Structure-Polymorphism Study of Fenamates: Toward Developing an Understanding of the Polymorphophore

Article abstract of DOI:10.1021/acs.cgd.5b00570

The ability of molecules to adopt more than one unique crystalline structure, polymorphism, is a phenomenon of considerable scientific interest because it challenges the notion that molecules arrange themselves exclusively in the thermodynamically most stable crystal form. The factors influencing this behavior are manifold and have defied simple prediction. To illustrate an approach to elucidating these factors, the solid-state behavior of a series of molecules that are derivatives of tolfenamic acid (TA), a pentamorphic system, was explored. In analogy to the manner in which drugs are discovered through structure-activity relationships and the identification of a pharmacophore, we test here the notion that when a collective ensemble structural motifs, a "polymorphophore," is incorporated into a molecule it renders the compound polymorphic. The structure-polymorphism relationship in six TA analogues, both commercial and newly synthesized, was undertaken with the intention of systematically understanding the factors that influence the polymorphism in the fenamic acid class through a combined computational as well as experimental approach. Ultimately, such studies may be used to experimentally derive the propensity for polymorphic behavior of a given molecular motif and perhaps provide a pathway to engineer molecular compounds with controlled properties in the solid state.

Full text of DOI:10.1021/acs.cgd.5b00570

Article
pubs.acs.org/crystal
Structure−Polymorphism Study of Fenamates: Toward Developing
an Understanding of the Polymorphophore
Vilmalí Lopez-Mejías†,§ and Adam J. Matzger*,†
́
†Department of Chemistry and the Macromolecular Science and Engineering Program, University of Michigan, 930 North University
Avenue, Ann Arbor, Michigan 48109-1055, United States
S
* Supporting Information
ABSTRACT: The ability of molecules to adopt more than one
unique crystalline structure, polymorphism, is a phenomenon of
considerable scientific interest because it challenges the notion
that molecules arrange themselves exclusively in the thermody-
namically most stable crystal form. The factors influencing this
behavior are manifold and have defied simple prediction. To
illustrate an approach to elucidating these factors, the solid-state
behavior of a series of molecules that are derivatives of tolfenamic
acid (TA), a pentamorphic system, was explored. In analogy to
the manner in which drugs are discovered through structure−
activity relationships and the identification of a pharmacophore,
we test here the notion that when a collective ensemble structural
motifs, a “polymorphophore,” is incorporated into a molecule it
renders the compound polymorphic. The structure−polymor-
phism relationship in six TA analogues, both commercial and
newly synthesized, was undertaken with the intention of
systematically understanding the factors that influence the
polymorphism in the fenamic acid class through a combined computational as well as experimental approach. Ultimately,
such studies may be used to experimentally derive the propensity for polymorphic behavior of a given molecular motif and
perhaps provide a pathway to engineer molecular compounds with controlled properties in the solid state.
classes.12−20 Analogues of the highly polymorphic compounds
INTRODUCTION
■
5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile
The existence of compounds exhibiting multiple crystalline
phases differing in the arrangements and/or conformations of
(ROY)17,21−25 and carbamazepine (CBZ)16,26−29 have been
the molecules within a crystal lattice,1 polymorphism, poses a
scrutinized for polymorphism (Supporting Information).
Collectively, these investigations present early evidence that
challenge to the notion that molecules can arrange themselves
an ensemble of steric and electronic features in a molecule
only in the thermodynamically most stable crystalline form.
Moreover, the economic impact of this long-standing challenge
provides a fine interplay of the interactions ultimately
responsible for the appearance of multiple crystal phases and
on the intellectual property, regulation, and manufacture of
crystalline materials is measured in billions of dollars.2
highlights the need for a systematic approach in order to gain
understanding of the structural factors that influence the
Therefore, it is important to understand not only the molecular
structure of a compound, but also how this structure influences
the packing behavior in the solid state in order to control a
appearance polymorphism in molecular compounds.
