First-Principles Nanocapacitor Simulations of the Optical Dielectric Constant in Water Ice

We introduce a combined density functional theory and nonequilibrium Green's function framework to compute the capacitance of nanocapacitors and directly extract the dielectric response of a subnanometer dielectric under bias. We identify that at the nanoscale conventional capacitance evaluations based on stored charge per unit voltage suffer from an ill-posed partitioning of electrode and dielectric charge. This partitioning directly impacts the geometric definition of capacitance through the capacitor width, which in turn makes the evaluation of dielectric response uncertain. This ambiguous separation further induces spurious interfacial polarizability when analyzed via maximally localized Wannier functions. Focusing on crystalline ice, we develop a robust charge-separation protocol that yields unique capacitance-derived polarizability and dielectric constants, unequivocally demonstrating that confinement alters neither ice's intrinsic electronic response nor its insensitivity to proton order. Our results lay the groundwork for rigorous interpretation of capacitor measurements in low-dimensional dielectric materials.