Structural analysis and multipole modelling of quercetin monohydrate--a quantitative and comparative study.

TL;DR: This quantitative and comparative study shows that in the absence of high-resolution diffraction data, the database transfer approach can be applied to the multipolar electron density features very accurately.

Abstract: The multipolar atom model, constructed by transferring the charge-density parameters from an experimental or theoretical database, is considered to be an easy replacement of the widely used independent atom model. The present study on a new crystal structure of quercetin monohydrate [2-(3,4-dihydroxyphenyl)-3,5,7-trihydroxy-4H-chromen-4-one monohydrate], a plant flavonoid, determined by X-ray diffraction, demonstrates that the transferred multipolar atom model approach greatly improves several factors: the accuracy of atomic positions and the magnitudes of atomic displacement parameters, the residual electron densities and the crystallographic figures of merit. The charge-density features, topological analysis and electrostatic interaction energies obtained from the multipole models based on experimental database transfer and periodic quantum mechanical calculations are found to compare well. This quantitative and comparative study shows that in the absence of high-resolution diffraction data, the database transfer approach can be applied to the multipolar electron density features very accurately.

Summary

Introduction

• Structural Science publishes papers in structural chemistry and solid-state physics in which structure is the primary focus of the work reported, also known as Acta Crystallographica Section B.
• The multipolar atom model, constructed by transferring the charge-density parameters from an experimental or theoretical database, is considered to be an easy replacement of the widely used independent atom model.
• The present study on a new crystal structure of quercetin monohydrate [2-(3,4- dihydroxyphenyl)-3,5,7-trihydroxy-4H-chromen-4-one monohydrate], a plant flavonoid, determined by X-ray diffraction, demonstrates that the transferred multipolar atom model approach greatly improves several factors: the accuracy of atomic positions and the magnitudes of atomic displacement parameters, the residual electron densities and the crystallographic figures of merit.

2.1. Crystallization, data collection and data reduction

• Quercetin dihydrate (CAS number 6151-25-3) purchased as a powder from Sigma–Aldrich was dissolved at 233 K in acetonitrile.
• The solution was left overnight to slowly cool down to room temperature.
• Analysis and multipole modelling Acta Cryst. (2011).
• Services for accessing these data are described at the back of the journal.
• The multi-scan absorption correction was applied in the scaling procedure.

2.3. Theoretical calculations

• Upon energy convergence ( E ’ 10 6), a periodic wavefunction based on optimized geometry was obtained.
• The index generation scheme proposed by Le Page & Gabe (1979) was applied to generate 18 404 unique Miller indices up to 1.2 Å 1 reciprocal resolution.
• The ADPs of the H atoms were scaled according to Ueq of the carrying atoms (URATIO restraint) in an analogous way to SHELX (Sheldrick, 2008).
• This restrained model is referred to as the IAM_R model (Table 1).

2.5. Database transfer

• A total of 12 unique atom types from the extended ELMAM database were assigned to 35 atoms of quercetin monohydrate.
• The multipolar parameters (including and 0) were then transferred to the quercetin monohydrate structure resulting from the final IAM_R and IAM_UR models.
• The resulting model is referred to as TAAM_OPT (Table 1).
• For all TAAM models, constructed using the extended ELMAM database, the electron density of the non-H atoms was described up to octupolar level, while for H atoms it was described only for the bond-directed quadrupole (q3z2 1) and Acta Cryst. (2011).
• ‘Empirical absorption correction using spherical harmonics was implemented in the SCALE3 ABSPACK scaling algorithm.’.

2.6. Theoretical modelling

• The MoPro package was used to perform the multipolar refinement (based on F) against the whole set of generated theoretical structure factors.
• The corresponding model is referred to as THEO_OPT (Table 1).
• The scale factor was fixed to the absolute value (1.0).
• An independent ( , 0) set was defined for the H6 atom as initial theoretical refinements showed dissimilar values.
• The same type and number of restraints and weighting scheme as used for other restrained models were also applied in this model.

2.7. Electrostatic interaction energy

• All the electrostatic interaction energy computations were performed with VMoPro, part of the MoPro package, using the numerical integration method on a spherical grid around selected atoms.
• The Gauss–Chebyshev (Becke, 1988) and Lebedev & Laikov (1999) quadratures were used for the radial and angular parts, respectively.
• Radial coordinates and weights were remapped using the formula of Treutler & Ahlrichs (1995).
• The integrations involved 100 radial and 434 angular quadrature points.
• Interaction energies were calculated between pairs of neighboring molecules in contact, for which two atoms were separated by a distance lower than or equal to the sum of their van der Waals radii.

