  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 to the equations of motion or the algorithm in
general, but rather by simply using different functional forms of the
observables.
