  The Caldeira-Leggett (CL) model, which describes a system bi-linearly coupled
to a harmonic bath, has enjoyed popularity in condensed phase spectroscopy
owing to its utmost simplicity. However, the applicability of the model to
cases with anharmonic system potentials, as it is required for the description
of realistic systems in solution, is questionable due to the presence of the
invertibility problem [J. Phys. Chem. Lett., \textbf{6}, 2722 (2015)] unless
the system itself resembles the CL model form. This might well be the case at
surfaces or in the solid regime, which we here confirm for a particular example
of an iodine molecule in the atomic argon environment under high pressure. For
this purpose we extend the recently proposed Fourier method for parameterizing
linear generalized Langevin dynamics[J. Chem. Phys., \textbf{142}, 244110
(2015)] to the non-linear case based on the CL model and perform an extensive
error analysis. In order to judge on the applicability of this model in
advance, we give handy empirical criteria and discuss the effect of the
potential renormalization term. The obtained results provide evidence that the
CL model can be used for describing a potentially broad class of systems.
