Electron transport properties of a carotene molecule in a metal-(single molecule)-metal junction

Article abstract of DOI:10.1021/jp0343786

Using a recently developed method for tethering gold contacts to single molecules, we have measured current versus voltage (I-V) data for single carotenedithiol molecules with a total length of 28 carbons (18 in the conjugated alkene chain). The molecules are inserted into a docosanethiol monolayer (C₂₂H₄₅SH) on Au(111), and a Au nanoparticle is tethered to each molecule via the protruding thiol group. Electrical contact is made by placing a gold-coated AFM probe in contact with the nanoparticle. The I-V curves are relatively insensitive to contact probe force and cluster around integer multiples of a fundamental curve, suggesting that members of the smallest set correspond to data obtained from a single molecule. First principles calculations based on tunnel transport yield results that are remarkably close (within a factor of 4) to the measured data. The remaining small discrepancy can be well accounted for by taking account of the effects of charging caused by a probe-to-gold particle contact resistance. Thus, it appears that electron tunneling dominates transport even in this 3-nm-long molecule. The carotenoid is a better conductor than a saturated n-alkane of equivalent length by a very large factor and is significantly more conductive than 2,5-di(phenylethynyl-4′-thioacetyl)benzene, another candidate "molecular wire".

Full text of DOI:10.1021/jp0343786

6162
J. Phys. Chem. B 2003, 107, 6162-6169
Electron Transport Properties of a Carotene Molecule in a Metal-(Single Molecule)-Metal
Junction
Ganesh K. Ramachandran,† John K. Tomfohr,† Jun Li,† Otto F. Sankey,† Xristo Zarate,‡
Alex Primak,‡ Yuichi Terazono,‡ Thomas A. Moore,‡ Ana L. Moore,‡ Devens Gust,‡
Larry A. Nagahara,§ and Stuart M. Lindsay*,†
Department of Physics and Astronomy, Arizona State UniVersity, Tempe, Arizona 85287-1504, Department of
Chemistry and Biochemistry, Arizona State UniVersity, Tempe, Arizona 85287-1604, and Physical Sciences
Research Laboratory, Motorola Labs, 7700 S. RiVer Parkway, Tempe, Arizona 85284
ReceiVed: February 13, 2003
Using a recently developed method for tethering gold contacts to single molecules, we have measured current
versus voltage (I-V) data for single carotenedithiol molecules with a total length of 28 carbons (18 in the
conjugated alkene chain). The molecules are inserted into a docosanethiol monolayer (C22H45SH) on Au(111),
and a Au nanoparticle is tethered to each molecule via the protruding thiol group. Electrical contact is made
by placing a gold-coated AFM probe in contact with the nanoparticle. The I-V curves are relatively insensitive
to contact probe force and cluster around integer multiples of a fundamental curve, suggesting that members
of the smallest set correspond to data obtained from a single molecule. First principles calculations based on
tunnel transport yield results that are remarkably close (within a factor of 4) to the measured data. The remaining
small discrepancy can be well accounted for by taking account of the effects of charging caused by a probe-
to-gold particle contact resistance. Thus, it appears that electron tunneling dominates transport even in this
3-nm-long molecule. The carotenoid is a better conductor than a saturated n-alkane of equivalent length by
a very large factor and is significantly more conductive than 2,5-di(phenylethynyl-4′-thioacetyl)benzene, another
candidate “molecular wire”.
Introduction
for measurements). The measured conductance of this molecule
in the gold-molecule-gold junction was surprisingly low.
Carotenoid polyenes appear to be excellent candidates for
molecular wires because of their conjugated nature and the
planar conformation of the alkene chain, which maximizes the
overlap of the π electrons. In earlier work,12 we showed that
carotenoids are orders of magnitude more conductive than
alkanes of the same length, but quantitative information was
difficult to obtain because these data were acquired by conduct-
ing atomic force microscopy in which one contact was not
covalently bonded. We have now examined this topic using the
contact pad approach developed by Cui et al.7 to contact carotene
molecules, and the results are reported here.
The carotenoids are intrinsically interesting molecules. Their
electronic delocalization is manifested in their optical properties
and used in their biological functions.13,14 Their electronic
properties are still a matter of some debate, but the current
understanding may be summarized as follows: The π-electron
system of the carotenoid pigment available to assist tunneling
(or actually to accept/donate electrons) can be obtained from
an analysis of the molecular orbital description of the low-lying
electronic excited states. As is usual for organic compounds
having large conjugated π-electron systems, the ground state is
well described by a set of occupied bonding molecular orbitals
and unoccupied antibonding orbitals. A strongly allowed
electronic transition gives rise to the intense light absorption in
the visible that is characteristic of carotenoids. Although this is
not the lowest-energy electronic transition, it is well described
in terms of promoting an electron from the HOMO to the
LUMO.15,16 In carotenoids having C2h symmetry, this state is
designated 11Bu+, and the absorption band onset is at ca. 2.4
Despite the demonstration of promising molecular-electronic
devices,1-4 questions remain about the nature of the contact
between molecules and electronic conducting materials.5,6 We
have shown previously that the conductivity of n-alkanes is
enhanced enormously when metal “contact pads” are covalently
bonded to each end of the molecule and a conducting atomic
force microscope (c-AFM) probe is used to contact the top metal
contact (a gold nanoparticle).7,8 By using an insertion process9
to support and separate the target molecules, single-molecule
measurements were made.7 The data were highly reproducible
and gave currents much closer to those predicted by first
principles theoretical simulations7 than was the case for
mechanically contacted molecules.8 Despite these successes,
discrepancies between theory and experiment remained.10
Subsequent (unpublished) work indicates that electrical resist-
ance between the nanoparticle and gold AFM probe can play
an important role and might account for these remaining
discrepancies.
