Inter- and Intramolecular Aryl–Aryl Interactions in Partially Fluorinated Ethylenedioxy-bridged Bisarenes**

Article abstract of DOI:10.1002/chem.202003259

Several ethylenedioxy-bridged bisarenes with a variety of type and number of aryl groups were synthesized to study non-covalent dispersion-driven inter- and intramolecular aryl–aryl interactions in the solid state and gas phase. Intramolecular interactions are preferably found in the gas phase. DFT calculations with and without dispersion correction show larger interacting aromatic groups increase the stabilization energy of folded conformers and decrease the intermolecular centroid–centroid distance. Single-molecule structures generally adopt folded conformations with short intramolecular aryl–aryl contacts. Gas electron diffraction experiments were performed exemplarily for 1-(pentafluorophenoxy)-2-(phenoxy)ethane. A new procedure for structure refinement was developed to deal with the conformational complexity of such molecules. The results are an experimental confirmation of the existence of folded conformations of this molecule with short intramolecular aryl–aryl distances in the gas phase. Solid-state structures are dominated by stretched structures without intramolecular aryl–aryl interactions but interactions with neighboring molecules.

Full text of DOI:10.1002/chem.202003259

Accepted Article
Accepted Article
Title: Inter- and intramolecular aryl-aryl-interactions in partially
fluorinated ethylenedioxy-bridged bisarenes
Authors: Jan-Henrik Weddeling, Yury Vishnevskiy, Beate Neumann,
Georg Stammler, and Norbert Werner Mitzel
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To be cited as: Chem. Eur. J. 10.1002/chem.202003259
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Inter- and intramolecular aryl-aryl-interactions in partially
fluorinated ethylenedioxy-bridged bisarenes
Jan-Henrik Weddeling, Yury V. Vishnevskiy,* Beate Neumann, Hans-Georg Stammler and Norbert W.
Mitzel*
Abstract: Several ethylenedioxy-bridged bisarenes with a variety of
type and number of aryl groups were synthesized to study non-cova-
lent dispersion-driven inter- and intramolecular aryl-aryl-interactions
in the solid state and gas phase. Intramolecular interactions are pre-
ferably found in the gas phase. DFT calculations with and without
dispersion-correction show larger interacting aromatic groups to in-
crease the stabilization energy of folded conformers and decrease the
intermolecular centroid-centroid-distance. Single molecule structures
generally adopt folded conformations with short intramolecular aryl-
aryl-contacts. Gas electron diffraction experiments were performed
exemplarily for 1-(pentafluorophenoxy)-2-(phenoxy)ethane. A new
procedure for structure refinement was developed to deal with the
conformational complexity of such molecules. The results are an
experimental confirmation of the existence of folded conformations of
this molecule with short -intramolecular aryl-aryl distances in the gas
phase. Solid-state structures are dominated by stretched structures
without intramolecular aryl-aryl-interactions but interactions with
neighboring molecules.
Strong intermolecular C6H6...C6F6 stacking interactions increase
the melting point by about 18 °C relative to the individual solid
substances.[9,10] This phenomenon was discovered by Patrick and
Prosser[10] and was first interpreted by an interaction of opposing
quadrupole moments of both substances (C6H6: −6.69, C6F6: 7.89
a.u.).[9] Later studies pointed out that London dispersion (LD) for-
ces, the attractive part of van-der-Waals interactions,[11] have a
significant impact on the total interaction energy.[12] To analyze
this phenomenon, different aromatic groups were linked with rigid
or flexible backbones and investigated in different phases and by
different methods.[13]
Recently, our group studied stacking interactions between diffe-
rent types of halogenated and non-halogenated phenyl groups
linked by different backbones in various phases. Compounds with
phenyl and perfluorophenyl rings bridged by (sila)propyl chains
receive stabilization by intermolecular aryl-aryl stacking interacti-
ons in the solid-state,[14] whereas free molecules, studied by gas
electron diffraction (GED), find their energetic minima as confor-
mers bearing intramolecular aryl-aryl interactions. 1,1,2,2-Tetra-
methyldisilanes, substituted with symmetric or asymmetric pairs
of phenyl and/or perhalogenated (F, Cl) phenyl groups also show
strong π-interactions.[15,16] The aggregation in solid-state was
found significantly stabilized by intramolecular aryl-aryl interac-
tions. Gas electron diffraction and SAPT (symmetry-adapted per-
turbation theory) calculations demonstrate the untypical syn-con-
formers to be stabilized by large dispersion contributions.
From our experience with bridged bisarenes we learned, that the
type of interaction partners and the linking-backbone is important
for the stabilization of gas-phase and solid-state structures. We
were interested if more flexibility and modified electronic surroun-
ding, by heteroatoms in the bridge, would influence such inter-
actions. Therefore, we report here investigations employing a new
four-atomic ethylenedioxy linker unit (-OCH2CH2O-) between a
variety of interacting aromatic systems.
