Superadiabatic Transitions in Quantum Molecular Dynamics

We study the dynamics of a molecule’s nuclear wave-function near an avoided crossing of two electronic energy levels, for one nuclear degree of freedom. We derive the general form of the Schrödinger equation in the n-th superadiabatic representation for all n ∈ N. Using these results, we obtain closed formulas for the time development of the component of the wave function in an initially unoccupied energy subspace, when a wave packet travels through the transition region. In the optimal superadiabatic representation, which we define, this component builds up monontonically. Finally, we give an explicit formula for the transition wave function away from the avoided crossing, which is in excellent agreement with high precision numerical calculations.