Three-Dimensional RISM Integral Equation Theory for Polarizable Solute Models

Modeling solute polarizability is a key ingredient for improving the description of solvation phenomena. In recent years, polarizable molecular mechanics force fields have emerged that circumvent the limitations of classical fixed charge force fields by the ability to adapt their electrostatic potential distribution to a polarizing environment. Solvation phenomena are characterized by the solute's excess chemical potential, which can be computed by expensive fully atomistic free energy simulations. The alternative is to employ an implicit solvent model, which poses a challenge to the formulation of the solute-solvent interaction term within a polarizable framework. Here, we adapt the three-dimensional dimensional reference interaction site model (3D RISM) integral equation theory as a solvent model, which analytically yields the chemical potential, to the polarizable AMOEBA force field using an embedding cluster (EC-RISM) strategy. The methodology is analogous to our earlier approach to the coupling of a quantum-chemical solute description with a classical 3D RISM solvent. We describe the conceptual physical and algorithmic basis as well as the performance for several benchmark cases as a proof of principle. The results consistently show reasonable agreement between AMOEBA and quantum-chemical free energies in solution in general and allow for separate assessment of energetic and solvation-related contributions. We find that, depending on the parametrization, AMOEBA reproduces the chemical potential in better agreement with reference quantum-chemical calculations than the intramolecular energies, which suggests possible routes toward systematic improvement of polarizable force fields.