Foiling Normal Patterns of Crystallization by Design. Polymorphism of Phosphangulene Chalcogenides

Article abstract of DOI:10.1021/acs.cgd.9b00907

Phosphangulene (1) has a well-defined hexacyclic structure with a distinctive conical shape and an electron-rich aromatic surface. Molecules of phosphangulene are disposed to crystallize in parallel π-stacks. This preference can be thwarted by adding a si

Full text of DOI:10.1021/acs.cgd.9b00907

Article
pubs.acs.org/crystal
Cite This: Cryst. Growth Des. XXXX, XXX, XXX−XXX
Foiling Normal Patterns of Crystallization by Design. Polymorphism
of Phosphangulene Chalcogenides
Published as part of a Crystal Growth and Design virtual special issue Remembering the Contributions and Life
of Prof. Joel Bernstein
Alice Heskia, Thierry Maris, and James D. Wuest*
́
́
́
́
́
Departement de Chimie, Universite de Montreal, Montreal, Quebec H3C 3J7 Canada
S
* Supporting Information
ABSTRACT: Phosphangulene (1) has a well-defined hex-
acyclic structure with a distinctive conical shape and an
electron-rich aromatic surface. Molecules of phosphangulene
are disposed to crystallize in parallel π-stacks. This preference
can be thwarted by adding a single atom and converting
phosphangulene into the corresponding oxide (2a), sulfide
(2b), and selenide (2c). This change creates an awkward
molecular shape that prevents effective stacking. As a
consequence, the formation of optimal intermolecular
interactions is inhibited, and multiple polymorphs with high
values of Z and Z′ are formed. The high polymorphism of chalcogenides 2a−c is particularly noteworthy because the
compounds have little flexibility. Analysis of the structures of phosphangulene, chalcogenides 2a−c, and related compounds
provides deeper understanding of crystallization, including how to design molecules that cannot pack efficiently, are unable to
achieve normal patterns of association, and are therefore predisposed to form multiple polymorphs, structures with high values
of Z and Z′, solvates, solid solutions, and cocrystals.
run along the C3 axis from the apex of the cone (with the atom
of phosphorus at the negative end) toward the base (with the
peripheral atoms of hydrogen at the positive end).4
INTRODUCTION
■
Phosphangulene (1) has a characteristic conical shape
reminiscent of traditional hats worn in parts of Asia (Figure
1). The compound was first reported by Krebs and co-workers,
In crystals of phosphangulene, topology works in harmony
with polarity to control molecular packing, which yields π-
stacks with dipole moments aligned in parallel (Figure 2a). No
other polymorph has been reported. Each stack is linked to six
neighboring stacks by short C−H···O interactions (2.395 Å),
as shown in Figure 2. Unexpectedly, the dipole moments of
neighboring stacks point in the same direction, thereby
yielding R3m crystals that are polar and pyroelectric.
Temporary voltages are generated when pyroelectric materials
are heated or cooled, making them suitable for use in high-
performance infrared detectors and other devices. Pyroelectric
Figure 1. (a, b) Representations of the molecular structure of
phosphangulene (1) in crystals grown from ethyl acetate, as viewed
along the C3 axis and perpendicular to the axis. Atoms of carbon
appear in gray, hydrogen in white, oxygen in red, and phosphorus in
orange.
who determined the structure of crystals grown from ethyl
acetate.1 The nonplanarity of phosphangulene gives rise to a
dipole moment, determined to be 3.3
0.2 D in CHCl3,1
which is slightly larger than the moment of triphenylphosphine
(1.49 D in benzene).2,3 On the basis of ab initio calculations
and multipolar modeling of X-ray structure factors, the
direction of the dipole in phosphangulene is considered to
Received: July 11, 2019
Revised: August 3, 2019
Published: August 6, 2019
© XXXX American Chemical Society
A
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The fingerprint plot in Figure 4 provides complementary
information by showing the frequency of finding points on the
Figure 2. Representations of the structure of crystals of
phosphangulene grown from ethyl acetate. (a) View perpendicular
to the c-axis, showing part of two adjacent π-stacks with aligned
dipoles. Principal interstack C−H···O interactions are marked by
broken lines, with distances given in Å. (b) View along the c-axis,
showing how a central stack (in red) is surrounded by six others.
Unless otherwise indicated, atoms are shown in standard colors.
carbon-based materials are uncommon, and their character-
istically low densities and small dielectric constants give them
advantages not normally shared by inorganic materials. As a
consequence, phosphangulene and its derivatives define a
structurally intriguing family of compounds with significant
potential utility.
Key features in the structure of phosphangulene can be
highlighted by Hirshfeld surfaces of molecules in the crystal
and by the corresponding two-dimensional fingerprint plots.5,6
Hirshfeld surfaces are typically constructed to show the locus
of points around a molecule in a crystal where the calculated
electron density contributed by the molecule equals that
contributed by all other atoms in the structure. The convex
and concave surfaces of phosphangulene are shown in Figure 3.
Figure 4. Two-dimensional fingerprint plot of the Hirshfeld surface
for molecules of phosphangulene in crystals grown from ethyl acetate.
The plot shows the frequency of finding points on the surface with
particular values of de and di (distances to the nearest external and
internal atomic nuclei). The colors at each point range from cool
(blue) to hot (red) as the frequency increases.
Hirshfeld surface with particular values of de (distance to the
nearest external atomic nucleus) and di (distance to the nearest
internal atomic nucleus). Colors at each point on the plot
range from cool (blue) to hot (red) as the frequency increases.
Two long spikes in Figure 4 denote the presence of important
intermolecular C−H···O interactions, and the reddish area
near di ≈ de ≈ 1.9 Å reflects the significant contribution made
by π-stacking, although the distances are relatively long. In
addition, the absence of points near di ≈ de ≈ 1.2 Å confirms
that H···H interactions are of minor importance; similarly, the
lack of points near (di, de) ≈ (1.7, 1.1) or (di, de) ≈ (1.1, 1.7)
demonstrates that C−H···π interactions are not significant.
Together, the Hirshfeld surface and fingerprint plot suggest
that the conical topology of phosphangulene allows molecules
to be stacked with a degree of efficiency, despite low mutual
affinity arising from any specific interactions other than dipolar
alignment.
Figure 3. (a) Hirshfeld surface of the convex face of a molecule of
phosphangulene in crystals grown from ethyl acetate. The surface is
colored according to the local value of de (distance from the surface to
the nearest atomic nucleus in another molecule), and the colors range
from cool (blue) to hot (red) as de decreases. (b) Corresponding
surface of the concave face.
As noted by Yamamura and Nabeshima,7 converting
phosphangulene into the corresponding oxide, sulfide, and
selenide (2a−c) makes the cone angle slightly less acute,
possibly as a result of decreases in the s-character of the orbital
of phosphorus involved in the P-chalcogenide bonds. In
addition, forming the chalcogenides adds only one atom to
phosphangulene but changes the topology markedly, creating
awkwardly shaped molecules that are no longer predisposed to
stack. These intriguing early observations suggested to us that
further analysis of phosphangulene, its chalcogenides, and
related compounds offered a unique opportunity to explore
what we have called the “dark side of crystal engineering,”
which focuses on what happens when normal patterns of
crystallization are thwarted.8−11 This approach has begun to
yield materials with unusual properties, as well as deeper
understanding of subtle factors controlling molecular organ-
ization. Previous studies of chalcogenides 2a−c and analogues
The surfaces are colored according to the local value of de,
which is the distance from the surface to the nearest atomic
nucleus in another molecule, and the colors vary from cool
(blue) to hot (red) as de decreases. Figure 3 underscores
several key features, including (1) the C3v molecular symmetry
of phosphangulene, (2) the presence of six significant C−H···
O interactions per molecule, denoted by conspicuous red spots
located on the convex surface near each atom of oxygen, and
(3) the weak affinity of the convex and concave π-surfaces, as
indicated by the high proportion of blue and green around the
center of each molecule. The primary driving forces for
stacking appear to be topology and dipolar alignment rather
than π−π interactions, and stacked molecules are separated by
a relatively long distance (4.259 Å), which corresponds to the
length of the unit cell along the c-axis.
