  Calculating relative free energies is a topic of substantial interest and has
many applications including solvation and binding free energies, which are used
in computational drug discovery. However, there remain the challenges of
accuracy, simple implementation, robustness and efficiency, which prevent the
calculations from being automated and limit their use in computational drug
discovery. Here we present an exact and complete decoupling analysis in which
the partition functions of the compared systems decompose into the partition
functions of the common and different subsystems. This decoupling analysis is
applicable to submolecules with coupled degrees of freedom and to any potential
function, enabling to remove less terms in the transformation. Then we show
mathematically, in the context of partition function decoupling, that the two
compared systems can be simulated separately, eliminating the need to design a
composite system. We demonstrate the decoupling analysis and the separate
transformations in an MD calculation of relative free energy for a general
force field which is in agreement with experiments. We present a unified soft
core technique that will ensure the monotonicity of the numerically integrated
function. Finally, we show that when the systems have rugged energy landscape
they can be equilibrated without introducing another sampling dimension. The
concepts presented in the article have implications in accuracy, efficiency,
simplicity and robustness of free energy calculations.
