Unusual Length Dependence of the Conductance in Cumulene Molecular Wires

Article abstract of DOI:10.1002/anie.201901228

Cumulenes are sometimes described as “metallic” because an infinitely long cumulene would have the band structure of a metal. Herein, we report the single-molecule conductance of a series of cumulenes and cumulene analogues, where the number of consecutiv

Full text of DOI:10.1002/anie.201901228

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Accepted Article
Title: Unusual Length-Dependence of Conductance in Cumulene
Molecular Wire
Authors: Wenjun Xu, Edmund Leary, Songjun Hou, Sara Sangtarash,
Teresa González, Gabino Rubio-Bollinger, Qingqing Wu,
Hatef Sadeghi, Lara Tejerina, Kirsten Christensen, Nicolás
Agraït, Simon Higgins, Colin Lambert, Richard Nichols, and
Harry Laurence Anderson
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To be cited as: Angew. Chem. Int. Ed. 10.1002/anie.201901228
Angew. Chem. 10.1002/ange.201901228
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Unusual Length-Dependence of Conductance in Cumulene
Molecular Wires
Wenjun Xu,+ Edmund Leary,+* Songjun Hou,+ Sara Sangtarash, M. Teresa González, Gabino Rubio-
Bollinger, Qingqing Wu, Hatef Sadeghi, Lara Tejerina, Kirsten E. Christensen, Nicolás Agraït, Simon J.
Higgins, Colin J. Lambert,* Richard J. Nichols,* and Harry L. Anderson*
Abstract: Cumulenes are sometimes described as ‘metallic’
because an infinitely long cumulene would have the band structure
of a metal. Here we report the single-molecule conductances of a
series of cumulenes and cumulene analogues, where the number of
consecutive C=C bonds in the core is n = 1, 2, 3 and 5. The
[n]cumulenes with n = 3 and 5 have almost the same conductance,
and they are both more conductive than the alkene (n = 1). This is
remarkable because molecular conductance normally falls
exponentially with length. The conductance of the allene (n = 2) is
much lower, due to its twisted geometry. Computational simulations
predict a similar trend to the experimental results and indicate that
where β is the exponential attenuation factor, which is normally
in the range 0.2–0.5 Å–1 for a conjugated organic π-system.[2] It
has been predicted that molecules with low bond length
alternation (BLA) will give unusual attenuation factors, such as β
≈ 0 (i.e. conductance independent of length) or even β < 0 (i.e.
conductance increasing with length).[3,4] Cumulenes are the
simplest type of neutral π-system not to exhibit substantial
BLA.[5–7] Here we report an experimental and computational
investigation of the length-dependence of charge transport
through these linear carbon chains. Recently, near length-
independent conductances were reported for a set of cyanine
dyes, which constitute a class of cationic π-system with BLA ≈
0.[8]
the low conductance of the allene is
a general feature of
[n]cumulenes where n is even. The lack of length-dependence in the
conductances of [3] and [5]cumulenes is attributed to the strong
decrease in HOMO-LUMO gap with increasing length.
R
R
R
R
R
R
• •
x
n
Long molecules generally conduct electricity less well than short
ones, and this can be a problem when designing molecular
wires for mediating efficient charge-transport over distances of
several nanometers. When a homologous series of oligomers
are connected between metal electrodes, and the transport
mechanism is coherent tunneling, the conductance G of each
oligomer typically decreases exponentially with its molecular
length L according to equation (1),[1]
[n]cumulene (n = 2x + 1)
polyyne
Figure 1. Cumulenes and polyynes: two types of linear sp carbon chains.
Cumulenes and polyynes are the two types of linear chains
of sp-hybridized carbon atoms: in cumulenes, the carbon atoms
are linked by double bonds, whereas in polyynes there are
alternating single and triple bonds (Figure 1). Cumulenes and
polyynes have fascinated chemists for many years as models for
carbyne, the infinite 1D form of carbon.[5,6] Cumulenes are said
to have a ‘metallic’ electronic structure,[4-7,9-11] because an
ꢀ ∝ ꢀ–!"
