Interplay between the crystal stability and the energy of the molecular conformation

Article abstract of DOI:10.1039/d0ce01673j

A specially designed new compound, 5,5′-bis(4-hydroxyphenyl)-2,2′-dihydroxy-1,1′-biphenyl, can crystallize in different crystallographic systems. The molecule adopts theC-conformation for the torsion angle of around 60° and theT-conformation for the angle of around 130°, which differ in energy by ～0.8 kJ mol^?1. Theoretical studies for the gaseous phase show that theC-conformer has a lower energy. However, crystallization experiments show that the most stable crystal structure consists of only the energetically less stableT-conformer. On the other hand, fast crystal growth at low temperature and crystal growth after milling both lead to the formation of metastable crystals in which the studied molecule adopts theC-conformation. Our study shows that the total crystal net energy is the main factor in determining the molecular conformations even if the molecular conformation has a higher energy in the gaseous phase.

Full text of DOI:10.1039/d0ce01673j

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Interplay between the crystal stability and the
energy of the molecular conformation†
Cite this: CrystEngComm, 2021, 23,
2683
Konrad Dyk, a Łukasz Baran, b Wojciech Rżysko,b
a
Marek Stankevič c and Daniel M. Kamiński
*
A specially designed new compound, 5,5′-bis(4-hydroxyphenyl)-2,2′-dihydroxy-1,1′-biphenyl, can crystallize
in different crystallographic systems. The molecule adopts the C-conformation for the torsion angle of
around 60° and the T-conformation for the angle of around 130°, which differ in energy by ∼0.8 kJ mol−1
.
Theoretical studies for the gaseous phase show that the C-conformer has a lower energy. However,
crystallization experiments show that the most stable crystal structure consists of only the energetically less
stable T-conformer. On the other hand, fast crystal growth at low temperature and crystal growth after
milling both lead to the formation of metastable crystals in which the studied molecule adopts the
C-conformation. Our study shows that the total crystal net energy is the main factor in determining the
molecular conformations even if the molecular conformation has a higher energy in the gaseous phase.
Received 18th November 2020,
Accepted 24th February 2021
DOI: 10.1039/d0ce01673j
rsc.li/crystengcomm
than 2 kJ mol−1. Based on our theoretical calculations, we have
Introduction
conducted
synthesized
a
number of crystallization experiments and
a new biphenol derivative, 5,5′-bis(4-
It is generally accepted that the molecule conformation in the
crystal lattice is determined by the energy of the conformer
and the crystal net energy. Both factors influence the
molecule packing in the crystal lattice.1 If the molecule can
adopt two or more conformations, the one with the lowest
energy should be dominant in the crystal. However, the
energy of the lattice can influence the conformation of the
molecule in the final crystal. The tendency of the system
(crystal net) to achieve the thermodynamic minimum energy
according to the 2nd law of thermodynamics is the general
rule in crystal growth. Although, during the crystal growth
process, less thermodynamically stable crystals can be formed
which might be related to the kinetics of the process.2–4
Usually, this may occur when the crystallization is conducted
far from equilibrium conditions like crystal growth during/
after milling or fast growth at low temperature.4,5
hydroxyphenyl)-2,2′-dihydroxy-1,1′-biphenyl (BHDB), which
consists of four connected phenol rings, as shown in Fig. 1. The
rotation around the C1–C1′ bond in 2,2′-biphenols has no real
restrictions, and thus a wide number of conformers in such a
case are possible. To achieve similar energy of two different
conformers, steric hindrance (two hydroxyl groups in the
o-position) was added to the designed molecule.
As a next step, the influence of the crystal grow conditions for
BHDB on the molecular conformation and crystal packing was
investigated. Surprisingly, the higher energy conformer builds
the crystals of the highest stability. We present a widely used
approach to combine the experimental and theoretical methods
to investigate the system of interest.6–8 Such a methodology
allows us to better understand the behavior of the system.
