The incommensurately modulated structure of a tricyclic natural-product-like compound of empirical formula C22H 20O3

Article abstract of DOI:10.1107/S010876810600930X

3,4-Diphenyl-2a,5a,6,7,8,8a,8b-heptahydro-furo[4,3,2-de]chromen-2-one (1) was prepared as part of a project aimed at the synthesis of polycyclic natural-product-like scaffolds. X-ray analysis of crystals grown from ethanol revealed an incommensurately mod

Full text of DOI:10.1107/S010876810600930X

research papers
Acta Crystallographica Section B
Structural
Science
The incommensurately modulated structure of a
tricyclic natural-product-like compound of
empirical formula C22H20O3
ISSN 0108-7681
Nicolas Guiblin,a* Cyril A.
3,4-Diphenyl-2a,5a,6,7,8,8a,8b-heptahydro-furo[4,3,2-de]-
chromen-2-one (1) was prepared as part of a project aimed
Received 20 October 2005
Accepted 13 March 2006
Fuhrer,b Robert Haner,b Helen
¨
Stoeckli-Evans,c Kurt Schenka
and Gervais Chapuisa
at the synthesis of polycyclic natural-product-like scaffolds.
X-ray analysis of crystals grown from ethanol revealed an
incommensurately modulated structure. Data include main
and satellite reflections up to second order. The modulation
vector was refined using the NADA program. The modulated
character of the structure of the organic compound C22H20O3
is interpreted in terms of the intermolecular C—Hꢀ ꢀ ꢀO
hydrogen bonds and close-contact approximation.
a
´
Laboratoire de Cristallographie, Ecole Poly-
´
´
technique Federale de Lausanne, Institut de
`
Physique de la Matiere Complexe, CH-1015
Lausanne, Switzerland, bDepartement fur
¨
Chemie und Biochemie, Universitat Bern,
¨
Freiestrasse 3, CH-3012 Bern, Switzerland, and
c
´
Institut de Microtechnique, Universite de
ˆ
Neuchatel, Rue Emile Argand 11, Case Postale
ˆ
158, CH-2009 Neuchatel, Switzerland
1. Introduction
Incommensurate modulated structures are part of a larger
group of aperiodic crystals also including composite and quasi-
crystalline materials. The diffraction pattern of crystals with an
incommensurate modulation is characterized by a series of
reflections, which require additional integers to define them.
In order to model the complete set of observations, it is
convenient to represent the structure in a space of dimension
larger than three. The dimension of the space is given by the
number of integer indices required to completely characterize
the diffraction pattern and is called the superspace. The
current method is essentially based on the work of de Wolff
(1974, 1977) and Janner & Janssen (1979).
Correspondence e-mail: nicolas.guiblin@epfl.ch
As part of the efforts aimed at the synthesis of natural-
product-like compounds (Messer et al., 2004, 2005), we
became interested in compound (1). This tricyclic compound
was synthesized in analogy with the previously published
procedure (Fuhrer et al., 2004). Upon recrystallization of (1)
from ethanol, preliminary structural investigations by X-ray
diffraction showed that this compound exhibits an incom-
mensurate character at 173 K.
Although incommensurate structures appear frequently in
inorganic (Baldinozzi et al., 1998; Boucher et al., 1996; Miles et
al., 1998; Shaw et al., 1988; Speziali & Pimenta, 2004) or metal-
organic materials (Lam et al., 1995; Meyer et al., 1994; Steurer
& Depmeier, 1989), fewer reports are available to date
¨
concerning organic compounds (Zun˜iga et al., 1989; Schon-
leber & Chapuis, 2004).
The present study is part of a project based on the under-
standing of the origin of the aperiodic character in organic
materials by diffraction methods (Bussien Gaillard et al., 1996,
1998) and also from molecular dynamical simulations (Pan et
al., 2002, 2003). The validity of the method presented here is
evident just by comparing the magnitude of the anisotropic
displacement parameters obtained from the superspace
refinement and the conventional refinement. In addition, via
the quality of the refinement it is possible to obtain very
# 2006 International Union of Crystallography
Printed in Great Britain – all rights reserved
506 doi:10.1107/S010876810600930X
Acta Cryst. (2006). B62, 506–512

research papers
Table 1
Experimental details.
circle goniometer and using Mo Kꢀ graphite monochromated
radiation. Experimental details are given in Table 1.
