Vacuum polarization in molecules II: higher order corrections

We outline a general formalism for treating vacuum polarization phenomena within an effective field expansion. The coupling between source charges and virtual fields is examined from the perspectives of electrostatic potentials, induced charge densities and form factors in momentum space. A strategy for the efficient calculation of vacuum polarization potentials is outlined, implemented, and applied towards the construction of fitting potentials that are suitable for molecular electronic structure calculations, which enclose no overall charge by construction. The order $\alpha(Z \alpha)$, $\alpha (Z \alpha)^{3}$ and $\alpha^{2}(Z\alpha)$ effects of a Gaussian nuclear charge on the electron-positron field are applied variationally towards the E119F molecule, as well as the order $\alpha(Z \alpha)$ effects arising from the virtual muon and charged pion fields.