3.1. Crystal structure

• Here the authors report the structure of a new hydrate form of quercetin crystallized in the monoclinic centrosymmetric space group P21/c with Z = 4 determined from X-ray diffraction data.
• Analysis and multipole modelling Acta Cryst. (2011).
• There are two structure determinations of quercetin dihydrate which have been previously published (Rossi et al., 1986; Jin et al., 1990).
• The majority of these are O—H O contacts, the dominating hydrogen bonds in this crystal structure (Table 5), rather than C—H O contacts.
• Further quantitative and qualitative analyses of intermolecular contacts based on their topological properties derived using Bader’s (1990, 1998) QTAIM (quantum theory of atoms in molecules) approach are discussed in a later section.

3.2. Improvement over spherical atom model

• In this section the authors draw comparisons between IAM_R versus TAAM_R and IAM_UR versus TAAM_UR models.
• This means that X—H distances obtained from the IAM_UR model are very much shortened when compared with neutron distances – a common observation in conven- tional X-ray structure analysis.
• A higher dissimilarity is observed for the C atoms than for the O atoms.
• It is apparent from Fig. 6 that the IAM_R model overestimates the displacement parameters for the C atoms in the plane of the molecule where covalent bonding occurs.
• The final refinement statistics listed in Table 3 suggest that the TAAM_R model is equally good or slightly better than the TAAM_THEO_R model.

3.3. Charge density analyses

• The deformation electron density and the derived oneelectron properties based on the TAAM_OPT and THEO_OPT models are compared quantitatively.
• To facilitate a better comparison and to avoid the influence of using different atomic positions, both models were constructed based on the optimized structure of the quercetin monohydrate.

3.4. Deformation electron densities

• The static deformation electron-density maps of the quercetin molecule are shown in Fig. S3 for both TAAM_OPT and THEO_OPT models (the water molecule is shown in Fig. S4).
• The grids were prepared in the following way.
• Fig. 8 shows the deformation electron density for the hydroxyl group O3—H3 in the plane bisecting the C—O—H triplet of atoms.
• The TAAM_OPT deformation electrondensity map in Fig. 8(a) appears to be slightly smeared and attenuated compared with the THEO_OPT model (Fig. 8b).
• In their study Farrugia et al. (2009) also observed that the electron lone pairs of similar O atoms are almost merged.

3.5. Topology of covalent bonds

• The topological description of the electron density at the bond-critical points (BCPs) in quercetin monohydrate for TAAM_OPT and THEO_OPT models is presented in Table 70 Sławomir Domagała et al.
• Analysis and multipole modelling Acta Cryst. (2011).
• The high discrepancy of the (rCP) and r2 (rCP) values for the carbonyl group may be connected to the higher uncertainty on the multipolar parameters of the O4 atom in the TAAM_OPT model.
• A smaller number of atoms were indeed available to build the average values in the databank for this aromatic carbonyl O-atom type.
• Additionally, the authors have analysed the relative agreement between the models in terms of the reliability factor R(p) of property p defined as RðpÞ ¼ X pTAAM OPT pTHEO OPT .X pTAAM OPT : ð3Þ.

3.6. Topology of intra- and intermolecular contacts

• Quantitative analysis of intra- and intermolecular interactions were performed in terms of the topology of the electron density.
• These interactions include contacts of the O C and C C type with separations ranging from 3.2 to 3.6 Å.
• In this context it is to be noted that the analyses may not necessarily be correlated as those two approaches are based on different partitioning schemes.
• For the TAAM_OPT and THEO_OPT models the topological properties of the electron density of intra- and intermolecular interactions are found to agree well.
• The largest discrepancies in (rCP) and r2 (rCP) values are observed for the six strongest hydrogen bonds (dH O < 1.9 Å).

3.7. Electrostatic interaction energies

• In the crystal lattice the quercetin molecule is in direct contact with 19 neighbouring entities (including water molecules).
• Pairs marked by A–H and I–M letters denote quercetin quercetin and quercetin water interactions.
• The sum over all interaction contacts is also given, with a weight of 12 for the involutional symmetry dimers (non duplicates).
• The values of the corresponding electrostatic interaction energies for the TAAM_OPT and THEO_OPT models are given in Table 7.
• The greatest difference in electrostatic interaction energy of 13 kJ mol 1 (14% in relative value) is noticed for the pair marked with ‘H’.

3.8. Electrostatic potentials

• The three-dimensional electrostatic potential (ESP) envelopes for the quercetin molecule mapped on the 0.0067 e Å 3 (0.001 e bohr 3) isosurface of the electron density are shown in Fig. 12.
• The most prominent difference is seen in the region of the catechol ring (C11–C16 and C2 atoms), which displays more negative ESP in the TAAM_OPT model.
• In order to quantify the ESP distribution in the quercetin molecule, the ESP surface quantities were calculated, as proposed by Politzer and co-workers (Murray & Politzer, 1998; Murray et al., 2000).
• All the notations used here to describe the quantities are from their original papers.
• A comparison of different surface quantities resulted in similar values for the TAAM_OPT and THEO_OPT models.