B
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Scheme 1
Table 1. Crystallographic Data for Polymorphs A, B, C, D, and E of Phosphangulene Oxide (2a)
a
polymorph
A
B
C
D
E
crystallization medium
formula
crystal system
space group
a (Å)
b (Å)
c (Å)
α (deg)
β (deg)
γ (deg)
V (Å3)
EtOAc
C18H9O4P
monoclinic
P21/n
10.0356(15)
25.043(4)
10.6453(16)
90
94.420(1)
90
2667.4(7)
8
EtOH
EtOH
EtOH
EtOH
C18H9O4P
monoclinic
P21/c
28.5547(11)
16.6794(6)
11.6200(4)
90
98.990(1)
90
5466.3(3)
16
C18H9O4P
orthorhombic
Pbca
12.0850(6)
7.4412(4)
29.7220(16)
90
C18H9O4P
orthorhombic
Pca21
11.6101(3)
16.6814(5)
28.2286(8)
90
C18H9O4P
monoclinic
P21
9.9199(5)
11.8932(5)
11.8950(6)
90
101.879(3)
90
1373.31(11)
4
90
90
90
90
2672.8(2)
8
5467.1(3)
16
Z
Z′
2
4
1
4
2
F(000)
1312
2624
1312
2624
656
T (K)
120
1.595
0.71073
0.226
150
1.556
1.34139
1.282
150
1.592
1.34139
1.307
150
1.556
1.34139
1.279
150
1.549
1.34139
1.272
ρcalc (g cm−3
λ (Å)
)
μ (mm−1
)
measured reflections
independent reflections
Rint
30172
6042
131053
12534
0.0351
0.0133
12089
0.0417
0.0426
0.1078
0.1090
1.055
21867
3063
0.0512
0.0325
2650
0.0491
0.0561
0.1238
0.1310
1.088
64961
11716
25072
6277
0.0229
0.0145
5812
0.0332
0.0343
0.0889
0.0904
1.033
0.0399
0.0294
10862
0.0475
0.0519
0.1217
0.1266
1.026
0.0362
0.0299
5983
0.0420
0.0447
0.1068
0.1099
1.025
Rσ
observed reflections
R1, I > 2σ(I)
R1, all data
wR2, I > 2σ(I)
wR2, all data
GOF
max/min (e Å−3
)
0.434/−0.352
N/A
0.428/−0.497
N/A
0.563/−0.51
N/A
0.590/−0.391
0.006(17)
1.190/−0.274
0.08(3)
Flack parameter
a
Data taken from the work of Krebs, Yamamura, and co-workers.7,13
C
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confirmed the intuitive expectation that their awkward shape
prevents stacking, but other important questions have not been
answered, such as what new patterns of organization emerge as
alternatives to stacking or what the observed structures reveal
about molecular crystallization in general. We have now found
that analysis of structural options available to phosphangulene,
its chalcogenides, and related compounds sheds light on
enduring mysteries, including the origin of high levels of
polymorphism, unusually large numbers of molecules in unit
cells, and pronounced tendencies to form solvates, solid
solutions, and cocrystals.
RESULTS AND DISCUSSION
■
Syntheses of Phosphangulene and its Chalcoge-
nides. Phosphangulene was synthesized by a modification of
the method reported by Krebs and co-workers (Scheme 1).1
Protection of 3-fluorophenol (3) as its tetrahydropyranyl
(THP) ether (4) was achieved efficiently in neat dihydropyran
with pyridinium p-toluenesulfonate (PPTS) as the acidic
catalyst. Metalation of THP ether 4 and subsequent reaction
with PBr3 afforded triarylphosphine 5, as described by Krebs
and co-workers,1 and the protective group was then removed
by acid-catalyzed methanolysis to give phosphine 6. Krebs and
co-workers reported preparing phosphangulene in 86% yield
by heating intermediate 6 with KO-t-Bu in N-methylpyrroli-
dinone at 200 °C, but we obtained lower yields despite various
attempts to use the reported method. Instead, we turned to an
intramolecular Ullmann-type coupling of the type described by
Zhang and co-workers.12 Treatment of intermediate 6 with
Cs2CO3 and CuI in DMF gave phosphangulene conveniently
and reproducibly in 56% yield. Further experiments showed
that CuI was necessary and that its use with other bases such as
KO-t-Bu or K2CO3 gave lower yields. Chalcogenides 2a−c
were obtained in high yields from phosphangulene by
modifications of published methods (Scheme 1).1,7 Specifi-
cally, oxide 2a was prepared by treatment with 30% aqueous
hydrogen peroxide, sulfide 2b by heating with elemental sulfur
in xylene, and selenide 2c by an analogous reaction with
elemental selenium.
Polymorphs of Phosphangulene Oxide. The character-
istic stacking of molecules of phosphangulene cannot be
maintained in crystals of chalcogenides 2a−c. The added P-
chalcogen bonds alter the dipole moment of phosphangulene
and create awkward molecular shapes that retain C3v molecular
symmetry but can no longer form efficiently packed conical
stacks. Confirmation is provided by the earlier work of Krebs,
Yamamura, and their co-workers, who reported the structure of
crystals of phosphangulene oxide (2a) grown from ethyl
acetate (polymorph A).7,13 More thorough analysis has
revealed four new polymorphs B−E. The new polymorphs
are described below, after a summary of the structure of known
polymorph A to allow comparison.
Figure 5. Representation of the structure of crystals of phosphangu-
lene oxide (2a) grown from ethyl acetate (polymorph A). Two
molecules that interact to form an offset clamshell pair are highlighted
in red, and a second pair is shown with atoms in normal colors.
Selected C−H···O interactions and C···O contacts are marked by
broken lines, with distances given in Å.
Figure 6. (a) Hirshfeld surface colored by de, showing an offset
clamshell pair formed by two molecules of oxide 2a in polymorph A.
(b) Corresponding surface of one of the convex faces of the pair.
oxygen bonded to phosphorus (2.505 Å in the illustrated
pairs), as well as unusually short C···O contacts (2.987 Å)
involving atoms of oxygen in the phosphangulene rings.
Key features of the structure are highlighted by the Hirshfeld
surfaces shown in Figure 6. In particular, conspicuous red spots
on the concave surface (Figure 6a) arise from multiple C−
H···π interactions, and red spots near the center of the convex
surface reflect the formation of C−H···O interactions involving
atoms of oxygen bonded to phosphorus (Figure 6b). The
striking dissimilarity of the structures of phosphangulene and
oxide 2a is underscored by the fingerprint plots in Figure 7.
The two symmetry-inequivalent molecules in the asymmetric
unit of polymorph A engage in closely similar interactions, as
demonstrated by the overall resemblance of Figures 7a and 7b.
Features of particular interest that distinguish the plots from
that of phosphangulene (Figure 4) are (1) numerous H···H
interactions, as indicated by the density of points near di ≈ de
≈ 1.1 Å, (2) significant wings near (di, de) ≈ (1.8, 1.1) and (di,
de) ≈ (1.1, 1.8), which correspond to C−H···π interactions,
and (3) the many large values of di and de observed in Figure 7,
which extend to approximately 2.7 Å. In sharp contrast, the
plot corresponding to phosphangulene is compact and
bounded by di ≈ de ≈ 2.3 Å (Figure 4).
Polymorph A of Oxide 2a. Crystals grown from ethyl
acetate belong to the monoclinic space group P21/n, with Z =
8 and Z′ = 2. The same structure is also produced by
crystallization from anhydrous ethanol. Other crystallographic
data are summarized in Table 1, and views of the structure are
presented in Figures 5, 6, and 7. Conical stacking is not
observed; instead, the structure consists of pairs of symmetry-
inequivalent molecules of oxide 2a (Figure 5), held in an offset
clamshell arrangement by multiple C−H···π interactions
despite a locally unfavorable orientation of molecular dipoles.
Adjacent pairs form C−H···O interactions involving atoms of
Together, the Hirshfeld surfaces and fingerprint plots
suggest that oxide 2a has no compelling reason to crystallize
in any particular way, despite its relatively rigid and symmetric
molecular structure. Instead, crystallization is forced to
produce a structure with many suboptimal interactions, and
D
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Figure 7. Fingerprint plots of Hirshfeld surfaces for the two symmetry-inequivalent molecules of oxide 2a in polymorph A.
Figure 8. (a) Representative fingerprint plot of the Hirshfeld surface of one of the four symmetry-inequivalent molecules of triphenylphosphine in
the triclinic P1 polymorph. (b) Fingerprint plot of the Hirshfeld surface of a molecule of triphenylphosphine oxide in the orthorhombic Pbca form.
multiple molecules are used to create a unit cell with
acceptable packing. The high frequency of large intermolecular
separations in the fingerprint plots of Figure 7, as indicated by
the density of points with coordinates exceeding 2.3 Å, reveals
that the behavior of oxide 2a resembles that of classic clathrate-
forming compounds such as hydroquinone and Dianin’s
compound. Both enclose suitable guests but can also form
guest-free R-3 crystals with significant unoccupied volume.14,15
Fingerprint plots of the Hirshfeld surfaces of molecules in such
structures are strikingly extended.
structures, as assessed by using spheres of variable radius to
probe accessible volumes lying between the van der Waals
surfaces of the constituent molecules. For crystals of
phosphangulene and polymorph A of oxide 2a, the
Kitaigorodsky packing coefficients are similar (0.689 and
0.705, respectively, at 293 K), but the structure of oxide 2a
incorporates much larger voids. For example, a probe sphere of
radius 0.8 Å can occupy 6% of the volume of crystals of
polymorph A but cannot be accommodated anywhere within
the structure of phosphangulene. Adding an atom of oxygen to
phosphangulene interferes substantially with molecular pack-
ing, as expected, whereas such changes do not result routinely
The markedly different packing of phosphangulene and its
oxide can also be underscored by comparing voids in their
E
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Figure 9. (a) Representation of the structure of needle-shaped crystals of oxide 2a grown from anhydrous ethanol (polymorph B). Two adjacent
inequivalent clamshell pairs are shown with atoms in normal colors. The shortest C−H···O interaction between pairs is marked by a broken line,
with the distance given in Å. (b) Superposition of representative clamshell pairs in the structures of polymorphs A and B, with different pairs shown
in shades of red.
when triarylphosphines are converted into the corresponding
oxides. For example, the structures of the triclinic P1
polymorph of triphenylphosphine16 and the orthorhombic
Pbca form of its oxide17 are related, as confirmed by comparing
the fingerprint plots in Figure 8, which are bounded by similar
values of di and de.
