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. Within this approximation correlated local hole states (CLHSs) are explicitely generated by correlating local Hartree-Fock (HF) hole states. The hole orbital and its occupancy is kept frozen during these correlation calculations. 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 MRCI(SD) (multi-reference 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 quasi-degenerate variational perturbation theory reveals that the leading contributions in the two approaches are identical. Thus, the FLHA is well-justified and provides a very promising and efficient alternative to fully correlated wavefunction-based treatments of the valence and conduction bands in extended systems. 
Elke Pahl and Uwe Birkenheuer