In analogy to how pharmacophores are identified, here we
performance of a material.3 To date, there is no experimental
method capable of determining if a given molecular structure is
prone to display polymorphism, nor is there a method to
establish the number of crystal phases that are energetically
accessible. Computational methods have shown promising
results in polymorph prediction,4−10 but their efficacy can only
be evaluated once every structure is experimentally deter-
mined.11 Hence, it would be beneficial if the relationship
between a molecular structure and its propensity to give rise to
polymorphism could be experimentally derived.
undertake a systematic study of the proposed structure−
polymorphism relationship among molecular analogues of
tolfenamic acid (TA). TA (Figure 1) is a highly polymorphic
nonsteroidal anti-inflammatory drug (NSAID) that possesses
complex solid-state chemistry including whole molecule
disorder (form V), varying numbers of molecules in the
asymmetric unit, as well as a diverse array of conformations and
packing arrangements; moreover, all of these occur within a
Received: April 23, 2015
Revised: June 10, 2015
Previous accounts have suggested a relationship between
molecular structure and polymorphism for specific compound
© XXXX American Chemical Society
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fritted filter and the solvent removed using rotary evaporation. The
resulting solid was dissolved in 5% Na2CO3 and precipitated with 0.5
M HCl. The precipitate was collected on a glass fritted filter and
dissolved in 5% Na2CO3 and precipitated again with 0.5 M HCl. The
final product was obtained by zone sublimation (∼15 mTorr) between
120 and 140 °C.
Crystallization in the Presence of Polymers. Polymer-induced-
heteronucleation (PIHn) was used as the primary method for
polymorph discovery.32−35 Solutions (∼12.5 mg/mL) of each
analogue were prepared in ethanol, methanol, or acetonitrile. Solutions
were dispensed equally (∼0.2 mL) into each well in the 96-well plate
containing nonpolar aromatic or acidic polymers. Crystals grew during
evaporation of the solvent in the presence of polymers.
Crystallization in the Absence of Polymers. Solutions (∼12.5
mg/mL) of each analogue were prepared in ethanol, methanol, 2-
propanol, 1-pentanol, ethyl acetate, methylene chloride, acetonitrile,
chloroform, isobutylalcohol, 1-butanol, 1-propanol, 1,4-butanediol, sec-
butanol, and acetone. Solutions were dispensed equally (∼0.2 mL)
into an uncapped 4 mL vial after dissolving the solute. Crystals grew
through evaporation of the solvent in the absence of polymer. Solvent
free crystallization was also explored by subliming the powdered
sample (∼100 mg) at 120−140 °C and ∼15 mTorr with collection
onto an ice-cooled coldfinger.
Polymorph Characterization. Crystals obtained in the 96-well
plates were first identified optically by differences in morphology and/
or color. Powder X-ray diffraction (PXRD) was utilized to confirm
structural dissimilarity among the suspected polymorphs of each
analogue. PXRD analysis was performed using a Rigaku R-Axis Spider
diffractometer equipped with an image plate detector and graphite
monochromated Cu Kα radiation (1.54178 Å, 50 kV, 40 mA). Samples
were mounted on a CryoLoop and images were collected for 5 min
while rotating the sample about the φ-axis at 10°/s, oscillating ω
between 120° and 180° at 1°/s with χ fixed at 45°. All images were
integrated from 5° to 50° with a 0.05° step size using AreaMax2
software. PXRD patterns were processed in Jade Plus3 (v 8.2) to
calculate peak positions (deg) and relative intensities (%). Ultimately,
if crystal quality permitted it, structures were determined through
single crystal X-ray diffraction.
Figure 1. Molecular structure of tolfenamic acid (TA), mefenamic acid
(MA), fenamic acid (FA), and synthesized analogues 1−4. Structural
changes in the noncarboxylated phenyl ring are indicated in blue for
the ortho position and red for the meta substituent.
very narrow free energy window.15 As such, this pentamorphic
compound is ideally suited to testing the notion that certain
structural motifs favor the formation of polymorphic crystals:
the polymorphophore.16,17 The polymorphophore does not
represent a real molecule or discrete association of functional
groups; it is an abstraction accounting for the common
structural motif in related compounds associated with their
propensity to display multiple crystalline phases. Systematic
studies of structure−polymorphism relationships, like the one
shown here, will assess polymorphic propensity of a given
molecular motif and, perhaps, ultimately provide a pathway to
engineer molecular compounds less prone to polymorphism.
