Sulfonamide molecular crystals: Thermodynamic and structural aspects

Article abstract of DOI:10.1021/cg1012389

The crystal structures of three sulfonamides with the structures C ₆H₅-SO₂NH-C₆H₅, C ₆H₅-SO₂NH-C₆H₄-R (R = 4-NO₂), 4-NH₂-C₆H₄-SO ₂NH-C₆H₄-R (R = 4-NO₂; 4-CN) have been determined by X-ray diffraction. On the basis of our previous data and the obtained results, comparative analysis of crystal properties was performed: molecular conformational states, packing architecture, and hydrogen bond networks using graph set notations. Conformational flexibility of the bridge connecting two phenyl rings was studied and described by a correlation equation. Hydrogen bonds were grouped according to the frequency of hydrogen bond appearance within the definite graph set assignment. The strength of the hydrogen bonds was evaluated. The influence of various molecular fragments on crystal lattice energy was analyzed. A correlation between melting points and fragmental molecular interactions in the crystal lattices was obtained. The thermodynamic aspects of the sulfonamide sublimation were studied by investigating the temperature dependence of vapor pressure using the transpiration method. A correlation between the Gibbs energy of the sublimation process and molecular H-bond acceptor factors was found. In addition, a regression equation was derived for describing the correlation between the sublimation entropy terms and crystal density data calculated from X-ray diffraction results. These dependencies allow us to predict sublimation thermodynamic parameters not knowing more than the molecular formula and crystal density.(Figure Presented)

Full text of DOI:10.1021/cg1012389

ARTICLE
pubs.acs.org/crystal
Sulfonamide Molecular Crystals: Thermodynamic and Structural
Aspects
German L. Perlovich,*,† Alex M. Ryzhakov,† Valery V. Tkachev,‡ and Lars Kr. Hansen§
†Institute of Solution Chemistry, Russian Academy of Sciences, 153045 Ivanovo, Russia
‡Laboratory of Structural Chemistry, Institute of Problems of Chemical Physics, Russian Academy of Sciences, 142432, Chernogolovka,
Russia
§University of Tromsø, Institute of Chemistry, Breivika, N-9037 Tromsø, Norway
S Supporting Information
b
ABSTRACT: The crystal structures of three sulfonamides with the
structures C6H5-SO2NH-C6H5, C6H5-SO2NH-C6H4-R (R = 4-
NO2), 4-NH2-C6H4-SO2NH-C6H4-R (R = 4-NO2; 4-CN) have
been determined by X-ray diffraction. On the basis of our previous
data and the obtained results, comparative analysis of crystal proper-
ties was performed: molecular conformational states, packing archi-
tecture, and hydrogen bond networks using graph set notations.
Conformational flexibility of the bridge connecting two phenyl rings
was studied and described by a correlation equation. Hydrogen bonds
were grouped according to the frequency of hydrogen bond appear-
ance within the definite graph set assignment. The strength of the
hydrogen bonds was evaluated. The influence of various molecular
fragments on crystal lattice energy was analyzed. A correlation
between melting points and fragmental molecular interactions in
the crystal lattices was obtained. The thermodynamic aspects of the
sulfonamide sublimation were studied by investigating the tempera-
ture dependence of vapor pressure using the transpiration method. A
correlation between the Gibbs energy of the sublimation process and molecular H-bond acceptor factors was found. In addition, a
regression equation was derived for describing the correlation between the sublimation entropy terms and crystal density data
calculated from X-ray diffraction results. These dependencies allow us to predict sublimation thermodynamic parameters not
knowing more than the molecular formula and crystal density.
’ INTRODUCTION
attention was paid to the hydrogen bond networks characteriza-
tion and systematization by using graph set notations. Moreover,
the authors tried to describe donor and acceptor affinities of
atoms in the molecules studied on the basis of the statistical
analysis of hydrogen bonds of solvated and nonsolvated crystals.
Furthermore, this class of substances attracted the researchers’
attention from the point of view of the fundamental aspects
of studying supramolecular aggregation in a cognate series of
substituted sulfonamides. Kelly et al.3 investigated the impact
of iodine and nitro groups at different positions of the aryl ring
on a wide range of different but competitive supramolecular
interactions.
Sulfonamides (SAs) are drugs extensively used for treating
certain infections caused by Gram-positive and Gram-negative
microorganisms, some fungi, and certain protozoa. Although the
extensive use of antibiotics has diminished the usefulness of SAs,
they still occupy a relatively small but important place in the
therapeutic resources of physicians.1 Usually the compounds
under consideration are poorly soluble in aqueous mediums, and
this fact is an essential obstacle for the drug delivery. Therefore,
the molecular structure design (without disturbing the pharma-
cological site), giving an opportunity to obtain the minimal values
of crystal lattice energies, is an important task for pharmaceutics
and crystal engineering. Sulfonamide molecules in crystals are
inclined to create hydrogen bond networks with complicated
topological structures. Therefore, it is sometimes difficult to esti-
mate crystal lattice energy on the basis of even crystal structure data.
A careful analysis of published SA crystal lattice structures has
been carried out by Adsmond and Grant.2 In this work, special
Understanding the structural conformation of sulfonamides is
vital for drug design, since the sulfonamide group is an extremely
important biological functional group and determines biological
Received: September 20, 2010
Revised:
January 5, 2011
Published: February 10, 2011
r
2011 American Chemical Society
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dx.doi.org/10.1021/cg1012389 Cryst. Growth Des. 2011, 11, 1067–1081
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Scheme 1
activity. Several works were devoted to the analysis of conforma-
tional states of sulfonamide molecules in crystals. It is essential to
mention the paper of Parkin et al.,4 who have carried out
comparative analysis of torsion angles of SA small molecules
on the basis of CDS.5 This work did not consider the phenyl
fragments connected with the sulfonamide bridge. Nevertheless,
the values, describing average statistical molecular conformations,
coincide with the torsion angles obtained by us in this work.
Adsmond and Grant2 analyzed three torsion angles characteriz-
ing the sulfonamide bridge mobility and concluded that sulfo-
namides in the amide tautomer have a large degree of confor-
mational mobility due to the three single bonds C-S-N-C
joining the two ends of the molecule. Moreover, all angles corres-
pond to the extended Huckel (EHMO) calculations, carried out
by Kalman et al.6 The exception connected with sulfamoxolez
was explained by hydrogen bond networks with motif R22(16).
The recent paper7 has used the results of the calculations on
sulfonamide conformations to explain the increase in the activity
of a particular potential drug compound over another. Although
their assumptions may be correct, the calculations as described
use information from the work of Bindal et al.8 that has since
been shown to contain erroneous assumptions about N-methyl-
methanesulfonamide in the solid state.9
phenyl)-benzene-sulfonamide (VII), 4-amino-N-(4-ethylphenyl)-
benzene-sulfonamide (VIII), 4-amino-N-(4-methoxyphenyl)-ben-
zene-sulfonamide (IX), and 4-amino-N-(5-chloro-2-methylphenyl)-
benzene-sulfonamide (X) with new ones: N-(4-nitrophenyl)-
benzene-sulfonamide (XI); 4-amino-N-(4-nitrophenyl)-benzene-
sulfonamide (XII); 4-amino-N-(4-cyanophenyl)-benzene-sulfonam-
ide (XIII); N-phenyl-benzene-sulfonamide (XIV) (Scheme 1).
The choice of the compounds was dictated by the following
aims. First, we aimed to analyze the influence of substituent
nature and molecular topology on the molecule conformational
state, the formation of crystal lattice architecture, and hydrogen
bond networks. Second, we planned to study the thermodynamic
and thermophysical properties of the crystals and find out the
relationship between the noted parameters and crystal structure.
