Symmetrical windowing for quantum states

The quasi-classical (QC) approach embodies a simple methodology, based purely on classical mechanics, for modeling transitions between quantum states in atomic and molecular dynamics (MD) simulation. In the standard quasiclassical
trajectory (QCT) simulation [4], molecular vibrational and/or rotational degrees of freedom (DOFs) are expressed in terms of classical actionangle variables, the action variables being classical generalized momenta serving as the classical analogues of the vibrational and/or rotational quantum numbers. "Quantization" is then accomplished by initializing classical trajectories
with integer values of the action variables-i.e., at the quantum energy level of the initial state-and the final distribution of quantum states is obtained by accumulating the values of the classical action variables in "bins" (or histograms) of unit-width centered about the integer quantum values corresponding to the accessible quantum states.