The Interaction of Graphene with Noble Metals

The Interaction of Graphene with Noble Metals

Petr Lazar, Jaroslav Granatier, Michal Otyepka, Pavel Hobza

Regional Centre of Advanced Technologies and Materials

Department of Physical Chemistry, Palacký University Olomouc, Czech Republic

Outline

Introduction

Quantum-mechanical calculations– wave-function based methods vs. density functional – How to overcome deficiencies of DFT?

Results for model systems:– metal-benzene– metal-coronene– metal-graphene

Conclusions

Graphene-Metal Interfaces

Ming Liu, et al. Nature

474, 64 (2011)

Nano(opto)electronics

interfaces between

graphene and

conventional electronics

Michael S. Fuhrer

University of Maryland

Key questions: How the particles bind to graphene?How will they affect the electronic properties of graphene?

Junfei Liang, Chem. Commun.

2011, DOI: 10.1039/C1CC10965K

Catalysts

and

Energy Storage

Devices

Nano Lett., 2010, 10 (2), 577

Biosenzors

metal nanoparticles on

graphene surface

Theoretical Modeling of Graphene-Metal system

Obstacles for theoretical modeling– Graphene sheet infinite – periodic boundary conditions necessary– Interaction involves van der Waals forces, relativistic effects (gold)...

Quantum-chemical methods- wavefunction based (WFT)- highly accurate (e.g. CCSD(T)/CBS as a golden standard)- atomic-like orbitals as a basis set (no spatial periodicity)- limited to small systems (scaling)

Density functional theory (DFT) methods– based on electron density– plane-wave basis set - applicable to extended systems (bandstructure)– depend on underlying functional

Pros and cons of DFT method

Graphene...Au complex

gold positioned over carbon atom

plane-wave (PW) DFT calculation using various functionals

LDA

PBE

HSE06

B3LYP

- none of functionals really works- no binding by B3LYP!- GGA, hybrids strongly underbound⇒ missing van der Waals int.

Which one should be used?

Strategy of Calculations

Benzene…Metal

Benchmark CCSD(T) calculations

Find the best MP2 (for coronene)

Find the best DFT (for graphene)

Coronone…Metal

Coronene as a model of the graphene sheet

Analysis of bonding

Graphene…Metal

Strategy of Calculations

Benzene…Metal

Benchmark CCSD(T) calculations

Find the best MP2 (for coronene)

Find the best DFT (for graphene)

Coronone…Metal

Coronene as a model of the graphene sheet

Analysis of bonding

Graphene…Metal

Benzene…Pd Benzene…Ag Benzene…Au

(t) (b) (h) (t) (b) (h) (t) (b) (h)

DFT-D3/TPSS/def2-QZVP

∆E -28.3 -29.4 -22.1 -3.7 -3.7 -4.0 -7.5 -7.2 -4.6

R 2.10 2.07 1.97 3.07 3.10 3.28 2.51 2.56 3.17

M06-2X/lanl2dz

∆E -15.1 -15.2 -12.3 -4.3 -4.6 -5.5 -5.8 -5.9 -6.3

R 2.36 2.37 2.45 3.09 3.10 3.12 2.97 2.99 3.10

DK rel. MP2/ANO-RCC-VDZP

∆E -18.5 -19.6 -12.3 -1.5 -1.6 -1.9 -4.2 -4.2 -3.6

R 2.11 2.08 1.97 3.34 3.33 3.34 2.66 2.69 3.07

DK rel. MP2/ANO-RCC-VTZP

∆E -28.0 -30.2 -27.5 -2.7 -2.9 -3.3 -8.2 -8.3 -6.1

R 2.05 2.01 1.83 3.01 3.01 3.11 2.41 2.39 2.83

DK rel. CCSD(T)/ANO-RCC-VTZP

∆E -18.8 -19.7 -12.8 -1.9 -2.0 -2.3 -4.2 -4.1 -3.2

R 2.13 2.11 2.04 3.18 3.18 3.24 2.63 2.67 3.09

DK rel. CCSD(T)/Pol-DK

∆E - - - -2.1 -2.2 -2.6 -3.7 -3.7 -3.1

R - - - 3.19 3.19 3.24 2.73 2.78 3.17

PBE

∆E -26.3 -27.3 -19.0 -1.3 -1.2 -1.0 -6.1 -5.6 -1.63

R 2.10 2.07 2.01 3.05 3.10 3.39 2.44 2.46 3.09

PBE + vdW

∆E -21.5 -21.8 -13.3 -2.7 -2.7 -2.6 -5.9 -5.5 -3.6

R 2.17 2.18 2.16 3.17 3.23 3.41 2.70 2.79 3.21

EE + vdW

∆E -17.2 -18.7 -10.6 -2.4 -2.3 -2.5 -5.1a -4.8 -3.4

R 2.18 2.15 2.16 3.22 3.32 3.41 2.64 2.74 3.22

a EE + vdW + spin-orbit coupling(soc) -5.7 kcal/mol

overbinding

overbinding

overbinding

Nature of Bonding of Pd, Ag, and Au differs• Pd bonding has partially covalent character

