Hydration‐Free Energies for Small Molecules With Physics‐Based Descriptors: Graph Neural Network With Cross‐Attention

Hydration-free energy (HFE) is a fundamental thermodynamic property with broad relevance in both chemistry and biology, particularly in solvation processes. Traditional methods for computing HFE, such as molecular dynamics simulations, are often computationally intensive and require significant domain-specific calibration. Recent advances in machine learning (ML) have enabled more efficient HFE predictions, especially for small molecules. However, many existing ML models lack interpretability and often rely on large, opaque feature sets. In this study, a graph neural network (GNN) model is used for predicting the HFE of small molecules from the FreeSolv dataset. Our model integrates graph representations of solute and solvent molecules and captures their mutual interactions through a cross-attention mechanism during message passing. To enhance physical interpretability, we incorporate a compact set of six global molecular descriptors: approximate electrostatic energy computed via a closed-form Generalized Born (GB) model, polar surface area (PSA), logarithm of the octanol-water partition coefficient ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>log</mml:mi> <mml:mi>P</mml:mi></mml:mrow> <mml:annotation>$$ \log P $$</mml:annotation></mml:semantics> </mml:math> ), hydrogen bond donors, hydrogen bond acceptors, and the number of rotatable bonds. We benchmark our model against classical ML methods and recent GNN-based baselines. Our attention-based GNN not only improves prediction accuracy but also maintains transparency in feature importance. Our method outperforms existing baselines, achieving a mean absolute error (MAE) of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mn>0</mml:mn> <mml:mo>.</mml:mo> <mml:mn>54</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0</mml:mn> <mml:mo>.</mml:mo> <mml:mn>04</mml:mn></mml:mrow> <mml:annotation>$$ 0.54\pm 0.04 $$</mml:annotation></mml:semantics> </mml:math> kcal/mol and a root mean square error (RMSE) of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mn>0</mml:mn> <mml:mo>.</mml:mo> <mml:mn>75</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0</mml:mn> <mml:mo>.</mml:mo> <mml:mn>03</mml:mn></mml:mrow> <mml:annotation>$$ 0.75\pm 0.03 $$</mml:annotation></mml:semantics> </mml:math> kcal/mol, which is approximately <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mn>23</mml:mn> <mml:mo>%</mml:mo></mml:mrow> <mml:annotation>$$ 23\% $$</mml:annotation></mml:semantics> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mn>36</mml:mn> <mml:mo>%</mml:mo></mml:mrow> <mml:annotation>$$ 36\% $$</mml:annotation></mml:semantics> </mml:math> improvement as compared to the best-performing baseline, respectively. The ablation study reveals that among the global descriptors used for the solute, electrostatic energy and PSA are the most critical in reducing prediction error, followed by features related to hydrogen bonding. This combination of high accuracy and strong interpretability makes our framework well-suited for large-scale, data-driven investigations of solvation-free energies. The validation of the proposed framework on datasets encompassing a broader range of solvents will be undertaken in future investigations.