Introduction
Intra- or intermolecular interactions between aromatic systems
are of importance for different categories in molecular science.
Supramolecular recognition processes,[1] interplay of DNA side-
chains[2] or host-guest complexation[3] as well as crystal enginee-
ring[4] are some prominent examples. Many experimental and the-
oretical studies dealt with such interactions, however, they are still
far from being completely understood. The simplest model for
aryl-aryl-interactions is the benzene dimer.[5] In the solid-state the
benzene rings arrange in T-shaped or herringbone structures,
described as σ–π-interaction;[6] a parallel arrangement of the
rings is not favored. In contrast to the arrangement in the solid-
state, the results of gas phase and theoretical studies show the
parallel displaced or offset as well as the rare sandwich structures
to be more important under these conditions.[7] Easier to predict
are the interactions between benzene (C6H6) and its perfluorina-
ted analogue hexafluoro-benzene (HFB, C6F6). Both pure sub-
stances arrange in herringbone-like structures in the solid-state,[8]
but the equimolar mixture of benzene and HFB crystallizes in a
parallel displaced structure of alternating HFB and benzene units.
Results and Discussion
Before we started synthesizing such model systems we perfor-
med preliminary calculations, in order to evaluate intramolecular
aryl–aryl-interactions to be also possible with the ethylenedioxy
linker unit. At first we investigated the electronic and mesomeric
effect of the new linker and whether the oxygen atoms have an
influence on conformations or electron-density of the interacting
aromatic systems. As the simplest model system for our linker-
unit we performed a potential energy scan (PBE0-D3/def2-TZVP)
around the C–C-bond of H3C-OCH2CH2O-CH3 (Figure S38). We
found two minima, gauche and anti, of nearly the same energy.
Therefore, we can assume that the relative positions of the
[a]
J.-H. Weddeling, Dr. Yu. V. Vishnevskiy, B. Neumann, Dr. H.-G.
Stammler, Prof. Dr. N. W. Mitzel
Lehrstuhl für Anorganische Chemie und Strukturchemie
Fakultät für Chemie, Universität Bielefeld
Universitätsstraße 25, 33615 Bielefeld (Germany)
E-mail: mitzel@uni-bielefeld.de
Supporting information for this article is given via a link at the end
of the document.
1
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10.1002/chem.202003259
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oxygen atoms to each another in the -OCH2CH2O- unit, do not
significantly influence the conformational energies.
With a series of calculations on compounds 1–10 (Scheme 1) we
decided if the examined compound was worthy of being synthe-
sized and analyzed experimentally. For one example, compound
2, we determined the structure of a free molecule in the gas phase
by means of gas electron diffraction (GED). This investigation was
supported by a more detailed description with computational
methods. This will be described below and is outlined in detail in
the Supporting Information.
The minima found for compounds 1–10 at the global search were
structure-optimized at the PBE0/def2-TZVP level of theory using
Gaussian 16[22] and are listed in the Supplementary Information.
The calculations were performed with and without D3 correction
for dispersion interactions,[21] in order to analyze if the intramole-
cular aryl−aryl-interactions for folded conformers are caused
solely by electrostatic effects. Along with the expected folded and
stretched structures, we also found minima with half-folded
structures (e.g. compound 2; see Figure 2).
The electronic effects of the oxygen substituents on the aryl
groups were analyzed by inspection of the electrostatic potential
(ESP) surface of compound 2 in its stretched form. As shown in
Figure 1, the effect of the oxygen atoms on the electron density
of both aromatic rings is not very pronounced, in terms of a disto-
rtion of the ESP. As earlier mentioned for aromatic systems inves-
tigated before[17] the electrostatic potential values on the surface
of the phenyl group are negative (blue) while the surface of the
perfluorophenyl group has a positive ESP (yellow/red). The com-
plementary polarization of the aryl groups should lead to attractive
interactions between these functions. These interactions would
necessarily be intramolecular for isolated molecules in the gas
phase, but difficult to predict for the solid state, where alternative
intermolecular interactions are possible.
Figure 2. Calculated folded and half-folded structures of 2.
For these conformers the aromatic ring systems are not in a
parallel offset orientation relative to one another; instead they are
twisted or adopt T-shaped arrangements of their aryl rings (similar
to the arrangements in the crystal structures of pure benzene or
hexafluorobenzene). They also have generally longer centroid-
centroid distances (see Supporting Information). These half-
folded structures represent in many cases the global minima if no
D3 dispersion correction was applied. For calculations with D3
dispersion correction, folded and half-folded conformers have
similar energies. The stretched conformers were modelled by
optimizing the structures found in the solid state (see below). In
general, the application of D3 corrections for dispersion leads to
significantly lower energies of (half)folded conformers, with small
centroid-centroid distances. For all compounds with at least one
pentafluorophenyl group the folded structures a more favorable
than the stretched ones by ΔE = 2–24 kJ mol−1 (Table 1).
