Accurate prediction of H${}_3$O${}^{+}$ and D${}_3$O${}^{+}$ sensitivity coefficients to probe a variable proton-to-electron mass ratio

Abstract

The mass sensitivity of the vibration-rotation-inversion transitions of H${}_3{}^{16}$O${}^{+}$, H${}_3{}^{18}$O${}^{+}$, and D${}_3{}^{16}$O${}^{+}$ is investigated variationally using the nuclear motion program TROVE~\citep{TROVE:2007}. The calculations utilize new high-level \textit{ab initio} potential energy and dipole moment surfaces. Along with the mass dependence, frequency data and Einstein A coefficients are computed for all transitions probed. Particular attention is paid to the $\Delta |k|=3$ and $\Delta |k-l|=3$ transitions comprising the accidentally coinciding $|J,K=0,v_2=0^{+}⟩$ and $|J,K=3,v_2=0^{-}⟩$ rotation-inversion energy levels. The newly computed probes exhibit sensitivities comparable to their ammonia and methanol counterparts, thus demonstrating their potential for testing the cosmological stability of the proton-to-electron mass ratio. The theoretical TROVE results are in close agreement with sensitivities obtained using the nonrigid and rigid inverter approximate models, confirming that the \textit{ab initio} theory used in the present study is adequate.