A Machine Learning Free Energy Functional for the 1D Reference Interaction Site Model - Towards Prediction of Solvation Free Energy for All Solvent Systems

Aug 5, 2026

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Understanding solute–solvent interactions is central to chemical science, and solvation free energy (SFE) is a key thermodynamic quantity for characterising molecular solvation. The One-Dimensional Reference Interaction Site Model (1D RISM) is widely used but produces large SFE errors. This work introduces a single machine-learning free-energy functional for 1D RISM using convolutional neural networks trained on RISM-derived solvation free-energy density functions across ~100 solvent systems. Reported performance reaches average RMSE 1.41 kcal/mol and R2 0.89, with accuracy improving for solvents with richer datasets.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages22

Reading Time55 min

AccessFree to download

Abstract

1. Introduction

Solvation Free Energy

Implicit Methods for SFE Prediction

Article A Machine Learning Free Energy Functional for the 1D Reference Interaction Site Model: Towards Prediction of Solvation Free Energy for All Solvent Systems Jonathan G. M. Conn, Abdullah Ahmad and David S. Palmer * Department of Pure and Applied Chemistry, University of Strathclyde, Thomas Graham Building, 295 Cathedral Street, Glasgow G1 1XL, UK * Correspondence: [david.palmer@strath.ac.uk](david.palmer@strath.ac.uk) Citation: Conn, J.G.M.; Ahmad, A.; Palmer, D.S. A Machine Learning Free Energy Functional for the 1D Reference Interaction Site Model: Towards Prediction of Solvation Free Energy for All Solvent Systems. Liquids 2024, 4, 710–731. [https://](https://)[ ](https://)[doi.org/10.3390/liquids4040040](doi.org/10.3390/liquids4040040) Academic Editors: William E. Acree, Jr., Juan Ortega Saavedra and Enrico Bodo Received: 28 June 2024 Revised: 14 October 2024 Accepted: 19 October 2024 Published: 8 November 2024 Copyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([https://](https://)[ ](https://)[creativecommons.org/licenses/by/](creativecommons.org/licenses/by/)[ ](creativecommons.org/licenses/by/)[4.0/](4.0/)) . Abstract: Understanding the interactions between solutes and solvents is vital in many areas of the chemical sciences. Solvation free energy (SFE) is an important thermodynamic property in characterising molecular solvation and so accurate prediction of this property is sought after. The One-Dimensional Reference Interaction Site Model (RISM) is a well-established method for modelling solvation, but it is known to yield large errors in the calculation of SFE. In this work, we show that a single machine learning free energy functional for RISM can accurately model solvation thermodynamics in multiple solvents. A convolutional neural network is trained on solvation free energy density functions calculated by RISM for small organic molecules in approximately 100 different solvent systems. We achieve an average RMSE of 1 .41 kcal/mol and an R2 of 0 .89 across all solvent systems. We also compare the performance for the most and least commonly represented solvents and show that higher accuracy is generally seen with higher volumes of data, with RMSE values of 0 .69–1.29 kcal/mol and R2 values of 0 .78–0.97 for solvents with more than 50 data points. We have shown that machine learning can greatly improve solvation free energy predictions in RISM, while demonstrating that the methodology is generalisable across solvent systems. This represents a significant step towards a universal machine learning SFE functional for RISM. Keywords: solvation free energy; RISM; machine learning; solvent systems; convolutional neural network 1. Introduction Solvation Free Energy The process of solvation, as defined by Ben-Naim, is the transfer of one solute molecule from a fixed position in the ideal gas phase to a fixed position in the liquid phase at a given temperature and pressure [1] . The solvation free energy (SFE) is the reversible work associated with the transfer of the solute molecule from the gas phase to the liquid phase. SFE is important in many areas, such as drug discovery, as it may be used in the predictions of solubility and octanol-water partition coefficient (logP) [2–4], and environmental chemistry, as it is useful in understanding pollutant distributions in different aqueous environments [5,6] . Generally, the SFE of solutes with low vapour pressures must be obtained indirectly from separate measurements of the solubility and pure compound vapour pressure by a thermodynamic cycle via the gas-phase. Experimental SFE determination is often a lengthy and difficult process, so many computational approaches have been developed for its prediction. SFE prediction methods can be separated into implicit and explicit methods. Implic

FAQs

What is the main goal of the study on 1D RISM and machine learning?

To build a single machine-learning free-energy functional for 1D RISM that accurately models solvation thermodynamics and improves prediction of solvation free energy across many solvent systems.

How is the machine learning model trained in this work?

A convolutional neural network is trained using solvation free-energy density functions calculated by 1D RISM for small organic molecules across approximately 100 solvent systems.

What predictive accuracy does the method achieve across solvent systems?

Across all solvent systems, the study reports an average RMSE of 1.41 kcal/mol and an R2 of 0.89, with higher accuracy generally for solvents with more than 50 data points.

Aug 5, 2026

Upload by Aria