Novel theoretical tools and applications for the study of electronic structure and optimizing reaction energetics

This thesis is comprised of two distinct areas: the first area representing the bulk of the work to be presented here, focusses on the development of novel analytical tools for the study of electronic structure. The second area highlights the refinement of potential energy surfaces algorithmically.;There is a great deal of interest in understanding electronic interactions within atoms and molecules. As we are confined to only 3-dimensions when visualizing a set of data, it is impossible to completely visualize the effects of particle interactions. Nonetheless, over the years, there have been numerous methods devised in order to analyze these interactions in different ways. In the first part of this thesis, the development of novel tools to examine electronic structure effects will be highlighted.;We introduce the intex density X (R, u), which combines both the intracular and extracular coordinates to yield a simultaneous probability density for the position of the centre-of-mass radius ( R) and relative separation (u) of electron pairs. The principle application of the intex density explored here is in the investigation of the recently observed secondary Coulomb hole. The Hartree-Fock (HF) intex densities for the helium atom and heliumlike ions are symmetric functions that may be used to prove the isomorphism 2P(2R) = E(R), where P( u) is the intracule density and E(R) is the extracule density. This is not true of the densities that have been constructed from explicitly correlated wave functions. The difference between these asymmetric functions and their symmetric HF counterparts produces a topologically rich intex correlation hole. We conclude that the probability of observing an electron pair with a very large interelectronic separation increases with the inclusion of correlation only when their centre-of-mass radius is close to half of their separation.;Despite providing more details regarding the correlation hole than the intracule alone, the intex density is still limited in nature by its lack of information regarding the spatial orientation of the R and u vectors. This led to the development of the probability density for the angle between these two vectors using both Hartree-Fock (HF) and explicitly correlated Kinoshita wave functions. This angular density, A(theta Ru), and the angular-dependent intex density, X (R, u, thetaRu), are explored for the helium isoelectronic series from He to Ne8+ to study the distribution of electron pairs in atomic systems (both HF and exact). We demonstrate that the most probable angle depends significantly on the scalar values of R and u for both the HF and exact treatments. As R and u simultaneously increase, the favoured angle for these densities approach 0 and pi.;With a more complete description and understanding of the secondary Coulomb hole, the focus of our study was directed towards determining the origin of the hole. These analyses were carried out by examining the correlation hole in intracules, DeltaP(u), for atoms with varying electron-nuclear potentials including systems with Coulombic potentials, harmonic potentials, and those with a zero potential (aside from an infinite confining potential). These studies have highlighted the role of a non-zero potential in the presence of the secondary hole and have suggested this counter-intuitive effect is the result of shielding. This theory is well supported by evidence in the literature including an analogous effect (i.e. contraction of electron pairs at large values of u) that has been observed for excited states and has been attributed to shielding.;In addition to these electronic structure analyses with respect to correlation, we also present findings regarding the effects of using polarization functions in basis sets to describe atoms and molecules. Previous research has indicated that the introduction of polarization functions into a basis set leads to an overall contraction of the intracule density. We examine this contraction of electron pairs through analysis of position intracules, various components of the energy, and differences in electron densities. This combined data has yielded conclusive evidence that the inclusion of polarization functions leads to an increase in density in the bonding regions in order to improve bond descriptions.;The second area explored in this thesis is regarding the development of novel software to be used for the optimization of chemical reactions. This optimization is based on a new method described herein, known as the linear combination of functional groups. In this process, a large set of substituents is superimposed at a functional site within a reactant complex. By allowing these substituents to interact with the fixed part of the molecule while prohibiting interactions between each of the functional groups, one can effectively determine the contribution of each moiety to the overall energy. Localized molecular orbitals are used in this study as they are highly transferable from molecule to the next. This allows for the construction of a library of coefficients specific for each functional group to determine the form of the molecular orbitals of said group that would be applicable in any chemical environment. Through the use of minimization/maximization algorithms one can optimize the energy difference between two states (e.g. products and reactants) with respect to each of these functional groups. The details of the method and the results of an optimization on the deprotonation of HO-X (X being the set of functional groups) is demonstrated herein. The results obtained in the proof-of-concept stage of this project demonstrate great merit for this concept.