Density functional. Theory and application to atoms and molecules

The density functional theory is one of the most efficient and promising methods of quantum physics and chemistry. It is a theory of electronic structure formulated in terms of the electron density as the basic unknown function instead of the electron wave function. According to the fundamental theorems of Hohenberg and Kohn, the electron density carries all the information one might need to determine any property of the electron system. However, the way of obtaining it, is not at all trivial. In this report, the recent advances are summarized. After a review of the Hohenberg–Kohn theorems, the method of constrained search and the Kohn–Sham scheme, exact theorems, relations and inequalities are discussed. There are several important concepts of chemistry (e.g. electronegativity, hardness, softness) that have recently obtained a firm foundation in the density functional theory. The optimized potential method and the methods that generate the potential from the electron density are reviewed. The local and nonlocal approximate functionals are compared. Extensions of the ground-state density functional theory (excited states, time-dependent, relativistic and finite temperature) are summarized. A review of the applications to atoms and molecules is presented.