Pseudo Jahn-Teller versus Renner-Teller effects in the instability of linear molecules

It is shown that for linear molecules in degenerate states the Renner-Teller effect (RTE) is not the only (and not even the main) source of bending instability; the pseudo Jahn-Teller effect (PJTE) is most important in the bending. Numerical estimates demonstrate that π-σ interactions with a limited number of excited states does not solve the problem. For a Π term with two perturbations a general formula of combined RTE plus PJTE is derived which does not involve excited states explicitly. It shows that the PJTE lowers the curvature of the energy surface in the direction of bending and contributes also to its splitting. By means of ab initio calculations the contributions of the RTE and PJTE to the bending instability are estimated for HBF, HNN, HCO, BH₂, NH₂, and AlH₂ molecules. The PJTE influence is significantly larger than the RTE one. This result may be similarly important for nonlinear systems.