Quantum interference distinguishes between constitutional isomers

Article abstract of DOI:10.1039/c0cc00125b

Matter waves, as introduced by de Broglie in 1923 (L. de Broglie, Nature, 1923, 112, 540),¹ are a fundamental quantum phenomenon, describing the delocalized center of mass motion of massive bodies and we show here their sensitivity to the molecular structure of constitutional isomers.

Full text of DOI:10.1039/c0cc00125b

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Quantum interference distinguishes between constitutional isomersw
Jens Tu
¨
xen,a Stefan Gerlich,b Sandra Eibenberger,b Markus Arndt*b and Marcel Mayor*ac
Received 25th February 2010, Accepted 19th April 2010
First published as an Advance Article on the web 10th May 2010
DOI: 10.1039/c0cc00125b
Matter waves, as introduced by de Broglie in 1923 (L. de
Broglie, Nature, 1923, 112, 540),1 are a fundamental quantum
phenomenon, describing the delocalized center of mass motion
of massive bodies and we show here their sensitivity to the
molecular structure of constitutional isomers.
different molecular conformations might eventually also be
distinguished in quantum interference experiments.7
For demonstration purposes we here compare two tailor-
made model compounds 1 and 2. The design of both is based
on our recent findings in molecular electronics which showed a
considerable delocalization of the p-system in rod-like oligo
phenylene ethynylene (OPE)8,9 on the one hand and a partition
of the p-system by conjugation interrupting subunits like e.g.
platinum complexes,10 perpendicular torsion angles11,12 or sp3-
carbon atoms on the other hand. The constitutional isomers 1
and 2 both have the chemical formula C49H16F52 and an
identical molecular weight of 1592 g molꢀ1, but different
polarizabilities. The tetrahedral model compound 1 consists
of four phenyl rings interlinked by a central sp3-carbon which
disables conjugation between the neighboring aromatic
subunits. In contrast to that, the p-system of the rod-like
OPE 2 extends over all three phenyl rings. Thus an increased
electron delocalization and polarizability is expected for com-
pound 2 as compared to 1.
In quantum textbooks, matter wave phenomena are often
associated with the equation ldB = h/mv, where the de Broglie
wavelength ldB is only determined by Planck’s constant h and
the particle’s momentum p = mv. It is a common conjecture
that this relation still holds for bodies of arbitrary mass, size
and complexity. But what is the role of the detailed internal
molecular composition if ldB does not include any such
information?
As already shown before,2 the centre of mass motion can be
well described by quantum delocalization and interference of
each entire molecule with itself—even if the internal atoms
may populate a thermal mixture of vibrational and rotational
modes at a temperature of about T = 500 K. The conceptual
separation of the internal and external degrees of freedom
allows us to discuss two different cases:
A simulation using Gaussian 03W13 with the basis set 3-21G
yielded a static polarizability of astat = 63(2) A3 ꢁ 4pe0 for
compound 1 and 70(2) A3 ꢁ 4pe0 for molecule 2, i.e. a
difference of about 10% between the two structures.
If the interaction between the molecule and its environment
makes it possible, even only in principle, to retrieve position
information, the initially delocalized particle will be localized
and quantum interference can no longer occur.3
The tetrahedral target compound 1 was synthesized in two
steps starting from tetraphenylmethane (3) (Scheme 1). Bro-
mination of all four para-positions of tetraphenylmethane (3)
was achieved according to an established procedure.14 Pure
tetrakis(4-bromophenyl)methane (4) was isolated as a yellowish
crystalline solid in a yield of 83%. By treating 4 with
n-perfluorohexyl iodide in a suspension of copper in dimethyl-
formamide (DMF) at 120 1C the perfluoroalkyl chains
were introduced. The tetrahedral target structure tetrakis-
(4-perfluorohexylphenyl)methane (1) was isolated by column
chromatography (CC) as a white crystalline solid in 27% yield.
The rod-like OPE structure 2 was assembled starting from
methyl 3,5-dibromobenzoate (5). In a copper catalyzed
Ullmann type coupling reaction both bromines were substituted
with fluorous ponytails to provide 6 as a white solid in 86%
yield after CC. The benzylic alcohol 7 was obtained in 64%
yield by reduction with lithium aluminium hydride (LiAlH4).
Subsequent oxidation with pyridinium dichromate (PDC)
provided the benzaldehyde 8 as a white solid in 88% yield
after CC. With a Corey–Fuchs reaction sequence the aldehyde
was transformed to the alkyne 10 in 79% yield over both steps.
