A multiple time step algorithm for trajectory surface hopping simulations

A multiple time step (MTS) algorithm for trajectory surface hopping molecular dynamics has been developed, implemented, and tested. The MTS scheme is an extension of the ab initio implementation for Born–Oppenheimer molecular dynamics presented in the work of Liberatore et al. [J. Chem. Theory Comput. 14, 2834 (2018)]. In particular, the MTS algorithm has been modified to enable the simulation of non-adiabatic processes with the trajectory surface hopping (TSH) method and Tully’s fewest switches algorithm. The specificities of the implementation lie in the combination of Landau–Zener and Tully’s transition probabilities during the inner MTS time steps. The new MTS-TSH method is applied successfully to the photorelaxation of protonated formaldimine, showing that the important characteristics of the process are recovered by the MTS algorithm. A computational speed-up between 1.5 and 3 has been obtained compared to standard TSH simulations, which is close to the ideal values that could be obtained with the computational settings considered.