Atoms and molecules in relativistic quantum mechanics

Abstract

Relativistic N-electron Hamiltonian can be written as a sum of the one electron Dirac Hamiltonians for an electron moving in the external field of nucleus, the Coulomb repulsion potential energy between electrons and the Breit operator representing the magnetic and retardation corrections to this interaction. Approximating many-electron wave function by a sum of anti- symmetrised products of orthonormal single particle spinors and using it as a trial function in a variational method leads to the Dirac-Fock equations for N-electron system. However the presence of a continuum of negative energy states below the bound states in the spectrum of Dirac Hamiltonian is a source of a several difficulties in atomic and molecular structure calculations: the Brown-Ravenhall disease, variational collapse and variational prolapse. Taking the boundary conditions properly into account, imposing the kinetic balance condition for small and large component basis sets, using correct strategy in developing basis sets and employing the finite nuclear size model results in the workable finite-difference and the basis-set methods of calculation for relativistic atomic and molecular structure.