Figure 1. Stretched conformation of 2 (a) and its total electrostatic potential
(ESP, b) mapped onto isosurface (0.0005 a.u.) of the electron density using
AIMAII[18] at PBE0-D3/def2-TZVP level of theory. Blue and red areas corres-
pond to the negative and positive ESP values with maximal magnitudes,
respectively.
In order to see whether folded conformers with intramolecular
stacking interactions represent the favored conformation in the
gas phase, we used the CREST procedure[19] for a global search
of stable conformers at the GFN2-xTB[20) level of theory for
compounds 2–10. We additionally inspected compound 1, the
analogue of 2, C6H5-(CH2)4-C6F5, with an oxygen-free four-atomic
bridge, to prove that the predicted conformers are largely inde-
pendent of the preferred stereochemical effects of the ethylene-
dioxy-linker.
Scheme 1. Model compounds 1–10.
2
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Figure 3. Minima for folded conformers of 1–6 and of 10 calculated at the PBE0-D3/def2-TZVP level.
The centroid-centroid distances are comparable to those in
bisarene compounds, which our group investigated earlier in the
solid state (XRD) and by gas electron diffraction (e.g. shortest
centroid distances: PhCH2CH2CH2Phf: 3.50(2) Å; PhSiMe2-
SiMe2Phf: 3.76(3) Å).[14,22] The enlargement of the non-fluorinated
(2, 3, 5) or fluorinated (4, 10) ring system influences the strength
of the interactions and can be seen by comparing the decreasing
centroid-centroid distances (Figure 3). Due to the greatest inter-
acting surfaces, we found the largest stabilization energies for
compound 10. The ethylenedioxy-bridge generally allows close
intramolecular aryl-aryl-contacts and there is a clear relationship
between the size of the aromatic systems and the centroid-centro-
id distances. Furthermore, the introduction of a second CH2CH2-
OPhf unit (2, 6) does lead to the significantly shorter aryl-aryl con-
tacts.
In order to explore cases without important stabilizing electrostatic
components, which are dominated by dispersion effects, we
investigated bisarenes with two identical aromatic substituents.
Due to the same electrostatic potential, both aryl groups should
repel each other, however surprisingly, the optimized minima for
the symmetric bisarenes 8 and 9 also reveal folded structures
(Figure 4).
Comparison of compound 2 to its oxygen-free analogue 1 again
shows, that the oxygen atoms in the linker-unit do not influence
the conformational preference significantly (Table 1). The relative
energy differences of the calculations for 1 and 2 – with and
without D3 correction – have the same tendency and range.
Figure 4. Folded minima of 8 (left) and 9 (right).
On first sight, this parallel displaced arrangement of the aromatic
groups seems to be disfavored because of the steric hindrance of
the halogen substituents and the electrostatic repulsion through
of the aromatic rings –although the centroid-centroid distances
are quite short. Such eclipsed conformations were also found for
the perhalogenated disilanes PhXSiMe2SiMe2PhX and are stabi-
lized by London dispersion interactions.[15] Symmetric bisarenes
without halogen substitution do not preferably arrange in folded
sandwich structures. This is also the case for compound 7.
Table 1. Relative energy differences between stretched and folded conformers
of compounds 1–10. The relative energies of the minima E are given in kJ mol−1
.
ΔE >0, folded conformer is more stable; ΔE < 0, stretched conformer is more
stable.
ΔE = Es−Ef[a]
method
1
2
3
4
5
6
7
8
9
10
[PBE0]
-0.3 1.1 −4.9 0.8 −16.5 3.2 −14.7 −13.2 −6.5 87.5
[PBE0-D3] 9.5 8.8 16.0 8.8 9.3 18.0 −5.6
[a] f: folded; s: stretched.
3.1
2.1 24.0
Considering the relative energy differences with and without D3
dispersion correction for each compound, 1–10 (Table 1), electro-
static interactions alone cannot explain the effect of stabilization
of the folded conformers. If that were the case, folded conformers
of compounds 3 and 5, calculated without D3 correction, would
be more stable than the stretched ones. Only by taking into
account electrostatic and dispersion forces, the stabilization of the
folded conformers of partially fluorinated bisarenes can be explai-
ned properly.
Figure 5. Calculated minimum structure for 7.
The minimum for 7 was found for a stretched structure (Figure 5).
In the latter the inclusion of dispersion correction lowers the
relative energy of the folded conformation but the repulsion
3
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between the phenyl groups still plays the dominant role. A similar
free-molecule structure for the same compound was already
found by calculations and fluorescence dip infrared spectroscopy
(FDIR) by Buchanan et al.[24]
Structures in the solid state
Single crystals, suitable for X-ray diffraction, were obtained by
slow evaporation of n-hexane solutions. Some selected structural
parameters characterizing the stacking interactions are listed in
Table 2. For ring systems bigger than phenyl, the centroid was
defined as the centroid of all condensed six-membered rings. A
aryl-aryl-interaction was defined by centroid–centroid distances
smaller than 4 Å.
