Assessing a First-Principles Model of an Electrochemical Interface by

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Assessing a First Principles Model of an Electrochemical Interface by Comparison with Experiment Stephan N. Steinmann, and Philippe Sautet J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b01938 • Publication Date (Web): 27 Feb 2016 Downloaded from http://pubs.acs.org on February 29, 2016

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The Journal of Physical Chemistry

Assessing a First Principles Model of an Electrochemical Interface by Comparison with Experiment Stephan N. Steinmann and Philippe Sautet∗ Univ Lyon, Ecole Normale Supérieure de Lyon, CNRS Université Lyon 1, Laboratoire de Chimie UMR 5182, 46 allée d’Italie, F-69364, LYON, France E-mail: [email protected]

∗

To whom correspondence should be addressed

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Abstract Electrified interfaces are central for electrocatalysis, batteries and molecular electronics. Experimental characterization of these complex interfaces with atomic resolution is highly challenging. First principles modelling could provide a link between the measurable quantities and an atomic scale understanding. However, such simulations are far from straightforward. Although approaches that include the effect of the potential and the electrolyte have been proposed, detailed validation has been scarce and "indirect" since atomically resolved experimental studies of systems that can be convincingly simulated are scarce. We introduce here the adsorption of pyridine on Au(111) as a convenient and relevant model: the adsorption mode of pyridine switches as a function of the electrochemical potential. We demonstrate that the primitive surface charging model gives qualitatively correct results at a low complexity. For quantitative agreement, however, the model needs to include a more realistic description of the electrical double layer. Approximating the latter through the linearized Poisson-Boltzmann equation leads to a quantitative improvement, lowering the error in the transition potential from 1 V to acceptable 0.3 V. Hence, we demonstrate the qualitative usefulness of the surface charging method and the excellent agreement that can be obtained by slightly more sophisticated electrolyte models.

Introduction In the dawn of green chemistry and the search for renewable energy sources, the importance of electrocatalysis has soared in recent years. In particular, electrocatalysis is the key technology for (water) electrolysis, fuel cells and electrosynthesis. Electrified interfaces are central in electrocatalysis, where the electrochemical potential determines the stability of adsorbed surface species and their reactivity. However, these interfaces are also of greatest importance in energy storage devices such as batteries, where their modifications are responsible for the losses upon charge-cycling. 1 Last but not least, electrified interfaces are also key in molecular electronics. 2,3 In all these examples an experimental atomically resolved characterization is very difficult due to the need of in-situ, surface 2 ACS Paragon Plus Environment

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sensitive techniques. First principles modelling provides a complementary atomic scale picture of these interfaces and allows to study the elementary processes in great detail, generating valuable information on how to improve the electrocatalytic reactivity. However, the description of electrified interfaces is highly challenging, as both, the electrochemical potential and the complex environment (electrolyte) need to be accounted for. Several approaches have been proposed in the literature, 4–12 but most of them come with at least one of the two following drawbacks: either they have only been implemented in private versions of electronic structure codes or the solvent description relies on few-layer ice-like water structures. Consistently embedding various adsorbates in these ice-like structures is far from obvious, reducing the attractiveness of this approach for many applications. Furthermore, this model is, of course, completely inadequate for other solvents than water which are especially relevant in batteries 1 or under aprotic, reducing conditions. 13 Implicit solvent models, which enjoy great popularity in molecular codes, 14 are, in contrast, straightforward to apply and can easily model different solvents by tuning the bulk dielectric constant of VASPsol. 15 Such models 16–19 have only very recently been made available to the public in periodic density functional theory (DFT) codes. 20 The question of the accuracy of these electrochemical models is seldom directly addressed, as only very limited experimental data is available that could be directly compared to the computations. The adsorption of pyridine on coinage metal surfaces has been studied in great detail, last but not least because of its strong Raman signal, which made it the archetype molecule studied by surface enhanced Raman spectroscopy (SERS). 21 As shown later, pyridine adsorption on gold is also a model system for molecular switches, as it shows a potential dependent, reversible, re-orientation. This phase transition has first been identified by spectroscopy (see ref 22 and therein) and later confirmed by electrochemical scanning tunneling microscopy (EC-STM). 23 Furthermore, pyridine has been identified to be a potent co-catalyst in CO2 reduction, notably over gold electrodes, 24 further increasing the interest in its potential-dependent behavior. Here we study the potential dependent adsorption of pyridine on gold surfaces by two electrochemical models in order to assess their accuracy. Both models explicitly include the effect



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of the electrode potential through charged surfaces, coupled to an implicit description of the bulk solvent effect. The surface charging (SC) model of Filhol and Neurock 7,11 applies a homogeneous background charge to neutralize the periodic cells, which does not need a special implementation. However, this simplicity comes at the cost of spurious interactions between the system and the homogeneous background, which have to be corrected for. 7 Despite the approximate character of the correction and of the double layer structure, the SC model has often delivered results compatible with experimental observations. 25–29 Herein, we apply the SC model in combination with the implicit solvent model, 30,31 VASPsol, 20 a methodology that we have previously applied to formic acid electro-oxidation 32 and electro-carboxylation of alkenes. 33 The second, more sophisticated, model considered here is based on the linearized Poisson-Boltzmann (PB) equation: the PB equation allows us to include an idealized electrolyte distribution in the electronic structure computations. This model has been very recently implemented in the Hennig group 15,34 and allows a more realistic description of the electric double layer. This electrolyte distribution also serves to balance the surface charge without the need for any correction terms.

