  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.
