Chapter 7 - The Generator Coordinate Dirac-Fock Method and Relativistic Calculations for Atoms and Molecules

Abstract

This chapter discusses the generator coordinator Dicra-Fock Method and Relativistic Calculations for Atoms and Molecules. There has been a great interest in using Gaussian-type functions (GTFs) as basis set for relativistic calculations. It has been emphasized that the imposition of finite nuclear boundary conditions for solutions of the Dirac-Fock (DF) equations results in a solution that is Gaussian at the origin. Therefore, the GTFs of integer power of r are appropriate basis functions for the finite nuclear model. The GTFs that satisfy the boundary conditions for the finite nucleus automatically satisfy the condition of the so-called kinetic balance for a finite speed of light. The idea of Matsuoka and Huzinaga of employing GTFs exponents was extremely practical, but the idea of generating GTFs exponents in the DF environment could not be forsaken. Other than the applications that are presented in the chapter with the generator coordinate Dirac-Fock and the polynomial version of the generator coordinate Dirac-Fock methods for Dirac-Fock-Coulomb (DFC), and Dirac–Fock–Breit (DFB) calculations. There are other applications with the relativistic generator coordinate formalism in atomic and molecular DFC and DFB calculations.