Truncated Hypernetted Chain Approximation: Accurate Functional for Energy Representation Theory

This study introduces the truncated hypernetted chain (tHNC) approximation for calculating solvation free energy (SFE) within the energy representation (ER) theory, demonstrating its improved accuracy. Conventional ER theory employs a hybrid functional that combines the hypernetted chain approximation for attractive interactions and the Percus-Yevick approximation for repulsive ones. However, this functional tends to overestimate SFEs in water, particularly for hydrophobic molecules such as alkanes and alcohols, due to unphysical solute-solvent overlap in the repulsive energy region. To address this, we introduce an energy cutoff parameter E_t, which truncates contributions from the high-energy interaction. This cutoff plays a role analogous to partial molar volume or hardsphere corrections proposed in other theoretical frameworks, effectively mitigating overestimation. Applied to the FreeSolv database (excluding 14 carboxylic acids), the tHNC functional achieved a mean absolute deviation of 0.37 kcal/mol relative to the benchmark Bennett acceptance ratio (BAR) method. The method notably improves predictions for hydrophobic molecules and maintains robust accuracy across variations in molecular size, polarity, and functional groups. The tHNC approximation thus offers a significant advance in accurate and efficient SFE calculation, supporting broader applications in solution-phase chemical and biological studies.