Candidate molecular ions for an electron electric dipole moment experiment

This paper is a theoretical work in support of a newly proposed experiment [R. Stutz and E. Cornell, Bull. Am. Soc. Phys. 89, 76 (2004)] that promises greater sensitivity to measurements of the electron’s electric dipole moment (EDM) based on the trapping of molecular ions. Such an experiment requires the choice of a suitable molecule that is both experimentally feasible and possesses an expectation of a reasonable EDM signal. We find that the molecular ions $\mathrm{Pt}{\mathrm{H}}^{+}$ and $\mathrm{Hf}{\mathrm{H}}^{+}$ are both suitable candidates in their low-lying ${}^3\Delta$ states. In particular, we anticipate that the effective electric fields generated inside these molecules are approximately 73 and $-17\mathrm{GV}∕\mathrm{cm}$, respectively. As a byproduct of this discussion, we also explain how to make estimates of the size of the effective electric field acting in a molecule, using commercially available nonrelativistic molecular structure software.