  Heavy polar diatomic molecules are currently among the most promising probes
of fundamental physics. Constraining the electric dipole moment of the electron
(eEDM), in order to explore physics beyond the Standard Model, requires a
synergy of molecular experiment and theory. Recent advances in experiment in
this field have motivated us to implement a finite field coupled cluster
approach (FFCC). This work has distinct advantages over the theoretical methods
that we had used earlier in the analysis of eEDM searches. We used the
relativistic FFCC to calculate molecular properties of interest to eEDM
experiments, that is, the effective electric field (Eeff), and the permanent
electric dipole moment (PDM). We theoretically determine these quantities for
the alkaline earth monofluorides (AEMs), the mercury monohalides (HgX), and
PbF. The latter two systems, as well as BaF from the AEMs, are of interest to
eEDM searches. We also report the calculations of the properties using a
relativistic coupled cluster approach with single, double, and partial triples'
excitations, which is considered to be the gold standard of electronic
structure calculations. We also present a detailed error estimate, including
errors that stem from the choice of basis sets, and higher order correlation
effects.
