Density Functional Calculations for Atomic Clusters

Abstract

The calculation of the adiabatic ground state energy ${\text{E}}\left[ {\{ \vec R_{\text{i}} \} } \right]$ of molecules, a long-standing problem in chemistry, is traditionally handled in one of two ways. Quantum chemists employ ab initio methods (meaning one or another brand of CI) which lead in principle to an exact solution of the many-electron wave-equation. Because the practical difficulties in achieving such a solution are formidable for all but the smallest systems, chemists over the years have developed empirical or semiempirical methods, such as extended-Hückel, which involves parameterization of a model Hamiltonian. These methods are not based on an attempt to solve the many-electron wave-equation, but rely on the transferability of chemical experience, i.e. the known behaviour of a given radical in a series of different environments is used to construct a model that can predict the behaviour of the same radical in a new environment. While this is an entirely legitimate scientific method giving useful results for very complex systems, it has obvious limitations. One might say that the two types of methods traditionally favoured by chemists are limited by placing either too much or too little emphasis on the many-electron wave-equation. This highlights the role that density functional methods might play in chemistry i.e. the many-electron problem is taken seriously, but not too seriously.