The influence functional coefficients that correspond to the QuAPI discretization of the path integral are available in several forms.  These are first obtained as time integrals of the appropriate bath correlation function, and can be expressed in the form of frequency integrals involving the spectral density.  We have given these coefficients in various forms, suitable for model calculations with a given spectral density, or for simulating processes where the effective harmonic bath is obtained in terms of time correlation functions of the actual polyatomic environment, for factorized or equilibrium initial conditions, and for a shifted bath that corresponds to the diabatic potential surface of the donor.

Related Articles:

T. C. Allen, P. L. Walters and N. Makri, “Direct computation of influence functional coefficients from numerical correlation functions”, J. Chem. Theory and Comput. 12, 4169-4177 (2016).

P. L. Walters, T. Banerjee and N. Makri, “On iterative path integral calculations for a system interacting with a shifted dissipative bath”, J. Chem. Phys. 143, 074112 (2015).

N. Makri, “Numerical path integral techniques for long-time quantum dynamics of quantum dissipative systems”, J. Math. Phys. 36, 2430-2457 (1995).

N. Makri and D. E. Makarov, “Tensor propagator for iterative quantum time evolution of reduced density matrices. II. Numerical methodology”, J. Chem. Phys. 102, 4611-4618 (1995).