Optimizing single-molecule conductivity of conjugated organic oligomers with carbodithioate linkers

Article abstract of DOI:10.1021/ja909559m

In molecular electronics, the linker group, which attaches the functional molecular core to the electrode, plays a crucial role in determining the overall conductivity of the molecular junction. While much focus has been placed on optimizing molecular core conductivity, there have been relatively few attempts at designing optimal linker groups to metallic or semiconducting electrodes. The vast majority of molecular electronic studies use thiol linker groups; work probing alternative amine linker systems has only recently been explored. Here, we probe single-molecule conductances in phenylene-ethynylene molecules terminated with thiol and carbodithioate linkers, experimentally using STM break-junction methods and theoretically using a nonequilibrium Greens function approach. Experimental studies demonstrate that the carbodithioate linker augments electronic coupling to the metal electrode and lowers the effective barrier for charge transport relative to the conventional thiol linker, thus enhancing the conductance of the linker-phenylene-ethynylene-linker unit; these data underscore that phenylene-ethynylene-based structures are more highly conductive than originally appreciated in molecular electronics applications. The theoretical analysis shows that the nature of sulfur hybridization in these species is responsible for the order-of-magnitude increased conductance in carbodithioate-terminated systems relative to identical conjugated structures that feature classic thiol linkers, independent of the mechanism of charge transport. Interestingly, in these systems, the tunneling current is not dominated by the frontier molecular orbitals. While barriers BT are expected to produce low β values, we show that the competition between tunneling and resonant transport processes allows barriers < k_BT to produce the low β values seen in our experiments. Taken together, these experimental and theoretical studies indicate a promising role for carbodithioate-based connectivity in molecular-scale electronics applications involving metallic and semiconducting electrodes.

Full text of DOI:10.1021/ja909559m

Published on Web 04/30/2010
Optimizing Single-Molecule Conductivity of Conjugated
Organic Oligomers with Carbodithioate Linkers
Yangjun Xing,† Tae-Hong Park,‡ Ravindra Venkatramani,§ Shahar Keinan,§
David N. Beratan,*,§,# Michael J. Therien,*,§ and Eric Borguet*,†
Department of Chemistry, Temple UniVersity, Philadelphia, PennsylVania 19122, Department of
Chemistry, UniVersity of PennsylVania, Philadelphia, PennsylVania 19104, Departments of Chemistry,
Biochemistry, and Physics, Duke UniVersity, Durham, North Carolina 27708, and Department of
Chemistry, French Family Science Center, Duke UniVersity, Durham, North Carolina 27708
Received November 16, 2009; E-mail: eborguet@temple.edu; michael.therien@duke.edu;
david.beratan@duke.edu
Abstract: In molecular electronics, the linker group, which attaches the functional molecular core to the
electrode, plays a crucial role in determining the overall conductivity of the molecular junction. While much
focus has been placed on optimizing molecular core conductivity, there have been relatively few attempts
at designing optimal linker groups to metallic or semiconducting electrodes. The vast majority of molecular
electronic studies use thiol linker groups; work probing alternative amine linker systems has only recently
been explored. Here, we probe single-molecule conductances in phenylene-ethynylene molecules
terminated with thiol and carbodithioate linkers, experimentally using STM break-junction methods and
theoretically using a nonequilibrium Green’s function approach. Experimental studies demonstrate that the
carbodithioate linker augments electronic coupling to the metal electrode and lowers the effective barrier
for charge transport relative to the conventional thiol linker, thus enhancing the conductance of the
linker-phenylene-ethynylene-linker unit; these data underscore that phenylene-ethynylene-based structures
are more highly conductive than originally appreciated in molecular electronics applications. The theoretical
analysis shows that the nature of sulfur hybridization in these species is responsible for the order-of-magnitude
increased conductance in carbodithioate-terminated systems relative to identical conjugated structures that feature
classic thiol linkers, independent of the mechanism of charge transport. Interestingly, in these systems, the
tunneling current is not dominated by the frontier molecular orbitals. While barriers <kBT are expected to produce
low ꢀ values, we show that the competition between tunneling and resonant transport processes allows barriers
.kBT to produce the low ꢀ values seen in our experiments. Taken together, these experimental and theoretical
studies indicate a promising role for carbodithioate-based connectivity in molecular-scale electronics applications
involving metallic and semiconducting electrodes.
Introduction
the field of molecular electronics and most recently a real molecule-
based memory device has even been fabricated.19
The development of molecular connects to metallic and semi-
conducting electrodes that possess controllable properties is a major
milestone in the molecular electronics roadmap.1-4 Recent years
have seen great theoretical5-10 and experimental11-18 progress in
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† Temple University.
‡ University of Pennsylvania.
§ Department of Chemistry, Duke University.
# Department of Biochemistry and Physics, Duke University.
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7946 J. AM. CHEM. SOC. 2010, 132, 7946–7956
10.1021/ja909559m  2010 American Chemical Society

Optimizing Single-Molecule Conductivity
A R T I C L E S
A key challenge in developing functional molecular connects
is to build a nanoscale electrode-molecule-electrode system
that can be probed experimentally in a repeated and controlled
fashion. At least one of the electrodes should be of nanoscale
dimensions to ensure that one molecule (or at most a few
molecules) is trapped between electrodes and probed. Research-
ers have created a number of methods to make nanoelectrodes,
including electro-migrated junctions,20,21 mechanical break-
junctions,17 mixed self-assembled monolayers (SAMs),11 and
scanning tunneling microscopy (STM) break-junctions.18,22
Since nanoscale molecular conductance is affected by many factors,
including the conformation of the molecules, the angle of linker-
electrode bonds, and the environment,23-26 individual measure-
ments may therefore fluctuate by orders of magnitude,14,24,27
underscoring the importance of repetitive measurements to
provide statistically significant results. The STM break-junction
method,18 one of the most widely used techniques for measuring
single-molecule conductivity, is designed to create, repeatedly
and rapidly, nanoscale electrode-molecule-electrode systems
so that thousands of experiments can be conducted in a few
hours or less.18,22,28-34 A closely related challenge presented
by single-molecule conductance data is to determine the relative
influence of the molecular “core” and the molecular “intercon-
nects” on observed currents; such analyses are necessary to
elucidate important structure-function relationships necessary
to design molecular electronic elements having the desired
functionality.
tunneling regime where molecular junctions usually operate,26,35,40
the junction resistance (R) increases approximately exponentially
with molecular length L: R ) R0exp(ꢀL). Here R0 is an effective
contact resistance and ꢀ is a constant, which depends on the
structure of the molecular backbone. An approximately expo-
nential decay of conductance with bridge length best describes
the bridge mediated tunneling (superexchange) in donor-bridge-
acceptor (D-B-A) systems where the donor/acceptor energies
are off resonance with the bridge. While single-step tunneling
is mediated by eigenstates of the bridging molecule, these states
are populated only virtually, and the tunneling rate decays
exponentially with the bridge length. On the other hand, when
donor/acceptor energy levels are resonant with those of the
bridge, electrons (or holes) are injected into the states of the
bridging molecule, and charge transfer (CT) from D to A takes
place via populated bridge states. In this case, the donor-acceptor
distance dependence of the charge transfer rate constant is very
soft. Thus, small values of ꢀ are consistent with transport via
carrier injection. It should be emphasized that the parameter ꢀ
described above, and used throughout this paper, is a decay
constant for transmission across a barrier extracted from fitting
an exponential to experimental (or computed) resistance values.
