Cluster Approaches to Solid State Problems: Necessary Complements to Band Structure Considerations

Abstract

Embedded clusters as models to study certain properties of real materials are defined as collections of atoms or ions at positions as they occur in solids and embedded in a (pseudo-) potential accounting for the short and long range, static and dynamic, influences of the rest of the material. The electronic structure is hence determined by the hamiltonian $$ H = {H^{N}}_{{cluster}} + {V_{{emb}}} $$ (1) where N indicates the number of electrons that are explicitly dealt with in the cluster chosen. The thus defined electronic problem can be treated by common ab initio or semi-empirical electronic structure methods and techniques, based on either wave functions or density functionals.