Modelling non-adiabatic effects in H₃⁺: solution of the rovibrational Schrödinger equation with motion-dependent masses and mass surfaces.

Introducing different rotational and vibrational masses in the nuclear-motion Hamiltonian is a simple phenomenological way to model rovibrational non-adiabaticity. It is shown on the example of the molecular ion H3(+), for which a global adiabatic potential energy surface accurate to better than 0.1 cm(-1) exists [M. Pavanello, L. Adamowicz, A. Alijah, N. F. Zobov, I. I. Mizus, O. L. Polyansky, J. Tennyson, T. Szidarovszky, A. G. Császár, M. Berg et al., Phys. Rev. Lett. 108, 023002 (2012)], that the motion-dependent mass concept yields much more accurate rovibrational energy levels but, unusually, the results are dependent upon the choice of the embedding of the molecule-fixed frame. Correct degeneracies and an improved agreement with experimental data are obtained if an Eckart embedding corresponding to a reference structure of D(3h) point-group symmetry is employed. The vibrational mass of the proton in H3(+) is optimized by minimizing the root-mean-square (rms) deviation between the computed and recent high-accuracy experimental transitions. The best vibrational mass obtained is larger than the nuclear mass of the proton by approximately one third of an electron mass, m(opt,p)((v))=m(nuc,p)+0.31224m(e). This optimized vibrational mass, along with a nuclear rotational mass, reduces the rms deviation of the experimental and computed rovibrational transitions by an order of magnitude. Finally, it is shown that an extension of the algorithm allowing the use of motion-dependent masses can deal with coordinate-dependent mass surfaces in the rovibrational Hamiltonian, as well.