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An improved experimental databank of transferable
multipolar atom models – ELMAM2. Construction
details and applications
Slawomir Domagala, Bertrand Fournier, Dorothee Liebschner, Benoit Guillot,
Christian Jelsch
To cite this version:
Slawomir Domagala, Bertrand Fournier, Dorothee Liebschner, Benoit Guillot, Christian Jelsch. An
improved experimental databank of transferable multipolar atom models – ELMAM2. Construction
details and applications. Acta Crystallographica Section A : Foundations and Advances [2014-..],
International Union of Crystallography, 2012, 68 (3), pp.337-351. �10.1107/S0108767312008197�. �hal-
01710503v2�
electronic reprint
ISSN: 2053-2733
journals.iucr.org/a
An improved experimental databank of transferable
multipolar atom models – ELMAM2. Construction details and
applications
Sławomir Domagała, Bertrand Fournier, Dorothee L iebschner, Benoˆıt
Guillot and Christian Jelsch
Acta Cryst.
(2012). A68, 337–351
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Acta Cryst.
(2012). A68, 337–351 Sławomir Domagała
et al.
· ELMAM2. Construction details and applications
Acta Cryst. (2012). A68, 337–351 doi:10.1107/S0108767312008197 337
research papers
Acta Crystallographica Section A
Foundations of
Crystallography
ISSN 0108-7673
Received 4 November 2011
Accepted 23 February 2012
# 2012 International Union of Crystallography
Printed in Singapore – all rights reserved
An improved experimental databank of transferable
multipolar atom models – ELMAM2. Construction
details and applications
Sławomir Domagała,
a,b
Bertrand Fournier,
a
Dorothee Liebschner,
a
Benoı
ˆ
t Guillot
a
and Christian Jelsch
a
*
a
Laboratoire de Cristallographie, Re
´
sonance Magne
´
tique et Mode
´
lisations (CRM2), CNRS, UMR
7036, Institut Jean Barriol, Faculte
´
des Sciences et Technologies, Nancy Universite
´
, BP 70239,
54506 Vandoeuvre-le
`
s-Nancy Cedex, France, and
b
Department of Chemistry, University of
Warsaw, Pasteura 1, 02-093 Warsaw, Poland. Correspondence e-mail:
christian.jelsch@crm2.uhp-nancy.fr
ELMAM2 is a generalized and improved library of experimentally derived
multipolar atom types. The previously published ELMAM database is restricted
mostly to protein atoms. The current da tabase is extended to common functional
groups encountered in organic molecules and is based on optimized local
axes systems taking into account the local pseudosymmetry of the molecular
fragment. In this approach, the symmetry-restricted multipoles have zero
populations, while others take generally significant values. The various
applications of the database are described. The deformation electron densities,
electrostatic potentials and interaction energies calculated for several tripep-
tides and aromatic molecules are calculated using ELMAM2 electron -density
parameters and compared with the former ELMAM database and density
functional theory calculations.
1. Introduction
Ultra-high-resolution X-ray diffraction crystallography is a
unique technique that allows one to obtain the experimental
distribution of the electron density in crystals. Charge-density
determination is now a mature branch of modern crystal-
lography with many publications in a variety of journals,
focusing on an increasing range of inorganic, organometallic,
organic and biological materials (Coppens, 1997; Spackman,
1997; Koritsanszky & Coppens, 2001; Munshi & Guru Row,
2005a). The electron-density distribution is frequently
modelled via the Hansen & Coppens multipolar model
(Hansen & Coppens, 1978), where the individual atomic
densities are described in terms of spherical core and valence
densities with an expansion of atom-centred real spherical
harmonic functions. Thus experim entally derived densities can
be compared with some success with the charge densities
obtained from high-level theoretical calculations, despite the
experimental errors and the approximations used in the
multipolar expansion model. A range of problems of chemical
and physical interest have been successfully resolved using this
technique (Spackman, 1992; Coppens, 1997; Tsirelson &
Ozerov, 1996). Unfortunately, because of the high demands of
the crystal quali ty and measurement conditions, the number of
publications involving new high-resolution structural studies
is rather limited. Owing to these constraints, the idea of
constructing the experimentally derived charge density has
emerged (Brock et al., 1991). This idea was quickly noticed
and the first database of experimentally obtained charge-
density parameters was constructed, ELMAM (Pichon-P esme
et al., 1995). Other initiatives have been undertaken to
construct such libraries from quantum-mechanical computa-
tions of selected small molecules. Two such libraries were
constructed: the University at Buffalo Pseudoatom Databank
(UBDB; Volkov et al., 2004; Dominiak et al., 2007) and the
Invariom database (Dittrich et al., 2004; Dittrich, Hu
¨
bschle et
al., 2006). Improvements to the residual electron density,
geometric parameters and atomic displacement parameters
when using database electron-density parameters have been
thoroughly discussed (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). The potential
applications of the databases to macromolecules (Muzet et al.,
2003; Guillot et al., 2008) and in the computations of elec-
trostatic interaction en ergies between host–guest protein
complexes were also investigated (Dominiak et al., 2009;
Fournier et al., 2009).
