Macro-Dipole-Constrainted Learning of Atomic Charges for Accurate Electrostatic Potentials at Electrochemical Interfaces

Abstract

Large thermal fluctuations of the liquid phase obscure the weak macroscopic electric field that drives electrochemical reactions, rendering the extraction of reliable interfacial charge distributions from ab initio molecular dynamics extremely challenging. We introduce SMILE-CP (Scalar Macro-dipole Integrated LEarning - Charge Partitioning), a macro-dipole-constrained scheme that infers atomic charges using only the instantaneous atomic coordinates and the total dipole moment of the simulation cell - quantities routinely available from standard density-functional theory calculations. SMILE-CP preserves both the global electrostatic field and the local potential without invoking any explicit charge-partitioning scheme. Benchmarks on three representative electrochemical interfaces - nanoconfined water, Mg2+ dissolution in water, and a kinked Mg vicinal surface under anodic bias - show that SMILE-CP eliminates the qualitative errors observed for unconstrained charge decompositions. The method is computationally inexpensive and data-efficient, opening the door to charge-aware machine-learning potentials capable of bias-controlled, nanosecond-scale simulations of realistic electrochemical systems.

Figures (4)

• Figure 1: (a) Atomistic model of the nanoconfined water between two Ne electrodes. The two electrodes carry opposite charges, creating a macroscopic field across the water layer. (b) The corresponding electrostatic potential calculated from DFT, Wannier centers (WCs), and the ML model learning from individual WCs (ML$^{\mathrm{WC}}$), with an applied field of $E^\mathrm{ext} =$ 0.2 V/$\mathrm{\AA}$. The gray dashed line represents the zero field DFT reference. (c) The externally applied field $\phi^{\mathrm ext}$ and the difference between the DFT electrostatic potential with and without field $\Delta \phi$. In the bulk water region, $\Delta \phi$ corresponds to an electric field smaller than $E^{\mathrm ext}$, which results from the electronic screening of water.
• Figure 2: (a) Schematic showing how a water molecule responds to an external electric field. The dipole moment of individual water molecule is represented by $\boldsymbol{\mu}^\mathrm{H_2O} = 8e(\mathbf{R^{\mathrm{el}}} - \mathbf{R^{\mathrm{core}}})$, where $\mathbf{R^{\mathrm{core}}}$ is the core charge center and $\mathbf{R^{\mathrm{el}}}$ is the electron charge center. When an external field is applied, the electrons are polarized, leading to change of $\mathbf{R^{\mathrm{el}}}$ and thus $\boldsymbol{\mu}^\mathrm{H_2O}$. (b) The dipole moments in the $z$ direction of individual water molecules $\mu_z^\mathrm{H_2O}$ (light blue dots) as a function of the applied field strength $E^\mathrm{ext}$. The corresponding grey shades show their value distribution. The red dots are the sum of the dipole moment in the $z$ direction $\mu^\mathrm{H_2O\text{-}tot}_z$, which clearly shows a linear relationship with $E^\mathrm{ext}$. The dark blue dots show $\mu^\mathrm{H_2O\text{-}tot}_z$ averaged to each water molecule, which is almost horizontal on the given scale.
• Figure 3: (a) Atomistic structure of nanoconfined water with a dissolved Mg$^{2+}$ ion. The compensating charge of the 2+ ion is evenly spread on the two Ne electrodes. (b) Predicted electrostatic potential $\phi$ of the SMILE0 and SMILE model, in comparison with DFT. The SMILE0 model is equivalent to SMILE at $\chi$ = 0. The black vertical line represents the average position of the Mg ion. (c) The distribution of the individual water molecule dipole magnitude $|\boldsymbol{\mu}^\mathrm{H_2O}|$ of the two models, in comparison to the values computed with WCs. The vertical lines show the corresponding averaged values, for which the lines of WC and SMILE overlap. (d) The RMSE of the SMILE model as a function of $\chi$. The purple vertical line shows the DFT-calculated electronic susceptibility of water $\chi_{\mathrm{DFT}}^{\mathrm{bulk}}$ = 0.96.
• Figure 4: (a) Atomistic model of the Mg(12$\bar{3}$5)/water interface. (b) The evolution of the macro dipole $\mu^\mathrm{tot}$ and the electrode charge $q_{\mathrm{electrode}}$ as a function of time in the AIMD simulation. The first 5 ps is under open circuit condition, followed by 45 ps of anodic bias. (c) The predicted electrostatic potential $\phi$ under open circuit condition and anodic bias predicted by the SMILE model (colored lines) in comparison to the DFT references (black dashed lines).