Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Randall W. Hall


Theoretical methods were used to study small sodium metal clusters. The goal was to find a simple way to model the electronic structure in these clusters that can be used to study large sodium clusters. Monte Carlo studies using Feynman's path integral formulation of quantum mechanics with Bose-Einstein statistics were used to study sodium metal clusters whose valence electrons with opposite spins were paired as bosons. Next, non-atom-based Gaussian s orbitals were used in a Hartree-Fock Monte Carlo procedure. Based on these results, standard quantum chemistry programs were used to test the utility of using non-atom-based basis sets made up of both s and p Gaussian functions to represent the valence electron density in sodium clusters. The Hartree-Fock Monte Carlo procedure was then modified to include Gaussian p functions in addition to the Gaussian s functions. Neutral and cationic clusters with three to six and eight atoms were studied to determine the geometries of the most stable isomers, the correlated energies, and the ionization potentials. Geometries were compared with published geometries and the ionization potentials were compared with experimental and theoretical ionization potentials. The small, non-atom-based basis set was found to be successful in modeling the electronic structure of small sodium metal clusters, and it is applicable to large sodium clusters and other metal systems.