the d-band model and heterogeneous catalysis – part 1xes.fysik.su.se/pdf/bligaard-1.pdf · the...

The d-band modeland

Heterogeneous Catalysis – Part 1

Chemical Surface Physics School, Stockholm May 19, 2010

Thomas BligaardCenter for Atomic-scale Materials Design

Department of PhysicsTechnical University of Denmark

Harvesting Harvesting sunlightsunlight

SustainableSustainable butbut-- LowLow intensityintensity-- WeatherWeather, , seasonseason and and

time dependenttime dependent

Chemical Chemical storagestorage-- HighHigh energyenergy densitydensity-- Storable/moveableStorable/moveable-- Bridges temporal Bridges temporal cyclescycles ofofproductionproduction & & consumptionconsumption

-- ExploitsExploits existingexistinginfrastructureinfrastructure

Global annual energyconsumption supplied by the sun in one hour

Part of the solution: Chemical Part of the solution: Chemical storagestorage

HoweverHowever......

High catalytic efficiency- Large surface area – nanoparticles- Optimal surface composition and

structure – design

• More efficient catalysts

• Stable catalysts

• Catalysts made from Earth-abundant materials

A catalyst is a material that speeds up a chemical reaction

The The CatalystCatalyst ChallengeChallenge

~80 years ago:Where is the hope ?

- for using calculations in solving atomic-scale problems

“The general theory of quantummechanics is now almost complete. The

underlying physical laws necessary for themathematical theory of a large part of

physics and the whole of chemistry arethus completely known, and the difficultyis only that the exact application of these

laws leads to equations much toocomplicated to be soluble.”

P.A.M. Dirac(Nobel PrizePhysics, 1933)

(Dirac, 1929)

R.S. MullikenNobel Prize,

Chemistry, 1966

“In conclusion, I would like to emphasize strongly my belief that the

era of computing chemists, when hundreds if not thousands of

chemists will go to the computing machine instead of the laboratory for increasingly many facets of chemical

information, is already at hand.”

~40 years ago: Here it is !

(Mulliken, Nobel Lecture, 1966)

~Today: The revolution is to come

New possibilities – eScience:“The next 10 to 20 years will see computational science firmly embedded in the fabric of science– the most profound development in the scientific method in over three centuries.”

A SCIENCE-BASED CASE FOR LARGE-SCALE SIMULATIONOffice of Science

U.S. Department of Energy, 2003

The big revolution is still to come !

Traditional simulation flowComputational design at the atomic scale

Nørskov, BligaardRossmeisl, Christensen

Nature Chemistry1, 37-46 (2009)

Outline of today’s lecture

Material design strategies- Surface activity:

• The d-band model (briefly)• Linear energy correlations/Scaling relations• Brønsted-Evans-Polanyi relations• Volcano-relations• Understanding the experimental trends for

the steam reforming reaction- Catalyst design

• Methanation• Selective hydrogenation• Hydrogen evolution

Outline of tomorrow’s lecture

The d-band model and its implications in more detail• The Newns-Anderson model• Effective medium theory• Electronic structure effects in alloying• Structure sensitivity of catalytic reactions• The electronic and geometrical effects in

heterogeneous catalysis

Three flavors of systematic“Computational Design”

A. Direct computational searchB. Data base screeningC. Descriptor-based search

Bligaard, Andersson, Skriver, Jacobsen, Christensen, NørskovMaterials Research Society Bulletin 31, 986 (2006)

Direct Computational Search

Pick a set ofstructures/compositions

Calculate their properties

Experimental testing

Good enough ?

Yes!

No ! Choose betterStructures/compositions

+ Adaptively improving- Difficult to addconstraints after a run

EvolutionaryAlgorithm

Johannessen, Bligaard, Ruban, Skriver,Jacobsen, Nørskov, Phys. Rev. Lett. 88,

255506 (2002)

EvolutionaryAlgorithm

The most stable 4-component

ordered metal alloy is found in the 11th

generation, and the 20 most stable

have been determined in 45

generations

Johannessen, Bligaard, Ruban,Skriver, Jacobsen, Nørskov,

Phys. Rev. Lett. 88, 255506 (2002)

Evolutionary algorithm for 4-component alloys

EAs outperform random search by a factor of 50 – even for this simple example

Structural stability of ordered alloyseV/atom

75 %

25 %

Formation energyof the

L12 binaryalloy structures

with respectto pure metals

LMTO-GGAcalculations

Johannessen, Bligaard, Ruban, Skriver, Jacobsen, Nørskov,Phys. Rev. Lett. 88, 255506 (2002)