It is not the same as the superexchange decay constant, which
we denote ꢀSE. The latter is defined only in the pure superex-
change limit and holds no meaning when carriers populate the
bridge states. Thus ꢀ ) ꢀSE only in the pure superexchange
limit.
π-Symmetry backbones present lower tunneling barriers than
σ-bonded systems, thus π-conjugated molecules have been
found to have much smaller ꢀ values than saturated ones. Many
groups have therefore focused on developing molecular cores
with π-conjugated building blocks to obtain ꢀ values in the range
of 0.2-0.6 Å-1.26,35,40 Recently, single-molecule junctions with
highly conjugated, low band gap oligomers have shown efficient
long-range charge transport with very small ꢀ values (e0.2
Å-1);13,31,41-43 for example, butadiyne-bridged porphyrin oli-
gomers have ꢀ of 0.04 Å-1, suggesting that resonant mechanisms
may be operative.41 Notably, Choi et al. found that the
systematic molecular length increase of the conjugated phenyl-
ene-imine oligomer core produced a transition from tunneling
to resonant transport.37 The nature of π-conjugation, the
magnitude of the band gap, and molecular length play important
roles in controlling transport mechanisms.
The choice of the linker connecting the molecular core to
the electrodes is equally crucial in determining transport
characteristics. A linker can shift the core states close to the
metal Fermi energy, thus lowering the tunneling barrier. In
addition, linkers can also decrease the contact resistance, so that
the intrinsic conductance of the molecular core dominates the
m-M-m response. Recent STM break-junction studies44-46
of alkane chain conductance varying both the electrode material
(Au, Pd, Pt) as well as the terminal linker group (dithiol,
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junctions has been investigated by measuring conductance (or
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A R T I C L E S
Xing et al.
diisothiocyanates) highlight the effect of linker-electrode
contact resistance on conductance. While the junctions with Pt
electrodes showed ∼3.5 times higher conductance compared
to conventional Au electrodes, the dithiol-terminated systems
showed roughly an order of magnitude higher conductances
relative to the diisothiocyanate-terminated systems.44 The high
affinity of thiolated compounds for gold surfaces, and their
synthetic flexibility, have led to their widespread use as linkers
to interconnect molecules with electrodes.26 However, gold-thiol
contacts appear to produce only modest interfacial interactions
between the molecule and the gold due to weak chemical
interactions at the contact.26,47,48 Hence, the quest for contacts
that provide enhanced electronic coupling has become a
principal interest in molecular electronics. Molecular conduc-
tance studies that probe junctions other than thiol-gold have
been reported.18,23,28,47-56 While the measured conductance of
molecules with amine linker groups has less variability than
molecules with thiol linkers,28 the conductance of the amine-
terminated molecules is smaller than that determined for
analogous compounds that feature thiol linkers, possibly a result
of the weaker binding of amines to gold.28,52 Tivanski et al.,
however have shown that carbodithioate linkers increase single-
molecule conductance through a biphenyl moiety by a factor
of 1.4 relative to that provided by thiols.57 Despite the appeal
of the carbodithioate linkers, no further conductance measure-
ments with carbodithioate-functionalized molecules have been
reported.
free thiols from oxidizing to disulfides. Similar to the acetyl
protection of thiols, (trimethylsilyl)ethyl (TMSE) protection
makes possible the synthesis of carbodithioate-terminated OPEs
via Sonogashira cross-coupling reactions; in situ deprotection
enables functionalization of gold nanoparticle surfaces.65 Thus,
it is possible to compare the conductance of m-M-m junctions
featuring OPE molecules having both thiol- and carbodithioate-
termini.
In a recent study, the conductance of OPE molecular wires
of different lengths terminated with amine linkers was explored
using STM break junction and CP-AFM measurements.66 The
authors demonstrated a tunneling (ꢀ ≈ 0.2 Å-1) to hopping
transition (ꢀ ≈ 0.03 Å-1) for OPE molecules at slightly longer
lengths than considered in this work (Vide infra). The present
work interrogates the extent to which conductance is augmented
through OPE molecules terminated with carbodithioate linkers
relative to identical structures that are terminated with dithiol
linkers. A surprising result is that carbodithioate-terminated OPE
molecules show small ꢀ (∼0.05 Å-1) values, even for modest
molecular length scales. Whether this value is maintained or
lowered further upon increasing the molecular length will be a
focus of future studies. The theoretical analysis66 of the amine-
terminated OPE conductance data, which did not take the full
electronic structure of the molecule into account, estimates a
barrier for charge injection which can be correlated with the
energies of the frontier orbitals (HOMO/LUMO). We employ
a more detailed model (Vide infra) that fully takes into account
molecular electronic structure. This approach allows us to
distinguish between hole (filled molecular orbitals)- or electron
(empty molecular orbital)-mediated charge transport. Further-
more, we show that the barrier for charge transport cannot, in
general, be determined from the knowledge of the molecular
frontier orbitals energies (or their separation from the Fermi
level) alone. It is essential to analyze whether the coupling
between the frontier orbitals and the electrode is sufficiently
strong that significant charge transport is mediated by these
MOs.
Over the past decade, nonequilibrium Green’s function
(NEGF) methods have become particularly useful in molecule-
mediated transport studies.10,67-72 The NEGF formalism for
charge transport,67 combined with ab initio density functional
theory (DFT) for electronic-structure calculations, forms the self-
consistent DFT-NEGF approach to compute the coherent
transport properties for modeled m-M-m systems.68,69 For
example, Sankey and Tomfohr calculated molecular conduc-
tances in agreement with experiments for a number of organic
molecules.10 This approach was extended to analyze inelastic
transport,70 and applied to conjugated oligo(phenylenevinylene)s
(OPVs), OPEs, and alkane bridges connected by thiol linkers
to gold electrodes.71 The influence of conformational sampling
on transport was recently investigated using NEGF calculations
Highly conjugated oligo(phenylene-ethynylene)s (OPEs)
have been key structures in molecular electronics.14,58-64 Most
OPE-based molecular junctions have featured thiol linkers and
have been assembled in m-M-m junctions by removing an
acetyl protecting group, thus enabling the synthesis of π-con-
jugated oligomers via cross-coupling reactions and preventing
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Optimizing Single-Molecule Conductivity
A R T I C L E S
on benzenedithiol, benzenediamine and biphenyldithiol72-75 In
the biphenyldithiol studies, DFT-NEGF calculations were
performed on three molecule-electrode geometries extracted
from MD simulations.73-75 In the benzenedithiol and benzene-
diamine studies, conductance calculations on hundreds of
molecule-electrode geometries, and four different electrode
separation distances were performed using a Hu¨ckel Hamilto-
nian.72
Chart 1. Structure of R,ω-Dithiol-Terminated (T1, T2, and T3) and
R,ω-Bis-carbodithioate-Terminated π-Conjugated Molecules (C1,
C2, and C3)
The self-consistent DFT-NEGF approach calculates the
interaction between metal electrodes and the molecule from first
principles. Each electrode is usually modeled as a finite set of
less than 50 lattice atoms. There are some issues regarding the
application of these methods to m-M-m systems, most of them
arising from the choice of the exchange correlational functional
(XCF).76-81 Compounding the standard limitations of DFT,
describing nonequilibrium processes with an equilibrium XCF
can lead to an overestimate of currents in molecules that weakly
couple to electrodes (see Supporting Information, SI). Li and
Kosov47 studied the enhancement of molecular conductance
through a biphenyl core structure when carbodithioate functional
groups were used in place of thiols. They used the DFT-NEGF
approach in the strong molecule-electrode coupling limit. Strong
coupling modifies the molecular eigenstates/eigenenergies and
strongly mixes molecule and electrode eigenstates. This ap-
proach is implemented in their analysis by considering an
extended molecule, i.e. including Au atoms at the interface as
part of the molecule.
