Supplementary information for How copper catalyzes the electroreduction of carbon dioxide into hydrocarbon fuels

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1 for How copper catalyzes the electroreduction of carbon dioxide into hydrocarbon fuels Andrew A. Peterson, Frank Abild-Pedersen, Felix Studt, Jan Rossmeisl, Jens K. Nørskov Center for Atomic-scale Materials Design, Department of Physics, Technical University of Denmark, DK-2800 Lyngby, Denmark. 1 Computational hydrogen electrode A reaction pathway (shown in Figure S1) involving 41 reaction intermediates was analyzed in the current work. The free energy change of each step that involves an electrochemical protonelectron transfer will be a function of the applied electrical potential. The effect of applying this potential was based upon a technique, described earlier by Nørskov et al. [1], which we are herein referring to as the computational hydrogen electrode (CHE) model. This technique also provides an elegant way of avoiding the explicit treatment of solvated protons. In this technique, zero voltage is defined based on the reversible hydrogen electrode (RHE), in which the reaction H + + e 1 2 H 2 (1) is defined to be in equilibrium at zero voltage, at all values of ph, at all temperatures, and with H 2 at Pa pressure. Therefore, in the CHE, the chemical potential of a protonelectron pair, µ(h + ) + µ(e ) is equal to half of the chemical potential of gaseous hydrogen (1/2 µ(h 2 )) at a potential of 0 V. In this way, the chemical potential of the proton-electron pair can be calculated simply by calculating the chemical potential of gas-phase H 2. The chemical potential of the proton-electron pair can be adjusted as a function of the applied potential by the standard relation between chemical and electrical potential, G = eu, where e is the elementary positive charge and U is the applied bias. Since the RHE is defined to be at 0 V at all ph values, a ph correction is not needed. Thus, the total chemical potential of the proton-electron pair as a function of applied potential, at all temperature and ph values, can be calculated as µ(h + ) + µ(e ) = 1 2 µ(h 2(g) ) eu (2) As an example, to calculate the free energy change from State 3 (adsorbed CO) to State 23 (adsorbed CHO), the free energy change of the below chemical reaction needs to be calculated: CO + (H + + e ) CHO (3) where an asterisk ( ) indicates that the species is adsorbed on the copper surface. The free energy change of this reaction would thus be: Page S1

2 Supplementary Material (ESI) for Energy & Environmental Science. Figure S1: Pathways in the electroreduction of carbon dioxide on a Cu(211) surface. The number at the top of each column corresponds to the number of proton-electron pairs transferred relative to CO2. Carbon is gray, oxygen is red, hydrogen is white, copper is orange. The lowest free-energy pathway to methane is highlighted. G(3 23) = µ(cho ) µ(co ) µ(h+ ) + µ(e ) 1 = µ(cho ) µ(co ) µ(h2(g) ) eu 2 (4) (5) Thus, the CHE model allows the potential (U ) to be explicitly contained within the free energy change of each step. The chemical potentials of each adsorbed species were calculated by standard DFT techniques, described in Section 2. To facilitate comparisons versus the data of Hori et al. [2], the literature data was converted from standard hydrogen electrode (SHE), which is defined at ph 0, to RHE by subtracting kt ph ln 10. This data was presented in Figure 1 of the main article. In the current study, the relative free energies of the intermediates were taken only as an indication of when different pathways in the electroreduction of CO2 open, since reaction barriers and coverage effects were not calculated. More exact prediction of onset voltages would require a full microkinetic model. Coverage effects are expected to be significant in a microkinetic model, but at the onset potential the coverages of key species should be low; coverage by spectator species causing poisoning may be a larger issue. These will be examined in future studies. Barriers for proton transfer to adsorbates from solution are expected to be quite small, as calculated for the protonation of adsorbed O2 [3] and for adsorbed OH [4]; in the latter case, the barrier for the proton transfer from solution (H3 O+ ) was reduced from about 0.25 ev to 0.02 ev as the potential was made more negative, from V to V (vs standard hydrogen electrode, SHE). A 0.25 ev barrier is very surmountable at room temperature, and barriers involving a proton transfer from solutions to an accessible atom are assumed to be small in the Page S2

