The Self-Consistent Field Concept in Density Functional Theory

Abstract

One can certainly say that it has been chiefly through its diverse applications that energy density functional theory has gained acceptance in physics and quantum chemistry. Of course, it is not always easy to decide on the relative importance of a “pure” theory separated from its applications. In the present Chapter we try to illustrate this fact. Nevertheless, from a present-day perspective, one may interpret most developments in density functional theory, after its inception sixty years ago in the works of Thomas and Fermi, as a series of pragmatic attempts geared at attaining simplifications in the quantum-mechanical treatment of many-body systems. Of course, at the different stages of development, justifications have been advanced for the purpose of validating the nature of the approximations. But, de facto or adhoc approximations usually comply with the principle “Ancepts remedium melius quam nullum”. In a way, one cannot be oblivious to the fact that all approximations are tinged to a smaller or larger degree by pragmatical considerations which overshadow more theoretical ones. And for this reason it is easy to understand why from the very outset the “pure” theoretical component of energy density functional theory has lagged behind its “empirical” component.

“-Where does the police start,… and where does Benja finish? -The police finishes where Benja starts, -wise folk answered…”.

I. Babel, “As it was done in Odessa” (1923)