Thermodynamics and kinetics of multi-electron transfer

Marc Koper

Leiden University

Redox reactions of water

E (vs.RHE)

currentdensity

0 1.23

2 H+ + 2 e- → H2

H2 → 2 H+ + 2 e-

diffusion-limitedcurrent

2 H2O → O2 + 4 H+ + 4 e-

O2 + 4 H+ + 4 e- → 2 H2O

diffusion-limitedcurrent

PtNilaccase

RuO2

PSIIplatinumhydrogenase

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-Cl0

Cl0 + 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+ + 2 e- H2

H+ + e- Hads (Volmer)

Hads + H+ + e- H2 (Heyrovsky)

H+ + e- Hads H2 freeenergy

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 + E2

0)/2 = E0

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

Thermodynamic volcano plot

zero thermodynamic overpotential

descriptor

M.T.M.Koper, H.A.Heering, in pressM.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- 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).

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

“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 H2 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*/Hads

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 + E2

0 + 2 E30)/4 = E0

Lining up energy levels

O2 OOHads OHads H2Ofreeenergy

Thermodynamic overpotential now dependson the ability of the catalyst to bind oxygenGold: weak oxygen bindingPlatinum: 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) 016105

Thermodynamic volcano plot

Bad news : because of the scaling relationships, we cannot line up the E0’s.

non-zero thermodynamic overpotential

Experiment volcano plot ORR

J.Greeley et al. Nature Chem. 1 (2009) 552

Pt3Ni 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

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

Volcano plot

non-zero thermodynamic overpotential

J.Rossmeisl et al. J.Electroanal.Chem (2007)

Comparsion RuO2 and OEC

J.Rossmeisl, K.Dimitrevskii, P.Siegbahn, J.K.Norskov, J.Phys.Chem.C 111 (2007) 18821

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)

Ni-doped RuO2

P.Krtil et al., Electrochim. Acta (2007)

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

Electrocatalytic CO2 reduction

CO2

CO

HCOOH

C2O42-

2e-

2e-

2e-

CH4, C2H4, CxHy

Cu

highoverpotential

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 CO2 to something useful?

Acknowledgments

• Dirk Heering (Leiden)

• Jan Rossmeisl, Jens Nørskov (Lyngby)

• ELCAT Marie Curie Initial Training Network, http://www.elcat.org.gu.se/

• NWO, NRSC-C