Ultra-fast rotors for molecular machines and functional materials via halogen bonding: Crystals of 1,4-bis(iodoethynyl)bicyclo[2.2.2]octane with distinct gigahertz rotation at two sites

Article abstract of DOI:10.1021/ja200503j

As a point of entry to investigate the potential of halogen-bonding interactions in the construction of functional materials and crystalline molecular machines, samples of 1,4-bis(iodoethynyl)bicyclo[2.2.2]octane (BIBCO) were synthesized and crystallized. Knowing that halogen-bonding interactions are common between electron-rich acetylenic carbons and electron-deficient iodines, it was expected that the BIBCO rotors would be an ideal platform to investigate the formation of a crystalline array of molecular rotors. Variable temperature single crystal X-ray crystallography established the presence of a halogen-bonded network, characterized by lamellarly ordered layers of crystallographically unique BIBCO rotors, which undergo a reversible monoclinic-to-triclinic phase transition at 110 K. In order to elucidate the rotational frequencies and the activation parameters of the BIBCO molecular rotors, variable-temperature ¹H wide-line and ¹³C cross-polarization/magic-angle spinning solid-state NMR experiments were performed at temperatures between 27 and 290 K. Analysis of the ¹H spin-lattice relaxation and second moment as a function of temperature revealed two dynamic processes simultaneously present over the entire temperature range studied, with temperature-dependent rotational rates of k_rot = 5.21 × 10¹⁰ s^-1·exp(-1.48 kcal·mol ^-1/RT) and k_rot= 8.00 × 10¹⁰ s ^-1·exp(-2.75 kcal·mol^-1/RT). Impressively, these correspond to room temperature rotational rates of 4.3 and 0.8 GHz, respectively. Notably, the high-temperature plastic crystalline phase I of bicyclo[2.2.2]octane has a reported activation energy of 1.84 kcal·mol^-1 for rotation about the 1,4 axis, which is 24% larger than E_a = 1.48 kcal·mol^-1 for the same rotational motion of the fastest BIBCO rotor; yet, the BIBCO rotor has three fewer degrees of translational freedom and two fewer degrees of rotational freedom! Even more so, these rates represent some of the fastest engineered molecular machines, to date. The results of this study highlight the potential of halogen bonding as a valuable construction tool for the design and the synthesis of amphidynamic artificial molecular machines and suggest the potential of modulating properties that depend on the dielectric behavior of crystalline media.

Full text of DOI:10.1021/ja200503j

ARTICLE
pubs.acs.org/JACS
Ultra-fast Rotors for Molecular Machines and Functional Materials via
Halogen Bonding: Crystals of 1,4-Bis(iodoethynyl)bicyclo[2.2.2]octane
with Distinct Gigahertz Rotation at Two Sites
Cyprien Lemouchi,† Cortnie S. Vogelsberg,‡ Leokadiya Zorina,†,§ Sergey Simonov,†,§ Patrick Batail,*,†
Stuart Brown,*,|| and Miguel A. Garcia-Garibay*,‡
†Laboratoire MOLTECH-Anjou, Universitꢀe d’Angers, CNRS, 2 Boulevard Lavoisier, 49045 Angers, France
‡Department of Chemistry, University of California—Los Angeles, 607 Charles E. Young Drive East, Los Angeles, California 90095-
1569, United States
§Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, 142432 MD, Russia
Department of Physics, University of California—Los Angeles, Box 951547, Los Angeles, California 90095-1569, United States
S Supporting Information
b
ABSTRACT: As a point of entry to investigate the potential of
halogen-bonding interactions in the construction of functional
materials and crystalline molecular machines, samples of 1,4-bis-
(iodoethynyl)bicyclo[2.2.2]octane (BIBCO) were synthesized and
crystallized. Knowing that halogen-bonding interactions are com-
mon between electron-rich acetylenic carbons and electron-defi-
cient iodines, it was expected that the BIBCO rotors would be an
ideal platform to investigate the formation of a crystalline array of
molecular rotors. Variable temperature single crystal X-ray crystal-
lography established the presence of a halogen-bonded network,
characterized by lamellarly ordered layers of crystallographically unique BIBCO rotors, which undergo a reversible monoclinic-to-
triclinic phase transition at 110 K. In order to elucidate the rotational frequencies and the activation parameters of the BIBCO
molecular rotors, variable-temperature 1H wide-line and 13C cross-polarization/magic-angle spinning solid-state NMR experiments
were performed at temperatures between 27 and 290 K. Analysis of the 1H spinꢀlattice relaxation and second moment as a function
of temperature revealed two dynamic processes simultaneously present over the entire temperature range studied, with
temperature-dependent rotational rates of krot = 5.21 ꢁ 1010 sꢀ1 exp(ꢀ1.48 kcal molꢀ1/RT) and krot = 8.00 ꢁ 1010 sꢀ1 exp-
3
3
3
(ꢀ2.75 kcal molꢀ1/RT). Impressively, these correspond to room temperature rotational rates of 4.3 and 0.8 GHz, respectively.
3
Notably, the high-temperature plastic crystalline phase I of bicyclo[2.2.2]octane has a reported activation energy of 1.84 kcal molꢀ1
3
for rotation about the 1,4 axis, which is 24% larger than Ea = 1.48 kcal molꢀ1 for the same rotational motion of the fastest BIBCO
3
rotor; yet, the BIBCO rotor has three fewer degrees of translational freedom and two fewer degrees of rotational freedom! Even
more so, these rates represent some of the fastest engineered molecular machines, to date. The results of this study highlight the
potential of halogen bonding as a valuable construction tool for the design and the synthesis of amphidynamic artificial molecular
machines and suggest the potential of modulating properties that depend on the dielectric behavior of crystalline media.
