Theory of
Electrocatalysis:
The Path Ahead
Wolfgang Schmickler
Institute of Theoretical Chemistry
University of Ulm
predictions are difficult to make, especially if they are to be about the future
old German saying
Menu
Hydrogen evolution - a prototype for a catalytic reaction
Catalysis of electron transfer - general principles
More about hydrogen catalysis
Remarks about oxygen
What will happen in the next few years?
outer sphere electron transfer
T. Iwasita, W. Schmickler, and J.W. Schultze, Ber. Bunsenges. 89 (1985) 138
E. Santos, T. Iwasita, and W. Vielstich, Electrochim. Acta 31 (1986) 431.
Hydrogen Oxidation - Evolution
an overly obsession with hydrogen evolution
has delayed the development of electrochemistry
by at least a decade
J. O’M. Bockris
Unfortunately, the hydrogen electrode must be considered to
be an extremely complicated example.
This may well be the reason for the relatively slow
development of electrode kinetics
K. J. Vetter
Trasatti’s Volcano Plot
oxide
covered
oxide
covered
theory
(wrong)
Volcano plot, Nørskov et al.
role of the solvent
the reaction
requires about 32 eV
about 23 eV come from proton solvation
about 9 eV come from metal work function
any rest comes from electrode potential
without a solvent hydrogen oxidation is impossible!
it is not possible to calculate electrochemical
reactions by ab initio methods
• too many particles: metal, reactants,
solvent
• how should we incorporate the potential?
• how should we find the transition state?
Our Philosophy
formulate general theories based on
model Hamiltonians
extract the parameters that govern the reaction
achieve a basic understanding
perform calculations for specific systems
using input from quantum-chemical calculations
and from simulations
Catalysis of Electron Transfer
Santos - Schmickler
Fermi level
interaction of level with a d-band
level at center
of d-band
level
strong and weak
interactions
catalysis by d-band
requires d band near Fermi level
strong coupling with reactant
E. Santos, W. Schmickler, ChemPhysChem 13 (2006) 282, Chem. Phys. 332 (2007) 39
evolution of
density of states
during reaction
DOS /eV
-1
bond breaking
electron transfer
energy / eV
center of gravity passes below barrier
metal d bands
on Pt(111)
hydrogen catalysis
what can we do now?
From DFT
calculate d- band DOS of metals
energy of adsorbed hydrogen for various distances
From theory
obtain coupling d-band to hydrogen
calculate effect of solvent reorganization
obtain free energy surfaces for reaction
coupling constants
Potential surfaces for Volmer-reaction
occupancy
eV
Activation energies / eV
Cd(0001) Cu(111) Ag(111) Ag(100) Au(111) Pt(111)
1.00
0.80
0.75
0.82
0.86
0
effect of nanostructure
monolayers of foreign metals (Pd/Au(111))
islands
surface alloys
steps
nanowires
monolayer of
Pd on Au(111)
(E. Santos)
Pd/Au(111)
island vs. surface alloy
(E. Santos)
Oxygen Reduction - the big challenge
many possible steps
energies of activation?
competition from adsorption and oxide formation
P.Vassilev, M.T.M.Koper,
J.Phys.Chem.C
111 (2007) 2607
can everything be explained
by O and OH adsorption?
Nørskov et al. JCP B 108 (2004) 17886
should we focus on the rate determining step?
in acid solutions:
reaction order with respect to
transfer coefficient about 1/2
is unity
what is the role of water at the interface
in reactions?
what is the solvation of ions near the
interface?
Can we learn something from
molecular dynamics?
some numbers
2
ab initio methods: area < 100 Å , time 10 ps
1 transition per run corresponds to 1.6 × 10 Acm
6
2
VB methods: area 500 Å , time 1 ns
1 transition per run corresponds to 300 Acm
−2
−2
Simulations for Pt(111)


Surface charge density: -7.5, -9.4, -11.3, -13.1, 2
15.0, -16.9, -18.8 µC/cm_:
elementary charges
distributed on bottom metal layer
At least 30 independent trajectories for each
surface charge value which showed transfer

Trajectory lengths: at least 500 ps if no transfer
occurs
• proton starts at 10 Å from surface
proton transfer
to Pt
trajectory for σ = −7.9µCcm
−2
adsorbed
Zundel ion
transfer to
surface
First Results for Ag(111)
nothing happens for σ > −17µCcm
remember
−2
φpzc ≈ −500mV
at equilibrium potential proton transfer is uphill
by about 0.4 eV
pre-adsorbed Zundel ion is not seen
Ag(111)
Zundel ion
only metastable
at interface
What can we expect in the near future?
For hydrogen:
Calculations for catalysis of nanostructures
For all systems:
Role of the solvent
For oxygen:
More about rate determining step
In general:
More DFT for thermodynamics and activation
energies of chemical steps
Molecular dynamics simulations
Recent works:
Nørskov et al., PCCP 9 (2007) 3241
Otani et al., PCCP 10 (2008) 3609
Expect more of the same
General Problem:
How to include electrode potential?
Constant background charge (Neurock)
Add a few ions (Nørskov)
Counter electrode
My wish list for theory / simulations
Include some water, if you have dipoles or charges
Do not try to simulate the whole interface,
It is impossible
Focus on well-defined aspects
Forget about the electrode potential –
use fields
Do not try to calculate CVs
My wish list for experiments
Provide kinetic data for well-defined systems
Use a fast kinetic method, NOT CVs!
Work together with theorists..
Thanks to
Elizabeth Santos
concepts, coauthor
Kay Pötting
DFT
calculations
Paola Quaino
DFT
Funding: DFG, EU (NENA and COST), DAAD, CONICET(Argentina)