Polymorph B of Oxide 2a. We observed that crystallizing
phosphangulene oxide from anhydrous ethanol yielded crystals
with different morphologies. Blocks proved to correspond to
known polymorph A, whereas needles were shown to be new
polymorph B, which crystallized in the monoclinic space group
P21/c with Z = 16 and Z′ = 4. Additional crystallographic data
are provided in Table 1, and representations of the structure
are shown in Figures 9−10. Again, oxide 2a forms offset
representative.18 Moreover, the plot closely resembles those
of molecules of oxide 2a in polymorph A (Figure 7). In both
polymorphs A and B, molecules of oxide 2a produce similar
fingerprints arising from H···H interactions (area near di ≈ de
≈ 1.0−1.2 Å), C−H···π interactions (small wings near (di, de)
≈ (1.8, 1.1) and (di, de) ≈ (1.1, 1.8)), and distant π-stacking
(light blue area centered on di ≈ de ≈ 1.8 Å). Of special note is
the highly extended nature of all plots, which reach out to di ≈
de ≈ 2.7 Å. This supports the notion that the molecular
structure of oxide 2a prevents efficient stacking and forces
crystallization to occur in various alternative ways, none
particularly favorable.
Polymorph C of Oxide 2a. Further evidence for this idea
is provided by the existence of polymorph C, which is
produced concomitantly with polymorphs A and B during
crystallization from anhydrous ethanol.19 Crystals of poly-
morph C proved to belong to the orthorhombic space group
Pbca with Z = 8 and Z′ = 1. Table 1 summarizes additional
crystallographic data, and Figure 12 provides a view of the
structure, which can be considered to consist of slipped stacks
of molecules of oxide 2a with their dipoles aligned
approximately along the b-axis. Each stack is surrounded by
six others, which are oriented so that there is no net dipole
along the b-axis.
The Hirshfeld surface (Figure 10b) shows two adjacent
molecules in a slipped stack and demonstrates the presence of
multiple C−H···π interactions. The close similarity of the
fingerprint plot (Figure 11b) to those of molecules in
polymorphs A and B confirms the notion that oxide 2a cannot
be packed efficiently in ways that create optimal interactions.
In particular, H···H and C−H···π distances are long, and π-
stacking is weak, as shown by reddish areas in the fingerprint
plot near di ≈ de ≈ 1.8 Å. In addition, the plot is notably
extended and reveals a high frequency of coordinates with large
values of di or de ranging up to 2.8 Å. The inability of oxide 2a
to crystallize in ways that allow its constituent atoms to engage
in normal intermolecular interactions leads to the formation of
multiple unappealing polymorphs with nearly equal stabilities,
as demonstrated by the concomitant crystallization of forms A,
B, and C.
Polymorph D of Oxide 2a. Additional polymorph D was
produced when oxide 2a was crystallized from anhydrous
ethanol or from thiophene. Crystals of polymorph D were
found to belong to the orthorhombic space group Pca21 with Z
= 16 and Z′ = 4. Other crystallographic data are summarized in
Table 1, and representations of the structure are provided in
Figures 13a and 14a. Again, the structure consists of offset
Figure 10. (a) Hirshfeld surface colored by de, showing a
representative offset clamshell pair of molecules of oxide 2a in
polymorph B. (b) Corresponding surface of adjacent molecules of
oxide 2a in a slipped stack in polymorph C.
clamshell pairs like those observed in polymorph A (Figure
9a). The resemblance of the pairs in the two polymorphs can
be highlighted by superimposition (Figure 9b) and by
comparison of the Hirshfeld surfaces (Figures 6a and 10a).
Conspicuous red spots on the concave surface of molecules in
polymorph B reflect C−H···π interactions that help hold the
pairs together, and the structure is also maintained by π-
stacking, dipolar alignment, and various C−H···O interactions,
including those with H···O distances as short as 2.329 Å (C−
H···O−P) and 2.426 Å (C−H···O−C). Portraying structural
details is complicated by the high value of Z′, and the
representative view in Figure 9a highlights only the shortest
C−H···O−P distance between adjacent inequivalent clamshell
pairs of oxide 2a.
All four inequivalent molecules of oxide 2a in the
asymmetric unit of polymorph B have very similar environ-
ments, and the single fingerprint plot in Figure 11a is
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Figure 11. (a) Representative fingerprint plot of the Hirshfeld surface corresponding to one of the four symmetry-inequivalent molecules of oxide
2a in polymorph B. (b) Fingerprint plot for molecules of oxide 2a in polymorph C.
clamshell pairs similar to those observed in polymorphs A and
B (Figure 13a), and fingerprint plots reveal a high frequency of
large intermolecular distances (Figure 14a).
Polymorph E of Oxide 2a. A fifth form (polymorph E)
resulted when oxide 2a was crystallized from anhydrous
ethanol or from CS2. Crystals of polymorph E proved to
belong to the monoclinic space group P21 with Z = 4 and Z′ =
2. Table 1 includes additional crystallographic data, and
Figures 13b and 14b provide representations of the structure,
which show the presence of offset clamshell pairs like those
present in polymorphs A, B, and D (Figure 13b), as well as a
similarly high frequency of abnormally long intermolecular
separations (Figure 14b).
No polymorph of oxide 2a adopts efficient conical stacking
of the type observed in crystals of phosphangulene 1 itself.
This underscores the disruptive effect of introducing a well-
placed atom of oxygen. Adding oxygen also alters the dipole
moment and gives rise to new C−H···O−P interactions in all
five polymorphs. The repeated observation of high values of Z′
and Z (8, 16, 8, 16, and 4 in polymorphs A, B, C, D, and E,
respectively) reinforces the hypothesis that the inherently
awkward shape of oxide 2a prevents crystallization from
yielding structures in which the constituent atoms have normal
intermolecular interactions. This favors the formation of
multiple polymorphs that are similar in energy and must use
multiple inequivalent molecules to ensure satisfactory pack-
ing.20−22 In essence, oxide 2a is condemned to crystallize in
ways that reflect unsatisfactory compromises: in particular, the
conical aromatic surface cannot be packed efficiently in the
manner of phosphangulene, nor can it engage fully in H···H,
C−H···π, and π···π interactions of the type that stabilize stacks
and herringbone arrangements of planar aromatic analogues.
As shown in Figure 15, various intermolecular interactions
make similar contributions to the Hirshfeld surfaces of all of
the polymorphs of oxide 2a, whereas the contributions differ
widely from those observed in the structure of phosphangulene
Figure 12. Space-filling representation of part of a slipped stack
observed in the structure of polymorph C of oxide 2a. Atoms are
shown in normal colors.
Figure 13. (a) Hirshfeld surface colored by de, showing a
representative offset clamshell pair formed by two molecules of
oxide 2a in polymorph D. (b) Corresponding surface of an offset
clamshell pair in polymorph E of oxide 2a.
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Figure 14. (a) Representative fingerprint plot of the Hirshfeld surface for one of the four symmetry-inequivalent molecules of oxide 2a in
polymorph D. (b) Fingerprint plot for molecules of oxide 2a in polymorph E.
used to estimate lattice energies and to compare the stabilities
of polymorphs; however, current methods cannot be expected
to provide reliable guidance in the case of forms A−E of oxide
2a, which have high values of Z/Z′ and closely similar energies,
as demonstrated by their coexistence under equilibrating
conditions.23
Only one polymorph of phosphangulene has been reported,
and earlier workers noted a single form of oxide 2a. In this
context, we were surprised to observe four new polymorphs,
without making any systematic effort to find others. Oxide 2a
is less highly polymorphic than the intensively studied
compound 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophene-
carbonitrile (ROY), which exists in 10 fully characterized
forms and remains one of the most highly polymorphic
substances in the Cambridge Structural Database (CSD).24−27
Unlike ROY, however, oxide 2a is a hexacyclic molecule with a
well-defined shape, so its rich polymorphic diversity does not
arise from an ability to adopt multiple conformations. The
Figure 15. Percentage contributions made by various intermolecular
CSD now includes more than one million entries, but recent
interactions to the Hirshfeld surfaces of representative molecules in
analyses have identified only 13 compounds that are known to
the structures of phosphangulene and oxide 2a (polymorphs A−E).
exist in more than four fully characterized polymorphic
Phosphangulene is shown as Phang, and polymorphs A−E appear in
order of the importance of C−H interactions.
forms.26 Nearly all of these special molecules are flexible and
crystallize as different conformers. Oxide 2a is among the rare
examples that are both highly polymorphic and virtually
inflexible. As a result, oxide 2a and its analogues allow the
origin of polymorphism to be probed in the absence of other
contributing factors. Our observations suggest that the
awkward topology of these compounds makes efficient
stacking impossible and forces crystallization to occur in
ways that lead to many suboptimal intermolecular contacts,
thereby expanding the scope for producing polymorphic forms
with similar energies. It is also possible that the conical
topology and polarity of oxide 2a inhibit displacements and
reorientations needed to convert metastable arrangements into
forms of lower energy.
