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Implementation and Application of
Advanced Density Functionals

Michael Christopher Gibson

A thesis submitted for the degree of

Doctor of Philosophy


Department of Physics
University of Durham



Density functional theory (DFT) is a method of effectively solving the many-electron Schrödinger equation, enabling the properties of condensed matter systems to be calculated from first principles. With the commonly used local density approximation (LDA), and generalised gradient approximations (GGAs), to the exchange correlation functional, it is currently possible to perform calculations on systems containing several hundred atoms. The accuracy of such calculations depends on the system under study and on which particular properties one wishes to calculate. The use of more advanced functionals has the potential to improve accuracy, at the expense of greater computational demand. In this work we use the LDA to calculate certain properties of GaN, such as geometry, band structure, and surface properties, including the reconstruction of GaN surfaces under the presence of hydrogen. We then describe our computational implementation of advanced density functionals, including screened exchange (sX-LDA), Hartree-Fock (HF), and exact exchange (EXX), within an efficient, fully parallel, plane wave code. The implementation of sX-LDA and HF is used to calculate band structure properties of Si, GaN, and other simple semiconductors, and it is found that sX-LDA can improve results significantly beyond the LDA. We also derive and implement the theory that allows one to calculate directly the contribution to the stress tensor from exchange and correlation when using these functionals, and demonstrate this with some simple test cases. Finally, we introduce some new theoretical ideas that may pave the way for yet more accurate density functionals in the future.


The work presented here has contributed to the following publications:

The work presented here was undertaken within the Department of Physics at the University of Durham between August 2002 and August 2005. I confirm that no part of this work has previously been submitted for a degree at this or any other institution and, unless otherwise stated, it is the original work of the author.

Michael C. Gibson

May 2006

The copyright of this thesis rests with the author. No quotation, figure, or any other part of it should be published in any format, including electronic and the Internet, without his prior written consent. All information derived from this thesis must be acknowledged appropriately.


First and foremost I would like to thank my supervisor Stewart Clark for his help, advice, curry, and malt whisky over the past few years. Thanks also to my co-supervisor Stuart Brand, head of research group Richard Abram, and everyone else who has been involved with the Durham condensed matter theory group during my time here. In particular I would like to thank Ian Bolland for helping learn the basics of Linux when I arrived, Paul Tulip for his entertaining office rants, and Dom Jochym for some Linux-related tips that have proved very useful in writing this thesis. Outside of work I would like to thank my girlfriend and my family for their constant support and encouragement, without which the completion of this work would not have been possible.

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Stewart Clark 2012-08-09