Landau-Zener Type Surface Hopping Algorithms

A class of surface hopping algorithms is studied comparing two recent Landau-Zener (LZ) formulas for the probability of nonadiabatic transitions. One of the formulas requires a diabatic representation of the potential matrix while the other one depends only on the adiabatic potential energy surfaces. For each classical trajectory, the nonadiabatic transitions take place only when the surface gap attains a local minimum. Numerical experiments are performed with deterministically branching trajectories and with probabilistic surface hopping. The deterministic and the probabilistic approach confirm the affinity of both the LZ probabilities, as well as the good approximation of the reference solution computed by solving the Schrödinger equation via a grid based pseudo-spectral method. Visualizations of position expectations and superimposed surface hopping trajectories with reference position densities illustrate the effective dynamics of the investigated algorithms.