Properties and applications of the average interparticle distance

Hollett, Joshua W. (2009) Properties and applications of the average interparticle distance. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

The first and second moment operators are used to define the origin invariant shape and size of a molecule or functional group, as well as expressions for the distance between two electrons and the distance between an electron and a nucleus. The measure of molecular size correlates quite well with an existing theoretical measure of molecular volume calculated from isodensity contours. Also, the measure of size is effective in predicting steric effects of substituents which have been measured experimentally. The electron-electron and electron-nuclear distances are related to components of the Hartree-Fock energy. The average distance between two electrons models the Coulomb energy quite well, especially in the case of localized molecular orbitals. The average distance between an electron and a nucleus is closely related to the electron-nuclear attraction energy of a molecule. -- The relationships discovered between the average interparticle distances and molecular energy components have led to the development of a new empirical approach to modelling the electronic structure of molecules. The general energy expression for a simulated electronic structure theory is defined, along with the functional form of the interatomic distance dependent energy functions. The theory is used to model the hydrogen molecule, the first-row hydrides, and ethane. The models, which have the correct RHF/6-31G(d) optimized geometries, also fit the RHF/6-31G(d) energy at equilibrium and the UHF/6-31G(d) energy at the bond dissociation limit, as well as some vibrational frequencies. -- Also directly related to the interelectronic distance, is the issue of electron correlation. Several new approaches to the electron correlation problem have emerged in recent years. Among the new methods is orbital functional theory, in which the correlation energy is a functional of the molecular orbitals. The correlation energy of different isoelectronic series as a function of nuclear charge is investigated in an effort to design a correlation operator. Insight is also gained by examining the explicit CISD energy expression.

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