Underlying theory of a model for the Renner-Teller effect in any-atomic linear molecules on example of the X 2Πu electronic state of C5−

In this study, we present the underlying theory of an extremely simple model for ab initio handling of the Renner-Teller effect in molecules with arbitrary number of nuclei and linear equilibrium geometry. A variational approach is developed for calculation of the vibronic spectra in Π electronic states. Particular attention is paid to the study of systematic crossings of the potential surfaces split upon bending vibrations, and the effect of them on the molecular geometry dependence, particularly on the magnitude of the non-adiabatic matrix elements. The model is tested on the example of the X 2Πu state of C5−. The results are compared with those generated in the corresponding perturbative calculations.