’ INTRODUCTION
research groups in Angers and in Los Angeles have been working
on the development of multicomponent crystalline conductors5ꢀ7
and the design of amphidynamic crystals with rapidly moving
parts.8ꢀ10 Now, we have joined forces to explore systems where
the dielectric modulation inherent to the rotor dynamics11,12
may affect the electrostatic potential of a charge carriers’ envir-
onment, which is expected to cause transitions between con-
ducting and localized states.5,13 Although this is a subject of
much current interest that has been stimulated by sound
theories,14,15 it has been only approached experimentally by
The field of artificial molecular machines represents one of the
most interesting challenges in basic science and modern
technology.1,2 While there has been much progress made in
the design of sophisticated small molecule analogs of macro-
scopic machines,1,2 one of the most promising perspectives is
based on the realization that complex molecular-level properties
and functions can be manifested in a collective manner at the
macroscopic scale in the form of complex functional materials.3,4
With materials applications in mind, one of the greatest chal-
lenges is the need to develop crystal engineering strategies to
control not only the number of components and their organiza-
tion but also their internal dynamics. In the past few years, our
Received: January 18, 2011
Published: April 06, 2011
r
2011 American Chemical Society
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analysis of charge-transfer processes and hole migration affected
by collective hydrogen-bond activation16 and dynamics.17 As a
starting point to engineer functional crystals modulated by ultra-
fast molecular rotors, we propose to take advantage of strategies
based on halogen-bonding interactions.18 The latter has been
used for the design of multicomponent crystalline conductors5,19
and appears to be significantly robust. Halogen bonds occur
between electron-deficient halogens and electron-rich atoms
with interaction energies that vary between ca. 1ꢀ43 kcal/mol,
depending on the electron density of the donor.20,21 To transi-
tion into molecular rotors, we set out to analyze the use of
halogen bonding as a lattice-directing interaction to control the
organization of a rotor array.8ꢀ10 It has been shown that
molecular structures inspired by macroscopic gyroscopes with
high-symmetry rotators22 linked by triple bonds to bulky stator
groups facilitate internal rotation in the crystalline state
(Scheme 1a). For this study we selected bis(1,4-iodoethynyl)
bicyclo[2.2.2]octane (BIBCO) as a promising test case. Based on
a previous report with the analogous 1,4-bis(iodoethynyl)
benzene,5,23 we recognized that iodine atoms covalently linked
to each terminal acetylenic carbon would provide the elements
required for a halogen-bonded network through iodine—acet-
ylene interactions at the two ends of each rotator, as shown in
Scheme 1b.24,25 The C3-symmetric bicyclo[2.2.2]octane rotator
was selected knowing that cylindrically shaped, higher-order Cn
rotators, with n > 2, pack in a manner that does not generate high
rotational barriers.22
(C2/c) to triclinic (P1) structures, with rotational disorder in
the high-temperature phase. To measure the rotational dynamics
of the cylindrical bicyclo[2.2.2]octane rotator, and expecting
frequencies in the megahertz (MHz) regime at ambient tem-
1
perature, we decided to use H NMR spinꢀlattice relaxation
(T1) as a function of temperature. Spinꢀlattice relaxation can be
used to probe dynamic processes occurring at frequencies that
are near the Larmor frequency of the nucleus being studied: 1H at
26.4 and 300 MHz in our experiments. In addition, spinꢀlattice
relaxation is particularly useful when the stimulated nuclear
transitions responsible for restoring thermal equilibrium in the
sample are determined by the modulation of dipolar interactions
caused by the rapid motion of internal rotors.26 The fastest
relaxation (a minimum in T1) occurs at the temperature when
the rotator matches the Larmor frequency. In the case of BIBCO
1
crystals, analysis of the H spinꢀlattice relaxation between 27
and 290 K revealed two T1 minima, indicating that there are two
distinct but simultaneous rotational processes over the entire
temperature range. This observation is in general agreement with
crystal structure, where BIBCO molecules are in two different
sites with different environments.
’ RESULTS AND DISCUSSION
Sample Preparation. Samples of bis(1,4-iodoethynyl)bicyclo-
[2.2.2]octane (BIBCO) were obtained in 76% yield by iodination of
1,4-diethynylbicyclo[2.2.2]octane (BCO) 9 with N-iodosuccinimide
(NIS). The terminal dialkyne was synthesized from diethylsuccinate
in a nine-step sequence developed in Angers using diverse literature
procedures, as illustrated in Scheme 2, with an overall yield of 11%. The
modified synthesis is analyzed in detail in the Supporting Information
Section along with all the spectroscopic and analytical data. Colorless,
diamond-shaped single crystals of BIBCO were obtained by recrystalli-
zation from hot ethanol.
As described in detail below, the desired packing arrange-
ment was obtained according to expectations. Extensive X-ray
diffraction experiments and structure analysis as a function of
temperature demonstrated that crystals of BIBCO undergo a
disorderꢀorder phase transition at 110 K from monoclinic
Scheme 1
X-ray Structures Determination at 295, 130, and 90 K.
Single crystal X-ray diffraction data was collected on a Bruker Nonius
KappaCCD diffractometer [λ(Mo KR) = 0.71073 Å] equipped with an
Oxford Cryosystems cryostream cooler. Unit cell parameters were
measured in the temperature range of 295ꢀ90 K with 5ꢀ30° steps
(Figure SI-1, Supporting Information). A reversible phase transition
from a monoclinic C2/c to a triclinic P1 structure was identified upon
cooling below 110 K. Full X-ray data sets were collected at 295, 130, and
90 K by a combined j- and ω-scan method. The triclinic structure is
twinned; diffraction intensities from both twin domains were integrated
into SHELX HKLF5 file using the EVALCCD software.27 Analytical
absorption corrections were applied for the 90 K data using WINGX,28
Scheme 2. Nine Step Sequence of BCOa
a Reagents for each step include: (a) NaH, dimethoxyethane, 60 °C, 15 h, 78% yield; (b) NaH, 1,2-dibromoethane, 110 °C, 96 h, 85% yield; (c) p-TsOH,
diethyleneglycol, toluene, reflux, 48h, 71% yield; (d) LiAlH4, Et2O, reflux, 5 h, 93% yield; (e) HCl 0.1 M, reflux, 24 h, quant.; (f) KOH, hydrazine
monohydrate, diethyleneglycol, reflux, 48 h, 41% yield; (g) Oxalylchloride, DMSO, CH2Cl2, Et3N, quant.; (h) CBr4, PPh3, CH2Cl2, R.T, 5 h, 65% yield;
and (i) n-BuLi (2.5 M), THF, ꢀ78 °C, 1 h, 95% yield. (See Supporting Information).