The crystal net energy might have a bigger impact on the
total lattice energy than the conformation of the single
molecule. To check this hypothesis, we designed a molecule
with a rotational degree of freedom which leads to two
conformers with an energy difference between them smaller
Materials and methods
5,5′-Bis(4-hydroxyphenyl)-2,2′-dihydroxy-1,1′-biphenyl (BHDB)
(empirical formula: C24H18O4, MW: 370.41 g mol−1, m. p.: >
a Department of General, and Coordination Chemistry and Crystallography,
Institute of Chemical Sciences, Faculty of Chemistry, Maria Curie-Skłodowska
University, Lublin, Poland. E-mail: daniel.kaminski@umcs.pl
b Department of Theoretical Chemistry, Institute of Chemical Sciences, Faculty of
Chemistry, Maria Curie-Skłodowska University, Lublin, Poland
c Department of Organic Chemistry, Institute of Chemical Sciences, Faculty of
Chemistry, Maria Curie-Skłodowska University, Lublin, Poland
† CCDC 2061380, 2061383, 2063307 and 2063312. For crystallographic data in
CIF or other electronic format see DOI: 10.1039/d0ce01673j
Fig. 1 The scheme of the BHDB molecule with atom numbering.
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Fig. 2 Synthesis of BHDB.
250 °C) consists of four connected phenol rings. The
synthetic route is presented in Fig. 2.
All structures were solved using the direct methods
implemented in SHELXT10 software and refined using
SHELXL.11 The C–H and O–H hydrogen atoms were located in
idealized average geometrical positions (O–H for structure III),
whereas O–H for structures I and II (all of them participate in
H-bonds) was found from differential electron density maps.
Scattering factors used are from Table 6.1.1.6 and 4.2.4.2 in ref.
12. Table 1 shows the experimental details for single crystal
X-ray measurements. Presented structures have been deposited
in the Cambridge Crystallographic Database with numbers: Ia –
2063312, Ib – 2063307, II – 2061383, and III – 2061380.
To obtain crystals suitable for further analysis, the
compound (2 mg each) was dissolved in different organic
solvents and left to evaporate at 293 K and 283 K. After
crystallization, three different structures were obtained.
Structure I (measured at: a – 293 K, b – 120 K) crystallized
from acetonitrile. Structure II was prepared by mechanical
grinding (30 minutes) with trimesic acid and subsequent
addition of acetonitrile (2 μL) and recrystallization in an
acetonitrile–acetic acid (1 : 1 v/v) mixture at room temperature
for 60 days. Structure III was obtained in an acetone–water
mixture (5 : 1 v/v) at 283 K. It was found that crystallization in
acetonitrile gives the crystals of the best quality. The crystals
of I appeared as yellow plates, II were transparent cubes and
III were colorless plates.
Attempted crystallization in acetone, acetic acid, ethyl
acetate, n-propyl acetate, a mixture of ethyl acetate and
chloroform (1: 1 v/v), 1,4-dioxane, 1,3-dioxane, a mixture of
methanol and water (3 : 2 v/v), and acetic acid gave crystals of
poor quality but the lattice parameters indicated the presence
of I.
Computational details
To check the relation between the energy of the molecule and
the C6–C1–C1′–C6′ torsion angle in BHDB in the gaseous
phase (without intermolecular interactions), density
functional, Møller Plesset (MP2) and zero-point energies were
calculated in Gaussian16 program.13 Importantly, the
geometry of the molecule was optimized at each rotation step.
In the calculations, the B3LYP, CAM-B3LYP, WB97XD, and
B3PW91 levels of theory were used with the 6-31G+(d, p) and
6-311+(d,p) basis sets and with standard convergence criteria.
