Ab initio calculation of the rotation–vibration energy levels of H3+ and its isotopomers to spectroscopic accuracy

Surfaces are fitted to the Born–Oppenheimer potential energy, electronic relativistic correction and adiabatic correction data calculated ab initio by Cencek et al. [J. Chem. Phys. 108, 2831 (1998)]. These surfaces are used in calculations of the rotation–vibration energy levels of ${\mathrm{H}}_{\mathrm{3}}^{\mathrm{+}},$ ${\mathrm{H}}_{\mathrm{2}}{\mathrm{D}}^{\mathrm{+}},$ ${\mathrm{D}}_{\mathrm{2}}{\mathrm{H}}^{\mathrm{+}},$ and ${\mathrm{D}}_{\mathrm{3}}^{\mathrm{+}}.$ Nonadiabatic corrections to the Born–Oppenheimer approximation are introduced following models developed for diatomics which involve the use of isotopomer independent scaled vibrational reduced masses. It is shown that for triatomics this approach leads to an extra term in the nuclear motion Hamiltonian. Our final calculations reproduce the known spectroscopic data for ${\mathrm{H}}_{\mathrm{3}}^{\mathrm{+}}$ and its isotopomers to within a few hundredths of a ${\mathrm{cm}}^{\mathrm{-1}}.$