1. The crystallographic parameters in Table 1, along with other
observations such as the formation of all five polymorphs A−E
during crystallization from anhydrous ethanol,19 do not
provide definitive evidence for placing the polymorphs in any
particular order of thermodynamic stability. However, the low
densities, high values of Z, and relatively low Kitaigorodsky
packing coefficients (0.704−0.707 at 150 K) found for
polymorphs B, D, and E suggest that they are the least stable.
Moreover, we observed the transformation of polymorph B
into polymorphs A and C during extended exposure to
anhydrous ethanol. Concomitant crystallizations and poly-
morphic interconversions prevented us from obtaining pure
samples for more detailed analysis by differential scanning
calorimetry. In principle, computational approaches can be
Previous statistical analyses of the CSD have led to
assertions that molecular flexibility and the incidence of
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Table 2. Crystallographic Data for Polymorphs A and B of Phosphangulene Sulfide (2b) and for Polymorphs A, B, and C of
Phosphangulene Selenide (2c)
a
a
compound
sulfide 2b polymorph A sulfide 2b polymorph B selenide 2c polymorph A selenide 2c polymorph B selenide 2c polymorph C
crystallization medium
crystal system
space group
a (Å)
b (Å)
c (Å)
α (deg)
β (deg)
γ (deg)
V (Å3)
CH2Cl2/hexane
monoclinic
P21/c
15.112(5)
13.276(4)
14.291(5)
90
93.096(3)
90
2863.1(16)
8
EtOH
orthorhombic
Pbca
14.7446(3)
13.0971(3)
14.9443(3)
90
CHCl3/hexane
orthorhombic
Pbca
12.9896(19)
15.120(2)
14.872(2)
90
CS2
monoclinic
P21/c
15.0217(6)
13.5252(5)
14.4528(5)
90
93.393(2)
90
CS2
monoclinic
I2/a
14.1307(8)
6.9551(4)
29.079(2)
90
90.359(2)
90
90
90
90
90
2885.92(11)
8
2920.8(8)
8
2931.25(19)
8
2857.9(3)
8
Z
Z′
2
1
1
2
1
F(000)
1376
1376
1520
1520
1520
T (K)
120
1.560
0.71073
0.350
105
1.548
1.34139
2.049
120
1.743
0.71073
2.692
150
1.737
1.34139
3.046
150
1.781
1.34139
3.124
ρcalc (g cm−3
λ (Å)
)
μ (mm−1
)
measured reflections
independent reflections
Rint
32254
6592
30130
3574
0.0274
0.0154
3406
0.0294
0.0306
0.0847
0.0857
1.051
15435
3339
0.0301
0.0216
2877
0.0512
0.0563
0.1339
0.1409
1.059
78953
6425
0.0536
0.0232
5234
0.0320
0.0456
0.0745
0.0825
1.056
52256
3240
0.0464
0.0183
3158
0.0632
0.0647
0.1756
0.1775
1.054
0.0425
0.0345
5294
0.0336
0.0521
0.0863
0.0934
1.034
Rσ
observed reflections
R1, I > 2σ(I)
R1, all data
wR2, I > 2σ(I)
wR2, all data
GOF
max/min (e Å−3
)
0.474/−0.348
0.456/−0.222
2.369/−0.494
0.397/−0.564
3.205/−1.56
Data taken from the work of Yamamura and Nabeshima.7
a
polymorphism are not correlated.28−30 Nevertheless, the quest
to identify general structural features favoring polymorphism
and high values of Z/Z′ remains an active area of study. If
predisposing features exist and can be identified, their
discovery would have a significant practical impact by
expanding the range of different ordered materials that can
be derived from a single molecular entity. However, the notion
that compounds with multiple polymorphic forms or high
values of Z/Z′ are exceptional and may have underlying shared
features is not universally accepted. Dissenting opinions
include those of McCrone, who famously stated “. . .that
every compound has different polymorphic forms and that, in
general, the number of forms known for a given compound is
proportional to the time and energy spent in research on that
compound.”31 In addition, Gavezzotti has suggested that each
case of elevated values of Z′ “. . .may be a story in itself.”32
Much of what is believed to be true about high levels of
polymorphism and large values of Z/Z′ reflects purely
statistical analyses of the CSD or smaller sets of data, often
related to drugs and intermediates used in their synthesis,
which do not represent the full scope of molecular diversity. In
contrast, surprisingly little effort has been devoted to close
comparative scrutiny of the structures of highly polymorphic
substances or to experimental studies of compounds
specifically devised to test conjectures about the origins of
polymorphism and high values of Z/Z′. Of the 13 compounds
recently highlighted because they are known to exist in more
than four polymorphic forms,26 only the 4-chloro-1,2,3,5-
dithiadiazolyl radical (7a)33,34 and 1,8-dihydroxyanthraqui-
none (8)35,36 resemble oxide 2a by existing primarily in a
single conformation.
This places compounds 2a, 7a, and 8 in an intriguing subset
of elite highly polymorphic compounds and challenges
chemists to identify specific structural features that explain
their special behavior. The polymorphic diversity of radical 7a
presumably arises in part from its strong self-association, which
creates isomeric dimers that resemble distinct covalently
bonded species and therefore crystallize differently. Notably,
however, the behavior of radical 7a does not extend to close
analogues such as fluoride 7b and bromide 7c, which have not
yielded multiple polymorphs despite efforts to make them.33
As a result, the example of radical 7a is “a story in itself” that
does not tell how to design any other highly polymorphic
compounds, even those with a close structural relationship.
1,8-Dihydroxyanthraquinone (8) is a natural product
derived from glycosides that have long been used as laxatives.
Its high polymorphism has complex origins, including the
ability to engage in multiple intermolecular O−H···O hydro-
gen-bonding motifs. However, none of the observed structures
exhibits any clear signs of inefficient packing. In particular, the
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values of Z′ are generally small (1, 2, 4, 1, and 0.5 for the five
known polymorphs), and the fingerprint plots are compact,
with a low frequency of abnormally long distances to atoms in
neighboring molecules (beyond di ≈ de ≈ 2.4 Å). As in the case
of radical 7a, the behavior of anthraquinone 8 does not point
unerringly to any other compounds that would also be
expected to be highly polymorphic. The examples of
compounds 7a and 8 thereby provide grounds for the gloomy
conjecture that “polymorphism is unpredictable on the basis of
molecular structure.”30
Phosphangulene chalcogenides 2a−c have let us put this
notion to a stringent experimental test. The special features
that appear to induce oxide 2a to form multiple polymorphs
with high values of Z/Z′ remain essentially unchanged in
analogues 2b−c; in particular, the retained awkward topology
is expected to continue to prevent crystallization from
occurring in fully satisfactory ways. If polymorphism is in
fact unpredictable, however, then sulfide 2b and selenide 2c
should not necessarily behave like oxide 2a.
Polymorphs of Phosphangulene Sulfide. Yamamura
and Nabeshima previously solved the structure of crystals of
sulfide 2b grown from CH2Cl2/hexane, which will be referred
to as polymorph A.7 By crystallizing sulfide 2b from anhydrous
ethanol, we obtained new polymorph B. Its structure is
described below, after a brief analysis of known polymorph A
to allow comparison.
Polymorph A of Sulfide 2b. Crystals of known form A
belong to the monoclinic space group P21/c with Z = 8 and Z′
= 2. Additional crystallographic data are provided in Table 2,
and representative views of the structure are shown in Figures
16 and 17a. Conical stacking is prevented, as expected, and
molecules form offset clamshell pairs like those present in
multiple polymorphs of oxide 2a (Figure 16). This observation
suggests that pairing is a fundamental preference of all
phosphangulene chalcogenides, not a phenomenon resulting
uniquely from C−H···O−P interactions in oxide 2a. The
Hirshfeld surface of paired molecules of sulfide 2b (Figure
17a) closely resembles the corresponding surfaces of various
polymorphs of oxide 2a and shows that the pairs are again
joined by multiple C−H···π interactions. The fingerprint plot
in Figure 18a demonstrates that the structure of polymorph A
of sulfide 2b is maintained by various interactions, including π-
stacking, C−H···π interactions, C−H···O interactions, and C−
H···S interactions. As in the case of polymorphs A−E of oxide
2a, the fingerprint plot is notably extended and shows a high
frequency of coordinates with values of di or de as large as 2.8
Å. The plot thereby confirms that sulfide 2b, like oxide 2a, is
forced by topology to pack in ways that poorly exploit the
potential of the constituent atoms to engage in stabilizing
intermolecular contacts. As a result, small changes in structural
parameters can be accommodated without incurring significant
energetic penalties, and the range of accessible polymorphs is
broadened.