weakly. The eigenstates do not lose either their symmetry or
their qualitative charge distribution characteristics compared to
the isolated molecule. As described below, our model param-
etrizes the conductance calculations so that we can analyze the
dependence of the absolute and relative conductance, contact
resistance, and distance-dependent conductance decay on the
relative location of the metal Fermi energy with respect to the
molecular eigenstate energies and the electrode-molecule
coupling. Moreover, in the weak coupling limit, the conductance
can be analyzed in terms of the isolated molecule properties.
Insights gained regarding molecular contributions are indepen-
dent of the electrode type and are transferable to other weak
coupling m-M-m systems.
We have experimentally measured the conductance of thiol
and carbodithioate-terminated OPEs using STM break-junctions,
and investigated the length dependence of the molecular
conductance with thiol and carbodithioate linkers. We also
performed nonequilibrium Green’s function calculations to
evaluate the effect of the linker on charge transport. Experi-
mental results show that the carbodithioate linkers not only
increase the molecular conductance compared to their thiol
counterparts (except for the shortest C1 (Chart 1) molecule)
but also provide a quasi-linear length dependence of conductivity
for the OPE molecular wires. Our theoretical analysis dissects
the contributions of individual molecular orbitals to the con-
ductivity and shows that the carbodithioate linkers facilitate
electronic coupling between the OPE molecules and the
electrodes as well as provide lower contact resistance compared
to the thiol linkers.
However, it is not clear that the gold-thiol linker coupling
is in fact strong. Rather, it was proposed that the thiol-Au
interactions are structural rather than chemical, suggesting that
there is negligible charge transfer between the thiol and the
gold.48 As such, interactions with the electrodes are unlikely to
significantly modify the energy and electron occupation of sulfur
3p orbitals.48 This was also noted by Li and Kosov.47
A
comprehensive DFT study82,83 of alkane, aromatic, and alkyne
molecules attached by thiol linkers to Au clusters showed (for
neutral systems): (a) negligible charge transfer between sulfur
and gold atoms, and (b) weak mixing of the molecule-metal
states. Thus, while we cannot eliminate the possibility of strong
electrode-molecule couplings in these systems, it is reasonable
to explore the conductivity of the OPE systems in the weak
electrode-molecule coupling regime.84 In this limit, the influ-
ence of the electrode is to broaden the molecular eigenstates
Experimental Section
Materials. 1,4-Benzenedithiol (T1) was purchased from Alfa
Aesar and used as received. The synthesis and characterization of
2-(trimetylsilyl)ethyl ester derivative of C1 are found in the SI.
The acetyl-protected versions of dithiol T2 and T362,85 and the
TMSE esters of C2 and C365 were synthesized according to
literature procedures.
Self-Assembled Monolayer (SAM) Preparation. A gold bead
was prepared using Clavilier’s method86 and cleaned by piranha
solution (H2SO4/H2O2 ) 3:1) and hydrogen flame annealed in air.
(Caution! Piranha solution is a very strong oxidizing reagent
and can be dangerous to handle. Protective equipment including
gloves and goggles should be used at all times.) After cooling,
the gold bead was immersed into a THF solution containing 100
µM of the target molecule (Chart 1) for 15-30 min to prepare a
self-assembled monolayer (SAM). The adsorbate solutions were
prepared by deprotection of the precursor molecules (SI) and used
immediately. The sample was rinsed by THF and dried under a
(73) Jang, S. S.; Jang, Y. H.; Kim, Y. H.; Goddard, W. A.; Choi, J. W.;
Heath, J. R.; Laursen, B. W.; Flood, A. H.; Stoddart, J. F.; Norgaard,
K.; Bjornholm, T. J. Am. Chem. Soc. 2005, 127, 14804–14816.
(74) Jang, S. S.; Jang, Y. H.; Kim, Y. H.; Goddard, W. A.; Flood, A. H.;
Laursen, B. W.; Tseng, H. R.; Stoddart, J. F.; Jeppesen, J. O.; Choi,
J. W.; Steuerman, D. W.; DeIonno, E.; Heath, J. R. J. Am. Chem.
Soc. 2005, 127, 1563–1575.
(75) Kim, Y. H.; Jang, S. S.; Goddard, W. A. J. Chem. Phys. 2005, 122,
244703.
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(78) Ke, S. H.; Baranger, H. U.; Yang, W. T. J. Chem. Phys. 2007, 126,
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Picconatto, C. A.; Ellenbogen, J. C.; Shashidhar, R. Ann. N.Y. Acad.
Sci. 2003, 1006, 235-251.
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Tetrahedron Lett. 1995, 36, 4525–4528.
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1980, 107, 205–209.
9
J. AM. CHEM. SOC. VOL. 132, NO. 23, 2010 7949

A R T I C L E S
Xing et al.
1
G(E) )
(1)
(EI - H - ΣL - ΣR)
H is the Hamiltonian and I is the identity matrix of the isolated
molecule. The self-energies Σ describe the broadening and shifts
in molecular energies induced by the right (R) and left (L)
electrodes. The transmission coefficient sums over all pathways for
charge transport at energy E from one electrode to the other:
Figure 1. Schematic for the separation of the electrode-molecule-electrode
system for NEGF calculations into the three subsystems: The device region
(center) with the molecule and thiol/carbodithioate and linkers (shown are
T2 and C2 from Chart 1); and the left and right featureless electrodes
(contacts) characterized purely in terms of the chemical potentials µL/µR.
εF is the Fermi energy, q is the electron charge and V is the applied potential
bias which is assumed to drop symmetrically across the two electrodes.
Note that the electronic structural calculations considered uncharged OPE
molecules.
T(E) ) Tr[ΓLGΓRG+]
(2)
The broadening matrix: Γ ) i [Σ - Σ+] is proportional to the
imaginary part of the self-energy. In conventional DFT-NEGF
schemes, the broadening matrices and Green’s functions are
computed for an explicit m-M-m system.10,47,68 Since we work
in the weak-electrode molecule coupling limit, we use the broaden-
ing matrix as a parameter represented in our calculations in the
basis of atomic orbitals. The molecule is assumed to contact the
metal electrodes only via the sulfur atoms, i.e. only orbitals of
the sulfur atoms are broadened, and the couplings among atomic
orbitals are not affected by the contacts. The elements of the
broadening matrix, are:
nitrogen stream, then put into the liquid cell of a PicoPlus Scanning
Probe Microscope (Molecular Imaging, Tempe, AZ) system and
covered with toluene.
