The three-dimensional reference interaction site model (3D-RISM) theory, an integral equation theory of molecular liquids, is one of the most powerful tools to calculate the solvation free energy (SFE). This theory produces accurate relative free energy change, and therefore has been used in many studies on chemical and biological processes in solution. However, the theory is also known to sometimes overestimate the absolute SFE. In 2001, Ten-no proposed the distributed partial wave (PW) expansion to solve the same problem in the 1D-RISM theory [S. Ten-no, J. Chem. Phys. 115, 3724 (2001).]. He derived an SFE expression by applying the PW expansion to the 1D-RISM theory (1D-RISM-PW) and succeeded in greatly improving the accuracy of calculated SFE. However, to utilize the idea of the PW expansion and accomplish accurate SFE calculations for large molecules like biomolecules, it is crucial to extend the PW expansion to the 3D-RISM theory. In this presentation, we propose a correction method for the 3D-RISM theory on the basis of the PW expansion. We first show a new SFE expression of the 3D-RISM theory based on the PW expansion (3D-RISM-PW). This expression takes account of the information on the orientation of solvent molecules, i.e., the anisotropy of the solvent molecules that is lacking in the conventional 3D-RISM theory. Then, we show some applications of the new expression to 467 small organic molecules and five proteins, and compare them with the results of the conventional SFE expressions based on the HyperNetted Chain (HNC) closure, the Kovalenko-Hirata (KH) closure, and the Gaussian Fluctuation. The results of the 1D-RISM theory and the implicit solvent models are also compared. From the results of the SFE for the 467 small organic molecules, it was found that the 3D-RISM-PW provided closer SFE values to the experimental values than the 3D-RISM-HNC and the 3D-RISM-KH (judging from the root-mean-squared errors from the experimental values). It was also found that the SFE values calculated by the 1D-RISM-PW were in better agreement with the experimental values than those of the 3D-RISM-PW, even though the 3D-RISM-PW is theoretically more rigorous than the 1D-RISM-PW. To assess the applicability of the 3D-RISM-PW to the biomolecular systems, the SFEs of the five proteins are compared with the results of previous studies which were calculated by the 3D-RISM theory with the HNC closure + repulsive bridge correction and the energy representation method.

Effect of the distributed partial wave expansion on the solvation free energy in the 3D-RISM theory

255th National Meeting (2018)

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