3 current study. This assumption will need to be validated for individual adsorbates in future studies, in particular when microkinetic modeling is undertaken. 2 Electronic structure calculations 2.1 Adsorbate energies Electronic structure calculations were performed using density functional theory (DFT) with the revised Perdew-Burke-Ernzerhof (RPBE) [5] exchange-correlation functional in a plane wave pseudopotential implementation [6, 7] using the Dacapo DFT calculator in the ASE simulation environment [8, 9]. Calculations were carried out on the 211 step of the fcc Cu surface, using a (3 2 3 for small-molecule adsorptions) periodic cell with a 3.71 Å lattice constant and with 12 Å of vacuum. A stepped surface is used because they are generally found to be most reactive for C-O bond-breaking [10] a process of critical importance here. Standard dipole corrections were employed, and field effects were investigated, but found to be minimal in accordance with Karlberg et al. [11] and not included. Plane wave and density cut-off energies of 340 and 500 ev, respectively, were employed with a Fermi-level smearing width of 0.1 ev and (4,4,1) k-point sampling. Geometries were optimized and the lowest energy binding location is reported. The electronic energies of all intermediate states reported in this study (and shown in Figure 2 of the main article) are summarized in Tables S1 and S2. In these tables, the lowest energy bonding site and optimized geometry are shown for all adsorbates. States with multiple adsorbates (e.g., state 2) are calculated by summing the calculations of the two individual adsorbates, thus keeping coverages consistent between states. The electronic energy difference between the (slab + adsorbate) and the clean slab is reported in the tables, not including any free energy corrections or hydrogen-bond stabilization. Free energies of adsorbates were calculated by treating all 3N degrees of freedom of the adsorbate as vibrational and assuming that any changes in the vibrations of the copper surface caused by the presence of the adsorbate were minimal, in accordance with Jones et al. [12]. Modes of vibration were found by performing a normal-mode analysis; all vibrations were treated in the harmonic oscillator approximation. Zero-point energies, entropies, and heat capacities were calculated from these vibrations by standard methods [13] and used to convert the electronic energies into free energies at 18.5 C (to permit comparison to the data of Hori et al. [2]). The contribution to the free energy for each adsorbate involved in the lowest-energy pathways are listed in Table S3. We include solvation at the water-solid interface approximately by exploiting the findings that hydroxyl adsorbates (OH*) exposed to the liquid water were found to be stabilized by approximately 0.5 ev [1, 14, 15], and hydroxyl that is indirectly bound to the surface through other atoms, *R-OH, may be stabilized by 0.25 ev (as shown for OOH) [4]. The solvent stabilization of adsorbed CO was calculated in the present study by an identical method, employing a hexagonal water overlayer above a CO group adsorbed on a Cu 111 surface. This resulted in a CO* stabilization of 0.1 ev which was applied to CO* and CHO*. 2.2 Non-adsorbed species and gas-phase correction Electronic structure calculations of non-adsorbed species were performed using the same techniques as described above for adsorbed species, except with a Fermi-level smearing of 0.01 ev. Electronic energies (E) of gas-phase species were converted into chemical potentials (µ) at Page S3

4 Supplementary Material (ESI) for Energy & Environmental Science. Table S1: Description and energies of states used in this study. E is the electronic energy of the state minus the electronic energy of the clean slab(s) associated with that state, with C atoms referenced to graphene, H atoms to 1/2 H2, and O atoms to (H2 O-H2 ). Geom. Slab size E (ev) Label Description 1 * OH* + CO* (CO*), (OH*) CO* * OCHO* * OCH2 O* O* + CH3 O* (O*), (CH3 O*) OH* + CH3 O* (OH*), (CH3 O*) 16 CH3 O* O* OH* * COH* CHO* CHOH* CH2 O* CH2 OH* * COOH* 1.22 Page S4-0.03

5 Supplementary Material (ESI) for Energy & Environmental Science. Table S2: Description and energies of states used in this study. E is the electronic energy of the state minus the electronic energy of the clean slab(s) associated with that state, with C atoms referenced to graphene, H atoms to 1/2 H2, and O atoms to (H2 O-H2 ). Geom. Slab size E (ev) Label Description 29 C* OH* CH2 * CH3 * H* * C* + OH* (C*), (OH*) CH* + O* (CH*), (O*) OH* + CH2 * (OH*), (CH2 *) O* OH* * C(OH)OH* O* + CHO* (O*), (CHO) OH* + CHO* (OH*), (CHO*) C* + O* (C*), (O*) OH* + CH* (OH*), (CH*) O* + CH2 * (O*), (CH2 *) O* + CH3 * (O*), (CH3 *) OH* + CH3 * (OH*), (CH3 *) Page S5-0.35