The ELMAM database has been extended from protein
atom types to common organic molecules. New chemical
environments (atom types) can be easily added to the data-
base when new charge-density diffraction data become
publicly available. The improv ed database hereafter referred
to as ELMAM2 is based on the optimal local coordinate
electronic reprint
systems (Domagała & Jelsch, 2008). The aim of the current
work is to present a thorough comparison of the improved
database with the previous experimental database as well as
with the AMBER point charges databank (Case et al., 2008)
and theoretically obtained elec tron-density distributions. The
comparison involves all the frequently studied features and
derived properties of the electron-density distribution. A
detailed comparison of the theoretical and experimental
databases of the aspherical atom types was presented by Ba˛k
et al. (2011). A typical example of applications of the new
ELMAM2 database for the common aromatic syste ms is given
in the study of quercetin monohydrate (Domagała et al., 2011).
The databank transfer procedure can be conveniently applied
to crystal structures of small molecules at usual resolution to
yield a more accurate structure and better crystallographic
statistics (Ahmed et al., 2011).
2. Construction of the generalized ELMAM2 database
2.1. Multipolar refinements of the selected structures
A set of 54 high-resolution structures was selec ted for the
construction of the generalized Experimental Library of
Multipolar Atom Model, hereafter called ELMAM2. The list
of all selected structures is given in Table 1S (the ‘S’ signifies
supplementary table or figure);
1
they are taken from the
following references: Benabicha et al. (2000); Birkedal et al.
(2004); Bouhmaida et al. (2009); Chen et al. (2007); Coppens et
al. (1999) ; Dahaoui et al. (1999); Destro et al. (1988); Dittrich
et al. (2002, 2007); Dittrich & Spackman (2007); Domagała et
al. (2009); Dominiak et al. (2003); Espinosa et al. (1996);
Fournier et al. (2009); Ghermani et al. (2004); Guillot et al.
(2003); Howard et al. (2009); Hu
¨
bschle et al. (2008); Kali-
nowski et al. (2007); Luger et al. (2004); Lutz et al. (2008);
Madsen et al. (2004); Martin & Pinkerton (1998); Meents et al.
(2008); Munshi & Guru Row (2002, 2005b; 2006a,b); Munshi et
al. (2006); Ogawa et al. (2006); Overgaard & Hibbs (2004);
Parrish et al. (2006); Pichon-Pesme et al. (2000); Rodrigues et
al. (2001); Scheins et al. (2004); Slouf et al. (2002); Sørensen et
al. (2003); Sparkes et al. (2008); Volkov et al. (2000); Wiest et
al. (1994); Zhurov et al. (2005); Zhurova et al. (2002, 2006);
Zhurova & Pinkerton (2001). The high-resolution structures
available in the literature were surveyed in order to find
accurate electron-density determinations. Their coordinates
and structure factors were obtained either from the journal
website (IUCr publications) or directly from the authors. All
structures found were refined using our standard strategy. The
‘good’ data were selected for further averaging. Several factors
were considered to qualify the data, e.g. featureless residual
density maps, reasonable multipolar parameters and no
convergence problems. Coordinated metal atoms were not
analysed and were not included in the present database.
The charge-density least-squares refinement program
MoPro (Guillot et al., 2001; Jelsch
et al., 2005) was used to
perform the multipolar refinements of the selected
compounds, applying a standardized refinement strategy.
