| Density functional theory can be used to define chemical concepts such as chemical potential and hardness. This dissertation begins with an overview of density functional theory. The results of three studies of hardness are then presented.; I. The hardnesses of diatomic molecules were determined on a contour of constant chemical potential. The analysis was prompted by previous findings that, for atoms, hardness correlates well with the difference in electrostatic potential between negative and positive ions on a certain contour. It was shown that diatomic molecules could also be investigated by generalizing this procedure. There is an unexplained discrepancy, however, of approximately a factor of 2 between theory (which works well for atoms) and the results obtained for diatomics.; II. A principle of maximum hardness was proven by others which related maximum hardness to minimum energy for electronic systems under the condition of constant chemical and external potential. Internal barrier energy calculations were carried out to test this hypothesis, and, although the conditions for the proof may not apply to experimental findings, the results do indicate that, in most cases, hardness and energy are related as required by the principle.; III. The Hammett equation provides quantitative information about chemical reactivity. Empirical relationships exist between reaction rates and variables representing electronic substituent effects. Hardness, in addition to being a measure of stability, also is a measure of chemical reactivity. Hammett-like relationships, therefore, were examined for hardness. Hardnesses of substituted molecules were plotted against the hardnesses of the molecules without the substituent attached. Linear relationships were found to exist in all cases, indicating that a Hammett-like equation for hardness does exist. |