Polymorph B of Sulfide 2b. Crystallization of sulfide 2b
from anhydrous ethanol yielded a new form, polymorph B.
The crystals were found to belong to the orthorhombic space
group Pbca with Z = 8 and Z′ = 1, and other crystallographic
data are summarized in Table 2. The Hirshfeld surface in
Figure 17b confirms that polymorph B incorporates offset
clamshell pairs joined by multiple C−H···π interactions, as
found in polymorph A of sulfide 2b and in polymorphs A, B,
D, and E of oxide 2a. Unlike polymorph A of sulfide 2b,
however, polymorph B does not have any C−H···O or C−H···
S contacts shorter than the sum of the van der Waals radii. The
fingerprint plot (Figure 18b) reveals that intermolecular
separations in polymorph B are unusually large; in particular,
there are no points on the Hirshfeld surface with values of di or
de less than 1.3 Å. Polymorph A is denser than polymorph B
and therefore appears to be more stable.
Polymorphs of Phosphangulene Selenide. With the
polymorphism of sulfide 2b established, we did not search
systematically for other forms, but instead examined the
crystallization of selenide 2c. We were confident that the
coherent behavior of oxide 2a and sulfide 2b, including their
polymorphism, formation of crystals with large values of Z/Z′,
and abnormally high frequencies of long intermolecular
distances, reflected basic principles of molecular design and
organization that would also govern the properties of selenide
2c. In previous work, Yamamura and Nabeshima reported the
structure of crystals of selenide 2c grown from CHCl3/hexane,
which will be referred to as polymorph A.7 We have found that
new polymorphs result when selenide 2c is crystallized under
other conditions. Their structures are described below,
following an analysis of known polymorph A to allow
comparison.
Figure 16. Representation of the structure of crystals of sulfide 2b
(polymorph A). Two adjacent offset clamshell pairs of molecules are
illustrated with atoms of carbon in gray, hydrogen in white, oxygen in
red, phosphorus in orange, and sulfur in yellow. C−H···S interactions
are marked by broken lines, with the distances given in Å.
Polymorph A of Selenide 2c. Crystals of selenide 2c
grown from CHCl3/hexane belong to the orthorhombic space
group Pbca with Z = 8 and Z′ = 1. Table 2 summarizes
additional crystallographic data, and Figure 19a provides a
representative view of the structure. Polymorph A of selenide
2c and polymorph B of sulfide 2b are isostructural. Conical
stacking is obstructed, as expected, and molecules of selenide
2c form offset clamshell pairs like those produced by oxide 2a
and sulfide 2b. Molecular association in the structure is
Figure 17. (a) Hirshfeld surface colored by de, showing a
representative offset clamshell pair formed by two molecules of
sulfide 2b in polymorph A. (b) Corresponding surface of an offset
clamshell pair in polymorph B of sulfide 2b.
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Figure 18. (a) Representative fingerprint plot of the Hirshfeld surface for one of the two symmetry-inequivalent molecules of sulfide 2b in
polymorph A. (b) Fingerprint plot for molecules of sulfide 2b in polymorph B.
Figure 19. Representations of the structures of crystals of selenide 2c grown from CHCl3/hexane (polymorph A) and from CS2 (polymorph B).
(a) Offset clamshell pair observed in polymorph A. (b) Three adjacent offset clamshell pairs in polymorph B. Both images show atoms of carbon in
gray, hydrogen in white, oxygen in red, phosphorus in orange, and selenium in yellow. Selected C−H···Se and Se···Se interactions are marked by
broken lines, with the distances given in Å.
governed primarily by C−H···π and C−H···O interactions, as
shown by the Hirshfeld surface of paired molecules in Figure
20a. Again, the fingerprint plot is abnormally extended, with
values of di or de reaching out beyond 2.7 Å.
Polymorph B of Selenide 2c. New polymorphs B and C
were obtained concomitantly by crystallizing selenide 2c from
CS2. Crystals of form B proved to belong to the monoclinic
space group P21/c with Z = 8 and Z′ = 2. Table 2 summarizes
additional crystallographic data, and Figure 19b shows that the
structure is composed of offset clamshell pairs like those
formed by polymorph A of selenide 2c and by various
polymorphs of oxide 2a and sulfide 2b. Form B of selenide 2c
and form A of sulfide 2b are isostructural. The Hirshfeld
surface corresponding to form B of selenide 2c confirms that
the pairs are held together by multiple C−H···π interactions
(Figure 20b). Other contacts shorter than the sum of the van
der Waals radii include C−H···Se interactions (2.973 and
3.030 Å) and Se···Se interactions (3.583 Å), as illustrated in
Figure 19b. The fingerprint plot (Figure 21b) is even more
extended than that of polymorph A of selenide 2c, and values
of di reach 2.9 Å.
Polymorph C of Selenide 2c. Crystals of concomitant
polymorph C were found to belong to the monoclinic space
group I2/a with Z = 8 and Z′ = 1. Other crystallographic
details appear in Table 2, and a view of the structure is
provided in Figure 22. The structure is devoid of noteworthy
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Figure 20. (a) Hirshfeld surface colored by de, showing an offset
clamshell pair formed by molecules of selenide 2c in polymorph A.
(b) Corresponding surface of a representative offset clamshell pair in
polymorph B of selenide 2c.
interactions, and it can be considered to be composed of
adjacent columns in which widely separated molecules (6.955
Å) are stacked with their P−Se bonds aligned approximately
with the b-axis. The convex and concave faces of the Hirshfeld
surface (Figure 23) indicate that the structure is maintained in
part by C−H···π interactions between columns, and the
corresponding fingerprint plot extends to large values of di and
de (Figure 24).
Figure 22. Representation of the structure of crystals of selenide 2c
(polymorph C). View along the b-axis, showing how a central column
of widely separated molecules (in red) is surrounded by eight other
loose stacks. Unless otherwise indicated, atoms are shown in normal
colors.
The inability to form stacks like those favored by
phosphangulene forces chalcogenides 2a−c to accept un-
attractive alternatives, particularly structures built from offset
clamshell pairs held together by multiple C−H···π interactions.
Figure 25 shows the superimposition of six representative pairs
that are present in the structures of oxide 2a (polymorphs A
and B), sulfide 2b (polymorphs A and B), and selenide 2c
(polymorphs A and B). The figure confirms that a similar
association is conserved throughout the series, but the
structural details vary substantially. This suggests that
chalcogenides 2a−c are highly polymorphic partly because
they can form a multitude of pairs that have slightly differing
geometries, closely similar energies, and numerous ways to
pack in crystal lattices.
Figure 23. (a) Hirshfeld surface colored by de, showing the convex
face of a molecule of selenide 2c in polymorph C. (b) Corresponding
concave face.
Figure 21. (a) Representative fingerprint plot of the Hirshfeld surface for one of the two symmetry-inequivalent molecules of selenide 2c in
polymorph A. (b) Fingerprint plot for molecules of selenide 2c in polymorph B.
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formed block-shaped crystals were found to have the structure
of polymorph C of oxide 2a, but they contained ratios of oxide
2a and phosphangulene that varied according to the changing
composition of the mother liquors. Blocks appearing early in
the crystallization were shown to have the 1:1 composition of
the initial mother liquors, whereas crystals formed later were
progressively enriched in oxide 2a as pure phosphangulene was
gradually removed from the liquid phase. The observation of
crystalline solid solutions strengthens the hypothesis that the
solid-state behavior of oxide 2a has a clear-cut structural basis,
rooted in its odd shape and inability to avoid suboptimal
intermolecular interactions. As a result, its crystallization is
prone to errors in which molecules of oxide 2a are replaced by
other compounds. A particularly attractive substitute is
phosphangulene itself, which is identical in symmetry,
topologically related, and smaller.
When isostructural compounds cocrystallize, the unit cell
parameters typically vary linearly as the ratio of the
components changes. This relationship, which is known as
Vegard’s law,37−39 unexpectedly also describes the behavior of
mixtures of phosphangulene and oxide 2a, even though they
are far from isostructural. Figure 26 shows that the volume of
the unit cell measured for single crystals of polymorph C of
oxide 2a decreases linearly as the amount of incorporated
phosphangulene increases.
Figure 24. Fingerprint plot for molecules of selenide 2c in polymorph
C.
Figure 25. Superimposition of six representative offset clamshell pairs
present in the structures of oxide 2a (polymorphs A and B in red and
dark red), sulfide 2b (polymorphs A and B in blue and dark blue), and
selenide 2c (polymorphs A and B in green and dark green).
Figure 26. Graph showing that the unit cell volume V (in Å3)
measured for single crystals of polymorph C of oxide 2a decreases
linearly as the molar fraction (1 − χ) of incorporated phosphangulene
increases.
