EPSRC Symposium Workshop on Quantum Simulations
Dynamics and Statistics of Electron Transport in
Single Molecules
Yi Luo
Theoretical Chemistry, Royal Institute of Technology, Sweden
&
Hefei National Lab, University of Science and Technology of China, China
Warwick, 2009-08-25
Scattering Theory: a bottom-up approach
Tunneling Current Density from Source to Drain:
DOS e
Ef
e
DOS
Ef
Simple estimation of potential drop in a junction with non-plannar metal surfaces
Solving Schrödinger Equation together with the Poisson equation
For atomic sharp contact, the potential drop on molecule is very small.
Fu and Luo, unpublished
S
H  H
S
0
 H
M
0
 H
D
0
U
M
U: interaction between subsystems
D
Transition matrix element
T ( E i )   1S 

1 S


i
V
Si
Coupling between reservoir
and end-sites of molecule
d
DN


1i
 1 |    | N 
z  

Interaction between orbital i of
molecule and orbital S of the reservoir
H |    |  
f

Z
DN


j
V
Wang, Fu, and Luo, Phys. Chem. Chem. Phys, 3 (2001) 5017
d
jN
expansion coefficient
 E i  i
a finite system: molecule + metal cluster
Injection energy
jD
escape rate
(Quantum Chemistry for Molecular Electronics)
QCME Program by J. Jiang, C.C.-K. Wang, and Y. Luo
Molecule-Gold-Cluster
DFT, B3LYP
Gaussian03, Dalton,
……
Results
Presented
here
QCME V1.0
Jiang, Kula, and Luo, J. Chem. Phys. , 124 (2006) 034708.
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Effects of the Size and the Shape of the Metal Clusters
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All calculated currents are of same order of magnitude
Li, Zou, Wang, and Luo , Phys. Rev. B, 73 (2006) 075326
Without field
With field
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I(μ A)
1.0
2.4
1.8
0.0
1.2
0.6
-1.0
Experiment: B.-Q. Xu, and T. J. Tao,
Science 301 1221(2003)
-1.0
-0.5
0.0
0.5
V bias (V)
0.0
1.0
DI/dVbias (μ S)
3.0
Exp.
Length Dependent Molecular Conductance
Exp: Wold et al., J. Phys. Chem. B, 106 (2002) 2813
I: circule
II: square III: triangle
Su, Jiang, and Luo, Chem. Phys. Lett., 412 (2005) 406
Dynamics of Nuclear Motion:
Inelastic Electron Tunneling Spectroscopy (IETS)
 Born-Oppenheimer approximation
 Electronic Hamiltonian can be considered parametrically as
dependent on the vibration normal modes Q:
 At electronic off-resonant region
 Harmonic approximation
With Scattering Theory Formulation
Transition Moment:
M. A. Reed et al., Nano Lett. 4, 643 (2004)
Gold-S-(CH2)8-S-Gold
J. G. Kushmerick et al., Nano Lett. 4, 639 (2004)
Gold-S-(CH2)11-H-Gold
 (C-C) FWHM
Exp.: 3.73 0.98 meV
Cal.: 6.1 meV
1)Jiang, Kula, Lu, and Luo, Nano Lett. 5 (2005) 1551
2). Kula, and Luo, J. Chem. Phys. , 124 (2006) 034708.
Jiang,
OPE
OPV
M. Kula, J. Jiang and Y. Luo, Nano Lett., 6 (2006) 1693 .
Exp: Kushmerick et al., Nano Lett. 4, 639 (2004)
OPE: Effects of the width of the junction on IETS
bg: background!
IETS for Surface Adsorbates: CO/Cu(001)
L. J. Lauhon and W. Ho, PRB, 60, R8525(1999)
H. Ren, J. L. Yang, and Y. Luo, J。Chem. Phys. 130 (2009) 134707
IETS for Surface Adsorbates: C2H4/Cu(100)
Dynamics of the Atomic Motion: Tautomerization Induced Molecular Switch
Conductance switching was
observed in a naphthalocyanin
molecule and attributed to the
hydrogen tautomerization process.
A slight but significant
deviation from purely
exponential dependence
Two tautomers were treated
as a perfect two-level system
Liljeroth, Repp, and Meyer, Science 317,1203 (2007)
Dynamics of the molecular switching: reaction paths
It is a four-state switch,
Not a two-state switch!
Q. Fu, J.-L. Yang, and Y. Luo, Appl. Phys. Lett., in press
Molecular Switch: Dynamic Motion of A Single Chemical Bond
Dehydrogenation
2.4 V plus
Switching
Pan, Fu, Huang, Zhao, Wang, Luo, Yang, Hou, PANS 00 (2009) 000.
Tautomerization
Switching rate : IN
Dynamics of Inelastic Scattering
Rate = kIN
Statistic distribution of multi-electron processes
P: probability of the inelastic scattering events
Ep: electron energy
T: tunneling probability
t: lifetime of the virtual state
Pan, Fu, Huang, Zhao, Wang, Luo, Yang, Hou, PANS 00 (2009) 000.
Orientation dependent molecular conductance
Orbitals
Calculations
Ning et al., J. Phys. Chem. C, 113 (2009) 26
Dynamic Motion of an Atom Inside a Molecule
Statistic Behavior of the Electron Transport
O atom
Molecular Dynamic Simulations
+ Quantum Chemistry Calculations
Li, Hihath, Chen, Masuda, Zang, and Tao, J. Am. Chem. Soc. 2007, 129, 11535.
Statistics of the molecular conductance of a junction
in water solution
30
298 K
308 K
25
298K
308K
30
298 K

