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Research
Note added 2006-10-15: Please note: this page is currently outdated.
My research is directed towards the development of more accurate approximations of the exchange-correlation energy functional in density functional theory. Density functional theory based calculations are a vital part of theoretical investigations in for example materials physics and quantum chemistry. The exchange-correlation functional is the limiting factor in the accuracy of such calculations. A long term goal is to get chemical accuracy using generic methods. This would open up new areas of application, as more automatized optimizations of materials and reactions can be realized.
Background: density functional theory and functional development
Density functional theory (DFT) is a formulation of quantum mechanics that utilizes a view of the particles known as electrons as a compound sea, focusing on the density of electrons as a fundamental property. This is opposed to so called wave-functional approaches that keep track of all individual electrons. The gain of DFT over the wave-functional approaches is that the density of electrons is a three-dimensional property, whereas the wave-function used to keep track of the electrons is of a dimensionality proportional to the number of electrons in the system (which usually is very large).
When the DFT formulation is transformed into a form suitable for computer calculations, the most difficult quantum mechanical behavior of the sea of electrons is put into the exchange-correlation energy functional. This is usually a part of minor size, but it is the only part that has to be approximated relative to an explicit wave-functional solution. Several approximations suitable for computer calculations have been developed, but there is a demand for even more accurate ones. The figure to the right illustrates LDA, the first approximation that was put forward.
Suggested reading:
- In Pursuit of the "Divine" Functional. A brief non-mathematical introduction to density functional theory and the development of better "functionals", Science 298, 759 (25 October 2002). This article was written by my research supervisor, Ann Mattsson, and the full text is also available from her publication list.
- 'Background' part of my PhD thesis. Available as pdf.
Subsystem functionals
Our idea is that a system can be split into several regions, and in each region different functionals can be used. Each such functional could then be specifically designed for the part of the system it is applied to. The aim is a better approximation of the total exchange-correlation energy.
Suggested reading:
- 'Scientific Contribution' part of my PhD thesis. Available as pdf.
- Subsystem functionals: Investigating the exchange energy per particle. PRB 66 165117 (2002). Reprint in pdf.
- Functional designed to include surface effects in self-consistent density functional theory. PRB 72 085108 (2005). Reprint in pdf.
Systems with electronic edges
The work on subsystem functionals described above is based on ideas presented in earlier work on how to treat systems with electronic edges.
Suggested reading:
- Edge electron gas, W. Kohn, A. E. Mattsson, PRB 81 3487 (1998). Also available in pdf format from Ann Mattssons publication list.
- Chapter 3 and 4 of my graduation thesis for the degree of Master of Science. Available as pdf.