The conductivity of the n-alkane chains bonded into an
electrical circuit now appears to be well enough understood to
justify a systematic comparison with other molecules that are
candidates for molecular electronic materials. We recently
completed an initial study of 2,5-di(phenylethynyl-4′-thioacetyl)-
benzene,11 a molecule specifically designed as a “molecular
wire” (i.e., the molecule is used in its deprotected thiol form
* Corresponding author. E-mail: stuart.lindsay@asu.edu.
† Department of Physics and Astronomy, Arizona State University.
‡ Department of Chemistry and Biochemistry, Arizona State University.
§ Motorola Labs.
10.1021/jp0343786 CCC: $25.00 © 2003 American Chemical Society
Published on Web 05/30/2003

ET Properties of a Carotene Molecule
J. Phys. Chem. B, Vol. 107, No. 25, 2003 6163
g, 0.019 mol) was dissolved in 10 mL of tetrahydrofuran (THF)
and heated to ∼50 °C. A solution of 2.0 g (0.018 mol) of
potassium thioacetate in 20 mL of THF was added dropwise.
The mixture was kept well stirred under a nitrogen atmosphere
overnight. After that time, the reaction mixture was diluted with
dichloromethane and extracted with water three times. The
organic solvent was distilled at reduced pressure, and crude 1
was purified by column chromatography on silica gel (5% ethyl
ether/hexane) to yield 0.81 g (17%) of the desired compound.
1H NMR (300 MHz, CDCl3): δ 7.29 (4H, m, ArH), 4.46 (2H,
s, -CH2Br), 4.10 (2H, s, -CH2S-), 2.35 (3H, s, -CH3).
4-Acetylthiomethylbenzyltriphenylphosphonium Bromide
(2). Ester 1 (0.81 g, 3.1 mmol) was dissolved in 30 mL of
toluene. To this solution was added 1.0 g (3.8 mmol) of
triphenylphosphine. The reaction mixture was stirred in an oil
bath at 110 °C overnight. After that time, it was cooled to 0 °C
and filtered, and the filter cake was washed two times with
toluene and two times with hexanes. The expected salt remained
as white crystals (1.5 g, 94% yield). 1H NMR (300 MHz,
CDCl3): δ 7.7 (15H, m, ArH), 7.04 (4H, m, ArH), 5.37 (2H,
m, -CH2P-), 4.01 (2H, s, -CH2S-), 2.34 (3H, s, -CH3); MS
(MALDI-TOF) m/z: 441.15 (calcd for C28H26OPS+, 441.14).
Figure 1. Sample preparation. (a) 7,7′-Bis(4-thiomethylphenyl)-7,7′-
diapocarotene (3), the dithiolated carotenoid used in this work. (On
the structure, all double bonds should be on the same side of the
backbonespreferably the lower side.) Arrows point to the bonds most
susceptible to cis-trans isomerization during synthesis. (b) A schematic
of the c-AFM experiment. A dithiolated carotene molecule is inserted
into a monolayer of the alkane monothiol C22H45-SH. The free thiol
group of the carotene is tethered with an Au nanoparticle, which is
then contacted by an AFM tip coated with gold. (c) Reverse-phase
HPLC of a sample of 3 synthesized showing 20% cis isomer content
(see text).
7,7′-Bis(4-thiomethylphenyl)-7,7′-diapocarotene (3). A por-
tion of crocetindial (0.10 g, 0.34 mmol) and 0.44 g (0.84 mmol)
of 2 were mixed with 10 mL of tetrahydrofuran, and enough
methanol was added to dissolve the salt (∼2 mL). An excess
of sodium methoxide (0.23 g, 4.2 mmol) was added to this
solution, which was kept well stirred in an inert atmosphere
overnight. The reaction mixture was diluted with dichloro-
methane and extracted with a dilute solution of citric acid and
then with water. The solvent was distilled from the organic phase
at reduced pressure, and column chromatography on silica gel
with 20% hexane/dichloromethane produced 23 mg (23% yield)
of the desired dithiol. Reverse-phase HPLC of this product
indicated that it consisted of a mixture of two major isomers in
an approximate ratio of 80:20 (Figure 1c), which is ascribed to
cis-trans isomerism in the carotene. (The arrows in Figure 1a
indicate the most likely position where cis isomerism would
occur as a consequence of the nonstereospecific Wittig-type
reaction used to expand the polyenic chain.) 1H NMR and COSY
eV. The lowest singlet excited state is designated 21Ag and
+
corresponds to electronic configurations that include promoting
two electrons from the HOMO to the LUMO and configurations
in which an electron is promoted from HOMO-1 to the LUMO
and from the HOMO to LUMO+1. Strong electron correlation
lowers the energy of this state below that of 11Bu+. The energy
of this electric-dipole-forbidden 21Ag+ state is uncertain in these
carotenoids but is thought to be in the vicinity of 1.7 eV. A
1
-
second forbidden state having B1u symmetry has also been
1
+
+
reported to lie between the allowed B1u state and the 21Ag
level.17-19 Its energy has not been determined. Nevertheless,
within the framework of modern molecular orbital treatments,
the electronic energy of the ground state-to-1Bu+ transition, ca.