Bligaard, Andersson, Skriver, Jacobsen, Christensen, NørskovMaterials Research Society Bulletin 31, 986 (2006)

Screening of Computed Data

Calculate properties for alarge number of systems

Look for systemshaving good qualities

Experimental testing

+ Ease of reusing data- Difficult to include enough

interesting systems

Bligaard, Johannessen, Ruban, Skriver, Jacobsen, Nørskov,App. Phys. Lett. 83, 4527 (2003)

Pareto optimality

(as a methodfor searchingdatabases)

The 82 alloys with the most relevant properties areeasily obtainedfrom the full database of> 64,000 alloys.

The Computational MaterialsData Repository

ternary

quaternary

International collaboration needed to reach relevant data base sizes

Munter, Landis et al.

The vision

The molecular engineering workbench

experimental data theory

understanding/concepts new experiments new design tools

computation



Developing the descriptorsBligaard, Andersson, Skriver, Jacobsen, Christensen, Nørskov

Materials Research Society Bulletin 31, 986 (2006)

The origin of catalytic trendsthe d-band model

Hammer, Nørskov, Nature 376, 238 (1995)Hammer, Nørskov, Adv. Catal. 45, 71 (2000)

Bligaard, Nørskov in Chemical bonding at surfaces, Elsevier (2008)

Corollary to the d-band model:adsorbate energies scale

Nilsson, Pettersson, Hammer,Bligaard, Christensen, Nørskov

Catal. Lett. 100, 111 (2005)

The 0th order d-band model:

Adsorption energies on 3d, 4d, and 5d metals is linear in the d-band center location

Corollary to d-band model:

The adsorption energy of any adsorbate scales with the adsorption energy of any other adsorbate on the d-metals

CHx adsorption energiesClose-packed surfaces

Scaling relations: CHx vs. C adsorption

Abild-Pedersen, Greeley, StudtRossmeisl, Munter, Moses

Skulason, Bligaard, NørskovPhys. Rev. Lett. 99, 016105 (2007)

Stepped surfaces CH

CH2

CH3

d-band modelHammer and Nørskov, Nature 376 (1995) 238

+ Scaling slopeEffective Medium Theory (EMT) rationalization:Nørskov and Lang, Phys. Rev. B 21, 2131 (1980)Nørskov, Rep. Prog. Phys. 53, 1253 (1990)

Rationalization of scaling relations

ξγ +Δ=Δ AAH ExE x )(

Abild-Pedersen, Greeley, Studt, Rossmeisl, Munter, Moses, SkulasonBligaard, Nørskov, Phys. Rev. Lett. 99, 016105 (2007)

maxmax /)()( xxxx −=γ

CHx adsorption energies Close-packed surfaces

Scaling relations: CHx vs. C

CH : 3/4

CH2 : 1/2

CH3 : 1/4



For AHx :slope = (xmax-x)/xmax Stepped surfaces

Close-packed surfaces

Stepped surfaces

Scaling relations: NHx vs. N



NH : a=2/3

NH2 : a=1/3

Scaling relations: OH vs. O

Stepped surfaces




OH : a=1/2


Scaling relations: SH vs. S

Stepped surfaces



SH : a=1/2

Predicting heats of reaction from scaling relations

Requires :1. Atomic C, O, and

S adsorption energies on all d-metals

2. Reaction intermediates on one metal (Pt)



Scaling: Methanation

Jones, Bligaard, Abild-Pedersen, Nørskov, J. Phys.: Cond. Mat. 20, 064239 (2008)

Scaling: Steam reforming

Scaling: Ammonia synthesis

Scaling: Water-gas-shift

Scaling: Methanol synthesis

Andersson, Bligaard, Kustov, Larsen, Greeley, Johannessen, Christensen, Nørskov, J. Catal. 239, 501 (2006)

Ediss (eV)

Brønsted-Evans-Polanyi (BEP) relations:e.g. CO dissociation

Ediss (eV)

CO diss.slow

C, Opoisoning

Sabatier, Ber. Deutsch. Chem. Gesell. 44, 1984 (1911)Bligaard, Nørskov, Dahl, Matthiesen, Christensen, Sehested, J. Catal. 224, 206 (2004)

Bligaard, Nørskov in “Chemical Bonding at Surfaces”, Elsevier (2008)

