Electron Density Distribution of Urea in Co-crystals with Rigid and Flexible Dicarboxylic Acids

Article abstract of DOI:10.1021/acs.cgd.5b01253

This is the first study on electron density distribution of urea and dicarboxylic acids co-crystals. The accurate electron density of two co-crystals of urea with oxalic acid and l-malic acid molecules is discussed, on the basis of high-resolution X-ray diffraction data collected at 80(2) K, and compared with density functional theory calculations in a crystal structure as well as in the gas phase. Rigid dicarboxylic acid favors two-dimensional planar hydrogen bond networks, whereas flexible acid promotes layers with helical arrangements of those molecules. The nature of chemical bonding is investigated using topological analysis based on quantum atoms in molecules theory, Hirshfeld analysis, noncovalent interactions approach, distributed atomic polarizabilities and electrostatic potential. In a co-crystal of oxalic acid and urea, uncommon carbonyl···carbonyl interaction is observed, representing an antiparallel motif between oxalic and urea molecules, which was so far identified only between the same molecules.

Full text of DOI:10.1021/acs.cgd.5b01253

Article
pubs.acs.org/crystal
Electron Density Distribution of Urea in Co-crystals with Rigid and
Flexible Dicarboxylic Acids
,†
†
‡
†
Anna Krawczuk,* Marlena Gryl, Mateusz B. Pitak, and Katarzyna Stadnicka
†
Faculty of Chemistry, Jagiellonian University, Ingardena 3, 30-060 Krakow, Poland
‡
UK National Crystallography Service, Chemistry, University of Southampton, Highfield, SO17 1BJ, Southampton, United Kingdom
S Supporting Information
*
ABSTRACT: This is the first study on electron density
distribution of urea and dicarboxylic acids co-crystals. The
accurate electron density of two co-crystals of urea with oxalic
acid and L-malic acid molecules is discussed, on the basis of
high-resolution X-ray diffraction data collected at 80(2) K, and
compared with density functional theory calculations in a
crystal structure as well as in the gas phase. Rigid dicarboxylic
acid favors two-dimensional planar hydrogen bond networks,
whereas flexible acid promotes layers with helical arrangements
of those molecules. The nature of chemical bonding is
investigated using topological analysis based on quantum atoms in molecules theory, Hirshfeld analysis, noncovalent interactions
approach, distributed atomic polarizabilities and electrostatic potential. In a co-crystal of oxalic acid and urea, uncommon
carbonyl···carbonyl interaction is observed, representing an antiparallel motif between oxalic and urea molecules, which was so far
identified only between the same molecules.
1
. INTRODUCTION
urea and L-malic acid exhibit both linear and nonlinear optical
properties, and the second harmonic efficiency at a fundamental
Structural diversity of urea and dicarboxylic acid co-crystals has
been the subject of many studies
dicarboxylic acids are considered as an ideal candidates for
forming those arrangements and are often used for crystal
engineering purposes.
bifunctional molecule where oxygen atom is a 4-fold hydrogen
bond (HB) acceptor, whereas nitrogen atoms are donors of
four HBs. It has been shown that the syn positioned HB
14
1
−10
wavelength of 1064 nm is around three times that of KDP. A
(Table 1). Both urea and
15
similar nature reveals urea L-tartaric acid and urea DL-tartaric
16
acid co-crystals, and for the second adduct second harmonic
generation (SHG) is 1 order of magnitude larger than that of
KDP.
1
1−13
Urea is a small, planar, and
So far co-crystals of urea and dicarboxylic acids were studied
in terms of classical crystal structure analysis where the
information about interatomic interactions comes from geo-
metrical criteria rather than from electron density distribution
1
1
donor and acceptor sites are employed in one-dimensional
(
1D) chain formation, whereas antipositioned HB donor and
(
EDD). To get more insight into the nature of weak
acceptor sites are responsible for the two- and three-
dimensional (2D and 3D) crystal structures. Dicarboxylic
acids, on the other hand, possess two HB sites which are not
used in the primary formation of a co-crystal, but ensure the
extension of this self-assembly in one and possibly two or three
directions. For example, in the case of urea succinic acid co-
interactions between atoms and therefore to design more
efficient co-crystals, it is desirable to use more sophisticated
tools where both qualitative and quantitative studies are
17
possible. One of the most powerful tools for analyzing
chemical bonding of the molecules in the crystal is Bader’s
1
8
5
quantum theory of atoms (QTAIM). By hard space
partitioning of electron density (ED) into atomic basins,
atomic volumes and electron populations of each atom are
obtained, and quantitative description of chemical bonding
within a system can be provided by characterization of electron
properties at bond critical points (BCP), where the gradient of
ED is equal to zero (∇ρ(r) = 0).
crystals (U-SA), with a 1:1 stoichiometry ratio all strong HBs
are involved in formation of 2D planar sheets, whereas for a 2:1
molar ratio strong HB are involved in formation of 1D chains
which are stabilized by weak C−H···O interactions resulting in
close packing. Moreover, by using different crystallization
methods (slow evaporation, neat grinding, or solvent-drop
grinding) under different experimental conditions (solution
composition, solvent, temperature, pressure, etc.) it is also
possible to obtain new polymorphic forms, i.e., urea glutaric
Taking into account the fact that the urea molecule is a
19
nonlinear optical (NLO) chromophore, within this paper we
6
,7
acid addition compound with a 1:1 molar ratio.
Such a variety of behavior of urea and dicarboxylic acids in a
crystal structure and combination of molar ratios in many cases
leads to multifunctional materials. For example, co-crystal of
Received: August 28, 2015
Revised: October 6, 2015
©
XXXX American Chemical Society
A
DOI: 10.1021/acs.cgd.5b01253
Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design
Article
a
Table 1. Summary of Known Cocrystals of Urea with Rigid and Flexible Dicarboxylic Acids
cell parameters Å, °
space
group
molar ratio
a
b
c
α
β
γ
solvent
Z
T/K
1
b
urea:oxalic acid
1:1
C2/c
C2/c
13.063
13.063
5.058
5.048
5.045
18.825
5.637
8.333
14.767
11.954
9.034
6.641
5.056
4.812
6.644
6.848
6.848
6.964
6.876
6.856
6.421
12.258
10.117
5.074
9.078
6.801
9.050
7.229
7.646
90
90
90
90
90
90
90
90
90
90
90
90
90
90
92.47
92.47
98.13
96.40
96.29
90.83
96.80
112.27
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
water
water
water
water
water
4
4
2
2
2
4
2
4
4
4
2
2
4
4
RT
RT
RT
100
80
X-ray
2
b
1:1
2:1
2:1
2:1
6.644
neutrons
X-ray
neutrons
X-ray
X-ray
X-ray
X-ray
X-ray
X-ray
X-ray
X-ray
X-ray
X-ray
3
4
P2 /c
1
12.400
12.374
12.375
6.512
P2 /c
1
this work
P2 /c
1
5
5
6
7
urea:succinic acid
urea: glutaric acid
1:1
:1
1:1
C2/c
acetonitrile/water (8:2)
2-propanol
no data
150
150
RT
RT
RT
RT
80
2
P2 /c
1
8.243
P2 /n
1
11.603
11.735
10.932
6.936
1
:1
:1
Pnma
C2/c
P21
no data
1
8
1
2
97.76
94.67
94.70
90
water/methanol (5:1)
methanol
urea:L-malic acid
1:1
this work
1
:1
P21
6.916
water
9
urea:L-tartaric acid
urea:DL-tartaric acid
1:1
1:1
P2 2 2
9.824
water
RT
RT
1
1
1
1
0
P21
23.080
101.08
water
a
b
Z refers to a number of asymmetric units in a unit cell. Reported cell parameters are the same although for different measurement techniques.
are especially interested how the electronic distribution of urea
in the solid-state deviates by changing the dicarboxylic acid
component, and how this modification could influence physical
properties of a given co-crystal. For those studies we have
chosen oxalic and L-malic acid representing rigid and flexible
molecules, respectively. By flexible we understand dicarboxylic
acids which are more susceptible on the chemical environment
and the covalent bonds may bend in order to stabilize the 3D
structure, especially when additional functional groups are
present like in L-malic acid, L-tartaric acid, or citric acid. In the
case of rigid dicarboxylic acids rather accompanying com-
pounds tend to adjust to form thermodynamically stable crystal
structure than the acid, for example, oxalic acid, malonic acid,
and glutaric acid.
(Rint = 0.019), whereas for MALUREA 13 223 reflections gave 9393
independent data (Rint = 0.020).