The Hirshfeld surface analysis was performed similarly to
that presented in a paper by Kaminski et al.14
Collection of the X-ray diffraction data for I and III was
accomplished at 293 K and 120 K using a SuperNova
diffractometer with CuKα radiation and a CCD detector
(ATLAS S2). Due to a small crystal size of II, a Rigaku XtaLAB
diffractometer with a rotated Cu anode and multilayer
focusing optics equipped with a Pilatus 3R (200K-A) detector
was used. Cell refinement and data collection, reduction and
analysis were performed with CRYSALISPRO software.9
Results
The most interesting parameter in this study is the torsion
angle between the atoms C6–C1–C1*–C6* (* – inversion
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Table 1 Data collection and refinement details for the measured structures
Ia
Ib
II
III
Empirical formula
C24H18O4
C24H18O4
C24H18O4
2× (C24H18O4) + 2× (C3H6O)
+ 3× (H2O)
293(2)
Temperature [K]
293(2)
120(1)
293(2)
Wavelength [Å]
Crystal system
Space group
1.54184
Monoclinic
C2/c
1.54184
Monoclinic
C2/c
1.54184
Regular
Fd3c
1.54184
Triclinic
P1
¯
a [Å]
b [Å]
c [Å]
α [deg]
20.3993(4)
8.8217(5)
9.7628(2)
90°
95.13(1)°
90°
1749.84(5)
4
1.406
20.3982(4)
8.7267(2)
9.6682(2)
90°
95.154(2)°
90°
1714.08(6)
4
1.435
36.4661(5)
36.4661(5)
36.4661(5)
90(0)°
90(0)
90(0)
48 491.8(12)
96
1.218
0.670
18 624
10.4718(6)
10.6341(5)
11.1086(6)
80.520(4)°
82.650(5)°
83.754(5)°
1205.24(11)
2
β [deg]
γ [deg]
Volume [Å3]
Z
Density [g cm3] (calculated)
Absorption coefficient
F(000)
1.236
0.715
474
0.774
776
0.790
776
Crystal size
Theta range for data collection
Index ranges
0.4 × 0.03 × 0.3
8.704 to 152.51°
−25 ≤ h ≤ 25,
−11 ≤ k ≤10,
−12 ≤ l ≤ 12
12 203
1821 [R(int) = 0.0282]
100%/152.51°
1821/129
1.078
0.4 × 0.03 × 0.3
8.71 to 152.46°
−17 ≤ h ≤25,
−10 ≤ k ≤ 10,
−12 ≤ l ≤ 12
5339
1766 [R(int) = 0.0201]
99.9%/152.46°
1766/132
1.063
0.2 × 0.2 × 0.18
3.43 to 68.77°
−42 ≤ h ≤ 43,
−43 ≤ k ≤ 43,
−43 ≤ l ≤43
125 860
1872 [R(int) = 0.0597]
98.9%/68.77°
1872/129
1072
0.4 × 0.05 × 0.3
4.06 to 76.12°
−13 ≤ h ≤ 13,
−12 ≤ k ≤ 12,
−12 ≤ l ≤13
8362
5726 [R(int) = 0.0672]
69%/76.12°
5726/625
Reflections collected
Independent reflections
Completeness/to theta
Data/parameters
Goodness-of-fit on F2
Final R indices
1.077
R1 = 0.0830
R1 = 0.03924
R1 = 0.03548
R1 = 0.0537
[I > 2sigma(I)]
R indices (all data)
R1 = 0.0407,
wR2 = 0.1093
0.22 and −0.20
R1 = 0.0.375,
wR2 = 0.0975
0.31 and −0.22
R1 = 0.0634,
wR2 = 0.1811
0.14 and −0.18
R1 = 0.1020
wR2 = 0.2597
0.32 and −0.34
Largest diff. peak and hole
center related atoms) for structures Ia, Ib and II and structure
III molecule A C6–C1–C13–C18 and molecule B C6′–C1′–C13′–
C18′ as shown in Fig. 4. The torsion angle of 0° leads to cis
like conformation (C-conformation) while 180° leads to trans
like conformation (T-conformation).
energy calculations (for all methods and basis sets) always
lead to the lowest energy for the C conformer, as shown in
Theoretical considerations
The theoretical scans of the torsion angle show that two
energy minima correspond to two conformations (Fig. 3). The
first minimum at 60° is analogous to structures II and III
obtained during crystallization. The second minimum at
130° is similar to the torsion angle observed in the crystal
lattice of molecule I. Table 2 shows that the DFT calculations
take into account electronic correlation to a varying degree,
which strongly depends on the experimental parameters
describing the correlation–exchange energy in each DSC
method. To clarify the role of the electron correlation,
additionally, the perturbation MP2 method was applied. It
can be seen that for MP2, the difference between the energies
for C and T is even bigger than that in DSC methods (see
Table 2). Calculations conducted in 6-31G+(d,p) and 6-311G
+(d,p) only in the CAM-B3LYP method exceptionally lead to a
lower energy for the T conformation. However, calculations
conducted in the extended 6-311G+(d,p) basis set always lead
to a lower energy for the C conformation. The zero-point
Fig. 3 Gaussian16 calculations for the gaseous phase of BHDB. The
diagram shows the changes of the potential energy due to the rotation
of the torsion angle. The geometry of the molecule was optimized at
each step of the calculations. The absolute minimum energy was
related to the minimum at 60° for each method.
