The Basic Machinery of Density Functional Programs
The preceding six chapters provided an overview of the theoretical background and current state of the art of modern approximate density functional theory. We now turn to the more practical problem of how the strategies developed so far can be mapped onto computational schemes. To this end, we first introduce the linear-combination-of-atomic-orbitals (LCAO) ansatz, which is the by far most dominant way to make the iterative self-consistent field procedure for solving the one-electron Kohn-Sham equations computationally accessible. This leads immediately to the problem of which kinds of basis sets are suitable in order to expand the Kohn-Sham orbitals in such calculations and according to which criteria one should choose a particular set of basis functions. One of the main questions in this context is, to what extent one can benefit from the vast experience regarding basis sets accumulated in wave function based techniques. Schemes for how the various components appearing in the KS equations are actually determined are discussed with particular emphasis on how the Coulomb energy can be approached. We also give a survey of the techniques employed for the numerical integration of the exchange-correlation potential including grid-free approaches, which circumvent the ubiquitous problems with numerical noise in the gridbased numerical integration. Finally, we will review the development of new algorithms that aim at a linear scaling of the computing time with respect to the size of the molecule which will allow the application of these methods to very large molecules occurring, for example, in biochemistry or material science.