Adsorption and reaction of hydrogen atoms on graphitic ...users.unimi.it/cdtg/download/beamer talks/Toulouse-2013.pdf · Hypercoordination(˘) sublattice imbalance ( ) Z = 2 )E Z

Point defects in graphene Eley-Rideal reaction

Adsorption and reaction of hydrogen atomson graphitic surfaces

Rocco Martinazzo

Dipartimento di ChimicaUniversità degli Studi, Milano, Italy

Exploring mechanisms for H2 formation on very smallcarbonaceous grains and PAHs of astrophysical interest

Toulouse, April 25, 2013


H2 in the ISM

Hydrogen is the most abundantelement of the UniverseH2 is formed on the surface ofdust grain

Hydrogen-graphite is an important model forunderstanding H2 formation in ISM

fgrain=ngrain/nH ∼ 10−12 i.e. ∼1%of ISM mass


Chemisorption and reaction

H + C2

CH2 CH2

2H + C

2 CH 2 CH

ortho dimer

single H adsortho−para conversion

Eley−Rideal

dimer recombination

diffusion

adsorption

adsorption

preferential sticking

4.75 eV

H + CH0.8 eV

0.8 eV1.9 eV

1.45 eV1.65 eV

0.2 eV

0.2 eV

1.0 eV

para dimer

R. Martinazzo, S. Casolo and L. Horneakerin Dynamics of Gas-Surface Interactions, Ed.s R. D. Muino and H. F. Busnengo, Springer (2013)


Technology: graphene physics and devices

Graphene is a true 2D-electron gas (2DEG) system withpseudo-relativistic charge-carriers

MIT occurs when hydrogenating graphene

..σ vs T agrees well with VRH in two dimensions

High nH : D. C. Elias et al., Science 323, 610 (2009)

Low nH : A. Bostwick et al., Phys. Rev. Lett. 103, 056404 (2009)


pz vacancies

-3 -2 -1 0 1 2 3( ε−εF ) / eV

0

15

30F

-3 -2 -1 0 1 2 3( ε−εF ) / eV

0

15

30

V2

Midgap states show up in the DOSsH, F, OH, CH3, etc. behave similarly to vacancies


Outline

1 Point defects in grapheneH adsorption and clusteringEdge effectsVacancies

2 Eley-Rideal reactionQuantum Dynamics at high EcollQuantum Dynamics at cold EcollAb initio molecular dynamics


Outline




Outline




Single-H chemisorption

1 2 3 4z / Å�

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

E /

eV

L. Jeloaica and V. Sidis, Chem. Phys. Lett. 300, 157 (1999)X. Sha and B. Jackson, Surf. Sci. 496, 318 (2002)

*


Midgap states

..patterned spin-density

-4 -2 0 2 4(ε−εF) / eV

-20

-10

0

10

20

DO

S

-4 -2 0 2 4(ε−εF) / eV

0

10

20

DO

S

Graphene

H-Graphene

+ H


Midgap states

Hπ ≈∑

τ,ij(tija†i,τbj,τ + tjib

†j,τai,τ ) + U

∑i ni,τni,−τ

n∗

nA + nB − 2n∗ n∗

*


Midgap states

M.M. Ugeda, I. Brihuega, F. Guinea and J.M. Gomez-Rodriguez, Phys. Rev. Lett. 104, 096804 (2010)D. Haberer et al., Phys. Rev. B 83, 165433 (2011)


Midgap states

ψ(x , y , z) ∼ 1/r

V. M. Pereira et al., Phys. Rev. Lett. 96, 036801 (2006);Phys. Rev. B 77, 115109 (2008)


Dimers


Dimers

S. Casolo, O.M. Lovvik, R. Martinazzo and G.F. Tantardini, J. Chem. Phys. 130 054704 (2009)S. Casolo, O.M. Lovvik, R. Martinazzo and G.F. Tantardini, arXiv:0808.1312 (2008)Preferential sticking: L. Hornekaer et al., Phys. Rev. Lett. 96 156104 (2006)


Dimers

[1] [2]

[1] L. Hornekaer, Z. Sljivancanin, W. Xu, R. Otero, E. Rauls, I. Stensgaard, E. Laegsgaard, B. Hammer and F.Besenbacher. Phys. Rev. Lett. 96 156104 (2006)

[2] A. Andree, M. Le Lay, T. Zecho and J. Kupper, Chem. Phys. Lett. 425 99 (2006) *


Role of edges


‘Geometric’ effect?

