Solvation potentials for flexible chain molecules in solution: on the validity of a pairwise decomposition

The effects of a solvent on the conformation of a flexible n-site solute molecule can be described formally in terms of an n-body solvation potential. Given the practical difficulty in computing such multibody potentials, it is common to carry out a pairwise decomposition in which the n-body potential is approximated by a sum of two-body potentials. Here we investigate the validity of this two-site approximation for short interaction-site chain-in-solvent systems. Using exact expressions for the conformation of an isolated chain, we construct a mapping between the full chain-in-solvent system and its solvation potential representation. We present results for both hard-sphere and square-well systems with n=5 that show that the two-site approximation is sufficient to completely capture the effects of an explicit solvent on chain conformation for a wide range of conditions (which include varying the solvent diameter in the hard-sphere system and varying the chain-solvent coupling in the square-well system). In all cases, a set of two-site potentials (one for each distinct site-site pair) is required. We also show that these two-site solvation potentials can be used to accurately compute a multisite intramolecular correlation function.