Resolving Interfacial Electrochemical Environment from Constrained Optimization

Madelung potential, or electrostatic potential felt by a given charged species, reports the Coulombic solvation around the host species in electrochemical systems. Fluctuations of the Madelung potential are thus a direct indictor of the structural-dynamical changes from charge reordering phenomena such as layering and screening. For nanoscale systems, a major challenge in the atomistic sampling of Madelung potential is that these potentials are spatially discrete and located sparsely in the electrochemical cell, especially with dilute electrolytes. This makes it difficult to exploit field-theoretic tools to characterize relevant spatial-temporal correlations. In this talk, we present a simple inferential approach to compute a continuous representation of the Madelung potential. Borrowing tools from classical differential geometry, we develop a compact workflow to feed molecular data, as both interior and boundary constraints, into an optimizer that allows the efficient construction of continuous Madelung potential surfaces. Fluctuations in the resulting potential profiles can be post-processed with canonical correlation analysis, revealing the emergence of species-specific interfacial driving forces.