Dependence of single-molecule conductance on molecule junction symmetry

Article abstract of DOI:10.1021/ja2033926

The symmetry of a molecule junction has been shown to play a significant role in determining the conductance of the molecule, but the details of how conductance changes with symmetry have heretofore been unknown. Herein, we investigate a naphthalenedithiol single-molecule system in which sulfur atoms from the molecule are anchored to two facing gold electrodes. In the studied system, the highest single-molecule conductance, for a molecule junction of 1,4-symmetry, is 110 times larger than the lowest single-molecule conductance, for a molecule junction of 2,7-symmetry. We demonstrate clearly that the measured dependence of molecule junction symmetry for single-molecule junctions agrees with theoretical predictions.

Full text of DOI:10.1021/ja2033926

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Dependence of Single-Molecule Conductance on Molecule Junction
Symmetry
,†
†
‡
‡
§
§
Masateru Taniguchi,* Makusu Tsutsui, Ryoji Mogi, Tadashi Sugawara, Yuta Tsuji, Kazunari Yoshizawa,
,†
and Tomoji Kawai*
†
The Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka 567-0047, Japan
‡
Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku,
Tokyo 153-8902, Japan
§
Institute for Materials Chemistry and Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
S Supporting Information
b
LUMO in the isolated molecular Green’s function (eq 1).
ABSTRACT: The symmetry of a molecule junction has
been shown to play a significant role in determining the
conductance of the molecule, but the details of how con-
ductance changes with symmetry have heretofore been
unknown. Herein, we investigate a naphthalenedithiol sin-
gle-molecule system in which sulfur atoms from the mole-
cule are anchored to two facing gold electrodes. In the
studied system, the highest single-molecule conductance,
for a molecule junction of 1,4-symmetry, is 110 times larger
than the lowest single-molecule conductance, for a mol-
ecule junction of 2,7-symmetry. We demonstrate clearly
that the measured dependence of molecule junction sym-
metry for single-molecule junctions agrees with theoretical
predictions.
CR;HOMOCꢁL;HOMO
CR;LUMOCꢁL;LUMO
EF ꢀ εLUMO
þ
ð1Þ
EF ꢀ ε
HOMO
where CR,HOMO and CR,LUMO are the molecular-orbital expan-
sion coefficient at a sulfur atom connected to the right electrode
at the HOMO and LUMO, respectively, and the other terms are
comparably assigned (see Supporting Information).
This equation implies that when the signs of the two products
CR,HOMOC*L,HOMO and CR,LUMOC*L,LUMO differ, Auꢀsingle-
moleculeꢀAu junctions are symmetry allowed and exhibit high
single-molecule conductance; when the signs of the two products
are the same, the junctions are symmetry forbidden and exhibit
low single-molecule conductance. For the case of two degenerate
states where the HOMO and LUMO in eq 1 are replaced by
singly occupied molecular orbital 1 (SOMO1) and SOMO2, the
opposite orbital symmetry rule applies: when the signs of the two
products CR,SOMO1C*L,SOMO1 and CR,SOMO2C*L,SOMO2 differ,
the junctions are symmetry forbidden. Consequently, the depen-
dence of single-molecule conductance on junction symmetry can
be predicted only by the phases of the sulfur atoms on the frontier
molecular orbitals.
To investigate our orbital symmetry rule for electron trans-
port, we selected ND as a small thiol molecule. We examined the
conductance of single-molecule junctions of 2,6-ND, 2,7-ND,
1,4-ND, and 1,5-ND (Figure 1), which we synthesized success-
fully (Figures S1 and S2).
We calculated transmission probabilities at the H €u ckel level of
theory for the four ND-isomer junctions. Figure 2 shows the
calculated electron transmission spectra. Resonance peaks for
ecent dramatic progress in creating single-molecule devices
R
has led to fabrication of semiconductor-related products
1 2
such as field-effect transistors, diodes, electroluminescence
3
devices, and even emerging nanodevices that use molecular
4,5
motion as a switching parameter. The key issue that determines
how single-molecule devices operate and how their character-
istics can be controlled is the symmetry of an electrodeꢀmolecule
junction where two atoms from the molecule are anchored to two
6
ꢀ15
facing electrodes.
A comprehensive understanding of how
single-molecule conductance changes with molecule junction
symmetry would facilitate the design and synthesis of functional
molecules for single-molecular devices.
We previously developed the orbital symmetry rule for
electron transport in single-molecule junctions. When we applied
the rule to single-molecule junctions of four naphthalenedithiol
2
,6-ND, 1,5-ND, and 1,4-ND appear at the Fermi level, indicat-
ing that frontier molecular orbitals interfere constructively, and
an antiresonance peak for 2,7-ND appear at the Fermi level,
indicating that frontier molecular orbitals interfere destructively.
1
6,17
(
ND) isomers,
the rule correctly predicted whether frontier
molecular orbitals on atoms anchored to two facing gold elec-
trodes should exhibit large or small single-molecule conductance.
We have carried out the present study to validate our previous
theoretical predictions.
Our orbital symmetry rule specifies that when the Fermi level
EF) of the electrodes is between the energies of the highest
This orbital symmetry rule for electron transport agrees well with
18ꢀ21
the quantum interference discussion.
Consequently, the
single-molecule conductance order becomes 2,7-ND (0 G , where
0
G is the conductance quantum, 77.5 μS) < 2,6-ND (0.82 G )
0
0
and 1,5-ND (0.82 G ) < 1,4-ND (0.94 G ) at the Fermi level.
0
0
(
occupied molecular orbital (εHOMO) and the lowest unoccupied
molecular orbital (εLUMO), the transmission probability is qua-
litatively predicted from the contribution of the HOMO and
Received: April 13, 2011
Published: July 08, 2011
r 2011 American Chemical Society
11426
dx.doi.org/10.1021/ja2033926
|J. Am. Chem. Soc. 2011, 133, 11426–11429