2
.1. Spherical Refinement. The spherical atom refinement, with
2
full-matrix least-squares on F using all data, was performed for both
co-crystals with SHELXL-97. Space groups, P2 /c for OXALUREA
23
1
and P2 for MALUREA, were assigned from the systematic absences
1
observed in the diffraction pattern, and the results of |E| distribution
and N(z) test clearly indicated the centrosymmetric and non-
centrosymmetric space groups, respectively. All non-H atoms were
allowed anisotropic thermal motion. Hydrogen atoms of the CH and
2
CH groups were found on the difference Fourier map, and then
refined at calculated positions (0.99 and 1.00 Å, respectively) with
U (H) = 1.2U (parent C). Hydrogen atoms of amine and hydroxyl
iso
eq
groups were found on the difference Fourier map and refined in a
riding model with U (H) = 1.5U (parent O/N) without constraints.
iso
eq
2
4
For structural drawings Mercury was used. All calculations were
carried out using the WinGX package. Selected crystal data and
2
5
experimental details are shown in Table 2.
2
. EXPERIMENTAL SECTION
2
.2. Multipole Refinement. The multipole formalism of Hansen
Colorless crystals of urea−oxalic acid adduct (OXALUREA) were
obtained by slow evaporation of an aqueous solution of urea and oxalic
acid (molar ratio 2:1). In the case of urea−L-malic acid co-crystal
2
6
2
7
and Coppens, implemented in the XD2006 program package, was
used. The aspherical atom electron density is given by
lmax
lmax
(
MALUREA), urea and L-malic acid were dissolved in water in a 1:1
3
3
ρ(r) = ρ(r) + P κ ρ(r) + ∑ κ R (κ′r) ∑ P
y
(θ, ϕ)
molar ratio, and crystals were obtained by slow evaporation of the
solvent.
c
v
v
l
lm± lm±
l=0
m=0
For both phases, well-faced crystals were cooled from ambient
temperature to 80 K using an Oxford 700 Series Cryostream cooler. X-
ray data collections were performed on Nonius KappaCCD
where ρ (r) and ρ (r) are core and spherical valence densities,
c
v
respectively, ylm± represents spherical harmonic angular functions, R is
l
the radial function, κ and κ′ are the expansion/contraction parameters,
20
diffractometer using Nonius COLLECT software.
P
and P
represent the population parameters. The function
v
lm±
For OXALUREA crystal a total of two runs were recorded using ω
scans at χ = 55°. In the main run (θmax = 50.58°, scan width = 1.7°/
frame) a total number of 458 images were collected with exposure
2
minimized in the least-squares procedure was ∑w(|F | − k|F |) , and
only those reflections with |F | > 4σ(F ) were included in the
0
c
0
0
refinement. Initially, the scale factor was refined against all data. In
order to obtain optimal and accurate positional and thermal
parameters for non-H atoms, the high-order refinement (sin θ/λ ≥
time of 1.7 min per frame, whereas in the additional run (θmax
=
30.03°, scan width = 1.5°/frame, total number of 160 images), the
−
1
−1
exposure time 0.70 min/frame was used to measure high-intensity low-
angle data more accurately. For MALUREA crystal also two runs were
recorded using ω scans at χ = 55°. In the main run (θmax = 53.87°, scan
width = 2°/frame) a total number of 399 images were collected with
exposure time of 3.30 min per frame. Similarly to OXALUREA
additional run (θmax = 40.25°, scan width = 1.7°/frame, total number
of 226 images, exposure time 1.7 min/frame) was used in order to
obtain accurate high-intensity low-angle data.
0
.7 Å ) was performed. Low-order refinement (sin θ/λ ≤ 0.7 Å )
was carried out to receive accurate thermal parameters for hydrogen
atoms. The hydrogen positional parameters were fixed at the
standardized distances determined from neutron studies at 1.092 Å
for the methylene group, 1.099 Å for methine group, 1.015 Å for
amine N−H groups, and 0.98 Å for hydroxyl O−H groups,
2
8
respectively. In the absence of neutron diffraction data, the H
atom anisotropic displacement parameters (ADPs) were estimated
2
9,30
For both co-crystals cell parameters and data processing were
using the SHADE2 web server,
and the obtained values were
2
1
performed using HKL DENZO and Scalepack. Absorption
subsequently kept fixed during the refinement. For the C, N, and O
atoms the multipole expansion was truncated at the octapole level. In
the case of H atoms the multipole expansion was kept up to the
21
corrections were introduced using multi-scan procedure. Reflections
22
were merged and sorted using SORTAV. In the case of OXALUREA
31
a total of 5660 reflections merged resulted in 4443 independent data
quadrupole level, as was previously advised by Hoser et al. No local
B
DOI: 10.1021/acs.cgd.5b01253
Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design
Article
3
2
gen atoms were fixed at the value of 1.13 for κ and 1.29 for κ′. For
both experimental and theoretical models the same κ′ parameters were
used for all the valence-deformation multipoles, since refinements with
individual κ′ for each multipole were unstable. The sequence of
multipolar refinement for both co-crystals was as follows: (1) scale
factor refinement against all data, (2) high-order refinement (sin θ/λ >
Table 2. Crystal Data and Experimental Details for
OXALUREA and MALUREA
co-crystal reference
chemical formula
formula mass
Crystal data
crystal system
a/Å
OXALUREA
MALUREA
C H O ·2(CH N O)
C H O ·CH N O
2
2
4
4
2
4
6
5
4
2
210.16
194.15
−
1
0
.7 Å ) with scale factor, (3) SHADE2 server used to obtain
estimated ADPs of hydrogen atoms, not refined further, (4)
refinement of population parameters together with scale factor against
all data, (5) refinement of multipole parameters and scale factor with
positional and thermal motions fixed, (6) refinement of expansion/
contraction parameters and scale factor with all other parameters fixed,
monoclinic
5.0451(1)
12.3754(2)
6.8563(1)
90
monoclinic
6.6411(2)
6.9162(2)
9.0495(2)
90.00
b/Å
c/Å
α/°
(
7) refinement of all parameters with κ and κ′ taken from previous
β/°
γ/°
96.289(1)
90
94.697(1)
90.00
step. The difference mean-square displacement amplitudes (Δ-msda)
for all bonds involving non-H atoms were within the Hirshfeld limits
−4
2
unit cell volume/Å3
temperature/K
space group
Z
425.498(13)
80(2)
414.26(2)
80(2)
(mean and largest Δ-msda were 1 and 2 × 10 Å for OXALUREA
and 2 and 4 × 10 Å for MALUREA). All static deformation
density and Laplacian maps were plotted using XDGRAPH.
Isosurface plots were generated using the MoleCoolQt program,
and the exact experimental electrostatic potentials were calculated
−4
2
22
2
6
P2 /c
1
P21
33
2
2
crystal size/mm
Data collection
diffractometer
radiation type
data collection method
absorption coefficient,
0.40 × 0.15 × 0.15
0.70 × 0.50 × 0.20
34
using the EP/MM method, as implemented in XD2006.
2
.3. Theoretical Calculations. The nature of intermolecular
Nonius KappaCCD
interactions has been studied by means of deformation density using
periodic density functional theory (DFT) calculations, which were
performed with B3LYP at the 6-311G** level using the CRYSTAL09
MoKα
ω scans at χ = 55°
0.144
3
5,36
0.153
5660
4443
program.
This basis set has proven to give reasonable results in the
−
1
37,38
μ/mm
case of intermolecular interactions for pure organic compounds.
Atomic coordinates were those determined from experimental
diffraction data, and positions of all atoms were kept frozen. Static
structure factors were computed from the resultant wave functions up
to the same resolution as that observed from the experiment and used
in multipole refinement with XD2006 package. No thermal or
positional parameters were refined in this model. For consistency,
multipolar refinement on theoretical data was carried out up to the
same level as the one used for the experimental charge density
modeling. This allows for the direct comparison of obtained results
with the experimental structure factors.