Conductivity Measurements. A fresh cut gold tip (0.25 mm,
99.999%, Alfa Aesar) was used to image a SAM-covered gold bead
surface immersed in toluene; the quality of the tip was judged by
the ability to resolve gold atomic steps in STM images. The tip
was then brought into contact with the surface and withdrawn at a
rate of ∼20 nm/s, while measuring current. This process was
repeated thousands of times and a current-distance curve was
recorded each time. When a molecule bridges the tip-substrate
gap, the current shows step-like features instead of a simple
exponential decay. Statistical analysis of the curves showing
quantized conductance peaks reflects the conductance of single
molecules.
Theoretical Methods. We calculated conductances for the thiol-
and carbodithioate-terminated OPE structures, using nonequilibrium
Green’s function (NEGF) methods67 on DFT-optimized structures.
As opposed to the conventional DFT-NEGF methods, which include
parts of the electrode in the DFT calculation, we worked in the
weak coupling limit, using DFT to calculate the geometry of the
isolated molecule (core plus linker) and used molecular orbital
information (as calculated using INDO/s) as input to NEGF
calculations. The effect of the electrodes is described with a
molecule-electrode coupling parameter that broadens the density
of states of the isolated molecule. Charge is injected into the
molecule at the electrode Fermi energy.
Γii
Γii
Γij
) γ for all sulfur atoms atomic orbitals
) 0 otherwise
) 0 for i * j
(3)
Here, i and j are atomic orbital indices and γ is the sulfur-gold
coupling parameter. The real parts of the self-energies are assumed
to be small compared to the energy separation of the sulfur atomic
orbitals (diagonal elements of the Fock matrix) from all other
molecular orbitals. The magnitude of the sulfur-gold coupling (γ)
was chosen to be small (relative to the separation among diagonal
elements of the Fock matrix). The transmission coefficient (or
current) can be partitioned into contributions from individual
molecular orbitals. The Green’s function in the basis of molecular
eigenstates is:
1
G(E) )
;
i
EI - Hꢀ + (Γ′ + ΓR′ )
L
[
]
2
1. Electronic Structure Calculations. Three carbodithioate-
terminated systems (CTS) and three dithiol-terminated systems
(DTS; Chart 1) were built, and the geometry was optimized using
DFT and a B3LYP exchange correlation functional with a 6-31G*
basis set, in Gaussian 03.87 The electronic structure of these
geometry optimized structures was calculated using an INDO/s
Hamiltonian88 as implemented in the CNDO code,89 and the
molecular orbitals were used as input to the NEGF analysis of
transport properties. The semiempirical INDO/s approach provides
a useful balance between cost and performance.88,90,91 Specifically,
for this investigation, we find the character of MOs and trends in
their relative energies within each molecule and across different
molecules to be the same qualitatively for INDO/s and DFT
calculations, as shown Figure S3 (SI).
Hꢀ ) U+HU;Γ′L/R ) U+ΓL/RU (4)
U diagonalizes the Fock matrix H. The current is given by the
Landauer expression:
q
h
I(V) )
T(E)[f (E) - f (E)]dE
(5)
∫
L
R
The Fermi function defines the electron occupancy for each
electrode:
1
fL/R(E) )
(6)
2. NEGF Calculations. In the NEGF approach67 the electrode-
molecule-electrode system is partitioned into three subsystems
(Figure 1): a device region (the isolated molecule) and two
structureless electrodes. The Green’s function describes the mol-
ecule and its interactions with the electrodes:
1 + exp[(E - µL/R)/kBT]
Here µL/R are the chemical potentials of the left/right electrodes:
µL ) EF + qV/2; µR ) EF - qV/2 (7)
The Fermi energy EF is the same for both electrodes if they are
made of the same metal, and V is an external potential bias (taken
in the range of 0-100 mV in the calculations here). The potential
drop is assumed to be symmetric across the electrodes. The small
biases applied here are not expected to cause significant changes
in molecular geometry or energies, and no potential drop is assumed
across the molecule. Our calculations are expected to capture
(87) Frisch, M. J.; et al. Gaussian 03, Revision D.02; Gaussian Inc:
Wallingford, CT, 2004.
(88) Ridley, J.; Zerner, M. Theor. Chim. Acta 1973, 32, 111–134.
(89) Zeng, J.; Hush, N. S.; Reimers, J. R. J. Am. Chem. Soc. 1996, 118,
2059–2068.
(90) Hutchison, G. R.; Ratner, M. A.; Marks, T. J. J. Phys. Chem. A 2002,
106, 10596–10605.
(91) Voityuk, A. A. Chem. Phys. Lett. 2006, 427, 177–180.
9
7950 J. AM. CHEM. SOC. VOL. 132, NO. 23, 2010

Optimizing Single-Molecule Conductivity
A R T I C L E S
Figure 3. Natural logarithmic plot of the resistance of dithiols (T1-T3)
and carbodithioates (C1-C3) versus molecular length. The ꢀ values are
calculated through the semilogarithmic plot of resistance and molecule length
based on R ) R0 exp(ꢀL).
has been proposed10,96 that this variation in conductance arises
due to multiple contact configurations of the benzedithiol
molecule with the electrodes. A careful reanalysis of break
junction experimental data was performed on alkanethiol
systems of varying length to reveal a second series of current
peaks corresponding to a lower conductance value.96 On the
basis of simulation studies10 the observed variation in conduc-
tance was attributed to two different contact configurations of
the sulfur atom with the gold surface; data obtained from
additional simulations showed further that this effect diminishes
with molecular length.
Comparing the conductances measured for C2-C3 and
T2-T3, it is clear that the carbodithioate linker improves the
conductance of OPE molecules by over an order of magnitude
and highlights the importance of optimizing the molecule-
electrode junction to enhance molecular conductivity and access
the intrinsic core conductivity. The order of magnitude improve-
ment in the conductivity of OPEs observed by changing to the
molecular termini from thiol to carbodithioate is significantly
greater than the 1.4-fold conductance enhancement observed
in experiments involving biphenyl junctions.57
Figure 2. (a) Scheme for single-molecule (C3) conductance measurements.
(b) Example of current-distance curves recorded with C3 in the junction
at 50 mV bias. (c) Histogram analysis of C3 conductance constructed from
∼150 I-S curves. (d) Conductance of C3 is determined by fitting the
measurements at different bias values.
Table 1. Conductance Measurement of T1-T3 and C1-C3
conductance/G0a
conductance/nS
resistance/MΩ
T1
T2
T3
C1
C2
C3
8.3 ((0.7) × 10-3
2.6 ((0.4) × 10-4
1.3 ((0.3) × 10-4
4.8 ((0.5) × 10-3
3.2 ((1.1) × 10-3
2.5 ((0.3) × 10-3
639 ( 54
20 ( 3
1.6 ( 0.13
50 ( 7.6
100 ( 25
2.7 ( 0.3
4.1 ( 0.9
5.2 ( 0.6
10 ( 2
367 ( 39
246 ( 54
193 ( 23
a G0 ) 2e2/h ) 77 µS ) 13 kΩ.
relative trends, and we analyze the relationship between molecular
structure and conductance trends for CTS and DTS.