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Table 2 Comparison of the energy differences with different methods
and basis sets between the C and T conformations
structure IIIB is bigger than that in other structures, as
shown in Table 5. This is related to the additional
intramolecular bonding O4–H4O⋯O2AC. Also, in structure
Ib we observed a valence angle of 106.69(3)° which is smaller
than typical and, again, this is due to the presence of an
additional intermolecular hydrogen bond O2–H2O⋯O1.
The specific design of the BHDB molecule limits the
torsion angle change for both conformers due to sterical
hindrance between hydroxyl groups: O2–H2O and O2*–H2O*
(* – inversion center related) and, for III, O2–H2O, O4–H4O,
O2′–H2O′ and O4′–H4O′. All examined molecules tend to
acquire a flat conformation but steric hindrance forces
deviation from the ideal 0° and 180° angles (Fig. 5) and the
molecules adopt either the C-conformation with an angle of
around 60° and T-conformation at around 120°, as shown in
Table 6. The torsion angles in structures Ia and Ib are similar
and equal to ∼116° but in structures II, IIIA and IIIB the
torsion angle is equal to 75.2(2)°, 46.4(2)° and 51.6(2)°
respectively. Differences in torsion angles are due to the
different arrangements of intramolecular and intermolecular
interactions. This angle around the bond between two
aromatic rings (C3–C7) fluctuates at around 150° in
structures Ia, Ib, II, and IIIB. In structure IIIA, the value of
the torsion angle around the C3–C7 bond is higher by 10°
than that in other cases, as shown in Fig. 6a and b. This
might be caused by the presence of hydrogen bonds between
the solvent and molecules and the crystal lattice might favour
the flattening of the compound.
Torsion
angle [deg]
Energy difference
Method
B3LYP
Basis set
[kJ mol−1
]
6-31G+(d,p)
6-311G+(d,p)
6-31G+(d,p)
6-311G+(d,p)
6-31G+(d,p)
6-311G+(d,p)
6-31G+(d,p)
60, 120
70, 130
70, 130
70, 130
70, 120
70, 120
70, 120
0.92
0.25
−0.31
0.38
0.78
0.83
2.02
CAM-B3LYP
WB97XD
MP2
Table 3. Based on these arguments, it can be concluded that
the theoretically evaluated minimum energy is for the C
conformation.
Comparison between theoretical and experimental data
leads to the conclusion that the biggest difference can be
observed in structure II, where the torsion angle is equal to
75.2(2)°. The difference might be a result of additional
hydrogen bonds present in crystal lattices which are not
considered in the calculations for the gaseous phase. Without
spherical hindrance, the torsion angle should be changed
without any restrictions but in the database, only PAZMIO
passed this condition with the torsion angle of 36.4(1)°,
which is close to that of the C-conformation.15 Although, in
this case, the angle is closer to 0°, than that for BHDB, which
confirms the effect of p-hydroxyl groups as rotation limiters.
The geometry of BHDB
Crystal net
The three obtained BHDB structures are presented in Fig. 4.
The structural analysis shows that in all cases the bond
lengths are similar (Table 4). The aromatic C–C bond lengths
have values in the 1.35(1) Å to 1.42(1) Å range which confirm
the aromatic character of the rings. The single bonds C3–C7
and C1–C1 (C1–C13 and C1′–C13′ in structure III) between
the rings have slightly shorter lengths (1.478(10)–1.489(12) Å)
than a typical single C–C bond which is distinct for such
systems.16–19
Structures Ia and Ib present the same crystal net at different
temperatures. The BHDB molecules are transformed by the
inversion center and have a different torsion angle than
molecules II and III, as shown in Fig. 4. Fig. 6a shows the
overlaying of the molecules from the asymmetric unit cell in
III. The differences between those two molecules are small
and can be seen in the torsion angle of C3–C7 and C15–C19
bonds and the valence angle of hydroxyl group O2′–H2O′.
