Thermodynamics and kinetics
of multi-electron transfer
Marc Koper
Leiden University
Redox reactions of water
current
density
H2 → 2 H+ + 2 eplatinum
hydrogenase
2 H2O → O2 + 4 H+ + 4 ediffusionlimited
current
RuO2
PSII
1.23
0
diffusionlimited
current
2 H+ + 2 e- → H2
PtNi
laccase
overpotential
O2 + 4 H+ + 4 e- → 2 H2O
E (vs.RHE)
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
Cl0
Cl-
Cl0 + e-  ClC.Hartnig, M.T.M.Koper, J.Am.Chem.Soc. 125 (2003) 9840
Nonlinear solvent reorganization
Effective radius gets smaller
with higher charge
C.Hartnig, M.T.M.Koper, J.Chem.Phys. 115 (2001) 8540
Orientation of water
depends on charge:
strongest change in
electrostriction from 0 to -1
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)
free
energy
H+ + e-
Hads
H2
Thermodynamics
2 H+ + 2 e-  H2
H+ + e-  Hads
Hads + H+ + e-  H2
E0 = 0 V
E10 = - ΔGads(H)/e0
E20 = ΔGads(H)/e0
Thermodynamic restriction: (E10 + E20)/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
R.Parsons,Trans.Faraday Soc. (1958); H.Gerischer (1958)
M.T.M.Koper, H.A.Heering, in press
J.K.Nørskov et al., J.Electrochem.Soc. (2004)
M.T.M.Koper, E.Bouwman, Angew.Chem.Int.Ed. (2010)
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 BronstedEvans-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 approximate 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 + E20 + 2 E30)/4 = E0
Lining up energy levels
free
energy
O2
OOHads
OHads
H2O
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) 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+ + eOHads  Oads + H+ + e2 Oads  O2
Oads + H2O  OOHads + H+ + eOOHads  O2 + H+ + e-
E 01
E02
Keq
E 03
E 04
Volcano plot
non-zero thermodynamic
overpotential
J.Rossmeisl et al. J.Electroanal.Chem (2007)
Comparsion RuO2 and OEC
Oads + H2O  OOHads + H+ + ePDS 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
Ni-doped RuO2
P.Krtil et al., Electrochim. Acta (2007)
Why chlorine electrolysis works
2 Cl-  Cl2 + 2 e-
E0 =1.36 V ηT = 0 V
2 H2O  O2 + 4 H+ + 4 e- E0 = 1.23 V ηT > 0 V
Both are catalyzed by RuO2/TiO2
Chlorine electrolysis works thanks to the
scaling relationships.
Electrocatalytic CO2 reduction
CO
2e-
CO2
2e-
high
overpotential
CH4, C2H4, CxHy
Cu
HCOOH
difficult
aldehyde
Calvin cycle
alcohol
2e-
C2O42-
fuel?
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