Quantum Crystallography in the Last Decade: Developments and Outlooks

Abstract

In this review article, we report on the recent progresses in the field of quantum crystallography that has witnessed a massive increase of production coupled with a broadening of the scope in the last decade. It is shown that the early thoughts about extracting quantum mechanical information from crystallographic experiments are becoming reality, although a century after prediction. While in the past the focus was mainly on electron density and related quantities, the attention is now shifting toward determination of wavefunction from experiments, which enables an exhaustive determination of the quantum mechanical functions and properties of a system. Nonetheless, methods based on electron density modelling have evolved and are nowadays able to reconstruct tiny polarizations of core electrons, coupling charge and spin models, or determining the quantum behaviour at extreme conditions. Far from being routine, these experimental and computational results should be regarded with special attention by scientists for the wealth of information on a system that they actually contain.

X-ray wavefunction refinement and comprehensive structural studies on bromo-substituted analogues of 2-deoxy-d-glucose in solid state and solution

“…However, recent development in both data collection and computational methods render IAM somewhat an obsolete method. 27 These more sophisticated approaches to structure refinement takes into consideration atomic non-sphericity, thus providing a better characterisation of bonding in the crystal state. Non-spherical refinement could be based on pre-calculated multipole populations approximating the molecular wavefunction of the investigated system (Hansen–Coppens multipole model and its variations), 28 or wavefunction computed for the system without any prior assumptions or pre-computed parameters (Hirshfeld atom refinement, HAR).…”

Real-Space Interpretation of Interatomic Charge Transfer and Electron Exchange Effects by Combining Static and Kinetic Potentials and Associated Vector Fields

“…To get more insight into the mechanisms of chemical bond formation beyond the orthodox topological analysis of electron density (ED) 𝜌(𝒓), we focus in this work on the analysis of electronic potentials 𝜑 𝑖 (𝒓) and corresponding local forces 𝑭 𝑖 (𝒓) 15,22,23 within the framework of quantum crystallography. [24][25][26][27][28][29][30][31] The orbital-free branch of quantum crystallography makes it possible to operate with ED and its derivatives, obtained either from theoretical calculations or experimental diffraction data for a many-electron multinuclear system in the stationary ground state. Each component of the inner potential field can be expressed starting from the one-electron Euler equation for ED: 22,23…”

QM/ELMO: A Multi-Purpose Fully Quantum Mechanical Embedding Scheme Based on Extremely Localized Molecular Orbitals

“…The QM/ELMO technique has been originally developed in the framework of the 109 Finally, the new embedding scheme has been also interfaced with the Hirshfeld atom refinement (HAR) technique 110-115 of quantum crystallography [116][117][118][119][120][121][122] for the accurate determination of hydrogen atom positions in crystal structures from X-ray diffraction data (see Subsection 3.4). 123 In the rest of the paper, after an overview on the theoretical bases of the QM/ELMO approach (Section 2), we will illustrate the main results obtained through our new embedding scheme in the different facets briefly mentioned above (Section 3).…”