A local diabatic representation of non-Born–Oppenheimer dynamics

We propose a new canonical procedure for investigating non-Born–Oppenheimer dynamics. This procedure is based on Van Vleckʹs theory and expressed in the normal coordinates of one of the diabatically coupled electronic surfaces. Up to intermediate energies, the successive unitary transformations convert the smooth, non-resonant part of the energy shifts due to the diabatic coupling into anharmonicities and off-diagonal couplings inside each surface. As a result, in this energy range, the two transformed electronic surfaces remain fairly decoupled. We also show that, because of the reduced coupling range, the size of the matrix needed to calculate the exact energy levels is substantially reduced, which is promising for future practical applications.