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