The atom model used for the description of the total
molecular electron density is based on the Hansen & Coppen s
(1978) multipole formalism. The ind ividual atomic densities
are described in terms of spherical core and valence densities
with an expansion of atom-centred real spherical harmonic
functions. The total atomic electron density is therefore a sum
of three components:
atom
rðÞ¼
core
rðÞþP
val
3
val
rðÞ
þ
P
l
max
l¼0
l
03
R
nl
0
rðÞ
P
l
m¼0
P
lm
y
lm
ð; ’Þ; ð1Þ
where
core
and
val
are spherical core and valence densities,
respectively. The third term contains the sum of the angular
functions y
lm
(, ’) to take into account aspherical deforma-
tions. The angular functions y
lm
(, ’) are real spherical
harmonic functions. The coeffi cients P
val
and P
lm
are multi-
pole populations for the spherical valence and multipolar
density, respectively. The and
0
are scaling parameters,
which determine the expansion/contraction of the spherical
and multipolar valence densities, respectively. In the Hansen–
Coppens (Hansen & Coppens, 1978) formalism, the P
val
, P
lm
,
and
0
are refined parameters together with the atomic
coordinates (noted as xyz) and atomic displacement para-
meters (ADPs).
Several authors have described the general strategies of
multipolar refinement (Hansen & Coppens, 1978; Coppens,
1997; Hoser et al., 2009). We also developed a suitable
approach for building the generalized multipolar database,
based on the high-order refinement of xyz and U
ij
for the non-
H atoms and low-order refinement for the H atoms. The
multipolar populations are refined in a stepwise manner, i.e.
they are added consecutively to the whole set of refined
parameters. The non-H atoms are refined up to octupolar level
with the exception of heavy atoms (Z > 10), which are refined
up to hexadecapolar level. For the H atoms, only one bond-
oriented dipole and one quadrupolar function (q
3z
2
1
) are
used. The SHADE program (Simple Hydrogen Anisotropic
Displacement Estimator; Madsen, 2006) was used to estimate
ADPs (noted as U
ij
) for H atoms. During the refinement,
numerous restraints and/or constraints are used to avoid
unphysical values of the refined parameters. The detailed
refinement procedure is summarized in the following steps:
(i) The X—H distances are restrained in the subsequent
refinements to the standard neutron distance (Allen et al.,
1987, 2006) with a restraint = 0.002 A
˚
. Restraints are also
applied to the isotro pic thermal displacement parameters
(noted as U
iso
) of H atoms, U
iso
= kU
eq
(X), where k = 1.2,
except for –CH
3
, –NH
3
+
, –OH and –SH groups for which k was
set to 1.5 as they have a rotational degree of freedom.
(ii) High-order refinement (sin / > 0.7 A
˚
1
) of the xyz and
U
ij
parameters for the non-H atoms. Then, considering the
whole resolution range, refinement of the scale factor, xyz and
U
iso
parameters of H atoms. These steps were repeated until
convergence was obtained.
research papers
338 Sławomir Domagała et al.
ELMAM2. Construction details and applications Acta Cryst. (2012). A68, 337–351
1
Supplementary material for this paper is available from the IUCr electronic
archives (Reference: PC5007). Services for accessing this material are
described at the back of the journal.
electronic reprint
(iii) The anisotropic ADPs of the H atoms were estimated
using the SHADE program and were kept strongly restrained
to the SHADE values in the subsequent refinements.
(iv) (a) Block refinement against high-order reflections of
xyz, U
ij
for non-H atoms. Block refinement against all reflec-
tions of: (b) scale factor; (c) xyz and U
ij
for H atoms; ( d) P
val
;
(e) P
lm
;(f) ;(g)
0
.
The charge-density parameters (P
val
, P
lm
, ,
0
) were
introduced in the refinement step by step, repeating every step
until convergence was obtained.
During the refinement,
0
parameters of H atoms were
strongly restrained (
R
= 0.01) to theoretical values which
depend on the type of the carrying atom to which the H atom
is attached (Volkov et al., 2001). For example, the
0
para-
meters were restrained to 1.18, 1.40 and 1.50 for H atoms
connected to C, N and O atoms, respectively. Restraints were
applied on (, P
val
) parameters to preserve a linear relation
between the expansion–contraction of the valence shell ()
and the net atomic charge q = P
neut
P
val
(Volkov et al., 2001;
Jelsch et al., 2005).