’ EXPERIMENTAL SECTION
Compounds and Solvents. The chemical synthesis of SAs
(XI-XIII) has been performed according to the procedures described
earlier10-12 by the reaction of a substituted aromatic amine with
4-acetylaminobenzenesulfonyl chloride in dry pyridine, followed by
hydrolytic deacetylation in alkaline aqueous medium (∼1 M NaOH)
and precipitation of the end product by acidification (∼1 M HCl) to
pH 5. The compounds were carefully purified by recrystallizing from
water-ethanol solution. The precipitate was filtered and dried at room
temperature under a vacuum until the mass of compounds remained
constant. The outlined procedure was repeated several times and the
product was checked by NMR after each recrystallization step until the
proton NMR signal correspondence to the purity of the compound was
over 99%. N-Phenyl-benzene-sulfonamide was obtained from Sigma
Chemical Co. (USA).
Our previous works10-12 studied the structures, packing
architecture, topology of hydrogen bond networks, sublimation,
solubility, and solvation characteristics of the 10 sulfonamides. As
a continuation of the study, this work focuses on the comparative
analysis of the published compounds N-(2-chlorophenyl)-benzene-
sulfonamide (I), N-(2,3-dichlorophenyl)-benzene-sulfonamide (II),
N-(4-chlorophenyl)-benzene-sulfonamide (III), 4-amino-N-(4-
chlorophenyl)-benzene-sulfonamide (IV), 4-amino-N-(2,3-di-
chlorophenyl)-benzene-sulfonamide (V), 4-amino-N-(3,4-dichloro-
phenyl)-benzene-sulfonamide (VI), 4-amino-N-(2,5-dichloro-
Single crystals of the title compounds were grown from a water-
ethanol solution (initial composition 20:1 v/v) by the vapor diffusion of
ethanol vapor into pure water.13
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Table 1. Crystal Lattice Parameters of the Substances under Investigationa
XI
XII
XIII
XIV
crystal system
monoclinic
P21/c
orthorhombic
Pbca
monoclinic
C2/c
tetragonal
P43212
space group
crystal size, mm
0.26 ꢀ 0.2 ꢀ 0.14
12.7510(19)
8.4820(17)
11.5790(12)
90.00
0.35 ꢀ 0.25 ꢀ 0.02
5.7526(11)
15.465(3)
30.087(6)
90.00
0.35 ꢀ 0.25 ꢀ 0.15
26.764(6)
24.756(5)
8.0027(17)
90.00
0.40 ꢀ 0.20 ꢀ 0.05
8.8551(19)
8.8551(19)
30.282(7)
90.00
a, Å
b, Å
c, Å
R, ꢀ
β, ꢀ
γ, ꢀ
volume, Å3
99.450(2)
90.00
90.00
100.543(4)
90.00
90.00
90.00
90.00
1235.3(3)
4
2676.7(9)
8
5212.9(19)
16
2374.5(9)
8
Z
Dcalc, g cm-3
1.496
1.455
1.393
1.305
3
radiation
Mo KR
Mo KR
Mo KR
Mo KR
T, K
293(2)
293.1
293.1
293.1
μ, mm-1
0.274
0.259
0.062
0.26
Data collection
measured reflections
independent reflections
independent reflections with >2σ(I)
Rint
2553
1916
1240
0.0283
25.0
10062
3591
1122
0.063
30.70
14665
6789
3085
0.037
30.72
5734
3105
2798
0.054
30.6
θmax, ꢀ
Refinement
refinement on
R[F2 > 2σ(F2)]
ωR(F2)
F2
F2
F2
F2
0.0389
0.0881
1.002
1916
177
0.054
0.069
1.15
0.0626
0.067
1.062
3160
377
0.0615
0.0537
1.135
2851
189
S
reflections
parameters
(Δ/σ)max
1605
198
0.000
0.189
-0.225
0.031
0.39
0.0048
0.27
0.0143
0.69
ΔFmax, e Å-3
3
ΔFmin, e Å-3
-0.39
-0.40
-0.68
3
a Standard deviations are presented in parentheses.
Methods. X-ray Diffraction Experiments. Single-crystal X-ray mea-
surements were carried out using a Nonius CAD-4 diffractometer with
graphite-monochromated Mo KR radiation (λ = 0.71069 Å). Intensity
data were collected at 25 ꢀC by means of a ω-2θ scanning procedure.
The crystal structures were solved using direct methods and refined by
means of a full-matrix least-squares procedure. CAD-414 was applied
for data collection, data reduction, and cell refinement. Programs
SHELXS-97 and SHELXL-9715 were used to solve and to refine
structures, respectively.
deviation being within 3-5%. Because the saturated vapor pressure of the
investigated compounds is low, it may be assumed that the heat capacity
change of the vapor with temperature is so small that it can be neglected.
The experimentally determined vapor pressure data may be described in
(ln P; 1/T) coordinates in the following way:
lnðpÞ ¼ A þ B=T
ð1Þ
The value of the sublimation enthalpy is calculated by the Clausius-
Clapeyron equation:
Sublimation Experiments. Sublimation experiments were carried out
by the transpiration method as was described elsewhere.16 In brief: a
stream of an inert gas passes above the sample at a constant temperature
andata knownslow constant flowrate inorder toachieve saturation ofthe
carrier gas with the vapor of the substance under investigation. The vapor
is condensed at some point downstream, and the mass of sublimate and its
purity are determined. The vapor pressure over the sample at this
temperature can be calculated by the amount of the sublimated sample
and the volume of the inert gas used.
ΔHsTub ¼ RT2 Dðln PÞ=DðTÞ
whereas the sublimation entropy at the given temperature T was calculated
ð2Þ
3
from the following relation:
ΔSTsub ¼ ðΔHsTub - ΔGTsubÞ=T
ð3Þ
with ΔGTsub = -RT ln(P/P0), where P0 is the standard pressure of 1.013 ꢀ
105 Pa.
For experimental reasons sublimation data are obtained at elevated
temperatures. However, in comparison with effusion methods, the
temperatures are much lower, which makes extrapolation to room
conditions easier. In order to further improve the extrapolation to room
conditions, we estimated the heat capacities (C2p,9c8r-value) of the crystals
using the additive scheme proposed by Chickos et al.18 Heat capacity
The equipment was calibrated using benzoic acid. The standard value
of sublimation enthalpy obtained here was ΔH0sub = 90.5 ( 0.3 J mol-1
.
3
This is in good agreement with the value recommended by IUPAC
of ΔH0sub = 89.7 ( 0.5 J mol-1 17
The saturated vapor pressures
were measured five times at each temperature with the standard
.
3
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Crystal Growth & Design
ARTICLE
was introduced as a correction for the recalculation of the sublimation
sub
(n = 10). The enthalpy of fusion at 298 K was calculated by the
following equation:
298
enthalpy ΔHTsub-value at 298 K (ΔH -value), according to the
298
equation18 (the procedure of C -value calculation is presented in
p,cr
298
fus
ΔH ¼ ΔHfus - ΔSfusðTm - 298:15Þ
ð5Þ
Table 7):
where the difference between the heat capacities of the melt and solid
states was approximated by the fusion entropy (as an upper estimate).