In order to understand the influence of oxalic and L-malic acid
molecules on atomic and molecular polarizabilities of urea, we have
calculated atomic and molecular polarizability tensors for above
models in isolation as well as in clusters (i.e., including intermolecular
interactions). For this purpose we performed first DFT calculations
with the GAUSSIAN09 package at the B3LYP/6-311++G(2d,2p)
level. For isolated molecules geometries were optimized, whereas in
the case of cluster geometries were taken from X-ray diffraction data
and kept frozen for further steps. Calculations were carried out at zero
field as well as under small (0.005 au) electric fields directed [±1, 0,
0], [0, ±1, 0], and [0, 0, ±1], respectively. Wave functions obtained
no. of reflections
measured
13223
9393
no. of independent
reflections
Rint
0.019
0.020
θ range/°
3.29−50.11
3.67−53.37
Spherical atom
refinement
no. of data in
4443/3740
79
9393/9160
139
2
refinement/with F >
2
2
σ(F )
no. of parameters
7
1
a
Flack parameter
0.1(2)
final R value (I > 2σ(I))
0.0352
0.0949
0.0251
0.0701
1
2
final wR(F ) values
(
I > 2σ(I))
final R value (all data)
0.0441
0.1002
0.0259
0.0709
1
2
final wR(F ) value (all
data)
2
goodness of fit on F
ρmin/ρmax/rms/e·Å−
1.000
0.972
3
−0.419/0.643/0.068
−0.265/0.515/0.05
3
9
Multipolar refinement
this way were used to perform QTAIM partitioning with the AIMAll
package. Atomic and molecular polarizabilities were then estimated
no. of data in refinement
F > 4σ(F)
4443/3739
196
9393/9206
360
4
0,41
using PolaBer,
which calculates numerical derivatives of the
no. of refined
parameters
electric dipole moment with respect to the applied field. So obtained
polarizabilities allowed more accurate reconstruction of molecular
polarizabilities.
final R value
0.024
0.019
(
F > 4σ(F))
final R value (all data)
final Rw(F) value
goodness-of-fit on F
N /N
0.036
0.024
1.217
19.08
0.021
0.025
1.904
25.57
3
. RESULTS AND DISCUSSION
3.1. Structural Details. Crystal structures, based on
conventional crystal structure analysis, of both co-crystals
ref
v
1
,8
−4
−4
max shift/esd in last
cycle
< 10
< 10
have been previously reported. Packing schemes for both co-
crystals are given in Figure 1. The crystal structure of
OXALUREA is built of layers, where molecules are held
together by a 2D hydrogen bond network. To develop the third
dimension, dipolar interactions of CO···CO type are
formed between urea and oxalic acid molecules. In the case of
MALUREA structure layers are observed where molecules of
ρmin/ρmax/rms/e·Å−
3
−0.199/0.194/0.046
−0.164/0.156/0.034
a
Configuration S of the malic acid molecule was determined from the
absolute structure of the crystal of its zinc salt, space group P2 , Flack
1
72
parameter −0.006(7).
malic acid form helices of 2 symmetry due to H-bonds, in
which the O−H group of the carboxylic group is a donor, and
the oxygen atom of the hydroxyl group is an acceptor of
symmetry constraints were applied. The expansion/contraction
parameters κ and κ′ parameters were employed for carbon, nitrogen,
and oxygen atoms. The expansion/contraction parameters of hydro-
1
C
DOI: 10.1021/acs.cgd.5b01253
Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design
Article
Figure 2. Molecular graphs based on experimental data, showing bond
paths and bond critical points in (a) OXALUREA and (b)
MALUREA. Red small spheres indicate the (3,−1) bond critical
points in ρ(r). Symmetry code: (i) −x, −y, −z.
the differences between values of charge density and Laplacian
at the BCP of CO bonds in both urea molecules (C5O51
and C3O3). This could be correlated with changed positions
of BCPs along the bond path with respect to the isolated urea
molecule. Those dissimilarities between O3 and O51 atoms
reflect their distinct hydrogen bond acceptor abilities. Subtle
bonding features in the regions of lone pairs on carbonyl
oxygen atoms can be seen on the static deformation density
maps of urea molecules (Figure 3). In both cases two lobes are
present at an angle higher than 120°, which is in agreement
with previously reported analysis of electron density distribu-
Figure 1. Crystal packing of (a) OXALUREA along [001] and (b)
MALUREA along [010]. Asymmetric units of both co-crystals are
labeled (for clarity of the drawing some of hydrogen atoms were not
labeled). Hydrogen bonds between molecules are marked with cyan
color.
hydrogen bond. Helices are connected via O−H···O and N−
H···O hydrogen bonds with urea molecules building layers
parallel to (100). The layers are linked into a 3D framework by
weak hydrogen bonds of C−H···O type.
43
tion around the carbonyl oxygen. The distribution of electron
density on both O3 and O51 atoms indicates preferences of the
urea molecule to form planar patterns of hydrogen bonds rather
than out of plane HB systems. The existence of intramolecular
interactions causes a slight redistribution of charge on the
carbonyl bond paths which could be seen on Laplacian profiles
along OC bonds (Figure 4a,b). An isolated molecule of urea
(black line) is compared with the urea molecule taken from the
crystal structures of MALUREA and OXALUREA (blue line
experimental and red line theoretical data). As expected,
lengthening of the CO bond is observed when going from
the isolated molecule to the co-crystal which is an effect of O3
and O51 acting as acceptors of two hydrogen bonds each. This
coincides with a decrease of ρ(r) at the BCP and an increase of
charge accumulation showed by the more negative values of
3.2. Electron Density and Topology of Chemical
Bonding. The validity of multipolar refinement was estab-
lished by plotting residual density maps for each co-crystal (see
Figure S1 in SI). Observed residuals are low and without
systematic features and the analysis of the residual density
4
2
according to Meindl & Henn results in a Gaussian
distribution for both cases (see Figure S2 in SI).
Both experimental and theoretical results, obtained from
multipolar refinements, have been used to characterize the
quantitative aspects in terms of electron density and Laplacian
values at bond critical points within molecules. Molecular
graphs representing bond paths and positions of BCPs for both
co-crystals are given in Figure 2. Since we are interested in the
differences between urea molecules depending on accompany-
ing dicarboxylic acid, the topological characteristics of covalent
bonds in urea molecules are given in Table 3. Key aspects are
2
∇ ρ(r) at the BCP. By comparing results from multipolar
refinements of charge density it is evident that the values of
D
DOI: 10.1021/acs.cgd.5b01253
Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design
Article
a
Table 3. Topological Analysis of Covalent Bonds in Urea Molecules, in Both Cocrystals
2
ρ(r)
∇ ρ(r)
Rij
d1
d2
λ1
λ2
λ3
ε
OXALUREA
0.48
C5−O51
2.64
−36.54
−26.71
−26.37
−22.04
−27.86
−21.06
−41.31
−23.94
−36.04
−23.41
−37.86
−23.31
−38.84
−25.34
1.26
1.26
1.34
1.34
1.35
1.35
1.02
1.02
1.02
1.02
1.02
1.02
1.02
1.02
0.78
0.79
0.78
0.77
0.77
0.76
0.76
0.74
0.76
0.74
0.77
0.74
0.74
0.73
−26.21
−21.42
−21.80
−19.69
−20.57
−19.29
−31.65
−26.56
−29.39
−26.32
−31.41
−26.59
−30.99
−27.05
−21.81
−19.51
−15.52
−15.66
−17.24
−15.26
−30.31
−24.66
−28.12
−24.75
−29.65
−24.73
−28.92
−25.10
11.48
14.22
10.95
13.31
9.94
0.20
0.10
0.40
0.26
0.19
0.26
0.04
0.08
0.05
0.06
0.06
0.07
0.07
0.08
2
.52
2.35
.31
2.30
.24
2.20
.13
2.14
.12
2.20
.09
2.29
.15
0.47
C5−N51
0.56
2
0.57
C5−N52
0.57
2
0.58
13.49
20.65
27.27
21.46
27.65
23.20
28.01
21.07
26.81
H511−N51
H512−N51
H521−N52
H522−N52
0.25
2
0.28
0.25
2
0.28
0.24
2
0.27
0.28
2
0.28
MALUREA
0.46
C3−O3
2.56
.47
2.33
.30
2.33
.27
2.21
.09
2.24
.08
2.27
.11
2.26
−35.16
−26.14
−32.48
−22.95
−33.18
−21.55
−36.31
−25.49
−36.06
−24.06
−36.41
−24.05
−34.74
−24.40
1.27
1.27
1.34
1.34
1.34
1.34
1.02
1.02
1.02
1.02
1.02
1.02
1.02
1.02
0.82
0.80
0.85
0.77
0.84
0.77
0.76
0.75
0.75
0.74
0.75
0.74
0.76
0.74
−23.77
−20.64
−20.94
−19.52
−20.48
−19.15
−30.69
−26.95
−30.54
−26.48
−30.87
−26.63
−30.64
−26.69
−22.19
−18.56
−16.99
−15.32
−17.06
−14.88
−29.24
−25.20
−28.78
−24.48
−29.31
−24.58
−29.11
−24.80
10.80
13.05
5.44
0.07
0.11
0.23
0.27
0.20
0.29
0.05
0.07
0.06
0.08
0.05
0.08
0.05
0.08
2
0.48
C3−N31
0.48
2
0.56
11.89
4.37
C3−N32
0.50
2
0.57
12.47
23.63
26.66
23.26
26.90
23.76
27.15
25.00
H312−N31
H322−N32
H311−N31
H321−N32
0.26
2
0.27
0.26
2
0.27
0.26
2
0.28
0.26
2
.11
0.27
27.09
−5
a
−3
2
−5
ρ(r)/e·Å , ∇ ρ(r)/e·Å , R /Å, d ,d - distance between BCP and atoms 1 and 2, respectively /Å, ε - ellipticity, λ λ λ /e·Å , G(r ) and V(r )
ij
1
2
1, 2,
−5
3
CP
CP
−
5
are local kinetic and local potential energy density (e·Å ), respectively, E(r ) is electronic local energy density (e·Å ). Abramov’s expression was
CP
7
3
used to obtain local kinetic and potential energy densities. Values in italics refer to periodic (CRYSTAL09) calculations.
