Chapter 4 - The Generator Coordinate Hartree-Fock Formalism

Abstract

This chapter discusses the generator coordinate Hartree-Fock formalism. It was probably only a matter of time that somebody would extend the integral transform idea of Griffin, Hill, and Wheeler to the one-electron functions of the Hartree-Fock (HF) scheme. So, at the 1986 Sanibel Symposia in Florida, Mohallem, Dreizler, and Trsic presented the Griffin-Hill-Wheeler (GHW) version of the Hartree-Fock (GHWHF) equations. In this work, example applications were for the He and Be atoms; it is interesting that from the beginning, the authors emphasized the role of the weight function, which actually has characterized the applications of the GCM. In 1913, Bohr presented his solution for the hydrogen atom as one of the most important pillars of what we now call Old Quantum Theory. The energies calculated with the Bohr model coincide with the exact values as obtained from the Schrödinger equation presented some ten years later. Thus, since the Old Quantum Theory required several numerical adjustments to meet the criteria for the experiment, in 1925 Heisenberg presented the formalism of his Quantum Mechanics, which allowed the treatment of both intensities and frequencies of spectral lines of atomic systems.