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Title: Aspects of density functional theory
Author: Chan, G. K.-L.
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2000
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The first part of our work, we describe investigations into the formal and conceptual aspects of density functional theory. These have been in four main areas. The first, is the theory of the derivative discontinuity, where we extended the theory to density matrix functionals, and carried out calculations of the effects of the discontinuity. Our second investigation concerned a new channel concept, namely, the shape and local chemical potentials. These describe the electron donating or accepting power of a density fragment. We demonstrated in simple model systems, that chemical features such as shell structure, or atoms in molecules, could be characterised as regions of constant shape chemical potential. Our third investigation concerned the homogeneous scaling of the Kohn-Sham kinetic energy. We disproved certain existing relations in the literature; we then went on to derive simple bounds on the kinetic energy, and to numerically calculate the approximate scaling of the kinetic energy in atomic systems. Our fourth investigation concerned an improved Lieb-Oxford bound for the exchange-correlation energy. By improving the numerical optimisation in the last part of the proof, we were able to tighten the bound. The second part of our work focused on the search for new energy functionals, and procedures for developing new functionals. Our efforts have been in two areas. The first was an investigation of the correlation functional of Hartree-Fock-Kohn-Sham theory. We observed the deficiencies of current functionals in the reproduction of the correlation potential, and attempted to correct this by fitting a functional to best reproduce numerical correlation potentials. In doing so, we observed the highly non-local nature of correlation in Hartree-Fock-Kohn-Sham theory, and the important effect of the derivative discontinuity on the energy. The second investigation attempted an exhaustive study of the Generalised Gradient Approximation (GCA), within a well-defined ab initio model. We developed a rigorous fitting methodology, and constructed well-converged fits to conclusively explore the limits of the accuracy of the GCA. A large number of observations were made concerning the choice of functional basis, the importance of additional gradient corrections, and the role of exact exchange. We also applied our fitting methodology to the construction of approximate Kohn-Sham kinetic energy functionals, with some success.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available