A van der Waals density functional study ofadsorption states of C60 on metal surfaces
Ikutaro Hamada
WPI-Advanced Institute for Materials Research, Tohoku University andCREST, Japan Science and Technology Agency
ikutaro@wpi-aimr.tohoku.ac.jp• Collaborators
Masaru Tsukada (Tohoku University)
Masaaki Araidai (Tohoku University)

Kazuhiko Hirakawa (The University of Tokyo)• Funding
Grant-in-Aid for Scientific Research on Innovative Area``Materials Design through Computics:
Complex Correlation and Non-equilibrium Dynamics"(No. 23104501)

1

Contents• Background- C60 as a component of molecular electronic devices• Franck-Condon process in a single-C60 transistor- Neutral C60 on a Au(111) surface- Negatively charged C60 on a Au(111) surface• Summary2

C60 as a component of a single-molecular transistor- “Franck-Condon blockade”
in a single-C60 transistor (Au/C60/Au)
Park et al., Nature 407, 57 (2000).

- Kondo effect in single-C60 transistors
with Au and Ni electrodes
Pasupathy et al., Science 306, 86 (2004).
Yu and Natelson, Nano Lett. 4, 79 (2004).

Park et al., Nature 407, 57 (2000).

Franck-Condon process in a single C60 transistor

C60- Negative differential resistance
Danilov et al., Faraday Discuss. 131, 337 (2006).

- Superconductivity
Winkelmann, et al., Nature Phys. 5, 876 (2009).

C603

Contents• Background- C60 as a component of molecular electronic device• Franck-Condon process in a single-C60 transistor- Neutral C60 on a Au(111) surface- Negatively charged C60 on a Au(111) surface• Summary4

Method
An accurate van der Waals density functional (vdW-DF)
for solids and surfaces: vdW-DF2C09x (vdW-DF2-C09)
Exc = ExGGA + EcLDA + EcNL
1NL
Ec =2!!

drdr! n(r)φ(r, r! )n(r! )A vdW-DF with the exchange of Cooper [Phys. Rev. B 81, 161104(R) (2010)] andthe nonlocal correlation of Lee et al. [Phys. Rev. B 82, 081101(R)(2010)]

IH and M. Otani, Phys. Rev. B 83, 245437 (2010).

C60/Au(111): accurate binding energy with
vdW-DF2C09x

Binding energy (eV)1Distance

0-1
PBE
C09
vdW-DF2 x-2

Expt.
0.1

0.2

0.3

0.4

Distance (nm)

IH and M. Tsukada, Phys. Rev. B 83, 245437 (2011).

0.5

0.66

PDOS and charge density difference
Charge density difference

PDOS (arb. unit)

HOMO(1)
HOMO(2)
HOMO(3)
HOMO(4)
HOMO(5)
LUMO(1)
LUMO(2)
LUMO(3)Charge accumulation
Charge depletion

-4

-3

-2

-1

E-EF (eV)012

There are weak covalent-like interface states, owing tohybridization of C60 LUMOs and substrate wave-functions
IH and M. Tsukada, PRB 83, 245437 (2011).

7

Contents• Background- C60 as a component of molecular electronic device• Franck-Condon process in a single-C60 transistor- Neutral C60 on a Au(111) surface- Negatively charged C60 on a Au(111) surface• Summary8Simulation of charged adsorbate on a metal surface
Neutral C60 on a metal surface
Electrode

Negatively charged C60 on a metal surface

C60

C60-

Electrode

LUMO
EF

HOMO

LUMO
EF

HOMO

C60

Electrode

-

EF

LUMO

-HOMO
9

Simulation of charged adsorbate on a metal surface
Neutral C60 on a metal surface
Electrode

Negatively charged C60 on a metal surface

C60

C60-

Electrode

LUMO
EF

HOMO

LUMO
EF

HOMO

C60

Electrode-EF

LUMO-HOMO
9Use Li@C60, instead of C60C60

Li@C60HOMO (spin up)

HOMO (spin down)

HOMO (spin down)

HOMO (spin up)

E=0.00 (eV)

E=-0.06 (eV)SOMO (spin down)
E=1.57 (eV)SUMO (spin up)

E=1.57 (eV)E=0.00 (eV)

E=-0.05 (eV)SOMO (spin up)
E=1.56 (eV)SUMO (spin down)
E=1.62 (eV)