Journal of the American Chemical Society
COMMUNICATION
Figure 1. Frontier molecular orbitals (HOMO, LUMO, and SOMO) of
the four studied ND isomers at the H €u ckel molecular orbital theory level.
SOMO1 and SOMO2 orbitals are degenerate. The phase and amplitude
of these frontier orbitals determine that the route for electron transmis-
sion is symmetry forbidden for 2,7-ND and symmetry allowed for the
other three isomers. Blue and red isosurfaces represent positive and
negative isovalues, respectively; green arrows show the routes for
electron transmission.
Figure 3. Measured conductance characteristics of AuꢀNDꢀAu sin-
gle-molecule junctions: Typical conductance traces of (a) 2,6-ND and
2,7-ND and (b) 1,4-ND and 1,5-ND junctions. Conductance histograms
of (c) 2,6-ND, (d) 2,7-ND, (e) 1,4-ND, and (f) 1,5-ND junctions
constructed from 328, 365, 443, and 142 conductance traces, respec-
tively (Figures S5 and S6). One thousand conductance traces were
accumulated for all molecular junctions. Measured single-molecule
conductances for the ND isomers are as follows: 2,6-ND, 1.4 mG0;
2
,7-ND, 0.1 mG ; 1,4-ND, 11 mG ; and 1,5-ND, 2.2 mG . Peak
0 0 0
conductances for 1,4-ND and 1,5-ND were obtained at integral multi-
ples of 11 and 2.2 mG , respectively. White lines are Gaussian fits to the
peak profiles. All electrical measurements were performed at room
0
ꢀ
5
temperature in a vacuum of 10 Torr.
conductances are 1.4 and 0.1 mG , respectively. For 1,4-ND and
0
1
,5-ND, plateaus appear at ∼10 mG and several mG , respec-
0
0
Figure 2. Calculated electron transmission spectra of AuꢀNDꢀAu
single-molecule junctions at the H €u ckel level of theory. Calculated
single-molecule conductances for the ND isomers are as follows: 1,
tively, and pronounced peaks appear at integral multiples of 11
and 2.2 mG (Figure 3e,f). Thus, the measured single-molecule
conductances of 1,4-ND and 1,5-ND are 11 and 2.2 mG0,
respectively, and the single-molecule conductance order is 2,
0
4
-ND, 0.94 G
where G is the conductance quantum, 77.5 μS. E
the electrodes.
0
; 1,5-ND, 0.82 G
0
; 2,6-ND, 0.82 G
0 0
; and 2,7-ND, 0 G ,
0
F
is the Fermi energy of
7
-DN (0.1 mG ) < 2,6-DN (1.4 mG ) < 1,5-DN (2.2 mG ) < 1,
0 0 0
4
-DN (11 mG ), where the highest conductance is 110 times
0
the lowest.
The single-molecule conductance order is retained in the small
bias window from ꢀ1 to +1 V.
We explored the voltage dependence of single-molecule
conductance by measuring currentꢀvoltage characteristics at
bias voltages of ꢀ0.8 to 0.8 V when the nanoelectrode gaps
were fixed in the state where single-molecule conductance was
obtained (Figure 4a). In the voltage window, the currentꢀvoltage
characteristics show single-molecule conductance in the order
1,4-ND > 1,5-ND > 2,6-ND > 2,7-ND.
We measured single-molecule conductances for the four
ND-isomer junctions (0.2 V, room temperature, in vacuum)
using nanofabricated mechanically controllable break junctions
2
2,23
(Figure S3).
Figure 3 shows the measured conductance
characteristics. Conductance traces obtained during the breaking
process show three conductance plateaus—at 1 G , ∼1 mG ,
We found a remarkable result that neither the theoretical nor
experimental conductance followed the exponential decay law
(Figure 4b), although the exponential decrease in single-molecule
conductance with increasing distance between sulfur atoms
0
0
and <1 mG (Figure 3a)—that correspond to the formation of a
0
single-gold atomic contact and of single-molecule junctions of
2
(
,6-ND and 2,7-ND, respectively. Traces of tetrahydrofuran
THF) solvent decrease exponentially with time, indicating
24,25
indicated electron tunneling.
is known to fail for either of the two scenarios:
Exponential-distance scaling
26,27
direct tunneling between electrodes (Figure S4). Conductance
(1) when
histograms show pronounced conductance peaks at ∼1.4 and
electrodeꢀmolecule coupling energy is strong compared to half
0
.1 mG (Figures 3c and 3d). For 2,6-ND and 2,7-ND, single-molecule
of the HOMOꢀLUMO gap or (2) when siteꢀsite interaction in
0
1
1427
dx.doi.org/10.1021/ja2033926 |J. Am. Chem. Soc. 2011, 133, 11426–11429

