Semiclassical treatment of electronic transitions in molecular collisions: Collinear H++D2→HD++D

Abstract

A semiclassical treatment is presented for the dynamics of the collinear reaction H++D2→HD++D as occurring by transition from the ground to the first excited singlet electronic state of the HD2+ system. The potential energy surfaces corresponding to the two singlet states of the same symmetry have an avoided intersection for real values of nuclear coordinates, and the surfaces are analytically continued to the complex intersection. Complex-valued classical trajectories are integrated on the analytically continued surfaces, and an electronic transition is effected by a trajectory switching surfaces continuously at the complex intersection. From the complex action calculated along appropriate trajectories, the classical limit of S-matrix elements is calculated for transitions from the ground vibrational state of D2 to the ground and first excited vibrational states of HD+ for initial relative translational energies in the range 3–6 eV. These two vibrational states of HD+ differ in that the energy of the ground state lies below the asymptotic real intersection point of interest of the two surfaces while the first excited state lies above the real intersection point. Furthermore, transition points, which are points in time when a trajectory switches surfaces, occur close together in pairs for the transition to the ground vibrational state of HD+, whereas transition points are well separated for the transition to the first excited vibrational state of HD+. The differences of the transitions to these two vibrational states of HD+ result in different dynamical behavior of the trajectories leading to these transitions and require different expressions for the classical limit of the S-matrix elements.