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

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

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

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

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

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

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

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

Thermodynamics 2 H 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 E 2 0 )/2 = E 0

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

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)

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).

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

“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

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

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

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

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

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)

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

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

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

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.

Mechanism for OER O H 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 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

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

Comparsion RuO 2 and OEC J.Rossmeisl, K.Dimitrevskii, P.Siegbahn, J.K.Norskov, J.Phys.Chem.C 111 (2007) 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)

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

Why chlorine electrolysis works 2 Cl -  Cl e - E 0 =1.36 V 2 H 2 O  O H 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

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

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?

Acknowledgments Dirk Heering (Leiden) Jan Rossmeisl, Jens Nørskov (Lyngby) ELCAT Marie Curie Initial Training Network, NWO, NRSC-C