Toward this goal, and drawing on principles of pharmacophore
identification, the polymorphic behavior of six analogues of TA
is studied in detail (Figure 1). Moreover, virtual crystal
structures of analogues adopting arrangements mirroring
those of TA polymorphs were examined, as were hypothetical
structures of TA adopting the arrangements experimentally
observed in analogues. This approach provides a paradigm for
systematic experimental−theoretical exploration of the crystal
polymorphism energy landscape.
RESULTS AND DISCUSSION
■
The factors leading to polymorphism in some molecules and
not in others are poorly understood. Here a systematic
investigation of the structure−polymorphism relationships
among analogues of TA is used to delineate the origin of
polymorphism in the molecular structure of TA, in other words
to identify, if one exists for this compound, the polymorpho-
phore. Toward this goal, an extensive experimental and
computational investigation into the solid-form diversity in
TA and structurally related analogues was carried out. A series
of molecular analogues, 1−4 (Figure 1), consisting of the TA
skeleton with different substitutions on the noncarboxylated
phenyl ring at the 2,3-positions were synthesized through
Ullman-Golberg condensations (Supporting Information).30,31
These four analogues and commercially available mefenamic
acid (MA) and fenamic acid (FA) yielded six structurally
related compounds to probe (Figure 1).
EXPERIMENTAL SECTION
■
Materials. Mefenamic acid (MA) and fenamic acid (FA) were
obtained from Sigma-Aldrich (St. Louis, MO). Analogues 1−4 were
synthesized according to literature procedures.30,31 The solvents
methanol, 2-propanol, 1-pentanol, ethyl acetate, methylene chloride,
acetonitrile, chloroform, 1-butanol, and acetone were purchased from
Fisher Scientific (Pittsburgh, PA). The solvents isobutanol and 1-
propanol were purchased from Burdick and Jackson Laboratories, Inc.
(Muskegon, MI), whereas 1,4-butanediol and sec-butanol were
purchased from Acros Organics (New Jersey). Ethanol was purchased
from Decon Laboratories, Inc. (King of Prussia, PA). The reagents 2-
bromobenzoic acid, 2-chlorobenzoic acid, 3-chloroaniline, and o-
toluidine were purchased from Aldrich (St. Louis, MO). The reagents
Cu powder (powder, 1 μm, 0.8 mmol), Cu2O (powder, <5 μm, 0.4
mmol), and 3-bromoaniline were purchased from Acros Organics
(New Jersey). The reagent 2-methyl-3-bromoaniline was purchased
from Alfa Aesar (Ward Hill, MA). All commercially available reagents,
compounds, and solvents were used without further purification.
General Procedure of the Cu-Catalyzed Amination of Aryl
Halides. A mixture of aniline (9.3 mmol), 2-bromobenzoic acid or 2-
chlorobenzoic acid (8.8 mmol), K2CO3 (8.8 mmol), Cu powder
(powder, 1 μm, 0.8 mmol), Cu2O (powder, <5 μm, 0.4 mmol), and 10
mL of 2-ethoxyethanol were heated to reflux for 24 h under a N2
atmosphere. The cooled reaction mixture was passed through a glass
At the outset of this investigation it was hypothesized that
subtle structural changes in the noncarboxylated phenyl ring at
the 2,3-positions has the potential to give rise to isostructural
analogues of TA, whereas disturbing the carboxylic acid
dimerization would prevent the appearance of the previously
observed packing motifs, all of which involve hydrogen bonded
dimers. Therefore, analogues were chosen to preserve the basic
monocarboxylated diphenylamine nucleus. In the molecular
structure of MA and analogue 1, the chlorine present in TA is
exchanged by methyl and bromine, respectively. For the chloro-
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Figure 2. Experimental PXRD patterns of the solid forms obtained for commercial TA analogues MA (top, left) and FA (top, center), as well as
synthesized analogues: analogue 1 (top, right), analogue 2 (bottom, left), analogue 3 (bottom, center), and analogue 4 (bottom, right) obtained
using PIHn.
methyl exchanged analogue MA, it was hypothesized that since
chlorine (19 Å3) and methyl (24 Å3) groups have similar
volumes,36−38 their substitution would lead to crystal forms
isostructural to TA forms if halogen interactions do not play a
critical role in controlling the packing of these crystals.
