  Recent work has shown that it is possible to circumvent the calculation of
the spectral density and directly calculate the coefficients of the discretized
influence functionals using data from classical trajectory simulations.
However, the accuracy of this procedure depends on the validity of the high
temperature approximation. In this work, an alternative derivation based on the
Kubo formalism is provided. This enables the calculation of additional
correction terms that increases the range of applicability of the procedure to
lower temperatures. Because it is based on the Kubo-transformed correlation
function, this approach enables the direct use of correlation functions
obtained from methods like ring-polymer molecular dynamics and centroid
molecular dynamics in determining the influence functional coefficients for
subsequent system-solvent simulations. The accuracy of the original procedure
and the corrected procedure is investigated across a range of parameters. It is
interesting that the correction term comes at zero additional cost.
Furthermore, it is possible to improve upon the correction using zero-cost
physical intuition and heuristics making the method even more accurate.
