  Feynman-Hibbs (FH) effective potentials constitute an appealing approach for
investigations of many-body systems at thermal equilibrium since they allow us
to easily include quantum corrections within standard classical simulations. In
this work we apply the FH formulation to the study of Ne$_N$-coronene clusters
($N=$ 1-4, 14) in the 2-14 K temperature range. Quadratic (FH2) and quartic
(FH4) contributions to the effective potentials are built upon Ne-Ne and
Ne-coronene analytical potentials. In particular, a new corrected expression
for the FH4 effective potential is reported. FH2 and FH4 cluster energies and
structures -obtained from energy optimization through a basin-hoping algorithm
as well as classical Monte Carlo simulations- are reported and compared with
reference path integral Monte Carlo calculations. For temperatures $T> 4$ K,
both FH2 and FH4 potentials are able to correct the purely classical
calculations in a consistent way. However, the FH approach fails at lower
temperatures, especially the quartic correction. It is thus crucial to assess
the range of applicability of this formulation and, in particular, to apply the
FH4 potentials with great caution. A simple model of $N$ isotropic harmonic
oscillators allows us to propose a means of estimating the cut-off temperature
for the validity of the method, which is found to increase with the number of
atoms adsorbed on the coronene molecule.
