1. Thermodynamics and kinetics of multi-electron transfer Marc Koper Leiden University

2. Redox reactions of water E (vs.RHE) current density 0 1.23 2 H + + 2 e - → H 2 H 2 → 2 H + + 2 e - diffusion- limited current 2 H 2 O → O 2 + 4 H + + 4 e - O 2 + 4 H + + 4 e - → 2 H 2 O diffusion- limited current PtNi laccase RuO 2 PSII platinum hydrogenase overpotential

3. Catalysis of multi-step reactions Practically every (interesting) chemical reaction happens in a series of steps; catalysis is often about optimizing that sequence 1 e - / 1 step / 0 intermediate 2 e - / 2 steps / 1 intermediate >2 e - / >2 steps / >1 intermediate

4. Single electron transfer Marcus Theory Activation energy determined by solvent reorganization energy λ (very difficult quantity to calculate accurately!)

5. Movie of electron transfer Cl - Cl 0 Cl 0 + e -  Cl - C.Hartnig, M.T.M.Koper, J.Am.Chem.Soc. 125 (2003) 9840

6. Nonlinear solvent reorganization Orientation of water depends on charge: strongest change in electrostriction from 0 to -1 Effective radius gets smaller with higher charge C.Hartnig, M.T.M.Koper, J.Chem.Phys. 115 (2001) 8540

7. What Marcus does not account for Proton transfer Bond making and bond breaking Catalysis

8. Two electron transfer 2 H + + 2 e -  H 2 H + + e -  H ads (Volmer) H ads + H + + e -  H 2 (Heyrovsky) H + + e - H ads H 2 free energy

9. Thermodynamics 2 H + + 2 e -  H 2 E 0 = 0 V H + + e -  H ads E 1 0 = - ΔG ads (H)/e 0 H ads + H + + e -  H 2 E 2 0 = ΔG ads (H)/e 0 Thermodynamic restriction: (E 1 0 + E 2 0 )/2 = E 0

10. Potential-determining step The potential-determining step is the step with the least favorable equilibrium potential The difference in the equilibrium potential of the potential-determining step and the overall equilibrium potential we will call the thermodynamic overpotential η T

11. Thermodynamic volcano plot zero thermodynamic overpotential descriptor M.T.M.Koper, H.A.Heering, in press M.T.M.Koper, E.Bouwman, Angew.Chem.Int.Ed. (2010) R.Parsons,Trans.Faraday Soc. (1958); H.Gerischer (1958) J.K.Nørskov et al., J.Electrochem.Soc. (2004)

12. Generalization H + + e -  H ads plus 2 H ads  H 2 (e-chem) H + + 2e -  H - plus H - + H +  H 2 (hydrogenase) The optimal electrocatalyst is achieved if each step is thermodynamically neutral. The H intermediate must bind to the catalyst with a bond strength equal to ½ E(H-H).

13. What about activation barriers? Can in principle be estimated with a more sophisticated model Contribution of water is constant (to a first approximation) as we vary the catalyst Activation barrier follows variations in the thermodynamics because of the Bronsted- Evans-Polanyi (BEP) relationship δE act = αδE react

14. “Marcus” model for HER/HOR Combines a Hückel-type model for a diatomic molecule with a coupling to the metal electronic levels and a Marcus-type coupling to the solvent Calculates approxi- mate activation barriers E.Santos, M.T.M.Koper, W.Schmickler, Chem.Phys. 344 (2008) 195

15. Experimental volcano for H 2 evolution J.Greeley, J.K.Nørskov, L.A.Kibler, A.M.El-Aziz, D.M.Kolb, ChemPhysChem 7 (2006) 1032

16. Good catalysts for HOR exist Platinum Hydrogenases (FeFe, FeNi) They optimize for the binding of H*/H ads

17. More than 2 electron transfers O 2 + 4 H + + 4 e -  2 H 2 OE 0 = 1.23 V O 2 + H + + e -  OOH ads E 1 0 OOH ads + H + + e -  2 OH ads E 2 0 2 OH ads + 2 H + + e -  2 H 2 OE 3 0 Thermodynamic restriction: (E 1 0 + E 2 0 + 2 E 3 0 )/4 = E 0

18. Lining up energy levels O 2 OOH ads OH ads H 2 O free energy Thermodynamic overpotential now depends on the ability of the catalyst to bind oxygen Gold: weak oxygen binding Platinum: stronger oxygen binding

19. Scaling relationships F.Abild-Petersen, J.Greeley, F.Studt, P.G.Moses, J.Rossmeisl, T.Munter, T.Bligaard, J.K. Nørskov, Phys.Rev.Lett. 99 (2007) 016105

20. Thermodynamic volcano plot Bad news  : because of the scaling relationships, we cannot line up the E 0 ’s. non-zero thermodynamic overpotential

21. Experiment volcano plot ORR J.Greeley et al. Nature Chem. 1 (2009) 552

22. Pt 3 Ni and Fe-based catalyst V.Stamenkovic et al., Science (2007) M.Lefevre et al. Science (2009)

23. ORR is a difficult case Man and nature have the same problem: Pt and laccase are good but not perfect catalysts for the ORR We need to beat the scaling relationships Fundamental problem with catalyzing reactions with more than 2 steps and more than 1 intermediate.

24. Mechanism for OER O 2 + 4 H + + 4 e -  2 H 2 OE 0 = 1.23 V H 2 O  OH ads + H + + e - E 0 1 OH ads  O ads + H + + e - E 0 2 2 O ads  O 2 K eq O ads + H 2 O  OOH ads + H + + e - E 0 3 OOH ads  O 2 + H + + e - E 0 4

25. Volcano plot non-zero thermodynamic overpotential J.Rossmeisl et al. J.Electroanal.Chem (2007)

26. Comparsion RuO 2 and OEC J.Rossmeisl, K.Dimitrevskii, P.Siegbahn, J.K.Norskov, J.Phys.Chem.C 111 (2007) 18821 O ads + H 2 O  OOH ads + H + + e - PDS on RuO 2 (η T =0.37 V) and on Loll et al. (η T =0.32 V) OOH ads  O 2 + H + + e - PDS on Ferreira et al. (η T =0.21 V)

27. Ni-doped RuO 2 P.Krtil et al., Electrochim. Acta (2007)

28. Why chlorine electrolysis works 2 Cl -  Cl 2 + 2 e - E 0 =1.36 V 2 H 2 O  O 2 + 4 H + + 4 e - E 0 = 1.23 V Both are catalyzed by RuO 2 /TiO 2 Chlorine electrolysis works thanks to the scaling relationships. η T = 0 V η T > 0 V

29. Electrocatalytic CO 2 reduction CO 2 CO HCOOH C 2 O 4 2- 2e - CH 4, C 2 H 4, C x H y Cu high overpotential aldehyde Calvin cycle alcohol fuel? difficult

30. Conclusions Optimizing the binding of key intermediates is the key to a good catalyst This is inherently more difficult for 2 or more intermediates than for 1 intermediate (scaling relationships) DFT is a useful tool in understanding and screening catalysts Can we efficiently and selectively reduce CO 2 to something useful?

31. Acknowledgments Dirk Heering (Leiden) Jan Rossmeisl, Jens Nørskov (Lyngby) ELCAT Marie Curie Initial Training Network, http://www.elcat.org.gu.se/http://www.elcat.org.gu.se/ NWO, NRSC-C