Hydrogen atoms on graphene: structure, energetics and …users.unimi.it/cdtg/download/beamer talks/Potsdam-2013.pdf · Hypercoordination(˘) sublattice imbalance ( ) Z = 2 )E Z =

Adsorption energetics Eley-Rideal reaction dynamics Sticking dynamics

Hydrogen atoms on graphene: structure,energetics and dynamics

Rocco Martinazzo

Dipartimento di ChimicaUniversità degli Studi, Milano, Italy

Scattering of Atoms and Molecules from SurfacesPotsdam, November 4-7, 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)


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


Outline

1 Adsorption energeticsSingle H adsorptionDimer formation and clusteringAdsorption at edgesH on Graphene/Ir(111)

2 Eley-Rideal reaction dynamicsReduced-dimensional quantum dynamicsAb initio molecular dynamics

3 Sticking dynamicsSystem-bath modelingVibrational relaxation dynamics


Outline





Outline





Outline





Chemisorption of a H atom

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: 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

H, F, OH, CH3, etc. behave similarly to vacancies



Hπ ≈∑

τ,ij(tija†i,τbj,τ + tjib

†j,τai,τ ) + U

∑i ni,τni,−τ

n∗

nA + nB − 2n∗ n∗

*



-100 -50 0 50 100x / a0

-0.20

-0.10

0.00

0.10

0.20

ψi

xV

M.M. Ugeda et al., Phys. Rev. Lett. 104, 096804 (2010)

ψ(x , y , z) ∼ 1/r

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



Resonating Valence Bond

Transport: resonantscatterers explain behavior ofσDC at zero and finite electrondensities

Magnetism: local magneticmoments responsible for theobserved paramagneticresponse

Chemistry: preferentialsticking leading to dimer andcluster formation


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


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

*


Graphitic vs edge carbons

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


Adsorption paths

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


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

Hypercoordination discriminates between edge sites..


Predicting reactivity


Ir(111)/graphene Moiré structure


Ir(111)/graphene Moiré structure

Top (hcp) Top (fcc) Hollow


Patterned H adsorption

R. Balog et al., Nat. Mater., 9 315 (2010)


Basis set selection

Too large cell for PW calculations.. ⇒ SIESTA

2.0 3.0 4.0 5.0z / Å

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

E (

per

C a

tom

) / e

V

Plane Waves (VASP)

SZSZPDZPTZ2PDZP enlarged

DZP enlarged2

DZP diffuse

Plain (no vdW)

2.0 3.0 4.0 5.0z / Å

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

E (

per

C a

tom

) / e

V

Plane Waves (VASP)

SZ SZP DZP TZ2P DZP enlarged

DZP enlarged2

DZP diffuse

CP corrected (no vdW)

2.0 3.0 4.0 5.0z / Å

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

E (

per

C a

tom

) / e

V

Plane Waves (VASP)

DZP diffuseDZP enlarged2

vdW corrected

1x1 Top (hcp) (similarly for Top (fcc) and Hollow )


Set up

Two-stage optimization

Stage IStandard Double ζ plus PolarizationThree 9× 9 Ir layers + 10× 10 graphene⇒ 443 atoms

Stage IIStandard Double ζ plus Polarization plus Diffuse plus vdWFive 9× 9 Ir layers + 10× 10 graphene⇒ 605 atoms


Graphene + 0H

Stage I : h = 2.94 Å, ∆hrms = 2× 0.39 ÅStage II : h = 3.38 Å, ∆hrms = 2× 0.39 Å

Exp[1] : h = 3.38 Å, ∆h = 0.6± 0.1 ÅExp[1] : h = 3.38 Å, ∆h = 1.0± 0.1 Å

η" bonding"

Top (fcc) HollowTop (hcp)

[1] C. Busse et al., Phys. Rev. Lett. 107 036101 (2011)


Graphene + 1H

Top (fcc)Top (hcp)

Hollow

7

86

2

1714

Up (stage I)

H2 : 2.68 eVH6 : 2.64 eVH7 : 2.87 eVH8 : 2.78 eVH14 : 1.08 eVH17 : 1.07 eV


Graphene + 1H

Top (fcc)Top (hcp)

Hollow

7

86

2

1714

Down (stage I)