(1)
[*]
W. Xu, Dr. L. Tejerina, Dr. K. E. Christensen, Prof. H. L. Anderson
Department of Chemistry, University of Oxford, Chemistry Research
Laboratory, Oxford OX1 3TA, UK
infinitely long cumulene would have
a
band structure
characteristic of a metal, with a partially occupied band derived
from the π and π* orbitals. In contrast polyynes have a π-π* gap
that persists even in long chains, and an infinite polyyne is
E-mail: harry.anderson@chem.ox.ac.uk
Dr. E. Leary, Prof. S. J. Higgins, Prof. R. J. Nichols
Department of Chemistry, Donnan and Robert Robinson
Laboratories, University of Liverpool, Liverpool L69 7ZD, UK
Dr. E. Leary, Prof. R. J. Nichols
Surface Science Research Centre, University of Liverpool, Oxford
Street, Liverpool L69 3BX, UK
E-mail: e.leary@liverpool.ac.uk, nichols@liverpool.ac.uk
S. Hou, Dr. S. Sangtarash, Dr. Q. Wu, Dr. H. Sadeghi, Prof. C. J.
Lambert
Department of Physics, Lancaster University, Lancaster LA1 4YW,
UK
expected to be
a
semiconductor.[10,12] This difference in
electronic structure is a direct consequence of the different BLA.
Although there is some BLA in cumulenes,[7] it is much more
subtle than the alternation between short C≡C and long C-C
bonds in polyynes.
Here, we report an experimental investigation of the
conductances of the family of cumulenes 1, 2, 3 and 5 shown in
Figure 2. The [4]cumulene 4 is included in our theoretical
investigation, but has not yet been tested experimentally. All
these molecules have two terminal 4-thioanisole substituents for
binding to gold electrodes. Single-molecule conductances were
measured using the scanning tunneling microscopy break-
E-mail: c.lambert@lancaster.ac.uk
Dr. M. T. González, Prof. N. Agräit
Instituto Madrileño de Estudios Avanzados (IMDEA), Calle Faraday
9, Campus Universitario de Cantoblanco, 28049 Madrid, Spain.
Prof. N. Agräit, Dr. G. Rubio-Bollinger
Departamento de Física de la Materia Condensada, IFIMAC and
Instituto “Nicolás Cabrera”, Universidad Autónoma de Madrid, E-
28049, Madrid, Spain.
junction (STM-BJ) method, using
a
gold tip and
a
gold
surface,[13] as described in detail previously.[2d]
[+]
These authors contributed equally to this work.
Supporting information for this article is given via a link at the end of
the document.
1
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MeS
MeS
Ph
•
Ph
Ph
Ph
SMe
Ph
1 (alkene, n = 1)
2 (allene, n = 2)
SMe
Ph
MeS
MeS
• •
•
Ph
• •
Ph
SMe
3 ([3]cumulene, n = 3)
4 ([4]cumulene, n = 4)
SMe
MeS
Ph
• • •
•
Ph
Figure 3. STM-BJ results on molecules 1–3 and 5 measured with a bias of 0.2
V. (a–d) 2D conductance histograms for the plateau-containing traces. The
number of traces in each (and percentage of the total) are as follows: n = 1:
1309 (56%), n = 2: 2988 (58%), n = 3: 1139 (47%), n = 5: 3402 (34%). (e) 1D
conductance histograms using all data points. (f) 1D conductance histogram
using only points from the end of the plateau distribution (g) Molecular
conductances from Gaussian fits to the data in (f); the experimental
uncertainties in these values are smaller than the size of the black squares.
5 ([5]cumulene, n = 5)
SMe
Figure 2. Structures of compounds 1–5. (Note that only 1, 2, 3 and 5 have
been tested experimentally.)
