Catastrophe theory, symmetry breaking and the pseudo Jahn-Teller effect

Abstract

This research focuses on the structural symmetry breaking observed in hypovalent silicon containing compounds. The structural symmetry breaking was studied from the perspective of the pseudo Jahn-Teller effect (pJTE). A density functional theory (DFT) based approach to assessing the pJTE parameters was developed to provide a computationally cost-effective alternative to the post Hartree-Fock procedures typically employed. Additionally, elementary catastrophe theory models were applied to gain a deeper insight into cases where the description of electronic structure by multiple quantum chemical methods are incongruous with one another. The symmetry breaking of hypovalent silicon containing compounds was studied by examining Si-analogs of a series of a planar cyanocarbons: tetracyanoethylene (TCNE), tetracyanoquinodimethane (TCNQ), tetracyanodiphenoquinodimethane (TCNDQ) and tetracyanopyrenoquinodimethane (TCNP). Si-substitution generally resulted in structural symmetry breaking of both the neutral and anionic forms which enhanced their electron affinities. Moreover, Si-substitution was found to enhance the singlet and triplet diradical character of the π-conjugated systems. The choice of density functional was found to have an impact on whether or not the pJTE was observed. This was studied in further detail by evaluating the effect of exact exchange on the description of the adiabatic potential energy surfaces (APESs) of disilene and 2Si TCNQ using the cusp catastrophe model. Functionals containing high amounts of exact exchange were found not to display the symmetry breaking effect. The elliptic umbilic catastrophe was also applied to the study of the electronic structure of isothiirane. Furthermore, commonly used post analysis tools, the Quantum Theory of Atoms in Molecules and Natural Resonance Theory, were critically assessed. The results of this study resolved an open question in the literature regarding the description of the electronic structure of isothiirane. The pJTE parameters were evaluated using DFT by employing a model Hamiltonian that accounts for vibronic interactions. This model Hamiltonian was fit to cross-sections of the APES along the distorting mode. Best practices regarding the evaluation of pJTE parameters were also described. The procedure outlined in this thesis is applicable to the study of any pJTE problem where post Hartree-Fock methods are not feasible.