Simulation of Potential-Dependent Activation Energies in Electrocatalysis: Mechanism of O–O Bond Formation on RuO₂

Abstract

Theoretical assessment of potential-dependent activation energies of electrochemical reactions is of critical importance but remains challenging. In this work, we present two computational tools to tackle this long-standing challenge. First, we implement a general computational framework for constant-potential saddle searches including both atomic positions and number of electrons as variables. Second, we develop a novel correction method to determine potential-dependent activation energies based on conventional zero-charge calculations. Different from existing capacitance-only schemes, our correction method takes into account the potential-dependent structural relaxation. This correction allows a significant reduction in computational overhead, but is still quite accurate, supplementing the direct constant-potential simulation. With these tools, we study the O–O bond formation reaction on the RuO2(110) surface. A number of new mechanistic insights are developed from the constant-potential calculations. The proton-coupled electron transfer pathway for the O–O bond formation has been determined to be favorable over the water dissociation mechanism. It is found that both H atoms strip from H2O successively to directly form adsorbed O2 without forming a stable intermediate OOH. With this example, we also demonstrate that the charge-structure coupling effect is not always negligible and can be captured by the full-Hessian correction. We expect the methods developed here to become useful tools in electrocatalysis.

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“…36,37 To simulate electrochemical conditions, the calculations adopted a full-Hessian correction method within the VASPsol calculator that allowed calculations to be performed within the framework of a grand canonical ensemble with a reservoir of electrons. 38 The number of electrons were treated as an additional degree of freedom as part of structural optimization, thereby enabling evaluation of potential-controlled DFT enthalpies. Thus, the resulting reaction enthalpy (H) was evaluated simultaneously as a function of the atomic positions in Cartesian coordinates (r) and the number of electrons (n) using the eq 1 using the total internal energy (E), the total number of nuclear charges in the system (n 0 ), and an effective energy level for the reference electrode (φ).…”

“…Thus, the resulting reaction enthalpy (H) was evaluated simultaneously as a function of the atomic positions in Cartesian coordinates (r) and the number of electrons (n) using the eq 1 using the total internal energy (E), the total number of nuclear charges in the system (n 0 ), and an effective energy level for the reference electrode (φ). 38 The effective energy level for the reference electrode (φ) is converted to an applied voltage (U) on the standard hydrogen electrode (SHE) scale as shown in eq 2, using a reference potential value of φ 0 = −4.6 eV for the SHE. The chemical potential of the electron (μ e ) can be thus derived as a function of the effective energy level of the reference electrode (φ) and the Fermi level of the working electrode (E F ) using eq 3.…”

“…The VASPsol package was used to describe the solvent electrolyte with the dielectric constant for water set to a relative permittivity value of 80. A Debye length of 9.7 Å was used, corresponding to an electrolyte concentration of 0.1 M solution. , To simulate electrochemical conditions, the calculations adopted a full-Hessian correction method within the VASPsol calculator that allowed calculations to be performed within the framework of a grand canonical ensemble with a reservoir of electrons . The number of electrons were treated as an additional degree of freedom as part of structural optimization, thereby enabling evaluation of potential-controlled DFT enthalpies.…”

“…The number of electrons were treated as an additional degree of freedom as part of structural optimization, thereby enabling evaluation of potential-controlled DFT enthalpies. Thus, the resulting reaction enthalpy ( H ) was evaluated simultaneously as a function of the atomic positions in Cartesian coordinates ( r ) and the number of electrons ( n ) using the eq using the total internal energy ( E ), the total number of nuclear charges in the system ( n 0 ), and an effective energy level for the reference electrode (φ) . The effective energy level for the reference electrode (φ) is converted to an applied voltage ( U ) on the standard hydrogen electrode (SHE) scale as shown in eq , using a reference potential value of φ 0 = −4.6 eV for the SHE.…”

“…The chemical potential of the electron (μ e ) can be thus derived as a function of the effective energy level of the reference electrode (φ) and the Fermi level of the working electrode ( E F ) using eq . We refer the reader to ref for comprehensive details of the methodology. …”