6 Table S3: Contributions to the adsorbate free energy from the zero-point energy correction, enthalpic temperature correction, entropy, and the total free energy correction, respectively. All values are given in ev. Adsorbate ZPE C P dt T S G E elec OH* CO* OCHO* H* COOH* CHO* CH 2 O* CH 3 O* O* Table S4: Faradaic yields of products of CO 2 electroreduction as reported by Hori [2]. The Faradaic yields are converted to molar yields, which are taken as the partial pressures (when multiplied by Pa) used in chemical potential calculations in the current study. Product Faradaic yield (%) Molar yield (%) CH C 2 H H HCOOH CH 3 CH 2 OH C 3 H 7 OH CO C by standard ideal-gas methods [13]. Pressure corrections were treated as follows: CO 2 was calculated at Pa (1 atm). Gaseous products in the pathway were calculated at partial pressures corresponding to the Faradaic yields reported by Hori et al. [2], converted to molar yields and multiplied by one atmosphere, as shown in Table S4. The free energy of liquid water was calculated as an ideal gas and adjusted to a fugacity of 3534 Pa, which is the vapor pressure of water (at which point the chemical potential of liquid and vapor phases are equal). Similarly, formic acid was calculated as an ideal gas with a fugacity of 2.0 Pa, which corresponds to an aqueous-phase activity of Methanol was calculated at a fugacity of 6080 Pa, which from its vapor-liquid equilibrium with water corresponds to a liquid mole fraction of The components of the energy calculations for all non-adsorbed species are summarized in Table S5; all fugacity assumptions are also contained in this table. As reported elsewhere [16], the gas-phase thermochemical reaction energies calculated with the RPBE functional were found to be inconsistent with experimental values. In particular, the reaction enthalpy of the water-gas shift reaction was found to be particularly deviant from its known experimental value; the thermochemistry of this reaction is of particular importance in this study. To quantify this inaccuracy, a set of 11 species in 21 reactions (listed in Table S6), focused on the energies of CO 2, CO, H 2, and H 2 O, was statistically analyzed. A sensitivity analysis was undertaken comparing the calculated reaction enthalpies ( rxn H) to literature enthalpies taken from NIST [17]. A systematic error was found in all species containing the OCO backbone, specifically CO 2, HCOOH, CH 3 COOH, and HCOOCH 3 (of which, only CO 2 and Page S6

7 Table S5: Assumed fugacity for each non-adsorbate species, along with calculated electronic energy, zero-point energy correction, enthalpic temperature correction, entropy contribution, and chemical potential, respectively. Electronic energies and chemical potentials do not include the gas-phase correction. H 2 is the value used for gaseous hydrogen, H 2 (ref) is used for the computational hydrogen electrode as described in Section 1. Species Fugacity E elec ZPE C P dt T S µ (Pa) (ev) (ev) (ev) (ev) (ev) CO CO H HCOOH CH 3 OH H 2 O CH CH 2 O C 2 H H 2 (ref) HCOOH are significant in the current study). The sensitivity analysis results of varying the energy of these species is shown in Figure S2. Fourteen of the 21 reactions in this set are affected by the OCO-containing species. The mean absolute error of the unaffected ( bystander ) reactions is ev; the mean absolute error of the affected reactions at 0 ev correction is ev. As shown, the optimal correction to these species is ev. This results in a reduction in the mean absolute error of the affected reactions to ev. This represents a reduction in the error of the affected reactions by 84%, and an overall reduction in error (including the bystander reactions) of 70%. The slope of the affected reactions curve is at its maximum absolute value at 0 correction, and remains at this maximum value almost until the optimal value of 0.45 ev correction is reached, indicating that the error is directionally constant. Table S7 shows the reactions with and without the OCO correction applied; as can be seen, with the correction applied all rxn H values are within 0.20 ev of their literature values. Thus, the correction of ev was applied to CO 2 and HCOOH in the current study. The sensitivity analysis revealed no other systematic errors in RPBE gas-phase values above 0.2 ev. To determine if the RPBE gas-phase correction to CO 2 and HCOOH was artificially skewing the results, the complete analysis was repeated with the Perdew-Burke-Ernzerhof (PBE) [18] exchange-correlation functional, rather than the RPBE functional. The sensitivity analysis in the gas-phase was repeated, and CO, rather than CO 2, was found to be the largest outlier, as summarized in Table S8. (Table S8 shows only single-molecule optimums, thus an optimal correction of ev is shown for CO 2, rather than the ev correction noted earlier for all OCO-containing species.) This table implies that the gas-phase error in PBE lies largely on the CO molecule. Thus, an independent set of calculations can be made with the PBE functional without the effect of systematically changing the crucial CO 2 energy; comparison of these results to the RPBE results may provide an indication of if the CO 2 correction was unfairly biasing the results. The full CHE model was repeated in the PBE functional with a CO correction. Gas-phase calculations were undertaken in a manner identical to that described earlier, and a correction of ev was made to the CO energy. Energies and vibrations were calculated in a relaxed and self-consistent manner in the PBE functional. Similarly, all adsorbate energies were calculated Page S7

