Date of Graduation


Document Type


Degree Name

Doctor of Philosophy in Physics (PhD)

Degree Level





William G. Harter

Committee Member

Daniel Kennefick

Second Committee Member

Peter Pulay

Third Committee Member

Gregory Salamo

Fourth Committee Member

Reeta Vyas


Using light to probe the structure of matter is as natural as opening our eyes. Modern physics and chemistry have turned this art into a rich science, measuring the delicate interactions possible at the molecular level.

Perhaps the most commonly used tool in computational spectroscopy is that of matrix diagonalization. While this is invaluable for calculating everything from molecular structure and energy levels to dipole moments and dynamics, the process of numerical diagonalization is an opaque one. This work applies symmetry and semi-classical techniques to elucidate numerical spectral analysis for high-symmetry molecules.

Semi-classical techniques, such as the Potential Energy Surfaces, have long been used to help understand molecular vibronic and rovibronic spectra and dynamics. This investigation focuses on newer semi-classical techniques that apply Rotational Energy Surfaces (RES) to rotational energy level clustering effects in high-symmetry molecules. Such clusters exist in rigid rotor molecules as well as deformable spherical tops. This study begins by using the simplicity of rigid symmetric top molecules to clarify the classical-quantum correspondence of RES semi-classical analysis and then extends it to a more precise and complete theory of modern high-resolution spectra.

RES analysis is extended to molecules having more complex and higher rank tensorial rotational and rovibrational Hamiltonians than were possible to understand before. Such molecules are shown to produce an extraordinary range of rotational level clusters, corresponding to a panoply of symmetries ranging from C4v to C2 and C1 (no symmetry) with a corresponding range of new angular momentum localization and J-tunneling effects.

Using RES topography analysis and the commutation duality relations between symmetry group operators in the lab-frame to those in the body-frame, it is shown how to better describe and catalog complex splittings found in rotational level clusters. Symmetry character analysis is generalized to give analytic eigensolutions. An appendix provides vibrational analogies.

For the first time, interactions between molecular vibrations (polyads) are de- scribed semi-classically by multiple RES. This is done for the ν3/2$nu;4 dyad of CF4. The nine-surface RES topology of the U(9)-dyad agrees with both computational and experimental work. A connection between this and a simpler U(2) example is detailed in an Appendix.