  The constraint coordinate-momentum phase space (CPS) formulation of
finite-state quantum systems has recently revealed that the triangle window
function approach is an isomorphic representation of the exact
population-population correlation function of the two-state system. We use the
triangle window (TW) function and the CPS mapping kernel element to formulate a
novel useful representation of discrete electronic degrees of freedom (DOFs).
When it is employed with nonadiabatic field (NaF) dynamics, a new variant of
the NaF approach (i.e., NaF-TW) is proposed. Extensive benchmark tests of model
systems in both the condensed phase and gas phase demonstrate that the NaF-TW
approach is competent in faithfully capturing the dynamical interplay between
electronic and nuclear DOFs. In comparison to the symmetrical quasi-classical
(SQC) method where triangle window functions were originally proposed, the
performance of NaF-TW is significantly better when the bifurcation
characteristic of nuclear motion in the asymptotic region is important.
