An ab initio model for handling the Renner-Teller effect in tetra-atomic molecules. I. Introduction of coordinates and the Hamiltonian

With the present paper we begin an extensive study of the Renner-Teller effect in linear and quasilinear tetra-atomic molecules. Although this topic has been the subject of considerable work carried out by the present authors and their colleagues, there are a number of critical points that have not been discussed profoundly enough, so that we feel it necessary to elucidate them in more detail. This particularly concerns the relationship between the Renner-Teller effect in tetra-atomic molecules and related coupling mechanisms appearing in triatomics, as well as avoided crossings, conical intersections and Jahn-Teller effect in nonlinear high-symmetry species. In the present paper we introduce various types of coordinates and derive general forms of the model bending Hamiltonian for molecules in Π, Δ, and Φ electronic states.