Density Functional Theory practical aspects

Kohl, H. and Dreizler, R.M. (1986). Time-dependent density-functional theory conceptual and practical aspects, Phys. Rev. Lett. 56, 1993-1995. 

The main purpose of this chapter is to present the basics of ab initio molecular dynamics, focusing on the practical aspects of the simulations, and in particular, on modeling chemical reactions. Although CP-MD is a general molecular dynamics scheme which potentially can be applied in combination with any electronic structure method, the Car-Parinello MD is usually implemented within the framework of density functional theory with plane-waves as the basis set. Such an approach is conceptually quite distant from the commonly applied static approaches of quantum-chemistry with atom-centered basis sets. Therefore, a main... 

Transition metal oxides are the systems which make a challenge to any quantum chemical theory. Thus their theoretical investigation constitute an excellent benchmark for Density Functional Theory in both aspects methodological and practical one. Two transition metal oxide molecules are considered here in detail, VO and MoO, with emphasis put on their electronic structure, spectroscopic properties and metal - oxygen bonding features. Applicability of DFT to various electronic states is discussed and the quality of results within various computational schemes is examined. 

In the next section, the different aspects and methods of ab initio quantum chemistry will be discussed. This will include a brief and incomplete discussion of the basics of solving a quantum-chemical problem, i. e. an electronic structure calculation. The practical calculation may proceed using either wave-function-based methods or density functional theory-based methods, and my focus will be on the latter as at the present time these methods are by far the most popular, giving the best accuracy for large systems in a limited amount of computer time. Different methods of analyzing the outcome of an ab initio calculation will also be discussed briefly. Finally, a development will be discussed which has become very important for modeling processes in condensed phases, namely the combination of electronic structure calculations (which are usually static and apply to a temperature of 0... 

An interesting approach to the quantum mechanical description of many-electron systems such as atoms, molecules, and solids is based on the idea that it should be possible to find a quantum theory that refers solely to observable quantities. Instead of relying on a wave function, such a theory should be based on the electron density. In this section, we introduce the basic concepts of this density functional theory (DFT) from fundamental relativistic principles. The equations that need to be solved within DFT are similar in structure to the SCF one-electron equations. For this reason, the focus here is on selected conceptual issues of relativistic DFT. From a practical and algorithmic point of view, most contemporary DFT variants can be considered as an improved model compared to the Hartree-Fock method, which is the reason why this section is very brief on solution and implementation aspects for the underlying one-electron equations. For elaborate accounts on nonrelativistic DFT that also address the many formal difficulties arising in the context of DFT, we therefore refer the reader to excellent monographs devoted to the subject [383-385]. 

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