T. Thorsteinsson.
Ph.d. thesis, University of Liverpool, 250 pages (1995).

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Abstract

Apart from incidental involvement in optimisation of the spin-coupled wavefunction by the so-called super-cofactor approach, and development of pair population analysis, the work in this Ph.D. has taken the form of three major projects: valence bond interpretation of complete active space self-consistent field (CASSCF) wavefunctions, biorthogonal orbital optimisation, and calculation of inter-ionic potentials. These are all related to non-orthogonal orbital optimisation in particular, and non-orthogonal methods in general, and so a fair amount of introductory detail has been given to these subject areas in the context of the spin-coupled method.
A new highly efficient method for exact transformations of general CASSCF structure spaces has been developed, which may be of interest for other researchers in the field of multi-configuration orbital optimisation. In this work it has been used to obtain valence bond representations of ‘N in N’ CASSCF wavefunctions based on the form of the spin-coupled wavefunction. Four optimisation criteria (CASVB1-CASVB4) have been investigated that seek either to maximise the covalent component of the CASSCF wavefunction, or to minimise the energy of this component. The results have not only highlighted the striking similarities between the spin-coupled and CASSCF methods for most cases, but also suggested alternative descriptions in the cases of ozone and diborane.
A method for biorthogonal orbital optimisation based on the form of the spin-coupled wavefunction has been developed. A fully second-order treatment was found to be necessary to ensure satisfactory convergence, and such a scheme has been implemented. In this context, we appear to be the first to consider general optimisation of non-linear, non-symmetrical wavefunction parameters. The results show good agreement with those obtained from the variationally optimised spin-coupled wavefunction. At the very least this offers qualitatively correct results if the number of active electrons in the optimisation is larger than what may at present be treated using the spin-coupled method.
The advantages of valence bond approaches for the study of intermolecular forces have been recognised for some time. Such a scheme may be applied with only minor modifications to the problem of obtaining reliable potentials for modelling of ionic solids. The main difference lies in the realistic simulation of the crystalline environment, and this has also proven to be the main factor determining the accuracy of the potentials. Provided that a Madelung field of appropriate strength is applied very good agreement with existing potentials can be obtained. This suggests defining a suitable variable to be fitted to experimental data, or alternatively estimating the strength of the field in a simulation from the local surroundings of each individual ion. This will provide a consistent set of transferable potentials for the modelling of a variety of important systems and phenomena.