This approach was used by Dannenfelser and Yalkowsky.19
The enthalpy of vaporization was calculated as
298
ΔH ¼ ΔHsTub þ ΔHcor
sub
298
¼ ΔHsTub þ ð0:75 þ 0:15C ÞðT - 298:15Þ
ð4Þ
p,cr
298
298
fus
ΔH ¼ ΔHs2u9b8 - ΔH
ð6Þ
Differential Scanning Calorimetry. Differential scanning calorim-
etry (DSC) was carried out using a Perkin-Elmer Pyris 1 DSC dif-
ferential scanning calorimeter (Perkin-Elmer Analytical Instruments,
Norwalk, Connecticut, USA) with Pyris software for Windows NT.
vap
Calculation Procedure. The free molecular volume in the crystal
lattice was estimated on the basis of the X-ray diffraction data and van der
Waals molecular volume (Vvdw), calculated by GEPOL:20
DSC runs were performed in an atmosphere of flowing (20 mL min-1
)
3
dry helium gas of high purity 99.996% using standard aluminum
Vfree ¼ ðVcell - ZVvdwÞ=Z
where Vcell is the volume of the unit cell, and Z is the number of
molecules in the unit cell.
ð7Þ
sample pans and a heating rate of 10 K min-1. The accuracy of
3
weight measurements was (0.005 mg. The DSC was calibrated with
an indium sample from Perkin-Elmer (P/N 0319-0033). The value
determined for the enthalpy of fusion corresponded to 28.48 J g-1
All descriptors were calculated by the program package HYBOT-
3
(reference value 28.45 J g-1). The melting point was 156.5 ( 0.1 ꢀC
PLUS (version of 2003 year) in Windows.21
3
Nonbonded van der Waals interactions of crystal lattice energy were
calculated as a sum of atom-atom interactions with the help of
Gavezzotti et al.28 force field and cutoff radius 16 Å. The hydrogen
ꢀ
bonding energy was calculated with the help of Mayo et al.24 force field:
10
EHB ¼ DHB½5ðRhb=RDA
Þ
12 - 6ðRhb=RDAÞ ꢁ cos4ðθDHA
Þ
ð8Þ
where DHB = 39.7 kJ mol-1 is a depth of potential well of pair potential
at the creation of the hydrogen bond of H2O dimer; Rhb = 2.75 Å; RDA
θDHA are the distance and angle between donor and acceptors atoms.
3
,
’ RESULTS AND DISCUSSION
Crystal Structure Analysis. Molecular Conformational Anal-
ysis. The results of the X-ray diffraction experiments are pre-
sented in Table 1.
In order to characterize the conformational states of the
molecules, Figure 1 shows the view of representative molecule
XI with atomic numbering. This numbering was used for all
Figure 1. A view of molecules IX-IV with atomic numbering.
Table 2. Some Parameters (ꢀ) Describing Molecular Conformational States in the Crystal Lattices
—C2-C1-S1-N1 (τ1)
—C7-N1-S1-C1 (τ2)
—C12-C7-N1-S1 (τ3)
—Ph1-Ph2
Ia
IIa
IIIa
-108.5(2)
-106.8(4)
-83.4(4)
-71.7(4)
-74.4(4)
-64.8(2)
-75.6(2)
-66.7(9)
-71.1(9)
-72.3(3)
-75.0(2)
-78.0(2)
-73.4(2)
-64.6(3)
-72.8(4)
-59.0(3)
-43.4(4)
-85.3(4)
-67.7(2)
-68.6(4)
-56.1(3)
-54.4(4)
-52.1(4)
-55.3(2)
-57.0(2)
-58.2(9)
-52.7(9)
-52.4(3)
-66.2(2)
-68.0(2)
-54.4(2)
-70.8(3)
-63.5(4)
-62.8(3)
-81.8(4)
-57.7(3)
-68.3(2)
-63.8(4)
-71.1(4)
-36.4(5)
-79.1(4)
-28.1(2)
-43.0(2)
-33(1)
49.14(9)
54.8(2)
54.4(2)
80.7(1)
60.5(2)
81.56(6)
79.11(7)
84.7(3)
60.7(4)
64.9(1)
64.4(6)
60.7(7)
67.61(8)
91.2(2)
89.5(4)
86.7(6)
83.1(7)
64.1(4)
IV(A)b
IV(B)b
V(A)b
V(B)b
VI(A)b
VI(B)b
VIIb
VIIIc
IXc
Xc
-80(1)
-65.9(3)
-72.7(2)
-77.0(2)
-62.1(2)
-31.2(4)
-22.3(6)
-21.4(5)
25.7(5)
XI
XII
XIII(A)
XIII(B)
XIV
a Ref 10. b Ref 11. c Ref 12.
-67.3(6)
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ARTICLE
Figure 2. Molecular packing architectures of (XI) (a), (XII) (b), (XIII) (c), and (XIV) (d) crystal lattices (stick corresponds to molecule A, whereas the
stick and ball correspond to molecule B).
compounds under investigation. The compound XIII has two
molecules (A and B) in the asymmetric unit of the crystal lattice.
On the basis of the presented numbering, it is possible to carry
out the comparative analysis of conformational states of mole-
cules I-XIV. The results are summarized in Table 2.
The molecular packing architectures of the four new sub-
stances under investigation are presented in Figure 2.
The conformational states of the molecules under investiga-
tion depend on the mobility of the bridge, connecting two phenyl
rings. In order to describe the conformational state we have
chosen three parameters (analogous to Parkin et al.4): the angle
between the SO2-group and the phenyl motif Ph1 (C1-C2-
C3-C4-C5-C6) —C2-C1-S1-N1 (τ1); the angle —C7-
N1-S1-C1 (τ2), describing the S1-N1 bond mobility and the
torsion angle —C12-C7-N1-S1 (τ3), which characterizes the
location of the second phenyl ring Ph2 (C7-C8-C9-C10-
C11-C12) relative to the NH-group. Moreover, we introduced
an angle between the two phenyl rings —Ph1-Ph2 (the acute
angle between the least-squares planes through the two phenyl
rings) (Table 2). In addition to the noted angles we introduced
an angle, equal to the sum of the dihedral angles (Στi = τ1 þ τ2 þ
τ3), which describes the integral flexibility of the bridge connect-
ing the phenyl rings.
Molecular conformational state in crystal lattice depends on
different factors: molecular topology, ability of atoms to take part
in donor-acceptor interactions, presence of hydrogen bonds
and their topological structure, availability of π-π interactions
and interactions with charge transfer, etc. Therefore, it is difficult
to pick out only one descriptor to describe both the molecular
conformational state and the physicochemical properties of
crystal. In our previous work12 we used the Vfree/Vvdw-parameter,
characterizing molecular packing density in crystal. In this work,
we have tried to find out a correlation of the studied properties
Figure 3. Dependencies of the torsion angles (τ1, τ2, τ3) characterizing
mobility of the bridge connecting the two phenyl motives and Στi versus
the angle between the phenyl fragments.
with HYBOT descriptors.21 It should be noted that primordially
32 descriptors were tested to find suitable correlations; they take
into account a whole diversity of interactions in the crystals
mentioned before. The τ1, τ2, and τ3 values versus the angle
between the phenyl fragments of studied SA are presented in
Figure 3. It should be mentioned that all compounds under
consideration break up into two conformational populations (if
the angles between the phenyl rings are taken into consider-
ation). The first one includes SA with angles 47ꢀ < —Ph1-Ph2
< 67ꢀ, whereas the second one - SA with angles: 77ꢀ < —Ph1-
Ph2 < 92ꢀ. It is not difficult to see that no correlation between the
introduced dihedral angles (τ1, τ2, τ3) and the angles between the
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Crystal Growth & Design
ARTICLE
phenyl rings is observed. For the integral angle (Στi) we observed
the following regularity. For the low-angle conformational
population, the angle between the phenyl rings increases with
decreasing the integral mobility of the bridge. For the large-angle
populations, a dependence with the extreme value for the
compound XIIIB is observed.
