With-Pair Relativistic Hamiltonians

Abstract

While the no-pair approximation widely used in relativistic quantum chemical calculations is good enough for most purposes, there is still a great need to go beyond it, not only for better accuracies but also for better understandings of relativistic quantum mechanics. It is shown here that, at variance with the usual top-down procedures for deriving relativistic Hamiltonians as approximations to quantum electrodynamics (QED), a with-pair relativistic many-electron Hamiltonian can be constructed in a bottom-up fashion without recourse to QED itself. It describes all virtual pair effects due to the instantaneous Coulomb/Gaunt/Breit interaction and is compatible with all wave function or density-functional-based correlation methods. As such, it serves as the basis for “with-pair relativistic quantum chemistry,” an extension of the traditional “no-pair relativistic quantum chemistry.” Due to the short range nature, the effective potential Q describing the electron vacuum polarization (EVP) and self-energy (ESE) can be fitted into a model operator and included in variational mean-field calculations. The major QED effects, including EVP and ESE, as well as the Coulomb/Gaunt/Breit screenings of them, can then readily be accounted for in subsequent treatments of electron correlation and properties.