title: A second-quantization framework for the unified treatment of relativistic and nonrelativistic molecular perturbations by response theory.
abstract: A formalism is presented for the calculation of relativistic corrections to molecular electronic energies and properties. After a discussion of the Dirac and Breit equations and their first-order Foldy-Wouthuysen [Phys. Rev. 78, 29 (1950)] transformation, we construct a second-quantization electronic Hamiltonian, valid for all values of the fine-structure constant alpha. The resulting alpha-dependent Hamiltonian is then used to set up a perturbation theory in orders of alpha(2), using the general framework of time-independent response theory, in the same manner as for geometrical and magnetic perturbations. Explicit expressions are given to second order in alpha(2) for the Hartree-Fock model. However, since all relativistic considerations are contained in the alpha-dependent Hamiltonian operator rather than in the wave function, the same approach may be used for other wave-function models, following the general procedure of response theory. In particular, by constructing a variational Lagrangian using the alpha-dependent electronic Hamiltonian, relativistic corrections can be calculated for nonvariational methods as well.
authors.affiliation: Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway. trygve.helgaker@kjemi.uio.no
authors.forename: Trygve
authors.initials: T
authors.lastname: Helgaker
authors.forename: Alf Christian
authors.initials: AC
authors.lastname: Hennum
authors.forename: Wim
authors.initials: W
authors.lastname: Klopper