As the number of the studied SAs was restricted by 14, we
declined to build multivariate correlation models due to their low
statistical significance. We collected as a dependent variable the
integral angle (Στi) describing the bridge flexibility. As indepen-
dent variables, physicochemical descriptors of program
HYBOT21 were chosen. The analysis of the 32 descriptors
showed that the integral angle can be best described by the
descriptor indicating the sum of H-bond acceptor factors (ΣCa)
of the molecule. The H-bond atom acceptor factor (Ca) has been
obtained from the database including Gibbs energies (binding
constants) of complexation processes between different com-
pounds in CCl4 solution. The results of the analysis are presented
in Figure 4. It is not difficult to see that the following regularity is
observed: while the H-bond acceptor factor increases, the
integral mobility of the bridge decreases. In other words,
donor-acceptor interactions and hydrogen bonding in the
crystals lead to a reduction of the bridge mobility.
Hydrogen Bond Networks Analysis. The considered com-
pounds create hydrogen bonds in the crystal lattices. Moreover,
the number of hydrogen bonds per molecule varies essentially
and depends on the molecular topology and presence of hydro-
gen bond centers. Furthermore, the hydrogen bonds in the
crystals create hydrogen bond networks with different topologi-
cal structures, which influence the thermodynamic and thermo-
physical properties: particularly the crystal lattice energy, and, as
a consequence, the solubility processes. Therefore, the next step
included analyzing the hydrogen bond network topology using
the graph set notation terminology introduced by Etter22 and
revised by Bernstein.23 The comparative characteristics of the
hydrogen bond geometric parameters, graph set assignments for
the two levels are summarized in Table 3. The graph set notations
mentioned in Table 3 are illustrated in Table 4.
In order to compare the strength of hydrogen bonds created in
the SA crystals, we calculated the hydrogen bond energies (EHB
)
according to Mayo et al.24 Therefore, the wide spectrum of
geometric characteristics, describing the hydrogen bonds, was
reduced to comparable values. For the analysis, we collected only
the diagonal elements of graph set assignments matrix (first
level). The hydrogen bonds were grouped in accordance with the
frequency of their appearance (within the graph set assignment)
for the chosen compounds (Table 5). As it follows from Table 5,
the graph set notations can be arranged (according to the
frequency of appearance in the studied crystals) in the following
way: C(8)-1 (type 1) (24times) > D-2 (10) > C(8)-2 (7) >C(4)-1
Figure 4. Plot of the integral angle (Στi) versus the sum of H-bond
acceptor factors (ΣCa).
Table 3. Hydrogen Bond Geometry and Graph Set Notations of the Molecules Studied
XI
a
D-H(X) A(Y)a,b
D-H[Å]
H
A[Å]
D
A[Å]
D-H A[deg]
a
3 3 3
3 3 3
3 3 3
3 3 3
N1-H1(A) O2i(A)
0.84(3)
2.156(3)
2.992(4)
173(3)
b
a
C(8)(type 3)
d
3 3 3
XII
D-H(X) A(Y)c
D-H
H
A
D
A
D-H
A
a
c
3 3 3
3 3 3
3 3 3
3 3 3
a
N2-H2B(A) O2i(A)
0.793
0.888
0.888
0.889
2.482
2.635
2.616
2.204
3.190
3.075
3.195
2.988
149.3
111.7
123.7
146.9
a
b
c
f
C(8)(type 1)
R44(22)
R44(22)
3 3 3
b
c
N2-H2A(A) O1 ii(A)
C(8)(type 1)
R33(18)
R44(22)
3 3 3
N2-H2A(A) O1 iii(A)
C(8)(type 1)
C(8)[ R22(6)]
3 3 3
d
N1-H1(A) N2iv(A)
R44(22)
C(8)(type 2)
f
3 3 3
XIII
D-H(X) A(Y)d
D-H
H
A
D
A
D-H
A
a
b
c
d
e
3 3 3
3 3 3
3 3 3
3 3 3
a
b
c
d
e
f
Nb1-Hb1(B) Oa1i(A)
0.889 2.028
Na2-Ha2B(A) Ob1 ii(B) 0.903 2.146
2.841
3.034
3.422
3.049
3.359
3.058
151.4
a
b
c
d
e
f
D(type 1)
R44(24)
C(18)
R44(24)
C(8);D
C(8);D
3 3 3
167.5
165.4
146.0
132.6
140.1
D(type 2)
R44(44)
C(18)
3 3 3
Nb2-Hb2B(B) Na3 iii(A) 0.967 2.478
D(type 3)
R44(44)
C(8);D
C(8);D
3 3 3
Na1-Ha1(A) Nb3iv(B)
0.889 2.271
D(type 4)
C(8);D
3 3 3
Nb2-Hb2A(B) Ob2v(B) 0.815 2.754
C(8);D
C(8);D
C(8)(type 1)
C(8);C(8)
3 3 3
Na2-Ha2A(A) Oa2vi(A) 0.828 2.377
C(8);D
C(8)(type 1)
a
3 3 3
XIV
D-H(X) A(Y)e
D-H
0.952
H
A
D
A
D-H
3 3 3
A
3 3 3
3 3 3
3 3 3
a
N1-H1(A) O2i(A)
1.913
2.862
174.25
a
C(4)(type 1)
3 3 3
a D-H(X) A(Y), where X and Y corresponds to molecule A or B of the asymmetric unit. b Symmetry code: (i) x, y - 1, z. c Symmetry code: (i) -x þ
3 3 3
1/2, -y þ 1, z - 1/2; (ii) x þ 1, y, z; (iii) x, y, z; (iv) x, -y þ 1/2, z- 1/2. d Symmetry code: (i) x þ 1, -y þ 1, z þ 1/2; (ii) -x þ 1 1/2, -y þ 1 1/2, -z
þ 2; (iii) x þ 1, y þ 1, z þ 1; (iv) -x þ 1, y þ 1, -z þ 1 1/2; (v) x þ 1, y þ 1, z þ 1; (vi) x þ 1, y þ 1, z þ 2. e Symmetry code: (i) x, y, z.
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Table 4. Graph Set Notations of the Hydrogen Bond Networks of the Crystal Structures Studied
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Table 4. Continued
(6) > C(8)-3 = D-1 = D-3 = D-4 = R22(16) (1 time).
The presented discrimination is quite conditional because for the
chosen compound the graph set assignment can occur several
times with different hydrogen bonds. Usually this fact is con-
nected with increase of a number of molecules in asymmetric unit
of crystal lattice. By our opinion, increase of a number of the same
type of graph set assignment within the substance leads to a
decrease of the accuracy of experimental measurements
(saturation vapor pressure, melting point, fusion enthalpy, and
so on).
It is interesting to analyze if there is some regularity between
E
HB (within the same topological graph) and the molecular van
der Waals volume. It should be noted that the graph set notation
C(8)-1 is observed for many compounds. Moreover, for each
substance this graph can appear several times since it can be
created by different hydrogen bonds. The analogous picture is
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Table 5. First Level Graph Set Notations of the Hydrogen Bonds Networks of Sulfonamides Studied, Frequency of Appearance,
and Energies (EHB, kJ mol-1) of the Hydrogen Bonds
3
a Labeling corresponds to the hydrogen bonds of Table 3.
observed for C(8)-2, whereas C(4)-1 motif is the only one for all
the substances where this graph appears (in other words, when
C(4) appears, there are no other hydrogen bonds in the
structure). The hydrogen bond energies versus molecular van
der Waals volumes for C(4)-1 (a), C(8)-2 (b), and C(8)-1 (c)
motives are summarized in Figure 5. For C(4)-1 a correlation
between the noted variables is observed: with an increase of the
molecular van der Waals volume the EHB-value decreases. For
C(8)-2 this trend is not obvious, whereas for C(8)-1 the
correlation is not observed at all. This behavior can be explained
by the following reasons. For the compounds, where the
regularity is observed (C(4)-1 graphs), there is only one hydro-
gen bond per molecule (no alternative hydrogen bonds). There-
fore, a variation of the molecular van der Waals volume does not
lead to a change of the molecular packing in the crystal lattice
(because it remains the same type of graph set) and affects only
the change of geometry and strength of the hydrogen bonds. On
the other hand, for the compounds with C(8)-1 and C(8)-2
motifs, besides these notations, there are alternative ones. As a
result, the increase of molecular van der Waals volume is relaxed
by all the hydrogen bonds available.
