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Simulating the nonadiabatic dynamics of condensed-phase systems continues topose a significant challenge for quantum dynamics methods. Approaches based onsampling classical trajectories within the mapping formalism, such as thelinearized semiclassical initial value representation (LSC-IVR), can be used toapproximate quantum correlation functions in dissipative environments. Suchsemiclassical methods however commonly fail in quantitatively predicting theelectronic-state populations in the long-time limit. Here we present asuggestion to minimize this difficulty by splitting the problem into two parts,one of which involves the identity, and treating this operator byquantum-mechanical principles rather than with classical approximations. Thisstrategy is applied to numerical simulations of spin-boson model systems,showing its potential to drastically improve the performance of LSC-IVR andrelated methods with no change to the equations of motion or the algorithm ingeneral, but rather by simply using different functional forms of theobservables.

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