Tunability in polyatomic molecule diffusion through tunneling versus pacing

Article abstract of DOI:10.1021/ja1027343

The diffusion temperature of molecular 'walkers', molecules that are capable of moving unidirectionally across a substrate violating its symmetry, can be tuned over a wide range utilizing extension of their aromatic backbone, insertion of a second set of substrate linkers (converting bipedal into quadrupedal species), and substitution on the ring. Density functional theory simulation of the molecular dynamics identifies the motion of the quadrupedal species as pacing (as opposed to trotting or gliding). Knowledge about the diffusion mode allows us to draw conclusions on the relevance of tunneling to the surface diffusion of polyatomic organic molecules.

Full text of DOI:10.1021/ja1027343

Published on Web 09/10/2010
Tunability in Polyatomic Molecule Diffusion through Tunneling versus Pacing
Zhihai Cheng, Eric S. Chu, Dezheng Sun, Daeho Kim, Yeming Zhu, MiaoMiao Luo, Greg Pawin,
Kin L. Wong, Ki-Young Kwon, Robert Carp, Michael Marsella, and Ludwig Bartels*
Department of Chemistry, UniVersity of California, RiVerside, California 92521
Received April 2, 2010; E-mail: ludwig.bartels@ucr.edu
substrate linkers and potential docking sites for molecular cargo,
Abstract: The diffusion temperature of molecular ‘walkers’,
inviting the question: in which fashion does a quadrupedal species
molecules that are capable of moving unidirectionally across a
move across a surface? Will it be in a walking style at all? And if
substrate violating its symmetry, can be tuned over a wide range
it is a walking style, which gait will its legs adopt: trotting, in which
utilizing extension of their aromatic backbone, insertion of a
diagonally opposed legs move in unison, or pacing, in which both
second set of substrate linkers (converting bipedal into quadru-
legs on one side of the molecule move together?
pedal species), and substitution on the ring. Density functional
theory simulation of the molecular dynamics identifies the motion
of the quadrupedal species as pacing (as opposed to trotting or
gliding). Knowledge about the diffusion mode allows us to draw
conclusions on the relevance of tunneling to the surface diffusion
of polyatomic organic molecules.
All measurements in this manuscript were performed in a
scanning tunneling microscopy (STM) instrument capable of
imaging molecular diffusion at 8 K and above in ultrahigh vacuum.
Preparation of the Cu(111) sample involved sequences of sputtering
and annealing, followed by cooling to 80 K. Deposition of the
molecules from a glass capillary proceeded on the cryogenic sample
followed by annealing to close to room temperatures to desorb
inevitable solvent residues. All coverages were ∼1 molecule per
The development of molecular machines as realization of the
100 substrate atoms, so that isolated molecules can be investigated.
ultimate miniaturization of macroscopic devices has become a
Temperatures were measured by a silicon diode attached to the
research topic of general and widespread interest. Molecular
STM scanner, which in turn had been calibrated by replacing the
machines are common in the biochemical arena (F1-motor of ATP
synthase, proton pump in cell membranes, transcription polymerase,
STM tip with a silicon diode in the tip-holder-sample junction. In
combination, this results in a temperature uncertainty of (1 K.
kinesin motor proteins, etc.). Much smaller and easier to handle
All density functional theory simulations (DFT) utilized the
molecules have been synthesized to resemble macroscopic devices
VASP code18 with the generalized-gradient approximation19 for
such as gears,1 cars,2 ratchets,3 walkers,4-6 turnstiles,7,8 pinwheels,9
the exchange-correlation functional and the plane-wave pseudopo-
shuttles,10 ‘sky-hooks’,11 and wheel-barrows12 when adsorbed at
tential method20 with ultrasoft pseudopotentials.21 Our calculations
use a 4 × 8 substrate atoms supercell with 4 substrate layers that
a metal surface.13-16 For surface molecular machinery to obtain
ultimate utility, it is necessary that their motion is reliable and their
provides a sufficiently large lateral extent to prevent intermolecular
rate of motion is tunable in a predetermined fashion to the task at
interactions despite circular boundary conditions. The atom positions
hand. Here we report on a class of molecules that allows us the
were optimized so that all forces in the system are smaller than
study of the transition from thermally assisted tunneling diffusion
to purely thermal diffusion17 and permits tuning of the diffusion
0.04 eV/Å.
We find that PQ adsorbs on Cu(111) very similar to AQ,6 i.e.
temperature between 20 and 80 K.
In previous work anthraquinone6 (AQ) (and its sulfur counterpart
with its anthracene body aligned with one of the substrate atomic
dithioanthracene,5 DTA) has been shown to diffuse on 6-fold
rows (Figure 1a). In STM images it appears as an elongated
protrusion with a slightly narrower waist at the carbonyl group
symmetric Cu(111) exclusively along the high-symmetry direction
positions. DFT simulation of its adsorption configuration shows
indicated by its aromatic moiety, i.e. violating the substrate
its carbonyl substrate linkers pinned to the substrate with the
symmetry, which is accomplished by sequential placement of its
remainder of the molecule bent upward (Figure 1c), similar to AQ.