Packing Architecture Analysis. The molecular packing archi-
tecture of crystals depends on the molecular structure and topology.
The compounds under consideration are structurally similar.
Therefore, variations of size, nature, and position of substituents
make it possible to analyze the influence of these factors on the
packing architecture. It is interesting to note that the free
volumes per molecule in the crystal lattices range within the
ꢀ3
limits 103-107 Å and are practically independent from the
molecular van der Waals volume (Figure 6) (except I, VI, XI, and
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Figure 5. Plot of the hydrogen bond energies versus the molecular van der Waals volumes of studied substances for C(4)-1 (a), C(8)-2 (b), and C(8)-1
(c) motives.
Scheme 2
Figure 6. Relationship between the free molecular volumes (Vfree) in the
crystal lattices and the van der Waals volumes (Vvdw) of the compounds.
XII). The deviation of the discussed values for VI is probably
connected with the following fact. The crystal lattices of IV and
VI are isomorphic:11 the same space groups - orthorhombic
Pna21; Vcell(IV) = 2560.0(9) and Vcell(VI) = 2632.1(9) Å3;
V
vdw(IV) = 216.1 and Vvdw(VI) = 231.8 Å3; Vfree(IV) = 103.9
and Vfree(VI) = 97.2 Å3. Therefore, the accommodation of the
additional Cl-atom of compound VI (in comparison with IV)
occurs in the free volume of the unit cell of substance IV.
Compounds I, XI, and XII require a more detailed analysis. It
can be assumed that the substances, included in the window, have
identical molecular packing architecture, whereas I, XI, and XII
sulfonamides have essential elements of distinction.
Figure 7. Plot of the contributions of nonbonded van der Waals
interactions to the packing energy from different fragment pairs of
adjacent molecules (Ei-i) versus Vfree/Vvdw for studied compounds
(asterisks correspond to correction for the hydrogen bond energy).
In order to understand the influence of various molecular
fragments on crystal lattice energy, we used the approach applied
by us earlier.25 The molecule was conditionally divided into a
certain number of fragments, depending on the molecular
topology. Segmentation for the six fragments (as a common
case) is shown in Scheme 2. After that we calculated the
contribution of nonbonded van der Waals interactions to the
packing energy from different fragment pairs of adjacent mole-
cules. The results of the calculation for various energetic terms of
the SA crystal lattices are shown in Figure 7.
stabilizing the crystal lattices, correspond to interactions between
R4-R4; R2-R3 and R2-R2. Moreover, when one of the
substituents is situated at para- position of Ph2, an inversion of
R2-R3 and R2-R2 contributions to the crystal lattice stabiliza-
tion is observed: for VI - E(R4-R4) > E(R2-R2) > E(R2-R3),
whereas for V, VII, X - E(R4-R4) > E(R2-R3) > E(R2-R2).
The absolute values of the maximal (R4-R4) contributions are
approximately the same (within 1 kJ mol-1). The analogous
3
conclusion can be made for R2-R3 as well. The R2-R2 con-
tributions (interactions between the second phenyl rings of adjacent
molecules in the crystal lattices) for compounds V, VII, X do not
Let us first consider the SAs with two substituents at the second
phenyl ring (V, VI, VII, X) (Figure 8). The main contributions,
differ essentially from each other; however, they are 5 kJ mol-1
3
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ARTICLE
Figure 9. Plot of Ei-i versus Vfree/Vvdw for I-V, VII, and XI.
Figure 8. Plot of Ei-i versus Vfree/Vvdw for V, VI, VII, and X.
lower than the analogous value for VI. Thus, for the sulfonamides
with substituents at the para position of Ph2 the main stabilizing
crystal lattice contributions correspond to the interactions
between the identical phenyl fragments (R4-R4 and R2-R2)
of adjacent molecules. For the rest of the compounds the bridge
connecting the two phenyl rings intervenes in the energetic
apportionment: R4-R4 and R2-R3. It should be noted that for
VI contributions of R2-R4 (Ph1-Ph2) and R4-R5 (Ph2-R5)
interactions are equal, whereas for the rest of the substances R2-
R4 > R4-R5 by 4 kJ mol-1. For SA VI there is a big energetic slit
3
(8 kJ mol-1) between the strongest contributions (R4-R4; R2-
3
R3 and R2-R2) and the other ones. For the other SAs, this slit is
not observed due to infilling them with R2-R2; R2-R3 and R2-
R4 interactions. One more peculiarity of the fragmental interac-
tions consists of the following: for VI - E(R4-R5) > E(R1-R2),
whereas for V, VII, X the opposite regularity is observed.
The fragments of the molecules take part in creating hydrogen
bonds. Therefore, in order to be correct, we tried to introduce a
correction on the hydrogen bonding energy at the R1-R3 interac-
Figure 10. Plot of Ei-i versus Vfree/Vvdw for IV, VIII, IX, XII, and XIII.
tion (Figure 8 asterisks): for VI - Etot(R1-R3) = 12 kJ mol-1
;
SA corresponds to the interactions between the second fragments
of the molecules E(R2-R2) (Ph1-Ph1 interactions), whereas
for the rest of the compounds the main contributions to packing
energy correspond to the two practically equal terms: E(R2-R4)
(Ph1-Ph2) and E(R3-R4) (bridge-Ph2). Moreover, the main
contributions to the packing energy for the para- substituted SA
exceed substantially the analogous term for the other com-
pounds. The impact of the substituent nature at the para position
can be analyzed on compounds III and XI. The crystal XI has a
3
for V - Etot(R1-R3) = 21.2 kJ mol-1; for VII - Etot(R1-R3) =
3
9.7 kJ mol-1; for X - Etot(R1-R3) = 11.7 kJ mol-1. It is not
3
3
difficult to see that the terms from interactions with account of
the hydrogen bond contribute an essential correction to the
packing energy. For example, this term for substance V exceeds
the maximal term E(R4-R4) by 5 kJ mol-1 and is dominant,
3
whereas for X this contribution is third and for VI and VII fourth.
It is interesting to note that contributions of R1-R3 interactions
(with account of hydrogen bond), creating graph sets C(8) (VI,
denser molecular packing in comparison with III: β(XI) = Vfree
V
/
VII, X), have approximately the same values (10-12 kJ mol-1).
vdw = 44.7 < β(III) = 50.7%. Probably this fact determines (at
3
In its turn the analogous contribution for V exceeds the previous
ones considerably. Moreover, the hydrogen bonds are integrated
in D organization of hydrogen bond networks. So, asymmetric
molecular structure (V) leads to D organization of hydrogen
bond networks and a considerable contribution of the hydrogen
bonding energy to the packing energy. This behavior is not
observed for more symmetric molecules.
approximately the same terms E(R2-R4) and E(R4-R4)) the
prevalence of the terms E(R2-R2) and E(R4-R5) for XI (NO2-)
in comparison with III (Cl-). If we compare SA I and II (i.e., the
molecules differing by additional Cl- atom at meta- position of
the second phenyl ring), the dominant energy contributions are
the same (E(R3-R4), E(R2-R4), E(R2-R2), and E(R2-R3)),
but their consecution is slightly changed.
