ARTICLE
DOI: 10.1002/zaac.201200498
Electron Localisation in Ga-Heterocyclic Compounds
James A. Platts,
[a]
Maja K. Thomsen,
[b]
and Jacob Overgaard*
[b]
Keywords: X-ray diffraction; Theoretical structure factors; Multipole modeling; Core polarisation; Main group metal complexes
Abstract. The present study shows that a successful description of
the electron density in a Ga-containing compound using the present
multipole model requires separation and independent radial scaling of
the three Ga core shells. It is also shown that two similar compounds
only differing in the oxidation state of the Ga atom provides similar
residual density maps and thus the deficiencies in the standard
multipole model are very similar in the two cases. Nevertheless, we
find two fundamentally different core modified multipole models. It is
Introduction
Over the last decade there has been an increased focus on
the accuracy of the scattering factors used in the process of
modelling single-crystal X-ray diffraction data for charge den-
sity studies. The single-zeta Slater functions that are normally
used to describe the radial dependency of the valence electrons
have been shown to be insufficient to accurately reproduce the
finer details of this electron density when structure factors to
high resolution have been used. Based on subsequent results
from analysis using theoretical structure factors Coppens et al.
suggested an approach using two different sets of radial func-
tions with very different values of the Slater exponent for each
atom. This was shown to significantly increase the ability of
the expression to fit the density. However, the approach was
at the same time deemed unfeasible for implementation in the
fitting of experimental structure factors.
[1]
For the intervening period it has therefore often been stated,
with reference to Ref. [1], that the multipole model in its nor-
mal form is not able to accurately describe the very fine fea-
tures of the electron density. However, a different approach
was recently advocated by Koritsanszky et al.,
[2]
representing
a significant step away from the traditional scattering factors
based on neutral, independent gas phase atoms. Instead, in or-
der to provide more accurate and physically meaningful scat-
* Prof. Dr. J. Overgaard
Fax: +45-86196199
E-Mail: jacobo@chem.au.dk
[a] School of Chemistry
Cardiff University
Cardiff, UK
[b] Department of Chemistry
Aarhus University
Langelandsgade 140
Aarhus, Denmark
Supporting information for this article is available on the WWW
under http://dx.doi.org/10.1002/zaac.201200498 or from the au-
thor.
Z. Anorg. Allg. Chem. 2013, 639, (11), 1979–1984 © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1979
found that introduction of the modified core parameters in the model-
ling of the experimental data has no significant impact. An analysis of
the ELI-D is introduced to study the localization of electrons in the
Ga-guanidinate moiety. There is a clear analogy between the Laplacian
and the ELI-D, however the latter is able to reveal details from the total
density which is not available in the Laplacian. Only in an analysis of
the valence density alone can the Laplacian reveal the finer details.
tering factors, this method involves calculation of a wave-func-
tion for the molecular system in question. The resulting molec-
ular electron density is partitioned into atomic contributions
using a stock-holder Scheme The new radial functions that are
derived from the projection of these atomic densities on real
spherical harmonic functions are m-dependent and fitted with
a number of Slater-functions. These are then carried over into
refinement against experimental data. This approach is shown
to be able to very accurately describe the density, but on the
other hand it may be significantly biased by the details of the
theoretical calculation, and hence strongly affected by any
shortcomings in the method used. Furthermore, it is not work-
able in the case of (inorganic) network structures or structures
with very heavy elements.
The two approaches mentioned above have in common that
they primarily focus on the problems related to the accurate
fitting of valence electrons, which are responsible for the
chemical bonding, while the core electrons are assumed to be
unperturbed by the chemistry that takes place. Nevertheless, a
few experimental charge density studies have over the years
described observations of spherical or even aspherical residu-
als centered exactly on the atomic positions. In most such stud-
ies these residuals are left un-modeled; however some authors
have tried to model these residuals by introducing extra radial
scale factors or even more complex functions. This core con-
traction or expansion reveals itself only in rather high order
data and may sometimes be out of reach for the experimental-
ists, although exceptions are present as we shall see in the
following. In this work, we refer to “core” density as that ap-
pearing on or very close to nuclear positions, even if subse-
quent analysis indicates that this is due to valence orbitals.
In a recent experimental charge density study
[3]
of a molecu-
lar Ga
I
complex it was realised – based only on experimental
data to a resolution of 1.08 Å
–1
– that a proper description of
the core density of Ga required different radial scaling param-