Counts
1.0
20
15
0.5
10
0.0
2
25
3
4
5
6
7
8
9
R (angstrom )
5
Counts
20
0
0 1
15
10
15
-3
Conductance (10 nS)
10
5
30
308 K
25
20
Counts
5
15
10
5
0
0
5
10
15
20
-3
C o n d u c ta n c e (1 0 n S )
H. Cao, J. Jiang, J. Ma and Y. Luo, J. Am. Chem. Soc. 130 (2008) 6674
20
Single Molecular Field Effect Transistor
Molecular Field Effect Transistor with
Electro-Chemically Controlled-Gate
Exp.: Xu et. al JACS., 127, 2386 (2005)
Su, Jiang, Lu, and Luo, Nano Lett., 6 (2006) 2091
Statistics of the molecular conductance under the external electric field
Cao, Ma and Luo, to be published
Conjugated polymer: poly(para-phenylene ethynylene)s (PPE)
=24
Hu et al. Institute of Chemistry, CAS
Au-Au: 18nm
Central Insertion Scheme (CIS)
Jiang, Liu, Lu, and Luo, J. Chem. Phys. 124 (2006) 214711.
An Elongation Method
Geometry elongation
Hamiltonian Matrix elongation
Poly10, Charging effect
Hu, Jiang, et al. Phys. Rev. Lett., (2006) 027801
poly 24 = 18.3 nm
A: =3, B: =10
i(Ei) =i(0)(1+ Ei)
 is the dephasing factor
SWCNT (5,5)
(a)
(b)
Electronic Structures of SWCNTs
(6,5)
Exp: 1.69eV
(8,3)
Exp: 1.72eV
Electronic transportation in (5, 5) CNT
Exp: Javey et al. PANS, 101 (2004) 13408
Jiang, Lu, and Luo, Chem. Phys. Lett. 416 (2005) 272 .
DNA
semi--conductor
semi
alike
Porath et al.
Nature,
403,635,2000
Hwang et al.
Appl. Phys. Lett.
81,1134,2002
Jiang, Liu, Lu, and Luo, J. Chem. Phys. 124 (2006) 214711.
Flow Chart of Bio
Bio--Nano
Nano--Lego Program
Step 1 (sequential)
1. Check the convergence of initial system
2. Write out matrices of intial system, such as
XXoverlap matrix, Hamiltonian matrix
Step 4 (parallel)
1. By using P_ARPACK, SuperLU and
XXSparse BLAS package to solve:
N
N
N
N
H CIS
 CIS
  CIS
S N CIS
Step 2 (parallel)
1. Compute the Hamiltonian matrix of each
XXrotated system:


H i  S i RiC RiC H 0 S 01 , i  1, 2 ,  , N
T
Step 3 (parallel)
1. By using the "centeral insertion scheme" to
XXgenerate a large cluster
2. Compute the overlap matrix S Nof this large
XXcluster in parallel
3. Combine each H i into a new Hamiltonian
N
XXmatrix H CIS
of this large cluster
Diomandiods with CH2 termination
Applications for Diamondoid (Step 4)
Diameter (nm)
Number of atoms
Number of electrons
Time
(min)
3.8
C2983H900
19518
5.3
4.3
C4312H1157
27934
9.6
4.8
C5989H1444
38478
16.6
5.3
C8051H1764
51390
28.4
5.8
C10539H2116
66910
48.1
6.3
C13493H2500
85278
76.4
6.8
C16953H2916
106734
123.3
7.3
C20959H3364
131518
188.5
The calculation were carried out at B3LYP/STO-6G level for 40 orbitals around gap. This
parallel version is double precision.
B. Gao, J. Jiang, K. Liu, Z. Wu, W. Lu, and Y. Luo, J. Comput. Chem., 29 (2008) 434
Applications for Diamondoid (Step 4)
2000
CPU x Time (min)
1500
1000
500
0
0
20000
40000
60000
80000
Number of orbitals
100000
120000
Hydrogen-terminated nanodiamonds
J. Jiang, et al. to be published
Hydrogen-terminated nanodiamonds
Hydrogen-terminated nanodiamonds
Experimental results for m*
Diamond (bulk): 0.20 to 0.25m; (surface): 0.17m
Silicon bulk: 0.92m, 1.09m
Acknowledgement
Dr. Jun Jinag, UC-Irvine, USA
Dr. Mathias Kula, Linköping University , Sweden
Dr. Bin Gao, University of Tromsø, Norway
Mr. Hui Cao, KTH
Mr. Hao Ren, KTH
Mr. Qiang Fu, KTH
Dr. WenYong Su, BIT, China
Dr. Chuan-Kui Wang, SDNU, China
Dr. Ying Fu, KTH
Swedish Research Council (VR)
Carl Trygger Fundation (CTS)
National Super-compter Center (NSC), Linköping, Sweden