Synthesis
For a preparative access to the model compounds, we used a
modified protocol of Guo et al.[25] Scheme 2 displays an exempla-
ry way to the asymmetric compound 1-(pentafluorophenoxy)-2-
(phenoxy)ethane (2).
Figure 6. Molecular structure and primary aggregation of 2 in the crystalline
state. a) Side view of aggregation in the crystal lattice. b) Interaction to
neighboring molecules with an intermolecular centroid–centroid distance of
3.668(1) Å. Displacement ellipsoids are drawn at 50% probability level.
Hydrogen atoms are omitted for clarity. Symmetry operations for generating
equivalent positions: 1−x, 1−y, 1−z.
Scheme 2. Synthesis of 2 starting from pentafluorophenol.[25]
Starting from pentafluorophenol, dibromoethane and potassium
carbonate we generated 2-(pentafluorophenoxy)ethyl bromide
(2a). Based on this building block we could introduce a second
aryloxy group under the same conditions. This procedure allowed
generating various asymmetric bisarenes (2–4, 6). The syntheses
of symmetric bisarenes (7–9) required extended reaction times for
the first etherfication step. In order to obtain compound 5 we
generated 2-(9-anthroxy)ethyl bromide (5a) from anthrone and 2-
bromoethanole. 5a and pentafluorophenole were then converted
into 5. Detailed information is provided in the Supporting Informa-
tion. Purification by column chromategraphy, sublimation and
crystallization afforded the bisarenes in moderate to good yields.
Compound 10 could not be synthesized yet. The compounds
were characterized by NMR-spectroscopy, high resolution mass
spectrometry, CHN analysis and single crystal X-ray diffraction.
Compounds 2–9 show no intramolecular aryl-aryl-interactions in
their solid-state structures. All molecules crystallize in stretched
conformations. The arrangement of molecules in the crystal lattice
follow different motifs. Compound 2 forms dimeric structures
whereas the phenyl and perfluorophenyl arrange in a head-tail
orientation to their neighboring counterpart and undergo aryl–aryl-
interactions with short centroid distances [3.688(1) Å]. A second
aryl–aryl-interaction was found between two perfluorophenyl
groups of neighboring dimers, with a distance of 3.944(1) Å, lea-
ding to an 1D-polymer along the a-axis.
Unlike 2, the crystal structure of 3 contains columnar alternating
stacks of perfluorophenyl and naphthyl groups from reversely ori-
ented alternating molecules. The ring systems arrange almost
perfectly above the centroid of the ring system of the neighboring
counterpart. Such sandwich
orientation is rarely observed.[26]
Table 2: Selected structural parameters from solid state structures of 2–9.
Within one column the centroid–
centroid distances alternate with
3.462(1) (A) and 3.550(1) Å (B)
(Figure 7). A is the shortest inter-
molecular aryl–aryl-distance for
partially fluorinated flexibly brid-
ged bisarenes found so far for
sandwich structures in solid state
[e.g. shortest centroid-centroid
2
3
4
5
6
7
8
9
̅
̅
̅
Space group
P21/c
3.18
P21/c
4.85
P21/n
4.03
P1
P21/c
4.47
P1
P21/c
2.00
P1
R [%]
3.69
5.55
2.74
3.338(3) 3.403(2)
(C2-C11) (C3-
(C6-C9)
3.348(2)
(C1…C14)
3.288(2)
3.278(3) 3.580(3) 3.585(3)
3.327(2)
(C13…C9)
dC–C [Å]
(C1…C19) (C3…C6) (C5…C9) C5…C4
C18)
distances:
F5C6(CH2)2SiMe2-
3.688(1)
3.462(1); 5.026(1) 3.660(1); 4.431(1)
4.431(1)
3.553(1)
3.729(1)
dcentr–centr [Å]
5.423(1) 3.971(1)
1.739(3)
C6H5: 3.535(1) Å; F5C6(SiMe2)2-
C6H5: 4.425(1) Å][14–15] and is
even shorter than in the
C6F6/C6H6 cocrystal (3.77 Å).[16]
3.944(1) Å 3.550(1) 5.247(1)) 3.721(1)
0.430(3);
0.418(3)
1.544(2); 3.004(3);
dplane-shift[Å]
1.554(2)
Ph/Phf
-
-
-
1.376(2)
1.371(2)
2.439(4)
Intermolecular
π–π interaction
Ph/Ph;
Phf/Phf
Naph/Phf
Anthr/Phf
Ph/Ph
-
Pho-Br/Pho-Br Phf/Phf
Aggregation
motif
polymeric columnar
columnar
-
columnar
chainlike
4
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Figure 7. Molecular structure and aggregation of 3 in the crystalline state. a)
Side view of aggregation in the crystal lattice. b) Interaction to neighboring
molecules with intermolecular centroid-centroid distance of A 3.462(1) / B
3.550(1) Å. Displacement of ellipsoids are drawn at 50% probability level.
