Crystallization of a racemate affords a P 21 chiral crystal structure: Asymmetric unit of two opposite handed molecules simulates achiral P 21/ n packing via pseudosymmetry

Article abstract of DOI:10.1021/cg1014994

A racemic mixture consisting of a secondary ammonium salt (±)-(1RS,3SR,4RS)-1-phenyl-cis-3,4-n-butano-5,6-dihydro-1H-2, 5-benzoxazocine hydrochloride (1) crystallized as a "false conglomerate" of crystals in the monoclinic system, Sohncke space group P2₁ with two molecules of opposite handedness in the asymmetric unit and at 295(2) K: a = 10.224(2) A, b = 13.969(2) A, c = 12.724(2) A, β = 98.996(2)°, V = 1794.9(5) A³, Z = 4, and Z′ = 2. The cis-3,4-n-butano-5,6-dihydro-1H-2,5-benzoxazocine fused-ring skeletons are approximately enantiotopic and exhibit pseudoinversion and pseudo-n-glide relationships. These noncrystallographic symmetries enable space filling in the chiral crystal structure to resemble that of a higher order achiral P2₁/n apparent space group (Z = 4, Z′ = 1). The secondary ammonium salt molecules crystallize in patterns influenced by a complex blend of N-H...Cl, C-H...Cl, C-H...O, and C-H...Ar interactions that seem to be responsible for different conformational twists of the phenyl rings in the structure. Avnir's CSM method was adapted for quantification of crystallographic pseudosymmetry. RmS(G) measurements of distortion from ideal G symmetries were developed for pure translation, screw rotation, and glide reflection, as well as point group symmetries. Low rmS(i) and rmS(n-glide) values show high fidelity for the emulation of P2₁/n space filling in crystalline 1.(Figure Presented)

Full text of DOI:10.1021/cg1014994

ARTICLE
pubs.acs.org/crystal
Crystallization of a Racemate Affords a P21 Chiral Crystal Structure:
Asymmetric Unit of Two Opposite Handed Molecules Simulates
Achiral P21/n Packing via Pseudosymmetry
Avital Steinberg,† Itzhak Ergaz,† Rubꢀen Alfredo Toscano,‡ and Robert Glaser*,‡
†Department of Chemistry, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
‡Instituto de Química, Universidad Nacional Autꢀonoma de Mꢀexico, Circuito Exterior, C. U., Coyoacꢀan, D.F., 04510, Mꢀexico
S Supporting Information
b
ABSTRACT: A racemic mixture consisting of a secondary ammonium
salt (()-(1RS,3SR,4RS)-1-phenyl-cis-3,4-n-butano-5,6-dihydro-1H-2,
5-benzoxazocine hydrochloride (1) crystallized as a “false conglomer-
ate” of crystals in the monoclinic system, Sohncke space group P21 with
two molecules of opposite handedness in the asymmetric unit and
at 295(2) K: a = 10.224(2) Å, b = 13.969(2) Å, c = 12.724(2) Å,
β = 98.996(2)°, V = 1794.9(5) Å3, Z = 4, and Z0 = 2. The cis-3,4-n-
butano-5,6-dihydro-1H-2,5-benzoxazocine fused-ring skeletons are ap-
proximately enantiotopic and exhibit pseudoinversion and pseudo-n-
glide relationships. These noncrystallographic symmetries enable space
filling in the chiral crystal structure to resemble that of a higher order achiral P21/n apparent space group (Z = 4, Z0 = 1). The
secondary ammonium salt molecules crystallize in patterns influenced by a complex blend of NꢀH Cl, CꢀH Cl, CꢀH O,
3 3 3
3 3 3
3 3 3
and CꢀH Ar interactions that seem to be responsible for different conformational twists of the phenyl rings in the structure.
3 3 3
Avnir's CSM method was adapted for quantification of crystallographic pseudosymmetry. RmS(G) measurements of distortion
from ideal G symmetries were developed for pure translation, screw rotation, and glide reflection, as well as point group symmetries.
Low rmS(i) and rmS(n-glide) values show high fidelity for the emulation of P21/n space filling in crystalline 1.
’ INTRODUCTION
unrelated molecules of opposite handedness as false conglomerates.
They estimate the frequency for false conglomerate formation to
be about 1% for organic compounds.6 False conglomerates differ
from true conglomerates in that dissolution of one chiral crystal
excised out of the bulk will now produce an optically inactive
solution of solvated enantiomers.
It is very common for both independent molecules to exhibit the
same (but not identical) conformation, and when they do, then their
corresponding bond lengths, angles, and torsion angles are usually
statistically similar.5 However, it is the relative energies of conforma-
tions and packing considerations that ultimately determine if one or
multiple conformations are to be found in the Z0 > 1 asymmetric
unit. When the conformations are the same, it is often possible to
show that the independent molecules are related to one another by
approximate symmetry transformations (pseudosymmetry).5 Pseu-
dosymmetrical independent molecules in the asymmetric unit
implies that structurally similar diastereomers mimic pairs of homo-
mers or enantiomers and show a particular intermolecular spatial
orientation approximating symmetry. Gavezzotti7 has investigated a
large population of crystals with two molecules in the asymmetric
unit (Z0 = 2) and noted that with an asymmetry tolerance of 0.5 Å
About 90% of the time, crystallization of a racemic mixture of
organic compounds yields achiral crystals known as racemic
compounds in the solid-state.1 The achiral crystal lattice contains
equal quantities of both enantiomers that reside in well-defined
positions.2 On the other hand, only about 10% of all racemic
mixtures of organic compounds crystallize as conglomerates of
chiral crystals.1 These are simple mechanical mixtures of (þ)- and
(ꢀ)-chiral crystals in a 1:1 statistical ratio.2 Usually, only one
molecule resides in the asymmetric unit (Z0 = 1) of these chiral
crystals. Dissolution of one crystal excised out of the bulk results
in a solution containing an enantiomerically pure compound.