Crystal data
Chemical formula
Mr
C22H20O3
332.4
2.2. Initial structure solution
Cell setting, space group
Temperature (K)
Monoclinic, P21/c
173
7.2527 (9), 24.951 (3), 9.8959 (10)
106.645 (8)
1715.8 (4)
4
1.286
Mo Kꢀ
6774
The observed systematic absences for main reflections are
compatible with the monoclinic space group P21/c (No. 14).
An initial structure solution was performed using direct
methods by means of the program SHELXS (Sheldrick, 1990).
The refinement and all further calculations were carried out
using SHELXL97 (Sheldrick, 1999). The H atoms were
included in calculated positions and treated as riding atoms
using SHELXL default parameters.
˚
a, b, c (A)
ꢂ (ꢄ)
3
˚
V (A )
Z
Dx (Mg mꢅ3
)
Radiation type
No. of reflections for cell para-
meters
ꢃ range (ꢄ)
1.6–25.6
0.09
ꢄ (mm–1)
˚
C—H distances were fixed at 0.97 A. 45 atoms were then
Crystal form, colour
Crystal size (mm)
Rod, colourless
0.50 ꢁ 0.22 ꢁ 0.20
used to describe the structure. In order to help with the
description of the structure, we propose to distinguish it by
considering three different parts (Fig. 1): the two phenyl rings
and the rest of the molecule, later referred to as RB3 (C1 to
C10, O1, O2 and O3), RB1 (the phenyl ring described by
atoms C17 to C22 and linked to the RB3 unit by C1) and RB2
(the phenyl ring described by atoms C11 to C16 and linked to
the RB3 unit by C2), the term RB meaning rigid body and this
approximation being used later in the refinement. H atoms,
not indicated here, are named according to their parent
C atom.
Data collection
Diffractometer
Stoe IPDS-II
! scans
None
Data collection method
Absorption correction
No. of measured, independent and
observed reflections
Criterion for observed reflections
Rint
12 976, 40 786, 12 976
I > 3ꢁ(I)
0.0375
51.6
–8 ) h ) 8
–29 ) k ) 29
–11 ) l ) 11
2
ꢃmax (ꢄ)
Range of h, k, l
Intensity decay (%)
The non-H atoms were refined using anisotropic atomic
displacement parameters (ADP). Hydrogen ADPs were
considered isotropic (IDP) and fixed to their respective linked
C atoms by the following equation: Uiso(H) = 1.2Ueq(C), with
Refinement
Refinement on
F2
R[F2 > 2ꢁ(F2)], wR(F2), S
No. of reflections
No. of parameters
H-atom treatment
Weighting scheme
0.039, 0.087, 0.79
40 786
328
Constrained to parent site
Based on measured s.u.’s
w = 1/[ꢁ2(I) + 0.0004I2]
0.001
P
P
3
i¼1
3
Ueq = ð1=3Þ
j¼1 U ijaꢂi ajꢂai ꢀ aj:
The average structure, corresponding to the Fourier trans-
form of the main reflections in real space (Schaniel et al.,
2002), is represented in Fig. 2. The corresponding R value,
obtained from 4977 reflections with I > 3ꢁ(I) and 226 refined
parameters, is 0.0546. The ORTEP (Farrugia, 1997) repre-
sentation of the structure shows large ADP ellipsoids. The
ADP values are large mainly along the b direction for all of
the atoms, i.e. along the long axis of the molecule.
(ꢀ/ꢁ)max
ꢀꢅmax, ꢀꢅmin (e A )
Extinction method
–3
˚
0.13, ꢅ0.14
B-C type 1 Gaussian isotropic
(Becker & Coppens, 1974)
0.78 (3)
Extinction coefficient
ˇ´ˇ
Computer programs used: JANA2000 (Petrıcek et al., 2003).
