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-