Sampling Matters: Molecular Dynamics Insights into How Sampling Density and Distribution Affect the Capacitance and Energy Predictions in Hydrated Ionic Liquid Supercapacitors

Abstract Accurate predictions of capacitance and energy storage in electrochemical systems depend critically on how the charge–potential response is sampled. In this work, we investigate how data resolution and sampling strategy affect capacitance and energy estimates in graphene-based supercapacitors using molecular dynamics (MD) simulations of a partially hydrated ionic liquid. To this end, we compare projected and differential capacitance approaches and their associated energy estimates using complete, uniformly reduced, and nonuniformly sampled data sets. Linear fits of the potential–charge relationship, Φ(σ), provide a robust estimate of the average projected capacitance and are relatively insensitive to sampling density. However, because the projected approach compresses the full electrostatic response into a single effective slope, it cannot resolve local capacitance variations or directly determine the capacitance at the point of zero charge (PZC). In contrast, the differential capacitance, derived from cubic fits of the charge–potential relationship, σ(Φ), provides a local, potential-resolved reconstruction of the electrostatic response, but is more sensitive to sparse or uneven sampling because it depends on the curvature of the fitted response. These methodological differences are propagated into the energy estimates: the projected energy follows the ideal quadratic voltage dependence of a constant-capacitance model, whereas the integrated energy reflects the voltage-dependent capacitance profile and captures deviations from ideal linear-capacitor behavior. By comparing edge-dominated and PZC-centered data sets, we show that different regions of the electrostatic phase space probe distinct electrostatic regimes. Sampling near the PZC captures the near-equilibrium response, whereas edge-dominated sampling emphasizes the strongly polarized regime. These results provide practical guidelines for molecular simulations of electrochemical interfaces and show that reliable capacitance and energy estimates require control not only over the number of sampled points, but also over their distribution across the full polarization range.