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spinꢀlattice relaxation (T1) measurements were carried out at UCLA at
two different 1H Larmor frequencies (300 and 26.4 MHz) and over a wide
range of temperatures in the solid state. Wide-line 1H spectra from 27 to
220 K were measured in single crystals with a commercial electromagnet
using a NMR spectrometer and probe built at UCLA. The typical NMR
frequency used was 26.4 MHz with the electromagnet set to a field strength
B0 of 0.6225 T. A very small NMR coil was constructed using bare copper
wire wound on a wire form. A few single crystals were loaded into the coil at
random orientations and held in place with a Teflon tube and caps. Acetone
was used for cleaning the coil and its surroundings to reduce spurious
proton signals relative to the BIBCO sample. 1Hspinꢀlattice relaxation was
measured using a saturation recovery sequence combined with a spinꢀecho
in which a saturation pulse comb (3 * π/2) was followed a time τ0 later
(τ0 values taken from the variable delay list) with a π/2 pulse p1 (typical pulse
width p1 = 1.3 μs) and subsequently a pulse p2. The angle of p2 is
adjustable to maximize the spinꢀecho magnitude, and pulses were
calibrated at different temperatures as necessary. Saturation recovery
traces from 220 to 50 K were fit well with a single exponential function
(Figure SI-4, Supporting Information). Data traces below 50 K began to
deviate from a monoexponential. Measurements between 189 to 290 K were
performed on a polycrystalline BIBCO sample and acquired with a Bruker
Avance 300 solid-state NMR spectrometer. 1H spinꢀlattice relaxation was
measured via the inversionꢀrecovery method using 13C CP/MAS detec-
tion. The 13C CP/MAS spectra were acquired at a 13C frequency of
75 MHz and a 1H frequency of 300 MHz. Details regarding the experimental
parameters of spectra acquisition may be found in the Supporting Informa-
tion. At each temperature between 189 to 290 K, the data was fit well with a
monoexponential function (Figure SI-5, Supporting Information).
Halogen Bonding as Crystal Engineering Strategy. The
crystal structure at ambient temperature was solved in the monoclinic
space group C2/c with eight molecules per unit cell. A view of the
structure along b in Figure 1a illustrates a layered topology where two
independent slabs, A and B, alternate along a. The layers differ by the
type of packing as well as the positional ordering of the bicyclo-
[2.2.2]octane rotators. Each layer contains one crystallographically
independent BIBCO molecule. Molecules in layer A lie on a two-fold
monoclinic axis and are fully ordered. Molecules in layer B are located on
inversion centers, and their acentric inner bicyclo[2.2.2]octane rotator
fragment is disordered between two distinct equilibrium positions of
equal weights. In order to investigate the fate of the disorder for
molecules B as a function of temperature, the structure was studied in
a wide temperature range. A series of unit cell parameters measured
between 295 and 90 K revealed a monoclinic to triclinic structural phase
transition at 110 K identified by the appearance of additional weak Bragg
reflections. Full X-ray diffraction data were collected at 295, 130, and 90
K. As the crystal structures at room temperature and 130 K are almost
identical, a detailed comparative analysis of the monoclinic structure at
130 K and the triclinic one at 90 K, above and below the phase transition
temperature, is presented below.
Figure 1. The high-temperature, monoclinic BIBCO structure. (a)
Structure projection along the b axis of unit cell. Layer A: layer of
molecules A with one equilibrium position; and layer B: layer of
molecules B with two equilibrium positions. The structure is directed
by a set of CꢀI π shown here in dashed red lines (I C distances at
3 3 3
3 3 3
130 K are 3.330(3) and 3.469(3) Å (IA CB) and 3.425(3) Å
3 3 3
(IB CA); CꢀI, 1.991(3) and 1.994(3) Å) and CꢀI IꢀC halogen
3 3 3
3 3 3
bonds drawn in dashed purple lines (I I, 3.9483(3) and 4.0028(4) Å).
3 3 3
(b) The BIBCO rotor axles in layer A are slightly bent. (c) While the
rotator is chiral as a result of a helical twist, the centrosymmetric crystal
contains a racemic mixture of the δ and λ conformers.
while empirical multiscan absorption correction with SADABS29 was
used for the 295 and 130 K data. The structures were solved by a direct
method followed by Fourier syntheses and refined by a full-matrix least-
squares method in an anisotropic approximation for all nonhydrogen
atoms using the SHELX-97 programs.30 Hydrogen (H)-atoms in the
bicyclo[2.2.2]octane fragments were introduced in calculated positions
with Uiso(H) = 1.2 Ueq(C). Table S1, Supporting Information sum-
marizes the main crystal and refinement data.