Hydrogen atoms are omitted for clarity. Symmetry operation for generating
equivalent positions: 1−x, ½+y, ½−z.
Figure 9. Molecular structure and aggregation of 6 in the crystalline state with
an intermolecular centroid-centroid distance of 4.311(1) Å. Displacement ellip-
soids are drawn at 50% probability level. Hydrogen atoms are omitted for clarity.
Symmetry operation for generating the second part of molecule (1−x, 2−y, 2−z)
and equivalent positions: +x, −1+y, +z.
The variation from phenyl- to naphthyl-group enables each group
to form two aryl contacts in solid state. A change in substitution
position – 1-naphthyl (3) to 2-naphthyl(4) – to the constitution
isomer 4 leads to an unexpected packing behavior. Compound 4
shows no preference for an arrangement in alternating columnar
structures. Instead we found multiple intermolecular aryl-contacts
(Phf/Phf, Naph/Naph, Naph/Phf) with long ranges (>5 Å) (see
Supporting Information). There is no recognizable impact of π–π-
interactions for the arrangement in the crystal lattice.
Compound 5 crystallizes in an alternating columnar structure with
slightly longer intermolecular centroid distances 3.660(1) Å and
3.721(1) Å than for 3. This offset or parallel displaced orientation
is commonly observed for aryl-aryl interactions. The angle
between the plane normal and the vector between the ring
centroids is about 20°.
The offset structure of 6 (Figure 9) seems to be disfavored
because the repelling surfaces of the aromatic systems and the
aryl-aryl-distance of 4.311(1) Å being too long for an aryl-aryl
interaction. The fact that benzene and HFB, as pure substances,
both prefer T-shaped arrangements in their solid-state structures,
makes this structure even more interesting. Due to the symmetry,
the Phf groups are coplanar and the central phenyl unit is twisted
by 64.1(1)° relative to them.
In order to analyze if the phenomenon of aryl-aryl interactions is
limited to partially fluorinated bisarenes, we also investigated
symmetric bisarenes with phenyl, perfluorophenyl, and 1,2-
dibromophenyl groups. The solid state structures of these
compounds do not feature typical intramolecular interactions.
Whereas compound 7 shows no stacking interactions in the solid-
state structures, compound 8 crystallizes in columnar structure
with a centroid–centroid distance slightly below the 4 Å limit
[3.971(1) Å].
Figure 8. Molecular structure and aggregation of 5 in the crystalline state with
intermolecular centroid-centroid distances of 3.660(1) and 3.721(1) Å. Displa-
cement ellipsoids are drawn at 50% probability level. Hydrogen atoms are omit-
ted for clarity. Symmetry operation for generating equivalent positions: 1−x, 1−y,
1−z.
Figure 10. Molecular structures and aggregations of 7 (a) and 8 (b) in the crys-
talline state. Displacement ellipsoids are drawn at 50% probability level.
Hydrogen atoms are omitted for clarity. a) Intermolecular centroid-centroid
distance: 5.423(1) Å; symmetry operation for generating equivalent positions:
−1+x, +y, +z. b) Intermolecular centroid-centroid distance: 3.971(1) Å;
symmetry operation for generating second part of the molecule (1−x, −y, −z)
and equivalent positions (1+x, +y, +z).
In order to study the influence of a second –OCH2CH2Phf group,
trisarene 6 was synthesized. Because the molecule has twice as
many fluorinated than non-fluorinated aryl rings, it is not possible
to arrange in 1:1 alternating structure as was observed for 3 or 5,
and consequently we expected a mixture of inter- and intramole-
cular aryl-interactions.
Because of long centroid distances to neighboring molecules, the
interaction between two phenyl groups seems to be disfavored.
The phenyl groups within one molecule of 7 are twisted against
each other by 63.1°. The substitution with bromine in ortho-posi-
tion (8) leads to co-planarity of the aromatic rings within the co-
5
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lumn and short centroid-centroid distance to neighboring molecu-
les. This phenomenon was recently discovered in our group by
investigating inter- or intramolecular π-stacking for perhalogena-
ted groups in symmetric disilanes (PhXSiMe2SiMe2PhX; X = H, Cl,
F); we recognized that π-stacking was limited to halogenated aryl
groups and was not observed for hydrocarbons.[23] Such stacking
interactions are stabilized primarily by London dispersion forces.
packing leads to columnar structures, similar to the benzene/HFB
co-crystal. The neighboring column, is displaced by a half of a
repetitive unit, that the structure is additionally stabilized by inter-
columnar H∙∙∙F-contacts [e.g.: 2.48(2) Å H(6)∙∙∙F(4)]. Within one
sheet (along the c-axis) the aromatic groups are coplanar, be-
tween two sheets twisted by 6.2(1) and 3.6(1)°. Other attempts of
co-crystallization could not be analyzed yet, because of the insuf-
ficient quality of the resulting crystals.
