Generalization of the local diabatization approach for propagating electronic degrees of freedom in nonadiabatic dynamics

In this Festschrift contribution in honor of Prof. Maurizio Persico, we present a systematic derivation and comprehensive assessment of several integrators for quantum–classical time-dependent Schrodinger (TD-SE) and Liouville (QCLE) equations. Our formalism is rooted in the basis set reprojection approach, but it naturally leads to a family of local diabatization (LD) integrators, including the one pioneered by Prof. Persico and co-workers. The formalism naturally accounts for trivial state crossing effects and helps solve related phenomena that often pose significant numerical problems in nonadiabatic molecular dynamics simulations. We adapt the LD-based methods for the QCLE integration. We generalize the symmetric splitting integrator proposed by one of us earlier and demonstrate how it can be applied to integrate both TD-SE and QCLE. Our analysis and computations suggest that the reprojection approach is critical for capturing correct qualitative dynamics in trivial crossing regimes, but the proper integration approach is still needed for high accuracy of calculations in general case. Our computations also reveal an interesting coherence discontinuity effect introduced by the LD approximation. We provide a detailed discussion of the algorithms and their implementation in the open-source Libra software and present their comprehensive assessment using several well-designed model problems.