Two-by-two diabatic approach for multi-channel curve crossing problems

A practically useful method is proposed to deal with multi-channel curve crossing problems. This method deals with each crossing based on the relevant two coupled diabatic states and provides a corresponding transition matrix (I-matrix). The total reduced scattering matrix can be expressed by a product of these I-matrices. In this way, the present method can make full use of the advantages of the newly completed semiclassical theory for two-state curve crossing problems, and can treat the multi-state curve crossing problems as simply as the two-state case. Some numerical demonstrations within a three-state model are presented.