Desiraju3 has noted that during the period of 1970ꢀ2006, the
percentage of organic compounds in the Cambridge Structural
Database4 with morethanone molecule inthe asymmetric unithas
remained virtually constant at approximately 11%. Two molecules
in the asymmetric unit (Z0 = 2) occur when it is difficult, by
symmetry alone, to simultaneously satisfy both the criteria of close
packing and the requirements of optimal intermolecular
interactions.5 This situation enables the intriguing possibility of
two molecules of either invariant or opposite handedness com-
prising the asymmetric units of these chiral crystal structures.
In most of those cases asymmetric units consist of two molecules
with the same handedness. Bishop and Scudder6 have referred to
conglomerates of chiral crystals containing two symmetry
Received: November 10, 2010
Revised:
February 22, 2011
Published: March 21, 2011
r
2011 American Chemical Society
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dx.doi.org/10.1021/cg1014994 Cryst. Growth Des. 2011, 11, 1262–1270
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Crystal Growth & Design
ARTICLE
atomꢀ1, 83% of the nonsymmetry related molecular arrangements in
the asymmetric unit revealed some kind of noncrystallographic
symmetry beyond that of the true symmetry imposed by the space
group. The presence of crystallographic pseudosymmetry empha-
sizes that the “...preconception that symmetry must rule exact and
uninterrupted throughout proper crystals for best packing and for
thermodynamic stability”7 sometimes is only achieved via multiple
content (Z0 > 1).
This paper describes the crystal packing within a false
conglomerate produced via crystallization of a racemic mix-
ture of the secondary ammonium salt (()-(1RS,3SR,4RS)-1-
phenyl-cis-3,4-n-butano-5,6-dihydro-1H-2,5-benzoxazocine hy-
drochloride (N-desmethyl-cis-3,4-n-butano-nefopam HCl, 1).
The oppositely handed fused-ring skeletons in these chiral
crystals exhibit pseudoinversion and pseudo-n-glide reflection
relationships. The crucial role of pseudosymmetry in space
filling within the false conglomerate will be discussed in this
report.
translation). The quantification of the pseudosymmetry operations in
this crystal will also be discussed below.
’ EXPERIMENTAL SECTION
NMR Spectroscopy. Solution-state 1H and 13C NMR spectrosco-
py were recorded at ambient temperature on a spectrometer at 500.13
and 125.76 MHz, respectively. The sample was measured in CD2Cl2
1
using the deuterium solvent as an internal lock. 13C and H chemical
shifts were based on the respective CD2Cl2 [53.8 ppm] and residual
CHDCl2 [5.32 ppm] signals as internal references. Homonuclear
decoupling was used to assign the spinꢀspin coupling constants. The
DEPT-135 pulse-sequence was used ascertain the hydrogen multiplicity
of the 13C signals. HMQC 2D-NMR spectroscopy was used to correlate
the 13C and 1H chemical shifts. NOE-DIFF experiments were performed
to aid in signal assignment.
(()-(1RS,3SR,4RS)-1-Phenyl-cis-3,4-n-butano-5,6-dihydro-
1H-2,5-benzoxazocine Hydrochloride (1). Using the method of
Glaser et al.34 for the analogous preparation of N-desmethylnefopam
HCl, phenylmagnesium bromide was reacted with phthaldialdehyde in
cold dried ether to give the 2-hydroxy-5-phenyl-2,5-dihydro-3,4-benzo-
furan crystalline intermediate (mp 120ꢀ122 °C). Reaction of this
intermediate with cis-2-aminocyclohexanol (from Acros Organics Inc.)
in warm toluene afforded cis-2-(3-phenyl-1,3-dihydro-isobenzofuran-1-
ylamino)-cyclohexanolasa crude intermediate which was thenreducedby
LiAlH4 to give cis-2-(2-hydroxy-cyclohexane)-aminomethylbenzhydrol as
a crystalline intermediate [mp100ꢀ103°]. Ringclosure ofthe benzhydrol
with p-CH3C6H4SO2OH/toluene and workup gave a crude viscous oil
containing a 1:10 mixture of (1RS,3RS,4SR)- and (1RS,3SR,4RS)-1-
phenyl-cis-3,4-n-butano-5,6-dihydro-1H-2,5-benzoxazocine (cis-3,4-n-bu-
tano-N-desmethylnefopam) free base diastereomers. After dissolving the
oil in ether and a few drops of methanol, ethereal HCl was carefully added
dropwise until acidic to pH paper to yield a solid that was recrystallized
from methanol/ethyl acetate/n-hexane to afford 1.4 g (73% yield)
(()-(1RS,3SR,4RS)-1-phenyl-cis-3,4-n-butano-5,6-dihydro-1H-2,5-ben-
zoxazocine hydrochloride (1), mp 259ꢀ261 °C; IR (KBr) ν 3416 cmꢀ1
(NH); 1H NMR (CD2Cl2) δ 5.77 [s, 1H, H(1)], 4.02 [dt, J(3ax-4eq) =
2.9(3) Hz, J(3ax-19eq) = 3.6(5) Hz, J(3ax-19ax) = 9.6(1) Hz, 1H,
H(3ax)], 3.52 [dt, J(3ax-4eq) = 2.9(3) Hz, J(4eq-22eq) = 3.5(2) Hz,
J(4eq-22ax) 6.5(2) Hz, 1H, H(4eq)], 7.77 [broad-s, 1H, NH(5)], 7.91
[broad-s, 1H, NH(50)], 5.39 [d, J = ꢀ12.6 Hz, 1H, H(6endo)], 4.25 [d, J =
ꢀ12.6 Hz, 1H, H(6exo)], 7.54 [dd, J(7-8) = 6.3 Hz, J(7-9) = 2.9 Hz, 1H,
H(7)], 7.16 [dd, J(9-10) = 6.2 Hz, J(8-10) = 2.9 Hz, 1H, H(10)],
7.22ꢀ7.36 [m, 7H, ArH], 2.14 [m, 1H, H(19ax)], 1.77 [m, 1H, H(19eq)],
1.42 [m, 1H, H(20ax)],1.87[m,1H,H(20eq)],1.97[m, 1H, H(21ax)], 1.54
[m, 1H, H(21eq)], 2.22 [m, 1H, H(22ax)], 1.77 [m, 1H, H(22eq)];
13C{1H} NMR (CD2Cl2) δ 85.28 [C(1)], 77.51 [C(3), broad], 52.79
[C(4)], 47.51 [C(6)], 134.82 [C(7)], 128.77 [C(10)], 29.03 [C(19)],
22.77 [C(20)], 21.47 [C(21)], 25.99 [C(22)]; 129.76, 128.35, 128.12,
127.65 [unassigned ArCH]; 143.04, 142.63 [ArC(quat)]. Anal. Calcd for
C20H24ClNO: C, 72.82; H, 7.33; N, 4.25. Found: C, 72.54; H, 7.41; N,
4.03. See Supporting Information for complete details of the synthesis
procedure.