8 Table S6: Reactions analyzed for the gas-phase H comparisons (at 25 C and Pa). Rxn Stoichiometry 0 CO 2 + H 2 CO + H 2 O 1 4 H 2 + CO 2 CH H 2 O 2 3 H 2 + CO CH 4 + H 2 O 3 CO 2 + H 2 HCOOH 4 CO + H 2 O HCOOH 5 3 H 2 + CO 2 CH 3 OH + H 2 O 6 2 H 2 + CO CH 3 OH 7 3 H 2 + CO 2 1/2 CH 3 CH 2 OH + 3/2 H 2 O 8 2 H 2 + CO 1/2 CH 3 CH 2 OH + 1/2 H 2 O 9 10/3 H 2 + CO 2 1/3 C 3 H H 2 O 10 7/3 H 2 + CO 1/3 C 3 H 8 + H 2 O 11 7/2 H 2 + CO 2 1/2 C 2 H H 2 O 12 5/2 H 2 + CO 1/2 C 2 H 6 + H 2 O 13 3 H 2 + CO 2 1/2 C 2 H H 2 O 14 2 H 2 + CO 1/2 C 2 H 4 + H 2 O 15 11/4 H 2 + CO 2 1/4 CH 2 CHCH CH H 2 O 16 7/4 H 2 + CO 1/4 CH 2 CHCH CH 2 + H 2 O 17 2 H 2 + CO 2 1/2 CH 3 COOH + H 2 O 18 CO + H 2 1/2 CH 3 COOH 19 2 H 2 + CO 2 1/2 HCOOCH 3 + H 2 O 20 CO + H 2 1/2 HCOOCH affected reactions bystander reactions 0.7 mean absolute error, ev correction, ev Figure S2: Sensitivity analysis to the enthalpy correction of OCO-containing gaseous species. affected reactions refers to the reactions in Table S6 that contain CO 2, HCOOH, CH 3 COOH and HCOOCH 3. bystander reactions contain none of these species and are thus not affected. The mean absolute error is the absolute error per reaction as compared to NIST values. Page S8

9 Table S7: Reaction enthalpies (in ev) of the reactions listed in Table S6, in both the uncorrected state ( H unc ) and corrected ( H cor ) with ev for CO 2, HCOOH, CH 3 COOH, and HCOOCH 3. Reference values ( H ref ) are from NIST [17]. Rxn H ref H unc error H cor error Table S8: Comparison of the gas-phase errors encountered with the RPBE and PBE exchangecorrelation functionals. MAE compares the mean absolute error (in ev) of the reactions in Table S6. The numbers next to the molecules indicate the optimal correction to each species to minimize the MAE, considering single molecules only. RPBE PBE MAE CO CO H H 2 O Page S9

10 Table S9: Comparison of limiting potentials and steps for RPBE and PBE functionals. Limiting step and potential Pathway RPBE PBE H 2 * H* V H* H V HCOOH * + CO 2 COOH* V OCHO* HCOOH V CO * + CO 2 COOH* V * + CO 2 COOH* V CH 4 CO* CHO* V CO* CHO* V self-consistently in the PBE functional with relaxed geometries and using the optimized lattice constant of 3.66 Å for PBE. Binding sites were assumed to be unchanged by the choice of functional. The results of this PBE verification are shown in Table S9. As can be seen, the limiting potential at which each product is first exergonic is unchanged (within 0.1 V) when using the gas-corrected PBE or the gas-corrected RPBE functional. The pathway to produce formic acid via a formate (OCHO*) intermediate is predicted to open at lower voltages in the PBE functional than the pathway via carboxyl (COOH*); however, this does not effect the conclusions of the present study (but may become significant in future studies). Note that the limiting step also changes in the hydrogen evolution reaction, but since the steps are very equally spaced this can be caused by only slight deviations in the numerical results. The PBE functional (with a CO correction) is in reasonable agreement with the RPBE functional (with CO 2 and HCOOH corrections), indicating that the CO 2 gas-phase correction did not significantly skew the results in this study. 3 Optimized geometries The optimized geometries of each state reported in the manuscript are given in cartesian coordinates (with atomic positions in Å) below. Clean copper slabs (3 2 3) 18 Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Page S10

