Vibrationally and rotationally nonadiabatic calculations on ${\mathrm{H}}_3{}^{+}$ using coordinate-dependent vibrational and rotational masses

Using the core-mass approach, we have generated a vibrational-mass surface for the triatomic ${\mathrm{H}}_3{}^{+}$. The coordinate-dependent masses account for the off-resonance nonadiabatic coupling and permit a very accurate determination of the rovibrational states using a single potential energy surface. The new, high-precision measurements of 12 rovibrational transitions in the ${\nu }_2$ bending fundamental of ${\mathrm{H}}_3{}^{+}$ by Wu et al. [Phys. Rev. A 88, 032507 (2013)] are used to scale this surface empirically and to derive state-dependent vibrational and rotational masses that reproduce the experimental transition energies to ${10}^{-3}{\mathrm{cm}}^{-1}$. Rotational term values for $J\le 10$ are presented for the two lowest vibrational states and equivalent transitions in D${}_3{}^{+}$ considered.

Figure 1

Visualization of the vibrational mass surface for configurations with the $C_{2v}$ symmetry. $r_1$ is the atom-diatom distance and $r_2$ is the diatomic distance.

Figure 2

Comparison of experimental ${\mathrm{D}}_3{}^{+}$ transition frequencies with calculated values obtained using different effective nuclear masses.