In contrast to the calculated gas-phase structures, most of the
molecular structures of compounds are found to adopt stretched
conformations in the solid state. Obviously, in this phase the
number of stabilizing inter- and intramolecular interactions is
larger for the stretched than for the folded conformer. As a
simplest approximation of intermolecular interactions, for com-
pound 2 we have optimized a system of two stacked molecules in
stretched conformations (Figure 13).
Figure 11. Molecular structure and aggregation of 9 in the crystalline state with
intermolecular centroid-centroid distances of 3.553(1) Å and 3.729(1) Å. Dis-
placement ellipsoids are drawn at 50% probability level. Symmetry operation for
generating equivalent positions: 1−x, 1−y, 1−z.
The perfluorinated compound 9 aggregates differently. The pri-
mary aggregation motif is a dimeric structure, with a short "inner"
centroid-centroid distance of 3.553(1) Å. The "outer" Phf groups
interact with the corresponding counterparts of neighboring di-
mers. This leads to endless chains running along 111 in the crys-
tal lattice with alternating shorter and longer aryl-aryl interactions.
In order to find out if we can intentionally generate the different
aggregation motifs, i.e. control the crystallization to some extent,
we attempted to co-crystallize compounds 2–9 with different aro-
matic compounds (HFB, benzene, octafluoronaphthalene) from
n-hexane solutions. We generated a 1:2 co-crystal of 7 and octa-
fluoronaphthalene (OFN). It has a columnar structure of alterna-
ting entities, either one molecule of 7 or a pair of OFN molecules.
Each phenyl group of 7 interacts with two neighboring OFN units
(Figure 12 b). The shorter contact of 3.548(1) Å is to the OFN
molecule within the same unit cell, the slightly longer [3.807(1) Å]
contact to an OFN molecule of a neighboring unit cell. This
Figure 13. Comparison of inter- and intramolecular stabilization of gas-phase
(B) and solid state structures (A) of 2 at PBE0-D3/def2-TZVP level of theory.
For this we used the Cartesian coordinates of the dimer (A) in the
crystal structure of 2, optimized its structure and calculated its
minimum energy at PBE0-D3/def2-TZVP level of theory. The
energy of this dimeric system (A) was 54 kJ mol−1 (BSSE correc-
ted) lower than the twice the energy of the best folded confor-
mation in the gas phase (B). Thus, the energetic stabilization due
to intermolecular interactions between stretched conformers is
more preferable than intramolecular stabilization in the folded
conformation.
Figure 12. a) Molecular structure and aggregation of a 1:2 co-crystal of 7 and octafluoronaphthalene in the crystalline state. Displacement ellipsoids are drawn at
50% probability level. a) Top view with intercolumnar H...F-contacts. b) Hydrogen atoms are omitted for clarity. Interaction in the unit cell with intermolecular
centroid-centroid distances of 3.548(1) and 3.807(1) Å. The neighboring unit cells are drawn at 50% transparency level. Symmetry operation for generating second
half of the co-crystal (−x, 2−y, −z) and equivalent positions: +x, −1+y, +z.
6
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Structure of 2 Determined by Gas Electron Diffraction
corrections to equilibrium structure implying the Qassandra
program.[29]
Gas-phase structures, i.e. the structures of free molecules undis-
torted by intermolecular interactions, ca be determined by means
of gas electron diffraction (GED). Due to the very high effort to be
spent, we chose 2 as a model compound for the partially fluori-
nated ethylenedioxy-bridged bisarenes to be studied exemplarily
in the context of this present study. The structure of 2 is suitable
for comparison with those of other flexibly bridged bisarenes, we
investigated earlier.[14,15,23]
First, a search for possible stable conformations of 2 was done
theoretically using the Crest program[19] utilizing the GFN2-xTB
method[20] for solving the electronic problem. Structures with rela-
tive energies below 3 kcal mol−1 were manually inspected and
(symmetry) duplicates were sorted out. This resulted in seven dis-
tinct conformations, denoted here as 2a – 2g (see Figure 14).
An additional stretched conformation 2h was also included into
this set as a structure with the largest distance between the
phenyl rings. The selected structures were optimized using the
CP2K program[27] and the implemented method GFN1-xTB
within.[28] The relative energies and the most important torsion
angles of the optimized structures are provided in Table S31. Path
integral molecular dynamics simulations were performed using
the same program and method. Eight simulations with 16 beads
were performed starting from structures of each conformation.
Each trajectory was 100 ps long with a step size of 0.5 fs. Distri-
butions of the most important torsion angles (φ1, θ1, τ, θ2, φ2; see
Scheme 3) were obtained from these trajectories and analyzed
(see Figures S69–S73).