‘Reorganization’ energyupon binding

δE = E(PAH∗)− E(PAHeq)

E sites: δE ∼ 1.4± 0.1eV

G sites: δE ∼ 1.0± 0.1eV

...purely electronic effect


Hints from the tight-binding Hamiltonian Hπ

Shape of low-energy orbitals..from a ‘lattice renormalization’

Coordination (Z )Hypercoordination (ξ)sublattice imbalance (η)

Z = 2⇒ E

Z = 3⇒ F,G

2

1

0

*


Systems

η = 0 η 6= 0


Graphitic vs edge carbons

M. Bonfanti, S. Casolo, G. F. Tantardini, A. Ponti and R. Martinazzo, J. Chem. Phys., 135 164701 (2011)


Adsorption paths



Predicting reactivity

η = 0

0.0 0.5 1.0 1.5 2.0 2.5 3.0N pi

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Ebi

nd /

eV

ξ = 0

ξ = 1

ξ = 2E sites

G sites

η 6= 0

0.00 0.10 0.20N pi

0.0

1.0

2.0

3.0

4.0

Ebi

nd /

eV

0.0 2.0 4.0N pi

0.0

1.0

2.0

3.0

4.0

Ebi

nd /

eV

ξ = 2

ξ = 1 ξ = 2

E* sites

G* sites

ξ = 1ξ = 0

E sites

G sites



Predicting reactivity


Spin-coupling around a carbon atom vacancy

Jahn−Teller

How the two e spins couple at a vacancy?How large is the splitting?Can that be used in applications? *


Magnetization constrained results

Partial geometrical relaxation,MS = 0,1 constrained

h

hh

triplet is stable, ω⊥ ∼ 200cm−1

singlet is bistable, ω⊥ ∼ 263cm−1

S = 1 is the ground-state up toh ∼ 0.5 Å

-1.0 -0.5 0.0 0.5 1.0 hC / Å

0.0

0.2

0.4

0.6

0.8

∆E /

eV

singlettriplet


CASPT2 results

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

hC / Å

0.0

0.1

0.2

0.3

0.4

0.5

∆E /

eV

0 0.025 0.05

0.2

0.3

0.4S=0

S=1 CASPT2

DFT

Magnetization constrained DFT results are reliable

Accurate energies from CASPT2

Singlet-state has a dominant open-shell character, Ψ ∝ (σπ + πσ)(αβ − βα)

M. Casartelli, S. Casolo, G.F. Tantardini and R. Martinazzo, submitted


Hydrogenation

3.64 eV

3.45 eV

1.36 eV

3.80 eV

2.14 eV

1.38 eV

3.68 eV2.35 eV

Mono-, Three- and Penta- hydrogenated vacancies are all spin-1/2 species


Outline




Reaction: technicalities

Rigid, flat surface approximation1

Split-Operator with FFT along cartesiancoordinates and DBT along ρ 1

propagation in both product andreagent coordinate sets2

⇒ state-to-state, energy-resolved crosssections for all possible processes

[1] M. Persson and B. Jackson, J. Chem. Phys. 102, 1078 (1995); D. Lemoineand B. Jackson, Comput. Phys. Commun. 137, 415 (2001)[2] R. Martinazzo and G.F. Tantardini, J. Phys. Chem. A, 109 (2005) 9379; J.Chem. Phys. 124, 124703 (2006); J. Chem. Phys. 124, 124704 (2006)


Reaction: Potential Energy Surfaces

Chemisorbed target H (zeq) Physisorbed target H (zeq)

X. Sha, B. Jackson and D. Lemoine, J. Chem. Phys. 116, 7158 (2002)


I. H-chemisorbed case

Oscillations in both ER and CID xsections



Quantum vs(quasi) classicaldynamics:quantum effects

R. Martinazzo and G.F. Tantardini,J. Phys. Chem. A109, 9379; J. Chem. Phys. 124124272 (2006)



Product moleculesare internally hotInternal excitation isa steep decreasingfunction of Ecoll