Compounds 1, 2, 3 and 5 were synthesized as described in
the Supporting Information (SI).[14] The alkene
1
was
Table 1. Single-molecule conductances, lengths and HOMO-LUMO gaps for
compounds 1–3 and 5.
recrystallized to give the E isomer, as confirmed by single crystal
X-ray diffraction.[15] Allene 2 is racemic. Cumulenes 3 and 5 are
1:1 mixtures of E and Z isomers (as confirmed by 1H NMR
spectroscopy); we were unable to separate these stereoisomers.
We expect them to convert readily under ambient conditions,[16]
and to have similar conductances (SI, Figure S7).
Lexp
Lcalc
Eg(UV)
Eg(DFT)
compound
log(G/G0)[a]
(nm)[b]
(nm)[c]
(eV)[d]
(eV)[e]
0.94
(1.32)
1 (n = 1)
2 (n = 2)
3 (n = 3)
5 (n = 5)
−4.09
–5.25
−3.74
−3.64
1.45
1.47
1.63
1.80
3.7
4.2
2.7
2.4
2.21
2.74
1.54
1.24
The experimental conductance results for compounds 1–3
and 5 are summarized in Figure 3 and Table 1. For reference,
we have also measured bis-4,4’-(thiomethyl)biphenyl, which has
no double bonds between the phenyl rings (SI, Section S3.7).
The 2D histograms (Figure 3a–d) show how the conductance
(G/G0, where G0 = 2e2/h) of each junction varies as the STM tip
is retracted from the surface (increasing distance, z) for a large
number of traces (see SI for details on the procedure and data
from multiple experimental runs). All the compounds give well-
defined plateaus, which become longer as the length of the
molecule increases, indicating that connection occurs at the
SMe groups (see Table 1 for experimental and calculated
molecular lengths, Lexp and Lcalc, and Figure S9 for the plateau-
length distributions). The percentage of junctions giving a
plateau for each compound is given in the caption to Figure 3
(and in Table S1). The measured conductances for the alkene
and allene vary slightly with distance across the plateau (z). The
molecular conductances plotted in Figure 3g and listed in Table
1 are quoted from the histograms in Figure 3f, where we have
considered only points from the end of the distribution, greater
than the median length determined from a Gaussian fit (see SI
for details). We validated this method previously for a family of
porphyrins.[17] This analysis procedure ensures that the
1.01
(1.34)
1.07
(1.46)
1.09
(1.64)
[a] Experimental conductance peak positions from data in Figure 3f; Run to
run variation in peak position is about 0.02, see SI Figure S19. [b] Lengths are
calibrated by adding 0.4 nm to the peak position of a Gaussian fit to the total
distribution of plateau lengths.[2d,17] Values in brackets are derived from the
95th percentile. See section 3.4 in the SI for the length distribution histograms.
[c] Calculated using the Spartan quantum chemical package at the semi-
empirical level. We bind a gold atom to each sulfur and measure the Au-Au
distance. [d] HOMO-LUMO gap calculated from the peak wavelength of the
lowest-energy absorption band in chloroform. [e] Calculated Kohn-Sham
HOMO-LUMO gaps from DFT for isolated molecules in vacuum.
conductance values can be attributed to fully-stretched single-
molecule junctions. It also results in good overlap between
histograms (of the same compound) from periods of
measurement giving different percentages of molecular junctions.
We often observe an apparent increase in the molecular
conductance when the percentage of molecular junctions
exceeds about 40%, which is attributed to the formation of
2
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junctions containing several wired molecules.[18] However, if we
only consider the data points at longer z values, the resulting
histograms are more reproducible, indicating that the probability
of multiple-molecule junctions diminishes as the junctions are
stretched (as discussed in the SI, Sections S3.8 and S3.9).
The [3] and [5]cumulenes have essentially the same
conductance, which is slightly larger than the alkene (see Figure
S19 for a comparison of multiple experimental runs showing
high reproducibility). The allene has a conductance about 50
times smaller than those of the [3] and [5]cumulenes, reflecting
its twisted geometry. The conductances of all compounds show
a weak voltage-dependence, suggesting that the Fermi level
(EF) lies far from any molecular levels, consistent with EF sitting
near the center of the HOMO-LUMO gap (see SI, Section S3.5).
