Fig. 1: Formulation and validation of the electric enthalpy in electrified interface within the MS-DFT formalism.
From: Ab initio theory of the nonequilibrium adsorption energy
a To describe the electrode potential Φ-dependent interaction between a working electrode L and a molecule C with the dipole moment \({{\boldsymbol{p}}}_{C}^{{V}_{b}}\) (green solid arrow), rather than introducing an electric field ε0 across C (➀) or assigning charges on electrodes (➁), MS-DFT explicitly introduces the bias voltage \({V}_{b}\) between L and the reference electrode R, which are characterized by the Fermi functions f with the electrochemical potentials \({\mu }_{L}\) and \({\mu }_{R}\), respectively (➂). Electrode potential Φ is defined as −\({V}_{b}/2\). b The atomic structure of the Au(111)-single water-Au(111) interface model overlaid with the two-dimensional contour plot of the bias-induced electrostatic potential change \(\Delta {v}_{H}\) (top) and the corresponding plane-averaged charge density difference or Landauer resistivity dipole \(\Delta \bar{\rho }\) (bottom) obtained at Φ = −2.0 V. c The \({{\mathcal{F}}}_{C}^{{V}_{b}}\) (red filled diamonds) is shifted downward from \({E}_{L+C+R}^{{V}_{b}}-{E}_{L+R}^{{V}_{b}}\) (orange open diamonds) by the \({{\boldsymbol{\varepsilon }}}_{0}\cdot {{\boldsymbol{p}}}_{C}^{{V}_{b}}\) contribution. The corresponding \({-}\nabla {{\mathcal{F}}}_{C}^{{V}_{b}}\) (dotted lines) curves match well with the z-component of the atomic forces \({F}_{z}\) (gray dashed line).