Exchange of chlorine in TA by bromine in analogue 1 will
allow similar intermolecular interactions to occur, possibility
permitting previously observed packing motifs for this
analogue.39 Analogues 2 and 3 display the absence of methyl
or chlorine groups compared to TA; the appearance of
isostructural forms of these analogues would provide insight
into the role that each of these functional groups plays in the
emergence of the multiple crystalline phases in TA. Analogue 4
will test the effect of halogen substitution in the absence of the
methyl group. The absence of both methyl and chlorine is
displayed by FA; to date, no polymorphs of this analogue have
been reported.40 The discovery of novel forms of FA would
provide insights on contribution of the monocarboxylated
diphenylamine nucleus to isostructural packing modes within
the polymorphophore. On the other hand, the absence of
experimentally observed polymorphs in FA would reinforce the
need for the steric and electronic features provided by the
methyl and halogen substituents in order to attain the multiple
packing modes observed experimentally in the polymorphs of
TA.
Polymorph Screening. Initial screening was carried out
using sublimation in the absence of polymers; this method did
not lead to new forms. The more traditional, solvent-based
crystallization method was also utilized employing 14
commonly used solvents with evaporation. Only a few of
these solvents were able to access a second crystalline phase for
some analogues. Polymer-induced heteronucleation (PIHn) is a
powerful technique for the selective discovery and control of
solid-state forms that utilizes polymers as heteronucleants.32−35
When this method was utilized as a general screening strategy, a
larger number of polymorphs were accessed. Therefore, the
majority of the polymorphs discussed here were grown using
PIHn. A comparison of the number of polymorphs found
during the crystallization of TA analogues in the 14 different
solvents and sublimation versus crystallization using polymers
as heteronuclei can be found in the Supporting Information.
The use of polymer heteronuclei allowed access to the two
previously reported forms of MA, and one previously reported
form of FA (Figure 2). No further polymorphs of these
commercial compounds were identified; in this context it
should be noted that a convincing case for a structural origin to
the lack of polymorphism in FA has recently been made based
on extensive computational studies showing the absence of low
energy hypothetical polymorphs.41 Both FA form I and MA
form I present unique PXRD patterns, while the comparison of
PXRD patterns of MA form II and TA form V indicates that
although both forms present disorder, these forms are
isostructural (Supporting Information).
Application of PIHn to analogue 1 yielded three polymorphs,
which were grown in the presence of nonpolar aromatic and
acidic polymers. PXRD patterns of the colorless needles (form
I), the yellow needles (form II), and the colorless plates (form
III) present unique reflections demonstrating that each form is
structurally distinct from one another (Figure 2). Furthermore,
the comparison of their PXRD patterns suggests that forms I
and II of analogue 1 are isostructural with forms I and II of TA
(Supporting Information).
Three polymorphs of analogue 2 were accessed through the
use of acidic polymers as heteronuclei. Form I is colorless and
crystallizes in a plate-like habit, whereas forms II and III are
light yellow needles. Examination of the PXRD patterns reveals
that forms I−III of analogue 2 are unique and are distinct from
those previously observed for TA and any of its analogues
(Figure 2).
PIHn allowed access to two polymorphs of analogue 3.
PXRD patterns of each form suggest structural dissimilarity
when compared to all other analogues and TA (Figure 2).
Three crystal forms of analogue 4 were discovered using PIHn.
PXRD patterns confirm the presence of unique packing
arrangements among analogue 4 polymorphs (Figure 2) and
these are distinct from the five forms of TA.
Structural Analysis. Classification of solid forms as
isostructural or structurally similar to one another is most
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effectively carried out from experimentally derived crystal
structures. Isostructural forms will share similar cell constants,
the same space group and almost identical packing motifs,
whereas structurally similar forms will present significant
deviations in cell constants and, potentially, space groups but
still preserve notable similarities in the packing arrangements.
