Analytic study of some excited state effects in a slightly bent Renner–Teller molecule

The two lowest electronic states (arising from X2Πu) are treated analytically with inclusion of excited state effects in a slightly bent Renner–Teller acetylene molecular ion. The aim is to explain the anomalous values of approximately π for the integrated non-adiabatic coupling term (NACT), recently obtained by ab initio calculations, as, e.g., in Halasz et al (2007 J. Chem. Phys. 126 154309). These occur when the molecular path twice coincides with symmetrically placed positions of degeneracies (conical intersections). However, the admixture of excited states into X2Πu removes these coincidences, creates two aligned conical intersections in a planar arrangement and perturbationally reduces the integrated NACT from its value of π.