  While first-principles calculations of electrode-molecule binding play an
indispensable role in obtaining atomic-level understanding in surface science
and electrochemistry, a significant challenge remains because the adsorption
energy is well-defined only in equilibrium. Herein, a theory to calculate the
electric enthalpy for electrochemical interfaces is formulated within the
multi-space constrained-search density functional theory (MS-DFT), which
provides the nonequilibrium total energy of a nanoscale
electrode-channel-electrode junction. An additional MS-DFT calculation for the
electrode-only counterpart that maintains the same bias voltage allows one to
identify the internal energy of the channel as well as the electric field and
the channel polarization, which together determine the electric enthalpy and
the nonequilibrium adsorption energy. Application of the developed scheme to
the water-Au and water-graphene interface models shows that the Au and graphene
electrodes induce very different behaviors in terms of the electrode
potential-dependent stabilization of water configurations. The theory developed
here will be a valuable tool in the ongoing effort to obtain an atomic-scale
understanding of bias-dependent molecular reorganizations in electrified
interfaces.