The packing of the structure is represented in Fig. 3. The
molecules are stacked perpendicularly to the c axis, two
nearest neighbours being related by the c glide. Such a row of
precise indications of the atomic interactions leading to the
incommensurability.
2. Experimental
2.1. Sample preparation and data collection
Compound (1) was prepared according to the previously
published method (Fuhrer et al., 2004). Full experimental
details have been deposited.1 Suitable crystals were obtained
after recrystallization from an ethanol solution. A colourless
rod-like crystal of dimensions 0.50 ꢁ 0.22 ꢁ 0.22 mm3 was
used for data collection. The intensity data were collected at
173 K on a Stoe IPDS II diffractometer equipped with a two-
Figure 1
The 3,4-diphenyl-2a,5a,6,7,8,8a,8b-heptahydro-furo[4,3,2-de]chromen-2-
one molecule. The different parts used in the text to describe the
molecule are represented. The (+/ꢅ) symbol indicates the racemic
composition of this molecule.
1 Supplementary data for this paper are available from IUCr electronic
archives (Reference: OG5016). Services for accessing these data are described
at the back of the journal.
ꢃ
Acta Cryst. (2006). B62, 506–512
Nicolas Guiblin et al.
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2.3. The incommensurately modulated structure
molecules is repeated along the a axis, thus forming a layer of
layer group Pc. These layers are then stacked on top of each
other perpendicularly to the b axis, realising the maximum
degree of order.
The modulated character of this structure is associated with
the existence of satellite reflections as indicated in Fig. 4. The
diffraction pattern can be fully indexed by introducing the
modulation vector q defined by the relation H = haꢂ + kbꢂ +
lcꢂ + mq: The symbol m represents the order of the satellite
reflections. The modulation is called commensurate if the
modulation vector components are rational, and incommen-
surate if at least one component is irrational.
Satellite reflections can be considered as a projection of a
four-dimensional lattice in four-dimensional space R4 onto
three-dimensional space R3.
A modulation can be displacive, i.e. displacement of atomic
coordinates, occupational, i.e. a probabilistic occupation of a
crystallographic site, or induced by thermal motion where the
modulation occurs in the ADPs. For a displacive modulation
the position r of an atom is described by the coordinates xi (i =
1, 2, 3, 4) in R4 with xi (i = 1 . . . 3) being the same coordinate as
in R3, and x4 the position along the supplementary dimension.
This position r is given by the relation r = r0 + u. In the average
structure the position of the atom is r0, and u defines the
perturbation generating the satellite reflections. The pertur-
bation is a periodic function of q ꢀ r, the ui components of
which can be decomposed into Fourier series, for the ith atom
in the unit cell, as
Figure 2
The molecular structure, obtained from the refinement of main
reflections, showing 50% probability displacement ellipsoids and the
crystallographic numbering scheme. For clarity, H atoms are drawn as
open circles of arbitrary diameter.
n
n
X
X
ui ¼
Ai;p sin 2ꢆpðq ꢀ r0Þ þ
Bi;p cos 2ꢆpðq ꢀ r0Þ:
p ¼ 1
p ¼ 1
The amplitude of the displacements is given by Ai;p and Bi;p
for the pth harmonic of the modulation function. The x4
coordinate in superspace is defined as t þ q ꢀ r, where t is a
continuous function between 0 and 1. Each section of the
superspace with a specific value of t represents a portion of
three-dimensional space.
Figure 3
Drawing of the unit cell of the packing arrangement corresponding to the
average structure. This packing shows the c-glide relation existing
between molecules stacked perpendicularly to the c axis. H atoms have
been omitted for clarity.
Figure 4
The (h0l) plane showing the main, first- and second-order satellite
reflections. The modulation vector q is indicated.
ꢃ
508 Nicolas Guiblin et al.
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The modulated structure was obtained by taking into
account the complete set of observations extracted from the
X-AREA integration software (Stoe, 2005). A reconstructed
h0l plane is represented in Fig. 4. Main and satellite reflections
up to second order are clearly visible, with some of the
satellites showing strong intensities.
