LECTURE 11 - CRCwschnei1/courses/CBE_547/Lectures/Lecture11/... · LECTURE 11 DFT Supercell Calculations of Surfaces W. F. Schneider CBE 547 Fall Semester 20071

LECTURE 11

DFT Supercell Calculations of Surfaces

Fall Semester 2007W. F. Schneider CBE 547 1

2

Alkaline Earth Oxide Bulk Structures2

-250

LDA VASP

experiment

MgOBulk MgO

-350

-300

ergy

(eV

)

LDA VASPGGA VASPLDA CPMD

Bulk MgO• Rocksalt structure

Represent as• Simple cubic unit cell

-400

EneSimple cubic unit cell

• 8 atom basis

• Optimize lattice constant-450

3.5 4 4.5 5

lattice constant (Ang.)

Exp’t 4.212 Å

Optimize lattice constant

LDA Vasp 4.182

GGA Vasp 4.255

LDA CPMD 4.240a

Fall Semester 2007W. F. Schneider CBE 547

3

Supercell Slab Models of Surfaces3

(MgO bulk) (MgO slab)Mg

c

g

O

ab

c

ab

f fSelection of a surface model• Surface cleavage plane

• “Thickness” of slab

• Lateral cell dimensions

• Size of vacuum spacing

Side view of 3 slab images


Top view of 4 “2x2” unit cells

4

Miller Index Naming for Surface Planes4

Specify cleavage plane in integer lattice vector coordinates of a vector orthogonal to the planeDescription thus depends on lattice vector choice

Complete definition also must include vertical location of planeS f ti hi hl d d t l lSurface properties highly dependent on cleavage plane

(001) (013)

z

y

x

z

Supercell model of a stepped surface“Basal” plane


y

x(Lattice vectors become more messy to determine)

5

More Miller Planes5

(111)

z y xPolar surface

Opposite faces have different compositions

Typically high energy and unstable to “reconstruction”


6

Supercell Dimensions6

Slab thickness typically a few “formula unit” layersVacuum spacing large enough to isolate slab from periodic image ( 10 15 Å)(~10-15 Å)Lateral dimensions based on need to isolate chemistry within a cellAlways test to be sure properties of interest are robust to model

a

2 atom

Nominally equivalent surface supercells

Different effective separation between

i hb

8 atom

4 atom

16 atom neighbors16 atom


7

Surface Relaxation7

Exposed surfaces will often relax in response to loss of bonding at surfaceTypical to “freeze” one side of slab to simulate constraints of the bulkIdeally converge results with respect to slab thickness

0.01 Å 0.03 Å

0.004 Å0.01 Å

4.212 Å

FixedMgO

0.02 J/m2 relaxation MgO (103) step relaxations


0.02 J/m relaxation MgO (103) step relaxations

8

Surface Energy8

(MgO bulk)

(MgO slab)slab bulkE nE−

ab

c

cslab bulk

2Aγ =

Energy cost to expose a surface by cleaving a bulk material

Always a positive quantityUseful for valdiation, experimental comparison

ab

Distance between steps

Comparison of energies between supercells of different shapes, requires

k-point convergenceEnergy cutoff convergenceEnergy cutoff convergenceEquivalent computational parameters

Slab k-pointsm × n × 1


m, n inversely proportional to lateral dimensions

9

Molecular mechanism of trapping on catalyzed oxides9

NO + ½ O2 NO2

CO, H2, HC+

NO2

N2, CO2, H2O

SO2 + ½ O2SO3

Pt O

NO2

Pt O

NO2

2 2

O

SO3

O

SO3

Lean ConditionsNOx and SOx oxidized & trapped

Trapping oxide (e.g. BaO)

Rich ConditionsNOx decomposed and reduced, SOx recalcitrant

Trapping oxide (e.g. BaO)

Key Questions:How does NOx get oxidized and adsorbed on a trapping material?How does the SO chemistry compete with NOx?How does the SOx chemistry compete with NOx?How can we select trap materials to optimize selectivity for NOx over SOx?