The diiodo derivative 12 as central building block of the rod 2
was obtained by iodination of 4-ethyltoluene (11) as white
crystals in 53% yield. With both building blocks in hand,
the rigid rod type target structure 2 was assembled with a
Sonogashira–Hagihara reaction. Thus the central diiodo
precursor 12 and two equivalents of the alkyne 10 were exposed
The second case is of particular relevance for our present
experiment: All individual atoms in a given molecular structure
will add up to determine its global properties, and in particular
also its electrical susceptibility. The susceptibility can couple to
an external electric field and thus influence the center of mass
motion of the entire particle. In this way, the internal structure
becomes influential for the external motion, even though the
molecule remains still widely delocalized and capable of
showing de Broglie interference.
First experiments along this line were recently able to apply
this idea to near-field interferometry for measuring the static4
and optical5 polarizability astat and aopt as well as the total
electric susceptibility wtot of molecules. The latter may also
contain additional information about static or time varying
electric dipole moments.6 It has therefore been suggested that
a Department of Chemistry, University of Basel, St. Johannsring 19,
4056 Basel, Switzerland. E-mail: marcel.mayor@unibas.ch
b Faculty of Physics, University of Vienna, Boltzmanngasse 5,
1090 Vienna, Austria. E-mail: markus.arndt@univie.ac.at
c Karlsruhe Institute of Technology, Institute for Nanotechnology,
P.O. Box 3640, 76021 Karlsruhe, Germany
w Electronic supplementary information (ESI) available: Synthetic
procedures, characterization data and details concerning the weighted
average of Fig. 2. See DOI: 10.1039/c0cc00125b
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Fig. 1 Sketch of the matter wave interferometer that was used to
distinguish the constitutional isomers 1 and 2. The isomers were
ejected from the effusive source to pass two nano-mechanical gratings
and one optical phase grating. Quantum interference leads to a
molecular density distribution at G3. Its lateral position is determined
by the interaction between the external electric field and the molecular
susceptibility wtot. The susceptibility varies for different atomic
arrangements even if they add up to the same chemical sum formula.
Scheme 1 Synthesis of the structural isomers 1 and 2. (a) Br2, rt,
25 min, 83%; (b) IC6F13, Cu, DMF, 120 1C, 12 h, 27%; (c) IC6F13, Cu,
DMF, 120 1C, 12 h, 86%; (d) LiAlH4, Et2O, rt, 16 h, 64%; (e) PDC,
CH2Cl2, rt, 24 h, 88%; (f) CBr4, PPh3, CH2Cl2, 0 1C, 1 h, 85%; (g)
1. n-BuLi, THF, ꢀ78 1C; 2. H2O, 93%; (h) I2, HIO3, glacial AcOH,
H2SO4, CHCl3, H2O, 85 1C, 4 h, 53%; (i) Pd(PPh3)4, CuI, (i-Pr)2NH,
THF, rt, 12 h, 22%.
The three gratings are spaced equidistantly at a distance of
105 mm one from another. G1 and G3 are absorptive masks
that are fabricated from a 190 nm thin SiNx membrane. The
central grating, which is responsible for diffraction, is realized
as a standing light wave that is generated by a retro-reflected
laser beam at lL E 532 nm. The light field imposes a position
dependent phase on the matter wave that is governed by the
laser power P and the optical polarizability aopt at the chosen
laser wavelength. For many molecules this value approximates
very closely the static value astat, when the dipole allowed
electronic resonances are sufficiently separated from the laser
wavelength. This is also the case for our structures 1 and 2.
The application of a pair of electrodes between gratings G1
and G2 allows us to subject the matter wave to a homogeneous
electric force field that is directed along the k-vector of the
grating laser and which is constant to within 1% across the
molecular beam. The electric field imprints an additional
phase onto the matter wave that results in a shift Dx3 of the
interference pattern at G3 parallel to the grating vector. This
to catalytic amounts of tetrakis(triphenylphosphine)palladium
and copper iodide in a tetrahydrofuran–diisopropylamine
mixture. Workup and purification by CC provided 2 as a
white solid in a yield of 22%.
The target structure 1 and the precursors 6–12 were soluble
1
in common organic solvents and were characterized by H-,
13C- and 19F-NMR spectroscopy, elemental analysis (EA)15
and mass spectrometry. 1H- and 19F-NMR spectra of the
poorly soluble compound 2 were recorded in mixtures of
deuterated chloroform with fluorinated solvents like hexafluoro-
benzene or 1,1,2-trichloro-1,2,2-trifluoroethane (Freon 113s).
Furthermore, the identity of 2 was corroborated by MALDI-ToF
mass spectrometry.
