Modelling the experimental electron density : only the synergy of various approaches can tackle the new challenge

International audienceElectrondensity is a fundamental quantity that enables understanding of the chemical bonding in a molecule or in a solid and the chemical/physical property of a material. Because electrons have a charge and a spin, two kinds of electron densities are available. Moreover, because electron distribution can be described in momentum or in position space, charge and spin density have two definitions and thez can be observed through Bragg (for the position space)or Compton (for the momentum space) diffraction experiments, using X-rays (charge density) or polarized neutrons (spin density). In recent years, we have witnessed many advances in this fiels, stimulated by the increased power of experimental techniques. However, an accurate modelling is still necessary to determine the desired functions from the acquired data. The improved accuracy of measurements and the possibility to combine information from differentexpirenmental techniques require even more flexibility of the models.In this short review, we analyse some of the most important topics that have emerged in the recent literature, especially the most thought-provoking at the recent IUCr general meeting in Montreal

Recent advances in understanding the similarities and differences of colombian euclases

Colombian euclase is rare and associated with emerald in medium-temperature hydrothermal veins hosted by Lower Cretaceous black shales (BS). The original sources of euclase production were the mining districts of Gachala and Chivor in the eastern emerald belt, but in 2016 euclases were also found at the La Marina mine in the western emerald belt. The present study is centered on a chemical and mineralogical examination of zoned Colombian euclase sold on the gem market as "trapiche'. Its texture is characterized by growth bands and sectors distinguished by the presence of numerous inclusions (mainly pyrite, carbonates, and organic matter) which represent around 0.2% of the total volume of the crystals. Xray computed tomography showed that the largest inclusions are randomly located, whereas the small inclusions are concentrated in the center of the crystals, along the crystallographic b axis, between neighboring growth sectors and between growth bands in each sector. The texture cannot be defined as "trapiche', like that of Colombian emeralds, because there is no matrix material from the surrounding BS trapped between the growth sectors and accumulated as dendrites. Three-phase fluid inclusions (FI) containing halite, liquid, and vapor phases are also observed in the euclase, and their volume is identical to that of the inclusions in emerald. Chromium and vanadium are the main chromophores, and the highest concentrations (1240 and 400 ppm, respectively) were found in deep blue-colored zones. Surprisingly, the euclase crystals have high Ge contents, between 230 and 530 ppm. The Rare Earth Element (REE) patterns of euclase are inherited from the enclosed BS or albitized and carbonatized BS. Euclase has the same REE pattern as emerald from the Gachala mines with an Eu anomaly (Eu/Eu* similar to 0.40) and a depletion in Heavy Rare Earth Elements (HREE). The present study allows for the reconstruction of the formation conditions of "trapiche' euclase and discussion about its probable geographic origin, i.e., the eastern emerald belt

Experimental spin-resolved electron densities: results of a joint refinement of XRD and PND data

International audienceSince the first works of Stewart on modelling charge density [1], huge improvements of X-ray sources, detectors and software has significantly increased the resolution and the qualities of diffraction data allowing an accurate determination of the charge density of a growing number of molecules. However, despite the technological improvement, no dramatic change of the experimental model was reached since the multipolar model of Hansen & Coppens in 1978 [2]. At the same time polarised neutron diffraction (PND) experiments were developed [3] to get access to the spin density at the molecular scale and the multipolar Hansen & Coppens model was adapted to model this quantity. These two quantities (charge and spin densities) are described by a similar multipolar atom centred model with a common parameterization, therefore a combined treatment of X-ray diffraction (XRD) and PND data, is not only possible but also useful as stated by Becker & Coppens in 1985 [4]. Recently an extended Hansen & Coppens model and the corresponding refinement program were developed [5, 6] in order to allow the joint refinement of data sets coming from three different experiments (X-ray, unpolarised and polarised neutron diffraction). By combining different data sets, the new model gives access to electron density with spin up (ρ↑) and electron density with spin down (ρ↓) separately. These two quantities (ρ↑ and ρ↓) can be observed experimentally for the first time, and this observation allows a further comparison with theoretical models. In a first part the presentation will focus on the common model and the refinement procedure. The second part will describe its application to the case of an end-to-end azido double-bridged copper(II) complex (Cu2L2(N3)2 where L=1,1,1-triuoro-7-(dimethylamino)-4-methyl-5-aza-3-hepten-2-onato) [7]. The experimental results will be presented and compared to the theoretical densities. Acknowledgments This work has been supported by l’Agence Nationale de la Recherche (CEDA project); M.D. thanks CNRS for PhD fellowship