This work: Compare SOx and NOx adsorption mechanisms on MgO(001)


x x

10

Sulfur Oxides10

SO2

O2-

∠OSO = 106°S

S O ∠OSO

SO 2

OOS-O ∠OSO

Exp’t 1.43 118.9

LDA 1.449 119.4

½ O2

SO32-

(sulfite)

SO3 ∠OSO = 109 5°3 ∠OSO = 109.5

S-O

Exp’t 1.42

LDA 1.439

O2-


SO42-

(sulfate)

11

MgO (001) + SO211

1.5021.47

117 0

1.5051.536

1.655

2.1321.755 2.0622.17117.0

2.211

2.132

Physisorbed SO2-16 kcal mol-1 LDA

Terrace chemisorbed SO2-42 kcal mol-1 LDA

2.448

Step chemisorbed SO2-62 kcal mol-1 LDA

Metastable dipolar physisorptionOnly structure found in cluster simulationsConverts to chemisorbed at ~200 K in MD simulations (Ea ≈ 0.5 kcal mol-1)

Strong “sulfite”-like chemisorption (MgO + SO2 MgO·SO2)Specific S–Os and O–Mgs interactions; significant charge transfer to adsorbatePronounced local lattice distortion, dies off over short range

SO2 chemisorbs preferentially on coordinatively unsaturated edge ionsSimilar sulfite-like adsorption geometry


SO2 oxygen fill vacant lattice sitesIntroduces pronounced lattice distortions along step edge

11

12

SO2 Chemisorption on MgO12

S O O LDA GGA1 2 3 4

BE, kcal mol-1

S O1 O2 LDA GGA (100) -37 -25 (103) 4 1 3 -62 -46 1 1 3 -60

3 3 2 59

1 2 3 4

1

3 3 2 -59 1 1 2 -52 2 1 2 -46 2 3 2 -34 S

O

O

(104) 4 1 3 -62 corner -92 -81

Multiple SO2 chemisorption sitesSO2 fills “virtual” lattice sitesAdsorption energy tracks with lattice ion coordinative


p gyunsaturation

13

MgO + SO313

1.470

1.454 1.4401.578

1.498

1.657 2.0662.603

2.420 Å

“Sulfate”-like chemisorption (MgO + SO3 MgO·SO3)

MgO (001) + SO3-69 kcal mol-1 LDA

MgO (103) + SO3-95 kcal mol-1 LDA

Primary S–Os bonding → approximately tetrahedral SO4 structures

Large, local relaxation of Os, charge transfer to SO3

Secondary O–Ms interactions fix orientation

Chemisorption energy ~30 kcal mol-1 greater than SO2


Chemisorption energy 30 kcal mol greater than SO2

Strong preference for coordinatively unsaturated ions

14

MgO + SOx Vibrational Spectroscopy14


15

NO•/NO2• Physisorption on MgO Terrace15

Physisorbed NO2

1.19

Physisorbed NO1.24

125º1 24

128º -0.23 e-0.26 e-0.19 e

2.27110º

2.252.25

1.24

MgO(001) + NO MgO(001) +NO2 O-downMgO(001) +NO2 N-down

NO and NO2 physisorb on MgO terraces

-7 kcal mol-1 -10 kcal mol-1-4 kcal mol-1

Low NOx Lewis basicity produces long, weak adsorbate-surface bondsCharge-dipole interaction, limited charge transfer to adsorbate

Not consistent with observations of “nitrite” and “nitrate” upon exposure of MgO to NOx!


g x

1616


17

Cooperative NO2 Adsorption on MgO(001)17

“nitrate”NO2

+ + Os2-

“nitrite”NO2

- + Mgs2+

1.28 1.28

e-

-0 23 e -0 73 e

1.41

1.22

2.322.09 2.11

1170.23 e -0.26 e

-1.22 e

-0.78 e0.73 e

-15 kcal mol-1

+

Isolated physisorbed NO2

Charge transfer generates cooperatively adsorbed NO2 pairStructural modifications consistent with chemisorptionMulliken populations reflect redistribution of charge between adsorbatesBinding energy enhanced by 15 kcal mol-1 (100%) over two isolated NO2!