Avnir and co-workers have shown that chirality and distortion
from ideal symmetry and from ideal shape should be considered
to be continuous properties. These have been quantified by
Continuous Symmetry Measures (CSM),8ꢀ14 Continuous Chir-
ality Measures,15 and Continuous Shape Measures (CShM).16,17
The CSM of a structure is a normalized root-mean-square (rms)
distance function from the closest theoretical structure which has
the ideal symmetry.8,9,11,14 The broad utility of the Avnir Con-
tinuous Symmetry Measures has been extensively demonstrated
for quantification of symmetry distortion within objects/mol-
ecules, and has led to correlations of these values for a wide range
of physio-chemical phenomena,18ꢀ23 and even anthropology.24
The application of Symmetry Operation Measures to inorganic
chemistry,25 and the use of CShM25ꢀ29 measurements for analysis
of complex polyhedral structures has also been discussed by
Alvarez and co-workers.
The fidelity of a pseudosymmetry relationship is a variable
which can be quantified, and its values should represent a
continuum. A number of measurements for pseudosymmetry
in crystals may be found in the literature.7,30ꢀ33 Avnir’s CSM
method is unique because it can treat two pseudosymmetric
molecules (or corresponding subunits in two molecules) as one
ensemble unit and calculate a root-mean-square (rms) distance from
the closest theoretical ensemble which has the specified symmetry. A
desire to calculate a single parameter value for the fidelity of the
intermolecular pseudosymmetry relationships in this crystal
prompted us to modify and extend the Continuous Symmetry
Measures of Avnir and co-workers. The classical CSM measurements
were based on distortion from ideal point group symmetries, and thus
they had to be modified for symmetry operations with translation
components observed solely in space groups, that is, pure translation,
glide-reflection (reflection-translation), and screw-rotation (rotation-
X-ray Crystallography of (()-(1RS,3SR,4RS)-1-Phenyl-cis-
3,4-n-butano-5,6-dihydro-1H-2,5-benzoxazocine
Hydro-
chloride (1).35 Crystallization was performed by vapor diffusion of
n-hexane into a methanol/ethyl acetate solution of salt 1. A clear prism
of C20H24ClNO having the approximate dimensions of 0.89 ꢁ 0.52 ꢁ
0.44 mm3 was chosen, mounted on a glass fiber, and then fixed to the
goniometer head of the X-ray diffractometer. Crystallographic mea-
surements were made on a Bruker SMART 1k CCD diffractometer with
graphite monochromated Mo KR (λ = 0.71073 Å) radiation. Data were
collected to a maximum θ value of 23.45° (96.7% completeness to θ),
and then reduced by the SAINT36 software package. Analysis of the data
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Crystal Growth & Design
ARTICLE
showed negligible decay during data collection, the intensities were
corrected for Lorentz and polarization factors, and an empirical
absorption correction was applied via SADABS37 (Tmin 0.8778, Tmax
1.00000). The structure was solved by application of direct methods
and refined by full matrix least-squares on F2 using the SHELXTL38
software package. Cell constants corresponded to a monoclinic system
with dimensions at 295(2) K of a = 10.224(2) Å, b = 13.969(2) Å, c =
12.724(2) Å, β = 98.996(2)°, and V = 1794.9(5) Å3. Systematic
absences correspond to either P21 (noncentrosymmetric) or P21/m
(centrosymmetric) space groups. Attempts to solve the structure in the
centrosymmetric space group P21/m were uniformly unsuccessful, but
the structure solved immediately in P21 and refined to a final R = 0.0241.
Refinement in the centrosymmetric space group P21/n (one molecule
in the asymmetric unit) was carried out after the proper origin shift. The
refinement and the molecular packing arrangement showed that the
pseudoinversion centers and pseudo-n-glide reflection planes are only
local pseudosymmetry elements. We conclude that the space group is
unambiguously P21. For Z = 4, Z0 = 2 and fw =329.85, the calculated
density is 1.221 g/cm3. 7556 reflections were measured, 3885 unique,
(Rint = 0.0151). Hydrogens attached to N-atoms were located in the
difference Fourier map and refined isotropically. The rest of the
H-atoms in this structure were introduced at calculated positions as
riding atoms, with CꢀH = 0.98 Å (CH), 0.97 Å (CH2), or 0.93 Å
(aromatic) and Uiso(H) = 1.2Ueq(C). All non-hydrogen atoms were
refined anisotropically. At convergence, the final discrepancy indices on
F were R(F) = 0.0241, Rw(F2) = 0.0596, and GOF S = 1.015 for the 3885
reflections with Inet > 2σ(Inet) and 431 parameters refined with 1
constraint. The residual negative and positive electron densities in the
final map were ꢀ0.133 and 0.117 e/Å3. The handedness of the polar
structure was determined by successful refinement of the Flack para-
meter (ꢀ0.06(4)).
