In this article it is shown that the decomposition of free energy diff
erences, as evaluated by molecular simulations using thermodynamic int
egration, in terms of components corresponding to terms in the Hamilto
nian, cannot be uniquely performed. This path dependence of the contri
butions to the total free energy difference is shown for the calculate
d difference in free energy of hydration of ethanol and ethane. The co
nclusion of this study is that the individual free energy difference c
ontributions from such calculations should, in general, be interpreted
with care.