II. H-physisorbed case


Reaction: technicalities (low Ecol)

Two-wavepacket approach1

Transmission-free2 absorbing potentialsand Fourier mapping3 in reagentcoordinates

In 3D Tf =25-30 ps and AP lengths ∼ 50Å inorder to get converged xsections down to∼ 10−5 eV, i.e. ∼ 0.1 K

[1] R. Martinazzo and G.F. Tantardini, J. Chem. Phys. 122, 094109 (2005)[2] D. Manolopoulos, J. Chem. Phys. 117, 9552 (2002)[3] A.G. Borisov, J. Chem. Phys. 114, 7770 (2001)



S. Casolo, M. Bonfanti, R. Martinazzo and G.F. Tantardini, J. Phys. Chem. A, 113 14545 (2009)




I. H-chemisorbed caseQCT comparison, v = 0

10-5

10-4

10-3

10-2

10-1

100

Ecoll / eV

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

σ / Α

2

100

101

102

103

104

Ecoll / K

No ZPE, Ts = 0 K

ZPE, Ts = 10 K

ZPE, Ts = 30 K

QCT, adiab

QD, diabQD, adiab

Diffuse clouds

M. Sizun, D. Bachellerie, F.Anguillon, V. Sidis Chem. Phys.Lett. 32 498 2010D. Bachellerie, M. Sizun, F.Anguillon, D. Teillet-Billy, N.Rougeau, Phys. Chem. Chem.Phys. 2715 11 2009


II. H-physisorbed case

S. Casolo, M. Bonfanti, R. Martinazzo and G.F. Tantardini, J. Phys. Chem. A, 113 14545 (2009)


H-chem vs H-phys

Cross-sections have to be corrected for the spin statistics (1/4)


H-chem vs H-phys

Cross-sections have to be corrected for the spin statistics (1/4)


Ab initio molecular dynamics

lattice corrugationlattice dynamicsdimer formation

..expensive, but solves the problem of computing and fitting amodel potential



0.0 0.2 0.4 0.6 0.8 1.0 1.2

Ecoll / eV

0.0

1.0

2.0

3.0

4.0

5.0

σ / A

2

Eley-Rideal

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Ecoll / eV

0.0

1.0

2.0

3.0

4.0

5.0

σ / A

2

Dimers

QM - adiab

QM - diab

AIMD

meta

ortho

paraAreou et al. J. Chem. Phys. 134, 0141701 (2011)

Zecho et al. Chem. Phys. Lett. 366, 188 (2002)

S. Casolo, G.F. Tantardini and R. Martinazzo, PNAS in press

*



10-5

10-4

10-3

10-2

10-1

100

101

Ecoll / eV

0

1

2

3

4

σ /

A2

S. Casolo, G.F. Tantardini and R. Martinazzo, PNAS in press



Tg = 300K , Ts = 15K

Latimer et al. Chem. Phys. Lett. 455, 174 (2008) AIMD for H/D @ 0.025 eV



0.0 0.3 0.6 0.9 1.2

Ecoll / eV

0.0

1.0

2.0

3.0

4.0

5.0

Eav

ail /

eV

0.0 0.3 0.6 0.9 1.2

Ecoll / eV

0

2

4

6

8

10

Esurf

Eint

Etrans

< v >

< j >

..most of energy is internal, but energy transfer to the surface isconsiderable


Summary

H dimers (clusters) which minimize sublattice imbalanceform easily in the bulkEdges and vacancies are chemically active and facilesticking is possible at these sitesEley-Rideal reaction out of chemisorbed species isreasonably efficientand dominates over dimer formationProduct molecules are hot, but up to ∼ 1eV can be left onthe surface


Chemical Dynamics Theory Group

Gian Franco Tantardini

Simone Casolo

Matteo Bonfanti

http://users.unimi.it/cdtg

Simona Achilli

Marina Casartelli

Paolo Bonardi

http://users.unimi.it/cdtg


Acknowledgements

Thank you for your attention!

