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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