Solid-State 13C CP/MAS NMR. The 13C cross-polarization/
magic-angle spinning (CP/MAS) spectra of a finely powdered crystal-
line BIBCO sample, acquired at UCLA on a Bruker Avance 300 solid-
state spectrometer operating at a 13C frequency of 75 MHz, displayed
three sharp signals at δ 102.50, 32.68, 29.14 ppm, corresponding to the
inner acetylenic C(sp), methylene C(sp3), and bridge head C(sp3),
respectively. These are similar to the 13C signals at 100.70, 31.43, 28.40
ppm, respectively, observed in a CD2Cl2 solution at 125 MHz. It is of
interest to note the signal corresponding to the acetylenic C(sp) bonded
to the iodine appears as a weak, broad signal at 0.79 ppm in the solid state
(Figure SI-2, Supporting Information) yet appears at ꢀ6.35 ppm in a
CD2Cl2 solution (Figure SI-3, Supporting Information).31 This is an
indication that the solid-state shielding effects of iodine may be due, to a
As shown in Figure 1b, the rotor axle is not linear, but it is instead
slightly bent toward one of the three bicyclo[2.2.2]octane rotor blades.
Another salient feature is the axial chirality of the bicyclo[2.2.2]octane
rotator, with a C3 point group that originates from a common tilt of the
three rotator blades. However, the crystal contains a racemic mixture of
the right (δ in Figure 1c) and left (λ) conformers, as required by the
centrosymmetric space group.33 The BIBCO molecules from adjacent
layers are orthogonal to each other in such a way that CꢀI
π
3 3 3
intermolecular interactions shown by red dashed lines in Figure 1a
significant extent, to CꢀI IꢀC halogen-bonding interactions. In
3 3 3
and CꢀI IꢀC halogen bonds are both satisfied. The I atoms of the
agreement with previous studies, MAS failed to completely remove
the dipolar coupling between the spin-1/2 13C nucleus and the quad-
rupolar spin-5/2 127I nucleus, thus resulting in the observed signal
broadening.32
3 3 3
ordered A molecule form two similar short I C contacts to both C
3 3 3
atoms of the triple CtC bond of the molecule in the other layer,
3.330(3) and 3.469(3) Å for (IA CB) at 130 K. In contrast, one of two
3 3 3
VT 1H SpinꢀLattice Relaxation (T1). To determine the rotational
dynamics and activation energy of the molecular rotors in BIBCO,
(IB CA) contacts from I atoms of the disordered B molecule is much
3 3 3
shorter than the other: 3.425(3) and 3.666(3) Å.
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Figure 3. Triclinic crystal structure at 90 K (drawn with 50% ellipsoid
0
probability). The set of shortest CꢀH I hydrogen bonds with HC ,
3 3 3
0
0
D0
IB ,A = 3.04ꢀ3.11 Å is shown by dashed lines.
3 3 3
the two rotator orientations, pointing to two relatively shallow minima for
the two equilibrium populations that are dynamically averaged out over
time during the X-ray data collection. At 130 K, the positional disorder
remains, but the anisotropic displacements parameters are smaller, as
expected for a smaller librational displacement. Finally, at 90 K, only one
equilibrium position remains, indicating that one of the two sites becomes
substantially lower in energy in the new P1 crystal phase. Relevant, striking
changes in experimental electron density maps are shown in Figure SI-8,
Supporting Information.
The low-temperature triclinic structure is shown projected along b in
Figure 3. Below the transition, each layer consists of two independent
molecules in general positions, each with only one equilibria position.
Layers A0B0 and C0D0 in the P1 crystal phase, respectively, correspond to
layers A and B of the C2/c structure shown in Figure 1a. Note that the
crystal remains achiral across the phase transition since the triclinic
structure is also centrosymmetric.
Figure 2. (a) Lattice transformation at the monoclinic to triclinic phase
transition. Monoclinic cell vectors are drawn in black, while two triclinic
lattices, 1 and 2, are marked by red and blue colors, respectively. The a
and b axes of the new triclinic lattice go along the diagonal directions of
bc monoclinic layer (i.e., the lattice periodicity becomes twice in both bm
and cm directions), while the new c-axis corresponds to C-centering
vector of the monoclinic C-lattice (see unit cell parameters in
Table S1, Supporting Information). Twin lattices 1 and 2 are related
by a 180° rotation around the bm-axis, which was the monoclinic
axis in the original monoclinic cell. The refined twin fraction is
0.4685(5). (b) Positional ordering upon the transition. As temperature
is decreased from 295 to 130 K, the anisotropic displacement parameters
of the rotor atoms become smaller. At 90 K, only one equilibrium
position remains.
The patterns of intermolecular interactions inside layers A0B0 and C0D0
are different (Figure 4). The rotor axles within layer A0B0 are close to
parallel. In contrast, the axles of molecules C0 and D0 are orthogonal. As a
result, rotors from the A0B0 and C0D0 layers have fundamentally different
molecular environments (see also Figures SI-9 and 10, Supporting
Information). Both layers consist of segregated rows of the alternating,
These CꢀI π intermolecular interactions can be seen as a
3 3 3
particular case of directional halogen bonding where the electron-
depleted polar regions of the polarized iodine atoms reach out toward
the electron-rich pπ orbitals of primarily one or eventually two carbon
atoms of the triple bond. Though an early example of this interaction was
documented in tetragonal crystalline diiodoacetylene (C2I2),24 this type
of halogen bond has been largely overlooked.21,25 A more recent
example comes from our earlier analysis of the crystal structure of 1,4-
bis(iodoethynyl)benzene (Figure SI-6, Supporting Information), which
inversionally related δ and λ molecules of the same name:
A0A0A0
3 3 3
rows run along b in layer A0B0 (Figure 4a), while
3 3 3
and
B0B0B0
3 3 3
3 3 3
and
C0C0C0
D0D0D0
rows are parallel to [110] in layer C0D0
3 3 3
3 3 3
3 3 3
3 3 3
(Figure 4b). The motif linking the ethynyl stator fragments via CꢀI
π
is similar to that of BIBCO. We also note that a loose, single Csp3ꢀI
I
3 3 3
3 3 3
and CꢀI IꢀC interactions remains intact across the transition,
halogen interaction is identified in the layered structure of 1,4-
diiodobicyclo[2.2.2]octane (Figure SI-7, Supporting Information).34
Cooling the crystal below 110 K reveals additional Bragg reflections
associated with a phase transition from the monoclinic C2/c to a twinned
triclinic P1 structure. Note that the orthogonality between the monoclinic
b-axis and the ac-plane is not affected and that the lattice distortion upon
the transition is minimal (Figure SI-1, Supporting Information). However,
the pattern of systematic diffraction absences as well as structural ordering
resulting from the transition could only be correctly described in a triclinic
lattice twinned by a two-fold rotation around the former monoclinic axis
(Figure2a). Themostimportant structuralchangesinthelow-temperature
phase concern the rotators in layer B (Figure 2b). Specifically, they lose
local inversion symmetry and become ordered below the phase transition.
