Vacuum polarization in molecules I: Uehling interaction

TL;DR

This paper presents a computationally convenient formulation for the leading-order vacuum polarization correction, specifically the Uehling interaction, in molecules, enabling more accurate relativistic electronic structure calculations.

Contribution

It introduces a new formulation for the Uehling interaction that facilitates implementation in molecular electronic structure computations.

Findings

Benchmark calculations for E119$^+$ and E119F demonstrate the method's effectiveness.

The approach accurately captures leading-order vacuum polarization effects.

Results improve the precision of relativistic molecular electronic structure models.

Abstract

Radiative corrections to electronic structure are characterized by perturbative expansions in $\alpha$ and $Z\alpha$, where $\alpha$ is the fine-structure constant and $Z$ is the nuclear charge. A formulation of the leading-order $\alpha(Z\alpha)$ 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.