Figure 1b and d show an STM image of several PT molecules on
a Cu(111) surface and a cross section of the PT adsorption
configuration obtained by integrating the charge density across
planes normal to the surface and the molecule. The molecular axis
is aligned with one of the atomic rows of the substrate. Its four
carbonyl oxygen legs come to rest on the surface, pulling the second
and fourth aromatic ring down onto the substrate, while allowing
the terminal rings to lift upward. DPT adsorbs similar to PT on
Cu(111).
chalcogen substrate linkers, a process dubbed ‘walking’. While AQ
movement proved useful in carrying cargo, its very low apparent
diffusion prefactor of just 102.4 Hz and barrier of 0.02 eV indicate
a diffusion mode that is not well understood. Here we show that
modification of AQ can lead either to similar or to much higher
diffusion barriers and prefactors, depending on whether the resultant
molecule can adopt a diffusion mode, in which tunneling of a single
atom only can forward it.
We investigated the surface diffusion of pentaquinone (PQ),
pentacenetetrone (PT), and a derivative of PT carrying methyl
groups at diagonally opposed ends of the aromatic backbone,
dimethylpentacenetetrone (DPT). The first two species were
obtained commercially, and DPT was synthesized through dimer-
ization of suitably substituted naphtaquions. While PQ differs from
AQ only by extension of the ring system and thus may be expected
to diffuse in a similar way across a surface, PT and DPT have four
Sequences of STM measurements reveal that PQ, PT, and DPT
diffuse exclusively along the axis indicated by their aromatic moiety,
similar to AQ.6 The Supporting Information shows a movie. We
acquired several days of diffusion data on each of the molecules;
in several thousand diffusion events investigated, no perpendicular
motion or rotation has been observed.
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C O M M U N I C A T I O N S
concerted lowering of prefactors and barrier has been described
already 70 years ago, named the Meyer Neldel rule or compensation
effect,27,28 and has since been observed for a range of phenomena
including conductivity of semiconductor, mobility of polymers,
grain and phase-boundary motion, etc.29 Yet the magnitude of
reduction observed here is larger than typical Meyer Neldel effects,
raising the question what in particular sets quadrupedal motion apart
from that of bipedal species.
To this end, we performed DFT simulations of how PT
overcomes the diffusion barrier. Starting out from the initial,
minimized configuration, we move the substrate linkers successively
by 0.1-0.2 Å at a time followed by renewed minimization of the
entire system so that all forces are smaller than 0.04 eV/Å, while
keeping only the forward motion of the manipulated oxygen atoms
fixed. In a previous mapping of the diffusion potential for AQ and
DTA we showed that the molecules move by alternatingly stepping
their substrate linkers, angling the molecule with regards to the
substrate atomic rows.5,6 For the quadrupedal species, mapping of
the entire parameter space is computationally prohibitive, because
it is not two-dimensional as in the case of AQ but four-dimensional.
Rather we investigate the diffusion barrier along three potential
pathways: the first, in which two diagonally opposed substrate
linkers move at a time resembling the gait of trotting (Figure 3 b);
the second, in which two adjacent substrate linkers move at a time
resembling pacing (Figure 3c); the last, in which the molecule glides
across the surface moving all oxygen atoms forward simultaneously
(Figure 3d). Using the mean forward motion of the substrate linkers
as a reaction coordinate, the diffusion barriers of Figure 3e result.
The Supporting Information contains movies illustrating these
motion modes.
Figure 1. (a,b) STM images of PQ (a) and PT (b) on Cu(111); (c,d)
Integrated charge density from DFT simulation5,22 of PQ (c) and PT (d) on
Cu(111). The carbonyl groups pin PQ and PT to the substrate leaving their
peripheral portions free to angle upward. STM image parameters: (a) 93
pA, -1.7 V, 37 Å × 22 Å; (b) 130 pA, -1.1 V, 32 Å × 19 Å. Note that
in panels c,d the substrate atoms appear twice as close because of the offset
of alternating atom rows on the fcc(111) surface.
Plotting the molecular diffusion rate versus the experimental
temperature leads to the Arrhenius plot of Figure 2, which, in
addition to the PQ, PT, and DPT, also shows the diffusion rate of
AQ for ref 6. The statistical error is smaller than the data markers.
From these data, diffusion barriers of 0.02 eV ( 0.01 and 0.03 eV
( 0.01 eV for AQ and PQ, respectively, and of 0.13 eV ( 0.02
and 0.19 eV ( 0.02 eV for PT and DPT, respectively, can be
extracted. Although the largest variation in diffusion barrier is found
between bipedal and quadrupedal species, the difference in diffusion
barrier induced by methyl substitution and elongation of the ring
system is substantial (i.e., ∼50% each). For example, extrapolation
of the diffusion rate of the methylated species to the unmethylated
one indicates almost a 1 × 106-fold difference in diffusion rate.