As shown in Figure 2b, the bicyclo[2.2.2]octane atoms in the C2/c
structure at 295 K display large anisotropic displacement parameters for
3 3 3
although the contact distances change in a way (see Figure SI-10 and
Table S2, Supporting Information for a comparison of contact distances at
different temperatures). The intermolecular interaction between rotors
and stator fragments occurs by hydrogen bonding with I atoms as
acceptors. The shortest CꢀH I bonds (dashed lines in Figure 3)
3 3 3
involve iodine atoms of molecules A0 and B0 and ꢀCH2 groups of formerly
0
disordered molecules C0 and D0 (HC
IB ,A = 3.07 and 3.09 Å; HD
0
0
3 3 3
0 3 3 3
0
0
IA ,B = 3.04 and 3.11 Å). These are likely to interfere in the process of
ordering the C0 and D0 rotors. For a comparison, other similar contacts of
0
0
0
0
0
0
0
0
0
0
0
the HA ,B
IC ,D, HA ,B
IA ,B , and HC ,D
IC ,D types both between
3 3 3
3 3 3
3 3 3
and inside the layers exceed 3.25, 3.27, and 3.24 Å, respectively.
Effects of Molecular and Crystal Symmetries on Rota-
tional Potentials. While crystals of BIBCO have two crystallographi-
cally independent moleculesabovethe phase transition and fourbelow, the
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Figure 5. (a) Proposed high-temperature rotational potential for the
ordered layer A (green) and disordered layer B (black) layers. (b)
Proposed low-temperature rotational potential for the ordered three-
fold layer A (green) and the formally ordered six-fold layer B (black)
rotators. Each layer has two crystallographically distinct molecules, but
each pair has a very similar environment.
Figure 4. These projections of the A0B0 layer (a) and C0D0 layer (b)
along c* exemplify the difference in molecular arrangement.
When cooling a BIBCO crystal to lower temperatures, the disorder of
molecules in the B layer lessens and then gradually disappears
(Figure 2b). Below the phase transition at 110 K, the inversion center
on molecule B is absent, and all molecules are ordered. The rotational
potential of the originally ordered, three-fold symmetric site of rotators
in the high-temperature A layer (A0B0 layer at T < 110 K) remains
essentially unchanged (shown in green), but the potential of the six-fold
symmetric site of rotators in the high-temperature B layer (C0D0 layer at
T < 110 K) is no longer isoenergetic with respect to the six sites. The
molecules at low temperature have a preferred orientation that corre-
spond to three low-energy minima, but the other three minima are
maintained, though slightly higher in energy, as shown in black in
Figure 5b. The crystal structure reveals the population corresponding to
the preferentially occupied sites, but rotational dynamics are likely to
occur in 60° jumps. The residence time in the higher energy sites should
be shorter, and their equilibrium populations smaller (note that a
two forms are essentially congruent. The local interactions remain relatively
unaltered at the disorderꢀorder phase transition. Although it could have
been expected that the spinꢀlattice relaxation in the BIBCO crystal might
have required double and triple exponential functions to fit the kinetics of
crystallographically independent rotors, relaxation was monoexponential
over a wide temperature range, suggesting a system under magnetic
equilibrium and with a common spin temperature. However, two energy
minima in the 1H T1 versus temperature plot (vide infra) clearly indicate
that relaxation is determined by two kinetically distinct rotational pro-
cesses, which contribute equally to the T1 relaxation of the crystal. Based on
these observations, our NMR analysis will rely on the assumption that the
steric environment of the rotator can be described in terms of two types
rotors located in the two different layers, A (A0B0 when T < 110 K) and B
(C0D0 when T < 110 K), over the entire temperature range investigated. In
layer A, the bicyclo[2.2.2]octane rotators are always ordered with a local
three-fold symmetry characterized by jumps that occur via 120° displace-
difference of ca. 0.5 kcal molꢀ1 between the high- and low-energy
3
minima would result in equilibrium populations of ca. 94:6 at T = 90 K,
which would be difficult to detect crystallographically).
VT 1H SpinꢀLattice relaxation (T1). The equilibration of
magnetic nuclei in condensed phases occurs by stimulated transitions
that result from the local magnetic fields generated by dynamic processes
of nearby spins in the lattice. It is well-known that spinꢀlattice relaxation
in solid samples may be dominated by a particular dynamic process if
some portions of the lattice are fairly static while others experience rapid
motion. When a single process with a correlation time τc is responsible
for the T1 relaxation, it is possible to determine the parameters that
ments and a barrier of 2.75 kcal molꢀ1 (vide infra). The potential assigned
3
to this site at high temperature is shown in green in Figure 5a. In layer B, the
bicyclo[2.2.2]octane rotators are positionally disordered at high tempera-
tures and, by symmetry, have a six-fold rotational potential with six
isoenergetic minima that have equal populations. The barrier of this site
is 1.48 kcal molꢀ1, and the potential assigned to this site is shown in black
3
in Figure 5a.
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While theꢀv1ariable-temperature data at 300 MHz is limited, the full range
of the T1 data estimated with the KuboꢀTomita equation at 26.4
MHz versus 300 MHz (vide infra) accounts for the small divergence
between green tilted squares and yellow circles below 200K, as expectꢀed1
for a change in the position of the inflection point for the two T1
maxima at the two different spectrometer frequencies.