11 (3 3 3) 27 Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu State 1 (Cu slab) See Clean copper slabs. (CO 2 ) 3 C O O State 3 (CO on Cu) 20 Cu Cu Cu Cu Cu Cu Page S11

12 Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu C O State 4 (Cu slab) See Clean copper slabs. (CO) 2 O C State 6 (Cu slab) See Clean copper slabs. (HCOOH) 5 O C O H H State 16 (OCH 3 on Cu) 32 H H H C O Cu Cu Cu Page S12

13 Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu State 18 (O on Cu) 19 Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu O (CH 4 ) 5 C H H H H Page S13

14 State 20 (OH on Cu) 29 H O Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu State 21 (Cu slab) See Clean copper slabs. (H 2 O) 3 O H H State 23 (CHO on Cu) 30 H O Page S14

15 C Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu State 25 (CH 2 O on Cu) 31 O C H H Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Page S15

16 Cu Cu Cu Cu Cu Cu Cu Cu State 28 (COOH on Cu) 31 Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu C O O H State 33 (H on Cu) 19 Cu Cu Cu Cu Cu Page S16

17 Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu H State 34 (Cu slab) See Clean copper slabs. (H 2 ) 2 H H References [1] Nørskov, J. K. et al. Origin of the overpotential for oxygen reduction at a fuel-cell cathode. The Journal of Physical Chemistry B 108, (2004). [2] Hori, Y., Murata, A. & Takahashi, R. Formation of hydrocarbons in the electrochemical reduction of carbon dioxide at a copper electrode in aqueous solution. Journal of the Chemical Society, Faraday Transactions 1 85, (1989). [3] Janik, M. J., Taylor, C. D. & Neurock, M. First-principles analysis of the initial electroreduction steps of oxygen over Pt(111). Journal of the Electrochemical Society 156, B126 B135 (2009). [4] Tripkovic, V., Skúlason, E., Siahrostami, S., Nørskov, J. & Rossmeisl, J. The oxygen reduction reaction mechanism on Pt(111) from density functional theory calculations. Electrochim. Acta (2010). Doi: /j.electacta [5] Hammer, B., Hansen, L. B. & Nørskov, J. K. Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals. Physical Review B 59, (1999). [6] Payne, M. C., Teter, M. P., Allan, D. C., Arias, T. A. & Joannopoulos, J. D. Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients. Reviews of Modern Physics 64, (1992). [7] Vanderbilt, D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Physical Review B 41, (1990). Page S17

18 [8] Bahn, S. R. & Jacobsen, K. W. An object-oriented scripting interface to a legacy electronic structure code. Computing in Science & Engineering 4, (2002). [9] Both Dacapo and ASE are open-source software packages available at [10] Nørskov, J. K. et al. Universality in heterogeneous catalysis. Journal of Catalysis 209, (2002). [11] Karlberg, G. S., Rossmeisl, J. & Nørskov, J. K. Estimations of electric field effects on the oxygen reduction reaction based on the density functional theory. Physical Chemistry Chemical Physics 9, (2007). [12] Jones, G. et al. First principles calculations and experimental insight into methane steam reforming over transition metal catalysts. Journal of Catalysis 259, (2008). [13] Cramer, C. J. Essentials of Computational Chemistry (Wiley, 2004), 2nd edn. [14] Rossmeisl, J., Greeley, J. & Karlberg, G. S. Electrocatalysis and catalyst screening from density functional theory calculations. In Koper, M. T. M. (ed.) Fuel Cell Catalysis: A Surface Science Approach, chap. 3, (Wiley, 2009). [15] Karlberg, G. S. & Wahnström, G. Density-functional based modeling of the intermediate in the water production reaction on Pt(111). Physical Review Letters 92, (2004). [16] Blaylock, D. W., Ogura, T., Green, W. H. & Beran, G. J. O. Computational investigation of thermochemistry and kinetics of steam methane reforming on Ni(111) under realistic conditions. The Journal of Physical Chemistry C 113, (2009). [17] Afeefy, H., Liebman, J. & Stein, S. Neutral thermochemical data. In Linstrom, P. & Mallard, W. (eds.) NIST Chemistry WebBook, NIST Standard Reference Database Number 69 (National Institute of Standards and Technology, Gaithersburg MD, USA, 2010). [18] Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Physical Review Letters 77, (1996). Page S18