Self-consistent-field (SCF) and multiconfiguration (MC) Hartree-Fock (HF) methods in atomic calculations: Numerical integration approaches

Abstract

The self-consistent field (SCF) and multiconfiguration (MC) Hartree-Fock (HF) methods are reviewed. The emphasis is on the specification, design and implementation of these methods as a part of an atomic structure software package, dealing with wavefunction determination. Numerical integration approaches will be used throughout. After outlining a class of MCHF problems, the derivation of the MCHF equations is reviewed and some theory developed on the variation of the energy functional with respect to a rotation of the orbital basis among orbitals of the same symmetry. Various procedures are proposed and evaluated for dealing with cases where the radial basis for a given total energy is not unique. A numerical MC SCF procedure is described using a top-down approach. The overall algorithm will be outlined first with numerical details provided later. Finally some test cases are proposed.