VT 1H T1 Data Analysis. Recognizing that the structures of the two
BIBCO polymorphs are closely related and that both arrange in
alternating lamellarly ordered layꢀer1s of rotators with different packing
motifs, we interpret the two T1 maxima as corresponding to the
rotational motion of the bicyclo[2.2.2]octane rotators about their 1,4-
axis in the two different crystallographic layers A and B. The low-energy
rotational process is associated with the less sterically hindered layer B,
which displays rotational disorder in both of the high-temperature
crystal structures obtained at 295 and 130 K, while the higher energy
process is associated with rotation in the more sterically hindered,
ordered layer A. This assignment is supported by the fact that the
shortest T1 relaxation times for each process are essentially equivalent
(53 ms versus 51 ms), suggesting that they do arise from two different
processes with effectively equal dipolar averaging but different frequen-
cies. Assuming that the reorientation of the BIBCO rotators in each
environment provides the dominant spinꢀlattice relaxation and that the
protons exist at a common spin-temperature within the lattice, the T1
behavior observed for the system may be expressed as the weighted sum
of the two distinct rotational processes:37
1
Figure 6. Temperature dependence of the H spinꢀlattice relaxation
time (T1) in BIBCO displaying two T1ꢀ1 maxima observed at 26.4 MHz
(yellow circles) and 300 MHz (green tilted squares). The heavy blue and
red lines correspond to a KuboꢀTomita fit for the two processes at 26.4
MHz, assuming Arrhenius-type behavior. The dotted black line corre-
sponds to the weighted sum of these two processes observed at 26.4
MHz and displays an excellent fit to the data. The light-blue and light-red
dotted lines correspond to a KuboꢀTomita fit for the two processes at
300 MHz, assuming Arrhenius-type behavior. The dotted gray line
corresponds to the weighted sum of these two processes observed at
300 MHz.
Tꢀ1 1
¼ ð0:5ÞTꢀ1 1fast þ ð0:5ÞTꢀ1
ð3Þ
total
slow
1
characterize its potential by measuring the T1 as a function of tempera-
ture. Specifically, if a motional process responsible for relaxation has a
correlation time τc equal to the inverse Larmor frequency of the
observed nucleus, then the relaxation will be most efficient and a
minimum in the spinꢀlattice relaxation time will be observed.26 Con-
sequently, the activation energy Ea for a thermally activated process
having a τc with Arrhenius-type temperature dependence (eq 1) may be
derived by fitting the T1 data to the KuboꢀTomita eq 2:
where the weighting factors (0.5) are related to the total fraction of
different nuclei responsible for motional averaging of the dipolar
interactions within the unit cell. The component T1 fast is the tempera-
ture-dependent spinꢀlattice relaxation for the low-energy rotational
process from rotators in layer B, and T1
is the temperature-
slow
dependent spinꢀlattice relaxation for the higher energy process for
rotators in layer A. The total number of molecules is the same in the
different layers. Therefore, each layer and its associated motional process
contribute equally to the total spinꢀlattice relaxation observed over the
entire temperature range studied.
τc ¼ τ0 expðEa=kTÞ
ð1Þ
ꢀ1
ꢀ1
ꢀ1
2
2
2
2
T1 ¼ C½τcð1 þ ω0 τc Þ þ 4τcð1 þ 4ω0 τc Þ
ꢂ
ð2Þ
To elucidate the activation energy and attempt frequency for BIBCO
dynamics, each individual rotational process from the T1 data was
subjected to a KuboꢀTomita fit by applying eq 2 and assuming an
Arrhenius-type temperature dependence for the corresponding correla-
tion times, τc fast and τc slow.. The corresponding variations shown as a
relaxation rate, or T1ꢀ1, as a function of temperature are illustrated in red
and blue lines in Figure 6. Adding the two processes together with the
corresponding weighting factors (eq 3) gave an excellent match with the
observed experimental data when the Arrhenius equation values, τo and
Ea, were optimized for the fast and slow components (Figure 6, black
dotted line). Notably, the sum of the two processes is required to obtain
a good fit at higher temperatures, helping dismiss the possibility that the
low-barrier process is present only in the low-temperature polymorph.
From the constant C of the KuboꢀTomita equation, the magnitude of
the local effective dipolar field Bnuc= ꢀ[γhμ0/(4πR3)](1 ꢀ 3cos2θ)m1,
where R is internuclear distance, can be found. This value was extracted
from the fit of the experimental T1ꢀ1 versus temperature data and found
2
where the constant C = (2/3) γ2 Bnuc corresponds to the dipolar
interactions related to the relative positions of the nuclei that participate
in the relaxation. Bnuc is the local effective dipolar field, and γ and ω0 are
the gyromagnetic ratio and the angular Larmor precession frequency,
respectively, of the observed nucleus in a magnetic field.35
From the spinꢀlattice relaxation (T1) measuꢀre1ments performed
between 27 and 290 K, a logarithmic plot of T1 as a function of
temperature displayed an excellent agreement with the 1H T1 measure-
ments acquired by the inversionꢀrecovery method at 300 MHz
(Figure 6, green diamonds) and by the saturation recovery methodꢀa1t
26.4 MHz (yellow circles). Interestingly, the plot revealed two T1
maxima, suggesting that spinꢀlattice relaxation occurs by two distinct
motional processes with dominant contributions at different tempera-
tures. At 26.4 MHz, a low-energy process resonates with the 1H Larmor
frequency at ca. 80 K, resulting in a T1 minimum of 53 ms. A second,
higher energy process reaches the frequency of 26.4 MHz at ca. 130 K
and results in another T1 minimum of 51 ms. No discontinuity in T1
values was observed at the phase transition determined by X-ray
diffraction at 110 K, confirming that the transition arises from minor
structural changes that affect the symmetry of the unit cell without
affecting the sterics and dynamics of the bicyclo[2.2.2]octane rotators.