Fig. 6b presents an overlay of the BHDB molecules from II
and IIIA. The biggest differences, in this case, are related to
Valence angle analysis of hydroxyl groups in the BHDB
molecules shows that the valence angle of 116.25° in
Table 3 Comparison of the zero-point energies with different methods and basis sets between the C and T conformations
Basis
set
Torsion
angle [deg]
Zero-point
energy
Energy difference
Method
B3LYP
[kJ mol−1
0.53
]
6-31G+(d,p)
6-311G+(d,p)
6-31G+(d,p)
6-311G+(d,p)
6-31G+(d,p)
6-311G+(d,p)
60
120
70
130
60
130
70
130
70
−1225.993328
−1225.993128
−1226.246886
−1226.246485
−1225.359739
−1225.359457
−1225.617432
−1225.617122
−1225.579135
−1225.578818
−1225.820274
−1225.819915
1.05
0.74
0.81
0.83
0.94
CAM-B3LYP
WB97XD
120
70
120
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Fig. 4 Atom labelling for the I, II and III BHDB structures with anisotropic displacement parameters at the 50% probability level.
Table 4 Bond distances in BHDB
III
Bond
Ia
Ib
II
Molecule A
Molecule B
Ring A
C1–C2
C2–C3
C3–C4
C4–C5
C5–C6
C6–C1
C6–O2
C3–C7
C7–C8
C8–C9
C9–C10
C10–C11
C11–C12
C12–C7
C10–O1
1.396(2)
1.397(2)
1.392(2)
1.382(2)
1.387(2)
1.399(2)
1.377(1)
1.486(1)
1.391(2)
1.387(2)
1.382(2)
1.387(2)
1.385(2)
1.397(2)
1.377(1)
1.401(2)
1.399(2)
1.393(2)
1.386(2)
1.391(2)
1.399(2)
1.379(2)
1.487(2)
1.391(2)
1.393(2)
1.388(2)
1.390(3)
1.386(2)
1.402(2)
1.379(2)
1.390(3)
1.393(2)
1.401(3)
1.363(3)
1.386(3)
1.395(3)
1.363(3)
1.481(3)
1.394(3)
1.370(3)
1.381(4)
1.378(4)
1.373(3)
1.387(3)
1.369(3)
1.389(8)
1.398(9)
1.391(9)
1.388(10)
1.372(11)
1.401(9)
1.377(8)
1.483(8)
1.391(9)
1.386(10)
1.360(10)
1.374(11)
1.389(11)
1.391(10)
1.375(8)
C13–C14
C14–C15
C15–C16
C16–C17
C17–18
1.393(9)
1.414(9)
1.396(10)
1.382(12)
1.356(11)
1.415(8)
1.372(9)
1.478(10)
1.406(9)
1.370(11)
1.359(12)
1.388(11)
1.394(12)
1.385(11)
1.378(10)
1.390(10)
1.378(10)
1.407(11)
1.366(15)
1.375(13)
1.420(9)
1.365(11)
1.489(12)
1.374(12)
1.392(13)
1.401(12)
1.383(14)
1.364(13)
1.407(10)
1.367(12)
C13′–C14′
1.394(9)
1.388(9)
C14′–C15′
C15′–C16′
C16′–C17′
C17′–C18′
C18′–C13′
C18′–O4′
C15′–C19′
C19′–C20′
C20′–C21′
C21′–C22′
C22′–C23′
C23′–C24′
C24′–C19′
C22′–O3′
1.402(10)
1.393(12)
1.371(12)
1.406(9)
1.365(10)
1.488(10)
1.354(11)
1.369(12)
1.419(11)
1.358(12)
1.376(11)
1.415(10)
1.371(10)
C18–C13
C18–O4
Ring B
C15–C19
C19–C2O
C20–C21
C21–C22
C22–C23
C23–C24
C24–C19
C22–O3
Table 5 Valence angles of hydroxyl groups of the BHDB structures
III
Angle
Ia
Ib
II
Molecule A
Molecule B
C10–O1–H1O
C6–O2–H2O
109.47(2)
109.47(2)
109.48(2)
106.69(3)
109.46(5)
109.49(5)
109.47(2)
109.47(2)
C18–O4–H4O
C22–O3–H3O
109.47(2)
109.47(2)
109.47(2)
109.47(2)
C18′–O4′–H4O′
C22′–O3′–H3O′
109.47(2)
109.47(2)
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In crystal I, we can observe columns connected by
hydrogen bonds in the [101] direction. In each column,
adjacent molecules are transformed by the presence of the
glide c plane in this direction while the adjacent columns are
made by the transformation through the inversion centre.
