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Abstract:
We resolve a seeming paradox arising from a common misinterpretation of Ben-Naim’s theorem, which rests on the decomposition of the Hamiltonian of a molecular solute/solvent system into solute–solvent and solvent–solvent interactions. According to this theorem, the solvation entropy can also be decomposed into a solute–solvent term and a remaining solvent–solvent term that is commonly referred to as the solvent reorganization term. Crucially, the latter equals the average solvent–solvent interaction energy such that these two solvent–solvent terms cancel and thus do not change the total solvation free energy. This analytical result implies that changes in the solvent–solvent interactions cannot contribute to any thermodynamic driving force. The solvent reorganization term is often identified with the contribution of many-body solvent correlations to the solvation entropy, which seems to imply that these correlations, too, cannot contribute to solvation. However, recent calculations based on atomistic simulations of a solvated globular protein and spatially resolved mutual information expansions revealed substantial contributions of many-body solvent correlations to the solvation free energy, which are not canceled by the enthalpy change of the solvent. Here, we resolved this seeming contradiction and illustrate by two examples─a simple Ising model and a solvated Lennard-Jones particle─that the solvent reorganization entropy and the actual entropy contribution arising from many-body solvent correlations differ both conceptually and numerically. Whereas the solvent reorganization entropy in fact arises from both solvent–solvent as well as solute–solvent interactions and thus has no straightforward intuitive interpretation, the mutual information expansion permits an interpretation in terms of the entropy contribution of solvent–solvent correlations to the solvation free energy.