Computational Details For more details on the surface charging methodology, see ref. 35 The electronic structure is described by the PBE density functional and the valence electrons expanded in a 400 eV cut-off basis set. Our density dependent dispersion correction dDsC has been applied throughout. 36 Symmetric slabs of 5 metallic layers were used to model the Au(111) surface. Most computations were performed in a p(4×4) unit cell, with results for p(3×3) only given in the supplementary information. The Brillouin zone is integrated by a 2 × 2 × 1 and 3 × 3 × 1 K-point mesh for p(4×4) and p(3×3) unit cells, respectively. The default dielectric constant, simulating aqueous solutions, has been used and the surface tension set to zero in order to avoid numerical instabilities. All geometries were optimized to reach a gradient smaller than 0.05 eV/Å with wave functions converged to 1·10−6 eV. The precision setting of VASP is set to "normal" and the automatic optimization of the real-space projection


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importance of applying a dispersion inclusive method. Since the perpendicular mode requires less space on the surface and dispersion interactions between adsorbates provides some stabilization, this mode would be favoured at higher coverages. However, in order to distinguish the effect of the electrochemical potential from the coverage effect, we place us in the low-coverage regime (p(4×4) unit cell), where lateral interactions are of no concern. Nevertheless, even in a smaller p(3×3) cell, qualitatively similar results are obtained (see SI). Turning to the electrochemical conditions, we first note that experimental evidence is quite clear. 22,23 At low potentials (1 V vs SHE), no pyridine adsorption is observed. At low potentials, the surface might be covered with hydrogen atoms and, more importantly, the adsorption energy of pyridine is weak compared to the loss of translational and rotational entropy. The entropy contribution to the adsorption free energy is not assessed herein, but can be estimated to be around 0.4 eV, assuming the loss of 0.5 (Srot + Strans ), evaluated for an ideal gas. At the oxidative potentials, on the other hand, the perchlorate electrolyte 38 and eventually a hydroxide layer 39 is likely blocking the pyridine adsorption. Note, however, that these species are absent in the STM images at the potentials considered. 23 In contrast, between -0.15 and 0.4 V, pyridine adsorbs in a co-planar mode, similar to benzene adsorption on transition metal surfaces. At 0.4 V, pyridine switches to a perpendicular adsorption mode, in which the nitrogen atom interacts strongly with the gold substrate. The application of an electrochemical potential in our computations affects the relative stability of the two adsorption modes dramatically (see Figure 2). The parallel adsorption mode (orange) is less strongly affected than the perpendicular (blue) one. This can be explained through the surface dipole moments, which are, obviously, very distinct. Based on electrostatic arguments, the variation of the adsorption energy as a function of the potential should be directly related to the interaction between the surface dipole and the electric field. Hence, the small/large dipole gives rise to a small/large slope of Eads for the parallel/perpendicular adsorption mode, respectively. The most important observation is, however, that the conformational switch is well reproduced by the SC method (broken lines), with a preferential adsorption of the co-planar mode at potentials


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0 -0.1 -0.2 Adsorption energy/eV

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-0.3 -0.4 -0.5 -0.6 SC, perpendicular SC, parallel PB, perpendicular PB, parallel

-0.7 -0.8

-1

-0.8

-0.6

-0.4 -0.2 0 0.2 Potential vs SHE/V

0.4

0.6

Figure 2: Adsorption energies of pyridine on Au(111) as a function of the electrochemical potential described by the surface charging (SC) model in broken lines. The full lines refer to the model implicitly including an electrolyte distribution through the Poisson-Boltzmann (PB) equation. The grey zone indicates the experimentally determined zone in which the adsorption mode switches from parallel to perpendicular (when scanning the potentials in the positive direction). < -0.5 V vs. SHE and the perpendicular adsorption mode being more stable for higher potentials. In comparison with experiment, the qualitative behavior is correct, but the switching potential is shifted by almost 1 V towards reductive potentials! In order to improve the description of the electrochemical interface, an idealized double layer can be included in the electronic structure computations through the linearized PB equation. Applying the PB equation with an ionic strength of 1 M, the qualitative behavior of SC is preserved. However, the switching potential is shifted to about 0.1 V vs SHE, leaving an error of only 0.3 V when compared to experiment. To the best of our knowledge, there is no precise experimental data available regarding the influence of the ionic strength of the supporting electrolyte on the switching potential of pyridine on Au(111). However, since most experiments are performed with concentrations in the range of 0.1 M, Figure 3 reports corresponding computations. The effect on the switching potential is rather small (0.1 V), increasing the discrepancy with experiment. This trend is easily understood considering that our SC model is the infinite dilution limit of the PB based model. We suspect three major factors to