Figure 1. Cluster of magenta colored graphically enlarged midpoints
(i.e., average coordinates) [x,y,z] between corresponding n-pairs of
hhh
atoms within the approximately enantiomeric fused-ring skeletons of
the (þ)-A and (ꢀ)-B molecules (1). For simplicity, only the nitrogens
and their ligated atoms have been illustrated for each molecule. Broken
lines indicate hydrogen bonds.
related atoms in molecules A and B is:
n
∑ xi
n
i¼1
The rmS(G) Pseudosymmetry Tool, Where G = i, σ, Cn, and
Sn. CSM calculations were performed at the Web site39 of the Avnir
group at the Hebrew University of Jerusalem, using the Advanced
mode. Input file format information and a tutorial are provided at the
site. These calculations include the deviation from ideal G point group
symmetries of G = i, σ, Cn, and Sn. The fractional coordinates of an
ensemble consisting of G pseudosymmetry related n-pairs of atoms
within two molecules/or fragments were converted to Cartesian space
and then arranged in an MDL (*.mol format) input file. Another input
file specifies the permutation of atom pairs for the desired G
pseudosymmetry relationship. The coordinates of the theoretical
xmean
¼
The point defined by the [xmean,ymean,zmean] fractional coordinates is
the statistical “best point”, and its estimated standard deviation (esd) is
the precision of this value. A statistically calculated “best line” or “best
plane” can be calculated from the set of midpoint [x,y,z] coordinates
hhh
between corresponding n-pairs of atoms in pseudoscrew and pseudo-
glide arrays of points using modules developed for MATLAB.40,41
Pseudo-Glide Translation. A crystallographic glide symmetry
operation is a composite of a translation and a reflection. If the
directional cosine values of the R, β, and γ angles, which the “normal
to the best plane”42 make with the positive directions of the coordinate
axes show that these lines are parallel to a cell face, then one is justified in
treating the glide reflection pseudosymmetries as separate translation
and reflection components, respectively (a similar argument can be
made for a pseudo-21 screw rotation ‘best line’41 which is parallel to a cell
axis). After molecule (ꢀ)-B is translated along the ‘best glide’ translation
line, it has a pseudo mirror relationship with respect to molecule (þ)-A
that can be quantified using the rmS(σ) tool. Similarly for a pseudo-21 screw
rotation relationship, if molecule (ꢀ)-B is translated along the ‘best screw’
translation line, it will now have a pseudo-C2 rotation arrangement relative
to molecule (þ)-A whose fidelity can be quantified using the rmS(C2) tool.
In the crystal under consideration, the ‘best pseudo-n-glide translation line’
lies within one of two ac-planes. Therefore, they each are composed of an
x-component and a z-component. The xi-translation of an atom in molecule
(ꢀ)-B with respect to one in molecule (þ)-A can be calculated from the
difference in their respective xi fractional coordinates, for example, Δxi =
xi(A) ꢀ xi(B). A Δzi value can be calculated in a similar fashion.
‘nearest ideal geometrical ensemble’ having bona fide
G
symmetry8,9,11,14 were calculated from the input coordinates using
the appropriate Avnir CSM algorithm.39 The size-dependent CSM
S(G) value, scaling factor, initial ensemble (structure) coordinates,
resulting ideal G-symmetry ensemble (structure) coordinates, direc-
tional cosines and the atom permutation list appear in the output
“Results” file.39 Then, atoms in the “nearest ideal G symmetry
ensemble of geometrical structures” were superimposed upon corre-
sponding atoms in the input ensemble of a G pseudosymmetry related
pair of molecules/or fragments to give the rms interatomic distance.
This is an average deviation from ideal G symmetry which is defined as
a crystallographic G pseudosymmetry measure called “the nonsize
normalized rmS(G) tool”.
Location of Statistically Determined Pseudosymmetry
Elements. The midpoints (i.e., average coordinates) [x,y,z] between
hhh
corresponding n-pairs of atoms within the approximately enantiomeric
fused-ring skeletons of the (þ)-A and (ꢀ)-B molecules generate either a
cluster of points (see Figure 1), or an approximately linear string of
points (not applicable for crystalline 1) or an almost planar array of
points, if the fragments are related by pseudoinversion, or pseudo-21
screw-rotation, or pseudoglide reflection, respectively. The xmean value
for all the midpoints between n-pairs of pseudoinversion symmetry
The rmS(translation) Pseudosymmetry Tool. An ideal trans-
lation Δxi value would obviously be exactly 0.5 fractional coordinate
units. The difference between an actual xi-translation (Δxi) minus the
ideal value for a bona fide glide reflection (or 21 screw-rotation) is
calculated for each of the n-pairs of atoms in the ensemble. The rms value
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Crystal Growth & Design
ARTICLE
Table 1. Selected Torsion Angles [°] for Eight-Membered
Ring BoatꢀBoat Conformation and Phenyl Twist in
(1R,3S,4R)-A (1A) and (1S,3R,4S)-B (1B) versus (1S)-Nefo-
pam HCl (2)
’ RESULTS AND DISCUSSION
The cis-3,4-n-butano-5,6-dihydro-1H-2,5-benzoxazocine fused-
ring skeletons in the P21 crystal are ‘almost enantiomeric’ in
structure and the eight-membered rings therein have boatꢀboat
(BB) conformations that are both very similar to that observed for
the parent non-narcotic analgesic drug (()-nefopam HCl (2),42
see selected torsion angles in Table 1. The close geometrical
similarity of the skeletons in salt 1 is seen by inverting the
handedness of one of them followed by superimposition of all
corresponding non-hydrogen atoms (but no phenyl atoms) to give
a very small root mean squared (rms) difference of only 0.051 Å.