2.4 eV, corresponds approximately to the HOMO-LUMO gap
in these systems. Spectroscopic studies on a wide range of
carotenoids indicate that this assignment of excited states is not
dependent upon strict C2h symmetry.
1
experiments were consistent with the proposed structure. H
NMR (500 MHz, CDCl3, major isomer): δ 7.39 (d, J ) 8 Hz,
ArH), 7.27 (d, J ) 8 Hz, ArH), 6.89 (d, J ) 16 Hz, 8-CH),
6.68 (m, 11-CH), 6.65 (m, 15-CH), 6.57 (d, J ) 16 Hz, 7-CH),
6.42 (d, J ) 15 Hz, 12-CH), 6.37 (d, J ) 15 Hz, 10-CH), 6.30
(m, 14-CH), 3.74 (d, J ) 8 Hz, -CH2-), 2.05 (s, 19-CH3),
1.97 (s, 20-CH3), 1.76 (br m, -SH); MS (MALDI-TOF) m/z:
536.24 (calculated for C36H40S2, 536.26); UV-vis (toluene) 379,
454 (sh), 477, 505 (sh) nm.
Experimental Section
Molecular Films. The dithiolated carotenoid 7,7′-bis(4-
thiomethylphenyl)-7,7′-diapocarotene (3) see Figure 1a) was
synthesized as described below. Samples for this study were
prepared by placing freshly annealed Au(111)-on-mica20 sur-
faces in 1 mM solutions of docosanethiol (C22H45-SH) in
toluene for 12-16 h. This process forms a uniform monolayer
of the alkanethiol on Au(111). After rinsing the monolayer in
toluene, the film was incubated in a fresh 0.022 mM solution
of the freshly thawed carotenedithiol (see below) for 6 h.
Subsequently, the film was rinsed in toluene and incubated in
a suspension (1 to 2 mg in CH2Cl2) of triphenylphosphine-
stabilized ∼1.5-nm-diameter gold nanoparticles21 for 12 h.7,10
Prior to experiments, samples were rinsed with freshly distilled
dichloromethane and toluene several times. The carotene
solutions were frozen until immediately prior to use. All rinsing
and depositions involving the carotene were performed in the
dark. Optical spectra collected before and after use of the
carotene solutions did not show any observable degradation or
oxidation.
Scanning Probe Microscopy. For c-AFM experiments
(shown schematically in Figure 1b), microfabricated contact-
mode silicon cantilevers with a spring constant of 0.35 N/m
(MikroMasch, CSC11) were coated with an underlayer of 50
Å Cr/100 Å Au followed by a second coating of 50 Å Cr and
400 Å of gold. The tips were cleaned in ozone-UV prior to
use. Measurements were made with a PicoSPM conducting
atomic-force microscope (Molecular Imaging, Phoenix) using
a hermetically sealed sample chamber flushed with argon to
reduce oxygen and water-vapor contamination. Contamination
was reduced by keeping the sample submerged in freshly
distilled toluene during measurement. This also serves to
minimize adhesion between the AFM tip and the sample,
permitting controlled contact between the tip and gold nano-
particles. All STM images were obtained with electrochemically
Synthesis of the Carotenedithiol. Thioacetic Acid (S)-(4-
Bromomethylbenzyl) Ester (1). R,R′-Dibromo-p-xylene (5.0

6164 J. Phys. Chem. B, Vol. 107, No. 25, 2003
Ramachandran et al.
molecules above the surrounding matrix. In consequence, images
with Au particles attached are only somewhat broadened relative
to those taken without the Au particles. However, the apparent
height of the “spots” associated with the inserted molecules is
more than doubled when Au particles are attached (Figure 2c).
(The apparent height in an STM image is only indirectly related
to true topographic changes when comparing images of samples
of different chemical composition.)
Current-voltage curves were obtained by lowering the gold-
coated c-AFM probe onto a gold particle and recording the
current as the probe bias was swept (typically at a rate of 3
V/s). Both the sweep rate and the range of the sweep were varied
to ensure that reproducible data were obtained and that the data
were free from hysteresis. A maximum bias of (1.5 V could
be applied without bias-dependent changes of the current-
voltage characteristics from sweep to sweep.
