Diabatic model for electrochemical hydrogen evolution based on constrained DFT configuration interaction

Abstract

The accuracy of density functional theory (DFT) based kinetic models for electrocatalysis is diminished by spurious electron delocalization effects, which manifest as uncertainties in the predicted values of reaction and activation energies. In this work, we present a constrained DFT approach to alleviate overdelocalization effects in the Volmer-Heyrovsky mechanism of the hydrogen evolution reaction (HER). This method is applied a posteriori to configurations sampled along a reaction path to correct their relative stabilities. Concretely, the first step of this approach involves describing the reaction in terms of a set of diabatic states that are constructed by imposing suitable density constraints on the system. Refined reaction energy profiles are then recovered by performing a configuration interaction (CDFT-CI) calculation within the basis spanned by the diabatic states. After a careful validation of the proposed method, we examined HER catalysis on open-ended carbon nanotubes and discovered that CDFT-CI increased activation energies and decreased reaction energies relative to DFT predictions. We believe that a similar approach could also be adopted to treat overdelocalization effects in other electrocatalytic proton-coupled electron transfer reactions, e.g., in the oxygen reduction reaction.

Revisiting the Volmer–Heyrovský mechanism of hydrogen evolution on a nitrogen doped carbon nanotube: constrained molecular dynamics versus the nudged elastic band method

“…This finding is understood by considering the ability of the hybrid functional to alleviate self-interaction error induced electron overdelocalisation in the initial and transition states and is qualitatively consistent with the results of charge-constrained DFT configuration interaction calculations. 80,81 Finally, the electrode potential dependence of the Volmer and Heyrovský energy profiles were found to be qualitatively reasonable and in satisfactory agreement with previous constant potential simulations, taking into account the differences in employed solvent structures resulting in an approximately constant positive shift in the energies of the present work.…”

“…Including exact Hartree-Fock exchange mitigates SIE induced electron overdelocalisation which spuriously stabilizes the reactant and transition states compared to the product state. This conclusion is consistent with earlier studies, 80,81 in which electron overdelocalisation effects were alleviated by employing a charge-constrained DFT based configuration interaction approach (CDFT-CI). Specifically, in the CDFT-CI study performed on the Volmer reaction on an open-ended CNT, 81 the barrier height was observed to increase by up to 0.2 eV while the reaction energy in the forward direction was lowered by 0.1-0.2 eV.…”

“…Whether this difference is significant is uncertain considering that the generally quoted DFT error is on the order of 100 meV. The observed trend is nevertheless in agreement with the CDFT-CI results presented previously 81 and suggests that adverse effects due to SIE may be even more pronounced for the Heyrovský reaction.…”

Grand Canonical Rate Theory for Electrochemical and Electrocatalytic Systems I: General Formulation and Proton-coupled Electron Transfer Reactions

“…Instead, as demonstrated herein, ET, PT, or PCET and bond rupture/formation are naturally captured with GCE-DFT. Bond formation s is also captured by diabatic models using cDFT as demonstrated herein for the Volmer reaction and previously for ET [138], PCET [139] and general chemical reactions [140,141].…”

Sensitivity of Intra- and Intermolecular Interactions of Benzo[h]quinoline from Car–Parrinello Molecular Dynamics and Electronic Structure Inspection

“…The charge density changes of the O-H...N proton reaction paths were examined. The CDFT simulations were carried out using the implementation of Holmberg and Laasonen [ 67 , 68 ] in the CP2K code version 8.0 [ 69 ]. The method is based on an external constraint potential acting on the electron density of the ground state and modifying its distribution according to the given parameters [ 67 ].…”