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/FASYZM58. https://resolver.caltech.edu/CaltechTHESIS:04212010085207566
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 secondorder optical properties and van der Waals coefficients. A basis set expansion technique is used and no continuumlike functions are included in the basis. However, unlike other methods we do not force the basis functions to satisfy any sumrule constraints but rather the formalism (RPA) is such that the Thomas ReicheKuhn 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 sumrules 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 SquareIntegrable 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 ThomasReichKuhn sum rule exactly and other energyweighted 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.
Item Type:  Thesis (Master's thesis) 

Subject Keywords:  Chemistry 
Degree Grantor:  California Institute of Technology 
Division:  Chemistry and Chemical Engineering 
Major Option:  Chemistry 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  30 January 1975 
Record Number:  CaltechTHESIS:04212010085207566 
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:04212010085207566 
DOI:  10.7907/FASYZM58 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  5725 
Collection:  CaltechTHESIS 
Deposited By:  Tony Diaz 
Deposited On:  17 Jun 2010 18:31 
Last Modified:  20 Dec 2019 19:43 
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