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

Charge density studies of multicentre two-electron bonding of an anion radical at non-ambient temperature and pressure

The variation of charge density of two-electron multicentre bonding (pancake bonding) between semi-quinone radicals with pressure and temperature was studied on a salt of 5,6-di-chloro-2,3-di-cyano-semi-quinone radical anion (DDQ) with 4-cyano-N-methyl-pyridinium cation (4-CN) using the Transferable Aspheric Atom Model (TAAM) refinement. The pancake-bonded radical dimers are stacked by non-bonding π-interactions. With rising pressure, the covalent character of interactions between radicals increases, and above 2.55 GPa, the electron density indicates multicentric covalent interactions throughout the stack. The experimental charge densities were verified and corroborated by periodic DFT computations. The TAAM approach has been tested and validated for atomic resolution data measured at ambient pressure; this work shows this approach can also be applied to diffraction data obtained at pressures up to several gigapascals.

Charge densities in actinide compounds: strategies for data reduction and model building

The data quality requirements for charge density studies on actinide compounds are extreme. Important steps in data collection and reduction required to obtain such data are summarized and evaluated. The steps involved in building an augmented Hansen-Coppens multipole model for an actinide pseudo-atom are provided. The number and choice of radial functions, in particular the definition of the core, valence and pseudo-valence terms are discussed. The conclusions in this paper are based on a re-examination and improvement of a previously reported study on [PPh4][UF6]. Topological analysis of the total electron density shows remarkable agreement between experiment and theory; however, there are significant differences in the Laplacian distribution close to the uranium atoms which may be due to the effective core potential employed for the theoretical calculations.

Relativistic quantum crystallography of diphenyl- and dicyanomercury. Theoretical structure factors and Hirshfeld atom refinement

Quantum crystallographic refinement of heavy-element-containing compounds is a challenge, because many physical effects have to be accounted for adequately. Here, the impact and magnitude of relativistic effects are compared with those of electron correlation, polarization through the environment, choice of basis set and treatment of thermal motion effects on the structure factors of diphenylmercury(II) [Hg(Ph)₂] and dicyanomercury(II) [Hg(CN)₂]. Furthermore, the individual atomic contributions to the structure factors are explored in detail (using Mulliken population analysis and the exponential decay of atomic displacement parameters) to compare the contributions of lighter atoms, especially hydrogen atoms, against mercury. Subsequently, relativistic Hirshfeld atom refinement (HAR) is validated against theoretical structure factors of Hg(Ph)₂ and Hg(CN)₂, starting from perturbed geometries, to test if the relativistic variant of HAR leads to multiple solutions. Generally, relativistic HAR is successful, leading to a perfect match with the reference geometries, but some limitations are pointed out.

Exploiting the full quantum crystallography

Quantum crystallography (QCr) is a branch of crystallography aimed at obtaining the complete quantum mechanics of a crystal given its X-ray scattering data. The fundamental value of obtaining an electron density matrix that is N-representable is that it ensures consistency with an underlying properly antisymmetrized wavefunction, a requirement of quantum mechanical validity. However, X-ray crystallography has progressed in an impressive way for decades based only upon the electron density obtained from the X-ray scattering data without the imposition of the mathematical structure of quantum mechanics. Therefore, one may perhaps ask regarding N-representability “why bother?” It is the purpose of this article to answer such a question by succinctly describing the advantage that is opened by QCr.

Insights on spin delocalization and spin polarization mechanisms in crystals of azido copper(II) dinuclear complexes through the electron spin density Source Function

The Source Function (SF) tool was applied to the analysis of thetheoreticalspin density in azido CuIIdinuclear complexes, where the azido group, acting as a coupler between the CuIIcations, is linked to the metal centres either in an end-on or in an end–end fashion. Results for only the former structural arrangement are reported in the present paper. The SF highlights to which extent the magnetic centres contribute to determine the local spin delocalization and polarization at any point in the dimetallic complex and whether an atom or group of atoms of the ligands act in favour or against a given local spin delocalization/polarization. Ball-and-stick atomic SF percentage representations allow for a visualization of the magnetic pathways and of the specific role played by each atom along these paths, at given reference points. Decomposition of SF contributions in terms of a magnetic and of a relaxation component provides further insight. Reconstruction of partial spin densities by means of the Source Function has for the first time been introduced. At variance with the standard SF percentage representations, such reconstructions offer a simultaneous view of the sources originating from specific subsets of contributing atoms, in a selected molecular plane or in the whole space, and are therefore particularly informative. The SF tool is also used to evaluate the accuracy of the analysed spin densities. It is found that those obtained at the unrestricted B3LYP DFT level, relative to those computed at the CASSCF(6,6) level, greatly overestimate spin delocalization to the ligands, but comparatively underestimate magnetic connection (spin transmission) among atoms, along the magnetic pathways. As a consequence of its excessive spin delocalization, the UB3LYP method also overestimates spin polarization mechanisms between the paramagnetic centres and the ligands. Spin delocalization measures derived from the refinement of Polarized Neutron Diffraction data seem in general superior to those obtained through the DFT UB3LYP approach and closer to the far more accurate CASSCF results. It is also shown that a visual agreement on the spin-resolved electron densities ραand ρβderived from different approaches does not warrant a corresponding agreement between their associated spin densities.

Quantum crystallography

Approximate wavefunctions can be improved by constraining them to reproduce observations derived from diffraction and scattering experiments. Conversely, charge density models, incorporating electron-density distributions, atomic positions and atomic motion, can be improved by supplementing diffraction experiments with quantum chemically calculated, tailor-made electron densities (form factors). In both cases quantum chemistry and diffraction/scattering experiments are combined into a single, integrated tool. The development of quantum crystallographic research is reviewed. Some results obtained by quantum crystallography illustrate the potential and limitations of this field.

Bonding in Uranium(V) Hexafluoride Based on the Experimental Electron Density Distribution Measured at 20 K

The electron density distribution of [PPh₄][UF₆] was obtained from high-resolution X-ray diffraction data measured at 20 K. The electron density was modeled with an augmented Hansen-Coppens multipolar formalism. Topological analysis reveals that the U-F bond is of incipient covalent nature. Theoretical calculations add further support to the bonding description gleaned from the experimental model. The impact of the uranium anomalous dispersion terms on the refinement is also discussed.

Challenges in the structural science of materials

Articles published recently in IUCrJ continue to exemplify the developments and challenges in the structural science of materials.