For the TA analogues discovered above, nine crystal structures
were obtained and these, in combination with the three crystal
structures for MA (forms I and II) and FA, provide a large basis
for comparison. A unifying theme among all analogues and TA
is the presence of hydrogen-bonded dimers assembled through
the carboxylic acid and the presence of an intramolecular
hydrogen bond between the carbonyl oxygen and the amine
hydrogen. Supramolecular synthons are essential for guiding
crystal packing; therefore, the hydrogen bonded dimer and its
stabilization through the intramolecular hydrogen bond seems
to be an important feature within the polymorphophore
connecting all of the TA analogues.
MA represents the chloro-methyl exchanged analogue of TA;
it was hypothesized that this substitution would lead to
isostructural crystal forms if the halogen interactions do not
play a critical role in controlling the packing of these crystals.
Experimentally, this was only observed in the case of MA form
II, which is isostructural to TA form V. Examination of the cell
parameters revealed identical space group (P1) and cell
̅
parameters for both forms. Both structures present similar
packing arrangements, although complete evaluation of the
resemblance present in each crystal form is difficult due to the
presence of disorder in both structures. TA form V exhibits
whole molecule disorder, whereas in the case of this chloro-
methyl exchanged analogue, only the noncarboxylated aromatic
ring in the molecule exhibits disorder. The emergence of an
isostructural form between MA form II and TA form V
indicates that halogen interactions do not play a critical role for
this specific packing motif.
The crystal structures for the three polymorphs of analogue 1
were elucidated (Supporting Information). Examination of the
space groups, cell parameters, hydrogen bonding, conforma-
tions, and packing motifs establishes that analogue 1 forms I
and II are isostructural to TA forms I and II, whereas analogue
1-form III shares only some structural similarities with TA form
III. Molecular conformations of forms I and II in both TA and
1 are equivalent, whereas the conformations present in form III
are not shared by any of the experimentally observed TA
polymorphs (Supporting Information). As in the case of TA
form II, 1-form II presents the most coplanar conformation
among all forms and this planarity causes the light yellow color
in the crystals of both forms. The root-mean-square (RMS)
value is defined as the square root of the mean squared
difference in the position of nominally equivalent atoms. The
RMS value is used to measure the geometric difference between
packing features in crystal structures.37 The resulting structural
overlay of 1-form I and TA form I yielded an RMS value of
0.119 Å (15 out of 15 molecules along the ac plane), indicating
that a close structural match exists between these polymorphs,
whereas a structural overlay of 1-form II and TA form II yielded
an RMS value of 0.132 Å (15 out of 15 molecules along the a-
axis), demonstrating that isostructurality exists between these
forms. Structural overlay of 1-form III and TA form III yielded
a RMS value of 0.207 Å (13 out of 15 molecules along the ac
plane), indicative of only structural similarity between these
forms (Figure 3). The presence of isostructural forms in the
case of analogue 1 and TA indicates that the substitution of the
Figure 3. Comparison of the molecular packing and hydrogen
bonding motif in (a) 1-form I along the a-axis, (b) TA form I along
the a-axis, (c) 1-form II along the c-axis, (d) TA form II along the c-
axis, (e) 1-form III along the b-axis, and (f) TA form III along the a-
axis.
chlorine by bromine allows for similar halogen···halogen
interactions to occur, therefore permitting nearly identical
packing modes to occur in the solid state.
Crystal structures for analogue 2 polymorphs I and II were
determined (Supporting Information), whereas that of form III
remains elusive. Both forms crystallize in the triclinic space
group P1 with one molecule in the asymmetric unit (Figure 4).
̅
A solid−solid transformation at low temperature (∼ −90 °C)
of 2-form II yielded 2-form IV (Supporting Information).
Notably, 2-form IV contains six unique molecules (P1) in the
̅
asymmetric unit, a rare occurrence in the Cambridge Structural
Database (CSD), with fewer than 200 examples for structures
with Z′ = 6.43,44 All conformations present in analogue 2
polymorphs present an anti-conformation between the
carboxylated phenyl ring and the chlorinated phenyl ring.
Although not isostructural, polymorphs II and IV of analogue 2
present a very similar columnar packing arrangement to TA
form IV. The absence of isostructural forms in the case of
analogue 2 (the TA analogue lacking the methyl group)
suggests the importance of the methyl group in accessing the
packing modes experimentally observed in the TA system.
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Figure 5. Molecular packing and hydrogen bonding motif of (a) 3-
form I and (b) 3-form II along the a-axis.