In the case (studied earlier) of alkanedithiol molecules inserted
into alkanethiol monolayers, the current measured via the
nanoparticle contact was found to be largely independent of
applied force,7 in contrast to measurements made without
bonded8,12 contact pads. It proved to be difficult to make a
similar measurement (measuring current while sweeping contact
force) in the present case, presumably because of the less rigid
molecular arrangement owing to the height difference between
the inserted molecule and the surrounding matrix. Nonetheless,
we were able to record a series of I-V curves as the force set-
point was changed, avoiding the problems of programming a
scan in the height of the probe at a fixed position in the plane
of the film (as would be required to record current vs force
change continuously). The I-V curves also served as an internal
control, becoming distorted if the tip moved during the voltage
scan. The quantity I/I0 (plotted in Figure 3a) was found by
obtaining the divisor that minimized the variance between each
I-V curve and the initial one, just as was done in the analysis
of the I-V curves (see below). It can be seen that the curves
Figure 2. STM images of the steps in insertion and contact tethering.
(a) STM image of the C22H45-SH alkane monothiol monolayer prior
to insertion of the dithiolated carotenoids. (b) Similar image after
insertion of the carotenoid and (c) after the carotenoid is subsequently
treated with a suspension of gold nanoparticles. The bright spots in b
correspond to the carotenedithiols, which are more conducting than
the alkanethiol matrix. These spots are rather broad, probably because
of the significant protrusion of the top of the inserted molecule (see
text), so the increase in width owing to the tethering of gold contacts
in c is not obvious. However, the apparent height of the spots increases
significantly after gold particles are attached. (A height scale is listed
below each image.) All images were obtained under toluene in an Ar
environment at a bias of -1.25 V and a set-point current of 18 pA.
etched PtIr tips using a PicoSPM with the sample under toluene
and operating in a dry argon environment. The operating set-
point current was between 12 and 20 pA with tip biases between
-0.8 and -1.2 V.
Experimental Results
The insertion process can be followed in STM images as
illustrated in Figure 2, which shows the docosanethiol monolayer
(a), the monolayer with inserted carotenoids (b), and the
assembly with tethered gold particles (c) all at the same
magnification. The insertion density (about 10 to 100 molecules
per 100 × 100 nm2) is typical. In contrast to our earlier work7,10
where the inserted molecule and surrounding matrix were nearly
identical, here the images of the inserted dithiolated carotenoids
(Figure 2b) are much broader (ca. 3-nm diameter), presumably
as a consequence of the ca. 4-Å overhang of the inserted
Figure 3. Current-voltage data from inserted molecules. (a) Contact-force dependence of the current. The I-V curves were recorded as the set
point was systematically increased. Every point on each curve was divided by the corresponding point on the first (lowest force) curve, and the
corresponding set of current ratios was averaged to produce the quantity I/I0 plotted here. Currents remained relatively constant until the contact
force exceeded 6 nN. (b) Current-voltage curves representative of the groups centered around 1, 2, and 3 units of conductance (see text). The data
shown here are averages of the curves selected using the divisor distribution shown in d, and error bars correspond to (1 standard error. (c) Curves
1, 2, and 3 from b divided by 1, 2, and 3 at each point. (d) Histogram of the value of a divisor chosen to minimize the variance between any pair
of measured curves and normalized so as to be 1 or greater. Clear peaks are seen at 1 ((0.22) and 2 ((0.22). There is also evidence of a peak at
3.04 ((0.41). The number of curves under each peak is in the ratio of 1:1.4:0.4.

ET Properties of a Carotene Molecule
J. Phys. Chem. B, Vol. 107, No. 25, 2003 6165
are quite stable up to contact forces of about 6 nN with this
particular tip (end radius ca. 30 nm).
Some typical I-V curves taken in the lower contact-force
range are shown in Figure 3b. These data are actually averages
of curves belonging to clusters selected as described below. The
curves are, within experimental uncertainty, symmetrical about
zero bias.
Curves were observed to cluster around certain values of
current at a given bias, as observed in our earlier work with
n-alkanedithiols.7,10 To characterize this variability, we analyzed
these curves in the following way. One of the curves with the
smallest current at the highest bias was arbitrarily assigned as
the “standard curve” for the complete data set (N ) 230). Then
the value of a divisor, X, was found for each of the other curves
such that dividing all points on the curve by X minimized the
variance between it and the standard curve. The resulting
histogram of X values shows two distinct peaks (Figure 3c) with
evidence of a third, implying that the currents cluster around
1X, 2X, and 3X of a fundamental current. (The first peak actually
occurs at X ) 1.04, reflecting the choice of a standard curve
that was a bit smaller than the peak values associated with the
first peak; numbers and widths have been rescaled in the Figure
caption so that the first peak is at X ) 1 to emphasize the integer
separation between peaks.) The corresponding I-V curves were
sorted according to the associated X value. Curves with 0.5 e
X < 1.5 were assigned to the 1X group, curves with 1.5 e X <
2.5 were assigned to the 2X group, and curves with 2.5 e X <
3.5 were assigned to the 3X group. The average of the curves
within each group (and the associated standard errors, shown
as the width of the lines) is plotted in Figure 3b. Dividing each
curve by 1, 2, and 3 at each voltage point yields the “master
curve” shown in Figure 3c.
The following conclusions can be drawn from this exercise:
(a) The I-V curves cluster around integer multiples of a
fundamental curve. The evidence for this lies in the width of
the peaks in the histogram of X values; the width of the first
two peaks is substantially less than their separation (see Figure
3 caption). Peak 3 is not as convincing. (Note that the small
error bars on curve 3 in Figure 3b reflect, in part, the exclusion
of curves for X g 3.5 as well as the use of the standard error
that understates the width of the distribution.)
