Model Hamiltonians and How to Determine their Parameters

Abstract

It is straightforward to write down the Hamiltonian for the electrons in molecules or solids within the Born-Oppenheimer approximation for the nuclei. Unfortunately the resulting electronic many-body problem is notoriously hard to solve. The idea of mean field theory has therefore very early been used in attempts to perform reasonable calculations for the properties of atoms and molecules.¹ In quantum chemistry a Hartree-Fock calculation is the usual starting point for configuration interaction (CI) calculations, which can yield very accurate results for small molecules. As this technique is not very well suited for solids, the Hohenberg-Kohn-Sham density functional theory (DFT) represented a major step forward.² These authors showed that the calculation of ground state properties can be formally exactly reduced to a problem of non-interacting electrons in an effective potential v_eff.