Relativistic self-consistent-field atomic calculationsusing a generalization of Brillouin's theorem

Abstract

When the one-body part of the relativistic Hamiltonian M is a sum of one-electron Dirac Hamiltonians, relativistic configuration interaction (CI) calculations are carried out on an ad hoc basis of positive-energy orbitals, t (=Ac2cc6, and more recently, with the full bases of positive-energy and negative-energy orbitals, t c (=Ac2cc6. The respective eigenproblems, + & =. & , &=1,2,..., E6 ,a nd+& =. & ; &=1,2,...,E26 are related through . $ . establishing a new variational principle for relativistic calculations of electronic structures. In this paper, on the basis of Brillouin's theorem and a relativistic multiconfiguration Hartree-Fock (RMCHF) expansion in the t c (=Ac2cc6 basis, we develop equations to annihilate the coefficients of all single excitations to obtain very accurate RMCHF solutions. Moreover, after nullifying the coefficients of single excitations, the above inequality among energies becomes an equality, leading to a particular instance of an exact decoupling of positive-energy and negative-energy orbitals, irrespective of any ad hoc choice of potentials, hence rigorously justifying, for the first time, the absence of explicit projection operators in all current relativistic work where one-electron Dirac Hamiltonians are involved. We present, also for the first time, relativistic Hartree-Fock approximations for the ground states of He through Ar, which are accurate to six decimals in a.u., and which converge to the nonrelativistic results when the speed of light S < . This accuracy was obtained by means of compact Slater-type orbital expansions through a direct translation of nonrelativistic Hartree-Fock without need to reoptimize nonlinear parameters. Our SCF equations are also valid for any open shells and for any excited states within a given symmetry, as exemplified with applications to odd-parity, a 'A *2, Ar 2r 2R ?R states of neutral nitrogen.