To distinguish between both constitutional isomers, the
substances were evaporated under high vacuum conditions
in a ceramic furnace at a temperature of T = 185 ꢃ 5 1C. The
molecular beam passed through a series of delimiters that
restricted the trajectory to the free-fall parabola that corresponds
to the desired velocity. The particles then traversed a Kapitza–
Dirac–Talbot–Lau (KDTL) interferometer,16 shown in Fig. 1,
before they were ionized by electron impact and injected into a
quadrupole mass spectrometer (QMS).
shift is proportional to the total electric susceptibility wtot
Dx3 p wstatU2/mv2
:
(I)
where m is the mass, n is the molecular velocity and U the
voltage applied between the electrodes.17 In order to obtain
absolute numbers, a geometry factor has to be determined
experimentally, in our case in a calibration measurement with
C60.
The matter wave interferometer consists of three gratings,
G1–G3, all with identical slit periods of d = 266 nm and slit
openings as small as about 100 nm. The first grating (G1)
prepares the necessary lateral wave coherence of the molecular
beam at the location of G2. Diffraction of the molecules at G2
then results in a regular density distribution of periodicity d at
G3. When G3 is scanned across this molecular pattern, the
detector records a sinusoidal intensity variation
Generally, the total electric susceptibility is determined by
the electronic contribution to the polarizability astat and,
according to the van Vleck formula18
wtot = astat + hd2i/3kBT
also by a thermal average over the square of all possible
electric dipole moments, be they permanent moments or those
related to thermally activated vibrations.6
As the polarizability is influenced by the molecular struc-
ture, in our case by the extent of delocalization of the central
p-systems, we expect even constitutional isomers to behave
differently under the influence of the external field. Effects of
the fluorous ponytails on the polarizability are expected to
be negligible mainly for two reasons: First, their electronic
coupling to the aromatic subunit is poor, and second their
S(x3) = O + Aꢄsin [2p(x3 ꢀ Dx3)/d]
as shown at the right-hand end of Fig. 1. Here, x3 denotes the
grating position, Dx3 is the position offset of the interference
fringe, which also depends on external forces, and we define
the quantum interference visibility V = A/O as the ratio of the
fringe amplitude A and its vertical offset O.
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the data point at U = 10 kV in the evaluation of the mean
value of w.
Interestingly, for both isomers the susceptibility values differ
from the computed static polarizabilities. This is consistent
with the presence of vibration-activated electric dipole moments
which emerge for flexible molecules at high temperature.6
Based on our earlier experiments with perfluoroalkyl-
functionalized azobenzenes19 we expect a thermal contribution
to the susceptibility of 10–15 A3 ꢁ 4pe0 per side chain.
Summarizing, the different total susceptibilities of both
constitutional isomers lead to different de Broglie interference
shifts in the presence of external fields. The isomers thus are
distinguishable even by pure center-of-mass interferometry, in
spite of their identical mass and chemical sum formula.
Our work was supported by the Austrian FWF within the
programs Wittgenstein Z149-N16, DK-W1210 CoQuS, the
Swiss National Science Foundation and ESF EuroQuasar
MIME.
Fig. 2 Experimental values of wstat for compounds 1 (blue full circles)
and 2 (red hollow circles) extracted from the interference fringe shift at
different settings of the deflection voltage. The error bars represent the
statistical errors (1s). The solid blue and red lines show the weighted
means of the susceptibility values of 1 and 2, respectively (see
Supporting Information).
contributions will be comparable for both constitutional
isomers 1 and 2.
Notes and references
Compounds 1 and 2 were examined in two separate experi-
mental runs. They were evaporated at identical temperatures,
but we chose slightly different velocity distributions. These
were centered at nmean = 110 m sꢀ1 for compound 1 and
nmean = 91 m sꢀ1 for 2 with DnFWHM/nmean = 0.15 and
DnFWHM/nmean = 0.10, respectively. This corresponds to a
mean de Broglie wavelength of about 2.5 pm.
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Each individual interference pattern was sampled in steps of
Dx3 = 26 nm over a range of 1064 nm, corresponding to four
full interference fringe periods. The interference patterns were
recorded at different voltage settings.
At high voltages the fringe visibility is reduced by a velocity
dependent dephasing of the interference pattern and the finite
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(eqn (I)), a large velocity spread will blur the interference
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In order to minimize the effect of thermal drifts of the
grating position, the field-dependent fringe shift was read for
each deflection voltage separately. For each position of G3 the
molecular beam transmission was measured both at the
desired deflection voltage and for a reference value of U = 1 kV.
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voltage step by fitting eqn (I) to the experimental value of Dx3
with wstat as the only free parameter. The calculation included
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runs for both molecules are depicted in Fig. 2. We find a
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and wstat = 126 ꢃ 0.5 A3 ꢁ 4pe0 for 2. We show only the
statistical error bar, which decreases because of the more
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Chem. Commun., 2010, 46, 4145–4147 | 4147