(b) Curves from the three groups have essentially the same
shape as shown by the superposition in Figure 3c. (Small but
significant differences are noticeable at higher bias, and
these contribute to the spread in X values for the 3X family of
curves.)
Figure 4. Contact geometry for the simulations. The terminal sulfur
sits in a 3-fold hollow on the gold surface with the molecular axis
inclined 30° to the surface normal, the C-S-Au (hollow site) angle
constrained to lie between 90 and 100°, and the S-C-C bond
maintained at 110°. The S-Au bond energy is relatively insensitive to
the rotations of S about the surface normal, so I-V curves were
calculated for the full range of values of this angle. The cis isomer
cannot be positioned on the surface within these constraints, and a
minimum-energy configuration was found with the Au-S-C bond
angle at 110°.
functions that are needed to compute the current versus voltage
curves were calculated from the Hamiltonian and overlap matrix
elements. Though the electronic structure calculation was
performed with gold slabs of finite thickness, we extended
Green’s functions to include semi-infinite contacts using a block-
recursion technique. Full details are given,31 and related
descriptions are available.26,10
The current is calculated as
2e
h
eV
2
eV
2
I(V) )
T(E, V) f E -
- f E +
dE (1)
∫
[
(
)
(
)
]
where T(E, V) is the transmission function,24,25 f is the Fermi
function, and V is the voltage. We have assumed that the electron
energies in the electrodes are shifted symmetrically by +eV/2
and -eV/2 for the left and right electrodes, respectively. The
calculations of the metal-molecule-metal system are fully self-
consistent at zero bias and thus include charge-transfer effects
at the interface; however, the effects of bias and the electric
field are approximated simply by shifts in the Fermi levels of
the left and right contacts.
The calculated conductance of the carotene molecule (3) is
sensitive to its geometric structure, particularly the alternating
double and single bonds in the molecule’s polyene (polyacet-
ylene-like) segment connecting the phenyl rings. The degree
of bond alternation, or “dimerization”, is characterized by R,
which is defined as the ratio of the single-bond length to the
double-bond length in the polyene backbone connecting the
phenyl rings. With no dimerization (R ) 1), the HOMO-
LUMO gap of the polyene chain goes to zero as its length
increases in the same way that the spacing between levels for
a particle-in-a-box goes to zero as the length of the box
increases. For short segments of an H-(CHCH)n-H chain
containing 2n carbon atoms, the HOMO-LUMO gap with R
being unity is given approximately by
Fits to the low-bias (linear I-V) region (Figure 5a) show that
the resistance of the 1X family of curves is 4.9 ( 0.2 GΩ at
low bias.
Theoretical Modeling
Calculations of the theoretical current-voltage curve for the
carotene molecule were based on the Landauer-Buttiker
formalism22,23 with the transmission function calculated using
quantum mechanical scattering theory.24,25 The model system
was an infinite 2D lattice (monolayer) of carotene molecules
sandwiched between gold contacts made up of eight ideal
Au(111) layers in a supercell structure, as discussed in detail
elsewhere.26 The self-consistent Kohn-Sham single-electron
states were obtained for this system using Fireballs-2000,27-29
a local atomic-orbital density functional theory (DFT)-based
method in the pseudopotential local density approximation
(LDA). The present procedures have been previously found to
give similar results using the related Siesta method.30 Green’s
π
∆E ) 4t sin
(2)
[
]
2(2n + 1)
This equation is derived from a simple tight-binding model
where t is an interaction Hamitonian matrix element. Dimer-
ization of the polyene chain (R > 1) leads to a substantial (∼1.8
eV) HOMO-LUMO gapsthe limit is approached as the length
of the chain increasessexactly analogous to the band gap of a
semiconductor. Tunneling current through an energy barrier
generally goes as I ) I0e-âL, where L is the length of the barrier
(here polyene) and the decay constant â due to tunneling goes

6166 J. Phys. Chem. B, Vol. 107, No. 25, 2003
Ramachandran et al.
Figure 5. Comparison of theory and experiment. (a) Calculated currents for the trans (l- - -) and doubly cis (- - -) geometries with error bars
showing the range owing to possible orientations with respect to rotations of the S-Au bond normal to the gold surface. The experimental data for
a single molecule are shown on the same scale as the solid line. The inset (lower right) shows the ohmic region at low bias with linear fits that yield
low-bias conductances of 0.2 nS (experimental), 0.45 nS (doubly cis, calculated), and 0.83 nS (trans, calculated). The corresponding resistances are
4.9, 2.2, and 1.2 GΩ. (b) Coulomb-blockade-corrected I-V curves showing improved agreement at low bias (s, experiment; O, theory) with
further improvement when the bias dependence of the tunneling rate is accounted for (4). The inset (lower right) shows the two-junction model.
to zero for energies near the HOMO and LUMO and reaches a
peak (most rapid decay), usually near the middle of the gap.
