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

Abstract

Theoretical estimation of the activation energy 2 of electrochemical reactions is of critical impor-3 tance but remains challenging. In this work, we 4 address the usage of an implicit solvation model 5 for describing hydrogen evolution reaction steps 6 on Pt(111) and Pt(110), and compare with 7 the 'extrapolation' approach as well as single-8 crystal measurements. We find that both meth-9 ods yield qualitatively similar results, which are 10 in fair agreement with the experimental data. 11 Care should be taken, however, in addressing 12 spurious electrostatic interactions between pe-13 riodically repeated slabs in the VASPsol im-14 plementation. Considering the lower computa-15 tional cost and higher flexibility of the implicit 16 solvation approach, we expect this method to 17 become a valuable tool in electrocatalysis. 18 157 tions involving H atoms adsorbed in threefold 158 hollow sites at a coverage of up to 1 ML. Also, 159 the HER steps on (110) facets are included, as experimental Tafel slopes are here easier to an-161 alyze and indicate a Volmer-Tafel mechanism 162 with the Tafel reaction as the rate-determining 163 step (RDS). 35 164 It should be noted that the above considera-457 face. The magnitude of the corresponding pre-458 exponential factor (circa 10 10 mA/cm 2) is char-459 acteristic of a process involving only surface 460 adsorbates, supporting the Tafel reaction as 461 the RDS. These findings therefore qualitatively 462 agree with the computational results described 463 in the previous paragraphs, where the same 464 Tafel RDS is found, though with a somewhat 465 higher activation energy (0.80-0.85 eV). As the 466 barrier for the Tafel step is not sensitive to the 467 water structure at the interface, this does not, 468 unfortunately, allow to discriminate between 469 different types of water models. 470 Comparison with other implicit solvent 471 calculations 472 Fang et al. have previously addressed 31 the 473 HER on Pt(111) using a similar method im-474 plemented in the SIESTA code. 32,33 At 0 V SHE 475 and a hydrogen coverage at or below 1 ML, the 476 Tafel barrier reported by Fang et al. (0.92 eV) 477 agrees well with our calculations, while the re-478 ported Volmer and Heyrovský barrier heights 479 are significantly lower than ours (< 0.2 eV and 480 0.93 eV, respectively). In attempting to locate 481 the origins of this difference for the Volmer re-482 action, we find that the inclusion of zero-point 483 vibrational energy corrections lowers the calcu-484 lated barrier by 0.10 eV, while applying the 485

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 ),…”

Practical Considerations for Continuum Models Applied to Surface Electrochemistry

“…F vac is printed in VASPsol as the negative of the output flag FERMI-SHIFT and decreases as a function of cell height. Figure 1 also shows that the electrolyte potential is already flat at typical cell sizes, and so the slow convergence of energies with respect to cell height [23][24][25][26][27] arises solely from variations in F vac rather than a slow decay of countercharge density in the continuum electrolyte. [26] In a charged LPB system, the absolute value of the potential is fixed even in the presence of periodic boundary conditions due to the additional ionic screening term in the Poisson equation.…”

DFT modelling of explicit solid–solid interfaces in batteries: methods and challenges

“…Under constant voltage conditions, ∆V e should be zero over the course of a reaction. To achieve this condition, constant V e ensembles 86 or extrapolation to large cell sizes87 have been applied in electrocatalysis calculations. Related methods have recently been applied to battery interfaces 88.…”