Consistent Construction of Density Matrix from Surface Hopping Trajectories

Proper construction of density matrix based on surface hopping trajectories remains a difficult problem. Due to the well-known overcoherence in traditional surface hopping simulations, the electronic wavefunction cannot be used directly. In this work, we propose a consistent density matrix construction method, which takes the advantage of occupation of active states to rescale the coherence calculated by wavefunctions and ensures the intrinsic consistency of density matrix. This new trajectory analysis method can be used for both Tully’s fewest switches surface hopping (FSSH) and our recently proposed branching corrected surface hopping (BCSH). As benchmarked in both one- and two-dimensional standard scattering models, the new approach combined with BCSH trajectories achieves highly accurate time-dependent spatial distributions of adiabatic populations and coherence compared with exact quantum results.