Self-consistent Field Orbital Methods

Abstract

This chapter discusses the concepts underlying the Hartree-Fock (HF) electronic structure method. First, it is shown how the energy expectation value is calculated for a Slater determinant (SD) wavefunction in the case of orthonormal orbitals. This leads to the definition of the electron repulsion integrals (ERIs). Next, the energy is minimized subject to the orthonormality constraints. This leads to the HF equation for the orbitals. The HF orbital energies are Langrange multipliers representing the constraints. An unknown set of orbitals can be determined from an initial guess via a self-consistent field (SCF) cycle. The HF scheme is discussed for closed-shell versus open shell systems, leading to the distinction between spin restricted and unrestricted HF (RHF, UHF). Kohn-Sham density functional theory (DFT) is introduced and its approximate version is placed in the context of ab-initio versus semi-empirical quantum chemistry methods.