2
ρ(r) and ∇ ρ(r) at the BCP are considerably lower from
theoretical studies than the ones obtained directly from the
experimental data. This is especially profound for OXALUREA
where the BCPs are more shifted toward the oxygen atom as a
result of the formation of a strong hydrogen bond of O−H···O
type.
values of the Laplacian of electron density at all BCPs. The
relation between local kinetic energy density G(r ) and
cp
distance R as well as potential energy densities V(r ) and R
ij
cp
ij
46
show exponential dependence. Both conditions for a positive
interpenetration of van der Waals spheres of the donor and
acceptor atoms are fulfilled: Δr > Δr and Δr + Δr > 0
H
A
H
A
3
.3. Analysis of Hydrogen Bonding. 3.3.1. Topological
(Table 5). Ultimately, it has been proven that all four Koch and
Popelier’s criteria are met, what confirms unambiguously the
existence of hydrogen bonds in both co-crystals (Table 4).
Energetic criteria based on analysis of local potential and
kinetic energy densities show that hydrogen bonds in both co-
Analysis of Electron Density. A full QTAIM analysis was
carried out on all experimental and theoretical electron density
models of OXALUREA and MALUREA. Topological proper-
ties at the hydrogen bonds BCPs in both co-crystals are listed in
44
Table 4 and shown in Figure 5. Koch and Popelier criteria
crystals (Table 4) show either closed shell character (|V(r )|/
cp
were applied to distinguish between hydrogen bonds and van
G(r ) < 1 E(r )/ρ(r ) > 0) or are intermediate between
cp
cp
cp
der Waals interactions.
The first four criteria can be successfully evaluated from the
closed and shared shell interactions with E(r ) < 0, |V(r )|/
cp
cp
G(r ) > 1, and E(r )|/ρ(r ) < 0.
cp cp cp
45
experimental charge density analysis. First criterion enforces
the existence of a bond path between hydrogen bond donor
and hydrogen bond acceptor. To fulfill second criterion a
nonzero charge density has to be evaluated at the BCP, and a
third criterion deals with positive value of the Laplacian at the
BCP and its correlation with the interaction energies. Fourth
criterion indicates that a mutual penetration of the hydrogen
atom and an acceptor atom has to take place for a hydrogen
bond to be formed.
The strongest hydrogen bond is that of O12−H12···O3 in
OXALUREA formed between oxalic acid and urea molecules. It
could be classified as an intermediate between closed and
shared shell with H12 shifting toward O3 atom. A covalent
contribution to the bond can be considered as a charge transfer
from H12−O12 bond of oxalic acid molecule to O3 atom of
urea as seen in Figure 6. Similar situation has been found for
the dimers of oxalic acid. The strong hydrogen bond formed
between two oxalic acid molecules has been classified as charge
delocalization assisted hydrogen bond. The charge redistrib-
ution over O−H···O bond has been a result of two σ and π
47
Analysis of the topology of ρ(r) for the examined weak
interactions revealed nonzero charge densities and positive
E
DOI: 10.1021/acs.cgd.5b01253
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Crystal Growth & Design
Article
−
−3
Figure 3. Static deformation electron densities of urea molecule for OXALUREA (a, c) and MALUREA (b, d). Isosurfaces are drawn at ±0.1 e ·Å .
Red and blue colors indicate negative and positive regions of electron density, respectively.
Figure 4. Laplacian profiles along OC bonds for urea molecule in (a) OXALUREA, (b) MALUREA. Blue and red lines represent experimental
and theoretical data, respectively. For the purpose of comparison black line stands for OC bond profile in isolated molecule of urea. Points
represent BCPs.
contributions to the bonding. Charge concentration around
H12 atom spreads between valence shell concentration of the
two oxygen atoms O12 and O3 (Figure 5b). A small region of
charge depletion is found between O3 and H12 atoms. A
similar situation can be found in other organic co-crystals
containing oxalic acid, i.e., O1−H1···N1 hydrogen bond in
The topological analysis of electron density indicated also the
presence of very weak hydrogen bonds of C−H···O type in the
co-crystal of MALUREA. Those interactions are observed
between the methylene group and oxygen atom of the hydroxyl
group of L-malic acid: C2−H2A···O3(−x, y − 1/2, −z) and
C2−H2B···O42(−x, y + 1/2, −z) and provide a full picture of
hydrogen bonding in the discussed co-crystal. The electron
densities and Laplacians are found to be very small (see Table
4), and the BCP properties classify them as pure closed shell
interactions, as expected.
48
isonicotinamide oxalic acid adduct. In MALUREA a slight
discontinuity in charge concentration can be also observed for
the O42−H42 bond (Figure 5e). According to the energetic
criteria only four hydrogen bonds in MALUREA show
intermediate character between shared and closed shell
interactions (|V(r )|/G(r ) > 1, although they can all be
3.3.2. Hirshfeld Surface Analysis. To facilitate the discussion
on intermolecular contacts in both co-crystals, Hirshfeld
cp
cp
4
9
50
classified as moderate hydrogen bonds.
surfaces were generated using CrystalExplorer. The
F
DOI: 10.1021/acs.cgd.5b01253
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Article
G
DOI: 10.1021/acs.cgd.5b01253
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Crystal Growth & Design
Article
Figure 5. Experimental Laplacian maps in the area of hydrogen bonds in OXALUREA and MALUREA. Contours are at logarithmic intervals in −
2
−5
∇
−
ρ(r) e·Å . Symmetry codes: (a) x − 1, −y − 1/2, z − 1/2; (b) −x + 2, −y + 1, −z + 1; (c) −x, y − 1/2, −z + 1; (d) −x + 1, y − 1/2, −z + 1; (e)
x + 1, y + 1/2, −z + 1; (f) −x + 1, y + 1/2, −z; (g) −x + 1, y − 1/2, −z.
Hirshfeld surface provides a unique signature for a molecule
within crystal structure and gives a measure of the portion of a
surface characterizing the range of a particular interaction. In
Figure 7a,b Hirshfeld surfaces of urea molecules from
experimental data are mapped with normalized contact distance
In the co-crystal of oxalic acid and urea, a rather unusual
dipolar interaction of CO···CO type is present and differs
significantly from the examples showed in the literature. So far,
carbonyl···carbonyl interactions were characterized between
molecules of the same type, whereas in the case of OXALUREA
those interactions occur between different molecules. Such a
behavior may come from the fact that the urea molecule is
somehow competitive with oxalic acid in the formation of a 3D
structure. The geometry of carbonyl and amine group of urea
“mimics” carboxylic group of oxalic acid, and, for example,
when a 2D layer is formed, no characteristic dimers of oxalic
acid are formed but pairs of urea and oxalic acid (see Figure
1a). The CO···CO interaction therefore acts as a “glue”
between those 2D layers built of strong hydrogen bond
networks (see Figure S5 in SI). Mutual arrangement of urea
and oxalic acid molecules involved in this “gluing” process,
shown in Figure 8a, and the geometrical parameters given in
Table 6, indicates that this pattern corresponds to type II
antiparallel arrangement introduced by Allen et al. Clearly,
since this motif is formed between different molecules, the
bond lengths of carbonyl groups vary, and therefore the
distances between neighboring carbon and oxygen atoms are
different; nevertheless they are within the limits of C···O
contacts, being less than 3.5 Å long (see Table 6). However,
although the geometrical requirements for forming the
antiparallel motif are fulfilled, the topological analysis of
electron density indicated the presence of only one bond
5
1
dnorm
,
which combines the external (from the point on the
surface to the atom outside the surface) and internal (from the
point on the surface to the atom inside the surface) distances
from the Hirshfeld surface to the nearest nucleus. Those plots
together with histograms, which reflect the relative contribution
of each interaction type in the crystal structure (Figure 7c,d),
indicate that the most dominant interaction in both co-crystals
is a hydrogen bond of X−H···O type (where X = N, O). In the
case of OXALUREA the percentage contribution of those
interactions is 45.9%, whereas for MALUREA is 55%. Other
interactions are also present including quite a significant
amount of nondirectional H···H contacts which may result for
example from interactions between neighboring amine groups
of urea molecules (2.25−2.35 Å), interactions between CH and
55
CH groups in MALUREA, or as in OXALUREA they may
2
occur as a result of specific planar HB network, which forces
relatively short distances between hydrogen atoms (2.46−2.5
Å). Fingerprint plots of urea are given in SI in Figure S4.
