Density Functional Theory in the Context of Local-Scaling Transformations and Its Prospects for Applications in Catalysis

Abstract

One of the most promising alternatives for quantum mechanical calculations of atoms, molecules and condensed matter systems is provided, nowadays, by density functional theory. In what follows, we give a succint description of the state of knowledge in density functional theory [for thorough up-to-date revisions, see Jones and Gunnarsson (1989), Parr and Yang (1989) and Kryachko and Ludena (1990 )]. We start, by characterizing some of the difficulties present in the usual orbital methods for the purpose of illustrating afterwards how density functional theory can be used to surmount them. Subsequently, we deal with the Hohenberg-Kohn-based versions of density functional theory and discuss some of their basic problems, such as their non-N-representable character. These theories are then contrasted to the local-scaling transformation version of density functional theory. The latter provides a rigorous variational approach permitting the construction of N-representable energy density functionals which can be iteratively improved in order to yield strict upper bounds to the exact energy. In particular, from the perspective of this new theory, we discuss the local-scaling version of Kohn-Sham-type equations and also indicate how the correlation functional of Colle and Salvetti may be incorporated into the local-scaling scheme. In addition, we deal with some possible extensions of these theory for the treatment of nuclear motion. Finally, we consider the prospects of applying these new developments to catalytic systems containing transition-metal atoms.