Let us consider the packing energy of the molecules, where the
first fragment does not contain NH2-group: I, II, III, XI (Figure 9).
It should be mentioned that for the para- substituted molecules
(III and XI) the apportionment of the fragmental contributions
differs essentially from the other substituted molecules (I and II).
For example, the dominant contribution for the para-substituted
As we had done before, we tried to introduce a correction for
hydrogen bonding energy in the packing energy of compounds I,
II, III, XI. In contrast to the previous SAs (with NH2- groups at
Ph1), this group of the compounds creates hydrogen bonds
between R3-R3 fragments, forming C(4) hydrogen bond net-
works. The result of the corrections is presented in Figure 9 by
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ARTICLE
Table 6. Temperature Dependencies of Saturation Vapor Pressure of the Compounds Studied
XIa
XIIb
XIIIc
XIVd
t [ꢀC]
P [Pa]
t [ꢀC]
P [Pa]
t [ꢀC]
P [Pa]
t [ꢀC]
P [Pa]
107.0
111.0
112.0
114.0
117.0
118.0
119.0
120.0
121.0
122.0
123.5
128.0
128.5
9.47 ꢀ 10-3
1.55 ꢀ 10-2
1.72 ꢀ 10-2
2.09 ꢀ 10-2
2.84 ꢀ 10-2
3.17 ꢀ 10-2
3.47 ꢀ 10-2
3.88 ꢀ 10-2
4.04 ꢀ 10-2
4.64 ꢀ 10-2
5.13 ꢀ 10-2
8.37 ꢀ 10-2
8.63 ꢀ 10-2
132.4
136.3
139.7
142.0
144.1
145.6
146.9
148.4
150.1
151.5
153.1
155.6
158.2
158.9
162.0
165.1
1.50 ꢀ 10-3
2.18 ꢀ 10-3
2.30 ꢀ 10-3
3.41 ꢀ 10-3
4.01 ꢀ 10-3
4.34 ꢀ 10-3
5.46 ꢀ 10-3
5.63 ꢀ 10-3
6.16 ꢀ 10-3
7.30 ꢀ 10-3
8.92 ꢀ 10-3
1.05 ꢀ 10-2
1.28 ꢀ 10-2
1.41 ꢀ 10-2
1.81 ꢀ 10-2
2.28 ꢀ 10-2
147.0
147.8
148.2
151.6
153.4
155.2
156.5
158.2
158.6
159.2
159.9
161.6
162.6
164.0
164.4
6.74 ꢀ 10-3
7.23 ꢀ 10-3
7.91 ꢀ 10-3
1.13 ꢀ 10-2
1.36 ꢀ 10-2
1.66 ꢀ 10-2
1.94 ꢀ 10-2
2.11 ꢀ 10-2
2.28 ꢀ 10-2
2.33 ꢀ 10-2
2.63 ꢀ 10-2
3.17 ꢀ 10-2
3.58 ꢀ 10-2
4.24 ꢀ 10-2
4.37 ꢀ 10-2
75.9
78.3
80.4
81.6
83.0
84.3
85.5
86.3
87.8
89.6
91.1
92.1
93.3
94.4
96.2
2.78 ꢀ 10-2
3.48 ꢀ 10-2
4.22 ꢀ 10-2
4.74 ꢀ 10-2
5.61 ꢀ 10-2
6.56 ꢀ 10-2
7.20 ꢀ 10-2
7.81 ꢀ 10-2
9.44 ꢀ 10-2
10.9 ꢀ 10-2
12.5 ꢀ 10-2
13.7 ꢀ 10-2
16.1 ꢀ 10-2
18.1 ꢀ 10-2
21.5 ꢀ 10-2
a ln(P[Pa]) = (35.8 ( 0.5) - (15378 ( 187)/T ; σ = 2.7 ꢀ 10-2; r = 0.999; F = 6742; n = 13. b ln(P[Pa]) = (30.5 ( 0.8) - (15041 ( 317)/T ; σ = 6.4 ꢀ
10-2; r = 0.9964; F = 2247; n = 16. c ln(P[Pa]) = (41.3 ( 0.6) - (19459 ( 272)/T ; σ = 3.2 ꢀ 10-2; r = 0.9996; F = 5129; n = 15. d ln(P[Pa]) = (33.9 (
0.4) - (13092 ( 131)/T ; σ = 2.3 ꢀ 10-2; r = 0.9988; F = 9916; n = 15.
asterisks. It is not difficult to see that the values of the contributions
> E(R4-R4), whereas for SA V: E(R4-R4) > E(R2-R3) >
E(R2-R2) > E(R2-R4). Moreover, the strongest terms of com-
are approximately situated within 3 kJ mol-1. The contributions
3
for substances I and II are dominant, whereas for III and IX second
throughout the energy. Thus, it can be assumed that hydrogen
bond networks of SA with substituents at the para position will
have less impact on the physicochemical properties in compar-
ison with the substituents at other positions. It can be assumed
that the first step of the nucleation process of the considered com-
pounds starts from creating hydrogen bonds (self-assembly),
whereas the second step can be connected with growing the nucleus
by the most dominant fragments interactions. In the case of SAs
III and XI the growth is driven by R2-R2 interactions (Ph1-
Ph1). The situation with compounds I and II is different from the
previous one. As dominant contributions (if it does not take into
account hydrogen bonding) several fragmental interactions can
appear: E(R3-R4), E(R2-R4), E(R2-R2), and E(R2-R3). This
variability can bring disordering of the molecules in the crystals
or creating various types of defects during the growing process.
On the contrary, for compounds III and XI more perfect single
crystals can be expected.
pound II are separated from the weakest ones by a 5 kJ mol-1
3
“energetic slit”. For SA V the mentioned slit is not observed.
Similarly, the terms for SA III can be arranged as: E(R2-R2) >
E(R4-R4) = E(R3-R4), whereas for SA IV: E(R4-R4) > E(R2-
R2) > E(R2-R3). The “energetic slit” for SA IV is equal to
9 kJ mol-1, whereas for SA III - to 6 kJ mol-1
.
3
3
Finally, let us consider the contributions in the packing energy
made by different fragments of para-substituted SA IV (Cl-), VIII
(C2H5-), IX (OMe-), XII (NO2-), XIII (CN-) (Figure 10). For the
studied compounds, the strongest contributions in the packing
energy cab be arranged as E(R4-R4) > E(R2-R2) > E(R2-R3).
For the crystals with big values of molecular packing density, a
considerable dispersion of the energetic terms is observed.
However, with a decrease of the molecular packing density the
differences between the contributions become negligible.
If we take into account the contributions to the packing energy
from the fragments creating hydrogen bonds, the following situa-
tion is observed (Figure 10). The discussed terms exceed the other
ones until reaching the defined value of the molecular packing
density. After passing the point, the difference between the con-
tributions becomes negligible. For all SAs the para-substituent
interacts more strongly with the second phenyl ring in compar-
ison to the first one: E(R4-R5) > E(R2-R5). Moreover, this
tendency is quite evident for XII (NO2-).