3
.4. CO···CO Interactions in OXALUREA. Carbon-
yl···carbonyl interactions have been a subject of many studies
mainly in the area of small biologically active molecules,
proteins, and protein−ligand complexes.
52−57
Allen and co-
5
5
workers identified those interactions as belonging to three
different types: perpendicular (type I), antiparallel (type II),
and sheared parallel (type III) (see Scheme 1 together with
Table 6). The contribution of those noncovalent interactions to
the molecular assembling was shown to be comparable to
moderate hydrogen bonds, and the interactions themselves may
determine three-dimensional crystal packing or as in the case of
critical point between C1 of oxalic acid and O3(x−1, y, z) of
2
urea molecule. The ρ
and ∇ ρ
values at BCP are 0.06
BCP
BCP
(0.04) e·Å− and 0.60 (0.55) e·Å , respectively. The
interaction is considered to be pure closed-shell as the ratio
of |V(r )|/G(r ) is found to be 0.75 and G(r )/ρ(r ) is 0.61.
3
−5
cp
cp
cp
cp
In Figure 8b,c we have shown the deformation density
isosurface in the close vicinity of both carbonyl oxygen atoms
O11 and O3. The distribution of electron density on atom O11
58
proteins they can stabilize the secondary structure motifs.
H
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Article
o
o
Table 5. Mutual Penetration in Terms of Nonbonded Radii (r , r ) and Bonded Radii (r , r ) of Hydrogen and Acceptor
Atoms
A
H
A
H
a
rA
rAo
OXALUREA
1.52
rHo
ΔrH
ΔrA
ΔrH + ΔrA
rH
b
H311···O11
0.67
1.21
1.23
1.29
1.30
1.24
1.26
1.02
1.04
1.33
1.35
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
0.53
0.54
0.48
0.47
0.51
0.53
0.70
0.72
0.40
0.40
0.85
0.86
0.80
0.79
0.83
0.85
1.02
1.04
0.72
0.72
1.38
1.40
1.28
1.26
1.34
1.38
1.72
1.76
1.12
1.12
0
.66
0.72
.73
0.69
.67
0.50
.48
0.80
.80
1.52
1.52
1.52
1.52
1.52
1.52
1.52
1.52
1.52
H322···O11
0
c
H312···O3
0
H12···O3
0
d
H321···O12
0
MALUREA
H521···O11
H511···O11
H522···O41
H521···O12
0.83
.88
0.76
.82
0.78
.80
0.97
.02
0.53
.51
0.55
.54
0.66
.72
0.59
.61
1.03
.06
0.99
.95
1.37
1.35
1.34
1.32
1.34
1.36
1.42
1.39
1.06
1.07
1.11
1.12
1.35
1.30
1.13
1.12
1.40
1.39
1.38
1.45
1.52
1.52
1.52
1.52
1.52
1.52
1.52
1.52
1.52
1.52
1.52
1.52
1.52
1.52
1.52
1.52
1.52
1.52
1.52
1.52
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
1.20
0.37
0.32
0.44
0.38
0.42
0.40
0.23
0.18
0.67
0.69
0.65
0.66
0.54
0.48
0.61
0.59
0.17
0.14
0.21
0.25
0.69
0.64
0.76
0.70
0.74
0.72
0.55
0.50
0.99
1.01
0.97
0.98
0.86
0.80
0.93
0.91
0.49
0.46
0.53
0.57
1.06
0.96
1.20
1.08
1.16
1.12
0.78
0.68
1.66
1.70
1.62
1.64
1.40
1.28
1.54
1.50
0.66
0.60
0.74
0.82
0
0
e
f
0
1
g
H42···O51
0
h
H12···O3
0
g
H512···O41
0
e
H3O···O51
0
i
H2B···O42
1
j
H2A···O3
0
a
Top line refers to experimental values, bottom line (italics) to theoretical values from periodic calculations. The non-bonded radii of hydrogen
acceptors were taken as the gas phase van der Waals radii and the corresponding bonding radii were taken as distances from the BCPs to nuclei.
b
−3
2
−5
ρ(r)/e·Å , ∇ ρ(r)/e·Å , R /Å, d ,d −distance between BCP and atoms 1 and 2, respectively /Å, ε - ellipticity, G(r ) and V(r ) are local kinetic
ij
1
2
CP
CP
−3
−3
c
d
and local potential energy density (e·Å ), respectively, E(r ) is electronic local energy density (e·Å ). x + 1,−y + 3/2, z + 1/2. −x + 2,−y + 1,
−
CP
e
f
g
h
i
j
z + 1. −x, −y, −z. −x + 1, y + 1/2, −z. −x + 1, y + 1/2, −z. −x + 1, y − 1/2, −z + 1. −x + 1, y − 1/2, −z. −x, y + 1/2, −z.
time involved in the formation of the strongest hydrogen bond
(
O12−H12···O3) and the carbonyl interaction with neighbor-
ing carbon atom C1 of oxalic acid. Nonetheless, in order to
confirm this rather unexpected result coming from the
topological analysis of electron density we have analyzed the
existence of CO···CO interactions by means of a
5
9,60
noncovalent interactions (NCI) approach.
The NCI
analysis provides a descriptor which enables visualization of
regions of space involved in either attractive or repulsive
interactions and depends on reduced electron density gradient
(RDG) defined as
Figure 6. Static deformation of electron density (a) and Laplacian of
electron density (b) in the area of charge delocalization assisted
hydrogen bond, O12−H12···O3, in OXALUREA. For electron density
maps positive (red lines) and negative (blue lines) contours are drawn
|∇ρ(r)|
s(r) =
1/3
4/3
−
3
2(3π) ρ(r)
at intervals 0.05 e·Å , whereas for Laplacian contours are at
2
−5
logarithmic intervals in −∇ ρ(r) e·Å .
where ∇ρ(r) is a gradient of electron density. Scatterplots of
s(r) against ρ(r) address noncovalent interaction and for those
contacts in a low-gradient and low-density region characteristic
spikes are present, which are absent in the case of covalent
(
not involved in CO···CO interaction, Figure 8b) shows
that both lone pairs are only involved in the formation of
hydrogen bonds; no electron excess regions of the oxygen atom
face deficiency regions of neighboring carbon atom. In the case
of atom O3 (Figure 8c), one of the lone pairs is at the same
bonds. Additionally the sign of second eigenvalue (λ ) of
2
Hessian matrix of electron density is taken into account and
provides an information whether identified noncovalent
I
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Figure 7. Hirshfeld surfaces of urea in OXALUREA (a) and MALUREA (b) mapped with dnorm; percentage contribution to the Hirshfeld surfaces of
various intermolecular interactions in OXALUREA (c) and MALUREA (d).
Scheme 1. Carbonyl···Carbonyl Interactions: (a)
Table 6. Geometries of Noncovalent Dipolar Interactions of
a
Perpendicular Motif, (b) Antiparallel Motif, (c) Sheared
CO···CO Type
a
Parallel Motif
b
b
b
c
Motif I
1.2
Motif II
1.2
Motif III
1.2
OXALUREA
1.27ur
.22ox
l1 (Å)
l2 (Å)
1
3.5
3.5
3.5
3.03 (C ...O )
ox
ur
3
.17 (C ...O )
ur ox
θ1 (deg)
75
15
180
90
0
90
90
90
90
0
90
90
55
55
0
88.7
98.2
82.0
89.2
17.3
θ2 (deg)
θ3 (deg)
θ4 (deg)
φ (C−O−C−O)
a
Experimental geometrical parameters from OXALUREA are
compared with idealized ones taken from the literature. Compare
b
55 c
Scheme 1. Idealized values given by Allen et al.
Experimental
values from this paper; ur refers to carbonyl group of urea, ox refers to
carbonyl group of oxalic acid.
a
l refers to the bond length of carbonyl groups, l refers to the
1
2
distance between interacting carbonyl groups.
interactions. Small disc-shaped regions denote strong intra-
molecular interactions within the oxalic acid molecule, whereas
broad multiform domain refers to carbonyl···carbonyl inter-
action which stabilizes the whole dimer. The shape and the area
of this surface suggest that not only C1···O3(x − 1, y, z)
interaction is present, but also C3(x − 1, y, z)···O11, which is
not observed via AIM. This might come from the fact that the
peak representing that interaction probably does not reach s(r)
= 0, so no critical point is associated with it, and therefore AIM
topology is somehow blind to this contact.
interaction is stabilizing (λ < 0) or destabilizing (λ > 0). In
2
2
other words, whereas the plots of s[ρ(r)·sign(λ )] recognize
the type of NCI, the amount of density itself gives the strength
of that interaction. Therefore, if a spike in the low-gradient,
2
low-density area at negative λ occurs, it indicates stabilizing
2
interaction like a hydrogen bond, when a smaller spike and
slightly negative λ are observed, the interaction is weakly
2
stabilizing, and finally when a spike is associated with positive
λ , no noncovalent interaction is present.