The tunneling current is “exponentially” sensitive to R because
a higher R leads to a larger HOMO-LUMO gap and a
corresponding increase in â.
I-V curves were computed for all allowed rotational arrange-
ments of this molecule as well. The rotationally averaged
computed I-V curves are shown in Figure 5a. The long-dashed
line is the calculated result for the trans isomer, the short-dashed
line is for the doubly cis isomer, and the solid line is the single-
molecule experimental curve. The theoretical “error bars”
indicate the range in currents spanned by rotating the molecule
about the Au-S bond. A magnified inset shows the low-bias
ohmic region with results for the doubly cis isomer and for the
all-trans isomer shown by solid triangles and open squares,
respectively. The corresponding resistances are 2.2 GΩ (cis)
and 1.2 GΩ (trans).
Structural optimization of the carotene molecule using density
functional theory was found to produce far too little dimerization
(R ) 1.03), resulting in 1.40 and 1.36 Å for the single- and
double-bond lengths, respectively. This results in a HOMO-
LUMO gap that is too small (about 1.0 eV) compared to the
experimental value, which is near 2.4 eV. (See the introductory
discussion.) It is known that Hartree-Fock (HF) calculations
generally do much better than LDA-DFT in predicting the
correct dimerization in the case of polyacetylene.32 Our Hartree-
Fock structural optimization33 of the carotene molecule yields
R ) 1.10 with 1.46 and 1.33 Å for the single- and double-bond
lengths, respectively, in excellent agreement with experiment.34
The resulting energy-optimized carotene geometry from HF is
then input into the DFT calculation, and a HOMO-LUMO gap
of around 1.8 eV is found. This value is in accord with existing
experimental data (2.4 eV).
To calculate the electronic current, we use the HF-optimized
carotene structure in DFT calculations of the carotene-gold
system. For testing purposes, we also performed current-voltage
calculations using carotene structures optimized by DFT and
found significant differences in the current compared to experi-
ment. The lower dimerization and resulting smaller HOMO-
LUMO gap predicted by DFT, for example, result in much
higher current values and a dramatic turn-on in current at around
0.5 V when conduction electrons access the HOMO and LUMO
levels.
The details of the molecule-metal contact are also important
(see Figure 4), and they were investigated as follows: The Au-
S-C bond angle was fixed at 90°, and the S-C-C angle was
fixed at 110°, resulting in an angle between the two sulfur end-
groups and the normal to the gold substrate of 30°, as might be
expected for insertion into the tilted docosanethiol matrix. There
are uncertainties concerning exactly how the carotene molecule
fits into the decosanethiol film. For the all-trans isomer, the
interaction between C and the Au surface was not strong enough
to identify a highly preferred orientation. On the basis of these
considerations, I-V curves were therefore computed for all
arrangements in which the molecule was rotated about the
surface normal on a fixed conical surface oriented 30° with
respect to the surface normal (see Figure 4). The doubly cis
isomer was more difficult to accommodate between two gold
slabs, and the Au-S-C bond angle had to be distorted to 110°.
Discussion
Origin of Quantized Molecular Conduction. By analogy
with our previous results for alkanedithiols,7,10 the simplest and
most reasonable explanation for the clusters of I-V curves
observed for the carotenedithiol is that the three curves in Figure
3b correspond to 1, 2, and 3 molecules bridging the gap between
the top gold contact and the underlying gold substrate, resulting
in resistance ratios R0, R0/2, and R0/3. However, a second
possibility should be considered. Approximately 20% of the
carotenedithiol preparation was a minor isomer. This most likely
has the cis configuration at a double bond adjacent to one aryl
ring because the method of synthesis produces a mixture of cis
and trans bonds at this location. Alternatively, the isomerization
of the all-trans carotene about any of its alkene double bonds
could have happened in solution or on the gold substrate because
such isomerizations are known to occur via chemical agents,
the carotenoid radical cation, and the carotenoid triplet state.
The theoretical calculations given above suggest that a carotene
with two cis double bonds is less conductive than an all-trans
carotene by about a factor of 2. Perhaps the first peak in the
histogram in Figure 3d represents a cis carotenedithiol, and the
second peak, a trans carotenedithiol (rather than two carotene-
dithiol molecules).
Although this latter interpretation cannot be totally excluded,
there are several factors that suggest that it is unlikely. In the
first place, there are approximately equal numbers of curves
under peaks 1 and 2 in Figure 3d, whereas the isomer ratio in
the solution used to form the monolayer was 4 trans/1 cis (Figure
1c). The observed ratio would therefore require either the cis
isomer to insert preferentially into the monolayer of docosane-
thiol or the trans isomer to isomerize preferentially to cis after
it has entered the monolayer. These possibilities seem unlikely,
given that the trans form is thermodynamically more stable in
solution and that the trans form would be expected to be less

ET Properties of a Carotene Molecule
J. Phys. Chem. B, Vol. 107, No. 25, 2003 6167
disruptive of the close packing of the alkanethiols in the
monolayer (by analogy with the similar packing in long-chain
carboxylic acid and phospholipid monolayers). Second, the
theoretical simulations suggest that dramatic differences in the
shapes of the I-V curves at higher bias should exist for the cis
and trans isomers (Figure 5a), but this is not observed (Figure
3c). Finally, the calculations show that a carotenoid with two
cis double bonds is almost exactly half as conductive as one
with none. The synthetic procedure is such that the formation
of a carotenoid with cis double bonds at both ends is highly
improbable. Presumably, a carotenoid with one double bond
would have a resistance somewhere between that of all-trans
and doubly cis. However, the histogram in Figure 3d clearly
shows a factor of 2 in conductivity difference between the two
families of curves. For these reasons, we favor the interpretation
that the curves in Figure 3b correspond to 1, 2, or 3 molecules
bridging the gap between gold contacts. It should be noted that
even if the other interpretation were correct the curve of lowest
conductivity would still represent the conductivity of a single
carotenoid molecule.
