LAUSR

Abstract The solvation thermodynamics is a molecular based statistical mechanics description of the solvation process, which provides a proper distinction from other processes that uniquely and unambiguously defines the solvation of any species in any environment. Because the activity coefficient involves the behavior of a given species in different environments, it is then related to the solvation process, which should be described within the solvation thermodynamics formalism. Indeed, the activity coefficient of a species i within an α phase, γ i , α o , ρ , is expressed in terms of the binding energy of i to the α phase, Bi, α, and to the dilute-ideal phase, Bi, o. In addition to this molecular description, the activity coefficient can also be related to the Gibbs solvation energies of these two phases within the solvation thermodynamics formalism, which can provide, for instance, unique values of the activity coefficients from the experimental Gibbs solvation energies. The relevance and advantages of using the binding energy (or the coupling work of the solute with its surroundings) as the main molecular quantity for evaluating the activity coefficient is explored in detail. For instance, several cancellations occur when evaluating the binding energies, especially those related to the non-additive corrections (many-body effects), which can more promptly justify the use of the pairwise approximation. In addition, by partitioning the potential energy into two or more contributions, the activity coefficient can also be partitioned into these contributions, yielding exact expressions that are suitable for approximations and interpretations. In fact, a direct connection with perturbation theories can be established and new partitions can be proposed to explore recent approaches based on embedded quantum calculations of the potential energy in condensed phases. It has been shown that the approximation 〈e−βBi, α〉 ≅ e−β〈Bi, α〉, with β−1 = kBT, can be valid even when the condition 〈Bi, α〉 ≪ kBT is not satisfied, as long as the fluctuations, 〈(Bi, α − 〈Bi, α〉)2〉, and the higher order deviations of the binding energy, 〈(Bi, α − 〈Bi, α〉)n〉, (n ≥ 3), are negligible. This small fluctuations approximation (SFA) can rationalize and justify the good results obtained for systems with large binding energies. The SFA can also provide a new interpretation and insights for the activity coefficient. The partition of the potential energy into hard sphere (cavity) and attractive (non-cavity) contributions and the SFA were employed to obtain approximate expressions that allowed to explore the general behavior of the activity coefficient of neutral systems. For instance, the activity coefficient of strongly interacting large molecules (hard-spheres interacting by Lennard-Jones potential in an implicit solvent) tends to decrease with the increasing of the concentration of the solute, which is accentuated by the increase of the dielectric constant of the medium. In addition, the cavity contribution (modeled by hard-sphere mixtures of different sizes) to the activity coefficient is influenced by the relative sizes of the molecules and by the pure liquid densities. This contribution dominates the behavior of the activity coefficient with the concentration.