Decreasing the temperature of the crystal to 120 K does not
affect the organization of the molecules in the crystal lattice
as shown in Fig. 8. The only effect observed at a lower
temperature was the reduction of thermal oscillations and
the quality improvement of the structure. The crystal lattices
of Ia and Ib are similar.
The main intermolecular hydrogen bonds in Ia and Ib are
O1–H1O⋯O2 and O2–H2O⋯O1. The lengths of these H-bonds
suggest that they are quite weak,20 as shown in Table 7.
Fig. 5 Overlay of cis (purple) and trans (light blue) conformations.
These bonds create a 3D net build in all crystallographic
directions (Fig. 9). In structures Ia and Ib despite the
presence of hydrogen bonds in the crystal, π⋯π stacking
(3.66(1) Å) and weak C–H⋯π interactions are present
(Fig. 10) which additionally stabilize the crystal lattice.
In the crystal lattices of I, we can observe layers of BHDB
molecules along the crystallographic [110] direction, where
aromatic rings form a hydrophobic core and the hydroxyl
groups bind the layers, as shown in Fig. 11.
Table 6 C6–C1–C1*–C6* torsion angles in studied molecules
III
Torsion angle
Ia
Ib
II
Molecule A Molecule B
51.6(2)
C6–C1–C1*–C6* 117.5(2) 115.9(2) 75.2(2) 46.4(2)
In structure II, the same functional groups are involved in
the intermolecular hydrogen bonding, and thus a similar
hydrogen bond pattern is observed. Despite the presence of
these interactions, the symmetrical intramolecular hydrogen
bonds O2–H2⋯O2 are observed which stabilize the
C-conformation. The angle and distance of this H-bond are
equal to 124.27(5)° and d(D–H⋯A) = 2.376(9) Å, respectively.
There are two intermolecular interactions: O2–H2⋯O2 and
O1–H1O⋯O1. In the crystal structure, each molecule
interacts with six others by hydrogen bonds, as shown in
Fig. 12. Also, weak interactions can be identified (C–H⋯π)
and additionally stabilizes the C-conformation (Table 8).
Structure II is the most interesting as it provides both
hydrophilic and hydrophobic pores. To refine this structure,
the solvent mask21 (included in Olex2) was used. This
the torsion angles between phenyl groups and the orientation
of hydroxyl groups. The C-conformation in the case of II is
stabilized by intramolecular hydrogen bonds O2–H2O⋯O2*
whereas the C-conformation in the case of III is stabilized by
intramolecular H-bonds (for molecule A: O2–H2O⋯O4 and
molecule B: O2′–H2O′⋯O4′) and also the intermolecular
hydrogen bonds between the compound and solvent
molecules (O4–H4O⋯O2AC, O5–H1O5⋯O2, O1′–H1O′⋯O5
and O3′–H3O′⋯O7).
Packing and intermolecular interactions
Crystal structures and hydrogen bonds of the three different
crystal nets of BHDB are presented in Fig. 7.
Fig. 6 Structure overlay after mirror imaging the asymmetric molecules. (a) Molecules A and B of structure III (magenta – A; light green – B); (b)
structure overlay after mirror imaging the asymmetric molecules (II – orange; IIIA – cyan).
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Fig. 7 Packing of the unit cell of the I, II and III BHDB crystals.
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gaps and interact with the surrounding BHDB molecules by
hydrogen bonds but they are not forming any stable motif in
the pores and thus they do not contribute significantly to the
stabilization of the C-conformation. In structure II, the
second type of pores has been observed to have a volume of
around 6.5 Å3 and cover 0.2% of the unit cell, as shown in
Fig. 13b. The small voids seem to be empty because they are
too small to host any molecules.
Fig.
8 Structure overlay after mirror imaging the asymmetric
molecules (Ia – red and Ib – green).
