Supporting Information
Transcription
Supporting Information
Supporting Information Modeling the HCOOH/CO2 Electrocatalytic Reaction: When Details Are Key Stephan N. Steinmann,[a] Carine Michel,[a, b] Renate Schwiedernoch,[c] Jean-Sebastien Filhol,[d] and Philippe Sautet*[a, b] cphc_201500187_sm_miscellaneous_information.pdf ´ 1 Computational Details The metal surface is modeled as a symmetric p(3×3) Ni(111) slab with a lattice constant of 3.52 Å and a thickness of 5 layers (the middle layer is frozen in its bulk position), in a periodic box of 37.35 Å. The spin-polarized electronic structure is described at the PBE level, 1 with an energy cut-off of 400 eV for the plane-wave basis set. The electron–ion interactions are described by the PAW formalism. 2,3 All computations are performed with a patched version (for the implicit solvent description) 4,5 of VASP 5.3.3 and VASP 5.3.5. 6,7 Accounting for solvation effects is achieved by exploiting the implicit solvation model 4,5 as implemented by Hennig and co-workers under the name VASPsol. 8 All technical settings are described in our previous publication 9 , except that we have set the bulk dielectric constant of the solvent to the value for water (ε = 80). Note, that when we started this study, VASPsol was incompatible with non-local van der Waals density functionals and we did therefore not apply them. Since we are mainly comparing two electrochemical approaches, we do not expect to obtain qualitatively different conclusions upon accounting for weak non-bonded interactions. All geometries were optimized to reach a gradient smaller than 0.05 eV/Å (some transition states proved to converge very slowly within the SC model) with wave functions converged to 5·10−5 eV. Note that we started from the geometries published by Jiao and coworkers 10 for the formate pathway. For the carboxylate pathway initial guess structures for the transition states were generated by nudged-elastic band computations and the transition states fully optimized with a quasi-Newton algorithm. Upon convergence, the number of frequencies has been verified to correspond to a minimum or a transition state. The precision setting of VASP is set to ”normal” and the automatic optimization of the real-space projection operators is used. To tune the electrode potential, the system is charged in the SC method. In order to reach an overall neutral cell, a uniform background charge of opposite sign is applied. This uniform charge is also present in the metal slab itself, where it is screened by the metal. Hence, the ”effective” applied charge is reduced and the DFT energy must be corrected accordingly. 11–13 We use a parabolic fit through at least 5 different charges for each system to access mol )−nsystem (U), arbitrary potentials. The charge injection for a given reaction is defined as ∆ads q(U) = (nslab surf (U)+N surf where N mol is the sum of the electrons in the isolated molecules (the proton is considered as a charged species) adsorbed on the surface and nslab surf (U) is the effective charge on the empty slab at potential U. Be reminded, that since the number of electrons is variable in the SC formalism, one should use electronic free energies, corresponding to the grand-canonical ensemble: 1 elec elec (1) ∆Gsurf (U vac ) = ∆Esurf (U vac ) − nsurf (U vac )FU vac ≈ ∆Esurf (U0 ) − C(U vac −U0vac )2 2 elec (U vac ) being the electronic energy at potential U vac and n with ∆Esurf surf is positive if electrons are removed and negative when electrons are added, i.e., nsurf is the surface charge of the system and U vac is the vacuum scale potential of the electrode. The reasoning behind 1 is that electrons removed from the system are transferred to the electrode that serves as the reservoir of electrons at the potential U vac . Similarly, adding an electron from the electrode is associated with the energetic cost of removing the electron from the reservoir. The approximate equality refers to the quadratic development of the electronic free energy, 13,14 which can serve to introduce the notion of the capacitance C of the surface and simplifies the link between SC and CHE results, which correspond to the zero charge result, ∆G(U0vac ). 1 For the reaction HCOOH → CO2 + 2(H+ + e− ) it is crucial to include thermal, i.e., free energy corrections: based on pure electronic energies, the reaction is 0.26 eV endothermic at zero bias potential, while the reaction is exergonic by -0.35 eV, corresponding to an equilibrium redox potential of 0.18 V vs. SHE, in close agreement with the about 0.2 V expected based on experimental data. These numbers refer to our level of theory and thus include the effect of an implicit solvent and an activity of unity for all chemical species involved. The free energy corrections are computed for the neutral systems by freezing the metal atoms and evaluating the frequencies for the adsorbate. Standard statistical mechanical formulae are applied to estimate the thermal corrections to the enthalpy and the entropy at 298.15 K. Only normal modes > 50 cm−1 are considered and rotations are neglected. This procedure leads to close agreement between the resulting free energy correction for CO2 + H2 → HCOOH and the corresponding free energy correction computed with Gaussian 09. 