With the use of NCIPLOT, we examined the isosufrace of
s(r) (Figure 9a) and plots of s(r) versus ρ(r) multiplied by the
We have calculated the total interaction energy (Eint)
between urea and oxalic acid molecules involved in carbon-
yl···carbonyl interaction, as pairwise interaction energy between
neighboring molecules, where the dispersion and exchange-
repulsion terms were estimated using Williams and Cox
potential. The interaction seems to be relatively strong
since the value of Eint is −38.41 kJ/mol and could be compared
with the interaction through moderate hydrogen bond of N−
2
61
sign of λ (Figure 9b) for a dimer built of urea and oxalic acid
2
involved in CO···CO interactions. These plots were
generated by evaluating the B3LYP 6-311G** density and
reduced gradient on cuboid grids with 0.1 au step size. Three
domains of RDG indicated the presence of three noncovalent
62
J
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Figure 8. Carbonyl···carbonyl interaction in OXALUREA: (a) mutual arrangement of urea and oxalic acid molecules involved in the interaction
(
values of θ , θ , θ , and θ are given in Table 6); distribution of electron density around O11 (b) and O3 (c) atoms. Dark red and transparent blue
1
2
3
4
−
+
−. −3
indicate electron excess (δ ) and electron deficiency (δ ) regions, respectively. Isosurfaces are drawn at ±0.1 e Å . Symmetry codes: (a) x − 1, y, z;
(
b) x − 1, −y + 3/2, z + 1/2; (c) −x + 1, y − 1/2, z − 1/2; (d) −x + 1,−y + 1, −z.
the polarization by the crystal field was not taken into account
in the reported paper.
.5. Atomic and Molecular Polarizabilities. The
3
importance of the surroundings on urea molecules in reported
crystals can be also evaluated through the analysis of atomic
polarizabilities. Although in the literature there are other
6
4−66
models available for calculating atomic polarizabilities,
have chosen a procedure proposed by some of us,
we
4
0,41
which
enables calculation of distributed atomic polarizabilities based
on QTAIM partitioning of a ground state electron density ρ(r)
67,68
69
of a molecular system. Bader et al.
and later Keith showed
that every molecular polarizability tensor can be decomposed
into additive atomic contributions:
Na
α = ∑ α(Ω) = ∑ α (Ω) + α (Ω)
p
c
Ω=1
Since the atomic polarizabilities are numerical derivatives of
the corresponding atomic dipole moments with respect to the
relatively small external electric field ε , thus the components of
j
polarizability tensors can be calculated as
ε
0
j
μ (Ω) − μ (Ω)
i
i
α (Ω) = lim
ij
ε
εj
j
εj
i
where μ (Ω) is a dipole moment component of the atomic
basin Ω along the i direction computed with applied electric
field in j direction. The atomic dipole moment on the other
hand can be defined as
Figure 9. Gradient isosurfaces of s(r) (0.1 au) (a) and plots of the
reduced density gradient versus the electron density multiplied by the
sign of the second Hessian eigenvalue (b) for urea and oxalic acid
dimer involved in carbonyl···carbonyl interaction. Symmetry code: (i)
x − 1, y, z.
μ(Ω) = −∫Ω [r − R ]ρ(r) dr+
Ω
∑
[R − R (Ω|Ω′)]Q(Ω|Ω′)
Ω
63
b
H···O type between glycine molecules in a crystalline state.
Ω′
We have also compared the obtained value of interaction
energy with previously reported theoretical one for antiparallel
where Q(Ω|Ω′) is the charge contributed to atom Ω by the
5
5
motif. Allen and co-workers used intermolecular perturbation
theory calculations on isolated acetone dimer in order to study
the interaction energies in terms of the change of the distance
between interacting carbonyl groups. The interaction energy for
the distance of 3.02 Å was found to be −22.3 kJ/mol and is
bond to atom Ω′, R is the position vector of atom Ω with
Ω
respect to the arbitrary origin and R (Ω|Ω″) is the positional
b
vector of the BCP between atom Ω and Ω′. The first part of the
equation describes atomic polarization μ (Ω) term, whereas the
p
second part is the charge translation μ (Ω) component, so the
c
smaller (in absolute value) than E in OXALUREA, because
atomic dipole moment can be rewritten as
int
K
DOI: 10.1021/acs.cgd.5b01253
Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design
Article
Figure 10. Atomic polarizability ellipsoids (a) in OXALUREA, (b) in MALUREA, (c) in isolated urea molecules from gas phase calculations. Arrows
indicate direction of a hydrogen bond from donor to acceptor. Symmetry codes: (i) −x + 2, −y + 1, −z + 1; (ii) x + 1, −y + 3/2, z + 1/2; (iii) −x +
1, y + 1/2, −z + 1/2; (iv) −x + 1, y + 1/2, −z; (v) −x + 1, y + 1/2, −z + 1; (vi) −x + 1, −y + 1/2, −z + 1.
Figure 11. Electrostatic potential of urea molecules in OXALUREA (a, c) and MALUREA (b, d) mapped in projections on experimental and
−3
theoretical (periodic calculations) electron density surfaces at ρ(r) = 0.5 e·Å .
μ(Ω) = μ (Ω) + μ(Ω)
Details of the procedure are given in a paper by Krawczuk et
p
c
41
al. Atomic and molecular polarizability tensors are then
visualized as ellipsoids in the same 3D space as the molecule,
The atomic polarization term comes from the integration of
the dipolar density function within the atomic basin and is
taken directly from the partitioning of the electron density. The
charge translation term, on the other hand, is given by the
weighted sum of atomic charge translations from the atom’s
nucleus to each BCP connected to that atom. The sign and
value of the charge translation component strongly depend on
the nature and number of the groups bonded to the selected
atom and some constrains need to be introduced in order to
compute this variable.
3
assuming 1 Å ≡ 1 Å, though for visualization purposes we used
a scaling factor of 0.4 Å− to reduce the size of polarizability
2
ellipsoids.
In Figure 10 we have compared atomic polarizabilities of urea
molecule in OXALUREA (Figure 10a), MALUREA (Figure
0b) and from gas-phase calculations (Figure 10c). A number
1
of characteristic features of atomic polarizabilities can be
observed. As expected polarizability ellipsoids are strongly
elongated toward covalent bonds. The stronger the bond is, the
more prolated the ellipsoids are (compare for example CO
L
DOI: 10.1021/acs.cgd.5b01253
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Crystal Growth & Design
Article
with N−H bonds). Because urea molecules in OXALUREA
and MALUREA are involved in the formation of hydrogen
bond networks, it is also clear why some of the polarizability
ellipsoids are modified and reoriented toward hydrogen bond
directions. For example, nitrogen atoms are donors of HBs, and
therefore their ellipsoids seem to be flattened comparing to
corresponding ellipsoids in urea in isolated state. H atoms have
very small polarizabilities due to their low electron population;
nevertheless it is noticeable that their polarizability ellipsoids
are also reoriented toward acceptors of hydrogen bonds.
Calculated atomic/molecular polarizability tensors of urea,
oxalic acid and L-malic acid both in isolation and in crystal
structures are listed in Table S2 in SI.
our knowledge, this is the first manuscript describing electron
density distribution in co-crystals of urea and dicarboxylic acids.
Our main purpose was to investigate whether the presence of
different dicarboxylic acid influences significantly the electron
density distribution of urea molecule. The analysis revealed
only subtle changes between those two molecules and
consistency in intramolecular electronic structure and bonding
properties. The most meaningful differences were observed for
carbonyl groups of urea molecules. Both oxygen atoms are
acceptors of two hydrogen bonds; however their nature and
origin differ significantly. In the case of OXALUREA the
geometry of carbonyl and amine group of urea molecule acts as
it was the carboxylic group of oxalic acid, and as a result pseudo
dimers between oxalic and urea molecules are formed. The
hydrogen bond of O−H···O type between the acid and urea
molecules is classified as an intermediate between closed and
shared shell, and influences the most the electron distribution
of carbonyl group.
During our studies we have also identified remarkable
carbonyl···carbonyl interactions in OXALUREA. To the best of
our knowledge, it is the first report on dipolar CO···CO
interaction which occurs between heteromolecules. So far those
interactions were identified only between molecules of the
same type. Although all the geometrical requirements were
fulfilled in order to classify the arrangement as so-called
antiparallel motif, surprisingly the topological analysis of ED
identified only one of C···O interaction. We confronted that
rather unexpected result of AIM topology with the NCI
approach. By examination of the isosurface of reduced electron
density gradient we identified two C···O interactions, showing
that the AIM approach somehow fails to identify a certain weak
interactions.