Temperature cycling around the phase transition revealed no hysteresis
in T1ꢀ1, again consistent with the X-ray crystallographic studies, further
to be ca. 3 gauss (G). This value is consistent with the magnitude Bnuc
=
[γhμ0/(4πR3)] calculated from the interhydrogen distances in the
BIBCO structure, where R g 2.70 Å corresponding to a Bnuc magnitude
of 2.7 G and lower for protons on adjacent carbons.
The low-energy process with a T1ꢀ1 maximum at ca. 80 K was fit to an
activation energy of 1.48 kcal molꢀ1 and a pre-exponential factor (or
3
attempt frequency) A = 5.21 ꢁ 1010 s
.
ꢀ1 38 The higher energy process,
suggesting that the two polymorphs are an enantiotropic pair.36 We
conclude that the position of the minimum in the relaxation rate (T1
versus temperature plot, also at ca. 110 K in Figure 6, is coincidental.
with a T1 minimum at ca. 130 K, has an activation energy of 2.75
ꢀ1
)
kcal molꢀ1 and an attempt frequency of A = 8.00 ꢁ 1010 sꢀ1 39
.
The
3
activation energies of the rotators in the two different layers are
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Table 1. Arrhenius and Eyring Parameters Derived from a KuboꢀTomita Fit of the T1 Data
Ea (kcal molꢀ1
)
ΔH‡ (kcal molꢀ1
)
A (sꢀ1
)
τ0 (s)
ΔS‡ (cal/K mol)
3
3
3
disordered layer
ordered layer
1.48
2.75
1.48
2.47
5.21 ꢁ 1010
8.00 ꢁ 1010
1.92 ꢁ 10ꢀ11
1.25 ꢁ 10ꢀ11
2.50
ꢀ0.45
consistent with the crystallographic data, which indicates two crystal-
lographically distinct environments with different steric barriers. The
activation parameters indicate that rotators in the disordered layer have a
frequency of ca. 4.3 GHz at ambient temperature, while the correspond-
ing frequency for the ordered layer is ca. 0.8 GHz. Comparatively, in the
high-temperature plastic crystalline phase I, pure bicyclo[2.2.2]octane
has an activation energy of 1.84 kcal molꢀ1 for rotation about the 1,4
3
axis.40 This is 24% larger than Ea = 1.48 kcal molꢀ1 for the same
3
rotational motion about the 1,4-axis of bicyclo[2.2.2]octane in the faster
BIBCO rotor. Yet, the BIBCO rotor has two fewer degrees of rotational
freedom!
Activation Parameters. Given that the two (three- and six-fold)
BIBCO rotators in the separate layers A and B have the same moment of
inertia and intrinsic (gas phase) molecular electronic barrier, a compar-
ison of their activation parameters is particularly interesting. Assigning
the high and low barriers to the ordered and disordered three- and six-
fold potentials, respectively, is consistent with the crystallographic data
and the two local BIBCO environments. Furthermore, differences in the
two pre-exponential factors (Afast and Aslow) are experimentally sig-
nificant. Specifically, the BIBCO rotators in the six-fold, low Ea layer
possess an attempt frequency that is ca. 35% smaller than that of the
ordered BIBCO rotators with the higher barrier. Given that the attempt
frequency represents the highest jumping frequency for the thermally
activated rotator in a particular environment, it is significant that rotators
in the two layers possess different rotational symmetry orders and
different potentials. According to transition-state theory, the attempt
frequency is related to the frequency of the librational mode that
describes the oscillation of the rotator, νLib, which is determined by
the shape of the potential. To gain a qualitative insight, we assume a
simple symmetric rotational potential with n-energy minima and a
barrier Emax as a function of the angle Θ, as described by a cosine
function of the form:
Figure 7. The 1H NMR second moment as a function of temperature.
= ꢀ0.45 cal/K mol for the higher energy, three-fold rotary process. The
3
ΔH‡ values are in excellent agreement with the Ea obtained from the
Arrhenius analysis, and the activation entropies are very small, and nearly
zero, for both the six- and three-fold rotators, respectively (Table 1). The
relatively small activation entropy for a single rotation step may be
interpreted as an indication that no correlated motion or changes in
order is required, and a small and positive value for the disordered layers
may reflect the “dissociative” nature of the lower energy potential.
Second Moment Analysis (M2). The proton second moment
(M2) is the mean square width of the proton wide-line curve and hence is
related to the spinꢀspin relaxation (T2).26 Like the spinꢀlattice
relaxation, both M2 and T2 are modulated by dipolar interactions, which
are averaged in the presence of molecular motion. While static molecules
in the solid-state display very broad signals, molecules undergoing fast
1
reorientation display narrowed signals. The H M2 for BIBCO was
measured as a function of temperature from 27 to 220 K at 26.4 MHz
(Figure 7). No distinguishable plateaus were observed, thus indicating
that BIBCO motion changes continuously throughout the entire
temperature range investigated. At 220 K, M2 is 0.97 G2. Cooling to
50 K resulted in observable line broadening, resulting in an increased M2
value of 4.5 G2. There is no discontinuity in M2 at the phase transition at
110 K, supporting the notion that there are no significant structural
changes that affect the dynamics of the rotators. Further cooling from 50
to 27 K resulted in a rapid increase in M2 up to 12 G2, indicating an
abrupt decrease in molecular rotation. Although temperatures below 27
K were not explored due to limitations of the NMR probe setup, the data
suggest that further line broadening would occur below 27 K, up to the
limit of the rigid lattice when BIBCO rotation is frozen or at the limit of
quantum mechanical tunneling if rotations may occur from zero point
energy levels.