3.9. Atomic charges and dipole moments

• The distribution of atomic charges in quercetin monohydrate, derived from the Hansen–Coppens (Hansen & Coppens, 1978) multipole formalism, for the TAAM_OPT and THEO_OPT models are listed in Table S6.
• The largest deviations between the two models are visible for the O4 atom and the C atoms of the C5–C10 ring of the benzopyran moiety.
• The direction of the dipole moments for the two models is found to deviate by 27 (Fig. S9).
• Nevertheless, their orientations follow the general distribution of the electrostatic potential as seen in Fig. 12.
• The authors also verified the values of dipole moments for the water molecule.

4. Concluding remarks

• This work was initiated with the aim of representing the transferred experimental multipolar atom model as an easy and better replacement for the widely used IAM.
• Indeed the present study on a new crystal structure of quercetin monohydrate determined from X-ray diffraction data convincingly demonstrates that the extended ELMAM database transfer approach greatly improves several factors, such as atomic positions, thermal motions and residual electron densities, when these were compared with the corresponding IAM.
• The Hirshfeld surface analysis of intermolecular contacts confirmed that the O—H O hydrogen bonds are the dominating contacts in this structure.
• This is not surprising as the charge-density parameters of the transferred model were obtained from a database of experimentally derived electron densities and the diffraction data are contaminated by some measurement errors and atomic thermal motion.
• The authors thank Dr Catherine Humeau for helpful discussions and for the quercetin sample.

Figures

Figure 2 ORTEP diagram of quercetin monohydrate at 110 K with 90% probability ellipsoids showing (a) the atomic labelling scheme and (b) the S12 similarity index (Whitten & Spackman, 2006) values. The ellipsoid diagrams from (a) IAM_R and (b) TAAM_R models were generated using ORTEPIII (Johnson & Burnett, 1996; Farrugia, 1997).

Figure 8 Static deformation electron-density maps in the plane of the lone pairs of O3 and O1W atoms. Maps show the deformation electron density in the region of the hydroxyl group for (a) TAAM_OPTand (b) THEO_OPT models, and of the water molecule for (c) THEO_OPT. Blue solid lines and red dashed lines denote positive and negative contours. Contour level at 0.05 e Å 3. Zero contours are shown in yellow dashed lines.

Figure 11 Representation of the unique contacts between the pairs formed by the quercetin molecule and the neighbouring molecules, including the water molecules.

Figure 12 Electrostatic potential mapped on the 0.0067 e Å 3 (0.001 e bohr 3) isosurface of the electron density in the quercetin molecule for (a) TAAM_OPTand (b) THEO_OPT models. The maximum negative (blue) and positive (red) values of the ESP correspond to 0.08 and 0.08 e Å 1 values. The view was generated using the program Pymol (DeLano, 2002).

Table 4 Comparison of selected torsion angles for quercetin monohydrate and dihydrate structures.

Figure 3 Molecular packing in the quercetin monohydrate structure showing the AABB stacking pattern. Quercetin and water molecules are highlighted in green and dark blue colours. This figure is in colour in the electronic version of this paper.

Figure 7 Difference static deformation electron-density map (THEO_OPT TAAM_OPT) models in the plane of the quercetin molecule. Blue solid lines and red dashed lines denote positive and negative contours, respectively. Contour level: 0.05 e Å 3. The zero contours are shown as yellow dashed lines.

Table 7 Electrostatic interaction energies (kJ mol 1) between interacting pairs of molecules shown for the TAAM_OPT and THEO_OPT models.

Figure 10 Laplacian [r2 (r)] maps of representative interactions from (a) TAAM_OPTand (b) THEO_OPT models. Blue (dashed) and red (solid) lines represent positive and negative values. Contours are drawn at 2m 10n e Å 5 (m = 1, 2, 3; n = 3, 2 . . . ) levels. Maps are plotted in the plane containing atoms C9, C8 and C11.

Figure 9 Laplacian [r2 (r)] maps of representative C—H O and O—H O hydrogen bonds from (a) TAAM_OPTand (b) THEO_OPTmodels. Blue (dashed) and red (solid) lines represent positive and negative values. Contours are drawn at 2m 10n e Å 5 (m = 1, 2, 3; n = 3, 2 . . . ) levels. Maps are plotted in the plane containing atoms O13, O7 and O1W.