Figure 4. Molecular packing and hydrogen bonding motif of (a) 2-
form I along the a-axis, (b) 2-form II along the a-axis, and (c) 2-form
IV along the b-axis.
Crystal structures were also determined for analogue 3, the
absence of the chlorine analogue. Colorless needles of 3-form I
crystallize in the monoclinic space group C2/c whereas
colorless plates of 3-form II crystallize in P21/n; both structures
present a unique molecular conformation and the one molecule
in the asymmetric unit (Supporting Information). The crystal
structure of 3-form I shows only a slight resemblance to that of
TA form III. This suggests that the absence of halogen (Cl···Cl)
contacts in 3-form I plays an important role in the packing
arrangement observed in this form versus that shown in TA
form III. Form II of analogue 3 presents a packing arrangement
that has not been previously observed (Figure 5b), but the
absence of halogen (Cl···Cl) contacts could also play an
important role in the differentiation of this packing mode
versus those presented by TA and analogue 2. It could be
implied that the absence of this contact does not allow for
analogue 3 to produce isostructural forms to that of TA or
analogue 2.
Figure 6. Comparison of the molecular packing and hydrogen
bonding motif in (a) 4-form I and (b) 2-form II along the a-axis.
Surprisingly, the packing mode present in 4-form I does not
resemble those of TA polymorphs; instead, packing modes
present in 4-form I resemble that of 2-form II demonstrating
that isostructurality exists between these polymorphs (Figure
6). This finding reinforces the importance of the presence of
the methyl group in order to access the packing modes
experimentally observed in the TA polymorphs.
Conformational Analysis. To probe the effect of
conformational changes on the polymorph−structure relation-
ships presented among these analogues and TA, a conforma-
tional search of the potential energy along the two torsion
angles (τ1 and τ2) connecting the diphenylamine functionality
was performed. Two-dimensional scans for each analogue and
TA were executed using Gaussian03. Optimized geometries and
corresponding energies were obtained at the HF/6-31G* level
at 10° intervals. The potential energies were used to construct
conformational plots (Figure 7). Based on their contours,
Although three polymorphs of analogue 4 were accessed
through the use of polymers as heteronuclei, only one form
yielded structural characterization. Form I crystallizes in the
triclinic space group P1 with a single molecule in the
̅
asymmetric unit (Figure 6a and Supporting Information).
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Figure 7. Conformational plots constructed using the results of a two-dimensional scan along torsion angles, τ1 and τ2, for TA and analogues using
Gaussian03. Optimized geometries and corresponding energies were obtained at the HF/6-31G* level at 10° intervals.
Figure 8. Lattice energy difference distribution (ΔUlatt) from lattice substitution calculations for analogues FA, MA, and 1−4 in the four crystal
structures observed experimentally for TA. The values for the lattice energy difference among the four “virtual” structures are shown in the graph;
form I (yellow), form II (red), form III (blue), form IV (green).
conformational plots can be divided into two groups: those that
present similar contours to TA and those that present different
contours. The conformational plots for MA, analogue 1, and
analogue 3 present similar contours to that of the conforma-
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tional plot of TA, whereas the conformational plots for FA,
analogue 2, and analogue 4 present distinct contours in their
conformational plots. It is therefore observed that substitution
of the ortho position in the noncarboxylated phenyl ring
provides conformational restrictions to the energetically
accessible conformations. These data provide a possible
explanation for the presence of isostructural analogues based
on the available conformations to these molecular structures.
They explain the presence of isostructural solid forms among
TA, MA, and analogue 1 based on the energetically viable
conformations due to the presence of the ortho substituent
while suggesting an important role of the meta substituent in
accessing isostructural packing modes.
Conformational plots reveal a connection between the
energetically relevant conformations present in analogue 2
and analogue 4 and the emergence of isostructural forms
between these molecular structures. It can also be concluded
that the diphenylamine functionality is not a sufficient
condition to harvest the multiple crystalline phases observed
in TA and its analogues, because although this molecular
structure is as conformationally flexible as analogue 2 and 4, it
lacks the directionality provided by the halogen group on the
meta position. The potential energy associated with the
experimentally determined conformation of each analogue
was calculated and compared to that of the lowest energy
conformation (Supporting Information). Analogues presenting
isostructural or structurally similar packing arrangements also
present similar conformations and therefore their conforma-
tional energy differences, ΔEconf, are of comparable magnitude.