A striking feature of the crystal structure is that the phenyl rings
ligated to each skeleton have different twist conformations
torsion angle
molecule A
molecule B
2
C(11)ꢀC(1)ꢀO(2)ꢀC(3)
C(1)ꢀO(2)ꢀC(3)ꢀC(4)
O(2)ꢀC(3)ꢀC(4)ꢀN(5)
C(3)ꢀC(4)ꢀN(5)ꢀC(6)
C(4)ꢀN(5)ꢀC(6)ꢀC(12)
N(5)ꢀC(6)ꢀC(12)ꢀC(11)
C(6)ꢀC(12)ꢀC(11)ꢀC(1)
C(12)ꢀC(11)ꢀC(1)ꢀO(2)
C(11)ꢀC(1)ꢀC(13)ꢀC(18)
H(1)ꢀC(1)ꢀC(13)ꢀC(14)
85.7(2)
ꢀ70.3(2)
ꢀ50.5(2)
59.8(2)
46.4(3)
ꢀ81.1(3)
2.1(3)
ꢀ82.7(2)
71.5(2)
ꢀ82.74
63.82
49.7(2)
57.87
ꢀ61.9(2)
ꢀ43.3(3)
81.8(3)
ꢀ59.29
ꢀ49.15
79.09
ꢀ1.9(3)
ꢀ9.0(3)
ꢀ77.8(2)
ꢀ16.5
3.23
(angle between planes = 60.1°). One phenyl ring C(18Aortho
almost eclipses a benzo-ring C(11Aipso) sp2-carbon in molecule A
[C(11A)ꢀC(1A)ꢀC(13A)ꢀC(18A) þ 20.1°], while C(14Bortho
in the other phenyl ring approximately eclipses an H(1Bbenzhydrylic
proton in molecule
)
5.9(3)
ꢀ6.56
ꢀ65.77
ꢀ4.2
20.1(2)
ꢀ42.8
)
)
B
[H(1B)ꢀC(1B)ꢀC(13B)ꢀC(14B)
for the set of n-differences is the deviation from an ideal xi-translation
(in fractional coordinates) along the corresponding direction, rmS
ꢀ16.5°]. The phenyl ring also eclipses the benzhydrylic-H in the
crystalline parent drug (2).
(x-translation)coordinate
:
For the sake of simplicity, the two molecules will be arbitrarily
referred to as (þ)-A and (ꢀ)-B, respectively. These molecules
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u
n
crystallize in patterns influenced by a complex blend of NꢀH
u
3
2
u ∑ ðΔxi ꢀ 0:5Þ
Cl, CꢀH Cl, CꢀH O, and CꢀH Ar interactions.
t
3 3
3 3 3
3 3 3
3 3 3
i ¼1
An R2 (8) ring hydrogen-bonding pattern graph set43 involves 2
rmSðx-translationÞcoordinate
¼
4
n
hydrogen-bond acceptors and 4 hydrogen-bond donors in an
8-atom ring cycle that links all pairs of (1R,3S,4R)-A and
(1S,3R,4S)-B molecules (see Figures 1ꢀ3). In this ring pattern,
N(5A)—H(5A) Cl(1) 2.30(2) Å, N(5A)—H(5B) Cl(2)
The rmS(x-translation)coordinate value was multiplied by the a-axis cell
length to give the relevant crystallographic translation pseudosymmetry
measure, rmS(x-translation) now in Å.
The rmS(glide) and rmS(screw) Pseudosymmetry Tools.
The xmean-translation (or ymean-translation, not applicable for 1) or
zmean-translation is the mean value of the Δxi (or Δyi) or Δzi fractional
coordinate distances between the n-pairs of atoms involved in a
translation of molecule (ꢀ)-B to (þ)-A. For example
3 3 3
3 3 3
2.18(3) Å, N(5B)—H(5C) Cl(2) 2.21(3) Å, and N(5B)—
3 3 3
H(5D) Cl(1) 2.14(3) Å, while the corresponding NꢀH
3 3 3
3 3 3
Cl angles are: 153(2)°, 175(2)°, 159(2)°, and 170(2)°. The
hydrogen-bonding interactions involve the pseudoinversion
symmetry related and more sterically demanding fused-ring
pseudoenantiomeric ‘skeletal’ fragments of the diastereomers.
These heterodimers extend the structure into infinite chains
n
∑ Δxi
n
along the b-direction by CꢀH Cl interactions {C(16A)—
3 3 3
i¼1
x-translationmean
¼
H(16A) Cl(2)[x, ꢀ1 þ y, z] 2.97 Å and C(16B)—H-
3 3 3
3 3 3
(16B) Cl(1)[x, 1 þ y, z] 3.11 Å}. Parallel chains generated
by 21 symmetry operations are held together by CꢀH Cl
3 3 3
If statistically insufficient midpoints are present in one unit cell to
calculate a “best line” or “best plane” that is parallel to a cell face, then
midpoints from adjacent unit cells should be added to the set. For a
pseudo n-glide in crystalline 1, a ‘dummy’ molecule (ꢀ)-B was created
from (ꢀ)-B by transforming its atomic coordinates by the respective
xmean and zmean values so that it was opposite (þ)-A. Now, from an input
file of the Cartesian coordinates of the ensemble of “dummy”-B and
actual A molecules, the coordinates of the closest theoretical geometrical
structure with bona fide reflection symmetry was calculated with the
Avnir CSM S(σ) program. The nondistance dependent deviation from
true reflection symmetry in the “dummy” (ꢀ)-B plus actual (þ)-A
ensemble of molecules [rmS(σ)glide] was calculated in a similar manner
to rmS(σ) described above. The rmS(glide) is the summation of its two
components: rmS(σ)glide þ rmS(translation)glide, and their values are in
Å. If a pseudo-21 screw relationship exists within the ensemble of
‘dummy’ and real molecules, then rmS(C2)screw is calculated by analogy
to rmS(C2) also described above, and rmS(screw) equals rmS(C2)screw
interactions {C(8A)—H(8A) Cl(1)[ꢀ1þx,y,z] 2.78 Å and
3 3 3
C(8B)—H(8B) Cl(2)[1 ꢀ x, 1/2 þ y, 1 ꢀ z] 2.83 Å} giving
3 3 3
3 3 3
rise to extra CꢀH O interactions {C(17B)—H(17B) O-
3 3 3
(2A)[x, 1 þ y, z] 2.62 Å} and C(aryl)—H π interactions
3 3 3
{C(15A)—H(15A) Aryl-C(7Af12A)centroid[2 ꢀ x,ꢀ1/2 þ
3 3 3
y, ꢀz] 2.83 Å, and C(15B)—H(15B) Aryl-C-
3 3 3
(7Bf12B)centroid[1 ꢀ x, 1/2 þ y, 1 ꢀ z] 2.87 Å}, which in turn
seem to be responsible for the different orientations of the phenyl
rings in the structure, see Figure 3.