Volcano: The methanation reaction:CO + 3H2 CH4 + H2O

Nørskov, Bligaard,Logadottir, Bahn, Hansen,

Bollinger, Bengaard, Hammer, Sljivancanin, Mavrikakis, Xu,

Dahl, JacobsenJ. Catal. 209, 275 (2002)

Universality of BEPsBEPs exist for a number of

small molecules– and happen to be identical

Omnipresence of volcanoes– and very similar kinetics

Generalized kinetic models

“BEPs” + “Contracted energy diagrams”

“Generalized Kinetic Models”

Models simplified to the level where they only contain the absolutely essential reaction steps

Bligaard, Nørskov, Dahl, Matthiesen, Christensen, Sehested,J. Catal. 224, 206 (2004)

A generalized kinetic model: A2+2B 2AB

A2 + 2* 2A* R1 = 2k1PA2Θ*2 - 2k-1ΘA

2 (= r1 - r-1)

A* + B AB + * R2 = k2ΘAPB - k-2PABΘ* (= r2 - r-2)

Site conservation: 1 = ΘA + Θ*

Three equations with four unknowns (R1 , R2 , ΘA , and Θ*)

The missing equation is obtained from either:

Stationary coverage: dΘi/dt = 0: r1 + r-2 = r-1 + r2 (R1 = R2)

Rate-limitation: E.g. reaction 1 is slow: r2 = r-2 (R2 = 0)

Stationary External ConditionsdPx/dt = 0

This reduces the differential equations to algebraic equations.

• Significantly reduces computation time.

A perfect local description of:

• Fixed bed reactors

• Fluidized bed reactors

• Trickle bed reactors

(But not applicable to Batch reactors)

Numerical problems

General micro-kinetic model:

• Singular differential equations

Stationary solution:

• Ill-conditioned algebraic equations

Therefore specialized numeric methods are required !?

Ill-conditioning of stationary state

-20

-15

-10

-5

0

5

-4 -3 -2 -1 0 1 2

Eadsorption (eV)

Log(

TO

F (1

/s))

r1 = r-1 , R2 << r1

Easy region

r2 = r-2 , R1 << r2

The approach to equilibrium

- This simple model can be solved by Taylor-expanding

the equations in the limits where they are ill-defined.

R1 = 2k1PA2Θ*2 - 2k-1ΘA

2 = 2k1PA2Θ*2(1-γ1), γ1 = r-1/r1

R2 = k2ΘAPB - k-2PABΘ* = k2ΘAPB (1-γ2), γ2 = r-2/r2

γ = γ1 γ22 = PAB

2/(PA2PB2) . 1/Keq

This allows one to define the Kinetic Switching Parameter (KSP):

KSP = [ 3 + (2 Log(γ2) – Log(γ1))/Log(γ) ]/2

(which is 1 when step 1 is rate-determining and 2 when step 2 is)

Simplest generalized kineticsA2+2B 2AB

Ea

ΔE1

BEP + All entropy lost on surface

Dissociation is rate-limiting at optimumIf the process follows the universal BEP-relations

The switching happens to the left of the maximum !In other words: The optimal catalyst can not directly be improved by lowering the barrier of the rate-determining step

Eads (eV)

KSP

TOF

Optimal catalysts– dependence on the approach to equilibrium

1. A2 + 2* ↔ 2A*

2. A* + B ↔ AB + *

eqBA

AB

KPPP 1

2

2

2

⋅=γ

Very exothermic reactions take place atsmall values of γ for a similar conversion

Optimal catalysts– dependence on temperature and pressure

High temperature and low reactant pressure “moves”the optimal catalyst towards more reactive surfaces.

Optimal catalysts– dependence on precursor stability

1. A2 + * ↔ A2*

2. A2* ↔ 2A*

3. A* + B ↔ AB + *

1. A2 + 2* ↔ 2A*

2. B + * ↔ B*

3. A* + B* ↔ AB + 2*

Le Chatelier-like principle for optimal catalysts:coverage conservation laws

The coverage of a key reactant on the surface of the optimal catalyst under given reaction conditions is constant.

( in the simple case “coverage of A” = “1-BEPslope” )

The optimal catalyst is located where the coverage switches – or where the adsorption free energy is close to zero.

More product poisoningnobler surface required

1. A2 + 2* ↔ 2A*

2. A* + B ↔ AB + *

eqBA

AB

KPPP 1

2

2

2

⋅=γ

Very exothermic reactions take place atsmall values of γ for a similar conversion

Lower temperature or high pressurePoisons surface

High temperature and low reactant pressure “moves”the optimal catalyst towards more reactive surfaces.

