3 - Self-consistent Field Molecular Orbital Theory

Abstract

This chapter develops the Hartree–Fock (HF) self-consistent field (SCF) theory for closed-shell and open-shell molecules within the Born–Oppenheimer approximation and goes beyond to include the various post HF methods that take into account electron correlation effects in a more accurate manner. Starting with the molecular orbital theory as linear combination of atomic orbitals (LCAOs-MO) and the valence bond theory of chemical bonding, illustrated by examples of H2+ and H2, it goes on to develop the HF theory and Roothan formalism for SCF calculations on polyatomic molecules. Different types of atomic orbitals, particularly, the Slater and Gaussian types, and the corresponding basis sets used for HF calculations have been described. Shortcomings of HF method and the quality of their results have been discussed. This is followed by a detailed treatment of the perturbative and variational post-HF theories that include electron correlation to the multielectron wavefunction and help to include repulsions between electrons more accurately than in the HF method. The approaches discussed are configuration interaction method, Møller–Plesset perturbation theory, multiconfiguration SCF method including complete active space SCF, and coupled-cluster theory.