Figure 4 The ‘fishing net’ pattern of quercetin monohydrate. View along the c axis.

Figure 5 Relative contributions of the intermolecular contacts in the quercetin monohydrate structure using Hirshfeld surface analysis. The chart is based on the IAM_R model.

Table 5 Intra- and intermolecular contacts obtained from the IAM_R model of quercetin monohydrate.

Table 1 Summary of the atom models.

Figure 1 Chemical structure of quercetin monohydrate.

Table 6 Topological properties of the electron density for the intra- and intermolecular contacts in the quercetin monohydrate for the TAAM_OPT (first entry) and THEO_OPT (second entry in italics) models.

Figure 6 PEANUT (Hummel et al., 1990) representations of the ADP differences between the IAM_R and TAAM_R restrained models. The root meansquare displacement difference surfaces are shown on a scale of 6:15. The positive differences appear in blue, while the negative ones are in red. H atoms were omitted as their displacement parameters were restrained to those of the carrying atoms. An equivalent orientation to the ORTEP plot was selected.

Full text

electronic reprint
Acta Crystallographica Section B
Structural
Science
ISSN 0108-7681
Editor: Carolyn P. Brock
Structural analysis and multipole modelling of quercetin
monohydrate – a quantitative and comparative study
Sławomir Domagała, Parthapratim Munshi, Maqsood Ahmed, Benoˆıt
Guillot and Christian Jelsch
Acta Cryst.
(2011). B67, 63–78
Copyright
c
 International Union of Crystallography
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For further information see http://journals.iucr.org/services/authorrights.html
Acta Crystallographica Section B: Structural Science
publishes papers in structural chem-
istry and solid-state physics in which structure is the primary focus of the work reported.
The central themes are the acquisition of structural knowledge from novel experimental
observations or from existing data, the correlation of structural knowledge with physico-
chemical and other properties, and the application of this knowledge to solve problems
in the structural domain. The journal covers metals and alloys, inorganics and minerals,
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Acta Cryst.
(2011). B67, 63–78 Sławomir Domagała
et al.
· Analysis and multipole modelling

research papers
Acta Cryst. (2011). B67, 63–78 doi:10.1107/S0108768110041996 63
Acta Crystallographica Section B
Structural
Science
ISSN 0108-7681
Structural analysis and multipole modelling of
quercetin monohydrate – a quantitative and
comparative study
Sławomir Domagała,
Parthapratim Munshi, Maqsood
Ahmed, Benoı
ˆ
t Guillot and
Christian Jelsch*
Laboratoire de Cristallographie, Re
´
sonance
Magne
´
tique et Mode
´
lizations (CRM2), CNRS,
UMR 7036, Institut Jean Barriol, Faculte
´
des
Sciences et Techniques, Nancy Universite
´
,BP
70239, 54506 Vandoeuvre-le
`
s-Nancy CEDEX,
France
Correspondence e-mail:
christian.jelsch@crm2.uhp-nancy.fr
# 2011 International Union of Crystallography
Printed in Singapore – all rights reserved
The multipolar atom model, constructed by transferring the
charge-density parameters from an experimental or theore-
tical database, is considered to be an easy replacement of the
widely used independent atom model. The present study on a
new crystal structure of querceti n monohydrate [2-(3,4-
dihydroxyphenyl)-3,5,7-trihydroxy-4H -chromen-4-one mono-
hydrate], a plant flavonoid, determined by X-ray diffraction,
demonstrates that the transferred multipolar atom model
approach greatly improves several factors: the accuracy of
atomic positions and the magnitudes of atomic displacement
parameters, the residual electron densities and the crystal-
lographic figures of merit. The charge-density features,
topological analysis and electrostatic interaction energies
obtained from the multipole models based on experimental
database transfer and periodic quantum mechanical calcula-
tions are found to compare well. This quantitative and
comparative study shows that in the absence of high-
resolution diffraction data, the database transfer approach
can be applied to the multipolar electron density features very
accurately.
Received 13 July 2010
Accepted 16 October 2010
1. Introduction
Quercetin is a naturally occurring flavonoid pigment fou nd in
coloured leafy vegetables, herbs and fruits. This biologically
active compound has gained immense attention from the
research community due to its medicinal properties. It is
reported to possess anticancer (ElAttar & Virji, 1999),
antithrombotic (Gryglewski et al. , 1987), antioxidant (Lamson
& Brignall, 2000) and antimicrobial (Formica & Regelson,
1995; Gatto et al., 2002) properties. Recent rese arch supports
the idea that quercetin may be helpful for patients with
chronic prostatitis with interstitial cystitis possibly because of
its action as a mast cell inhibitor (Shoskes et al., 1999). The
presence of quercetin along with other flavonols in our daily
diet is also reported to be associated with a reduced risk of
fatal pancreatic cancer in tobacco smokers (No
¨
thlings et al.,
2007).
Charge-density analysis of accurate high-resolution single-
crystal X-ray diffraction data is now a matured branch of
modern crystallography, published in a variety of jour nals,
focusing on an ever-increasing range of inorganic, organo-
metallic, organic and biological materials (Coppens, 1997;
Spackman, 1997; Koritsa
´
nszky & Coppens, 2001; Munshi &
Guru Row, 2005a). This technique has now reached a level at
which the experimentally derived electron density can be
compared with the charge density obtained from high-level
theoretical calculations. Experimental and theoretical charge
densities can be used to analyse a range of problems of
chemical (Coppens, 1997) and physical (Tsirelson & Ozerov,
electronic reprint

