Chapter 2 - The Generator Coordinate Method

Abstract

This chapter describes the coordinating method of the generator. The Hartree-Fock theory at its limit may provide about 98% of the energy of an atom or molecule. Several alternatives are available if the endeavour to recover the missing portion of energy (correlation energy), such as much body perturbation theory (MBPT), density functional theory (DFT), and the variational configuration interaction (CI) method, often at the cost of nontrivial computational efforts continues. The generator coordinate method (GCM) introduces an integral transform capable, in principle of finding the best functional form for a given trial function through the Griffin-Hill-Wheeler (GHW) integral equation. The GCM was introduced in the field of Nuclear Physics. The proposition of Wheeler and collaborators was one of the first attempts to incorporate collective and single-particle nuclear motions into a single coherent quantum-mechanical formulation. Physics and chemistry have been interacting and feeding each other with questions and answers for centuries. However, the speed of interpenetration is variable. The analytical solution of the GHW equation for many electron atoms and molecules (or many particle systems in general) is beyond present mathematical capabilities. Thus most applications have relied on either approximations, which is the case for nuclei, or discretization techniques, as in the case of atoms and molecules.