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Title: On Total Energy Calculations for Electronic Systems
Author: Silva Carneiro, Nuno Filipe da
Awarding Body: University of York
Current Institution: University of York
Date of Award: 2007
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The accurate calculation of the total energy, ET of an electronic system, using as our starting point simply the properties of the interactions between the particles that constitute such a system, is a source of immense power. With it we can understand and control, properties of materials, chemical and biological processes. The problem is complex; approximations must be introduced. There exist two main families of methods. One tries to follow the theory that describes these interactions:. Many Body Perturbation Theory (MBPT). The other usesĀ· a different formulation, based on the electronic density, Density Functional Theory, (DFT) and a new technique: Kohn-Sham scheme. The first is numerically expensive and can't be used for most systems. The second is simple, but lacks accuracy. We introduce a third way, based on a generalised Kohn-Sham (GKS) scheme, which retains some of the simplicity of the standard Kohn-Sham scheme, but being more flexible, allows the use of non-local potentials and orbital-dependent quantities. We realised this meant the Kohn-Sham scheme was now able to process concepts from MBPT; this last theory is based on non-local quantities like the self-energy. operator, ~, and the Green's function, G, which, if we ignore frequency dependence in the self-energy operator, can be represented by the one-particle orbitals. We produced models for screened interaction, W, and ~ and calculated ET for different systems. Results showed the strong points and weaknesses of these models. With this experience we introduce a new method, based on a frequency-dependent W, and theGW approximation to obtain a model ~. This final model, gave excellent results for homogeneous systems, and promising results for inhomogeneous systems; the way to proceed and the remaining tests that need to be done, are also mentioned.
Supervisor: Not available Sponsor: Not available
Qualification Name: Not available Qualification Level: Doctoral
EThOS ID:  DOI: Not available