VBSCF Methods: Classical Chemical Concepts and Beyond

The aim of this research has been to extend the ab initio Valence Bond Self-Consistent Field (VBSCF) methodology and to apply this method to the electronic structure of molecules. The valence bond method directly deals with the chemical structure of molecules in a pictorial language, which chemists are familiar with. One of the problems in this case is the manual generation of the structures where the spin-coupling patterns of the electrons correspond to the classical (Kekule valence) structures for polycyclic conjugated systems, which is cumbersome because the number of such structures grows very rapidly with the size of the system. A procedure has been developed which can generate these structures automatically using the geometry of the molecules. Further, it has also been shown that, for cyclic conjugated systems, the consideration of only Kekule valence structures in the VB wave functions already gives an excellent description of their electronic structure. Another methodological improvement that has been made in this work is on improving the convergence of the VBSCF wave function. A second-order converging VBSCF method has been developed in this thesis based on a Newton-Raphson scheme. The new method shows excellent convergence when the singly occupied orbitals do not mix with each other. When good starting orbitals are available, the same convergence behaviour has been found in the full optimisation. The convergence efficiency of the method has been compared with the Super-CI method. Finally, a combination of Super-CI and Newton-Raphson methods has been shown to be computationally more efficient than either the Super-CI or the Newton-Raphson method alone. In the combined method the first few iterations are performed with Super-CI until reasonably small orbital gradients or correction vectors, and then the final iterations are performed using the Newton-Raphson method. Finally, the VBSCF method has been applied to calculate the resonance energies of cyclic conjugated systems. The resonance energy of cyclic conjugated systems is considered as an important measure of their aromaticity. The effect of the choice of the orbitals on the calculated resonance energies has been explored. It has been shown that resonance energies calculated with the VB-delocal method are more reliable than those obtained from the VB-local method. Furthermore, the results for phenanthrene and anthracene show that the extra stability of the kinked benzenoid systems over their linear counterparts is a result of the larger resonance energies in the bent benzenoids. At last, the empirical parameters used in other semi-empirical VB methods and conjugated circuit theory have been quantified with the results of the VBSCF calculations on cyclic conjugated molecules.