With R1 corresponding to the probe-to-particle tunnel junction
resistance, C1 corresponding to its capacitance, R2 corresponding
to the particle-to-substrate tunnel junction resistance, and C2
corresponding to its capacitance and allowing for a charge
accumulation Q0 on the nanoparticle, the current is obtained
from
∞
I(V) ) -e
σ(n)[Γ+(n) - Γ-(n)] )
2 2
∑
n)-∞
∞
-e
σ(n)[Γ-(n) - Γ+(n)] (3)
1 1
∑
n)-∞
where σ(n) is the steady-state probability that the nanoparticle
is charged with n electrons. Here,
-∆E(j
1
Γ(j (n) )
j ) 1, 2
(4)
Rje2
∆E(j
1 - exp
(
)
(
)
kBT
and
Magnitude of Molecular Conductance. The experiment and
theory agree remarkably well, as shown in Figure 5a. It is
important to stress that neither experimental data nor calculated
data are scaled in any way: the absolute values of current are
shown. Given the uncertainties in the simulation, this means
that the measured currents may be accounted for by electron
tunneling. This degree of agreement in the absolute magnitude
of tunnel current is unusual and was only recently achieved for
the simple n-alkanedithiols.7
-e
C1 + C2
1
∆E(1 )
∆E(2 )
- n ( e + Q0 + C2V
(5)
(6)
(
(
)
)
2
(e
1
2
n ( e - Q0 + C1V
((
)
)
C1 + C2
The superscripts + or - refer to an electron hopping on or off
the nanoparticle, respectively, through the junction.
Role of Contact Resistance. A close inspection of the
experimental and calculated curves (for the trans isomer where
the overall shape agreement is better) shows small but significant
differences in shape when the theory is scaled to give a best fit
to experiment (not shown): the experimental current in the
ohmic region is too small (compared with theory), and the
experimental curve grows less rapidly than the calculated curve
at high bias. This suppression of current in the low-bias re-
gion and a smaller-than-expected growth as resonance is
approached are both possible consequences of contact resistance
between the AFM probe and the gold nanoparticle. The
nanoparticles are ligand-stabilized, and it is not clear whether
the contact stresses used in this work are adequate to penetrate
the ligand layer. The large tip radius (ca. 30 nm) and the
relatively large cluster diameter (∼1.5 nm) should result in a
significant contact area (when compared to a tip-single-
molecule contact). Nonetheless, the contact may not be formed
from metallic bonds because of the possibility of an intervening
ligand layer.
The residual charge on the nanoparticle, Q0, was set equal to
zero in the fits that follow because nonzero values give
asymmetric I-V curves, contrary to experiment. In eq 3, the
electron distribution abides by detailed balance
Γ-1 (n + 1) + Γ-2 (n + 1)
σ(n)
)
(7)
Γ+1 (n) + Γ+2 (n)
σ(n + 1)
and normalization of probability
∞
σ(n) ) 1
(8)
∑
n)-∞
We can estimate C2 as being of the same order of magnitude
as the free-space capacitance of a sphere, 4πꢀ0R, where R ≈
1.5 nm, giving 0.08 aF (1 aF ) 10-18 F). Previous fits of data
for a number of different n-alkanes using the same gold spheres
showed that good results are obtained with C1 ) 0.318 aF and
C2 ) 0.085 aF (J. Tomfohr, unpublished data). Therefore, we
started with these values for the capacitance and used a value
for R2 of 1.2 GΩ calculated quantum mechanically for the trans
isomer (inset, Figure 5a). We found that the resulting I-V curves
were essentially independent of R1 so long as R1 , R2. The
results of a calculation for R1 ) 1 MΩ are shown as circles in
Figure 5b. Given that, with the exception of the unimportant
R1, the parameter values were obtained independently, and the
fit at low bias is quite striking.
We previously found that the approach outlined above worked
well in accounting for I-V curves measured for various
n-alkanes over the entire range of biases. Here, it clearly fails
at higher bias. However, this is not surprising because of the
assumption of a fixed value for R2. This approximation (i.e., a
constant resistance R2) is valid for the alkanes that have a very
large HOMO-LUMO gap; however, it fails for carotene when
If the probe-to-cluster contact resistance is significantly higher
than the quantum of resistance (h/2e2 ≈ 12.9 kΩ), then the
current will be dominated by a sequential electron-transport
process in which electrons transfer one at a time across the
probe-to-cluster and cluster-to-substrate junctions. This will
result in a suppressed current flow for biases below that required
to overcome the Coulomb charging energy (i.e., “Coulomb
blockade”) of the cluster.35
This possibility can be treated by considering the junction as
a resistance (proportional to the inverse tunneling rate) in parallel
with a capacitor to represent the AFM-to-gold particle contact
and a second parallel resistor-capacitor combination in series
with the first to represent the gold particle-to-gold substrate
contact. (See the inset in Figure 5b.) Such an arrangement has
been treated in detail by Averin and Likharev36 and by Hanna
and Tinkham.37

6168 J. Phys. Chem. B, Vol. 107, No. 25, 2003
Ramachandran et al.