Journal of the American Chemical Society
COMMUNICATION
orbital phases of the two sulfur atoms anchored to the electrodes.
Thus, we have demonstrated clearly that molecular orbital theory
provides an orbital symmetry rule for describing electron trans-
port in single-molecule junctions as well as in chemical reactions.
Further, the rule holds true even if the effects of molecu-
30
leꢀelectrode coupling by sulfur atoms are included. The orbital
symmetry rule for electron transport in single-molecule junctions
provides a guiding principle for the design of molecules that
exhibit desirable levels of single-molecule conductance.
Figure 4. Measured electron-transport characteristics through
AuꢀNDꢀAu single-molecule junctions for the four studied ND isomers.
(
a) Currentꢀvoltage characteristics of the four ND single-molecule
’ ASSOCIATED CONTENT
junctions. (b) Single-molecule conductance as a function of distance
between S atoms. The distances were obtained from optimized molec-
ular structures, where the calculated SꢀS distances are as follows: 1,
S
Supporting Information. Synthesis and single-molecule
b
measurements of dithiolnaphthalene and theoretical calculations of
electron transmission for single-molecule junctions. This material is
available free of charge via the Internet at http://pubs.acs.org.
4
0
-DN, 0.644 nm; 1,5-DN, 0.684 nm; 2,7-DN, 0.784 nm; and 2,6-DN,
.856 nm. The dependence of single-molecule conductance on SꢀS
distance obtained from experiments is similar to that obtained from
theoretical calculations, and both disobey the exponential decay law with
respect to distance.
’
AUTHOR INFORMATION
Corresponding Author
taniguti@sanken.osaka-u.ac.jp; kawai@sanken.osaka-u.ac.jp
the molecule is sufficiently strong to drive the single-molecule
junction close to resonance tunneling. Our density functional
theory (DFT) calculations yield the following HOMOꢀLUMO
gaps: 2,6-ND, 4.3 eV; 2,7-ND, 4.5 eV; 1,4-ND, 4.1 eV; and 1,
’
ACKNOWLEDGMENT
5
-ND, 4.3 eV. However, theoretical calculations also yield electrodeꢀ
28,29
This research is partially supported by the Japan Society for
molecule coupling energies of <1 eV;
hence, the first scenario
the Promotion of Science (JSPS) through its Funding Program
for World-Leading Innovative R&D on Science and Technology.
K.Y. acknowledges Grants-in-Aid (No. 18GS0207 and 22245028)
for Scientific Research from JSPS and MEXT, the Kyushu
University Global COE Project, the Nanotechnology Support
Project, the MEXT Project of Integrated Research on Chemical
Synthesis, and CREST of the Japan Science and Technology
Cooperation.
is not applicable to ND junctions. However, the second scenario
is applicable because for 2,6-ND, 1,4-ND, and 1,5-ND, π electrons
on carbon and sulfur atoms interact strongly with each other at
the frontier molecular orbitals (Figure 1). In addition, the theo-
retical and experimental conductance values differ. Theoretical
calculations predict that, if the sole mechanism of electron trans-
port is π tunneling, single-molecule conductance for 2,7-ND
should become 0 at the Fermi level and for 1,4-ND, 1,5-ND, and
2
,6-ND, single-molecule conductance should become close to 1G0.
We carried out molecular projected self-consistent Hamiltonian
MPSH) analysis at the DFT level, which shows us the spatial
’
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