Vacuum polarization in molecules I: Uehling interaction

Radiative corrections to electronic structure are characterized by perturbative expansions in α and Zα, where α is the fine-structure constant and Z is the nuclear charge. A formulation of the leading-order α(Zα) Uehling contribution to the renormalized vacuum polarization is reported in a form that is convenient for implementation in computational studies of the relativistic electronic structures of molecules. Benchmark calculations based on these methods are reported that include the leading-order vacuum polarization effects within relativistic mean-field methods for the E119⁺ ion and the closed-shell diatomic species E119F.