1996) interest since the charge density is a physically obser-
vable quantity. One of the most exciting applications of charge
density analysis is the eval uation of one-electron properties in
molecular crystals (Spackman, 1992).
Bader’s Quantum Theory of Atoms In Molecules (QTAIM)
is an ultimate approach to studying the topological features of
the charge-density distribution (Bader, 1990, 1998). Topolo-
gical analysis via the QTAIM approach is capable of providing
the information about the existence and the nature of
hydrogen bonds. The eight criteria suggested by Koch and
Popelier (Koch & Popelier, 1995; Popelier, 2000; hereafter
referred as KP) based on QTAIM allow a hydrogen bond to
be distinguished from a van der Waals interaction. In this
study we focus on the first four of the criteria.
The possibility of using previously extracted electron-
density parameters within Hirshfeld’s (1971) aspherical
formalism in crystallographic modelling was first realised by
Brock et al. (1991). This work was followed by Pichon-Pesme
et al. (1995), resulting in the construction of the first experi-
mental database of peptide and amino-acid fragments, called
the experimental library of multipolar atom models
(ELMAM) based on the Hansen–Coppens (Hansen &
Coppens, 1978) multipolar formalism. Two more aspherical
atom libraries based on the same formalism but using
computed electron densities were also constructed: University
at Buffa lo Pseudoatom Databank (UBDB; Volkov et al., 2004)
and the Invariom database (Dittrich et al., 2004). All three
libraries are in continuous development and were revised
several times. ELMAM was updated in 2004 (Pichon-Pesme et
al., 2004), UBDB in 2007 (Dominiak et al., 2007) and Invariom
was improved in 2006 (Dittrich, Hu
¨
bschle et al., 2006). The
advantages of using aspherical atom databases in routine
crystallographic modelling were pointed out in several studies
(Jelsch et al., 1998, 2005; Dittrich et al., 2005, 2007, 2008;
Dittrich, Hu
¨
bschle et al., 2006, 2009; Dittrich, Stru
¨
mpel et al.,
2006; Dittrich, Weber et al., 2009; Volkov et al., 2007; Zarychta
et al., 2007; Ba˛k et al., 2009 ). Improvements to the residual
electron density, geometrical parameters and atomic displa-
cement parameters have been thoroughly discussed. More-
over, some of the databases were also used to compute the
electrostatic interaction energies between host–guest protein
complexes (Dominiak et al., 2009; Fournier et al., 2009).
The ELMAM database ha s been extended from protein
atom types to common organic molecules and is based on the
optimal local coordinate systems (Domagała & Jelsch, 2008).
New chemical en vironments (atom types) can be easily added
to the database when new charge-density diffraction data
become publicly available. Details of the construction of this
extended database will be published in a separate paper. In
this work we present the application of the extended database
for the multipolar atom modelling of quercetin monohydrate
(Fig. 1). The most important features of the modelled electron
density of this compound are discussed and are the subject of a
detailed comparison with the theoretical multipole model
based on periodic quantum mechanical calculations. All the
atom models discussed here are summarized in Table 1. The
charge-density parameters transferred to quercetin are
described in the CIF files in the supplementary material.
1
2. Experimental and theoretical details
2.1. Crystallization, data collection and data reduction
Quercetin dihydrate (CAS number 6151-25-3) purchased as
a powder from Sigma– Aldrich was dissolved at  233 K in
acetonitrile. The solution was left overnight to slowly cool
down to room temperature. Yellow crystals of prismatic shape
were crystallized from the solution. A crystal of size 0.35 
research papers
64 Sławomir Domagała et al.