Stronger precursor bindingPrecursor competes with key reactant

1. A2 + * ↔ A2*

2. A2* ↔ 2A*

3. A* + B ↔ AB + *

1. A2 + 2* ↔ 2A*

2. B + * ↔ B*

3. A* + B* ↔ AB + 2*

Le Chatelier-like principle for optimal catalysts:coverage conservation laws

The coverage of a key reactant on the surface of the optimal catalyst under given reaction conditions is constant.

( in the simple case “coverage of A” = “1-BEPslope” )

The optimal catalyst is located where the coverage switches – or where the adsorption free energy is close to zero

ΔEads = -0.6eV at 300K or ΔEads = -1.8eV at 900K

Implications of ”Universality”

General insights into”How to pick optimal catalysts”

Bligaard, Nørskov, Dahl, Matthiesen, Christensen, Sehested,J. Catal. 224, 206 (2004)

Which is the best catalyst?

Ammonia synthesis :N2+3H2 2NH3 (Ru, Fe, (Os))

Fischer Tropsch synthesis, methanation:nCO+(2n+1)H2 CnH2n+2+nH2O (Co, Ru, Rh, Ni)

NO reduction:2NO+2H2 N2+2H2O (Pt, Pd, Rh)

Oxidation:O2+2X 2XO (Pt, Pd, Ag)

……..

Understanding trends in catalytic activity

Nørskov, Bligaard, Logadottir, Bahn, Hansen, Bollinger, Bengaard, Hammer, Sljivancanin, Mavrikakis, Xu, Dahl, JacobsenJ.Catal. 209, 275 (2002)

-4 -3 -2 -1 0 1 2 3 4

Ea (

eV)

-1012345

CONOO2

N2

100 bar673 KH2:N2 = 3:1

γ = 10-10, 10-5, 0.5

Flat surface

Step sites

Step kinetics

ΔE (eV)-4 -3 -2 -1 0 1 2 3 4

Nor

mal

ized

TO

F

0.0

0.2

0.4

0.6

0.8

1.0

Ea

(eV

)

-2-101234

Understanding trends in catalytic activity-4 -3 -2 -1 0 1 2 3 4

Ea (

eV)

-1012345

CONOO2

N2

100 bar673 KH2:N2 = 3:1

γ = 10-10, 10-5, 0.5

Flat surface

Step sites

Step kinetics

ΔE (eV)-4 -3 -2 -1 0 1 2 3 4

Nor

mal

ized

TO

F

0.0

0.2

0.4

0.6

0.8

1.0

Ea

(eV

)

-2-101234

Ammonia synthesis :

N2+3H2 2NH3

Ru

Fe

CoMo

-4 -3 -2 -1 0 1 2 3 4

Ea (

eV)

-1012345

CONOO2

N2

100 bar673 KH2:N2 = 3:1

γ = 10-10, 10-5, 0.5

Flat surface

Step sites

Step kinetics

ΔE (eV)-4 -3 -2 -1 0 1 2 3 4

Nor

mal

ized

TO

F

0.0

0.2

0.4

0.6

0.8

1.0

Ea

(eV

)

-2-101234

Fischer Tropsch synthesisand methanation:

nCO+(2n+1)H2

CnH2n+2+nH2O

Ni

Co

Fe Ru


Understanding trends in catalytic activity-4 -3 -2 -1 0 1 2 3 4

Ea (

eV)

-1012345

CONOO2

N2

100 bar673 KH2:N2 = 3:1

γ = 10-10, 10-5, 0.5

Flat surface

Step sites

Step kinetics

ΔE (eV)-4 -3 -2 -1 0 1 2 3 4

Nor

mal

ized

TO

F

0.0

0.2

0.4

0.6

0.8

1.0

Ea

(eV

)

-2-101234

NO reduction:

2NO+2H2 N2+2H2O

Pt

PtRh

Pd

-4 -3 -2 -1 0 1 2 3 4

Ea (

eV)

-1012345

CONOO2

N2

100 bar673 KH2:N2 = 3:1

γ = 10-10, 10-5, 0.5

Flat surface

Step sites

Step kinetics

ΔE (eV)-4 -3 -2 -1 0 1 2 3 4

Nor

mal

ized

TO

F

0.0

0.2

0.4

0.6

0.8

1.0

Ea

(eV

)

-2-101234

Oxidation:

O2+2X 2XO

Ag

Pt


the d-band model and heterogeneous catalysis – part 1xes.fysik.su.se/pdf/bligaard-1.pdf · the...

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