Physisorption

HF-MP2 / aug-cc-pVDZ + BFs / CP-BSSE

De = 39.5 meV vs De(exp)=39.2±0.5 meV

Ebarr = 4.0 meV, DT =0K = 1.7 10−4 cm2s−1

M. Bonfanti, R. Martinazzo, G.F. Tantardini and A. Ponti, J. Phys.Chem. C,111, 5825 (2007)

Exp: E. Ghio et al., J. Chem. Phys., 73, 596 (1980)*

Midgap states

Hπ ≈∑

σ,ij(tija†i,σbj,σ + tjib

†j,σai,σ)+U

∑i ni,τni,−τ

Electron-hole symmetrybi → −bi =⇒ Hπe → −Hπe

εi , |ψ(+)i 〉 =

∑k αk |ak 〉+

∑j βi |bj 〉

⇓

−εi , |ψ(−)i 〉 =

∑k αk |ak 〉 −

∑j βi |bj 〉

Midgap states

Hπ ≈∑


†j,σai,σ)+U

∑i ni,τni,−τ

Imbalance ruleLet nA > nB , T(nBxnA)

[0 T†T 0

] [αβ

]=

[00

]=⇒ Tα = 0 has nA − nB solutions

Midgap states

Hπ ≈∑


†j,σai,σ) + U

∑i ni,τni,−τ

Spin alignmentIf U > 0, the ground-state at half-filling has

S = |nA − nB |/2 = nI/2

E.H. Lieb, Phys. Rev. Lett. 62, 1201 (1989)

*

3-atom clusters

µ = 1µB ⇒µ = 2µB⇒ µ = 3µB

µ = 1µB ⇒ µ = 2µB ⇒ µ = 3µB

3-atom clusters

A2B A3

4-atom clusters

*


Hπ ≈∑


†j,σai,σ)+U

∑i ni,τni,−τ

t

tt

t

‘Lattice renormalization’H̃AA = HABHBA

ε̃i , |ψA,i 〉⇓

ε±i = ±√ε̃i , |ψ

(±)i 〉 = |ψA,i 〉 ± |ψB,i 〉

|ψB,i 〉 = ε̃−1/2i HBA |ψA,i 〉


H̃π ≈∑

i Zi t2a†i ai +∑

ij t2a†i aj


ε̃i , |ψA,i 〉⇓

ε±i = ±√ε̃i , |ψ

(±)i 〉 = |ψA,i 〉 ± |ψB,i 〉

|ψB,i 〉 = ε̃−1/2i HBA |ψA,i 〉


H̃π ≈∑

i Zi t2a†i ai +∑

ij t2a†i aj

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20ε / eV

0

500

1000

1500

2000

ρ /

eV-1

-0.01 0 0.01 0.02 0.03 0.04

ε / eV2

0

2000

4000

6000

8000

10000

ρ /

eV

-2

HOMO LUMO

GSMO


ε̃i , |ψA,i 〉⇓

ε±i = ±√ε̃i , |ψ

(±)i 〉 = |ψA,i 〉 ± |ψB,i 〉

|ψB,i 〉 = ε̃−1/2i HBA |ψA,i 〉

*

E ⊗ e JT problem

a’’

a’

a’

a’

a’1

e’ a’’2

A’1

1

2 0 2

1...(a’) e’ a’’

2σ π

A’’1

1A’’3

11E’’

1 2 1

1...(a’) e’ a’’

2 σ σ

E’’13

E’’2 1 1

1...(a’) e’ a’’

2

A’1

1A’3

11E’’

2 2 0

1...(a’) e’ a’’

2π σ

E x e

Qθ

Qε

σ

σ

σ

π

σ

σ π

e’

..with interacting higher-energy statesOut-of-plane, E ′′ vibrations do not lift degeneracy at first order..

e’’

h

..but give corrections to second order, either positive ornegative *

Zecho’s kinetic experiments

*

Documents

Adsorption and reaction of hydrogen atoms on graphitic ...users.unimi.it/cdtg/download/beamer talks/Toulouse-2013.pdf · Hypercoordination(˘) sublattice imbalance ( ) Z = 2 )E Z