Pseudoinversion Symmetry. Figure 2 clearly depicts a
pseudoinversion relationship between the fused-ring skeletons
of molecule (þ)-A and molecule (ꢀ)-B if the disparately twisted
phenyl rings are overlooked. If the inversion was bona fide, then
the [x,y,z] midpoints between pairs of corresponding atoms in
hhh
the two molecules would all converge at one single point located
at a specific spatial location in the crystal lattice (a special position
of inversion symmetry). But, since pseudosymmetry between
oppositely handed diastereomeric (rather than enantiomeric)
skeletons is involved, then the distribution of midpoints becomes
a cluster of points occupying a general position of symmetry, where
local site symmetry is only identity (see enlargement in Figure 1).
þ rmS(translation)screw
.
CSM Error Estimation. The errors in the CSM values are
estimated using the Avnir CSM Error Estimation Program, which takes
the number of unique reflections, the thermal factors, and the CSM value
into account as input, and returns a CSM range or an upper bound for
the CSM values.12
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Crystal Growth & Design
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Figure 2. Molecular structure, numbering diagram, and hydrogen-bond pattern for (1R,3S,4R)-A and (1S,3R,4S)-B in the asymmetric unit of P21 salt 1.
Displacement ellipsoids are drawn at the 50% probability level. Broken lines indicate hydrogen bonds. A statistically determined ‘best point’ of
pseudoinversion at coordinates [0.779(3),0.501(2),0.249(4)] lies near the center of the R2 (8) ring hydrogen-bonding pattern graph set.
4
Figure 3. The heterodimers extend the structure into infinite chains along the b-direction by C(16A)—H(16A) Cl(2) and C(16B)—
3 3 3
H(16B) Cl(1) interactions. Parallel chains generated by 21 symmetry operations are held together by a complex blend of CꢀH Cl, CꢀH O,
3 3 3
3 3 3
3 3 3
3 3 3
and CꢀH Ar interactions which seem to be responsible for the different orientations of the phenyl rings in the structure.
The location of the above-mentioned pseudoinversion cluster of
points is a statistically determined [xmean,ymean,zmean] best point
at coordinates [0.779(3),0.501(2),0.249(4)]. The estimated
standard deviation of these coordinates is the precision of the
pseudosymmetry inversion cluster.
The 21 screw-rotation operator generates (þ)-A[1 ꢀ x, y þ
0.5, 1 ꢀ z] and (ꢀ)-B[1 ꢀ x, y ꢀ 0.5, 1ꢀ z], the remaining two
molecules within the unit cell. An additional pseudoinversion
relationship exists between their fused-ring skeletons (i.e., again
neglecting the phenyls), see Figure 4. Now, the coordinates of
the statistically determined best point are [0.221(3), 0.501(2),
0.751(4)], about midway between the edge-to-face phenyl rings.
Once again, the different phenyl-ring twists of the aromatic edge-
to-face44 interaction (centroid centroid 4.84 Å) break bona
3 3 3
fide inversion symmetry, but this is dismissed when discussing
pseudoinversion between the larger fused-ring skeletal frag-
ments. Within the unit cell are two additional pseudoinversion
relationships. Each involves one of the two (ꢀ)-B molecules
from within the unit cell plus a nearby (þ)-A molecule in an
adjacent cell: Figure 5 shows molecules (ꢀ)-B and (þ)-A[x ꢀ 1,
y, z] whose statistical best point is [0.279(3), 0.501(2),
0.249(4)], and Figure 6 depicts the molecules (ꢀ)-B[1 ꢀ x, y
ꢀ 0.5, 1 ꢀ z] and (þ)-A[2 ꢀ x, y þ 0.5, 1 ꢀ z] whose statistical
best point is [0.721(3), 0.501(2), 0.751(4)].
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Figure 4. An edge-to-face phenylꢀphenyl interaction (centroid
3 3 3
centroid 4.84 Å) between the 21-screw generated molecules (þ)-A[1 ꢀ x,
y þ 0.5, 1 ꢀ z] on the left and (ꢀ)-B[1 ꢀ x, y ꢀ 0.5, 1 ꢀ z] on the
right. A statistically determined best point of pseudoinversion for the
fused-ring skeletons is between the asymmetrically arranged phenyls and
has coordinates [0.221(3),0.501(2),0.751(4)].
Figure 6. Statistically determined best point of pseudoinversion for the
fused-ring skeletons of molecules (þ)-A[2 ꢀ x, y þ 0.5, 1 ꢀ z] on the
right and (ꢀ)-B[1 ꢀ x, y ꢀ 0.5, 1 ꢀ z] on the left is at coordinates
[0.721(3), 0.501(2), 0.751(4)].