The effect of methylation is even sufficient to put the observation
of uniaxial diffusion within reach of LN2 cooling. These results
make it clear that terminal methyl substitution and backbone
elongation, despite their chemically inert nature, and remote location
from the fulcrum of the motion, are very sensitive handles for tuning
the diffusion rates of walking molecules.
Figure 2. Arrhenius plot of the uniaxial motion of AQ (pink), PQ (red),
PT (blue), and DPT (purple).
The difference between bipedal and quadrupedal species is even
more striking, if the prefactors are compared. For AQ and PQ they
are 102.4(1 and 102.3(1, respectively, whereas for PT and DPT they
are both 1013(1 Hz. The prefactors for the bipedal species are much
lower than the conventional 1010-1013 Hz, yet low prefactors have
been reported in a number of STM diffusion experiments at low
temperatures: CO/Cu(111), ∼107 Hz;23 CO chevrons/Cu(111), ∼105
Hz;24 CO/Cu(110), ∼107 Hz;25 Al/Au(111), ∼103 Hz26). A
Figure 3. Setup of PT on Cu(111) as obtained from DFT-based minimiza-
tion (a) and schematic representation of trotting (red), pacing (blue), and
gliding (green). Panel e shows the corresponding energy barriers, with
trotting on the right y-axis and pacing as well as gliding on the left axis.
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C O M M U N I C A T I O N S
d
Each of the diffusion pathways is associated with more than one
barrier. During trotting, only one pair of diagonally opposed
substrate linkers moves whereas the other stays stationary, leading
to a distortion of the molecule. The maximum distortion is reached
at 1/4 (and 3/4) of the step distance coinciding with the maximum
barrier height of 0.7-0.8 eV. At the diffusion midpoint, the
distortion of the molecule is released and the total energy is at a
local minimum, despite the fact that here the interaction with the
substrate is not optimal. The diffusion barrier encountered during
trotting is significantly higher than the measured value, and it is
prohibitive at the temperatures of our experiments. It reflects the
great energetic cost associated with distorting the molecule’s
aromatic backbone.
P ) exp -2/
2mE (x) dx
√
atom
∫
(
)
p
0
Assuming the central portion of the pacing barrier (Figure 3e)
as Eatom(x) + Ebarr, a tunneling probability of ∼10-10 results. Thus,
if the rate at which the bipedal AQ species approaches the
vibrationally excited state is assumed to be a typical value of
1012-1013 Hz, an apparent attempt frequency of 102-103 Hz is
expected, which corresponds to the values measured here.
Why then do we observe low prefactors for the bipedal species
and conventional ones for the quadrupedal species? The simulation
shows that the molecular distortion required to place the substrate
linkers sequentially (as it is possible in the trotting gait) is
energetically prohibitive. Pacing, however, requires concerted
motion of both substrate linkers on one side of the molecule; yet
concerted tunneling of them has a probability of P2 ≈ 10-20, too
unlikely to occur. Thus, tunneling is only an option for a molecule,
in whose motion no concerted displacement of substrate linkers is
required.
On the gliding pathway (and to a lesser degree on the pacing
pathway), initial displacement from the equilibrium adsite encoun-
ters a small barrier. While pacing, the second set of substrate linkers
starts to move once the first set reaches 1/4 of the diffusion distance.
At the diffusion quarterpoint (≈ 0.6 Å) the molecular setups for
pacing and gliding merge at an energetic minimum. Similarly, all
diffusion pathways merge at the diffusion halfpoint and the molecule
is aligned parallel to the diffusion direction. In gliding, PT
approaches this point via a considerable barrier, whereas, in pacing,
the molecule angles itself barrierless into this configuration. In
contrast to trotting motion, pacing and gliding motions are inversion
symmetric at the diffusion midpoint.
The combination of modeling of the diffusion mode and
calculation of the tunneling probability provides a strong argument
in favor of the relevance of tunneling for the bipedal species.
Moreover, the apparent barriers obtained from the Arrhenius fit of
AQ and PQ diffusion of 0.02 and 0.03 eV are a much better match
for vibrational modes of oxygen atoms at surfaces, as required for
thermally assisted tunneling, than for actual diffusion barriers.35
The absolute height of the simulated diffusion barrier of ∼0.07
eV is somewhat lower than the experimental value of 0.13 eV;
van der Waals (vdW) interactions are absent from our DFT
simulations for reason of computational feasibility, although they
are known to contribute substantially to the acene-substrate
interaction, thus explaining the difference in total barrier.30,31 While
we wish to caution that this may also impact our assignment of the
gait, we believe that the 0.02 eV difference in energy between
pacing and gliding will not be superseded by vdW interactions given
their typically slow spatial variation.30
Acknowledgment. Supported by U.S. Department of Energy
Grant DE-FG02-07ER15842 and by NSF Grant 0749949. Com-
putational resources were made available by the NSF Teragrid and
the Beran group at UCR.
Supporting Information Available: Description of synthetic meth-
ods; movies and animation of the molecular motion. This material is
available free of charge via the Internet at http://pubs.acs.org.
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