Multicapacitor Approach to Interfacial Proton-Coupled Electron Transfer Thermodynamics at Constant Potential

Abstract

Theoretical calculations of interfacial thermodynamics at constant potential enhance understanding of heterogeneous electrocatalytic reactions. Herein, a strategy is devised for computing reaction thermodynamics for electrochemical proton-coupled electron transfer (PCET), a key elementary step in a wide range of electrocatalytic processes. In this approach, Gibbs free energies obtained from constant charge periodic density functional theory calculations are transformed to grand potentials by using a grid-based mapping procedure in conjunction with a multicapacitor model that accounts for constantly charged surface adsorbates. The energetic contribution of the adsorbate capacitor to the grand potential is found to be essential for computing proton-coupled redox potentials at constant potential. This strategy is applied to graphite-conjugated catalysts, wherein organic acids are attached to carbon surfaces through a conductive phenazine bridge. In these systems, PCET occurs at both the phenazine bridges and the organic acids, which can be negatively or positively charged. For a given graphite-conjugated catalyst active site, the charge of the organic acid adsorbate remains virtually constant for the relevant range of electrode potentials. Moreover, the potential-dependent graphite surface charge density, which excludes this adsorbate charge, is consistent across all systems studied. Within this framework, the potential-dependent PCET reaction free energies are independent of cell size, thereby avoiding the need for computationally expensive cell size extrapolation techniques. The proton-coupled redox potentials computed with this strategy are in agreement with experimental data. This computational strategy, as well as the conceptual insights about the impact of charged adsorbates on electrochemical interfaces, is applicable to other materials and processes.

Theoretical Modeling of Electrochemical Proton-Coupled Electron Transfer

“…This result was consistent with earlier work, which demonstrated that constant-charge PCET reaction energetics are uniquely defined as a function of the effective surface charge . The computational analysis of the graphite-conjugated organic acids showed that the internal energy U [ q graph ( E )] can be calculated using the DFT energy U DFT and a shift associated with the capacitive contributions of the constantly charged surface adsorbate: …”

“…A computational analysis of PCET reactions at the surface of graphite-conjugated organic acids showed that the energetics of interfaces containing adsorbates with constant charge are determined by the graphite electrode surface charge, q graph . In this case, the Taylor series expansion for an interface that is polarized by both counter-charges in the EDL, denoted q , and constantly charged adsorbates, q ads , simplifies to a function of q graph only (Figure A–B): where E 0 is the graphite electrode potential of zero free charge (PZFC).…”

Force-based method to determine the potential dependence in electrochemical barriers

“…Note that this method, combined with the extrapolation procedure in Equation 4, provides a direct way to determine potential dependent electrochemical barriers by using just the outputs of a DFT calculation along with the transition state structures, without the need for any a priori assumptions to its value. 16,22…”

“…11,12,14 In the past decade, a variety of methods to address this challenge have been developed. 11,12,[14][15][16][17][18][19][20][21][22][23][24][25] These methods can be broadly grouped into two categories, extrapolation and grand-canonical schemes. Extrapolation methods seek to determine activation energies at the limit of infinite cell size by correcting DFT energies for finite cell size effects.…”

“…performing DFT calculations which change the workfunction by adding or subtracting excess electrons while using the capacitor equations to interpret the obtained energies. 13,22 In theory, it has been shown that both GC and extrapolation methodologies are equivalent in specific limiting cases, such as adsorption reactions of polar species. For example, Ref 17 showed that for CO 2 → CO * 2 both GC and extrapolation procedures provide the same potential dependent energies.…”