High-Precision Solvation Free Energy Calculation via Multi-Input Linear Correction in 3D-RISM Theory

This study introduces the multi-input linear correction (MILC) method to enhance the accuracy of solvation free energy (SFE) calculations with the three-dimensional reference interaction site model (3D-RISM) theory. While the 3D-RISM theory offers significant computational efficiency compared with molecular simulation-based methods, conventional energy functionals─such as the Singer-Chandler or Gaussian fluctuation formulas─often suffer from systematic overestimation of SFEs. In general, partial molar volume (PMV) corrections are employed to account for errors related to hydrophobic and cavity formation energies. To further improve the prediction accuracy, the MILC method employs a physically motivated data-driven approach that incorporates not only the standard SFE components but also physical quantities obtained when the solute atomic charges are set to zero. Accordingly, the method requires two independent 3D-RISM calculations per solute. The robustness and transferability of the MILC method were rigorously validated using a nested cross-validation protocol on 628 molecules in the FreeSolv database (excluding carboxylic acids). By averaging over 10 conformers per molecule, the method achieved a mean absolute deviation (MAD) of 0.38 kcal/mol relative to the benchmark Bennett acceptance ratio (BAR) method. Furthermore, we demonstrate that the MILC method outperforms conventional volume-based corrections and provides predictive performance superior or comparable to complex machine learning models while maintaining high physical interpretability. This level of accuracy and statistical reliability demonstrates that the 3D-RISM theory with the MILC method is a robust and efficient tool for high-throughput applications in drug discovery and material design.