Thermodynamics and kinetics of multi-electron transfer

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

2. Redox reactions of water current density 2 H2O → O2 + 4 H+ + 4 e- H2→2 H+ + 2 e- diffusion- limited current RuO2 PSII platinum hydrogenase 1.23 0 E (vs.RHE) PtNi laccase diffusion- limited current overpotential O2 + 4 H+ + 4 e-→ 2 H2O 2 H+ + 2 e- → H2

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 Cl0 Cl- Cl0 + 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- H2 H+ + e- Hads (Volmer) Hads + H+ + e- H2 (Heyrovsky) H+ + e- Hads H2 free energy

9. Thermodynamics 2 H+ + 2 e- H2 E0 = 0 V H+ + e- Hads E10 = - ΔGads(H)/e0 Hads + H+ + e-  H2 E20 = ΔGads(H)/e0 Thermodynamic restriction: (E10 + E20)/2 = E0

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 ηT

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

12. Generalization H+ + e- Hads plus 2 Hads  H2 (e-chem) H+ + 2e- H- plus H- + H+  H2 (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 δEact = αδEreact

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 H2 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*/Hads

17. More than 2 electron transfers O2 + 4 H+ + 4 e- 2 H2O E0 = 1.23 V O2 + H+ + e-  OOHads E10 OOHads + H+ + e-  2 OHads E20 2 OHads + 2 H+ + e-  2 H2O E30 Thermodynamic restriction: (E10 + E20 + 2 E30)/4 = E0

18. Lining up energy levels O2 OOHads OHads H2O 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 E0’s. non-zero thermodynamic overpotential

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

22. Pt3Ni 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 O2 + 4 H+ + 4 e- 2 H2O E0 = 1.23 V H2O  OHads + H+ + e- E01 OHads  Oads + H+ + e- E02 2 Oads  O2 Keq Oads + H2O  OOHads + H+ + e- E03 OOHads  O2 + H+ + e- E04

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

26. Comparsion RuO2 and OEC Oads + H2O  OOHads + H+ + e- PDS on RuO2 (ηT=0.37 V) and on Loll et al. (ηT=0.32 V) OOHads  O2 + H+ + e- PDS on Ferreira et al. (ηT=0.21 V) J.Rossmeisl, K.Dimitrevskii, P.Siegbahn, J.K.Norskov, J.Phys.Chem.C 111 (2007) 18821

27. Ni-doped RuO2 P.Krtil et al., Electrochim. Acta (2007)

28. Why chlorine electrolysis works 2 Cl- Cl2 + 2 e- E0 =1.36 V 2 H2O  O2 + 4 H+ + 4 e-E0 = 1.23 V Both are catalyzed by RuO2/TiO2 Chlorine electrolysis works thanks to the scaling relationships. ηT = 0 V ηT > 0 V

29. Electrocatalytic CO2 reduction CO CH4, C2H4, CxHy high overpotential 2e- Cu difficult CO2 HCOOH aldehyde 2e- Calvin cycle alcohol 2e- C2O42- fuel?

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 CO2 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/ • NWO, NRSC-C