The R (R-weighted) values are 0.0331 (0.0657), 0.0434
(0.0766) and 0.0697 (0.1581) for main, first- and second-order
satellite observed reflections, respectively.
The C—H distances and H-atom positions were constrained
as for the average structure. Nevertheless, a refinement
without constraints was also performed. This should give
better accuracy in C—H distances (Schomaker & Trueblood,
1968). However, the equation applied for calculating
hydrogen IDPs was kept. The R (R-weighted) values are
0.0332 (0.0648), 0.0435 (0.0761) and 0.0703 (0.1597) for main,
first- and second-order satellite reflections, respectively. The
C—H distances vary in all the molecules from 0.967 (6) to
The description of the modulated character of this structure
requires a precise value for the components of the modulation
¨
vector. The program NADA (Schonleber et al., 2001) was used
for this purpose. This program re-indexes the main and
satellite reflections using the orientation matrix and the spatial
peak positions. The refined modulation vector is obtained with
standard uncertainties calculated analytically.
˚
0.977 (7) A. As the deviations in C—H distances are very
The refined modulation vector was q = 0:2530 ð6Þ aꢂ
ꢅ
limited, and if we consider the error in the distances, equal to
the distance chosen for the constrained C—H bond, then
the applied constraints on the H-atom positions are justified.
This was done in order to reduce the number of refined
parameters. The total number of refined parameters in the
constrained model is then 328, to be compared with 418 in the
non-constrained model.
In the constrained refinement, the atomic positions vary
mainly with the modulation along the b axis. This variation is
represented in Fig. 5, showing the displacement of atoms C1,
C17, C20, O3, C4 and C11 as a function of the variable t.
By considering the amplitude of the variations of the
displacement for atoms C1, C17 and C20, we notice an
analogous variation for all displacements along y, and an
increase in amplitude for the x and z components from atoms
C1 to C17 and to C20. We can deduce that the molecule moves
as a whole along the b axis, and that the phenyl rings possess
0:2123 ð7Þ cꢂ: The corresponding superspace group is
P21=cðꢀ0ꢇÞ. Using this modulation vector, satellite reflections
are attached to main reflections that are systematically absent.
As no satellite reflections are attached to main reflections, a
reconsideration of the modulation vector had to be carried
out. The modulation vector was transformed into an equiva-
lent one, consistent with the previously indicated superspace
group with the new modulation vector
0:2530 ð6Þ aꢂ ꢅ 1:2123 ð7Þ cꢂ:
q
=
The average structure was introduced as the starting model
ˇ´ˇ
in the JANA2000 software (Petrıcek et al., 2003). The
incommensurately modulated structure was refined by
considering positional parameters with harmonic functions up
to third order. The modulation functions were applied to the
three rigid-body units, thus considerably reducing the number
of refined parameters.
Figure 5
Modulation function of selected atoms along the a, b and c axis (represented by x, y and z coordinates, respectively), describing the displacement as a
function of the incommensurate parameter t. The similar variation along the b axis is clearly visible. The displacement for the phenyl rings (represented
by atoms C17 and C2) is more important along the three axes than the rest of the molecule. All diagrams present the same y-axis scale.
ꢃ
Acta Cryst. (2006). B62, 506–512
Nicolas Guiblin et al.
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more degrees of freedom to move along the other directions.
We observe that C11 and C17 present the same displacement
along t, and that all of the C atoms from the RB1 and RB2
phenyl rings move with approximately the same amplitude.
All the O atoms (only O3 is presented in Fig. 5) present the
same behaviour with a slight displacement along the x and
z axis.
and 166.2 (3)ꢄ for C3—C2—C1—C17, which correspond to
the average value considering the modulation parameter.
Bending angles are 10.1 (2)ꢄ for O1—C1—C2—C3 and
9.9 (3)ꢄ for C17—C1—C2—C11. We must mention that the
first torsion angle is constant whatever the modulation para-
meter t considered, while the second torsion angle varies from
8.5 (3) to 10.9 (3)ꢄ (Fig. 6).
