Multiconfigurational\nSurface Hopping: a Time-Dependent\nVariational Approach with Momentum-Jump Trajectories

The\nEhrenfest mean field dynamics and trajectory surface hopping\nhave been widely used in nonadiabatic dynamics simulations. Based\non the time-dependent variational principle (TDVP), the multiconfigurational\nEhrenfest (MCE) method has also been developed and can be regarded\nas a multiconfigurational extension of the traditional Ehrenfest dynamics.\nHowever, it is not straightforward to apply the TDVP to surface hopping\ntrajectories because there exists momentum jump during surface hops.\nTo solve this problem, we here propose a multiconfigurational surface\nhopping (MCSH) method, where continuous momenta are obtained by linear\ninterpolation and the interpolated trajectories are used to construct\nthe basis functions for TDVP in a postprocessing manner. As demonstrated\nin a series of representative spin-boson models, MCSH achieves high\naccuracy with only several hundred trajectory bases and can uniformly\nimprove the performance of surface hopping. In principle, MCSH can\nbe combined with all kinds of mixed quantum-classical trajectories\nand thus has the potential to properly describe general nonadiabatic\ndynamics.