Let us consider the identical molecules with and without NH2-
groups at the first phenyl ring: II and V, III and IV, XI and XII. It
is interesting to note,= that introducing the NH2- group in com-
pounds II and III (it gives V and IV) leads to an increase of
molecular packing density in the crystals: β(V) = Vfree/Vvdw
=
48.1 < β(II) = 44.9%; β(IV) = 48.3 < β(III) = 50.7%. In contrast
to this, for substances XI and XII the opposite regularity is
observed: β(XI) = 44.7 < β(XII) = 51.3%. For the compounds
with the asymmetric location of Cl- atoms (II and V) the fragments,
taking part in creating hydrogen bonds, bring in the dominant con-
tribution in the crystal packing energy. For the SAs with the
location of Cl- atom at para- position (III and IV) the noted terms
are not dominant. It is evident, that with introducing the NH2-
group an essential redistribution of the terms in the crystal packing
energy is observed. For example, the four maximal contributions
of SA II can be arranged as: E(R3-R4) > E(R2-R4) > E(R2-R2)
Sublimation Characteristics. The temperature dependen-
cies of saturated vapor pressure of V-VII are shown in Table 6.
The thermodynamic functions of the drugs sublimation, fusion,
and vaporization processes are presented in Table 7.
We have tried to search the correlation between the sublima-
tion thermodynamic functions and the descriptor describing the
sum of H-bond acceptor factors (ΣCa) of the molecule, as it was
done before to analyze the conformational states of SAs. The
dependence between the sublimation Gibbs energies and ΣCa is
shown in Figure 11. It is not difficult to see that with an increase
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Crystal Growth & Design
Table 7. Thermodynamic Characteristics of Processes of Sublimation, Fusion, and Vaporization of the Compounds Studied
ARTICLE
XI
XII
XIII
XIV
ΔG [kJ mol-1
]
67.7
127.9 ( 1.6
132.5 ( 1.6
327.5
78.0
125.1 ( 2.6
131.4 ( 2.6
340.1
88.0
161.8 ( 2.3
168.3 ( 2.3
326.3
53.4
108.9 ( 1.1
111.5 ( 1.1
280.4
298
sub
3
ΔHTsub [kJ mol-1
ΔH2su9b8 [kJ mol-1
C2p,9c8r [J mol-1 K-1 a
T ΔSs2u9b8 [kJ mol-1
]
3
]
3
]
3
3
]
64.7
53.4
80.3
58.1
3
3
ΔS2su9b8 [J mol-1 K-1
]
217 ( 7
67.2
179 ( 7
71.1
269 ( 9
67.7
195 ( 6
65.7
3
3
ςH [%]b
ςTS [%]b
Tm [K]
ΔHTfus [kJ mol-1
ΔH2fu9s8 [kJ mol-1
ΔSTfus [J mol-1 K-1 c
ΔH2va9p8 [kJ mol-1
32.8
28.9
32.3
34.3
411.3 ( 0.2
28.7 ( 0.5
20.8
438.9 ( 0.2
27.9 ( 0.5
18.9
451.5 ( 0.2
30.9 ( 0.5
20.4
383.5 ( 0.2
23.5 ( 0.5
18.3
]
3
]
3
]
69.8
63.6
68.4
61.3
3
3
]
111.7
112.5
147.9
93.2
3
a
298
p,cr
C
has been calculated by additive scheme with the following group values (in J K-1 mol-1): Cp(-SO2-) = 88.7; Cp(quaternary aromatic C sp2 =
3
3
CaR-) = 8.5; Cp(tertiary aromatic C sp3 = CaH-) = 17.5; Cp(-NH-) = -0.3; Cp(-NO2) = 56.1; Cp(-NH2) = 21.6; Cp(-CN) = 42.3 the error of the
calculation procedure corresponds to significant digit; b ςH = (ΔH /(ΔH þ TΔS )) 100%; ςTS = (TΔS /(ΔH þ TΔS )) 100%. c ΔSfus
=
298
sub
298
sub
298
sub
298
sub
298
sub
298
sub
3
3
ΔHfus/Tm.
298
sub
Figure 11. Relationship between the sublimation Gibbs energies (ΔG
and the sum of H-bond acceptor factors (ΣCa).
)
Figure 12. Correlation between the sublimation entropic terms
(TΔS2su9b8) and calculated molecular densities (Dcal) in the crystal lattices
(see text for numbering of the compounds).
of the molecule acceptor ability to create hydrogen bonds the
sublimation Gibbs energy increases as well. Unfortunately,
substance VI deviates from the trend. If we do not take this
value into consideration, the discussed trend can be described by
the regression equation:
Moreover, it is difficult to explain why the compounds VIII, XIII,
and XIV create their own branches. The rest of the SAs can be
described by the correlation equation:
298
298
TΔS ¼ ð - 214 ( 19Þ þ ð186 ( 13ÞDcal
sub
ΔG ¼ ð8 ( 6Þ þ ð13:5 ( 1:5ÞΣCa
sub
ð10Þ
ð9Þ
r ¼ 0:980; σ ¼ 2:44; n ¼ 11
r ¼ 0:9375; σ ¼ 4:3; n ¼ 13
Thus, the Gibbs energy of the compound belonging to the group
under consideration can be estimated simply on the basis of the
structural formula. It should be noted that the mentioned thermo-
dynamic function is very important for predicting the solubility
values of poorly soluble drugs, since the calculation approaches
to estimating solvation/hydration terms have been recently
improved greatly.
As the Dcal parameter is an entropic characteristic of a crystal,
we tried to compare these values with the entropic terms of the
sublimation process (TΔS2su9b8) of the compounds (Figure 12). It
is not difficult to see that all data break up into two branches.
The experimentally obtained crystal density values can be
expected to be correlated with the calculated ones. Therefore, the
entropic sublimation term can be directly estimated by the
experimental density values, without any knowledge of the crystal
structure. If we take into account the eqs 8 and 9 obtained before,
the sublimation enthalpy term can be estimated. In other words,
on the basis of crystal density values and structural formulas it is
possible to describe the sublimation thermodynamic functions of
the processes for the studied group of molecular crystals.
It is well-known that the melting point (Tm) and fusion enthalpy
(ΔHTfus) of molecular crystals are usually used in pharmaceutics
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Hydrogen bond network topology of the sulfonamides by the
graph set notations has been analyzed. The graph set notations
can be arranged (according to the frequency of their appearance
in the studied crystals) in the following way: C(8)-1 (type 1) >
C(4)-1 > C(8)-2 > D-2 > C(8)-3 = D-1 = D-3 = D-4 = R22(16).
We have also studied the relationships between hydrogen bond
energies and molecular van der Waals volumes within the definite
graph set assignments. For C(4)-1 a correlation between the noted
variables is observed: with an increase of the molecular van der
Waals volume the EHB-value decreases. For C(8)-2 this trend is not
obvious, whereas for C(8)-1 the correlation is not observed at all.
The free volumes per molecule in the crystal lattices of SAs
ꢀ3
range within the limits of 103-107 Å and are practically
independent from the molecular van der Waals volume. The
influence of various molecular fragments on the crystal packing
energy was analyzed. For most of the studied compounds the
main contributions, stabilizing the crystal lattices, correspond to
the interactions between: the second phenyl rings Ph2-Ph2; the
first ones Ph1-Ph1 and the bridge - Ph1. We have also found
the correlation between the melting points and the contributions
in the packing energy from the nonbounded van der Waals
interactions: the melting point values rise, while the interactions
between the second phenyl fragments increase as well.
The thermodynamic aspects of the sulfonamide sublimation
processes have been studied by investigating the temperature
dependence of vapor pressure by means of transpiration method.
A correlation between the Gibbs energy of sublimation and the
molecular H-bond acceptor factors was found. Also a regression
equation was derived describing the correlation between the
sublimation entropy terms and the crystal density data calculated
by the X-ray diffraction results. These dependencies allow us to
predict the sublimation thermodynamic parameters not knowing
more than the molecular formula and crystal density.