• Ag binds by dispersion interactions

• Au binding involves charge transfer, dispersion and relativity

Methods• neither LDA nor GGA work

• van der Waals term (vdW-DF; PBE+vdW) improves results

• a combination with HF exchange (EE+vdW) yields the best agreement

• empirical dispersion terms (DFT-D) doubtful

- MP2/DZ good agreement (cancelation of errors)

Conclusions – Benzene Complexes

Strategy of Calculations

Benzene…Metal

Benchmark CCSD(T) calculations

Find the best MP2 (for coronene)

Find the best DFT (for graphene)

Coronone…Metal

Coronene as a model of the graphene sheet

Analysis of bonding

Graphene…Metal

Graphene...Ag complex

➥ negligible bonding by PBE

➥ van der Waals forces dominant

➥ all positions equal in energy

silver glides easily on graphene

surface

32 atoms modeling the graphene sheet

5x5x1 k-points, 450 eV energy cut- off

one total energy point: ~1h GGA

~8h vdW term

~20h exact exchange

Single atom over graphene sheet-test the method (EE+vdW)-calculate Fermi level shift (or band gap)-find absorption positions and diffusion barriers

Graphene...Pd complex

➥ the strongest bonding (covalent character)

➥ PBE overestimates bonding energy

➥ vdW term repulsive

➥ top position preferred

➥ center site the least favorable

Calculated charge distribution of bonds

for coronene and its Pd, Ag, and Au complexes

Graphene...Au complex

➥ bonding distances longer (than benzene)

➥ PBE underestimates bonding energy

(in contrast to benzene...Au)

➥ vdW term essential

➥ top and bond sites equal

Graphene...Pd Graphene...Ag Graphene...Au

(t) (b) (h) (t) (b) (h) (t) (b) (h)

EE + vdW

∆E -17.4 -15.9 -12.0 -4.3 -4.3 -4.2 -5.6 -5.5 -5.2

R 2.21 2.17 2.18 3.35 3.35 3.39 3.14 3.07 3.33

-Pd binds much stroger-Ag and Au very mobile

Preliminary TEM data

Graphene + Pd = all sheets

covered with nanoparticles; a

high degree of coverage; no NPs

observed out of sheets

Graphene + Au = some sheets

covered with nanoparticles;

lower degree of coverage

compared to G-Pd system but

higher degree of particle

aggregation; a lot of NPs

observed out of the sheets (red

circles)

Graphene + Ag = all sheets

covered rather accidentally

with Ag nanoparticles; very low

NPs loading; majority of

nanoparticles located out of

sheets (bottom image)

Exfoliated Graphene sheet + Metal Nanoparticles

Metal clusters on graphene

Metal/graphene interface-planar geometric of clusters -larger clusters represent increasing coverage-many positions available

Metal dimers and tetramers on graphene-planar geometries similar in energy in DFT(valid for Ag and Pd as well)

-Binding energies in same order as atoms

Pd4...coronene Ag4...coronene Au4...coronene

structure

1 2 3 4 1 2 3 4 1 2 3 4

MP2/ANO-RCC-VDZP

∆E 70.6 71.8 39.0 44.6 13.9 18.1 16.4 16.2 18.5 25.0 23.6 23.31

R 2.09 2.08 2.09 2.08 3.22 3.22 3.28 3.26 3.07 3.08 3.10 3.12

TEM tip/graphene interaction-tetrahedral geometries

Metal clusters on graphene

Triplet-singlet transition in Pd dimer interacting with graphene

-the triplet groundstate of Pd dimer has multireference character(problems for both; CCSD(T) and DFT)

-DFT calculations reveal singlet Pd dimer on graphene

Isolated Pd dimer calculated by:

CCSD (blue)

CCSD(T) (black)

MRCI (red) … multi refrerence CI

--each metal cluster has unique properties

Bonding of Pd, Ag, and Au -Pd has the strongest bonding -Ag binds weakly through dispersion interactions-Au combines charge transfer and dispersion; relativistic effects important-EE+vdW method reproduces very well results of CCSD(T)

Clusters of Pd, Ag, and Au-planar geometries follow the same pattern as atoms (Pd>Au>Ag)-calculations resemble experimental results-change of spin state may occur (Pd dimer)-calculations more difficult (multireference character of some clusters)-tetrahedral clusters reveal strong bonding of Cu and Pt

Granatier J, Lazar P, Otyepka M, Hobza P: J. Chem. Theor. Comput. 7, 3743, (2011)

Granatier J, Lazar P, Prucek R, Šafářová K, Zbořil R, Otyepka M, Hobza P: J. Phys. Chem C, submitted

Conclusions

Funding Research Project No. Z40550506 of the Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic. Korea Science and Engineering Foundation (World Class Univ. program R32-2008-000-10180-0), Nos. LC512 and MSM6198959216 from the Ministry of Education, Youth and Sports of the Czech RepublicNo. P208/10/1742 from the Grant Agency of the Czech Republic.

The Operational Program Research and Development for Innovations ofEuropean Regional Development Fund (CZ.1.05/2.1.00/03.0058)

The Operational Program Education for Competitiveness of European Social Fund (CZ.1.07/2.3.00/20.0017).

…and you for your attention.

Acknowledgments