Accurate prediction of H3O+ and D3O+ sensitivity coefficients to probe a variable proton-to-electron mass ratio

The mass sensitivity of the vibration-rotation-inversion transitions of H₃¹⁶O⁺, H₃¹⁸O⁺, and D₃¹⁶O⁺ is investigated variationally using the nuclear motion program TROVE (Yurchenko, Thiel & Jensen). The calculations utilize new high-level 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 Δ|k| = 3 and Δ|k - l| = 3 transitions comprising the accidentally coinciding |J, K = 0, v₂ = 0⁺> and |J, K = 3, v₂ = 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 non-rigid and rigid inverter approximate models, confirming that the ab initio theory used in the present study is adequate.