The most interesting feature of atomic polarizabilities in urea
molecule is the behavior of carbonyl group CO. We have
70
compared the values of a bond polarizability, which is a
projection of atomic polarizabilities of carbon and oxygen
atoms along the CO bond, calculated with the use of
following formula:
T
αΩ−Ω′ = r ·(α + α )·r
ΩΩ′
Ω
Ω′ ΩΩ′
where rΩΩ′ is a unit vector in the direction of the Ω−Ω′ bond.
The bond polarizability of CO in OXALUREA is 19.75
3
Bohr , whereas in MALUREA the value is slightly higher, 21.10
3
Bohr . The difference comes from the fact that in OXALUREA
oxygen atom O3 is involved in very strong hydrogen bond of
O−H···O type (see section 3.3), which reorients the polar-
izability ellipsoid of O3 toward this strong interaction. The
deviation of the O3 ellipsoid’s axis αzz from the direction of
carbonyl bond is 11(1)°, whereas in MALUREA it is only
1
(1)°, which is in the limit of error.
3
.6. Electrostatic Potential. Electrostatic potential (ESP)
On the basis of the above observation of carbonyl interaction
in OXALUREA a question arises if this formation is
characteristic only for the reported structure or is it a more
general behavior present in co-crystals of urea and rigid
dicarboxylic acids. In order to get a complete answer, we plan
to perform accurate electron density studies on a series of
crystal structures where carbonyl interactions can be identified.
has been calculated based on experimental and theoretical
charge densities for both co-crystals and visualized with the
33
MoleCoolQT program. The electrostatic potential is very
useful to rationalize intermolecular interactions and plays a key
role in molecular recognition in a given system. In Figure 11 we
have shown electrostatic potential for the urea molecule in
OXALUREA and MALUREA. The most negative areas, ca.
−
1
−
0.1033 e·Å , are associated with the electronegative atoms,
ASSOCIATED CONTENT
Supporting Information
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.cgd.5b01253.
■
such as oxygen atoms, and indicate nucleophilic character,
whereas the highest positive regions, ca. 2.8943 e·Å , are
concentrated on hydrogen atoms of amine groups.
*
S
−1
The most pronounced difference of electrostatic potential is
observed on carbonyl oxygen atoms. The ESP on O51 in
MALUREA is evenly distributed around the atom, confirming
that syn positioned hydrogen bonds with L-malic acid are
equally strong. On atom O3 of OXALUREA, on the other
hand, quite pronounced anisotropy of potential is observed.
The electronic charge is displaced toward very strong hydrogen
bond with neighboring oxalic acid (O12−H12···O3), causing
depletion of the charge along the CO bond. What is also
worth noticing is the behavior of hydrogen atoms in both urea
molecules. In MALUREA hydrogen atoms of amine groups are
more electrophilic than the ones in OXALUREA, which
indicates their greater preference to form hydrogen bonds.
Figure S1 Final residual maps from experimental data for
both co-crystals. Figure S2 Fractal dimension distribution
of residual density plots. Figure S3 Static deformation
maps of dicarboxylic acids. Figure S4 Fingerprint plots of
Hirshfeld surfaces of urea in both co-crystals. Figure S5
2D layers in OXALUREA connected through carbonyl···
carbonyl interactions. Figure S6 Electrostatic potential of
dicarboxylic acids in OXALUREA and MALUREA.
Table S1 Full topological analysis of BCPs for oxalic
acid and L-malic acid. Table S2 Polarizability tensor for
urea, oxalic acid and L-malic acid, both in isolation and
taken from crystal structures (PDF)
Crystallographic information files (CIF1, CIF2)
4
. CONCLUSIONS
AUTHOR INFORMATION
Corresponding Author
*Tel. +48 12 6632059; fax: +48 12 6340515; e-mail:
krawczuk@chemia.uj.edu.pl.
In this paper we have analyzed the accurate electron density
distribution for two co-crystals, representing a case in which the
urea molecule either co-crystallizes with rigid dicarboxylic acid,
here oxalic acid, or flexible one, here L-malic acid. To the best of
■
M
DOI: 10.1021/acs.cgd.5b01253
Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design
Article
Funding
Multipole Refinement, Topological Analysis of Charge Densities and
Evaluation of Intermolecular Energies from Experimental and Theoretical
Structure Factors, 2006.
This work was partially supported by the Polish Ministry of
Science and Higher Education No. N204 124 32/3169. This
research was supported in part by PL-Grid Infrastructure.
(
2
(
28) Allen, F. H.; Bruno, I. J. Acta Crystallogr., Sect. B: Struct. Sci.
010, 66, 380−386.
29) Madsen, A. Ø. J. Appl. Crystallogr. 2006, 39, 757−758.
Notes
The authors declare no competing financial interest.
(30) Munshi, P.; Madsen, A.Ø.; Spackman, M. A.; Larsen, S.; Destro,
R. Acta Crystallogr., Sect. A: Found. Crystallogr. 2008, 64, 465−475.
(31) Hoser, A. A.; Dominiak, P. M.; Wozniak, K. Acta Crystallogr.,
Sect. A: Found. Crystallogr. 2009, 65, 300−311.
ACKNOWLEDGMENTS
■
We thank the X-ray Laboratory, Faculty of Chemistry,
Jagiellonian University, for making the Nonius KappaCCD
diffractometer available. We also thank Mr. Roberto Alvarez-
Boto for valuable hints in NCI analysis.
(
32) Volkov, A.; Abramov, Y. A.; Coppens, P. Acta Crystallogr., Sect.
A: Found. Crystallogr. 2001, 57, 272−282.
33) Hubschle, C.; Dittrich, B. J. Appl. Crystallogr. 2011, 44, 238−
240.
34) Volkov, A.; Koritsanszky, T.; Coppens, P. Chem. Phys. Lett.
2004, 391, 170−175.
35) Dovesi, R.; Orlando, R.; Civalleri, B.; Roetti, C.; Saunders, V. R.;
Zicovich-Wilson, C. M. Z. Kristallogr. - Cryst. Mater. 2005, 220, 571.
36) Dovesi, R.; Saunders, V. R.; Roetti, C.; Orlando, R.; Zicovich-
(
̈
(
REFERENCES
■
(
(
1) Harkema, S.; Ter Brake, J. H. M. Acta Crystallogr., Sect. B: Struct.
Crystallogr. Cryst. Chem. 1979, 35, 1011−1013.
(
(
2) Harkema, S.; Ter Brake, J. H. M.; Helmholdt, R. B. Acta
Crystallogr., Sect. C: Cryst. Struct. Commun. 1984, 40, 1733−1734.
3) Harkema, S.; Bats, J. W.; Weyenberg, A. M.; Feil, D. Acta
Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 1972, 28, 1646−
648.
4) Van Hummel, G. J.; Helmholdt, R. B. Acta Crystallogr., Sect. C:
Cryst. Struct. Commun. 1991, 47, 213−215.
5) Alhalaweh, A.; George, S.; Bostrom, D.; Velaga, S. P. Cryst.
Wilson, C. M.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N. M.;
Bush, I. J.; D’Arco, Ph.; Llunell, M. CRYSTAL09, User’s Manual;
University of Torino: Torino, 2009.
(
(
37) Munshi, P.; Guru Row, T. N. Acta Crystallogr., Sect. B: Struct. Sci.
006, 62, 612−626.
38) Munshi, P.; Thakur, T. S.; Guru Row, T. N.; Desiraju, G. R. Acta
Crystallogr., Sect. B: Struct. Sci. 2006, 62, 118−127.
39) Keith, T. A. AIMAll, Version 13.11.04; TK Gristmill Software:
Overland Park, KS, USA, 2013.
40) Krawczuk-Pantula, A.; Per
Trans. Am. Crystallogr. Assoc. 2011, 42, 1−25.
41) Krawczuk, A.; Perez, D.; Macchi, P. J. Appl. Crystallogr. 2014, 47,
452−1457.
42) Meindl, K.; Henn, J. Acta Crystallogr., Sect. A: Found. Crystallogr.
008, 64, 404−418.
43) Ahmed, M.; Jelsch, C.; Guillot, B.; Lecomte, C.; Domagała, S.
1
(
2
(
(
̈
(
Growth Des. 2010, 10, 4847−4855.
(6) Videnova-Adrabinska, V. J. Mater. Chem. 1995, 5, 2309−2311.
(7) Chadwick, K.; Davey, R.; Sadiq, G.; Cross, W.; Pritchard, R.
(
́
ez, D.; Stadnicka, K.; Macchi, P.
CrystEngComm 2009, 11, 412−414.
