Variational incorporation of negative-energy orbitals in relativistic electronic structure calculations

Abstract

Significant effects of negative-energy orbitals in molecules with light atoms have recently been observed in calculations by perturbation theory from wave functions expressed in terms of positive-energy orbitals. We give a detailed discussion of how to incorporate, through a rigorous variational theorem, negative-energy orbitals in relativistic calculations of bound electronic states without any a priori knowledge of positive-energy orbitals, neither ad hoc potentials nor self-consistent-field (SCF) equations. The energy contribution of negative-energy orbitals, generally shown to be of positive sign, can be minimized by resorting to a minimax theorem or in other more practical ways, thus allowing large-scale configuration interaction (CI) with (+) orbitals obtained from correlated calculations, rather than from uncorrelated ones as in the conventional no-pair approach. General SCF equations are derived yielding positive-energy orbitals in the limit of the independent-particle model. The method is illustrated with relativistic CI calculations taken from the recent literature. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 461–470, 2000