Solvent-Environment Dependence of the Excess Chemical Potential and Its Computation Scheme Formulated through Error...

Solvent environment may significantly affect the equilibria involving flexible solute species, such as proteins and polymers. In the present work, a computation scheme is formulated for the change in the excess chemical potential of a flexible solute molecule upon variation of the solvent condition. The formulation adopts the scheme of error minimization in parallel to the method of Bennett acceptance ratio, and an exact expression is presented that provides the change in the excess chemical potential from solvation free energies computed in two solvent conditions of interest. The formulated scheme is applied to n-hexanol as the solute in water and n-octanol as the two solvent systems and to an oligomer of ethylene glycol as the solute in water with urea or NaCl added as a cosolvent. It is demonstrated that the change in the excess chemical potential of the solute due to the variation of the solvent condition (composition) can be obtained from the solvation free energies calculated over ∼10 to ∼10² solute configurations, without referring to any intermediate states between the two solvent conditions concerned. The connection to the solvent-condition dependence of the solute structure is further discussed for the systems of the ethylene-glycol oligomer, and the role is addressed for the probability distribution functions of the cosolvent-induced changes in the solvation free energies.