Results and Discussion
1. Molecular Conductance Measurements. The single-
molecule conductance of π-conjugated organic molecules with
thiol or carbodithioate linkers (Chart 1) was measured via the
STMbreak-junctionmethod18 (Figure2a).Typicalcurrent-distance
curves, showing clear conductance steps, are shown for C3 in
Figure 2b. The histogram analysis (Figure 2c) shows well-
defined peaks in which the magnitude of the second current
peak is about twice that of the first. This suggests that the first
current peak corresponds to single-molecule junctions, while
the second peak corresponds to the junction formed from pairs
of molecules.18 The conductances for all six systems in Chart
1 were obtained by linear fitting of the current peaks acquired
at multiple biases and are listed in Table 1. Out of the six
molecules studied here, two (T1 and T3) have been studied
previously using the STM break-junction method by Tao and
co-workers. Our conductance values for T1 and T3 are
comparable to those obtained previously (T1, 833 ( 90 nS;92
T3, ∼13 nS).64
The ꢀ value determined from the length dependence of
T1-T3 resistances is 0.32 ( 0.10 Å-1 (blue dashed line, Figure
3). The data, however, deviate significantly from the fitting line,
because of the atypical behavior of T1. We exclude the
conductance of T1 from further analysis due to the uncertainties
in measuring the conductances of short molecules such as T1
using break-junction methods (vide supra). Omitting the T1
resistance in this analysis suggests ꢀ ) 0.11 ( 0.06 Å-1 (black
line, Figure 3), a value much lower than the theoretical estimate
of 0.27 Å-1 determined for dithiol OPE wires,10 and rather close
to tunneling decay constants measured for other R,ω-dithiol-
terminated π-conjugated molecules using the STM break-
junction methods.29,31,42
Carbodithioate-terminated C1-C3, on the other hand, show
a ꢀ of 0.05 ( 0.01 Å-1 (green line, Figure 3), a value lower
than their dithiol analogues and other dithiol π-conjugated
oligomers.29,31,42 A comparably low ꢀ value derived from single-
molecule conductance measurements has only been realized with
dithiol-terminated butadiyne-bridged porphyrin oligomers (ꢀ )
0.04 ( 0.006 Å-1).41 In these systems, the extension of
π-conjugation reduces the gap between the donor and the bridge
states (in butadiyne-bridged D-B-A systems) or between the
electrode Fermi level and the bridge states (in these m-M-m
junctions). In Figure S3 (SI), we report the calculated
Table 1 shows that with the exception of benzene-based C1
and T1, the carbodithioate linker enhances the conductance of
OPE molecules by an order of magnitude relative to corre-
sponding phenylene-ethynylenes that possess thiol linkers.
The conductance of benzenedithiol (T1) does not follow the
decay trend of T2 and T3 (Figure 3) and is roughly two times
higher than C1. The T1 system has proved notoriously difficult
to characterize using break junction experiments, exhibiting a
wide range of conductance values (0.01G0-0.1G0).16,92-95 It
(94) Ghosh, S.; Halimun, H.; Mahapatro, A. K.; Choi, J.; Lodha, S.; Janes,
D. Appl. Phys. Lett. 2005, 87, 233509/1–233509/3.
(95) Tsutsui, M.; Teramae, Y.; Kurokawa, S.; Sakai, A. Appl. Phys. Lett.
2006, 89, 163111/1–163111/3.
(96) He, J.; Sankey, O.; Lee, M.; Tao, N. J.; Li, X. L.; Lindsay, S. Faraday
Discuss. 2006, 131, 145–154.
(92) Xiao, X. Y.; Xu, B. Q.; Tao, N. J. Nano Lett. 2004, 4, 267–271.
(93) Ulrich, J.; Esrail, D.; Pontius, W.; Venkataraman, L.; Millar, D.;
Doerrer, L. H. J. Phys. Chem. B 2006, 110, 2462–2466.
9
J. AM. CHEM. SOC. VOL. 132, NO. 23, 2010 7951

A R T I C L E S
Xing et al.
Table 2. Calculated Resistance Values for Tunneling Currents in
HOMO-LUMO gaps for both the C1-C3 and T1-T3 systems,
calculated using DFT as well as INDO/s methods. The computed
CTS HOMO-LUMO gaps are lower than those evinced for
DTS, for identical phenylene-ethynylene cores.65 However, the
CTS HOMO-LUMO gaps are also much larger than those
previously reported for the butadiyne-bridged porphyrin oligo-
mers (1.8-2.1 eV); thus, in order for the CTS to exhibit a low
ꢀ value comparable to that determined for butadiyne-bridged
porphyrin oligomers in m-M-m junctions, the carbodithioate-
mediated coupling strength between the contacts and the bridge
states must exceed that for thiol-mediated coupling. These results
thus show the critical importance of the nature of the molecule-
to-metal contact upon bridge electronic structure, and suggest
that the OPE core is much more conductive than previously
thought.
2. Calculations of Molecular Conductances. The computa-
tions described above were performed to explore the origins of
improved conductance in CTS and its weaker dependence on
OPE length relative to the analogous thiol-terminated systems.
In the following sections, we first analyze the conductance of
CTS and DTS in the limits of both deep tunneling and resonant
transport regimes. Connections to the experimental results are
then made in calculations which do not a priori assume any
particular transport mechanism.
CT and DT Systemsa
system
R (MΩ)
system
R (MΩ)
C1
C2
C3
3.2613 × 103
3.7858 × 104
9.8815 × 105
T1
T2
T3
2.8474 × 104
5.6488 × 105
1.04 × 107
a EF ) -5.1 eV and γ ) 0.1 eV.
current-voltage curves. Table 2 shows that the calculated
resistances for DTS are about an order of magnitude larger than
for CTS. The computed ꢀ values are comparable for both
systems (0.42 Å-1 for CTS and 0.43 Å-1 for DTS), while the
evaluated contact resistance, R0, for CTS (C1-C3, 1.94 MΩ)
is nearly an order of magnitude smaller than that for DTS (T2
and T3, 12.02 MΩ), providing evidence that improving the
coupling at the contacts enhances the conductivity of CTS
relative to the corresponding DTS.
Figure 4 plots the scoring factor as a function of MO energy.
While the barrier for hole injection is lower than that for electron
injection in both systems, the electron current through empty
states cannot be disregarded (relative to the hole current) for
CTS. Both contribute comparably in CTS while hole transport
dominates for DTS. Visualization of MO contributions (parts
A and B Figure 5) show that the strongest contribution to the
current comes from delocalized MOs with large amplitudes on
the terminal sulfurs (not necessarily the HOMO or LUMO).