Ability of Phosphangulene Chalcogenides 2a−c To
Form Crystalline Solid Solutions, Pseudo-Polymorphs,
and Cocrystals. The distinctive shape of chalcogenides 2a−c
prevents efficient packing and forces crystallization to occur in
ways that are significantly flawed, with high frequencies of long
intermolecular contacts. Polymorphism is thereby favored, and
multiple molecules are needed to construct unit cells with
acceptable packing. We reasoned that if chalcogenides 2a−c
cannot in fact crystallize in fully satisfactory ways, then they
should be disposed to form structures that accommodate other
molecules.
To test this notion, we crystallized equimolar mixtures of
phosphangulene and oxide 2a from ethyl acetate, and we
observed the formation of both needles and blocks. The
needles proved to be phosphangulene uncontaminated by
oxide 2a. This indicates that crystallization of phosphangulene
by stacking is kinetically favorable, as well as topologically
attractive, and that the lattice effectively excludes molecules of
oxide 2a, which are larger and awkwardly shaped. Concurrently
The rapid high-fidelity crystallization of phosphangulene
differs sharply from the promiscuous behavior of oxide 2a. The
contrast is an impressive example of how patterns of molecular
organization can be altered substantially by simple structural
modifications. The ability of oxide 2a to include phosphangu-
lene over a wide range of compositions is noteworthy because
crystals of the pure components are not isomorphous,
isostructural, or even structurally similar. The special tendency
of oxide 2a to form solid solutions appears to have the same
origin as its high degree of polymorphism; specifically, the
awkward shape inhibits effective packing, weakens intermo-
lecular interactions, and broadens the opportunities to produce
crystals in which the orientation and even the identity of
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adjacent molecules can be varied without imposing a
significant energetic penalty.
exhibit polymorphism in only about 37% of the single-
component crystals examined;30 moreover, only two inflexible
compounds in the entire CSD (0.0002%) are known to exist in
more than four polymorphic forms. As a result, the consistently
unusual behavior of all three compounds 2a−c is statistically
improbable and refutes the notion that there are no
correlations between molecular structure and high levels of
polymorphism.
These conclusions are reinforced by the results of related
experiments. For example, crystallization of equimolar mixtures
of oxide 2a and sulfide 2b from CH2Cl2/hexane yielded
crystals of oxide 2a incorporating approximately 28% of sulfide
2b. This surprising observation reveals that packing in the
lattice of oxide 2a is so susceptible to variations that sulfide 2b
can be accommodated, even though it is a larger molecule.
Remarkably, examination of multiple mixed crystals showed
that they all had similar compositions but formed two different
structures. One corresponded to known polymorph A of oxide
2a (monoclinic P21/n), but the other appears to be a new
polymorph of oxide 2a (monoclinic P21/c) that we have not
yet been able to prepare in pure form. This observation
suggests that further study of oxide 2a will yield more
polymorphs, beyond the five forms A−E already characterized
in detail. Moreover, the promiscuous formation of mixed
crystals is not a phenomenon limited to a single polymorph but
rather is a more general consequence of the peculiar structural
features of chalcogenides 2a−c. The finding that oxide 2a can
be induced to crystallize in new ways by traces of additives
provides further evidence that its molecular organization can
be altered with unusual facility.
Chalcogenides 2a−c also readily form pseudo-polymorphs
incorporating molecules of various solvents, as well as
cocrystals with diverse partners.40 We have found that
particularly suitable partners are fullerenes such as C60 and
C70, which have convex surfaces that are topologically and
electronically complementary to the concave faces of
phosphangulene and its derivatives.40−43 The related propen-
sity of triphenylphosphine oxide to cocrystallize with many
partners has been noted in previous work and attributed in part
to a strong capacity to accept hydrogen bonds.44 Phosphangu-
lene oxide (2a) promises to be an even more effective agent for
promoting cocrystallizations, because it cannot crystallize
effectively by itself in ways that properly exploit its latent
ability to form hydrogen bonds and other interactions.
Our work builds on earlier investigations of phosphangulene
and its derivatives but extends these previous studies in
unexpected ways. Our observations reveal that the behavior of
the compounds is not merely a curiosity, but rather a source of
broadly useful new understanding of molecular crystallization
overlooked in earlier work. Phosphangulene and its chalcoge-
nides may appear to be exotic compounds, but they are not
odd exceptions to normal molecular behavior. In fact, the
series of compounds is aptly chosen to help reveal how
molecular organization can be altered and controlled.
Crystallization is an undeniably complex phenomenon, but
our findings confirm that it is not futile to seek to identify
specific structural features that underlie particular solid-state
behavior. The approach used in our study of phosphangulene
and its chalcogenides is based on purposeful interference with
established patterns of crystallization, followed by extensive
analysis of the consequences. Our results confirm that the
approach is an effective way to probe the origins of molecular
organization and to engineer materials with useful properties
that arise predictably from structural features present in the
individual molecular components.
Our results underscore the shortcomings of efforts to
understand molecular crystallization based solely on statistical
analyses of the CSD and other structural databases. Previous
surveys have failed to identify any specific molecular features
that predictably underlie high levels of polymorphism.
Reported structures with high values of Z/Z′ are also diverse,
although certain organizing principles have been identified.20
However, the guidelines are far too vague to allow confident
extrapolation from the behavior of one compound to that of an
analogue. We are not aware of any previous study in which the
origin of high polymorphism and elevated values of Z/Z′ has
been traced back to specific structural features in a set of
compounds, in the way that we have probed the behavior of
phosphangulene chalcogenides 2a−c. Moreover, the correla-
tion we observe between molecular structure and crystalline
organization is tight, allowing key features of the solid-state
behavior of the entire set of compounds to be predicted with
confidence, on the basis of the properties of a single example.
This has not been achieved in previous efforts to understand
the origin of polymorphism and elevated values of Z/Z′.
Analyses of large databases are valuable tools for discovery, but
they must be complemented by parallel experimental studies,
using molecules purposefully devised to reveal and test
principles of organization in crystals. Mining databases,
however large, cannot yet replace sound chemical intuition
as a way to locate promising areas for exploration within the
infinite realm of molecular structures.
CONCLUSIONS
■
The distinctive conical shape of phosphangulene allows
efficient molecular packing and helps direct crystallization by
favoring the formation of π-stacks. As confirmed earlier by
Krebs, Yamamura, and their co-workers, this preferred mode of
association can be foiled by converting phosphangulene into
the corresponding oxide 2a, sulfide 2b, or selenide 2c. Only
one atom is added, but molecular packing is altered
profoundly. The shape of chalcogenides 2a−c consistently
disfavors efficient stacking and forces crystallization to occur in
other ways. Detailed structural analysis of multiple polymorphs
shows that none of the alternatives is particularly favorable, and
the frequency of large intermolecular separations is always
abnormally high. Chalcogenides 2a−c are structurally unable
to exploit the full potential of their constituent atoms to engage
in stabilizing intermolecular contacts. A high degree of
polymorphism is favored because various structural alterations
can be accommodated without incurring significant energetic
penalties, and the unit cells and asymmetric units of crystals
must typically include large numbers of molecules to allow
acceptable packing to be achieved.
EXPERIMENTAL SECTION
■
All reagents and solvents were obtained from commercial sources and
used without further purification unless otherwise indicated.
Phosphangulene and chalcogenides 2a−c were prepared by
modifications of published procedures, as described below.1,7,13
Phosphangulene chalcogenides 2a−c are richly polymorphic
despite having little conformational flexibility. Statistical
analysis of the CSD has established that molecular compounds
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2-(3-Fluorophenoxy)tetrahydro-2H-pyran (4). To a stirred
solution of pyridinium p-toluenesulfonate (0.305 g, 1.39 mmol) in
3,4-dihydro-2H-pyran (50 mL) was slowly added 3-fluorophenol
(12.5 mL, 138 mmol) at 25 °C under N2. After 30 min, the resulting
mixture was concentrated by evaporating volatile components under
reduced pressure, and ethyl acetate (200 mL) was added to the
residue. The organic phase was washed with saturated aqueous
NaHCO3 (200 mL), water (200 mL), and brine (200 mL). The
washed solution was then dried over Na2SO4 and filtered. Evaporation
of volatiles under reduced pressure left an oily residue that was
purified by flash chromatography (hexane, silica gel) to afford ether 4
Phosphangulene Sulfide (2b). A solution of phosphangulene
(1; 304 mg, 1.00 mmol) in p-xylene (3 mL) was sparged with N2, and
elemental sulfur was added (48.1 mg, 1.50 mmol). The resulting
suspension was stirred and heated at reflux for 12 h. Volatiles were
then removed by evaporation under reduced pressure, and the residue
was purified by elution with hexane through a short column of silica.