The last BHDB structure is a solvate which has additional
two acetone and three water molecules in the unit cell. As in
previous structure II, the intramolecular hydrogen bond
stabilizes the C-conformation of BHDB. Furthermore, acetone
molecules play an important role in stabilizing the BHDB
conformation by hydrogen bonds which fix the torsion angle
C6–C1–C13–C16. The intermolecular hydrogen bonding
occurs mainly through solvent (water, acetone) molecules
and, as in the other structures, strong hydrophilic and
hydrophobic areas might be distinguished. Structure III in
the [100] direction has perpendicularly ordered BHDB
molecules interacting via the C–H⋯π interactions in the crystal
lattice, as shown in Fig. 14. Only this crystal has several H-
bonds, which have a typical range between d(A⋯D) 2.5–2.8 Å.
According to Brown,20 this donor–acceptor distance of the
hydrogen bond can be regarded as a strong one (Table 9).
Table 7 Hydrogen bonds in structures Ia and Ib
D–H⋯A
d(D–H)
d(H⋯A)
d(D⋯A)
<DHA
Ia
Ib
O1–H1O⋯O2
O2–H2O⋯O1
O1–H1O⋯O2
O2–H2O⋯O1
0.820(1)
0.820(1)
0.820(1)
0.854(20)
2.166(1)
2.104(1)
2.076(1)
2.092(1)
2.980(1)
2.910(1)
2.871(1)
2.939(1)
172.00(7)
167.37(2)
163.34(6)
171.1(18)
operation helps to hide the electron density, which
contributes to the structure, from the disordered water
molecules occupying hydrophilic pores, as shown in Fig. 13a,
and, therefore, helps in the further analysis of the molecular
crystal. The disordered water molecules are enclosed in the
Fig. 9 Hydrogen bonds of structure I in an elemental cell.
Fig. 10 The π⋯π stacking between two I molecules.
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Fig. 11 Layering in the unit cell of structure I.
Fig. 12 Intermolecular hydrogen bonds between the BHDB molecules in crystal II.
conformers of BHDB. It appears that both conformations C
and T occur in the crystals but structure I (T-conformation) is
the most favourable as it was observed in several conducted
crystallization experiments close to the equilibrium
conditions (see Materials and methods). Structures II and III
were observed only in two cases. The first one was obtained
after mechanical grinding which usually leads to the
formation of less energetically stable forms22–27 and the
second by fast crystallization at low temperature. In the first
approximation, the Boltzman distribution suggests (based on
the energy from theoretical calculations) that in solution, two
conformers are almost in a 1 : 1 ratio (295 K T: C 43.8 : 56.2;
285 K T: C = 43.5 : 56.5) and the temperature has little
influence on the ratio between these two conformers. The
kinetics of the crystal growth, which also depends on the
temperature, is here the main factor in determining the
crystal structure. To prove this hypothesis, the crystallization
of III was conducted at room temperature with the other
parameters the same as previously described but without any
success. This effect might be easily understood if the crystal
lattice energy is taken under consideration.28
Table 8 Hydrogen bonds in the unit cell of II
D–H⋯A
d(D–H)
d(H⋯A)
d(D⋯A)
<DHA
O2–H2O⋯O2
O1–H1O⋯O1
0.822(9)
0.820(9)
2.376(9)
2.14(9)
2.923(3)
2.940(3)
124.27(5)
165.49(5)
Similar to structure II, in solvate III we can observe empty
spaces in the unit cell which cover 5.1% of the volume of the
unit cell (Fig. 15). These voids occur in hydrophobic areas where
the crystal lattice cannot be stabilized by the solvent molecules
and their interactions. This might be the reason for the
instability of the crystal. This crystal disintegrated during the
X-ray measurement. This was probably related to the weak
association of acetone molecules in the crystal lattice.