Mixed nitrite/nitrate consistent with experimental observation for NO2-exposed M


MgO

18

Distance Dependence of Cooperative Chemisorption18

“Lewis Basic” NO2

Unique “Lewis Acidic” NO2 Sites

OMg Mg O

MgO Mg O

2

253035

nerg

y

OMg

O Mg

Mg O Mg O

MgOA Mg O10152025

Ads

orpt

ion

en(k

cal/

mol

)

Mg O

O Mg

05

10

Tota

l A B C D E F oo

Adsorption site

Mg OB Mg O

MgOD Mg OE

Mg OC

OF Mg

Cooperative effect decreases slowly with adsorbate separatione- transfer/pairing can occur over several Angstroms

“3x3” MgO supercellAdsorption site


/p g gForced charge separation yields physisorption

19

Bulk and Surface Structures of FCC Metals19

2.95

3

-5.6

-5.5

Lattice ConstantTotal energyÅ)

Bulk FCC Pt

2.7

2.75

2.8

2.85

2.9

-6.1

-6

-5.9

-5.8

-5.7Total energy

attic

e C

onst

ant (

Å

2.5

2.55

2.6

2.65

0 50 100 150 200-6.5

-6.4

-6.3

-6.2

k points

La

a aa

k-points

Theory Expt’

Lattice Constant Lattice Constant (Å)

3.986 3.923

Surface energy (J/m2)

1.48 --


20

FCC (111) Surface Supercell Models20

11.271 Å8.453 Åa

3 Pt × 3 Pt 4 Pt × 4 Pt

1×1

2×2

20.9

21 Å

√3×√3

b a

c

1×2

-120

-100

-80

y (k

cal m

ol-1

)

NO

(a)4×4

-60

-40

-20Ad

sorp

tion

Ene

rgNO2

NO


03 layer 4 layer 5 layer

A

21

Adsorption Sites on FCC (111) Surfaces21

Adsorption sites on the (111) facet:

bridge – 2-fold

hcp – 3-fold coordination

fcc – 3-fold coordination

atop – 1-foldcoordination

atop 1 fold coordination

Hexagonal arrays of sites

o DFT calculations performed with Vasp

o 3×3, 4×4, 5×5 Pt(111) supercell models

o 8×8×1, 6×6×1, and 4×4×1 Monkhorst‐Pack k‐point grids

o “PAW” electron core treatment

91 li d di i i


o PW91 generalized gradient approximation

22

Oxygen adsorption and interactions on Pt(111)22

Low coverage (1/16 ML) O preference for FCC adsorption

fcc: -1.29 eV atop: +0.18 eVfcc-hcp bridge (TS)hcp: -0.89 eV

Pt(111) + ½ O2 < < <

Lateral interaction effects on O adsorption (4 x 4 supercell)

2.4 Å

fcc-fcc: 1NN fcc-fcc: 2NN fcc-fcc: 3NN fcc-hcp: 1NN fcc-hcp: 2NN

+0 20 eV +0 10 eV +0 01 eV +0 82 eV +0 32 eV


+0.20 eV +0.10 eV +0.01 eV +0.82 eV +0.32 eV

Characterizing Pt(111)-O Surface Coverage

+Adsorbates

O atom

Pt atom

Clean Pt(111) surface p(1 × 1)—O orderingAdsorbatesinteract with each other to produce different stable configurations at different 60

80Atop onlyHCP onlydifferent

coverages

rm(m

eVÅ‐2)

0

20

40y

Mixed

E for

-60

-40

-20

0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000O Coverage (ML)

W. F. SchneiderACS ‐ 21 August 2007

Surface free energies

( , , ) OF T V N E TS= − (1) ( , , )O O OF T V E TS Nμ μ= − −

Canonical ensembleHelmholtz free energyConstant atom number

Grand canonical ensembleTransformed Helmholtz energyConstant oxygen potential

(1) (1)F F (1) (1)F F(1)(1) (1)

surf bulk(111) Pt

F F

Aγ

−=

Bulk Pt Pt(111)

(1)(1) (1)

Pt(111) F F

Aθ

θγ−

Δ =

Pt(111)‐θ(O)

( ) ( )

( , )

, ,

DFT DFTSurf Bulk

ZP ZPSurf Bulk

Vib VibSurf Bulk

E T V E E

E E

E T V E T V

Δ = −

+ −

+ −

( )

( ) ( )

Pt (111)

Pt (111)

Pt (111)

