Relativistic linear combination of Gaussian-type orbitale density functional method based on a two-component formalism with external field projectors

A two-component scalar relativistic method which is based on the no-pair projection operator formalism of quantum electrodynamics has been studied within the framework of local density functional theory. This projection operator formalism, first proposed by Sucher for wave function based methods, provides a stable approach to the relativistic electronic structure problem without the well-known deficiencies of some variational procedures for the Dirac equation. Several approximations of increasing accuracy have been investigated. Besides the method based on free-particle projectors and on external field projectors for the singular nuclear potential, projectors on the full electronic potential are presented here for the first time. Atomic all-electron calculations within this framework give excellent results compared to a fully numerical solution of a scalar relativistic approximation to the corresponding one-particle Dirac problem. Calculations for cerium and for lead are analyzed in detail. About 96% of the relativistic shift of the one-electron energies and about 98% of the relativistic effect on the total energy are covered within this method. The method allows for a rather straightforward generalization to molecular systems with multinuclear potentials.