Junctions of [5]cumulene were stable generally to ±1.2 V,
whereas the shorter allene was stable only to ±0.5 V. At 1.2 V,
series of compounds alkene, [3]cumulene and [5]cumulene can
be attributed to the decreasing HOMO-LUMO gaps, which
compensate for the increasing length.[13,23] The lower molecular
conductance of the
the maximum current through
a
[5]cumulene molecule
approaches microamperes (see Figure S10).
In order to gain further insight into the conductance trends in
the family of cumulene molecular wires, and how their
conductances change with length, transmission spectra T(E)
were calculated by combining the DFT package SIESTA[19] with
the quantum transport code Gollum[20] (for further details see SI).
For alkene, [3]cumulene and [5]cumulene, the energetically
preferred conformations have two terminal thioanisole rings that
are not coplanar (see details in SI, Section S2.2), in agreement
with crystallographic studies.[15,21] The conformations of relaxed
molecules embedded in Au-Au junctions are shown in Figure 4a.
The frontier molecular orbitals (see SI, Figure S3) show that the
HOMO of alkene, the HOMO and LUMO of [3]cumulene and
[5]cumulene form extended π-conjugated transport paths
through the whole molecule. In contrast, the molecular orbitals of
the allene and [4]cumulene are formed from pz and px orbitals
and follow chiral paths through the molecules, leading to
terminal thioanisole rings which are orthogonal to each other,
and the absence of an extended π-system in the HOMO and
LUMO. As shown in Figure 4b, these differences between the
even and odd-numbered cumulenes are reflected in their
transmission functions. Over a range of EF within the HOMO-
LUMO gap, (indicated by the shaded region in Figure 4b), the
conductances of allene and the [4]cumulene are expected to be
lower than those of the other three molecules. More interestingly,
the conductances of the [3]cumulene and the [5]cumulene are
predicted to be about the same, despite the substantial change
in length. This prediction is consistent with previous
computational studies of charge transport through cumulene
molecular wires.[4,9] The local density of states (LDOS) of alkene
and allene (Figure 4c) reveals a clear transport path for the
alkene (magenta surface), while there is no such LDOS path on
the allene molecule. The alkene is predicted to have a slightly
lower conductance than both the [3] and [5]cumulenes, due to
the larger angle between the two thioanisole rings in the alkene,
which is the result of steric interactions between the thioanisole
and phenyl substituents.
Figure 4. (a) Calculated conformations for alkene, allene, [3]cumulene,
[5]cumulene attached to two gold leads, where the grey, white and pale yellow
balls represent carbon, hydrogen and sulfur respectively. The yellow balls at
both ends represent gold leads. (b) Transmission spectra. The shaded region
indicates the range of Fermi energies within the HOMO-LUMO gap that
contribute towards conduction at room temperature. (c) The LDOS with
magenta color in the energy window from –0.5 eV to 0 eV for alkene and
allene incorporated in two gold leads separately at the isosurface 0.00002.