Molecular orbitals of Li@C60 resemble those of C60-, validating the use of Li@C60 to mimic C60NOTE: Li atom is placed at the center of the case, to avoid strong interaction with C60-

10Interaction energy of negatively charged C60
with Au(111)
Eint(C60-/Au)=Etot(C60-/Au) - Etot(C60-) - Etot(Au)11Interaction energy of negatively charged C60
with Au(111)
Eint(C60-/Au)=Etot(C60-/Au) - Etot(C60-) - Etot(Au)Eint(C60-/Au)= [Etot(Li+@C60-/Au) - Eint(Li+/Au)]-[Etot(Li+@C60-)-Eint(Li+/C60-)]-Etot(Au)11Interaction energy of negatively charged C60
with Au(111)
Eint(C60-/Au)=Etot(C60-/Au) - Etot(C60-) - Etot(Au)Eint(C60-/Au)= [Etot(Li+@C60-/Au) - Eint(Li+/Au)]-[Etot(Li+@C60-)-Eint(Li+/C60-)]-Etot(Au)=Eint(Li@C60/Au)

11

Interaction energy of negatively charged C60
with Au(111)
Eint(C60-/Au)=Etot(C60-/Au) - Etot(C60-) - Etot(Au)=Eimage(Li)Eint(C60-/Au)= [Etot(Li+@C60-/Au) - Eint(Li+/Au)]-[Etot(Li+@C60-)-Eint(Li+/C60-)]-Etot(Au)=Eint(Li@C60/Au)

11

Interaction energy of negatively charged C60
with Au(111)
Eint(C60-/Au)=Etot(C60-/Au) - Etot(C60-) - Etot(Au)=Eimage(Li)Eint(C60-/Au)= [Etot(Li+@C60-/Au) - Eint(Li+/Au)]-[Etot(Li+@C60-)-Etot(Au)-Eint(Li+/C60-)]=-ΔE=Eint(Li@C60/Au)

Eint(C60-/Au)=Eint(Li@C60/Au)-Eimage(Li)-ΔE

11

Calculated interaction energies of C60 and C60

on Au(111)Interaction energy (eV)

0.0
C60

-0.5

C60

C60
Distance-0.9
-1.0

-1.0

C60

-1.1
-1.2
-1.3

-1.4

-1.5

0.20

0.30

0.22

0.24

0.40

0.26

0.28

0.50

Distance (nm)C60 : d=0.243 nm, Eint=-1.335 eVC60- : d=0.247 nm, Eint=-1.105 eV

Negatively charged C60 shifts away from the surface!

12Discussion• Our result suggest that negatively charged C60
interacts (slightly) more repulsively with the Au
substrate than neutral C60, and C60- is shiftedaway from the surface• This is in sharp contrast with naive explanationthat the negatively charged C60 interacts
attractively with induced image charge

Interaction energy (eV)

0.0
C60

-0.5

C60

C60
Distance

-0.9
-1.0

-1.0

C60

-1.1
-1.2
-1.3

-1.4

-1.5

0.20

0.30

0.220.24

0.26

0.40

0.28

0.50

Distance (nm)• What is the origin of the repulsive interaction?

Park et al., Nature 407, 57 (2000).

13PDOS and COOP analysis:
Comparison with C60
C60-/Au(111)

C60/Au(111)

HOMO(1)(c)

HOMO(2)
HOMO(3)

COOP (arb. unit)

PDOS (arb. unit)(a)

HOMO(4)
HOMO(5)
LUMO(1)
LUMO(2)
LUMO(3)

(b)

-2(d)

-1

0
E-EF (eV)12-2-10
E-EF (eV)12Antibonding components (negative COOPs) are partially occupied,suggesting Pauli repulsion between C60- and Au substrate14

Summary• Application of vdW-DF2C09x to C60 on a Au(111) surface• Weak covalent-like C60 LUMO - Au substrate hybridized states• Negatively charged C60 moves away from the electrode surface• Pauli repulsion of LUMOs with the substrate state is larger than
the attractive interaction with induced image charge, resulting in
repulsive interaction of C60- with the Au electrode• Importance of orbital hybridization in typical ``physisorption systems”
IH and M. Tsukada, PRB 83, 245437 (2011).
IH, M. Araidai, and M. Tsukada, PRB 85, 121401(R) (2012).
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