Discussion
Despite the C-conformation having the lowest energy, the
difference between the C and T-conformations is only an
average of 0.8 kJ mol−1 which is related to the spherical
Unfortunately, the calculated lattice energies of obtained
structures I, II and III cannot be compared because of
hindrance that forbids
a
flat conformation of both
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Fig. 13 Packing of the unit cell of crystal II; (a) presents a packing with the disordered water molecules as a spacefill and (b) shows the empty
space in the crystal hydrate.
different unit cell arrangements. However, the Hirshfeld
surface analysis provides qualitative information about the
bonds important for crystal stability. Structure I has 20.4%
O–H hydrogen bonds and 8.6% C–C interactions including
π⋯π stacking. This structure lacks the repulsive O–O
interactions. Structure II has 23.9% O–H bonds which are
more than in structure I but additionally has 4.9% repulsive
O–O interactions that destabilize the structure. The number
of C–C interactions is negligible in this case. Structure III has
two BHDB molecules in the asymmetric part of the unit cell
which on average have 19.65% O–H bonds. This is less than
in structure I. Also, the amount of C–C interactions is
negligible in this case. The average amount of repulsive O–O
interactions per molecule is 1.0%. Comparison of all the
intermolecular interactions suggests that structure I is the
most stable, as shown in Fig. 16.
This experiment clearly shows that the thermodynamic
global minimum is a function of molecular energy and lattice
energy. Considering the energy of a single molecule as the only
parameter might lead to wrong conclusions as the results of the
experiment shows. The analysis of similar molecules in the
CCDC database (Table 10) shows that there are two main
torsion angles between the single C1–C1′ bond for similar
molecules. First, the angle of around 120° corresponds to our
T-conformation and second, 44–57° for C. Only structure
NUTSUQ, which contains biphenol molecules, is similar to
Table 9 Intramolecular and intermolecular hydrogen bonds in crystal III
Intramolecular hydrogen bonds
D–H⋯A
d(D–H)
d(H⋯A)
d(D⋯A)
<DHA
O2–H2O⋯O4
0.82
0.82
1.905(4)
2.216(4)
2.617(4)
2.699(4)
144.54(5)
117.83(5)
O2′–H2O′⋯O4′
Intermolecular hydrogen bonds
O4–H4O⋯O2AC
O4′–H4O′⋯O1
O3′–H3O′⋯O7
O1′–H1O′⋯O5
O3–H3O⋯O1AC
O7–H1O7⋯O1AC
O1–H1O⋯O3
0.82
0.82
0.82
0.82
0.82
0.85
0.82
0.85
0.85
0.85
0.85
0.85
0.85
0.85
1.930(3)
1.886(4)
1.836(3)
1.893(4)
1.952(3)
2.701(3)
2.201(4)
2.701(3)
1.826(4)
2.383(5)
2.078(5)
2.534(4)
1.960(5)
2.433(5)
2.658(3)
2.684(3)
2.610(4)
2.693(3)
2.764(3)
2.855(3)
2.778(4)
2.855(3)
2.555(3)
2.555(3)
2.814(3)
2.555(4)
2.693(3)
2.693(3)
147.50(5)
164.10(6)
156.91(5)
164.67(5)
170.26(6)
91.63(5)
127.52(5)
91.63(6)
142.76(5)
91.79(6)
144.28(5)
81.78(5)
143.60(5)
98.45(5)
O7–H1O7⋯O1AC
O7–H1O7⋯O6
O6–H1O6⋯O7
O5–H1O5⋯O2
O7–H2O7⋯O6
O6–H2O6⋯O1′
O5–H2O5⋯O1′
Fig. 14 Solvent occupancy in the unit cell of crystal III.
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Conclusions
In this work, we have shown that the most important factor
in determining the crystal lattice packing is the minimum of
crystal energy if crystallization is conducted close to the
equilibrium conditions. The conformation of molecules in
the crystal lattice plays
a minor role in the present
experiment. It has been shown that under normal conditions
(close to the equilibrium), crystal growth of BHDB leads to
the energetically less favorable T-conformer in a crystal
lattice, whereas the conditions such as lower temperature or
milling lead to a crystalline product with molecules packed
in the C-conformation. This suggests that in these cases,
crystallization kinetics plays a dominant role. Our study
clearly shows that considering only single molecule energy in
the gaseous phase can lead to wrong conclusions regarding
molecule arrangement in the crystal lattice.
Additionally, it has been shown that it is possible to
design a molecule with a small energy difference between
two conformers by simply adding spherical hindrance.
Fig. 15 Empty spaces in the unit cell of crystal III.
Conflicts of interest
There are no conflicts to declare.
Acknowledgements
This research was supported in part by the PL-Grid
Infrastructure and Wroclaw Centre for Networking and
Supercomputing (grant no. 424). The X-ray diffraction
measurements were supported by the EcoTech Complex in
Lublin.
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