Figure 13. Relationship between the melting points and E4-4 con-
tributions in the packing energy made by the nonbounded van der Waals
interactions.
as parameters modeling crystal lattice energy. As an example we
can present the general solubility equation obtained by Yalk-
owsky and Valvani.26 The popularity of the parameters is
connected with the fact that they can be obtained in a very easy
way through the routine DSC method. The melting points and
fusion enthalpies of the studied SAs are presented in Table 7. It
should be mentioned that in the literature there are still certain
discussions about the nature and mechanism, determining the
outlined parameters.27 We tried to find out the correlation
between the melting points and the contributions in the packing
energy made by the nonbounded van der Waals interactions. It is
interesting to note that a linear trend is observed between Tm and
E4-4: the melting point values are raised while the interactions
between the second phenyl fragments are increased as well
(Figure 13). As it was shown before (Figure 7), E4-4 term in
the packing energy is dominant in comparison with the other
ones. Therefore, it can be assumed that the melting process starts
with the loss of contact between the second phenyl fragments of
SA. The hydrogen bonding energy between definite fragments of
adjacent molecules can be higher or lower than E4-4 (it depends
on the compounds). Therefore, it could be assumed that in the
case when EHB < E4-4 the hydrogen bonds break up before the
melting temperature. In the opposite case, breaking up of the
hydrogen bonds goes on at higher temperatures in comparison
with the melting one.
’ ASSOCIATED CONTENT
S
Supporting Information. The cif files of the XI-XIV
b
compounds. This material is available free of charge via the
Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION
Corresponding Author
*Phone: þ7-4932-533784; fax: þ7-4932- 336237; e-mail glp@
isc-ras.ru.
’ ACKNOWLEDGMENT
’ CONCLUSION
This work was supported by ISTC (Project No. 0888) and the
Russian Foundation of Basic Research N 09-03-00057.
The crystal structures of four sulfonamides (XI-XIV) have
been solved by X-ray diffraction experiments. Comparative
analysis of molecular conformational states has been carried
out. All the considered compounds break up into two conforma-
tional populations (if the angles between the phenyl rings are
taken into account). The first one includes SAs with angles 47ꢀ <
—Ph1-Ph2 < 67ꢀ, whereas the second one, SAs with angles: 77ꢀ
< —Ph1-Ph2 < 92ꢀ. For the low-angle conformational popula-
tion, the angle between the phenyl rings increases with decreas-
ing the bridge integral mobility. For the large-angle populations, a
dependence with the extreme value for the compound XIIIB is
observed. On the basis of the correlation analysis, we found out
that donor-acceptor interactions and hydrogen bonding in the
crystals lead to a reduction of the bridge mobility.
’ REFERENCES
(1) Korolkovas, A. Essentials of Medicinal Chemistry, 2nd ed.; Wiley:
New York, 1988; pp 699-716.
(2) Adsmond, D. A.; Grant, D. J. W. J. Pharm. Sci. 2001, 90 (12),
2058–2077.
(3) Kelly, C. J.; Skakle, J. M. S.; Wardell, J. L.; Wardell, S. M. S. V.;
Low, J. N.; Glidewell, C. Acta Crystallogr. 2002, B58, 94–108.
(4) Parkin, A.; Collins, A.; Gilmore, C. J.; Wilson, C. C. Acta
Crystallogr. 2008, B64, 66–71.
(5) Allen, F. H. Acta Crystallogr. 2002, B58, 380–388.
(6) Kalman, A; Czugler, M; Argay, G. Acta Crystallogr. 1981, B37,
868–877.
1080
dx.doi.org/10.1021/cg1012389 |Cryst. Growth Des. 2011, 11, 1067–1081

Crystal Growth & Design
ARTICLE
(7) Senger, S.; Chan, C.; Convery, M. A.; Hubbard, J. A.; Shah, G. P.;
Watson, N. S.; Young, R. J. Bioorg. Med. Chem. Lett. 2007, 17, 2931–
2934.
(8) Bindal, R. D.; Golab, J. T.; Katzenellenbogen, J. A. J. Am. Chem.
Soc. 1990, 112, 7861–7868.
(9) Higgs, T. C.; Parkin, A.; Parsons, S.; Tasker, P. A. Acta Crystal-
logr. 2002, E58, o523–o525.
(10) Perlovich, G. L.; Strakhova, N. N.; Kazachenko, V. P.; Volkova,
T. V.; Tkachev, V. V.; Schaper, K. J.; Raevsky, O. A. Int. J. Pharm. 2007,
334, 115–124.
(11) Perlovich, G. L.; Strakhova, N. N.; Kazachenko, V. P.; Volkova,
T. V.; Tkachev, V. V.; Schaper, K. J.; Raevsky, O. A. Int. J. Pharm. 2008,
349, 300–313.
(12) Perlovich, G. L.; Tkachev, V. V.; Strakhova, N. N.; Kazachenko,
V. P.; Volkova, T. V.; Surov, O. V.; Schaper, K. J.; Raevsky, O. A.
J. Pharm. Sci. 2009, 98, 4738–4755.
(13) Guillory, J. K. Polymorphism in Pharmaceutical Solids; Brittain,
H. G., Ed.; : Marcel Dekker Inc.: New York, 1999; pp 183-226.
(14) CAD-4 Software, Version 5.0; Enraf-Nonius: Delft, The Nether-
lands, 1989.
(15) Sheldrick, G. M. SHELXL97 and SHELXS97; University of
G€ottingen: Germany, 1997.
(16) Zielenkiewicz, W.; Perlovich, G.; Wszelaka-Rylik, M. J. Therm.
Anal. Calorim. 1999, 57, 225–234.
(17) Cox, J. D.; Pilcher, G. Thermochemistry of Organic and Organo-
metallic Compounds; , Academic Press: London, 1970.
(18) Chickos, J. S.; Acree, W. E., Jr. J. Phys. Chem. Ref. Data 2002, 31
(2), 537–698.
(19) Dannenfelser, R.-M.; Yalkowsky, S. H. J. Pharm. Sci. 1999, 88
(7), 722–724.
(20) Pascual-Ahuir, J. L.; Silla, E. J. Comput. Chem. 1990, 11, 1047.
(21) Raevsky, O. A.; Grigor’ev, V. J.; Trepalin S. V. HYBOT program
package, Registration by Russian State Patent Agency N 990090 of
26.02.99.
(22) Etter, M. C. Acc. Chem. Res. 1990, 23, 120–126.
(23) Bernstein, J.; Davis, R. E.; Shimoni, L.; Chang, N.-L. Angew.
Chem., Int. Ed. Engl. 1995, 34 (15), 1555–1573.
(24) Mayo, S. L.; Olafson, B. D.; Goddard, W. A., III J. Phys. Chem.
1990, 94, 8897–8909.
(25) Perlovich, G. L.; Rodionov, S. V.; Bauer-Brandl, A. Eur. J.
Pharm. Sci. 2005, 24, 25–33.
(26) Yalkowsky, S. H.; Valvani, S. C. J. Pharm. Sci. 1980, 69, 912–
922.
(27) Li, Z. J.; Ojala, W. H.; Grant, D. J. W. J. Pharm. Sci. 2001, 90,
1523–1539.
(28) Gavezzotti, A.; Filippini, G. . Energetic aspects of crystal
packing: Experiment and computer simulations. In Theoretical Aspects
and Computer Modeling of the Molecular Solid State; Gavezzotti, A., Eds.;
John Wiley & Sons: Chichester, 1997; Chapter 3, pp 61-97.
1081
dx.doi.org/10.1021/cg1012389 |Cryst. Growth Des. 2011, 11, 1067–1081