On the identity of the identity operator in nonadiabatic linearized semiclassical dynamics

Simulating the nonadiabatic dynamics of condensed-phase systems continues to pose a significant challenge for quantum dynamics methods. Approaches based on sampling classical trajectories within the mapping formalism, such as the linearized semiclassical initial value representation (LSC-IVR), can be used to approximate quantum correlation functions in dissipative environments. Such semiclassical methods however commonly fail in quantitatively predicting the electronic-state populations in the long-time limit. Here we present a suggestion to minimize this difficulty by splitting the problem into two parts, one of which involves the identity and treating this operator by quantum-mechanical principles rather than with classical approximations. This strategy is applied to numerical simulations of spin-boson model systems, showing its potential to drastically improve the performance of LSC-IVR and related methods with no change in the equations of motion or the algorithm in general, but rather by simply using different functional forms of the observables. (C) 2019 Author(s).