Crystallization of the product from anhydrous ethanol afforded
phosphangulene sulfide (2b) as a colorless solid (259 mg, 0.770
1
mmol, 77%). The H and 13C NMR spectra matched those reported
previously.7
Phosphangulene Selenide (2c). A solution of phosphangulene
(1; 304 mg, 1.00 mmol) in p-xylene (3 mL) was sparged with N2, and
elemental selenium was added (118 mg, 1.50 mmol). The resulting
suspension was stirred and heated at reflux for 12 h. Volatiles were
then removed by evaporation under reduced pressure, and the residue
was purified by elution with hexane through a short column of silica.
Crystallization of the product from anhydrous ethanol afforded
phosphangulene selenide (2c) as a colorless solid (283 mg, 0.738
1
as a colorless solid (21.6 g, 110 mmol, 79%). The H and 13C NMR
spectra matched those reported previously.1
Tris[2-fluoro-6-(tetrahydro-2H-pyran-2-yloxy)phenyl]-
phosphine (5). A stirred solution of ether 4 (20.7 g, 105 mmol) in
dry THF (320 mL) was cooled to −85 °C under N2 and treated
dropwise with a solution of n-BuLi (42 mL, 2.5 M in hexane, 110
mmol) during 15 min. After 1 h at −85 °C, freshly distilled PBr3 (9.23
g, 34.1 mmol) was added dropwise during 10 min. The resulting
mixture was stirred for 2.5 h at −85 °C, then MeOH (5.5 mL) was
added, and the temperature was allowed to rise to 25 °C. The
quenched mixture was poured into brine (300 mL), and the mixture
was extracted with diethyl ether (3 × 200 mL). The combined
extracts were dried over Na2SO4 and filtered. Evaporation of volatiles
under reduced pressure left a residue of solid, which was purified by
trituration with boiling MeOH or by recrystallization from a boiling
mixture of MeOH (1 L) and CHCl3 (50−100 mL). The resulting
solid was washed with MeOH and dried under vacuum to give
1
mmol, 74%). The H and 13C NMR spectra matched those reported
previously.7
ASSOCIATED CONTENT
* Supporting Information
■
S
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.cgd.9b00907.
Supplementary two-dimensional fingerprint plots of
Hirshfeld surfaces and additional crystallographic details,
including ORTEP drawings (PDF)
1
phosphine 5 as a colorless solid (15.6 g, 25.3 mmol, 74%). The H
and 13C NMR spectra matched those reported previously.1
2,2′,2″-Phosphinetriyltris(3-fluorophenol) (6). Phosphine 5
(8.00 g, 13.0 mmol) was suspended in N2-sparged MeOH (800 mL),
and 36% aqueous HCl (16 mL, 190 mmol) was added. The mixture
was stirred at 25 °C under N2 until a solution was formed (about 1−
1.5 h), and then volatile components were removed by evaporation
under reduced pressure. The residue was dissolved in N2-sparged
CHCl3 (300 mL), and N2-sparged aqueous NaHCO3 (1 N, 300 mL)
was added. The two phases were vigorously stirred for 2 h under N2
and then separated. The aqueous phase was extracted with diethyl
ether (2 × 100 mL), and the combined organic phases were dried
over Na2SO4 and filtered. Volatiles were removed by evaporation
under reduced pressure, and the residue was then dissolved in boiling
toluene (about 125 mL). Subsequent careful addition of heptane (200
mL) caused a colorless solid to precipitate. The resulting suspension
was kept overnight at −25 °C to induce further precipitation. The
product was separated by filtration, washed with hexane, and dried
under vacuum to afford phosphine 6 as a colorless solid (4.31 g, 11.8
Accession Codes
CCDC 1912956−1912970 contain the supplementary crys-
tallographic data for this paper. These data can be obtained
free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by
emailing data_request@ccdc.cam.ac.uk, or by contacting The
Cambridge Crystallographic Data Centre, 12 Union Road,
Cambridge CB2 1EZ, UK; fax: +44 1223 336033.
AUTHOR INFORMATION
Corresponding Author
*E-mail: james.d.wuest@umontreal.ca.
■
ORCID
Thierry Maris: 0000-0001-9731-4046
James D. Wuest: 0000-0003-1847-6923
Notes
1
mmol, 91%). The H and 13C NMR spectra matched those reported
previously.1
The authors declare no competing financial interest.
Phosphangulene (1). Under dry N2, a mixture of phosphine 6
(1.82 g, 5.00 mmol), Cs2CO3 (12.2 g, 37.4 mmol), and CuI (0.0952
g, 0.500 mmol) was treated with dry DMF (75 mL) and freshly
distilled tetramethylethylenediamine (TMEDA; 38 μL, 0.25 mmol).
The mixture was heated at reflux for 2 days and then allowed to cool.
Water was added until no more precipitate was formed. The solid was
separated by filtration, washed thoroughly with water, and dried under
vacuum at 25 °C. Decolorization could be achieved by dissolving the
solid in CH2Cl2 and passing the solution through a pad of silica. This
yielded phosphangulene (1) as a colorless solid (0.850 g, 2.79 mmol,
56%). The 1H and 13C NMR spectra matched those reported
previously.1
ACKNOWLEDGMENTS
We are grateful to the Natural Sciences and Engineering
Research Council of Canada, the Ministere de l’Education du
■
́
̀
́
Quebec, the Canada Foundation for Innovation, the Canada
́
́
Research Chairs Program, and Universite de Montreal for
financial support.
DEDICATION
■
Dedicated to the memory of the late Joel Bernstein, whose
deep understanding of molecular solids and infectious
enthusiasm made him a valued friend and colleague.
Phosphangulene Oxide (2a). A solution of phosphangulene (1;
304 mg, 1.00 mmol) in CHCl3 (8 mL) was treated with 30% aqueous
hydrogen peroxide (10 mL), and the mixture was stirred vigorously at
25 °C for 12 h. The phases were separated, and the organic phase was
dried over sodium sulfate and filtered. Removal of volatiles by
evaporation under reduced pressure left a residue that was
recrystallized from anhydrous ethanol to afford phosphangulene
REFERENCES
■
(1) Krebs, F. C.; Larsen, P. S.; Larsen, J.; Jacobsen, C. S.; Boutton,
C.; Thorup, N. Synthesis, Structure, and Properties of 4,8,12-Trioxa-
12c-phospha-4,8,12,12c-tetrahydrodibenzo[cd,mn]pyrene, a Molecu-
lar Pyroelectric. J. Am. Chem. Soc. 1997, 119, 1208−1216.
1
oxide (2a) as a colorless solid (307 mg, 0.959 mmol, 96%). The H
and 13C NMR spectra matched those reported previously.7
O
DOI: 10.1021/acs.cgd.9b00907
Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design
Article
(2) Carlson, R. R.; Meek, D. W. Dipole Moments of Several Tertiary
Phosphine Oxides, Sulfides, and Selenides and of Some Tertiary
Arsine Oxides and Sulfides. Inorg. Chem. 1974, 13, 1741−1747.
(3) Cumper, C. W. N.; Foxton, A. A.; Read, J.; Vogel, A. I. Physical
Properties and Chemical Constitution. Part XXXIX. The Electric
Dipole Moments of Some Tri-n-alkylphosphines, of Triphenylphos-
phine, and of their Oxides. J. Chem. Soc. 1964, 430−434.
(4) Madsen, G. K. H.; Krebs, F. C.; Lebech, B.; Larsen, F. K.
Evaluation of the Solid State Dipole Moment and Pyroelectric
Coefficient of Phosphangulene by Multipolar Modeling of X-ray
Structure Factors. Chem. - Eur. J. 2000, 6, 1797−1804.
(5) Hirshfeld surfaces and two-dimensional fingerprint plots were
generated by using CrystalExplorer17. Turner, M. J.; McKinnon, J. J.;
Wolff, S. K.; Grimwood, D. J.; Spackman, P. R.; Jayatilaka, D.;
Spackman, M. A. Crystal Explorer17; University of Western Australia,
2017.
(21) Steed, K. M.; Steed, J. W. Packing Problems: High Z’ Crystal
Structures and Their Relationship to Cocrystals, Inclusion Com-
pounds, and Polymorphism. Chem. Rev. 2015, 115, 2895−2933.
(22) Bernstein, J.; Dunitz, J. D.; Gavezzotti, A. Polymorphic
Perversity: Crystal Structures with Many Symmetry-Independent
Molecules in the Unit Cell. Cryst. Growth Des. 2008, 8, 2011−2018.
(23) Thomas, S. P.; Spackman, P. R.; Jayatilaka, D.; Spackman, M.
A. Accurate Lattice Energies for Molecular Crystals from
Experimental Crystal Structures. J. Chem. Theory Comput. 2018, 14,
1614−1623.
(24) Zeidan, T. A.; Trotta, J. T.; Tilak, P. A.; Oliveira, M. A.;
Chiarella, R. A.; Foxman, B. M.; Almarsson, O.; Hickey, M. B. An
Unprecedented Case of Dodecamorphism: The Twelfth Polymorph
of Aripiprazole Formed by Seeding with its Active Metabolite.
CrystEngComm 2016, 18, 1486−1488.
(25) Gnutzmann, T.; Thi, Y. N.; Rademann, K.; Emmerling, F.