H2 : 2.68 eVH6 : 2.64 eVH7 : 2.87 eVH8 : 2.78 eVH14 : 1.27 eVH17 : 1.35 eV


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

DFT PES fitted to modified LEPS3

⇒ 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)[3] X. Sha, B. Jackson and D. Lemoine, J. Chem. Phys. 116, 7158 (2002)


I. H-chemisorbed case

Oscillations in both ER and CID xsections



Product moleculesare internally hotInternal excitation isa steep decreasingfunction of Ecoll



R. Martinazzo and G.F. Tantardini, J. Phys. Chem. A 109, 9379; J. Chem. Phys. 124 124272 (2006)


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)


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

[ Corrected for the spin statistical factor (1/4) ]


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


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 110 6674 (2013)

*



10-5

10-4

10-3

10-2

10-1

100

101

Ecoll / eV

0

1

2

3

4

σ /

A2

para-mediated reaction weighted QM/AIMD xsections



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

5.0E

avai

l / 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


Kinetic modeling

dnH2v

dt' kskER

ksΣs + kERΣgng

v nHv = RnnH

v

Facile sticking: σs ' 20 Å2

n∗ ' 10−2 per C atomPorous grains:Σg ' 30− 40× Σ

geomg

10 100 1000T (K)

10-20

10-19

10-18

10-17

10-16

10-15

R (

cm3 /s

)


Outline





H chemisorption on graphene

Challenging huge-dimensionalstrongly coupled quantum problem..

I Convert the graphene lattice intoa quasi-equivalent HarmonicOscillator bath

II Convert the bath to a LinearChain form suited for largedimensional quantum calculations


System-bath modeling

Lattice

Hlatt =p2

H2mH

+p2C

2mC+ V (xH , zC , q) +

∑i

p2i

2mi

⇓

System-bath

Hsb =p2

H2mH

+p2C

2mC+ V (xH , zC , qeq) +

∑k

p2k2 +

ω2k

2

(qk −

ckω2

kf (zC )

)2

ωk , ck ⇔ J(ω)⇔ κ(t)


Spectral densities

H→ C→ latticeCanonical MD (AIMD in the near future): δz i

H(t)

δz iH(ω) =

∫ +∞−∞ eiωtδz i

H(t)dt

C(ω) = 1N∑N

i=1 |δz iH(ω)|

2

JH(ω) = kBT σ(ω)

|S+(ω)|2 σ(ω) = C(ω)ω/2

JC(ω) = mCD2

0JH (ω)

|W+(ω)|2 D20 = 2

π

∫ +∞−∞ JH(ω)ωdω


Spectral densities

∗ Jackson’s CH and lattice potential


Spectral densities

Lattice - Normal Bath - Linear Chain


Linear chain representation

J0JM

XMX2 X3X1

Ω2 Ω3Ω1

D1D0 D2

s s

Universal Markovian reduction1

Unraveling the memory kernel2

Efficient quantum simulations3

[1] R. Martinazzo, B. Vacchini, K.H. Hughes and I. Burghardt, J. Chem. Phys. 134 011101 (2011)[2] R. Martinazzo, K.H. Hughes and I. Burghardt, Phys. Rev. E 84 030102 (2011)[3] M. Bonfanti, G.F. Tantardini, K.H. Hughes, I. Burghardt and R. Martinazzo,J. Phys. Chem. A, 11406 116 (2012)


Quantum dynamics with MCTDH

Ψ(x1, x2, .., xN) =∑

i1,i2,...iN ci1,i2,...iN φ(1)i1

(x1)φ(2)i2

(x2) . . . φ(N)iN

(xN)

ci1,i2,...iN = ci1,i2,...iN (t) are time-evolving amplitudes for theconfigurations

φ(k)i (x) = φ

(k)i (x , t) are time-evolving single-particle

functions〈φ(k)i |φ

(k)j 〉 = δij for any k = 1, ..N

Equations of motion from DF variational principle

M.H. Beck, A. Jackle, G.A. Worth, H.-D. Meyer, Phys. Rep. 324 1 (2000)


A simple MCTDH ansatz

System + Primary + Secondary modes

Ψ(x,y, z) =∑

IJ cIJ φi1(x1).. φj1(y1).. ψ1(z1)ψ2(z2)..ψN(zN)

Linear scalingAccuracy depends on the primary modes onlyRecurrence times can be enormously increasedEffective-mode based variants for G-MCTDH1, LCSA2, etc.are possible