For these molecules, the frontier orbitals need not dominate the
conductance. Further, even if the frontier orbitals couple strongly
to the electrodes, they may have low scoring factors because
contact-induced couplings to neighboring orbitals with phase
opposite to those of the frontier orbitals can lead to destructive
interferences. In eq 8c the pure contributions for an orbital (m
) n) can cancel with a cross term (m * n) if orbitals m and n
are energetically close and have opposite phases. As an example,
Figure 5C shows two neighboring high-lying filled C1 orbitals
(HOMO-2 and HOMO-1), which are strongly coupled to the
electrodes as seen from the large amplitudes on the terminal
sulfurs. This MO pair has nearly equal energy. Yet, one MO
has terminal group amplitudes of the same sign; the other MO
has terminal group amplitudes of opposite sign. Thus, these two
nearly degenerate MOs interfere destructively (see eq 8c),
leading to nearly canceling scoring factors highlighted in Figure
4. To see this more clearly, consider the three leading terms in
the scoring factor (eq 8c) for the C1 HOMO-1:
2.1. Tunneling Currents. In the tunneling regime, the elec-
trode Fermi level lies in the gap between filled and empty
molecular orbitals. The Fermi level is far enough (energetically)
from the HOMO or LUMO that the dominat contribution to
the current (eq 5) arises from transmission near the Fermi
energy. The tunneling current is given by:
q2V
h
I
Tun(V) )
× T(E ) E )
(8a)
(
)
F
with
and
T(E ) E ) )
SFTun
(8b)
∑
F
m
m
ΓLmnΓRnm
SF )
(8c)
∑
m
(EF - Em)(EF - En)
n
where n and m are MO indices and the sums run over all MOs.
Here, the transmission coefficient in eq 2 (and the current) were
decomposed into contributions from specific molecular orbitals
m given by the scoring factor SFm. Equation 8c uses EF - Em
+ 0.5i(ΓLmm + ΓmRm) ≈ EF - Em. When m ) n, the score
represents a pure contribution from orbital m with broadening
matrix elements ΓLmm and ΓmRm, which are positive in nature.
When m * n, the score represents a contribution arising from
the electrode induced coupling of orbital m to orbital n. These
contributions can be positive or negative, depending on the sign
of the broadening matrix elements. We assumed EF ) -5.1 eV
(typical for Au) and a sulfur-gold coupling parameter γ ) 0.1
(eq 3) for all six systems (C1-C3 and T1-T3). While γ is the
same for sulfur atomic orbitals in all systems (CTS and DTS),
the differences in mixing of each molecule’s sulfur atomic
orbitals with the molecular core leads to completely different
couplings between the molecule and the electrodes. The
computed current-voltage curves are linear over the range of
the applied bias (0-100 mV). The conductance (or resistance)
for each system was computed from the slope of the
ΓLHOMO-1,HOMOΓHROMO, HOMO-1
SFHOMO-1
)
+
(EF - EHOMO-1)(EF - EHOMO
ΓLHOMO-1,HOMO-1ΓHROMO-1,HOMO-1
)
+
2
(EF - EHOMO-1
)
ΓLHOMO-1,HOMO-2ΓHROMO-2,HOMO-1
(EF - EHOMO-1)(EF - EHOMO-2
)
The denominators of all three terms are virtually identical,
since energetic differences between the HOMO, HOMO-1, and
HOMO-2 are negligible compared to their separation from the
Fermi level (see Figure 4A). The magnitude and sign of the
three terms are then decided by the numerator ΓLmn and ΓRmn terms,
which represent the coupling of orbital m with orbital n induced
by their mutual coupling to the left and right contacts,
respectively; these are directly proportional to the product of
MO amplitudes on the terminal sulfurs. Since the C1 HOMO-1
9
7952 J. AM. CHEM. SOC. VOL. 132, NO. 23, 2010

Optimizing Single-Molecule Conductivity
A R T I C L E S
Figure 4. Plots of the scoring factors (eq 8a) for each molecular orbital vs MO energies in the tunneling transport limit wherein the Fermi level is located
deep in the HOMO-LUMO gap. The Fermi level and MO energies are plotted with respect to a common vacuum level (Evac ) 0 eV). The value chosen
for the Fermi level energy matches reported values of the gold workfunction (5.1 eV) from the literature. (A) CTS and (B) DTS. For both CT and DT
systems, the orbitals with the strongest contributions are labeled. These orbitals are also visually depicted in A and B of Figure 5.
and HOMO-2 orbitals have much larger amplitudes on the
terminal sulfurs (Figure 5) than on the C1 HOMO, the second
and third terms give the strongest contributions. Further, from
Figure 5C, we can infer that the product of MO amplitudes on
the terminal sulfurs for the HOMO and HOMO-1 would lead
to nearly equal magnitudes but opposite signs for the second
and third terms. Thus, a cancellation of the dominant contribu-
tions leads to a weak scoring factor for HOMO-1. Parts A and
B of Figure 5 show MOs giving the strongest conductance
contributions for CTS and DTS respectively. Contact-induced
couplings (cross terms in eq 8a) further enable these orbitals to
boost the contribution of energetically close neighboring orbitals
(via constructive interference), which are more weakly coupled
to the electrodes.
Figure 4 shows that the contribution of the HOMO to the
tunneling current in CTS is much larger than in DTS, despite
the higher barrier for hole injection in CTS. Since the contribu-
tion to the tunneling current from a single MO with energy E
is proportional to ΓLΓR/ [EF - E]2, the broadening matrix
elements ΓL and ΓR for the CTS HOMO are bigger than those
for the analogous DT constructs. In contrast to thiol, the
carbodithioate unit is delocalized; for CTS, the combination of
π conjugation and an additional terminal sulfur, promotes a
π-mediated coupling pathway to the Au surface. The contribu-
tion of this π pathway to the current is much larger than that
which derives from a pathway involving a single thiol sulfur.
We have calculated tunneling currents in CTS for hypothetical
cases where the linkers are coupled to the contacts at either
end through both carbodithioate sulfurs by setting the coupling
of one of the terminal sulfurs on both sides to zero in eq 3.
Treating the carbodithioate moiety for the purpose of computa-
tion as a linker where one sulfur features a single bond to the
terminal carbon while the other features a full C-S double bond
(Table 3), shows that the smallest resistance path is mediated
by the double-bonded sulfurs. These data underscore the
importance of π conjugation in fixing the magnitude of
linker-electrode coupling. The couplings to the contacts through
double-bonded sulfurs (Figure S2 (SI), Table 3) at both ends
give currents that are 2 orders of magnitude larger than those
obtained by coupling through single-bonded sulfurs. Thus, the
calculated tunneling currents in CTS point to the importance
of augmented carbon-sulfur conjugation (Table 3) in the
enhancement of molecule-electrode coupling compared to
the dithiol OPE benchmarks.
2.2. Resonant Currents. In the resonant regime, the electrode
Fermi levels are resonant with molecular energies, and a ballistic
9
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A R T I C L E S
Xing et al.
Table 4. Resonant current (IRmes(m ) HOMO/LUMO) for V ) 100
mV) for CTS and DTS
Res
m)HOMO
Res
m)HOMO
system
I
(µA)
system
I
(µA)
C1
C2
C3
74
26
24
T1
T2
T3
37
4.1
0.7
Res
m)LUMO
Res
m)LUMO
system
I
(µA)
system
I
(µA)
C1
C2
C3
42
35
25
T1
T2
T3
2.4
0.1
23
MO and the electrodes. However, in the resonant regime, the
conductance depends only on the strength of the broadening
matrix elements (the energy line width over which the current
is integrated in eq 9). In our calculations, we find that
contributions from off resonant cross terms (n * m) are
negligible in the summation of the integrand in eq 9, and the
summation is always positive. This further simplifies the picture,
as the currents in eq 9 are the intrinsic contributions of orbital
m, free of any interference from other MOs. As the Fermi level
approaches resonance with the HOMO or LUMO, the orbital
nearest EF, will dominate ballistic transport (IRes ) ImResm )
Figure 5. (A) Filled and empty MOs that show the strongest contributions
(see Figure 4) to the current for CTS. (B) Filled MOs that show the strongest
contributions (see Figure 4) to the current for DTS. Empty MOs give
negligible contribution to the current for DTS and are not shown. (C) A
pair of energetically close MOs with strong coupling to the electrode and
with opposite phases whose contributions to the current destructively
interfere.