Electron-density studies of magnetic di-nuclear complexes

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Electron-density studies of magnetic di-nuclear complexes

International audienceIn the aim to rationalise the conception of single molecular magnets the first step is to explore the interactions in molecular magnetic complexes and to understand their role. To this end we modeled the experimental electron density distributions in di-nuclear complexes. For example, we studied a cobalt(II) compound ([Co2(sym-hmp)2](BPh4)2) which was theoretically studied by Tone et al. in 2007[1]. When decreasing the temperature, the magnetic susceptibility of this complex deviates from the Curie law (Fig. 1) because of the anti-ferromagneticexchange interaction, but the susceptibility increases sharply at low temperature (< 20K). The theoretical analysis of Tone et al. showed that this behavior is explained by a tilt of local distortion axes around cobalt atoms and not by a paramagnetic impurity. A polarized neutron diffraction experiment was carried out in order to model the spin density and verify this hypothesis (Borta et al. (2011), accepted in Phys. Rev. B.)To support this electronical approach and to better describe the metal-ligand interactions, we determined the charge density of this complex using high resolution X-ray diffraction at 100 K. We will present our multipolar model[2] and its description using various tools(Fig. 2). The different interactions will be described and comparison will be made with spin density results from polarized neutron diffraction experiments. We will finally introduce our project of a new program for joint refinements of a unique electronic model based on X-rays and polarized neutrons diffraction data

Les rayon X et les neutrons se combinent pour révéler la densité résolue en spin

International audienceLa distribution des électrons dans un cristal peut être reconstruite avec une grande précision au moyen de la diffraction des rayons X à haute résolution, alors que la diffraction des neutrons polarisés en spin permet de retrouver la densité d’aimantation. Bien que les grandeurs ainsi mesurées soient toutes deux une traduction du comportement des électrons, ces deux types d’expérience de diffusion sont de nos jours interprétées par des modèles différents.Nous retraçons ici les étapes ayant conduit à la première détermination expérimentale de la densité d’électrons résolue en spin par un traitement combiné des données de diffraction de rayons X et de neutrons polarisés

Experimental determination of spin-dependent electron density by joint refinement of X-ray and polarized neutron diffraction data

International audienceNew crystallographic tools were developed to access a more precise description of the spin-dependent electron density of magnetic crystals. The method combines experimental information coming from high-resolution X-ray diffraction (XRD) and polarized neutron diffraction (PND) in a unified model. A new algorithm that allows for a simultaneous refinement of the charge- and spin-density parameters against XRD and PND data is described. The resulting software MOLLYNX is based on the well known Hansen-Coppens multipolar model, and makes it possible to differentiate the electron spins. This algorithm is validated and demonstrated with a molecular crystal formed by a bimetallic chain, MnCu(pba)(H2O)3 2H2O, for which XRD and PND data are available. The joint refinement provides a more detailed description of the spin density than the refinement from PND data alon

When combined X-ray and polarized neutron diffraction data challenge high-level calculations: Spin-resolved electron density of an organic radical

Joint refinement of X-ray and polarized neutron diffraction data has been carried out in order to determine charge and spin density distributions simultaneously in the nitronyl nitroxide (NN) free radical Nit(SMe)Ph. For comparison purposes, density functional theory (DFT) and complete active-space self-consistent field (CASSCF) theoretical calculations were also performed. Experimentally derived charge and spin densities show significant differences between the two NO groups of the NN function that are not observed from DFT theoretical calculations. On the contrary, CASSCF calculations exhibit the same fine details as observed in spin-resolved joint refinement and a clear asymmetry between the two NO groups.Experimental joint refinement against X-ray and polarized neutron diffraction data has been performed to simultaneously model the charge and spin density of a free radical; the resulting model challenges density functional theory (DFT) calculations, but is in fair agreement with ab initio complete active-space self-consistent field (CASSCF) calculations

Joint densities and density matrices refinements: first attempts and first results

International audienceAlthough analysis of joint experimental data as diverse as x-rays structure factors, polarized neutron flipping ratios, neutron structure factors, CBED measurements, x-ray Compton magnetic (and non magnetic) profiles, among others, is theoretically feasible and desirable, to this day only few attempts have been made. We will remind some of the important strategies that have been elaborated in the past and we will propose a new possible way of combining and exploiting the richness of the diversity of experimental methods. We will show that as long as the data are issued from elastic coherent scattering experiments only marginal changes have to be made to the usual pseudo-atoms model. This will be illustrated with recent results obtained on magnetic compounds. We will finally address a critical discussion concerning the difficulties occurring in combining real and momentum space data