(
́
(
8) de Matos Gomes, E.; Venkataramanan, V.; Nogueira, E.; Belsley,
1
(
2
(
M.; Proenca, F.; Criado, A.; Dianez, M. J.; Estrada, M. D.; Perez-
Garrido, S. Synth. Met. 2000, 115, 225−228.
(
9) Meng, F.; Lu, M.; Yin, X.; Yu, W.; Wang, Y. Mater. Res. Bull.
1
(
996, 31, 1127−1131.
10) Kostyanovsky, R. G.; Kostyanovsky, V. R.; Kadorkina, G. K.
Mendeleev Commun. 2009, 19, 17−18.
11) Videnova-Adrabinska, V.; Etter, M. C. J. Chem. Crystallogr. 1995,
Cryst. Growth Des. 2013, 13, 315−325.
(
44) Koch, U.; Popelier, P. L. A. J. Phys. Chem. 1995, 99, 9747−9754.
(45) Farrugia, L. J.; Kocovsky, P.; Senn, H. M.; Vyskocil, S. Acta
(
Crystallogr., Sect. B: Struct. Sci. 2009, 65, 757−769.
46) Espinosa, E.; Molins, E.; Lecomte, C. Chem. Phys. Lett. 1998,
85, 170−173.
47) Mitoraj, M. P.; Kurczab, R.; Boczar, M.; Michalak, A. J. Mol.
Model. 2010, 16, 1789−1795.
48) Schmidtmann, M.; Farrugia, L. J.; Middlemiss, D. S.; Gutmann,
M. J.; McIntyre, G. J.; Wilson, C. C. J. Phys. Chem. A 2009, 113,
2
(
(
5, 823−829.
(
2
(
12) Custelcean, R. Chem. Commun. 2008, 295−307.
13) Nangia, A. In Organic Crystal Engineering: Frontiers in Crystal
Engineering; Tiekink, E. R. T.; Vittal, J.; Zaworotko, M., Eds.; Wiley:
New York, 2010; pp 151−187.
(
(
14) Dixit, V.; Vanishri, S.; Bhat, H.; de Matos Gomes, E.; Belsley,
M.; Santinha, C.; Arunmozhi, G.; Venkataramanan, V.; Proena, F.;
1
(
(
3985−13997.
Criado, A. J. Cryst. Growth 2003, 253, 460−466.
49) Spackman, D.; Jayatilaka, D. CrystEngComm 2009, 11, 19−32.
(
15) Lu
16), 1392−1395.
16) Lu, M. K.; Meng, F. Q.; Yang, H.; Yu, T.; Zeng, H. Cryst. Res.
̈
, M.; Meng, F.; Zeng, H.; Yu, W. Chin. Sci. Bull. 1996, 41
50) Wolff, S. K.; Grimwood, D. J.; McKinnon, J. J.; Turner, M. J.;
(
Jayatilaka, D.; Spackman, M. A. CrystalExplorer (Version 3.1);
University of Western Australia, 2012.
(
̈
Technol. 1996, 31 (7), 833−836.
(
(
(
51) McKinnon, J. J.; Jayatilaka, D.; Spackman, M. A. Chem.
Commun. 2007, 3814−3816.
(52) Burgi, H. B.; Dunitz, J. D.; Shefter, E. Acta Crystallogr., Sect. B:
17) Krawczuk, A.; Macchi, P. Chem. Cent. J. 2014, 8 (68), 1−15.
18) Bader, R. F. W. Atoms in Molecules. A Quantum Theory;
Clarendon Press: Oxford, UK, 1990.
̈
(
(
(
19) Zyss, J.; Ledoux, I. Chem. Rev. 1994, 94, 77−105.
20) COLLECT; Nonius BV: Delft, The Netherlands, 1997.
21) Otwinowski, Z.; Minor, W. Methods in Enzymology, Vol. 276,
Struct. Crystallogr. Cryst. Chem. 1974, 30, 1517−1527.
(53) Taylor, R.; Mullaley, A.; Mullier, G. W. Pestic. Sci. 1990, 29,
197−213.
Macromolecular Crystallography; Carter, C. W., Jr.; Sweer, R. M.,
Eds.; Elsevier: Amsterdam, 1997; Part A, 307.
(54) Gavezzotti, A. J. Phys. Chem. 1990, 94, 4319−4325.
(55) Allen, F. H.; Baalham, C. A.; Lommerse, J. P. N.; Raithby, P. R.
Acta Crystallogr., Sect. B: Struct. Sci. 1998, 54, 320−329.
(56) Fischer, F. R.; Wood, P. A.; Allen, F. H.; Diederich, F. Proc. Natl.
Acad. Sci. U. S. A. 2008, 105, 17290−17294.
(
(
22) Blessing, R. H. J. Appl. Crystallogr. 1997, 30, 421−426.
23) Sheldrick, G. M. Acta Crystallogr., Sect. A: Found. Crystallogr.
2
(
008, 64, 112−120.
24) Macrae, C. F.; Bruno, I. J.; Chisholm, J. A.; Edgington, P. R.;
(57) Choudhary, A.; Gandla, D.; Krow, G. R.; Raines, R. T. J. Am.
Chem. Soc. 2009, 131, 7244−7246.
McCabe, P.; Pidcock, E.; Rodriguez-Monge, L.; Taylor, R.; van de
Streek, J.; Wood, P. A. J. Appl. Crystallogr. 2008, 41, 466−470.
(58) Maccallum, E. H.; Poet, R.; Milner-White, E. J. J. Mol. Biol.
1995, 248, 361−373.
(59) Johnson, E. R.; Keinan, S.; Mori-Sanchez, P.; Contreras-Garcia,
́ ́
(25) Farrugia, L. J. J. Appl. Crystallogr. 1999, 32, 837−838.
(26) Hansen, N. K.; Coppens, P. Acta Crystallogr., Sect. A: Cryst. Phys.,
Diffr., Theor. Gen. Crystallogr. 1978, 34, 909−921.
27) Volkov, A.; Macchi, P.; Farrugia, L. J.; Gatti, C.; Mallinson, P.;
Richter, T.; Koritsanszky, T. XD2006: A Computer Program Package for
J.; Cohen, A. J.; Yang, W. J. Am. Chem. Soc. 2010, 132, 6498−6506.
(60) Contreras-Garcia, J.; Yang, W.; Johnson, E. R. J. Phys. Chem. A
2011, 115, 12983−12990.
(
́
N
DOI: 10.1021/acs.cgd.5b01253
Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design
Article
(
61) Contreras-Garcia,
Piquemal, J.-P.; Beratan, D. N.; Yang, W. J. Chem. Theory Comput.
011, 7, 625−632.
62) Williams, D. E.; Cox, S. R. Acta Crystallogr., Sect. B: Struct. Sci.
984, 40, 404−417.
63) Dominiak, P. M.; Espionosa, E.; Angyan
́
J.; Johnson, E. R.; Keinan, S.; Chaudret, R.;
2
(
1
(
́
́
, J. G. In Modern Charge
Density Analysis; Gatti, C., Macchi, P., Eds; Springer: Dordrecht, 2012;
Chapter 11, pp 387−433.
(
(
(
(
64) Applequist, J. Acc. Chem. Res. 1977, 10, 79−85.
65) Thole, B. T. Chem. Phys. 1981, 59, 341−350.
66) Stone, A. J. Mol. Phys. 1985, 56, 1065−1082.
67) Bader, R. F. W.; Keith, T. A.; Gough, K. M.; Laidig, K. E. Mol.
Phys. 1992, 75, 1167−1189.
68) Bader, R. F. W.; Larouche, A.; Gatti, C.; Carroll, M. T.;
MacDougall, P. J.; Wiberg, K. B. J. Chem. Phys. 1987, 87, 1142−1152.
69) Keith, T. A. In The Quantum Theory of Atoms in Molecules: From
(
(
Solid State to DNA and Drug Design; Matta, C. F., Boyd, R. J., Eds.;
Wiley-WCH: Weinheim, 2007; Chapter 3, pp 61−95.
(
70) Macchi, P.; Krawczuk, A. Comput. Theor. Chem. 2015, 1053,
1
(
3
(
65−172.
71) Flack, H. D. Acta Crystallogr., Sect. A: Found. Crystallogr. 1983,
9, 876−881.
72) Reed, A. T.; Karipides, A. Acta Crystallogr., Sect. B: Struct.
Crystallogr. Cryst. Chem. 1976, 32, 2085−2088.
73) Abramov, Y.; Volkov, A.; Wu, G.; Coppens, P. Acta Crystallogr.,
Sect. A: Found. Crystallogr. 2000, 56, 585−591.
(
O
DOI: 10.1021/acs.cgd.5b01253
Cryst. Growth Des. XXXX, XXX, XXX−XXX