Adiabatic-diabatic transformations for molecular systems: a model study of two interacting conical intersections

A model is presented for studying the interaction between two conical intersections (e.g. a dimer of two bound molecules each characterized by a conical intersection). The model is an extension of a previous model for a single conical intersection formed by an electron housed in a vibrating molecule (Baer M. and Englman, R., 1992, Molec. Phys., 75, 293). We distinguish between two situations: when the coupling is weak (for instance when it takes place in the asymptotic region) and when it is strong. The study is accomplished by calculating the adiabatic-diabatic transformation (ADT) matrix. Whereas the features of the ADT matrix for weak coupling seem reasonable (and to a certain extent expected), we find some unexpected features in the case of strong coupling. In particular, the two characteristic ADT angles of the uncoupled systems namely (phi(1)/2) and (phi(2)/2) are replaced by two new ADT angles, namely, (phi(1) + phi(2))/2 and (phi(1) - phi(2))/2. This implies that the corresponding nuclear wavefunctions, which originally were multi-valued, become single-valued in cases of strong interaction.