[1] I. Burghardt, H.-D.Meyer and L. S. Cederbaum, J. Chem. Phys. 111 2927 (1999)[1] R. Martinazzo, M. Nest, P. Saalfrank and G. F. Tantardini, J. Chem. Phys. 125 194102 (2006)


Model systems

H = p2

2M + V (s) +∑

k

p2

k2 +

ω2k

2

(xk − ck f (s)

ω2k

)2

f (s) = 1−e−αs

α → s for s → 0V (s) = Dee−αs (e−αs − 2),with De = 1.55eVM = mH

Several J(ω)s


A simple MCTDH ansatz: vib relax

Non-Markovian SDs, N = 100

0 100 200 300 400 500t / fs

-1.450

-1.400

-1.350

-1.300

E /

eV

normal bathncorr = 5

ncorr = 10

ncorr = 15

0 100 200 300 400 500t / fs

-1.450

-1.400

-1.350

-1.300

E /

eV

normal bathncorr = 5

ncorr = 10

ncorr = 15

M. Bonfanti, G.F. Tantardini, K.H. Hughes, R. Martinazzo and I. Burghardt, J. Phys. Chem. A, 11406 116 (2012)


A simple MCTDH ansatz: vib relax

Non-Markovian SDs, N = 100

0 50 100 150 200 250 300t / fs

-0.10

-0.05

0.00

0.05

0.10

Im<

x(t)

x(0)

> /

a 02

0 50 100 150 200 250 300t / fs

-0.10

-0.05

0.00

0.05

0.10

0.15

Re<

x(t)

x(0)

> /

a 02

0 50 100 150 200 250 300t / fs

-0.10

-0.05

0.00

0.05

0.10

0 50 100 150 200 250 300t / fs

-0.10

-0.05

0.00

0.05

0.10

0.15


A simple MCTDH ansatz: sticking

0.0 0.5 1.0Einc / eV

0.0

0.2

0.4

0.6

0.8

1.0

P st

ick

0.0 0.5 1.0Einc / eV

0.0

0.2

0.4

0.6

0.8

1.0

P st

ick

0.0 0.5 1.0Einc / eV

0.0

0.2

0.4

0.6

0.8

1.0

Pst

ick

normal bathNcorr = 5

Ncorr = 10

Ncorr = 15

Normal bath vs. Linear chain N = Ncorr + Nscf = 300


CH: vibrational relaxation

ClassicalQuasi ClassicalNormal bath, N = 75Chain bath 1, N = 200Chain bath 2, N = 200

τ ' 1.0 ps


Summary

Midgap states modulate reactivity: dimers (cluster) whichminimize sublattice imbalance form easilyEdges are chemically active and facile sticking is possibleat these sitesSubstrates (even if not strongly binding) may modulatechemical activityEley-Rideal reaction out of chemisorbed species isreasonably efficient and dominates over dimer formationHydrogen chemisorption is a challenging dynamicalproblem


Chemical Dynamics Theory Group

Gian Franco Tantardini

Simone Casolo

Matteo Bonfanti

http://users.unimi.it/cdtg

Special thanks to:

Eckart Hasselbrink

Geert-Jan Kroes

Bret Jackson

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’HAA = HABHBA

εi , |ψA,i 〉⇓

ε±i = ±√εi , |ψ

(±)i 〉 = |ψA,i 〉 ± |ψB,i 〉

|ψB,i 〉 = ε−1/2i HBA |ψA,i 〉


Hπ ≈∑

i Zi t2a†i ai +∑

ij t2a†i aj


εi , |ψA,i 〉⇓

ε±i = ±√εi , |ψ

(±)i 〉 = |ψA,i 〉 ± |ψB,i 〉

|ψB,i 〉 = ε−1/2i HBA |ψA,i 〉


Hπ ≈∑

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


εi , |ψA,i 〉⇓

ε±i = ±√εi , |ψ

(±)i 〉 = |ψA,i 〉 ± |ψB,i 〉

|ψB,i 〉 = ε−1/2i HBA |ψA,i 〉

*

Zecho’s kinetic experiments

*

Documents

Hydrogen atoms on graphene: structure, energetics and …users.unimi.it/cdtg/download/beamer talks/Potsdam-2013.pdf · Hypercoordination(˘) sublattice imbalance ( ) Z = 2 )E Z =