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 modeling 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 describe 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 (DFT) with fixed electron and ion chemical potentials in the grand canonical (GC) ensemble is established for modeling electrocatalytic and electrochemical interfaces. Starting from a fully quantum mechanical description of multi-component GC-DFT for 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 various (modified) Poisson-Boltzmann (mPB) implicit solvent models. 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 within a linear dielectic continuum in the GPAW code and test their capabilities to model capacitance of electrochemical interfaces as well as study different approaches for modeling 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.

Assessment of Constant-Potential Implicit Solvation Calculations of Electrochemical Energy Barriers for H2 Evolution on Pt

“…This 322 behavior is possibly connected to the observa-323 tion that standard Poisson-Boltzmann models 324 do not necessarily enforce strict charge neutral-325 ity. 54 We therefore performed single-point cal-326 culations using the JDFTx code which imple-327 ments a truncated Coulomb scheme to fully de-328 couple periodically repeated slabs. 55 As shown 329 in Table 1, the JDFTx activation energies in-330 deed agree well with the VASPsol results ex-331 trapolated to L z = ∞.…”

Influence of Van der Waals Interactions on the Solvation Energies of Adsorbates at Pt‐Based Electrocatalysts

“…In computational electrocatalysis adsorbate‐solvent and adsorbate‐electrolyte interactions at the interface can be evaluated implicitly (where the solvent is modelled as a continuum with certain dielectric constant), explicitly, or through combinations of the two . Furthermore, efforts have been devoted to determine the minimal number of explicit water molecules needed to stabilize a given adsorbate .…”

Recent Advancements Towards Closing the Gap between Electrocatalysis and Battery Science Communities: The Computational Lithium Electrode and Activity–Stability Volcano Plots

“…Section 2.3). Therefore, furtherm odel development in ab initio electrochemistry is called for that facilitates the incorporation of the appliede lectrode potentiald irectly into the underlying calculations, such as in ar ecent contribution of Melander et al, [124] in whichagrand canonical approach was used to investigatee lectrocatalyticsystems at constant ionand electrode potentials. The application of MD simulations [125,126] is required for ap roper sampling of solventc onfigurations, which can be linked to the applied electrode potential.…”