For the refinement of molecular structures a new method has
been implemented into the UNEX program.[30] This method is ba-
sed on the well-known regularization technique[31] and allows de-
coupled definition of refined structural parameters and regulariza-
tion parameters of different types. For example, in this work we
defined and refined molecular structures in terms of Cartesian co-
ordinates but the regularization was applied in terms of internal
parameters, that is bond lengths, valence, torsion and out of plane
angles. In contrast, the already available methods[32–35] apply
flexible restraints only to the refined parameters. In some cases,
e.g. for carbaboranes,[36] it is convenient to refine and regularize
Cartesian coordinates simultaneously. However, for flexible and
large molecules this can either hinder the fitting of the model or
can lead to highly unstable solutions. Thus, in this work the follo-
wing least squares functional was minimized:
2
)
2
)
∑
∑
푗
푄 = 푤푖 (푠푀( ),exp − 푠푀( )
+ 훼 푤 (푝( ,reg − 푝(
(1)
)
)
,model
푖
푖
푖
,model
푗
푗
푗
where sM(i),exp and sM(i),model are experimental and model molecu-
lar intensity functions, p(j),reg and p(j),model are regularization and
model internal geometrical parameters, wi and wj are respective
weighting factors, α is the global regularization factor. Weighting
factors for the experimental data were calculated from corres-
ponding individual standard deviations σi as wi = σi-2. In the regu-
larization part of the functional weighting factors wj had different
values depending on the location of parameters. Relative values
of wj for valence angles in the -O-CH2-CH2-O- chain were by factor
102 smaller than for all other valence angles. Analogously, for the
torsion angles in this fragment (φ1, θ1, τ, θ2, φ2) wj were 25 times
smaller than for other torsion angles. Thus, in the refinements the
inverse problem was more flexible for parameters determining
conformations while for the benzene rings and atoms connected
to them a stronger regularization was applied. For obtaining regu-
larization parameters of reasonable accuracy the structures were
additionally optimized at the PBEh-3c level of theory[37] as imple-
mented in the Turbomole 7.4 program package.[38] The obtained
torsion angles and relative energies are collected in Table S32.
Note, that functional (1) consists of two parts, (a) the first part built
Scheme 3. Torsion angles for ethylenedioxy-bridged bisarenes 2.
Guided by the distributions the individual trajectories were used
for calculations of interatomic vibrational amplitudes and
Figure 14. Selected conformers 2a–h obtained using GFN1-xTB method.
7
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10.1002/chem.202003259
Chemistry - A European Journal
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on experimental sM(s) functions and (b) the
second regularizing theoretical part. As the
structures are determined by minimizing the
complete functional Q, both parts of the
functional can determine the refined parame-
ters. However, the extent of influence of each
part of Q on different parameters can also be
different. Accordingly, contributions can be
defined (as a measure of influence) of the
parts of Q onto refined parameters.
The global regularization factor α was manu-
ally adjusted so that contributions of the ex-
perimental GED data onto the refined para-
meters were maximized while the solutions
were still stable. The contributions of experi-
mental data and regularization data, respec-
tively, were calculated according to the W2
method.[39] Amplitudes of vibrations were
refined in groups keeping the ratios within
Table 3: Refined torsion angles (in degrees), weighted R-factors (in %) and relative energies ΔE (in
kJ mol−1) for all tested conformers of 2.a
ΔE
(GFN1-
xTB)
ΔE
(PBEh-
3c)
φ1
θ1
τ
θ2
φ2
wRb
2a −17.8(32) −65.9(34) −59.8(21) 75.9(14)
72.8(22)
3.62
0.00
3.89
3.10
6.44
7.78
6.23
5.69
8.83
0.00
0.46
2b −8.1(71) −120.7(31) 82.1(25) −54.3(47) −76.4(16) 4.78
2c 14.6(59)
2d
166.7(51) −71.0(36) 71.6(36) −105.0(18) 3.59
36.7(24) −129.6(14) 3.60
43.0(18) 71.4(17) 5.15
0.21
−47.1(45) −104.8(28) 58.9(19)
6.02
2e 23.3(150)
70.9(43)
50.2(10)
9.92
2f −20.0(300) −80.5(130) −179.7(25) −78.5(88) −57.2(20) 5.24
12.38
13.05
18.66
2g 157.3(74) 109.7(21) −70.9(33) 145.3(25) 63.4(20)
2h
0.0 180.0 180.0 180.0 180.0
4.14
11.10
a In parentheses are 1σ pure experimental errors, see text for details.
b Calculated as wR = [∑wi{sM(i),exp − sM(i),model}2/∑wi{sM(i),exp}2]½ × 100 %
Other detailed information on refinements, including complete
structures, is provided in the Supporting Information. The radial
distribution functions are shown in Figure 15. Summarizing the
results of the structural analysis of 2 by GED we conclude that the
experimental gas electron diffraction intensities are best descri-
bed by the models of conformers with folded structures 2a, 2c and
2d (see Figure 16). However, it was impossible to determine
exactly which of these three conformations exist in the gas phase
at the experimental conditions.
groups fixed at theoretical values. Models of all conformers were
refined in exactly the same manner with the same extents of
regularization. The resulted wR-factors of all models and corres-
ponding torsion angles are collected in Table 3. Note, the stated
uncertainties are purely experimental errors, which were calcula-
ted using a method removing the influence of regularization.[40] In
comparison to these values, the least squares standard deviati-
ons were unrealistically small in many cases (see Table S33).