15 The main difference between the two approaches is that VASP does not project out translations and rotations during a normal mode analysis and hence the low energy modes are not very meaningful. Table 1: Comparison of overpotentials for the surface charging method (SC) and the computational hydrogen electrode (CHE). Thermodynamic overpotential (ηthermo ): potential (relative to the ideal potential of 0.18 V) at which all intermediates are formed exothermically with respect to the reactants. Kinetic limitation ηkin potential (relative to the ideal potential of 0.18 V) at which all transition states are formed exothermically with respect to the reactants. Thermodynamic overpotential Limiting species SC: 5 CHE: 5 Kinetic limitation Limiting species SC: TSdes CHE: TSCH Ulimit /(V vs. SHE) -0.01 0.24 ηthermo /V 0.17 0.42 Ulimit /(V vs. SHE) 0.14 0.34 ηkin /V 0.32 0.52 References [1] J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865. [2] P. E. Blochl, Phys. Rev. B, 1994, 50, 17953. [3] G. Kresse and D. Joubert, Phys. Rev. B, 1999, 59, 1758. [4] K. Letchworth-Weaver and T. A. Arias, Phys. Rev. B, 2012, 86, 075140. [5] D. Gunceler, K. Letchworth-Weaver, R. Sundararaman, K. A. Schwarz and T. A. Arias, Modelling and Simulation in Materials Science and Engineering, 2013, 21, 074005. [6] G. Kresse and J. Hafner, Phys. Rev. B, 1993, 47, 558. [7] G. Kresse and J. Furthmuller, Phys. Rev. B, 1996, 54, 11169. [8] K. Mathew, R. Sundararaman, K. Letchworth-Weaver, T. A. Arias and R. G. Hennig, J. Chem. Phys., 2014, 140, 084106. [9] S. N. Steinmann, C. Michel, R. Schwiedernoch and P. Sautet, submitted. [10] Q. Luo, G. Feng, M. Beller and H. Jiao, J. Phys. Chem. C, 2012, 116, 4149. [11] C. D. Taylor, S. A. Wasileski, J.-S. Filhol and M. Neurock, Phys. Rev. B, 2006, 73, 165402. [12] M. Mamatkulov and J.-S. Filhol, Phys. Chem. Chem. Phys., 2011, 13, 7675. [13] J.-S. Filhol and M.-L. Doublet, Catal. Today, 2013, 202, 87. [14] J.-S. Filhol and M.-L. Doublet, J. Phys. Chem. C, 2014, 118, 19023. [15] Gaussian 09, Revision A.1, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. 2 1 TSOH 2 3 TSrot 4 Tsrot' 5 TSCH 6 7 TSdes A TSCH B C TSR(O-H) D TSOH E Figure 1: Geometries of intermediates along the electro-oxidation of formic acid to CO2 on the Ni(111) surface. The ”formate” and ”carboxyl” pathways are shown in the top and bottom scheme, respectively. 3 HCO2 H CO2 H+ H+ + e− CO2 + 2(H+ + e− ) HCO2 + H+ + e − HCO2 H -0.25 V 0.0 V 0.8 Reaction Free Energy/eV 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 HCO2 H A B C D TSads TSads TSR(O–H) TSOH TSCH -1 E 7 TSCH 7 6 RefR TSrot’ 5 TSrot 4 TSOH 3 2 1 HCO2 H Figure 2: Free energy profile for the electroreduction relative to the reference for reduction RefR (CO2 , a slab of Ni(111) and 2 (H+ + e− )) of CO2 according to CHE (thin lines) and SC (thick lines) approach at three different electrochemical potentials (vs. SHE): 0 V and -0.25 V where the electrochemical cell is operating at a minimal overpotential. The path to the right goes through the formate pathway, while on the left the alternative carboxyl path is shown. Note that until the first proton coupled electron transfer occurs (change from dark to light gray background), all the CHE lines overlap by construction. The second formally electrochemical step occurs with the change from light gray to white. 0.3 Fit: y(x)=0.97x 0.2 d(GSC −GCHE )(U ) dU 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.3 -0.2 -0.1 0 ∆ SC−CHE ads 0.1 0.2 0.3 q Figure 3: Derivative d∆ dU ∆G(U) as a function of ∆ads q(U) at U = 0 V. The derivative of the difference in reaction energy between the SC and the CHE model has been computed numerically with the data at 0 and -0.25 V. Energies are in eV and the potential in V. 4 0.3 Fit: y(x)=0.235x +0.02 0.2 d(GSC −GCHE )(U ) dU 0.1 0 -0.1 -0.2 -0.3 -0.4 -1.5 -1 -0.5 0 0.5 1 ∆W SC−CHE Figure 4: Derivative d∆ dU ∆G(U) as a function of ∆W at U = 0 V. The derivative of the difference in reaction energy between the SC and the CHE model has been computed numerically with the data at 0 and -0.25 V. Energies are in eV and the potential in V. 0.05 ∆GSC (0V ) − ∆GCHE (0V ) 0 -0.05 -0.1 -0.15 -0.2 -0.25 -0.3 -0.35 Fit: y(x)=−0.14 · x2 − 0.14 · x -1.5 -1 -0.5 0 0.5 1 ∆W Figure 5: ∆SC G(U) − ∆CHE G(U), i.e., the difference between the SC free energy and the CHE prediction as a function of the difference in the workfunction (∆W ). Energies and workfunctions are relative to the Ni(111) slab and, for the energies, to isolated formic acid. Energies are in eV and the potential in V. 5 0.2 CO2 CO2 H HCO2 H HCO2 CO2 0 d∆GSC,rel (U ) dU -0.2 -0.4 -0.6 -0.8 TSrot TSOH TSCH TSOH TSR(O–H) TSdes TSrot’ TSdes TSCH -1 7 E D C B A 1 2 3 4 5 6 7 -1.2 rel,SC Figure 6: Derivative dG dU (U) , i.e., the SC free energy change from one step to the next, along the formic acid electro-oxidation pathway at U = 0 V. The derivative has been computed numerically with the data at 0 and -0.25 V. Energies are in eV and the potential in V. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. 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