A study of the geometrical phase effect on scattering processes: Validity of the extended-Longuet-Higgins formalism for a four-fold Jahn-Teller type model system

摘要

The Longuet-Higgins theorem has recently been extended to Jahn-Teller type electronic degeneracy manifolds of arbitrary dimension and suggested to obtain generalized Born-Oppenheimer equations including the geometrical phase effect [A.J.C. Varandas, Chem. Phys. Lett. 487 (2010) 139]. By replacing the traditional sign-change diagnostic of the adiabatic electronic wave vectors (upon adiabatic transportation in configuration space along a loop that encircles the point of degeneracy) with a sign-change criterion based upon their rotation by π in the N-dimensional electronic wave-vector space, it has been shown that only one pair of adiabatic electronic states changes sign upon encircling the degeneracy in configuration space. Here, we examine in detail the four-fold problem and report relevant dynamics studies. The results are compared with those obtained from the simple Born-Oppenheimer approximation (geometrical phase ignored) as well as two- and three-fold single-surface generalized Born-Oppenheimer equations. A rationalization is provided based on the symmetry-allowed reactive probabilities.