Analysis and multipole modelling Acta Cryst. (2011). B67, 63–78
Figure 1
Chemical structure of quercetin monohydrate.
Table 1
Summary of the atom models.
Model Description
IAM_R xyz, ADPs and scale factor refined versus experimental
structure factors
X—H distances, angles involving H atoms and ADPs of
the H atoms restrained
IAM_UR xyz, ADPs and scale factor refined versus experimental
structure factors
ADPs of the H atoms restrained
TAAM_R xyz, ADPs and scale factor refined versus experimental
structure factors
X—H distances, angles involving H atoms and ADPs of
the H atoms restrained
Multipolar parameters transferred from the extended
database
TAAM_UR xyz, ADPs and scale factor refined versus experimental
structure factors
ADPs of the H atoms
Multipolar parameters transferred from the extended
database
TAAM_OPT Optimized geometry used
Multipolar parameters transferred from the extended
database
THEO_OPT Optimized geometry used
Multipolar parameters refined versus theoretical struc-
ture factors
 and 
0
parameters for some H atoms restrained
TAAM_THEO_R xyz, ADPs and scale factor refined versus experimental
structure factors
X—H distances, angles involving H atoms and ADPs of
the H atoms restrained
Multipolar parameters transferred from the THEO_OPT
model
1
Supplementary data for this paper are available from the IUCr electronic
archives (Reference: GW5011). Services for accessing these data are described
at the back of the journal.
electronic reprint

0.19  0.16 mm was selec ted for the experiment. Data
collection was performed using an Oxford Diffraction Super-
Nova Dual Wavelength Microfocus diffractometer equipped
with an ATLAS CCD detector. Reflections were collected at
110 K up to sin / =0.63A
˚
1
resolution using Cu radiation.
Data were collected using 91 ! runs, with a 1.0

scan width and
15 s per frame exposure time, resulting in a total of 4921
frames. The average redundancy was 6.7. Indexing, integration
and scaling were performed with CrysAlisPro, Version 1.171
(Oxford Diffraction, 2009). In total, 39 962 reflections were
measured and then merged to 2652 unique reflections. The
multi-scan absorption correction was applied in the scaling
procedure. Further details of the data collection and red uction
are given in Table 2.
2.2. Spherical atom refinements
Structure solution and the initial stages of refinement were
carried out using SHELX97 (Sheldrick, 2008) with full-matrix
least-squares and based on F
2
. The final refinements on F were
performed using the MoPro package (Guillot et al., 2001;
Jelsch et al., 2005).
2.3. Theoretical calculations
Periodic quantum mechanical calculations using
CRYSTAL06 (Dovesi et al. , 2008) were performed for the
crystal structure obtained from X-ray diffraction and, using
this as a starting point, full geometry optimization was
performed using density functional theory (DFT; Hohenberg
& Kohn, 1964) and with the B3LYP hybrid functional (Lee et
al., 1988; Becke, 1993) using the 6-31G(d,p) basis set (Hari-
haran & Pople, 1973). Upon energy conver-
gence (E ’ 10
6
), a periodic wavefunction
based on optimized geometry was obtained.
The index generation scheme proposed by Le
Page & Gabe (1979) was applied to generate
18 404 unique Miller indices up to 1.2 A
˚
1
reciprocal resolutio n. Option XFAC of the
CRYSTAL06 program was then used to
generate a set of theoretical structure factors
from the computed electron density and using
a set of prepared indices.
2.4. Experimental modelling
Initially the quercetin monohydrate struc-
ture was modelled using the independent atom
model (IAM) approximation. Atomic displa-
cement parameters (ADPs), positions (xyz
coordinates) and the scale factor were refined
with the appropriate weighting scheme and
restraints. X—H (where X = C or O) distances
were shifted and restrained to the average
neutron diffraction distances (Allen et al.,
1987, 2006). Angles involving C—H bonds
were also restrained using similarity restraints.
The ADPs of the H atoms were scaled
according to U
eq
of the carrying atoms (URATIO restraint) in
an analogous way to SHELX (Sheldrick, 2008). This
restrained model is referred to as the IAM_R model (Table 1).
Further, restraints on the distances and angles were released
from IAM_R, while the URATIO restraints were maintained.
This partially unrestrained mode l is referred to as IAM_UR
(Table 1).
2.5. Database transfer
A total of 12 unique atom types from the extended
ELMAM database were assigned to 35 atoms of quercetin
monohydrate. For some atoms, the same atom type was
selected (see Table S1 of the supplementary material). The
multipolar parameters (including  and 
0
) were then trans-
ferred to the quercetin monohydra te structure resulting from
the final IAM_R and IAM_UR models. The corresponding
transferred aspherical atom models (TAAM) are referred to
as TAAM_R and TAAM_UR (Table 1). Subsequently, the
charge-density par ameters were kept fixed and the ADPs,
atomic positions and the scale factor were refined until
convergence was reached. The same weighting scheme and
restraints were applied as in the IAM_R and IAM_UR
models. Further, the multipolar parameters from the extended
ELMAM database were transferred to the set of coordinates
obtained from the optimized quercetin monohydrate struc-
ture. The resulting model is referred to as TAAM_OPT (Table
1).
For all TAAM models, constructed using the extended
ELMAM database, the electron density of the non-H atoms
was described up to octupolar level, while for H atoms it was
described only for the bond-directed quadrupole (q
3z
2
1
) and
research papers
Acta Cryst. (2011). B67, 63–78 Sławomir Domagała et al.

