Modern methods of electronic structure calculations

Abstract

In this Chapter we shall consider methods that are currently widely used for calculating the electronic structure of solids. Essentially, there are two groups of methods. The methods of the first group are built upon the Hartree-Fock (HF) theory and have historically been developed by theoretical chemists, while the methods of the second group are based on the Density Functional Theory (DFT) and have been mainly developed by solid state physicists. We shall consider the main ideas of both these theories for several reasons. First of all, there is the fundamental reason that it is impossible to understand the DFT without the HF theory; after all, such notions as the exchange interaction and the correlation energy arise in the latter in the first place. Secondly, if the situation some 5–10 years ago was that physicists used mainly the DFT-based methods, today the application of methods developed by chemists for solving physical problems has substantially increased. Thus there are strong benefits in familiarising solid state physicists with the HF-based techniques as well. On the other hand, chemists have been increasingly using the DFT based methods, so that both techniques should be discussed, in order to benefit young researches from both communities.