Lattice Energy Calculations. To further explore the
structural relationships that emerged in the TA analogues,
lattice energy calculations were carried out in which the six
analogues were substituted in turn into each of the four distinct
experimental lattices observed for ordered polymorphs of TA.
Four simulated, or “virtual”, structures were obtained for each
analogue. These structures were then optimized and their
lattice energy, Ulatt (virtual analogue), was compared to that of the
lowest lattice energy calculated, Ulatt (analogue), for the different
polymorphs of each analogue (Figure 8). For a detailed
procedure on the Lattice Energy Calculations see section five of
the Supporting Information. Among these structures, those
corresponding to analogue 1-forms I−IV are low on the lattice
energy plot and comparable in stability with the forms I−IV of
TA (Supporting Information). As suggested by these
calculations, isostructural forms to TA in the case of analogue
1 (forms I and II) where experimentally accessed with the aid
of polymers as heteronuclei, those analogue 1 (forms III and
IV) remained experimentally elusive.
Figure 9. Lattice energy difference (ΔUlatt) from lattice energy
substitution calculations of TA in the ordered crystal structures
observed experimentally for analogues FA, MA, and 1−4. Only the
average values for the lattice energy difference are shown in the graph.
CONCLUSIONS
■
Understanding the structural basis for polymorphism in
molecular crystals has been a vexing problem in solid-state
chemistry. The concept of the polymorphophore, tested here
within the prominent fenamic series, has the potential to shed
light on this issue; the structure−polymorphism relationship is
clearly established in this series and tied to structural features
present within the analogues. This is the most extensive study
of its type and lays the groundwork for application to further
molecular classes. The correlation with the (readily calculable)
potential energy as a functional of molecular conformation is an
intriguing observation that suggests the approach could be
applied to finding compounds prone to, or resistant to,
polymorphic crystallization if data on one analogue is
established. This investigation advances understanding of the
structural factors responsible for the appearance of multiple
polymorphs and supports the notion that a collective ensemble
of conformational, steric, and electronic features is responsible
for the adoption of multiple packing modes in molecular
compounds. Ultimately, these studies will help to experimen-
tally derive the propensity for polymorphic behavior of a given
molecular motif and perhaps provide a pathway to engineer
molecular compounds with controlled properties in the solid
state.
ASSOCIATED CONTENT
* Supporting Information
■
S
In order to determine if all energetically accessible forms of
TA have been kinetically accessed, lattice energy calculations
were carried out in which TA was substituted in turn into each
of the experimental lattices determined for polymorphs of all six
analogues. The lattice energy difference, ΔUlatt, for several
virtual structures fall within 2 kcal/mol (Figure 9 and
Supporting Information). Although experimentally some of
these crystal structures have not been observed for TA, most of
the virtual structures that fall within this minimum represent
isostructural or structurally similar packing arrangements to TA.
This approach of combining experimental screening and lattice
energy substitution calculations provides a strategy to maximize
the probability that all energetically viable crystalline phases are
accessed.
Experimental preparation, PXRD patterns, and cif files. The
Supporting Information is available free of charge on the ACS
Publications website at DOI: 10.1021/acs.cgd.5b00570.
AUTHOR INFORMATION
Corresponding Author
*E-mail: matzger@umich.edu.
■
Present Address
§
́
́
Vilmalı Lopez-Mejıas, Department of Chemistry, University of
́
Puerto Rico, Rio Piedras Campus, PO Box 23346 San Juan, PR
00931−3346.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
■
This work was supported by the National Institute of Health
Grant Number GM072737 and National Science Foundation
(CHE-0840456). The authors thank Dr. Jennifer L. Knight for
her contributions to the calculations of the conformational
energies and development of the conformational energy plots,
and Dr. Kira Landenberger and Dr. Jeff W. Kampf for providing
technical advice and refinement to some of the structures
presented in this manuscript.
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DOI: 10.1021/acs.cgd.5b00570
Cryst. Growth Des. XXXX, XXX, XXX−XXX