Analysis and multipole modelling 65
Table 2
Experimental details.
For all structures: C
15
H
10
O
7
H
2
O, M
r
= 320.24, monoclinic, P2
1
/c, Z = 4. Experiments were carried
out at 110 K with Cu K radiation using a SuperNova, Dual, Cu at zero, Atlas diffractometer.
Absorption was corrected for by multi-scan methods. ‘Empirical absorption correction using
spherical harmonics was implemented in the SCALE3 ABSPACK scaling algorithm.’ Refinement
was on 256 parameters with 29 restraints. H-atom parameters were constrained.
IAM_R TAAM_R TAAM_THEO_R
Crystal data
a, b, c (A
˚
) 8.737 (1), 4.852 (1), 30.160 (1)
 (

) 95.52 (1)
V (A
˚
3
) 1272.6 (3)
 (mm
1
) 0.138
Crystal size (mm) 0.35  0.19  0.16
Data collection
T
min
, T
max
0.672, 1.000
No. of measured, independent and
observed [I >2.0(I)] reflections
69 706, 2652, 2565
R
int
0.017
Refinement
R[F
2
>2(F
2
)], wR(F
2
), S 0.039, 0.054, 2.19 0.020, 0.028, 1.11 0.020, 0.027, 1.11
No. of reflections 2652 2652 2652

max
, 
min
(e A
˚
3
) 0.39, 0.24 0.14, 0.16 0.15, 0.18
Computer programs used: CrysAlisPro (Oxford Diffraction, 2009), SHELXL97 (Sheldrick, 2008), MoPro
(Jelsch et al., 2005).
electronic reprint

dipole (d
z
) components along with the monopole function.
After transfer, the resulting excess charge for the quercetin
monohydrate was 0.765 e (0.022 e per atom on average).
Therefore, the quercetin molecule and water molecule were
neutralized separately, using the charge-scaling procedure of
Faerman & Price (1990).
2.6. Theoretical modelling
The MoPro package was used to perform the multipolar
refinement (based on F) against the whole set of generated
theoretical structure factors. The corresponding model is
referred to as THEO_OPT (Table 1). The non-H atoms were
modelled up to the octupolar level. All H atoms were refined
with one dipole d
z
component, except the H atoms connected
to the O atoms for which a quadrupole q
3z
2
1
component was
also refined. The scale factor was fixed to the absolute value
(1.0). To consider a static model, the U
ij
tensor elements were
set to zero. During the refinement only valence and multipole
populations, and  and 
0
parameters were allowed to refine,
but no atomic positions were refined. No restraints/constraints
were imposed on any atoms, except  constraints on the H
atoms. In particular, one set of  and 
0
parameters was used
for all H atoms of the hydroxyl groups and a separate (, 
0
)
set was used for H atoms bound to the C atoms. An inde-
pendent (, 
0
) set was defined for the H6 atom as initial
theoretical refinements showed dissimilar values. However,
the final  and 
0
values of the H6 atom [1.149 (5) and 1.36 (1)]
were very simil ar to those of other H atoms [1.162 (3) and
1.35 (1)] bound to the C atoms. The H atoms of the water
molecule shared a fourth set of  and 
0
parameters. In order
to keep both molecules neutral and to allow better comparison
with the transferred model, during the refinement no charge
transfer was allowed between the quercetin and the water
molecule.
Additionally, the multipolar parameters from the
THEO_OPT model were transferred to the IAM_R model
and only the ADPs, atomic positions and the scale factor were
re-refined against the experimentally observed reflections. The
same type and number of restraints and weighting scheme as
used for other restrained models were also applied in this
model. The corresponding model is referred to as
TAAM_THEO_R (Table 1).
2.7. Electrostatic interaction energy
All the electrostatic interaction energy computations were
performed with VMoPro, part of the MoPro package, using
the numerical integration method on a spherical grid around
selected atoms. The Gauss–Chebyshev (Becke, 1988) and
Lebedev & Laikov (1999) quadratures were used for the
radial and angular parts, respectively. Radial coordinates an d
weights were remapped using the formula of Treutler &
Ahlrichs (1995). The integrations involved 100 radial and 434
angular quadrature points. Interaction energies were calcu-
lated between pairs of neighboring molecules in contact, for
which two atoms were separated by a distance lower than or
equal to the sum of their van der Waals radii.
The interaction energy values were computed as an integral
over the electron density (obtained from the multipolar
refinement) of molecule A multiplied by the electrostatic
potential of molecule B, or reciprocally
E
elec
¼
Z