Solvent-Triggered Crystallization of Polymorphs Studied in Situ.
Cryst. Growth Des. 2014, 14, 6445−6450.
(6) McKinnon, J. J.; Spackman, M. A.; Mitchell, A. S. Novel Tools
for Visualizing and Exploring Intermolecular Interactions in Molecular
Crystals. Acta Crystallogr., Sect. B: Struct. Sci. 2004, 60, 627−668.
(7) Yamamura, M.; Nabeshima, T. Relationship between the Bowl-
Shaped Geometry of Phosphangulene and an Axial Group on the
Phosphorus Atom. Bull. Chem. Soc. Jpn. 2016, 89, 42−49.
(8) Maly, K. E.; Gagnon, E.; Wuest, J. D. Engineering Molecular
Crystals with Abnormally Weak Cohesion. Chem. Commun. 2011, 47,
5163−5165.
́
(26) Lopez-Mejías, V.; Kampf, J. W.; Matzger, A. J. Nonamorphism
in Flufenamic Acid and a New Record for a Polymorphic Structure
with Solved Structures. J. Am. Chem. Soc. 2012, 134, 9872−9875.
(27) Yu, L. Polymorphism in Molecular Solids: An Extraordinary
System of Red, Orange, and Yellow Crystals. Acc. Chem. Res. 2010, 43,
1257−1266.
́
(28) Bras, E. M.; Henriques, M. S. C.; Paixao, J. A.; Fausto, R. High
̃
Z’ Crystal Structure of a New Polymorph of a Thioimidazole
Disulfide: Importance of Conformational Flexibility. Cryst. Growth
Des. 2018, 18, 4167−4173.
́
(9) Gagnon, E.; Halperin, S. D.; Metivaud, V.; Maly, K. E.; Wuest, J.
D. Tampering with Molecular Cohesion in Crystals of Hexaphe-
nylbenzenes. J. Org. Chem. 2010, 75, 399−406.
(29) Kersten, K.; Kaur, R.; Matzger, A. Survey and Analysis of
Crystal Polymorphism in Organic Structures. IUCrJ 2018, 5, 124−
129.
(10) Zhou, H.; Dang, H.; Yi, J.-H.; Nanci, A.; Rochefort, A.; Wuest,
J. D. Frustrated 2D Molecular Crystallization. J. Am. Chem. Soc. 2007,
129, 13774−13775.
(30) Cruz-Cabeza, A. J.; Reutzel-Edens, S. M.; Bernstein, J. Facts
and Fictions about Polymorphism. Chem. Soc. Rev. 2015, 44, 8619−
8635.
(31) McCrone, W. C. In Polymorphism in Physics and Chemistry of
the Organic Solid State; Fox, D., Labes, M. M., Weissenberg, A., Eds.;
Interscience: New York, 1965; Vol. II, pp 726.
(32) Gavezzotti, A. Structure and Energy in Organic Crystals with
Two Molecules in the Asymmetric Unit: Causality or Chance?
CrystEngComm 2008, 10, 389−398.
(33) Knapp, C.; Lork, E.; Gupta, K.; Mews, R. Structure
Investigations on 4-Halo-1,2,3,5-dithiadiazolyl Radicals XCNSSN•
(X = F, Cl, Br): The Shortest Intradimer S···S Distance in
Dithiadiazolyl Dimers. Z. Anorg. Allg. Chem. 2005, 631, 1640−1644.
(34) Clarke, C. S.; Pascu, S. I.; Rawson, J. M. Further Studies on the
Polymorphic Dithiadiazolyl Radical, ClCNSSN. CrystEngComm 2004,
6, 79−82.
(35) Cheuk, D.; Khamar, D.; McArdle, P.; Rasmuson, Å. C. Solid
Forms, Crystal Habits, and Solubility of Danthron. J. Chem. Eng. Data
2015, 60, 2110−2118.
(36) Rohl, A. L.; Moret, M.; Kaminsky, W.; Claborn, K.; McKinnon,
J. J.; Kahr, B. Hirshfeld Surfaces Identify Inadequacies in
Computations of Intermolecular Interactions in Crystals: Pentam-
orphic 1,8-Dihydroxyanthraquinone. Cryst. Growth Des. 2008, 8,
4517−4525.
(37) Lusi, M. Engineering Crystal Properties through Solid
Solutions. Cryst. Growth Des. 2018, 18, 3704−3712.
(38) Vegard, L. Die Konstitution der Mischkristalle und die
̀
(11) Lebel, O.; Maris, T.; Perron, M.-E.; Demers, E.; Wuest, J. D.
The Dark Side of Crystal Engineering: Creating Glasses from Small
Symmetric Molecules that Form Multiple Hydrogen Bonds. J. Am.
Chem. Soc. 2006, 128, 10372−10373.
(12) Zhang, X.; Liu, F.; Wei, Z.; Wang, Z. Synthesis of Diaryl Ethers
by CuI-Catalyzed C-O Bond Formation via Ullman Coupling:
Assessing the Reactivity of Aryl Halides. Lett. Org. Chem. 2013, 10,
31−36.
(13) Faldt, A.; Krebs, F. C.; Thorup, N. Synthesis, Structure and
Properties of Various Molecules Based on the 4,8,12-Trioxa-
4,8,12,12c-tetrahydrodibenzo[cd,mn]pyrene System with an Evalua-
tion of the Effect Differing Molecular Substitution Patterns has on the
Space Group Symmetry. J. Chem. Soc., Perkin Trans. 2 1997, 2, 2219−
2227.
(14) Eikeland, E.; Thomsen, M. K.; Overgaard, J.; Spackman, M. A.;
Iversen, B. B. Intermolecular Interaction Energies in Hydroquinone
Clathrates at High Pressure. Cryst. Growth Des. 2017, 17, 3834−3846.
(15) Lee, J. J.; Fuller, R. O.; Sobolev, A. N.; Clausen, H. F.;
Overgaard, J.; Koutsantonis, G. A.; Iversen, B. B.; Spackman, M. A.
Temperature-Dependent Crystal Structure of the Isopropanol
Clathrate of Dianin’s Compound. Chem. Commun. 2011, 47, 2029−
2031.
(16) Kooijman, H.; Spek, A. L.; van Bommel, K. J. C.; Verboom, W.;
Reinhoudt, D. N. A Triclinic Modification of Triphenylphosphine.
Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 1998, 54, 1695−
1698.
(17) Brock, C. P.; Schweizer, W. B. Internal Molecular Motion of
Triphenylphosphine Oxide: Analysis of Atomic Displacement
Parameters for Orthorhombic and Monoclinic Crystal Modifications
at 100 and 150 K. J. Am. Chem. Soc. 1985, 107, 6964−6970.
(18) Views of the structures of other inequivalent molecules in the
asymmetric unit are provided in the Supporting Information.
(19) Bernstein, J.; Davey, R. J.; Henck, J.-O. Concomitant
Polymorphs. Angew. Chem., Int. Ed. 1999, 38, 3440−3461.
(20) Brock, C. P. High-Z’ Structures of Organic Molecules: Their
Diversity and Organizing Principles. Acta Crystallogr., Sect. B: Struct.
Sci., Cryst. Eng. Mater. 2016, 72, 807−821.
Raumfullung der Atome. Eur. Phys. J. A 1921, 5, 17−26.
̈
(39) Vegard, L.; Shelderup, H. Die Konstitution der Mischkristalle.
Phys. Z. 1917, 18, 93−96.
(40) Heskia, A.; Maris, T.; Wuest, J. D. Putting Fullerenes in Their
Place: Cocrystallizing C60 and C70 with Phosphangulene Chalcoge-
nides. Cryst. Growth Des. 2019, 19, in press. DOI: 10.1021/
acs.cgd.9b00954.
(41) Yamamura, M.; Hongo, D.; Nabeshima, T. Twofold Fused
Concave Hosts Containing Two Phosphorus Atoms: Modules for the
Sandwich-Type Encapsulation of Fullerenes in Variable Cavities.
Chem. Sci. 2015, 6, 6373−6378.
P
DOI: 10.1021/acs.cgd.9b00907
Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design
Article
(42) Yamamura, M.; Sukegawa, K.; Nabeshima, T. Tuning the
Depth of Bowl-Shaped Phosphine Hosts: Capsule and Pseudo-Cage
Architectures in Host-Guest Complexes with C60 Fullerene. Chem.
Commun. 2015, 51, 12080−12083.
(43) Yamamura, M.; Saito, T.; Nabeshima, T. Phosphorus-
Containing Chiral Molecule for Fullerene Recognition Based on
Concave/Convex Interaction. J. Am. Chem. Soc. 2014, 136, 14299−
14306.
(44) Etter, M. C.; Baures, P. W. Triphenylphosphine Oxide as a
Crystallization Aid. J. Am. Chem. Soc. 1988, 110, 639−640.
Q
DOI: 10.1021/acs.cgd.9b00907
Cryst. Growth Des. XXXX, XXX, XXX−XXX