Step 3. Molecular junction between Au electrodesCurrent-Voltage (I-V) Characteristics

Periodic QM (DFT) with surface Green’s function formalism

Au

Au

I

V

Kim, Jang, YHJ, Goddard III, Phys. Rev. Lett., 95, 156801 (2005)

Density-functional theory (Hohenberg-Kohn-Sham)

)()(),(

21221 dEEfEfVET

h

eI T(E,V)

2,12,12,1

121mmmm )(

i

HSEGbroadeningself-energy

GGVET 21Tr),(

1m

2

Non-Eqm. Green’s ftn. Formalism (Fisher-Lee)

Ballistic transport theory (Landauer, Buttiker)

“Extended molecule” + separate bulk electrode calc. -> H, S

Calculated with SeqQuest periodic DFT code (Peter Schultz, Sandia)

I-V : DFT + Green’s Function + Landauer formalism

Au Au

V=0

0(EF) V

Au Au

Small V

Au Au

V

Large V

I=0 I=0 I0

I

V

I

V

CBPQT@TTF

(TTF)(CBPQT)

(PF6)4(DNP)

“CBPQT@TTF”

(TTF)(DNP)(CBPQT)(PF6)4

“CBPQT@DNP”

No HOMO level close to EF

TTF HOMO level close to EF

Implication of QM to switching mechanism

(TTF)(DNP)

“finger only”

Au AuTTF DNP AuTTF DNPAu

CBPQT@DNP

Au AuTTF DNP AuTTF DNPAu

[2]rotaxane

[2]catenane CBPQT

Au

Au

TTF TTF+CBPQT DNP DNP+CBPQT

~CBPQT@TTF ~CBPQT@DNP

1.5nm

Key components between Au(111) slabs

Rotaxane ~ Catenane~ sum-up of components

-0.2 -0.1 0.0 0.1 0.2

E EF (eV)

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

T(E)

TTF+CBPQT TTFT (

E)

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

T(E)

DNP DNP+CBPQT

T (

E)

-0.2 -0.1 0.0 0.1 0.2

E EF (eV)

Transmission within the energy window

Switch OFF

TTF TTF+CBPQT DNP DNP+CBPQT

~CBPQT@TTF~CBPQT@DNPSwitch ON

Model junction: [2]Catenane between Au(111) slabs

Folded rotaxane ~ Catenane

CBPQT@TTF“Green” state

CBPQT@DNP“Red” state

(TTF):(DNP)(CBPQT)

(PF6)4

“CBPQT@DNP”

-6-5-4-3-2-101

-1.0 -0.5 0.0 0.5 1.0

E-EF (eV) (EF = 4.75 eV)

log

10T(TTF)(CBPQT)(PF6)4:(DNP)

“CBPQT@TTF”1.8nm

1.8nm

-4

-2

0

2

0.0 0.1 0.2 0.3 0.4 0.5

V (V)

log

10I

(A

)

CBPQT@TTF

CBPQT@DNP

ON

OFF

-6-5-4-3-2-101

-1.0 -0.5 0.0 0.5 1.0

E-EF (eV) (EF = 4.77 eV)

log

10T

Model: -stacked components between Au(111)

0.2 – 0.3 V (choice in experiments) CBPQT@DNP: Switch ON CBPQT@TTF: Switch OFFON/OFF ratio ~ 5(agreement with experiments)

Summary

(1) Electronic structure of key components: QM Role of the ring 1: provide low-lying LUMO Role of the ring 2: stabilize energy level of station -orbitals dominant around HOMO-LUMO

(2) SAM packing on Au(111): MD simulation Coverage-dependent conformation

(3) I-V Calculation: periodic QM + Green’s function formalismAu(111) Model catenane/fully-folded-rotaxane Au(111)

(2) MD (1) QM (3) Periodic QM + I-V