A
’
B
dr
A
¼
Z

B
’
A
dr
B
: ð1Þ
3. Results and discussions
3.1. Crystal structure
Here we report the structure of a new hydrate form of
quercetin crystallized in the monoclinic centrosymmetric
space group P2
1
/c with Z = 4 determined from X-ray
diffraction data. In the present case quercetin crystallized with
one water molecule in the asymmetric unit. The structural
details and the statistical parameters from the spheric al atom
refinement of X-ray diffraction data are listed in Tables 2 and
research papers
66 Sławomir Domagała et al.

Analysis and multipole modelling Acta Cryst. (2011). B67, 63–78
Figure 2
ORTEP diagram of quercetin monohydrate at 110 K with 90%
probability ellipsoids showing (a) the atomic labelling scheme and (b)
the S
12
similarity index (Whitten & Spackman, 2006) values. The ellipsoid
diagrams from (a) IAM_R and (b) TAAM_R models were generated
using ORTEPIII (Johnson & Burnett, 1996; Farrugia, 1997).
electronic reprint

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Structural analysis and multipole modelling of quercetin monohydrate – a quantitative and comparative study" ?

Copyright c © International Union of Crystallography Author ( s ) of this paper may load this reprint on their own web site or institutional repository provided that this cover page is retained. Republication of this article or its storage in electronic databases other than as specified above is not permitted without prior permission in writing from the IUCr. For further information see http: //journals. iucr. org/services/authorrights. 

Q2. What is the transferability approximation for the electron density?

The transfer provides values for the electron-density derived properties (dipole moments, electrostatic potentials and electrostatic interaction energies) only within a transferability approximation. 

Q3. Why was no charge transfer allowed between the hydroxyl groups?

In order to keep both molecules neutral and to allow better comparison with the transferred model, during the refinement no charge transfer was allowed between the quercetin and the water molecule. 

Q4. What is the way to estimate the accuracy of the predicted properties?

To estimate the accuracy of the predicted properties, analysis of a greater sample of the transferred electron-density parameters for several molecules is required. 

Q5. What is the deviation from the neutron mean distances?

The deviation from the neutron mean distances, defined as dmodel dneutron, is smaller than 1 neut for O—H and 2.6 neut for C—H bonds in TAAM_UR. 

Q6. What are the limitations of the transferred model?

note the limitations of the transferred model, which does not take into account atom polarization owing to local chemical environments. 

Q7. What is the correlation coefficient for the TAAM_OPT model?

The electron lone pairs of the O atom are separated by three contour levels in the THEO_OPT model, whereas for the TAAM_OPT model the lone pairs are separated by only one contour level. 

Q8. What are the parameters of the quercetin monohydrate?

The calculated 13C shielding parameters and bond-order parameters indicate that the quercetin monohydrate with syn conformation is the favoured one (Olejniczak & Potrzebowski, 2004). 

Q9. What is the c axis of the fishing net?

While viewed down the c axis, the molecules are found to intersect each other almost perpendicularly (inter-planarangle 85 ) to form the parallel stripes of the ‘fishing net’ running along the a axis (Fig. 4). 

Q10. What is the dihedral angle between the benzopyran rings and the catechol?

In the case of the quercetin dihydrate structure, the dihedral angle (O1—C2— C11—C16) between the benzopyran rings and the catechol ring is 175.0 (anti orientation). 

Q11. What is the role of the water molecule in the formation of three-dimensional networks?

The water molecule bridging the same type of molecule (AA and BB) via O—H O and C—H O hydrogen bonds plays a major role in the formation of three-dimensional networks (Table 5). 

Q12. What is the similarity index for the two ADP tensors?

2. This index, introduced by Whitten & Spackman (2006), is expressed as S12 = 100(1 R12), where R12 describes the overlap between probability density functions for the two ADP tensors U asR12 ¼ Z ½p1 xð Þp2 xð Þ 1=2 d3x ¼ 23=2 det U 11 U 1 21=4 det U 11 þU 12 1=2 : ð2ÞTherefore, the similarity index can be used to describe the percentage difference of two probability density functions. 

Q13. What is the difference between the ADPs from the bonding density?

The introduction of multipolar parameters allows deconvolution of the ADPs from bonding density and improves the reliability of the displacement parameters (Brock et al., 1991; Jelsch et al., 1998).