Figure 5. Statistically determined best point of pseudoinversion for the fused-ring skeletons in molecules (þ)-A[x ꢀ 1, y, z] on the right and (ꢀ)-B on
the left is at coordinates [0.279(3), 0.501(2), 0.249(4)].
Measures for Crystallographic Pseudosymmetry. Pseudo-
symmetry measurements were confined to ensembles of two
fused-ring skeletal fragments since only they are capable of
showing intermolecular symmetry. When the Avnir CSM S(i)
calculation was used to measure the departure from true inversion
within the four ensembles of two pseudoenantiomeric skeletons
(i.e., neglecting the phenyls) depicted in Figures 2 and 4ꢀ6, the
results varied from0.020 to0.040(where idealinversionsymmetry
is S(i) = integer zero). Despite the fact that there can be no
symmetry (and thus no pseudosymmetry) between the edge-to-
face phenyls due to their asymmetric arrangement, S(i) was
calculated for four ensembles of just phenyl pairs in order to
provide comparative numerical values when inversion symmetry
was impossible. The closer the two noninversion related phenyl
rings were to each other, the higher was their S(i) value: S(i) =
ensembles were a reminder that the CSM S(i) method treats an
ensemble of two skeletons as one object and calculates the closest
theoretical geometry for that ensemble having ideal inversion
symmetry within. A size normalization scaling factor is included in
these calculations, so that an object’s size would not influence its
S(G) value for distortion from an ideal G symmetry. However,
when the “object” is a composite of two molecules/fragments,
then the distance between them influences the object’s size. Since
the four pseudoinversions in our crystal involved pairs of diaster-
eomeric skeletons with different intermolecular distances, the
distance normalization function had to be removed from the
Continuous Symmetry Measures. This was previously done by
YogevꢀEinot and Avnir18 to afford a nearly constant chirality
measure thatwas independent of the lengthof a quartzhelix. Using
their modification, atoms in the input ensemble were super-
imposed on those of the closest theoretical ideal ensemble
(coordinates listed in the output file prior to the distance normal-
ization step). Now, the same rms distance value of 0.088(1) Å
was calculated for all four skeletal ensembles. We called this rmS(i)
2.64(1) (Figure 4, centroid centroid 4.84 Å), S(i) = 1.37(1)
3 3 3
(Figure 5, centroid centroid 7.18 Å), S(i) = 0.32(1) (Figure 2,
3 3 3
centroid centroid 15.72 Å), and S(i) = 0.29(1) (Figure 6,
centroid centroid 16.60 Å). The results for these more simple
3 3 3
3 3 3
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Figure 8. Axes of 21 screw-rotation [colored black] are a feature
common to symmetry element diagrams of both the P21 (Z = 4, Z0=
2) chiral unit cell of 1 (conventional black outline and analogous green
on the left) and of a P21/n (Z = 4, Z0 = 1) achiral unit cell (on the right).
The red colored pseudosymmetry elements in the diagram for the P21
crystal structure of 1 are located in a spatial arrangement approximating
that of the black colored P21/n special positions of inversion and n-glide
reflection symmetry. The positive direction of both b-axes in this figure is
toward the viewer.
The Cartesian coordinates of the closest theoretical ensemble
having ideal reflection were extracted from the CSM S(σ) output
file. The rms of superimposition of similar atoms in the ideal and
input ensembles provided a 0.076(1) Å nondistance normalized
rmS(σ) value (denoted as the crystallographic pseudoreflection
tool, to distinguish it from the CSM S(σ)). To also put this value
into quantitative perspective, rmS(σ) = 0.91(1) Å when just the
ensembles of edge-to-face phenyl ring pairs were calculated. As with
inversion, the asymmetric ensembles of these phenyl rings are
incompatible with n-glide symmetry.
Figure 7. Illustration of graphically enlarged magenta colored mid-
points (i.e., average coordinates) [x,y,z] between corresponding n-pairs
hhh
of atoms in the approximately enantiomeric fused-ring skeletons of 1.
This array of points represents an almost planar pseudo-n-glide reflec-
tion projection [y = 0.251(3)] between molecules (þ)-A[x ꢀ 1, y, z] on
left-bottom and (ꢀ)-B[1 ꢀ x, y ꢀ 0.5, 1 ꢀ z] at right-top. The positive
direction of the b-axis in this figure is toward the viewer.
Pseudo-x- or z-Translation. The difference between an actual
xi-translation (Δxi = xi(A) ꢀ xi(B)) minus the ideal 0.5 value for
a bona fide glide reflection operation (or 21 screw-rotation) was
calculated for each of the n-pairs of atoms in the ensemble. The
rms value for the set of n-differences is the deviation from an ideal
crystallographic x-translation (in fractional coordinates), rmS(x-
translation)coordinate = 0.059 x-units. Similarly, rmS(z-transla-
tion)coordinate = 0.013 z-units. These values were multiplied by
the respective 10.224(2) Å a- or 12.724(2) Å c-axes cell lengths
to give the relevant crystallographic pseudotranslation measures:
0.608 Å rmS(x-translation) and 0.160 Å rmS(z-translation). The
rmS(n-translation) is the 0.38(6) Å average value of the rmS(x-
and z-translations). Finally, the 0.45(6) Å rmS(n-glide) measure-
ment is the sum of its two components: rmS(σ) þ rmS(n-
translation): 0.076(1) Å þ 0.38(6) Å.
(a crystallographic pseudoinversion tool) to distinguish it from the
standard CSM method. The lower the rmS(i) distortion value, the
higheristhepseudosymmetryfidelity. ToputthisrmS(i) 0.088(1)
Å value in perspective, distance normalization was removed from
the calculations on the four asymmetric ensembles of phenyl pairs,
and the result was a ca. five times higher 0.46(1) Å rmS(i) value,
that was the same for all ensembles.
