Grand-Canonical Approach to Density Functional Theory of Electrocatalytic Systems: Thermodynamics of Solid-Liquid Interfaces at Constant Ion and Electrode Potentials

Abstract

Properties of solid-liquid interfaces are of immense importance for electrocatalytic and electrochemical systems but modelling such interfaces at the atomic level presents a serious challenge and approaches beyond standard methodologies are needed. An atomistic computational scheme needs treat at least part of the system quantum mechanically to include adsorption and reactions while the entire system is in thermal equilibrium. The experimentally relevant macroscopic control variables are temperature, electrode potential, choice of the solvent and ions and these need to be explicitly included in the computational model as well; this calls for an thermodynamic ensemble with fixed ion and electrode potentials. In this work a general framework within density functional theory with fixed electron and ion chemical potentials in the grand canonical ensemble is established for modelling electrocatalytic and electrochemical interfaces. Starting from a fully quantum mechanical description of nuclei and electrons, a systematic coarse-graining is employed to establish various computational schemes including i) the combination of classical and electronic density functional theories within the grand canonical ensemble and ii) on the simplest level a chemically and physically sound way to obtain the (modified) Poisson-Boltzmann (mPB) implicit solvent model. The detailed and rigorous derivation clearly establishes which approximations are needed for coarse-graining as well as highlights which details and interactions are omitted in vein of computational feasibility. The transparent approximations also allow removing some the constraints and coarse-graining if needed. We implement various mPB models in the GPAW code and test their capabilities to model capacitance of electrochemical interfaces as well as study different approaches for modelling partly periodic charged systems. Our rigorous and well-defined DFT coarse-graining scheme to continuum electrolytes highlights the inadequacy of current linear dielectric models for treating properties of the electrochemical interface.<br><br>

On the Mechanistic Origins of the pH-Dependency in Au-Catalyzed Glycerol Electro-Oxidation: Insight from First Principles Calculations

“…For oxygen and hydrogen, standard cavity radii 64 were used but for Au a larger radius of 2.0 Å was adapted based on our previous results. 65 The Au lattice constant was calculated to be 4.142 Å, which agrees well with the experimental value (4.065 Å 66 ). An Au(111) surface was selected to model the electrode surface as it is the most stable and abundant Au surface.…”

“…While we did not explicitly address the potential-dependent kinetics, we confirmed that the Fermi-levels coincide well with the experimentally relevant potential range of 0.6-1.0 V vs. RHE (henceforth referred as V RHE ). The Fermi-levels correspond to absolute electrode potentials, 65 and can be converted to the RHE scale by U (RHE) = −e(E F + 4.4eV ). The Fermi-levels (electrode potentials vs. RHE) are -4.9 eV (0.5 V), -4.8 eV (0.4 V), -4.8 eV (0.4 V), and -4.9 eV (0.5V) for the bare Au surface, GLY adsorption, neutral/acidic NEB calculations, and alkaline NEB calculations, respectively.…”

A Challenge to the G ∼ 0 Interpretation of Hydrogen Evolution

“…This interfacial water geometry has been shown to be the most stable geometry for protonated, that is, acidic water bilayers, at the potentials of interest for HER. 47,[53][54][55] The reaction pathways are all performed at constant potential within a tolerance of 0.01 V, and the relevant energy comparison is therefore the energy at constant potential (often referred to as Ω [38][39][40][41][44][45][46][47][48][49]56 ),…”

“…The advent of grand-canonical electronic structure schemes has allowed for explicit control of applied potential in atomistic studies of electrocatalytic systems by varying the number of electrons, allowing the workfunction to be tuned relative to some reference potential. [38][39][40][41][42][43][44][45][46][47][48][49] These methods provide a straightforward way of calculating reaction barriers at constant potential. In particular, the solvated jellium (SJ) method 47 accomplishes potential control for periodic systems by employing a counter charge in a solvated jellium slab, which localizes the excess charge on the reactive side of the electrode surface.…”

Revisiting the Active Sites at the MoS2/H2O Interface via Grand-Canonical DFT: The Role of Water Dissociation

“…45 To better understand the details of HER the electrified MoS 2 interface immersed in the electrolyte solution needs to be simulated. We herein apply the computationally efficient grand-canonical DFT approach [46][47][48] and investigate the competition with adsorption of the water solvent. In contrast to the computational hydrogen electrode (CHE) method, 49 grandcanonicl DFT allows to explicitly take the polarization of the electrode into account, thus going beyond the purely thermodynamic effects of the electrochemical potential on the energy of proton/electron pairs.…”