[en] The nonadiabatic couplings which arise when two potential energy surfaces of a polyatomic molecule get close in energy can be classified as follows: (A) avoided crossings, (B) genuine intersections (Jahn-Teller and conical), (C) glancing intersections (Renner-Teller interactions). The characteristics of the potential energy surfaces in the adiabatic and diabatic representations
are discussed for each case. The three coupling cases differ in the structure of the Hamiltonian matrix. When the latter is written in the diabatic representation, it is meaningful to retain the leading term only in its power series expansion. This gives rise to a so-called minimum-order model which is found to be surprisingly accurate (at least in a restricted zone of nuclear coordinates) when compared to the results of ab initio calculations. The characteristic features of each coupling case can only be understood in a two-dimensional configuration space, Le., when two nuclear degrees of freedom, often with different symmetry properties, are explicitly considered. A simple expression of the nonadiabatic transition probability between two electronic states can be worked out in the framework of the minimum-order models. Two-dimensional extensions of the Landau-Zener formula are obtained, which can be used to study the consequences of the anisotropic properties of the coupling. In the case of avoided crossings, only nuclear trajectories having a well-defined direction are able to bring about surface hopping, wheras there exists two active degrees of freedom for conical intersections. Hence, nonadiabatic processes which are controlled by genuine intersections are expected to take place faster than those controlled by avoided crossings.
Fonds pour la formation à la Recherche dans l'Industrie et dans l'Agriculture (Communauté française de Belgique) - FRIA ; Fonds de la Recherche Fondamentale Collective d’Initiative des Chercheurs - FRFC ; Politique Scientifique Fédérale (Belgique) = Belgian Federal Science Policy