Pseudo-n-Glide Reflection. The combination of bona fide 21
screw-rotation acting on the pseudoinversion related molecules
affords additional pseudosymmetry, providing that the differ-
ently skewed phenyl rings are once again ignored, see Figure 7.
The array of [x,y,z] midpoints between corresponding atoms
hhh
within the approximately enantiotopic fused-ring skeletons of the
(þ)-A[1 ꢀ x, y, z] and (ꢀ)-B[1 ꢀ x, y ꢀ 0.5, 1 ꢀ z] molecules
represents an almost planar projection that portrays a pseudo
n-glide reflection. The statistical best plane of these points cuts the
y-axis at 0.251(3), and the rms deviation from the best plane was
only 0.009 Å. The 21 screw-rotation afforded a second pseudo-
n-glide reflection plane relating skeletons (ꢀ)-B and (þ)-A[2 ꢀ x,
y þ 0.5, 1 ꢀ z], and its best plane cuts the y-axis at 0.751(3).
The directional cosines of the R, β, and γ angles that the normal
to the best plane made with the positive directions of the coordinate
axes were 0.0095, ꢀ0.9999, 0.0137. This showed that the normal to
the statistical best plane was parallel to the a,c-cell face and justified
treating the pseudoglide reflection as separate translation and
reflection components. Observation of the glide relationship
showed that it was an n-glide, with xmean 0.441(6) x-unit and zmean
0.50(1) z-unit pseudotranslations on the a- and c-axes. Transforma-
tion of the (ꢀ)-B atom coordinates by the xmean and zmean
pseudotranslation values afforded a new ensemble containing
a dummy (ꢀ)-B molecule opposite to a real (þ)-A molecule.
Pseudosymmetry and Apparent Packing. Axes of 21 screw-
rotation (colored black) are a feature shared by both an achiral
P21/n supergroup cell (P21/c with unique axis b, cell choice 2 in
the International Tables,45 Figure 8 right drawing aꢀ0ꢀc) and by
a chiral P21 cell (with unique axis b, Figure 8 left drawing
a0ꢀ00ꢀc0). The special positions of inversion and n-glide reflec-
tion symmetry in this illustration [colored black] in a P21/n
crystal have been desymmetrized into approximately located
statistical best points [0.779(3),0.501(2),0.249(4)], [0.221(3),
0.501(2),0.751(4)], [0.279(3),0.501(2),0.249(4)], [0.721(3),
0.501(2),0.751(4)], and best planes [b = 0.251(3) and
b = 0.751(3)] of pseudosymmetry [colored red] in P21 crystals
of 1. As a result, molecules in the P21 crystals were freed from
symmetry positional constraints and have slightly realigned
themselves for both an optimal fit and for auspicious interactions
while their overall space filling still approximates that of the
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supergroup. The major significance of this emulation of P21/n
space filling is highly efficient packing. Of the 230 space groups,
the monoclinic P21/c space group and its glide equivalents are
exhibited by more than one-third of all the entries in the CSD.46
Pseudosymmetry and Accuracy. Intermolecular interac-
tions may be considered to be chemical constraints. The hydro-
gen-bond ring pattern places the set of molecules (þ)-A and
(ꢀ)-B within close proximity to each other (Figure 2). Another
chemical constraint is the aromaticꢀaromatic interaction which
keeps the phenyl centroids in the set of molecules (þ)-A[1 ꢀ x, y
þ 0.5, 1 ꢀ z] and (ꢀ)-B[1 ꢀ x, y ꢀ 0.5, 1 ꢀ z] also close
(Figure 4). The statistically determined best points of pseudoin-
version between the almost enantiotopic skeletons in each set of
two molecules in the chiral crystal structure are located at the
respective positions [0.779(3),0.501(2),0.246(4)] and
[0.221(3),0.501(2),0.751(4)]. Corresponding ideal special posi-
tions in an achiral P21/n cell are at [3/4,1/2,1/4] and [1/4,1/
2,3/4] using the same origin. Thus, the pseudosymmetry ele-
ments have been relocated from ideal positions. The largest
deviation in the accuracy of the best points appears to be along
the a-axis (the x-coordinates). The pseudoinversion point in the
hydrogen-bonding set is between the two molecules and is
þ0.029(3) x-fractional coordinate units (ca. 0.3 Å) above the
ideal x = 3/4 location. The pseudoinversion point in the
aromaticꢀaromatic interaction set is also between the two
molecules and is ꢀ0.029(3) x-fractional coordinate units
(∼0.3 Å) below the ideal x = 1/4 location. Therefore, pseudoin-
version symmetry in the P21 lattice has enabled a relative
displacement of ca. 0.6 Å along the a-axis between the two sets
of chemically constrained molecules. By Group Theory, this
separation is also manifested by the relative large rmS(x-trans-
lation) of 0.608 Å for the n-glide.
’ AUTHOR INFORMATION
Corresponding Author
*E-mail: rglaser@bgu.ac.il.
’ ACKNOWLEDGMENT
This work would not have been possible without the gener-
osity of Prof. David Avnir (Hebrew University of Jerusalem) who
provided us with access to his CSM and Error Estimation
Programs. The authors express their gratitude to him and his
co-workers for their warm encouragement and kindness.
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’ ASSOCIATED CONTENT
S
Supporting Information. A CIF file, scheme, and synth-
b
esis details of salt 1, seven tables of crystal data and structure
refinement, non-hydrogen atomic coordinates and equivalent
isotropic displacement parameters, bond lengths and angles,
anisotropic displacement parameters, hydrogen coordinates
and isotropic displacement parameters, torsion angles, and
hydrogen-bonds for 1, explanation of the Avnir CSM calculation,
and Figure 9 showing the deviation of a distorted C3h structure
from one of ideal C3 symmetry. This material is available free of
charge via the Internet at http://pubs.acs.org.
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