HOMO/LUMO). Table 4 shows the resonant current (IRes
)
IRmes for V ) 100 mV) for CTS and DTS. The data in Table 4
clearly indicate that the HOMO for CTS is more strongly
coupled to the electrodes than that for the corresponding DTS,
producing higher ballistic currents in the resonant regime.
Table 3. Resistance (in MΩ) for CT Systems with the Interaction
of One of the Terminal Sulfurs with the Electrodes Turned offa
system
C1
C2
C3
LS1:RS1
LS1:RS2
LS2:RS1
LS2:RS2
2.4819 × 105
3.7492 × 104
3.7473 × 104
4.0122 × 103
6.7417 × 106
5.4714 × 105
5.5459 × 105
4.4179 × 104
1.2994 × 108
1.3455 × 107
1.3252 × 107
1.1703 × 106
2.3. Mixed Mechanisms: Combinations of Tunneling and
Resonant Currents. The measured ꢀ value of 0.05 Å-1 suggests
an effective charge injection barrier height <kBT (kB is Boltz-
mann’s constant and T the temperature, 300 K) for the
carbodithioate-terminated OPEs, indicating that tunneling trans-
port likely competes with thermally activated carrier injec-
tion.37,41,97 Recent studies indicate that conformational fluctua-
tions can bias individual members of an ensemble toward one
mechanism or another.98,99 We show in this section that indeed
such a competition between transport mechanisms is at play in
our experiments. However, our analysis shows that very small
charge injection barriers <kBT are not a prerequisite to produce
the low ꢀ values seen in our experiments. Such small barriers
require small ꢀ values only in the limit where broadening of
the MO energies due to coupling to the electrodes is negligible.
For negligible broadening, the transmission function T(E) in
eq 5 would be sharply peaked at the MO energies. Resonant
contributions to the current from an MO are thus significant
only when the separation between the Fermi level and the MO
energies is within the line width (∼kBT) of the function fL(E)
- fR(E) in eq 5. On the other hand, when broadening of the
MO energies due to coupling with the electrodes is non-
negligible, the finite linewidths of the peaks in T(E) and the
thermal width of the difference function fL(E) - fR(E) in eq 5
tend to increase the range of separations between the Fermi level
and MO energies at which resonant transport become significant.
By calculating the combined tunneling plus ballistic transmission
using eqs 4 and 5, we show that the small ꢀ values observed
a In these computations, the carbodithioate moiety was treated as a
linker in which one sulfur features a single bond to the terminal carbon
(S1) while the other features a full C-S double bond (S2). L and R
represent right and left contacts to the electrodes. Thus LS1:RS2, for
example, represents a system where only the single bonded sulfur is
coupled to the left electrode and only the double bonded sulfur is
coupled to the right electrode.
current flows through the molecule. Intuitively, this current
should depend only on the contact resistance as defined by the
coupling strength of each MO to the electrodes. We can define
the resonant current through MO m using eq 5 and, in analogy
with eq 8a, as:
EHigh
q
h
IRmes
)
×
∫
∑
( )
ELow
n
ΓLmnΓRnm
×
i
2
i
2
E - Em + (ΓLmm + ΓRmm) E - En - (ΓLnn + ΓRnn)
[
][
]
[fL(E) - fR(E)]dE (9)
The integration extends over the line width ΓLmm + ΓmRm
associated with molecular orbital m with energy Em: ELow
)
Em - 0.5(ΓLmm + ΓRmm);EHigh ) Em + 0.5(ΓLmm + ΓmRm) and the
Fermi level is assumed to be resonant with the energy of the
orbital (EF ) Em). In this orbital approximation, virtual oxidized
or reduced states of the bridge are treated in an orbital
approximation, so virtual state lifetimes appear as orbital energy
linewidths. The sulfur-gold coupling parameter is γ ) 0.1 eV.
In the tunneling regime, the conductance mediated by an MO
depends on both the energy separation between the MO and
the Fermi level and the strength of the coupling between the
(97) Bixon, M.; Jortner, J. J. Chem. Phys. 1997, 107, 5154–5170.
(98) Berlin, Y. A.; Kurnikov, I. V.; Beratan, D.; Ratner, M. A.; Burin,
A. L. In Long-Range Charge Transfer in DNA II; Springer-Verlag
Berlin: Berlin, 2004; Vol. 237, pp 1-36.
(99) Hatcher, E.; Balaeff, A.; Keinan, S.; Venkatramani, R.; Beratan, D. N.
J. Am. Chem. Soc. 2008, 130, 11752–11761.
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Optimizing Single-Molecule Conductivity
A R T I C L E S
Figure 6. Change in (A) the decay constant ꢀ and (B) contact resistance R0 as a function of Fermi energy EF of the electrodes. The scans shown are for
γ ) 0.1 eV. Solid (dashed) green lines represent data for CTS (DTS). The vertical lines represent HOMO/LUMO energies for C1/T1 (black), C2/T2 (red),
and C3/T3 (blue) systems.
experimentally can result from barriers .kBT as a result of the
competition between tunneling and resonant processes. Since
neither the Fermi energy location relative to the molecular
eigenstate energies, nor the details of the linker interactions with
gold are known precisely, we treat EF and γ as parameters and
study the dependence of ꢀ and R0 on these parameters. EF is
restricted to energies in the HOMO-LUMO gap, for cases
where the Fermi energy lies 0.4-0.6 eV away from these
orbitals; these boundaries on the EF energy level ensure that
the current/voltage dependence in the applied bias range of 100
mV is linear and that the conductance can be calculated directly
from the slope of the I-V plots. The sulfur-gold coupling
parameter γ is varied over several orders of magnitude (Figure
S2, SI), while maintaining the weak coupling limit.
Figure 6 shows the dependence of the effective contact
resistance R0 and the electronic coupling constant ꢀ on EF in
the HOMO/LUMO gap. The dependence of ꢀ on EF in the
HOMO/LUMO gap is theoretically well-known from extensive
studies on hydrocarbon bridges.100,101 ꢀ is expected to become
larger as the EF energy level becomes further removed from
the frontier orbital energies. Asymmetries in the decay can be
introduced due to the interfering contributions of many filled
and/or empty MOs. This is precisely the case for CTS and DTS
where the frontier orbitals (shown by dashed and solid vertical
lines in Figure 6) do not even give the strongest contributions
in the tunneling limit (Figure 4). The situation is more
complicated for CTS, as the LUMO shifts to higher energies
(Figure 6) with augmented OPE conjugation length; note that
this behavior contrasts that of the CTS HOMO, and the observed
HOMO and LUMO shifts for DTS, which shift to more
favorable energies (CTS and DTS HOMOs shift to higher
energies and DTS LUMO shifts to lower energies) with
increasing conjugation. This effect results in an increase in ꢀ
for CTS as EF comes within ∼0.6 eV of the LUMO energy
(data not shown). Similarly, the dependence of the contact
resistance on EF for both systems is complex, because of the
contributions from many different MOs. While the ꢀ values for
the two linker systems remain close within the HOMO-LUMO
midgap region (varying from 0.45 to 0.15 Å-1 at EF values of
-6.5 eV < EF < -2.5 eV; Figure 6A), the CTS system is
theoretically capable of achieving very low ꢀ values (<0.1 Å-1)
even in the weak sulfur-gold coupling limit (γ ) 0.1 eV) as
EF approaches the HOMO. Moreover, the relative contact
resistance value (R0) of CTS is always lower (ranging from
5-180 times) than that of DTS for all values of EF considered
in Figure 6; note that R0 varies by 2 orders of magnitude for
CTS, and approximately an order of magnitude for DTS as the
Fermi energy is varied within the HOMO-LUMO gap. These
observations are consistent with the order of magnitude increase
in resistance of DTS relative to CTS highlighted in the
experimental data. The computations suggest that, in the weak
coupling limit, the differences in resistance values between CTS
and DTS could be increased (decreased) by shifting the Fermi
level toward the LUMO (HOMO).