Although the models described above fit the data well, there are
still small systematic differences between experimental and mo-
del radial distribution functions (Figure 15) and molecular intensity
functions (Figure S68). This was also seen by comparing the very
low experimental wR-factors of 1.6 %, demonstrating the ex-
cellent reproducibility of the experimental sM(s) functions, with the
best structural wR-factors of 3.6 %. It is possible that all three
conformers, 2a, 2c and 2d, exist in the gas phase simultaneously.
Figure 16. Conformers 2a, 2d, 2c with best description of GED.
However, a refinement of the conformational composition could
not be done with sufficient accuracy using solely the GED data
due to instability of the inverse problem.
Interestingly, model 2b had a somewhat larger wR-factor in spite
of its folded structure and low relative energy at the PBEh3-c level.
We do not exclude that this was due to imperfections in the de-
scription of molecular vibrations on the level of molecular dyna-
mics used in this work. For 2 this problem is very complicated due
the occurrence of large amplitude motions and its rich conforma-
tional landscape, which can be seen on distributions of torsion
angles (Figures S69–S73). In general, the stretched structures
showed a worse agreement with the experimental intensities. This
is also clear by comparing the difference curves of the radial dis-
tribution functions in Figure 15. The model of 2g showed an
Figure 15. Experimental (dots) and best model (line) radial distribution functions
of 2. Below are ordered difference curves for all tested models, highest for the
first conformation 2a, lowest for 2h. Vertical bars indicate positions of
interatomic distances in 2a.
8
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interesting possible case of a σ-π interaction. The energy of this
conformer was fairly high but the wR-factor was relatively low. We
cannot exclude small fractions of this conformer in the gas phase.
The worst agreement with experimental data had model 2h with
the largest distance between phenyl rings. A special note should
be made concerning the refined torsion angles in Table 3. Due to
the aforementioned vibrational complexity and ambiguity in the
conformational composition they can be significantly biased away
from true equilibrium values. Moreover, in the rejected models
they do not indicate a correspondence to real structures, possibly
existing in small fractions under experimental conditions.
The best GED models have folded structures with short intra-
molecular aryl-aryl interactions. The respective centroid-centroid
distances (see Figure 16) are slightly longer than for our prelimi-
nary calculations for the gas phase (Figure 3) and comparable to
GED data for bisarenes our group investigated recently
(PhCH2CH2CH2Phf: 3.50(2) Å; PhSiMe2SiMe2Phf: 3.76(3) Å).[14,23]
Note, the distances between centroids in 2 refined in this work
were essentially experimental in spite of using quantum-chemi-
cally calculated restraints. W2-contributions of the GED data to
these parameters as described above and which were 97, 57 and
82 % in 2a, 2c and 2d, respectively.
Acknowledgements
We thank Klaus-Peter Mester and Marco Wißbrock for recording
NMR spectra and Barbara Teichner for elemental analyses. We
also thank Timo Glodde and Dr. Jan Schwabedissen for the gas
electron diffraction experiments. This work was funded by DFG
(German Research Foundation) in the Priority Program SPP 1807
„Control of LD in molecular chemistry“ (grant MI477/28-2, project
no. 271386299) and the core facility GED@BI (grant MI477/35-1,
project no. 324757882). Yury Vishnevskiy is grateful for financial
support by Deutsche Forschungsgemeinschaft (DFG, Grant VI
713/1-2, project no. 243500032) and to HPC facilities at the
Universität zu Köln for providing computational time and pro-
grams.
Keywords: bridged arenes • dispersion • halogenated arenes •
inter/intramolecular stacking interactions• solid-state structures •
gas electron diffraction
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Entry for the Table of Contents
Inter- and intramolecular aryl-aryl-interactions in partially fluorinated
ethylenedioxy-bridged bisarenes
J.-H. Weddeling, Yu. V. Vishnevskiy, B. Neumann, H.-G. Stammler and N. W.
Mitzel
London dispersion driven interactions between two aryl groups, separated by
ethylenedioxy-bridged linkers, lead to different conformations, dependent on the
size and nature of the aryl groups and the phase, studied by X-ray (solid) and
electron diffraction (gas).
11
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