Deep learning of committor for ion dissociation and interpretable analysis of solvent effects using atom-centered symmetry functions

TL;DR

The paper addresses the challenge of identifying reaction coordinates for solvent-mediated ion dissociation by training a neural network on committor values $p_B^*$ while encoding the solvent environment with atom-centered symmetry functions. The approach yields an interpretable RC, highlighted by two ACSF descriptors, $G^5_{58}$ and $G^5_{1217}$, which correspond to water O coordination around Na and water-bridging O atoms, respectively; SHAP analysis links these descriptors to the transition pathway and correlates them with conventional bridging CVs such as the interionic density $\rho$ and bridging waters $N_B$. The results show that water bridging structures play a central role in the association/dissociation process, and the RC exhibits a separatrix near the saddle point consistent with the underlying mechanism. This framework provides a general, interpretable methodology for solvent-influenced transitions and can be extended to processes like ligand binding, nucleation, and biomolecular conformational changes.

Abstract

The association and dissociation of ion pairs in water are fundamental to physical chemistry, yet their reaction coordinates are complex, involving not only interionic distance but also solvent-mediated hydration structures. These processes are often represented by free-energy landscapes constructed from collective variables (CVs), such as interionic distance and water bridging structures; however, it remains uncertain whether such representations reliably capture the transition pathways between the two associated and dissociated states. In this study, we employ deep learning to identify reaction coordinates for NaCl ion pair association and dissociation in water, using the committor as a quantitative measure of progress along the transition pathway through the transition state. The solvent environment surrounding the ions is encoded through descriptors based on atom-centered symmetry functions (ACSFs), which serve as input variables for the neural network. In addition, an explainable artificial intelligence technique is applied to identify ACSFs that contribute to the reaction coordinate. A comparative analysis of their correlation with CVs representing water bridging structures, such as interionic water density and the number of water molecules coordinating both ions, further provides a molecular-level interpretation of the ion association-dissociation mechanism in water.

Figures (6)

• Figure 1: (a) PMF $F(r_\mathrm{ion})$ as a function the interionic distance $r_\mathrm{ion}$. (b) Distribution of Committor $p_\mathrm{B}^*$ evaluated for configurations sampled within the range $3.2~{\AA} < r_\mathrm{ion} < 4.3$ Å.
• Figure 2: Relationship between committor $p_\mathrm{B}^*$ and the RC $q$ predicted by the neural network trained model using the test dataset (3040 points). The blue curve represents the sigmoidal function, $p_\mathrm{B}(q)=(1+\tanh(q))/2$.
• Figure 3: Feature contribution of each CV evaluated by the absolute SHAP value. (a): Summed SHAP values for each atom combination ($i$-$Z_1$) in $G^2$ and ($Z_1$-$i$-$Z_2$) in $G^5$ descriptors. (b): Index dependence of SHAP values for $G^2$ descriptors. (c) and (d): Index dependence of SHAP values for $G^5$ descriptors.
• Figure 4: Schematic illustration of water O atoms within 2 Å of Na (a) and water O atoms within the 4 Å hydration shell of Cl (b), characterized by two ACSF descriptors, $G^5_{58}$ and $G^5_{1217}$, respectively.
• Figure 5: Distribution of committor $p_\mathrm{B}^*$ dataset in the two-dimensional surface using the interionic distance $r_\mathrm{ion}$ and $G^5_{58}$ (a) and $G^5_{1217}$ (b). Committer values are colored according to the bottom color bar. The black lines are drawn as follows. The ranges of the $x$- and $y$-axis values were each divided into 200 grid points (forming a 200 $\times$ 200 grid), and the average committor value $p_\mathrm{B}^*$ within each grid cell was computed. After applying cubic interpolation for smoothing, contour lines corresponding to $p_\mathrm{B}^*=0.5$ were plotted.