A Caltech Library Service

Applications of the Equations of Motion Method


Yeager, Danny Lee (1975) Applications of the Equations of Motion Method. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/xny7-ve74.


Part I

In Part I several applications of the equations of motion method for c1osed shell around states are discussed. The equations of motion method is used to study the excitation energies and intensities of formaldehyde, water, and CH+. A formalism is developed for studying intraexcited state transition densities, and applications are made to He and N2. This section is composed of three published manuscripts and two manuscripts submitted for publication.

In H2CO the calculated excitation energies and oscillator strengths agree well with experiment and suggest explanations for some unusual features recently observed in the optical absorption and electron scattering spectrum in the vacuum ultraviolet.

To explain the inelastic feature at 4.5 eV in the spectrum of water and to study its spectrum in some detail, several calculations on the excited states of water using the equations of motion method are made. We conclude that the calculated vertical excitation energy of 6.9 eV for the 3B1 state corresponds to the strong feature at 7.2 eV observed in low-energy electron scattering spectrum. The 4.5 eV inelastic process almost certainly does not correspond to a vertical excitation of water at the ground state geometry. The other excitation energies and oscillator strengths agree well with experiment.

The equations of motion method is used to study the X'Σ+ -A'π 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 with the best CI calculations to date.

An approximation for transition moments between excited states consistent with the approximations and assumptions normally used to obtain transition moments between the ground and excited states in the random phase approximation and its higher order approximations is derived . The result is applied to the calculation of the photoionization cross sections of the 23S and 2'S metastable states of helium by a numerical analytical continuation of the frequency dependent polarizability. The procedure completely avoids the need for continuum basis functions. The cross sections agree well with the results of other calculations. We also predict an accurate two-photon decay rate for the 2'S metastable state of helium. The entire procedure is immediately applicable to several problems involving photoionization of metastable states of molecules .

We report the transition moments between the excited states of molecular nitrogen including their dependence on internuclear distance. These moments are calculated non-empirically using a many-body approach --the equations of motion method. These results suggest that it may be simpler to calculate these transition moments and their variation with internuclear distance rather than to attempt to extract this information from available experimental intensity data.

Part II

A straightforward scheme is developed for extending the equations of motion formalism to systems with simple open shell ground states. Equations for open shell random phase approximation (RPA) are given for the cases of one electron outside of a closed shell in a nondegenerate molecular orbital and for the triplet ground state with two electrons outside of a closed shell in degenerate molecular orbitals. Application to other open shells and extension of the open shell EOM to higher orders are both straightforward. Results for the open shell RPA for lithium atom and oxygen molecule are given.

Part III

A simple method for directly calculating ionization potentials and electron affinities is discussed. Formulas are given through third order in interaction matrix elements and described in detail . Results are presented for the ionization potentials of He, N2, and OH- using several different approximations.

Item Type:Thesis (Dissertation (Ph.D.))
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):
  • McKoy, Basil Vincent
Thesis Committee:
  • McKoy, Basil Vincent
Defense Date:7 February 1975
Funding AgencyGrant Number
Record Number:CaltechTHESIS:02282022-185309824
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for Chapter I.A. adapted for Chapter I.B. adapted for Chapter I.C. adapted for Chapter I.D.
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14510
Deposited By: Benjamin Perez
Deposited On:01 Mar 2022 23:15
Last Modified:01 Mar 2022 23:17

Thesis Files

[img] PDF - Final Version
See Usage Policy.


Repository Staff Only: item control page