A similar analysis was performed for the dependence of R0
and ꢀ on the sulfur-gold coupling parameter γ, at fixed values
of the Fermi energy EF. The results (Figure S2, SI) show that
ꢀ is insensitive to changes in γ over several orders of magnitude.
Also, the R0 difference between CTS and DTS is independent
of γ over several orders of magnitude, while R0 decreases
quadratically with increases in γ. However, the dependence of
R0 and ꢀ on the Fermi energies in the HOMO-LUMO gap are
more complicated (ꢀ is sensitive to γ; change in R0 with γ is
not quadratic), especially for Fermi energies for with EF - Em
≈ γ. A more detailed discussion is presented in section 2.2 of
the SI.
Having explored the dependence of the conductance, contact
resistance, and decay constant on our modeling parameters, we
now address the question of whether our theoretical approach
in the weak sulfur-electrode coupling regime explains our
experimental data. The experiments show low ꢀ values (∼0.11
Å-1 for DTS and ∼0.05 Å-1 for CTS), which is plausible when
the Fermi energy is close to a frontier orbital, and both tunneling
and resonant currents contribute. ꢀ values as low as ∼0.05 Å-1
for the CTS can be realized from the plots of ꢀ vs EF in Figure
6(A) only if the Fermi level lies close to the filled orbitals for
the CTS. While the ordering of the LUMO energies for the CTS
(C1 < C2 < C3) tends to make ꢀ large as EF shifts toward the
empty orbitals, the ordering of the HOMO energies for both
CT and DT OPEs (C1 < C2 < C3 and T1 < T2 < T3) tends to
reduce ꢀ as EF shifts toward the filled orbitals. Since both linker
systems couple to the electrodes through a sulfur-gold bond,
we expect the Fermi levels for both systems to be close
energetically. However, near the HOMO energy (Figure 6A),
the CTS show a larger ꢀ value than the DTS at the same EF, in
contrast to the experimental values. These data suggest that the
Fermi level might be pinned at different energies for CT and
DT OPEs. The physical basis for this assumption arises from
differences at the linker-electrode interface. The π-conjugated
sulfur atoms of the carbodithioate group likely serve to modify
the contact considerably with respect to the thiol function,
altering the alignment between the Fermi level with the HOMO/
(100) Beratan, D. N.; Hopfield, J. J. J. Am. Chem. Soc. 1984, 106, 1584–
1594.
(101) Onuchic, J. N.; Beratan, D. N. J. Am. Chem. Soc. 1987, 109, 6771–
6778.
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A R T I C L E S
Xing et al.
LUMO of the OPE molecules. Both the extent of delocalization
and the number of terminal sulfurs connected to the conjugated
molecular cores differ in DTS and CTS, leading to differences
in the orbital symmetry and energy levels that mediate the
coupling. Such an end group effect on the alignment of MOs
with the Fermi level has been invoked previously to explain
the different decay constants for the thiol and pyridine-
terminated carotenoid molecular junctions.43
Our calculations show that a hole injection barrier (separation
between the Fermi level and the filled MOs) of ∼0.4 eV, is
sufficient to produce the experimentally observed low ꢀ values.
The value of ∼0.4 eV is an upper limit for the barrier at which
resonant transport processes start competing with tunneling
transport, significantly lowering the ꢀ value. Note that this
barrier value is an upper limit due to the assumption of coherent
transport; incoherent transport resulting from the coupling of
the charge to molecular and solvent vibrational degrees of
freedom would lead to a smaller barrier.
ductances than do the analogous thiol-terminated systems (DTS).
We predict that this trend will be retained in general for other
metal and semiconducting electrodes which couple weakly to
conjugated organic molecules via a thiol linker: replacement
of thiol with carbodithioate will augment electronic coupling
and reduce the effective barrier for charge transport. Our
calculations further suggest that the experimental data can be
explained via a weak coupling limit analysis in which the Fermi
energies lie close to those of the CTS/DTS filled orbitals, such
that a mix of tunneling and resonant transport mechanisms
operate. Our calculations suggest an upper limit of ∼0.4 eV
for the charge injection barrier, at which resonant transport
processes become competitive with tunneling transport to
produce the low values of ꢀ observed experimentally in our
systems. Collectively, these experimental and theoretical data
emphasize the promise for using carbodithioate-based linkers
in molecular electronics applications.
Acknowledgment. We thank Dr. NongJian Tao and Dr. Yufan
He for useful discussions. We thank Prof. Jeffery R. Reimers for
providing the CNDO program. Financial support from the National
Science Foundation (NSEC DMR04-25780, CHE-0628169, and
CHE-0628218) is gratefully acknowledged. M.J.T. is grateful to
the Francqui Foundation (Belgium), and VLAC (Vlaams Acade-
misch Centrum), Centre for Advanced Studies of the Royal Flemish
Academy of Belgium for Science and the Arts, for research
fellowships.
Conclusion
We have probed single-molecule conductances in phen-
ylene-ethynylene molecules terminated with thiol and
carbodithioate linkers, using STM break-junctions and nonequi-
librium Green’s function analysis. Experimental data demonstrate
that the carbodithioate linker not only augments electronic coupling
relative to thiol, but reduces the effective barrier for charge
transport, making possible mixed tunneling/hopping transport
mechanisms, and underscoring that phenylene-ethynylene-based
molecular wires are more highly conductiVe than originally
appreciated. Theoretical analysis considered three regimes of
charge transport: tunneling, the resonant conduction, and a
mixed regime where both tunneling and resonant transport
processes operate. Interestingly, for the tunneling regime, the
frontier molecular orbitals are not the major tunneling current
mediators. Independent of the mechanism of charge transport,
the carbodithioate-terminated systems (CTS) show larger con-
Note Added after ASAP Publication. This article posted on
April 30, 2010 with incomplete corrections. The corrected version
published May 19, 2010.
Supporting Information Available: Synthetic procedures;
characterization and spectroscopic data; theoretical and com-
putational details; complete references 35 and 87. This material
is available free of charge via the Internet at http://pubs.acs.org/.
JA909559M
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7956 J. AM. CHEM. SOC. VOL. 132, NO. 23, 2010