Chapter 7 Post Dirac-Hartree-Fock methods—properties

Abstract

Abstract This chapter first gives a general introduction to the theory of molecular properties, primarily in terms of (quasi)energy derivatives, valid for time-dependent as well as static perturbations and for both variational and non-variational wave functions. Alternative definitions based on perturbation expansions of expectation values or with recourse to propagator theory is discussed as well. Perturbations are primary external fields, and a whole section is accordingly devoted to a careful review of electromagnetic interactions, with particular emphasis on the proper non-relativistic limit. It is suggested that all effects of retardation and magnetic interaction constitute relativistic effects. Magnetic and electric multipoles are derived using multipolar gauge. A third section discusses the form and characteristics of perturbation operators in the relativistic as well as non-relativistic domain. In the next section the theory of linear and quadratic response functions at the 4-component relativistic Hartree-Fock level is derived and further approximations related to the description of excitation energies discussed. In closing I outline difficulties associated with the use of quasirelativistic or even non-relativistic wave functions as starting point for the calculation of molecular properties with inclusion of relativistic effects.