The interaction between charged or polarizable solids and surrounding liquid environments is central to electrochemistry, catalysis, and materials design. Implicit solvation models offer an efficient framework for simulating such systems by treating the solvent as a continuum dielectric and, where relevant, including ionic response through modified electrostatic equations. These models replace explicit solvent molecules with position-dependent dielectric and ionic fields, dramatically reducing computational cost and enabling integration with quantum-mechanical descriptions of the solute.
In this tutorial, I will introduce the theoretical foundations of implicit solvation models, focusing on their continuum formulations and energy functionals. I will outline the core assumptions, such as locality, linear or nonlinear dielectric response, time-independent mean-field treatments, and sharp or diffuse cavity boundaries, and discuss which of these are intrinsic to the continuum approximation and which may be relaxed to incorporate fluctuations or time-dependent effects. This perspective connects directly to the goals of the IPAM program: to bridge deterministic and stochastic descriptions of electrochemical interfaces and explore how implicit models can be extended or hybridized to account for spatial and temporal solvent fluctuations.
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