TABLE 1: Measured Resistances at Low Bias for Various
Dithiolated Molecules Contacted with Gold Nanoparticlesa
the applied bias begins to approach the HOMO-LUMO gap
separation energy. We therefore introduced a bias-dependent
R2 in an ad hoc manner by modifying eq 4 for the transfer rate
across junction 2 as
R(low bias)
GΩ
12.9 exp(âN) kΩ
GΩ
molecule
N
octanedithiol
decanedithiol
dodecanedithiol
TPEb-dithiol
8
0.965 ( 0.02
2.89 ( 0.5
8.26 ( 1
0.038
0.277
2.05
10
12
16
28
I(Va) + I(Vb)
2e
1
Γ(2 (n) )
(9)
∆E(2 /kT
52 ( 18
112
1 - e
carotenedithiol
4.9 ( 0.2
1.8 × 107
a Variances are estimated from repeated attempts to fit the linear
portions of the curves near zero bias. N is the minimum number of
carbons in a direct path through the molecule. For comparison, an
estimated resistance based on a â of 1.0 per carbon is shown. b TPE-
dithiol is 2,5-di(phenylethynyl-4′-thioacetyl)benzene.
where I(V) is the current at voltage V determined from the
calculated I-V curve for the trans isomer and Vb and Va are the
(n-dependent) voltages across junction 2 before and after the
electron transfer. Physically, the voltage across the junction will
change (from Vb to Va) during an electron transfer, and we use
the average of currents I(Vb) and I(Va) from the I-V calculation
for the molecule to approximate the average transfer rate. For
an ohmic junction I(V) ) V/R, we recover eq 4 because ∆E is
given by the electron charge multiplied by the average voltage
(Vb + Va)/2. The I-V curve resulting from this modification
fits the experimental data quite well (triangles in Figure 5b). A
better fit is obtained if we increase R1 to 10 MΩ.
taken into account (unpublished work). In contrast, the unsat-
urated molecule 2,5-di(phenylethynyl-4′-thioacetyl)benzene has
a resistance close to that predicted using a â of unity, even
though â has been expected to be much smaller for this
molecule.38,39 The carotenoid is by far the longest molecule
studied using bonded contacts, yet its low-bias resistance is less
than that of dodecanedithiol!
Comparison with Other Measurements. Comparative stud-
ies of conduction through saturated and unsaturated com-
plexes38,39 show evidence of enhanced transport in the unsat-
urated systems, together with a significant decrease in the inverse
electronic decay length,38 as might be expected given the
enhanced overlap and delocalization in the unsaturated molecular
systems. To date, however, the only published study of
carotenoids appears to be our earlier conducting AFM work on
a monothiol derivative, contacted mechanically (i.e., no chemical
bonding between the probe and the molecule).12 In the case of
n-alkanes, we found a very large (3 orders of magnitude)
difference between similar sets of measurements when mechan-
ical and bonded contacts were compared.7,8 In the case of the
carotenoid, it is surprising that the resistance measured for the
ohmic region in both the early work (mechanical contact) and
the present work (bonded contact) is about 5 GΩ! However,
the earlier (mechanical contact) measurements on inserted
carotenoids were made in quite a different manner from the
mechanical contact measurements on n-alkane monolayers. In
the work of Letherman et al.,12 current images were obtained
at a series of fixed biases, and the maximum current was
extracted by fitting the “image” of the conducting molecule so
as to remove uncertainties associated with the relative tip-to-
molecule positioning. Clearly, this tedious procedure was
successful (but it yielded much noisier data than the procedure
presented here).
In conclusion, we have now obtained current versus voltage
data for single carotene molecules with a total length of 28
carbons (18 in the conjugated chain). Despite some uncertainty
about the role of isomers, the data give, at worst, an estimate
of the single-molecule resistance for all-trans carotenedithiol 3
to within a factor of 2. At best, the single-molecule I-V curve
for all-trans 3 in a gold-molecule-gold junction has been
determined to within the width of the measured single-molecule
distribution (i.e., about (20%). These data are in remarkable
agreement (factor of 4) with the results of a theory based on
tunnel transport, and the agreement can be made almost
complete when some reasonable corrections for contact resist-
ance are made. This suggests that the conductance can be
accounted for largely by tunnel transport, despite the electro-
active nature of this molecule. Overall, the molecule is an
excellent mediator of tunneling, having a conductance similar
to that of an n-alkane of less than half its length.
Acknowledgment. This work was supported by the NSF
(ECS 01101175 and CHE 0078835) and Molecular Imaging.
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