The phenyl rings described as RB1 and RB2 units present
small deviations compared with the basic hexagonal geometry.
The C—C—C angles vary from 118.5 (4) to 120.9 (4)ꢄ for RB1
and from 117.8 (4) to 121.2 (4)ꢄ for RB2, with a small variation
along t. The atomic deviations from the planes of the two
phenyl rings are very small, with a maximum distance from the
The opposite behaviour of the two angles characterizing the
position of the phenyl rings from the rest of the molecule
indicates that they are displaced in phase, but with a larger
variation for the RB1 unit.
If we consider the torsion angles of the two phenyl rings
around the C1—C17 (respectively C2—C11) axis (Fig. 7) we
observe that the two phenyl rings are also rotated in opposite
directions. This can be understood if we consider the molecule
viewed along its long axis. The clockwise rotation of the RB1
phenyl ring then induces an anticlockwise rotation for the
RB2 phenyl ring.
˚
basal plane of ꢆ0.009 A for C atoms.
The C1 C2 double bond presents a slight variation from
planarity. This can be interpreted as a combination of twisting
and antisymmetric out-of-plane torsion (Ermer & Mason,
1982). The twist angles are 173.8 (3)ꢄ for O1—C1—C2—C11
Observation of the distances between the C17 and C18
atoms, and the C11 and C16 atoms from the RB1 and RB2
phenyl rings, respectively, shows that these distances are in
fact less than the sum of the van der Waals radii, which
corresponds to the close-contact approximation. The average
˚
˚
values are 3.133 (7) A (C17—C11), 3.262 (7) A (C17—C16),
˚
˚
3.155 (7) A (C18—C11) and 3.180 (7) A (C16—C18). This
explains the behaviour of the phenyl rings observed both in
Figs. 6 and 7.
3. Discussion
As expected, the refinement of the modulated structure
greatly reduces the ADP values for all the atoms obtained
from the average structure. The corresponding ADPs are very
Figure 6
Variation of the angle of the two phenyl rings attached to the RB3 unit.
Figure 7
Figure 8
Variation of the torsion angles of the phenyl rings attached to the RB3
unit. Torsion angles are defined by C2—C1—C17—C18 for the RB1 unit
and by C1—C2—C11-C16 for the RB2 unit.
ORTEP view of the structure showing the quasi-isotropic behaviour of all
the atoms after the refinement of the modulation parameters. The
ellipsoids are shown for the 50% probability level.
ꢃ
510 Nicolas Guiblin et al.
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Acta Cryst. (2006). B62, 506–512

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regular for all atoms, leading to a quasi-isotropic behaviour of
all the atoms. Fig. 8 shows an ORTEP representation of the
molecule and must be compared with Fig. 2. The elongation of
the ADP ellipsoids was corrected by the displacement of the
structure along the b axis induced by the modulation.
With the crystal packing shown in Fig. 3, some interactions
between the molecules, in the form of hydrogen bonds, must
be considered (Steiner, 1997). The layer stacking is exclusively
mediated by van der Waals forces. In this structure the C—
Hꢀ ꢀ ꢀO interactions can occur in three ways, with the partici-
pation of the three different O atoms of the molecule.
Considering that the hydrogen bond is preferentially aligned
with a bonding angle between 150 and 180ꢄ (Steiner &
Desiraju, 1998), only intermolecular hydrogen bonds occur in
the crystal structure.
The O3ꢀ ꢀ ꢀH22 distances vary from 2.554 (8) to
ꢄ
˚
3.016 (10) A, and ꢃ angles from 142.3 (7) to 153.7 (7) . This
hydrogen bond is established between the RB3 unit of a
molecule and the RB1 phenyl ring of a neighbour molecule
considering the c axis. This interaction can be seen in Fig. 10.
The difference in the amplitude of the C—Hꢀ ꢀ ꢀO bond
lengths with t is essentially due to the displacement of the C
atoms. The amplitude of C3—H3ꢀ ꢀ ꢀO2 is three times larger
than for C4—H4ꢀ ꢀ ꢀO1, which can be compared with the
amplitude of the displacement of the respective C atoms (see
Fig. 5, C3 atom is displaced like C1). The same occurs for
C22—H22ꢀ ꢀ ꢀO3 compared with, for example, C3—H3ꢀ ꢀ ꢀO2
with twice the distance amplitude.