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charges are modeled as point-charges, which implies that, due to the neglect of finite size effects, the charge distribution at high ionic strengths is not realistic. Figure 4 compares the isodensity surface of the electrolyte density (green) and the electronic density (grey) for pyridine on Au(111) at a surface charge of 0.25. In other words, the electrolyte provides an anionic countercharge of -0.25 e. Despite having the same (negative) charge, the electrolyte density partially overlaps with the electron density at the same iso-density value. This illustrates that the electrolyte approaches the surface very closely. Hence, for more realistic simulations, one should either apply lower ionic strengths (PB is known to be reliable for ≤ 0.001 M) or apply models that take the size of the ions into account. 40–43 Unfortunately, these models are numerically more involved and the physical model behind them is less well defined. Applying lower ionic strengths is technically straight forward. However, one hurts an other issue: the size of the "vacuum" or, rather, "solvent". The ionic strength I in M is related to the Debye screening length: λ ≈

√3 Å I

at room temperature. Hence, for 1 M, λ = 3 Å, but for 0.001

M, λ already reaches 95 Å. What does this mean for the size of the "solvent" required for reliably describing the electrolyte distribution? Based on empirical models 42 it has been suggested that the unit cells should have a size of about 5 × λ , which would mean 500 Å for 0.001 M. In Figure 5 we trace the average electrolyte charge as a function of the out-of-plane distance for two cell sizes: about 45 Å, a size which has proofed adequate for the SC model, and 140 Å, which has been used for the PB results presented, including the ones with I = 0.1, corresponding to λ = 9.5 Å in Figure 3. As can be seen, in the "small" cell, the electrolyte charge does not fall to zero in the middle of the cell, despite the void being about 30 Å and therefore about 10×, and not only 5 × λ . Two explanations can rationalize this observation: first, when computing the "void", we only subtract the metal, and not the adsorbate. However, the surface charge and the adsorbate are likely taking some space, reducing the effective z-distance for the electrolyte. Second, we are working with symmetric slabs. Therefore, the space required for neutralizing a given surface charge needs to be roughly doubled. Hence, the "void" beyond the surface and its adsorbate needs to be ≥ 10 × λ , which leads 9 ACS Paragon Plus Environment


to a significant increase in the cell size compared to the SC model. As shown in the SI, the induced charge in the polarizable continuum decays much faster than the charge accumulation in the electrolyte. This explains why smaller unit-cells are sufficient for the SC model with its homogeneous background charge. Average charge(z)/a.u.

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0

130 Å 30 Å

-0.0002 -0.0004 -0.0006 -0.0008 -0.001 -50

0

50 z-distance/Å

100

150

Figure 5: Average electrolyte charge density as a function of the out-of-plane distance. Negative distances (in red) and positive distances (blue line) refer to a "regular" and "large" cell size, with 30 Å and 130 Å void between the metal surfaces. A surface charge of -0.25 e is applied to the parallel adsorption mode of pyridine. A last point concerns numerical precision: As presented in Figure 3, increasing the plane wave cut-off for the wave function expansion from 400 to 600 eV and the quality of the numerical grids improves the agreement with experiment for the switching potential by 0.1 V. However, this encouraging result comes at a computational cost that is about 6 times higher, implying that routine applications will seldom apply such stringent settings.

Conclusion To summarize, even the rather primitive surface charging model, combining an implicit solvent with a homogeneous background charge, delivers qualitatively correct results for the potential dependent adsorption of pyridine on Au(111). However, getting the transition potential right requires more sophisticated models. The linearized Poisson-Boltzmann equation yields a very fair description of this phenomenon, although the countercharge distribution is found too close to the surface at practical ionic strengths. The implicit solvent models applied herein neglect all specific interactions 10 ACS Paragon Plus Environment

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between the solvent and metal surface, and are, therefore, inadequate for the description of the competitive adsorption of water and its dissociation products at strongly reductive and oxidative potentials. However, describing this adsorption would be crucial in order to simulate the desorption of pyridine at these potentials. Hence, more advanced electrochemical models need to be developed. An other shortcoming of the present approach is the neglect of thermal (entropic) contributions to the adsorption (free) energy. Including these corrections and assessing the coverage dependence would, eventually, enable a quantitative comparison with the experimentally determined adsorption isotherms. We propose that the pyridine adsorption on Au(111) is an ideal model system to validate electrochemical models. Ultimately, a model seamlessly accounting for specific solvent effects would be able to also reproduce the competitive adsorption with the solvent.

Acknowledgement We are very grateful to K. Mathew and R. Hennig who have shared their recent implementation of the linearized Poisson-Boltzmann equation in VASP with us. Computational resources generously provided by the mesocenter PSMN. This work was granted access to the HPC resources of CINES and IDRIS under the allocation 2014-080609 made by GENCI.

Supporting Information Available The supplementary information contains additional Figures; in particular, the adsorption of perchlorate, pyridine adsorption in a 3×3 unit cell and the polarization charge of the implicit solvent are shown. The coordinates for neutral systems optimized in the presence of an implicit electrolyte are given as well.

This material is available free of charge via the Internet at

http://pubs.acs.org/.

References (1) Goodenough, J. B.; Kim, Y. Chem. Mater. 2010, 22, 587.



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