Orbital Theories of Electronic Structure

Abstract

We show that in the Hartree—Fock approximation there exists a uniquely defined Hermitian potential which describes the interaction of a model subgroup of electrons with the rest of the system. This potential can be divided into two parts. The first part is the difference between the Hartree—Fock Hamiltonian for the system and the model Hamiltonian. The second part is a nonlocal potential which cancels (screens) some of the first part. The essential point in the derivation is our choice of definition for model orbitals in the system. The only condition that must be satisfied by the occupied orbitals of the system is that they be linearly independent. It is also shown that there exist equations describing the best orbitals to use in a calculation by a linear combination of atomic orbitals method. They are the best orbitals to use because they give the exact answer. As a concrete example of our ideas we have treated numerically the LiH molecule. In order to link our method with others that have been described we indicate how the pseudopotential form of the orthogonalized plane wave method may be derived.