EðΘÞ ¼ 1=2Emax½1 ꢀ cos nΘꢂ
ð4Þ
The frequency of the active librational mode, νLib, will depend on the
shape of the function as determined by Emax and n. Steeper potentials
will result the higher the librational frequencies and greater the pre-
exponential factors. Steeper potentials will arise from higher barriers and,
for a given barrier height, from a greater number of minima. In the case of
BIBCO, a barrier of Ea = 2.75 kcal molꢀ1 for the ordered three-fold
3
symmetric layers is almost twice as large as that for the disordered layers
with the six-fold energy minima, which has an Ea = 1.48 kcal molꢀ1
.
3
Using these values in eq 4 demonstrates that the depth and shape of the
potentials are very similar, suggesting that the corresponding librational
modes should have analogous frequencies and that the different attempt
frequencies result from the additional vibrational activation required to
reach the top of the barrier.
In order to qualitatively evaluate line-broadening effects as a function
of temperature, the motionally narrowed line width at 220 K was related
to the correlation time of the BIBCO rotors in the disordered layer B and
the magnitude of the local effective field Bnuc determined from the
KuboꢀTomita fit. In the high-temperature limit, when ω02 τc2 , 1:
2
A potentially important limitation of the Arrhenius analysis is that it
assumes the pre-exponential factor is constant over the entire tempera-
ture range studied. To account for such variations one may apply the
Eyring eq 5:
τc ¼ h=kBT expð ꢀ ΔS‡=RÞ expðΔH‡=RTÞ
ð5Þ
mean 1H linewidthhighT ꢃ Tꢀ2 1
ꢃ Tꢀ1 1
ꢃ ð2=3Þγ2Bnuc τc,fast
ð6Þ
highT
highT
to substitute the τc in the KuboꢀTomita expression (Figure SI-12,
Supporting Information). An excellent fit to the T1ꢀ1 data was obtained
with a ΔH‡ = 1.48 kcal molꢀ1and ΔS‡ = 2.50 cal/K mol for the low-
At T = 220 K, the mean width of the motionally narrowed 1H wide-line
spectrum is at a minimum of ca. 4.1 kHz. According to the above eq 6,
3
3
energy, six-fold rotary process and with ΔH‡ = 2.47 kcal molꢀ1and ΔS‡
3
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Journal of the American Chemical Society
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line-broadening effects due to a decrease in the rotational dynamics
should become relevant when the fastest rotator layer becomes suffi-
ciently slow to cease partial averaging of dipolar interactions, i.e., when
the averaged dipolar interactions become the same order of magnitude
as the motionally narrowed line width. Using the narrowed line width at
T = 220 K, eq 6 reveals this temperature to be approximately 70 K.
Consistent with the results of this calculation, the 1H M2 data reveal a
dramatic increase in spectral line width below 70 K. Above this
temperature, the rotational correlation time becomes very small, and
the rotational processes sufficiently fast, leading to a partial averaging of
dipolar interactions. This result confirms the validity of the Ku-
boꢀTomita fit and relates the dynamic rotational processes affecting
and a KuboꢀTomita fit using the Eyring analysis. This material is
available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION
Corresponding Author
mgg@chem.ucla.edu; Patrick.Batail@univ-angers.fr; brown@
physics.ucla.edu.
’ ACKNOWLEDGMENT
We thank the National Science Foundation for support
through grants DMR-0605688 (MGG), 0804625 (SB), and
DGE-0654431 IGERT: Materials Creation Training Program
(CSV) as well as the California NanoSystems Institute (CSV).
We thank the CNRS and the Rꢀegion des Pays de la Loire for
support through a joint Ph.D. grant (C.L.), an associated CNRS
researcher position (L.Z.), a PDL Post-Doctorate grant (S.S.),
and grant MOVAMOL-2010 10306.
1
1H M2 to the averaged internuclear H dipolar fields of the BIBCO
rotors.
’ CONCLUSIONS
In order to investigate the potential of halogen bonding for the
design and the synthesis of functional materials and molecular
machines, a halogen-bonded network of BIBCO molecular
rotors was synthesized and structurally characterized using single
crystal X-ray diffraction data from 295 to 90 K. The structural
solution revealed a halogen-bonded, lamellar structure com-
posed of alternating ordered (A) and disordered (B) layers of
BIBCO rotors in two crystallographically unique environments,
which undergo a disorderꢀorder phase transition at 110 K. The
Brownian rotational dynamics of the crystallographically distinct
bicyclo[2.2.2]octane rotators in the two layers were each as-
signed a distinct, clearly resolved dynamic process due to the
relaxation contribution from each kinetically distinguishable A
and B site based upon variable-temperature solid-state NMR
studies from 290 to 27 K. Remarkably, the rotational dynamics of
both layers are ultra-fast at room temperature, with frequencies
corresponding to 0.8 and 4.3 GHz, respectively. The activation
energy for rotation about the 1,4-bicyclo[2.2.2]octane axis is 24%
lower in the disordered B layer of BIBCO, as compared to the
high-temperature plastic crystalline phase I of the bicyclo-
[2.2.2]octane molecule. This study validates an unprecedented
approach to the construction of amphidynamic molecular ma-
chines where the extended framework itself provides the tem-
plate to differentiate rotor dynamics and to sustain engineered
rotation down to very low temperatures. With respect to the
frequency factors of the BIBCO rotators in the ordered and
disordered layers, analysis of the data suggests that different
rotational potentials and solid-state packing dictate the limiting
rotational dynamics, even though the rotors possess the same
intrinsic electronic (gas phase) barrier. Although spinꢀlattice
relaxation measurements cannot discern the type of rotational
motion present, analysis of the crystal structure suggests that
rotational symmetry order of three- and six-fold symmetries may
play an important role on the dynamics of the two distinguishable
rotators. Future studies involving deuterium-enriched BIBCO
rotors may help elucidate the jumping mechanism of the two
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