Jean-Michel Gillet

First spin-resolved electron distributions in crystals from combined polarized neutron and X-ray diffraction experiments

A method to map spin-resolved electron distribution from combined polarized neutron and X-ray diffraction is described and applied for the first time to a molecular magnet and it is shown that spin up density is 5% more contracted than spin down density.

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

New 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)(H(2)O)(3)·2H(2)O, 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 alone.

Determination of a one-electron reduced density matrix using a coupled pseudo-atom model and a set of complementary scattering data

A possible model of one-electron reduced density matrices is presented, adapted from the Hansen-Coppens pseudo-atomic description of electron density [Hansen & Coppens (1978). Acta Cryst. A34, 909-913]. Potential benefits from a joint refinement of the model from X-ray diffraction and deep inelastic scattering data are illustrated.

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

The most recent research in charge spin and momentum density is presented and discussed.

d-Orbital orientation in a dimer cobalt complex: link to magnetic properties?

The experimental charge-density distribution of the dinuclear cobalt(II) complex [Co(2)(sym-hmp)(2)](BPh(4))(2)·2H(2)O·2C(3)H(6)O was determined at 100 K. When decreasing the temperature, the magnetic susceptibility of this complex deviates from Curie law because of anti-ferromagnetic exchange interactions, but the susceptibility increases sharply at low temperature (< 20 K). To explain this magnetic behaviour a tilt angle between the Co-atom environments was previously theoretically predicted. The structure and experimental charge density determined in this study show a tilt angle. The calculated value, based on the 100 K experimental d-orbital model, is in agreement with the theoretical one.

Charge and momentum densities of cubic tetracyanoethylene and its insertion compounds

Charge and momentum electron densities provide complementary views of cohesive forces in solids. This is particularly true for molecular crystals. The examples of cubic tetracyanoethylene (1,1,2,2-ethenetetracarbonitrile) and its alkali-metal insertion compounds are analyzed from a theoretical point of view. Besides the usual deformation density maps and anisotropy of Compton profiles, it is shown that interaction charge density and interaction Compton profiles can be defined and reveal the subtleties of the intermolecular interactions. It is shown that owing to the large cavities in the crystal, alkali-metal atoms can be inserted, leading to a strong charge transfer to the molecules and to a metallic character; the mechanism of insertion is revealed well by the combination of charge and momentum density studies. The combination of the two techniques of X-ray diffraction and Compton scattering should be of great help in the study of rather weak interactions present in molecular solids.

Towards a refinement of bonding features in MgO from directional Compton profiles

Abstract Adhesive properties of metals on oxide substrates, such as MgO, critically depend on the effective covalent character of metal-oxygen. In ionic solids (J.M. Gillet, P. Becker, G. Loupias, Acta Cryst. A 51 (1995) 405–413) the anisotropy among directional Compton profiles was shown to be strongly dependent upon the iono-covalent character of cohesive interactions. A systematic study of momentum density was thus undertaken for MgO, both experimental and theoretical. Reliable DCPs were obtained at ESRF, anisotropies being in fair agreement with Hartree–Fock calculations. In order to refine coupling parameters among valence orbitals, a three-dimensional (3D) reconstruction of momentum density is necessary. Various approaches are considered: besides spherical harmonics reconstruction, we propose a simple and efficient Gaussian fit of DCPs, followed by an extrapolation to the 3D momentum density. Preliminary results are discussed.

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.

Quantum Crystallography: Current Developments and Future Perspectives

Crystallography and quantum mechanics have always been tightly connected because reliable quantum mechanical models are needed to determine crystal structures. Due to this natural synergy, nowadays accurate distributions of electrons in space can be obtained from diffraction and scattering experiments. In the original definition of quantum crystallography (QCr) given by Massa, Karle and Huang, direct extraction of wavefunctions or density matrices from measured intensities of reflections or, conversely, ad hoc quantum mechanical calculations to enhance the accuracy of the crystallographic refinement are implicated. Nevertheless, many other active and emerging research areas involving quantum mechanics and scattering experiments are not covered by the original definition although they enable to observe and explain quantum phenomena as accurately and successfully as the original strategies. Therefore, we give an overview over current research that is related to a broader notion of QCr, and discuss options how QCr can evolve to become a complete and independent domain of natural sciences. The goal of this paper is to initiate discussions around QCr, but not to find a final definition of the field.

Past, Present and Future of Charge Density and Density Matrix Refinements

Basic theoretical and some practical aspects of the interpretation of X-ray scattering experiments are described. Our focus is on model building and refinement associated with retrieving information related to electron density matrices from the measured data. The ill-posed nature of this inverse problem is emphasised and the physical significance, reliability and reproducibility of the properties obtained by data fitting are discussed through representative examples taken from recent studies. A special attention is devoted to the pseudoatom formalism widely used to interpret high-resolution single-crystal X-ray diffraction data to map the static electron distribution in solids.