Prospects for an electron electric-dipole moment search in metastable ThO andThF+

The observation of an electron electric-dipole moment (EEDM) would have major ramifications for the standard model of physics. Polar molecules offer a near-ideal laboratory for such searches due to the large effective electric field $\left({\mathbf{F}}_{\mathrm{eff}}\right)$, on order of tens of GV/cm that can be easily oriented in the laboratory frame. We present an improved method for simply and accurately determining ${\mathbf{F}}_{\mathrm{eff}}$, in a heavy polar molecule, allowing for a quick determination of candidates for an EEDM experiment. We apply this method to ThO and $\mathrm{Th}{\mathrm{F}}^{+}$, both of which possess metastable ${}^3\Delta$ electronic states. The values of ${\mathbf{F}}_{\mathrm{eff}}$ in ThO and $\mathrm{Th}{\mathrm{F}}^{+}$ are estimated to be $104\mathrm{GV}∕\mathrm{cm}$ and $90\mathrm{GV}∕\mathrm{cm}$, respectively, making them two of the best known candidates for the EEDM search.