Rovibrational energies of triatomic molecules by means of the Rayleigh-Schrodinger perturbation theory

A Rayleigh-Schrodinger perturbation theory approach based on the adiabatic (Born-Oppenheimer) separation of vibrational motions was previously develop ed and used to evaluate for a system of coupled oscillators the adiabatic e nergy levels and their nonadiabatic corrections. This method is applied her e to calculate rotation-vibration energies of the triatomic molecular ions HeH2- and ArNO+ consisting of a strongly bound diatomic fragment and a rela tively loosely bound rare gas atom. In these systems the high-frequency str etching motion of the diatomic fragment can be separated from the other two low-frequency motions without substantial loss of accuracy. Treating the d iatomic fragment as a rigid rotor, the low-frequency stretching motion is d ecoupled from the bending motion in analogy to the concept of the adiabatic (Born-Oppenheimer) separation of motions and the strong nonadiabatic coupl ings between these two motions are accounted for perturbationally. Although the resulting perturbation series may show poor convergence, they turn out to be accurately summable by applying standard techniques for the summatio n of divergent series. Comparison with the results obtained from full-dimen sional calculations for the two ions shows that the approach is capable of providing accurate energies for quite a few of the bound rotation-vibration states and that in the case of the HeH2+ ion it is even able to predict th e positions and widths of some low-lying resonance states with good accurac y. The perturbation approach yields zeroth-order energies and corrections i n terms of the relevant quantum numbers. It thus allows a direct assignment of the energy levels without any reference to the corresponding eigenfunct ions. The weak couplings between the high- and low-frequency motions can ea sily be treated by the same perturbative approach and numerically exact ene rgies can finally be obtained. (C) 2000 Academic Press.