.

Thesis Files