Path dependence of free energy components in thermodynamic integration

In this article it is shown that the decomposition of free energy differences, as evaluated by molecular simulations using thermodynamic integration, in terms of components corresponding to terms in the Hamiltonian, cannot be uniquely performed. This path dependence of the contributions to the total free energy difference is shown for the calculated difference in free energy of hydration of ethanol and ethane. The conclusion of this study is that the individual free energy difference contributions from such calculations should, in general, be interpreted with care.