Theory of Electric Enthalpy of Formation in Electrified Interfaces

Despite the recent developments in the modern theory of polarization and density polarization functional theory, defining the concept of electric enthalpy for the nanoscale channel sandwiched by biased electrodes remains an open question. While the non-equilibrium Green’s function (NEGF) formalism coupled with density functional theory (DFT) has become a standard approach for finite-bias junction calculations, DFT-NEGF has a fundamental limitation in defining the total energy due to the Landauer or grand-canonical framework it adopts. In this work, we establish a theory of the electric enthalpy in nanoscale junctions based on the multi-space constrained-search DFT (MS-DFT) formalism, in which the microcanonical ensemble is employed and the quantum transport process is mapped to the multi-electrode optical excitation counterpart. A key challenge in defining the electric enthalpy for biased nanojunctions is identifying the electric displacement of the electrodes-only system and the polarization of the channel-only systems that exactly correspond to those from the combined non-equilibrium junction system. We devise a self-consistent method to achieve this identification, and validate the methodology for the gold and graphene electrode-based nanocapacitor models. We verify that the capacitances calculated from the developed theory are comparable to experimental data, and particularly reveal how electrified graphene electrodes exhibit nontrivial responses due to interfacial water.