Frozen local hole approximation

The frozen local hole approximation (FLHA) is an adiabatic approximation which is aimed to simplify the correlation calculations of valence and conduction bands of solids and polymers or, more generally, of the ionization potentials and electron affinities of any large system. Within this approximation correlated local hole states (CLHSs) are explicitly generated by correlating local Hartree-Fock (HF) hole states, i.e., (N-1)-particle determinants in which the electron has been removed from a local occupied orbital. The hole orbital and its occupancy are kept frozen during these correlation calculations, implying a rather stringent configuration selection. Effective Hamilton matrix elements are then evaluated with the above CLHSs; diagonalization finally yields the desired correlation corrections for the cationic hole states. We compare and analyze the results of the FLHA with the results of a full multireference configuration interaction with single and double excitations calculation for two prototype model systems, (H2)n ladders and H-(Be)n-H chains. Excellent numerical agreement between the two approaches is found. Comparing the FLHA with a full correlation treatment in the framework of quasidegenerate variational perturbation theory reveals that the leading contributions in the two approaches are identical. In the same way it could be shown that a much less demanding self-consistent field (SCF) calculation around a frozen local hole fully recovers, up to first order, all the leading single excitation contributions. Thus, both the FLHA and the above SCF approximation are well justified and provide a very promising and efficient alternative to fully correlated wave-function-based treatments of the valence and conduction bands in extended systems.