An Efficient, Augmented Surface Hopping Algorithm That Includes Decoherence for Use in Large-Scale Simulations

We propose and implement a highly efficient augmented surface hopping algorithm that (i) can be used for large simulations (with many nuclei and many electronic states) and (ii) includes the effects of decoherence without parametrization. Our protocol is based on three key modifications of the surface hopping methodology: (a) a novel separation of classical and quantum degrees of freedom that treats avoided and trivial crossings efficiently, (b) a multidimensional approximation of the time derivative matrix that avoids explicit construction of the derivative coupling at most time steps, and (c) an efficient approximation for the augmented fewest-switches surface hopping decoherence rate. We will show that this protocol can be several orders of magnitude more efficient than the traditional protocol for large multidimensional problems. Furthermore, the marginal cost for including decoherence effects is now negligible.