Owing to the existence of two hydrogen bonds between the
RB3 unit in the crystal packing, this part of the molecule is
stable with only a displacement along the b axis with the t
parameter. The stability of this molecular part is also observed
with the constant value of the O1—C1—C2—C3 torsion angle.
If we consider the two phenyl rings, one is linked to the RB3
unit of a neighbour molecule by a hydrogen bond and the
other one is free of intermolecular bonds. As these two rings
move in phase owing to geometrical constraints, the C22—
H22ꢀ ꢀ ꢀO3 hydrogen bond acts as a spring. The small displa-
cements of these rings relative to the rest of the molecule
induces small displacements generating deviation from three-
dimensional periodicity. The less constrained behaviour of the
RB2 phenyl ring is also observed in Fig. 6, with a larger
evolution along t for RB2 compared with RB1.
The strongest hydrogen bond of the structure is C4—
1
1
H4ꢀ ꢀ ꢀO1 (x, ꢅ y, + z). The distance varies with the
2
2
˚
modulation from 2.443 (5) to 2.510 (5) A. This hydrogen bond
links the RB3 units within the layers of the molecule, as shown
in Fig. 9. The ꢃ angle C—Hꢀ ꢀ ꢀO describing the geometry of the
hydrogen-bonding system varies from 167.30 (8) to 172.4 (4)ꢄ
along the t parameter.
1
1
The C3—H3ꢀ ꢀ ꢀO2 (x, ꢅ y, + z) hydrogen bond occurs
2
2
approximately in the same direction as the first described, with
˚
Oꢀ ꢀ ꢀH distances varying from 2.707 (6) to 2.917 (6) A and ꢃ
angles from 142.5 (5) to 147.4 (4)ꢄ.
The third hydrogen bond to be considered is C22—
H22ꢀ ꢀ ꢀO3 (ꢅ1 + x, y, z). In fact, three different hydrogen
bonds should be considered which share the O3 atom, the
other two being C6—H62ꢀ ꢀ ꢀO3, with Hꢀ ꢀ ꢀO distances varying
RB1 is less distorted than RB2. This must be related to the
existence of a hydrogen bond between H22 from RB1 and O3
from a neighbour RB3 molecular part, constraining the posi-
tion of RB1 constituent atoms. RB2 atoms are then less
constrained in position, leading to a more distorted ring,
˚
from 2.870 (7) to 3.091 (6) A, and C5—H5ꢀ ꢀ ꢀO3, with Hꢀ ꢀ ꢀO
˚
distances from 2.631 (4) to 2.914 (4) A. The reason why these
two bonds are not retained is essentially due to the C—Hꢀ ꢀ ꢀO
angle, 112.3 (5) and 123.3 (3)ꢄ for the average values, respec-
tively, which are in the lower limit of acceptance for a direc-
tional bond.
Figure 9
Packing of the structure showing the hydrogen bonds between atoms O1
Figure 10
Two different views of the packing structure showing the disposition of
the O3ꢀ ꢀ ꢀH22 hydrogen bonds [symmetry code: (i) ꢅ1 + x, y, z].
1
and H4 and atoms O2 and H3 [symmetry code: (i) x, ꢅ y, 12 + z].
2
ꢃ
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¨
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The refinement of the structure without taking into account
the modulation information (commonly referred to as the
average structure) yields quite large ADP values for the C and
O atoms. The introduction of a displacive modulation leads to
satisfactory ADP values for all atoms.
This modulation is adequately described with harmonics up
to third order. All the molecules are displaced along the b axis.
The phenyl rings are also displaced in the two other directions
(Fig. 5), with an increase of the displacement from the centre
to the exterior of the molecule. The phenyl rings are displaced
and rotated in phase with the modulation parameter t.
ˇ´ˇ
ˇ
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of Physics, Praha, Czech Republic.
ˇ´ˇ
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