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Title: New approaches to calculating the electronic structure of small molecules
Author: Case, David
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 2012
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Post Hartree-Fock methods provide a well tested and theoretically sound route to the determination of the electronic wavefunction. The problem is that the computational expense of calculating the required amplitudes of the determinants that make up the wavefunction grows quickly with respect to the size of the system. Specifically, if a wavefunction contains n excitations from the HF reference determinant, then the cost of solving the associated equations scales as JV2n+2 where JV relates to the number of orbitals. The jump from a doubles wavefunction (cost JV6) to one with triply excited determinants (carrying a cost of JVS) is too great to be made in most applications, yet this extra effort would make a considerable difference when the required accuracy in energy is of the order of a few kJ mol-I. If these wavefunctions are used to predict static properties, or integrated into dynamics simulations, then they must be accurate in a variety of chemical environments. Theories must perform robustly in their treatment of pairs of electrons whether they are in different kinds of chemical bond or lone pairs on an atom. They must predict reaction energies with reliability as well as maintain performance when describing transition states or stretched bonds. There are also artifacts which arise from mathematical constraints on the method such as size-extensivity and orbital-invariance. New approaches tested in this thesis are compared to standards with all of this in mind. There are two methods which are developed in this text. Neither exceeds the JV6 scaling which is common to doubles theories, and both draw some of their ideas from older theories in physics. The first is the random phase approximation (RPA) and is presented after an analysis of coupled cluster doubles theory based on intracules. The intracule is a probability density function relating to electrons separated by a particular distance. The RPA has found itself the subject of renewed interest of late and this intracule analysis provides insight behind the method's successes and failures in different situations. A method involving a scaling parameter is presented and analysed. The method was found to perform well in many systems but was found to systematically overestimate bond strengths. The second method is based on work from classical fluid theory. Ornstein and Zernike formulated an equation that relates the total correlation function.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available