2.1.1. Constraints, restraints and atom-type selection rules.
During the multipolar refinements, atoms within a similar
chemical environment had their charge-density parameters
P
val
, P
lm
, and
0
values constrained to be identical. Moreover,
optimal local axes were used and the highest possible
symmetry was imposed on the refined multipoles (Domagała
& Jelsch, 2008). An algorithm built into the MoPro program
generates automatically the multipolar local axes systems of
all the atoms of the molecule in a unique manner.
At first, a connectivity list is generated for all the atoms. For
unique ordering of the neighbours of a central atom, the list of
considered atoms is sorted according to the following criteria
of decreasing importance: (a) decreasing atomic numbers, (b)
decreasing number of bonds, (c) decreasing atomic numbers of
neighbours, (d) increasing distances to the central atom.
The type of local axes system is assig ned to an atom
according to the number of neighbours and its symmetry. The
multipolar refi nement, as described before, is performed and
the final multipolar parameters, including estimated standard
deviations (e.s.d.’s), are stored in the output file.
2.2. Averaging atoms from different molecules
The electron-de nsity parameters resulting for each mole-
cule from its final multipolar refinement were used as an input
to a Perl script to create the atom types stored further in the
database. Atom-selection procedures and averaging of atom
types from different molecules were carried out. Non-H atoms
with kappa parameters outside a well defined range (0.9 < <
1.1 and 0.7 <
0
< 1.3) were automatically removed from the
atom list. This was done to check the correctness of the
electron-density parameters and also to ensure that all atoms
are coherent with the standard radial function parameters
used in the refinements. When the charge-density parameters
of several atoms in a given molecule were constrained toge-
ther by chemical equivalence constraints, only one reference
atom was retained in the list of atoms contributing to an atom
type.
The chemical surrounding of a given atom type can be
represented as a graph. The node s denote the atoms which are
in the vicinity of the considered atom. The atoms connected
directly to the considered atoms are called the first-shell
neighbours. The atoms connected to the first-shell atoms are
called the second-shell neighbours etc. The connectivity graphs
were represented as strings to facilitate the comparison of
atom types. An example of graph and string representation is
shown in Fig. 1. The distinc tion of the different shells is made
according to the different parentheses.
Atoms were assigned to the same atom type when the
following parameters were exactly the same: chemical type,
type of local axes, number and type of neighbours (first shell),
planarity. Distances and angles between the considered atom
and the first neighbours were compared within a certain
tolerance (0.05 A
˚
and 5
). A new atom type was created in the
databank every time the program encountered an atom with
different parameters. In total, the 68 different atom types were
encountered when parsing the multipolar parameters of the
refined structures.
For most of the atom types, only the first shell of neighbours
was exactly compared. These include C, S, F and N atoms. The
second- and the third-shell neighbours were also comp ared for
certain cases of atom types. For example, in the case of H
atoms, the second-shell neighbours were also taken into
account, whereas oxygen, with its many chemical properties, is
an atom type which is sensitive to the type of third-shell atoms.
This was the case, for instance, to distinguish between
carboxylate Oc[o
()c(x)], carboxylic Oc[o(h)c(x)] and ester
Oc[o
(c)c(x)] oxygen atoms, as the values of multipoles and the
chemical properties are different for these atoms. The differ-
ences in the third shell are here marked using underlined bold
typeface. The electron-density parameters for each atom type
were represented as the weighted mean over all atoms
contributing to one atom type. The weights were set recipro-
Acta Cryst. (2012). A68, 337–351 Sławomir Domagała et al.
ELMAM2. Construction details and applications 339
research papers
Figure 1
Graph representation of the following chemical string Wx
1
[y
1
(z
1
z
2
)-
y
2
(z
3
z
4
)]x
2
[y
3
(z
5
)y
4
(z
6
z
7
)]x
3
. W denotes the main atom. The x, y and z
atoms correspond to neighbours in the first, second and third shell,
respectively. In the case of the string representation, the beginning and
the end of each shell is denoted by parentheses, if it is necessary to do so.
Therefore, the second shell is distinguished by the ‘[’ and ‘]’ characters,
whereas the third one is differentiated by the ‘(’ and ‘)’ characters.
electronic reprint
