While first-principles calculations of electrode-molecule adsorption 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 electrified 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 atomic-scale understanding of bias-dependent molecular reorganizations in electrified interfaces.

虽然电极分子吸附的第一原理计算在获得表面科学和电化学的原子级理解方面发挥着不可或缺的作用，但仍然存在重大挑战，因为吸附能仅在平衡状态下才能明确定义。在此，在多空间约束搜索密度泛函理论（MS-DFT）中制定了计算带电界面电焓的理论，该理论提供了纳米级电极-通道-电极结的非平衡总能量。对保持相同偏置电压的纯电极对应物进行额外的 MS-DFT 计算，可以识别通道的内能以及电场和通道极化，它们共同确定电焓和非平衡吸附能。将所开发的方案应用于水-金和水-石墨烯界面模型表明，金和石墨烯电极在水构型的电极电势依赖性稳定性方面引起非常不同的行为。这里开发的理论将成为一个有价值的工具，有助于我们不断努力获得对带电界面中偏压依赖性分子重组的原子尺度理解。