allene is consistent with the large HOMO-LUMO gap which
leads to a higher barrier to electron transport. ‘Odd-even’
conductance oscillations are anticipated from previous studies
on metal atomic chains (e.g. Au, Pt and Ir) as a function of the
number of atoms in the chain.[24] For example, Au and Na chains,
with single conductance channels, show an odd-even effect that
originates from quantum interference.[25,26] Odd-even oscillations
have also been predicted for monoatomic carbon chains
between carbon nanotubes.[27] The odd-even effect that we
observe here is probably dominated by the fact the 4-thioanisole
groups connecting the chains to the electrodes are only π-
conjugated in the odd [n]cumulenes (i.e. even number of carbon
atoms). Another obvious difference between our measurements
and the metal atomic chains is the fact that the chain and
The experimental conductances of molecules 1, 2, 3 and 5
correlate well with their HOMO-LUMO gaps, as illustrated by the
optical gaps, Eg(UV) from the wavelength of the lowest-energy
UV-vis absorption band, and the Kohn-Sham gaps, Eg(DFT) in
Table 1.[22] The lack of attenuation in the conductance for the
3
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In conclusion, this study reveals that the conductance of a
series of cumulenes shows remarkably little dependence on the
molecular length (n). This behavior is a consequence of the lack
of strong BLA in these compounds, which results in a steep
reduction in the HOMO-LUMO gap with increasing length.[6,7] In
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bias voltage).[28] The [5]cumulene exhibits a high conductance of
log(G/G0) = −3.7 (± 0.5) and shows stable junctions up to a bias
of 1.2 V. The discovery that cumulenes exhibit length-
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All individual G−z traces for the STM experiments are freely
available
http://dx.doi.org/10.17638/datacat.liverpool.ac.uk/659
at
the
following
repository
address:
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Acknowledgements
We thank the EPSRC (grants EP/M016110/1, EP/M014452/1,
EP/M014169/1 and EP/M029522/1) and ERC (grant 320969) for
support, and the EPSRC UK National Mass Spectrometry
Facility at Swansea University for MALDI spectra. H.S. and S.S.
acknowledge the Leverhulme Trust for Leverhulme Early Career
Fellowship no. ECF-2017-186 and ECF-2018-375. H.S.
acknowledges the UKRI Future Leaders Fellowship no.
MR/S015329/1. IMDEA Nanociencia acknowledges support
from the ’Severo Ochoa’ Programme for Centres of Excellence
in R&D (MINECO, Grant SEV-2016-0686). N.A. and C.J.L.
acknowledge EC H2020 FET Open project 767187 “QuIET”. N.A.
and G.R.B. were funded by Spanish MINECO (grants MAT2014-
57915-R, MAT2017-88693-R and MDM-2014-0377) and
[15] Low temperature single crystal X-ray diffraction data for compound 1
were collected using
a (Rigaku) Oxford Diffraction SuperNova
diffractometer. Raw frame data were reduced using CrysAlisPro and
the structures were solved using 'Superflip’ [L. Palatinus, G. Chapuis, J.
Appl. Cryst. 2007, 40, 786–790] before refinement with CRYSTALS [a)
P. Parois, R. I. Cooper, A. L. Thompson, Chem. Cent. J. 2015, 9:30; b)
R. I. Cooper, A. L. Thompson, D. J. Watkin, J. Appl. Cryst. 2010, 43,
1100–1107] as per the SI (CIF). Crystallographic data have been
deposited with the Cambridge Crystallographic Data Centre as
supplementary publication no. CCDC 1893619 and can be obtained via
www. ccdc.cam.ac.uk/data_request/cif.
Comunidad
de
Madrid
(grant
NANOFRONTMAG-CM,
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S2013/MIT-2850). We thank Dr. P. Gawel for valuable
discussion.
Keywords: cumulene • single-molecule • conductance •
molecular wire • break-junction
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4
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10.1002/anie.201901228
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Entry for the Table of Contents
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Wenjun Xu, Dr. Edmund Leary, Songjun
Hou, Dr. Sara Sangtarash, Dr. M.
Teresa González, Dr. Qingqing Wu, Dr.
Hatef Sadeghi, Dr. Lara Tejerina, Dr.
Kirsten E. Christensen, Prof. Nicolás
Agraït, Prof. Simon J. Higgins, Prof.
Colin J. Lambert, Prof. Richard J.
Nichols, and Prof. Harry L. Anderson
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C
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Text for Table of Contents
Cumulene wires, such as that show above, with an odd number of double bonds,
are more conductive than expected for their length, as revealed by experimental
single-molecule break-junction results and computational simulations. The
conductance is almost independent of length because the HOMO-LUMO gaps
decreases steeply as the molecules become longer.
Page No. – Page No.
Title: Unusual Length-Dependence of
Conductance in Cumulene Molecular
Wires
6
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