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

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 (Scalar Macro-dipole Integrated LEarning) charge partition, 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 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, Mg^{2+} dissolution in water, and a kinked Mg vicinal surface under anodic bias-show that SMILE 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.