, ,

, ,

DFT DFT

ZP ZP

Vib Vib

E T V E E

E E

E T V E T V

θ

θ

θ

θΔ = −

+ −

+ −( ) ( )f

( ) ( ) ( ), , ,Vib VibSurf BulkS T V S T V S T VΔ = − ( ) ( ) ( )Pt(111), , , ,Vib VibS T V S T V S T VθθΔ = −

Supercell calculations on thick slabsPhonon calculations for bulk and surface

4‐layer supercellsO atom vibrations

W. F. Schneider ACS ‐ 21 August 2007

Phonon calculations for bulk and surfaceEinstein vibrational model

O atom vibrationsEinstein vibrational model

Pt(111)/O2 Phase Diagram

2

2 2 2O1 ( ) ln2 1

ODFT ZPO O O B

PE E G T k T

barμ

⎛ ⎞⎛ ⎞= + + Δ +⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

O2 (T,P)

O coverage limited by accessible O2 T

O2 (g) + 2* 2O*12001200

O O O O

Pt(111) surface

g y 2and PXPS performed to determine O coverage at various O2 exposures

Ribeiro et al.

W ll k l θ = 0 25 800

900

1000

1100

800

1000

re (K

)

clean surface

p(4×4)–O(2 4) O

O atom

Pt atom

Well known low-pressure θ = 0.25 coverage used to calibrate XPS

Consistent with p(2×2)-O ordering

High-pressure θ = 0.5 coverage consistent with p(2×1)-O ordering 500

600

700

800

600

800

Tem

pera

tur

θ = 0.39θ = 0.40

θ = 0.52

p(2×2)–O

p(2×4)–Oc(4×4)–3O

Likely highest coverage accessible with O2 at ambient conditions

Kinetics limit rate of O2 loss from surface 200

300

400

-13 -11 -9 -7 -5 -3 -1 1

-1-3-5-7-9-11 1

400

-13200

θ = 0.25 θ = 0.49

θ = 0.48

c(4×4)–7O p(2×1)–Oc(2×4)–3O

1357911log10(PO2/1 bar)

113


Coverage-dependent O binding energies

1.5

2

NO→ NO

¼ ML ½ ML

V/O)

OxygenformdE

BEdθ

∝

0.5

1

p(2×1)‐O

p(√3×√3)‐2ONO + O* → NO2½ O2 → O*

+ NO → + NO2

ΔE2 (θ)

Apparent window of

favorable ΔEng ene

rgy (eV

-1

-0.5

0

+ ½ O2 →

ΔE1 (θ)

favorable ΔE1and ΔE2

xygen bind

in

S f hibit t l t t di ti t bi di i

-1.50 0.2 0.4 0.6 0.8 1

ΔE1 (θ)

Oxygen coverage (ML)

Ox

Surface exhibits at least two distinct binding energy regimesLow coverage BE in middle of experimentally available values

O2 dissociation exothermic only up to a limiting coverage near θ = 2/3NO oxidation exothermic only at coverages above about θ = ½


Based on experimental NO oxidation energy

O2 adsorption on Pt(111)-O(X)

• TBT and TFB isomers energetically

θO = 0.25θO = 0 θO = 0.5

equivalent

• Exothermically bound at low θO

• Adsorption energy diminishes greatly with coverage– Strong electrostatic

l i

ΔE = ‐0.80 eV ΔE = ‐0.23 eV ΔE = +0.57 eV

repulsion

• Endothermicallybound at catalytic coverage ΔE = ‐1.56 eV ΔE = ‐1.03 eV ΔE = ‐0.41 eVg– O2* unlikely precursor to

dissociation

• How does O2participate in the

ti ??


reaction??

O2 dissociation on Pt(111)-O(X)28

“Nudged l b d”

28

a) O2 (g) + 2* → 2O*

elastic band” (NEB) calculations of reaction

h 2

3

2.14 eVpathways

Reaction barrier depends on

0

1

2

O2 (g)

ergy

(eV

)

-0.05 eV

surface coverage

-3

-2

-1

2O (g)transTS

Ene

p(2×1)-O Pt(111)


p( ) ( )

LECTURE 11 - CRCwschnei1/courses/CBE_547/Lectures/Lecture11/... · LECTURE 11 DFT Supercell Calculations of Surfaces W. F. Schneider CBE 547 Fall Semester 20071

Documents