A variational method for the calculation of spin-rovibronic levels of Renner-Teller triatomic molecules

Abstract

This paper reports an extension of our method, introduced several years ago, for the variational treatment of the rovibronic levels of Renner-Teller triatomic molecules. A more complete treatment now introduces the effect of electron spin. Thus new terms enter the Hamiltonian because (a) the total-angular-momentum operator is replaced by - Ľ - Š in the kinetic-energy operator, and (b) spin-orbit effects must be introduced. Here we include the latter through a semi-empirical form AĽ · Š . Expansion functions having the correct symmetry (Σ_g ⁺, Σ_u ⁺, Σ_g ^-, Σ_u ^-), for D_∞h molecules are derived. Hence the present approach takes into account the full dimensionality, anharmonicity and rotation-vibration coupling, as well as the coupling of all relevant angular momenta. This is particularly important for open-shell molecules and/or for electronically degenerate states. For the ²Π_g electronic ground state of the CO₂ ⁺ ion the spin-rotation and spin-orbit split Renner-Teller levels have been calculated using three-dimensional electronic potential-energy functions, for both Renner-Teller surfaces, derived from ab initio computation. The fundamental frequencies are in very good agreement with the available experimental data. In particular, the low antisymmetric stretch frequency and its negative anharmonicity are reproduced. Previously it had been postulated that this anharmonicity was due to a vibronic coupling between the ²Π_g and à ²Π_u states; these calculations, however, show that it arises naturally from accurate representations of the adiabatic surfaces.