Exploring charge density analysis in crystals at high pressure: data collection, data analysis and advanced modelling

Abstract

The possibility to determine electron-density distribution in crystals has been an enormous breakthrough, stimulated by a favourable combination of equipment for X-ray and neutron diffraction at low temperature, by the development of simplified, though accurate, electron-density models refined from the experimental data and by the progress in charge density analysis often in combination with theoretical work. Many years after the first successful charge density determination and analysis, scientists face new challenges, for example: (i) determination of the finer details of the electron-density distribution in the atomic cores, (ii) simultaneous refinement of electron charge and spin density or (iii) measuring crystals under perturbation. In this context, the possibility of obtaining experimental charge density at high pressure has recently been demonstrated [Casati et al. (2016). Nat. Commun. 7, 10901]. This paper reports on the necessities and pitfalls of this new challenge, focusing on the species syn-1,6:8,13-biscarbonyl[14]annulene. The experimental requirements, the expected data quality and data corrections are discussed in detail, including warnings about possible shortcomings. At the same time, new modelling techniques are proposed, which could enable specific information to be extracted, from the limited and less accurate observations, like the degree of localization of double bonds, which is fundamental to the scientific case under examination.

Electron Density Studies in Materials Research

“…These include the use of high pressure, which induces new and exotic structural and electronic transformationsa sa lready predicted theoretically for the high pressure electrides highlighted in this Review.T he first experimental ED study at high pressure appeared recently evaluating changes in aromaticity at high pressure, and the experimental consideration forr ealizing these challenging conditions were discussed. [123] Another external perturbation that has been pursued for al ong time is laser irradiation to measure the ED in an excited electronic state. Due to the great experimental challenges, only one study of this type has appeared, [124] but with the introduction of more powerful X-ray sources and faster detectors, this mayb ecome feasible in the future.S ince the properties of many materials, for example, for optical,e lectronic or catalytic applications, arise from excited states, this will open completely new possibilities for understandingt hesep rocesses that are also very difficult to model theoretically.O ther external perturbations that could be pursued in the future with relevance for materials science are externale lectric and magnetic fields.…”

Halogen in materials design: Revealing the nature of hydrogen bonding and other non-covalent interactions in the polymorphic transformations of methylammonium lead tribromide perovskite

“…Two of its charge density-based topological descriptors, viz., the presence of a bond path (bp), and the presence of the (3,-1) bond critical point (bcp) between interacting atomic basins have proved very useful in inferring the presence of a chemical bonding in chemical systems [35][36][37][38][39][53][54][55][56][57][58][59][60]. Two of its other signatures, the sign of the Laplacian of the charge density ( 2  b ) and the sign of the total energy density (H b ) at a bcp, can be used (and have been recommended) to determine whether the interaction between two atomic basins in a given pair is ionic, covalent, or a mixture of the two [59][60][61][62][63][64][65]. We have suggested in a recent study that these, together with other indicators for non-covalent interactions, can be used in the unambiguous characterization of hydrogen bonding in chemical systems [61].…”

Quantum Crystallography: Current Developments and Future Perspectives

“…[16] Furthermore, the modeling of atomicd isplacements initially led to additional problems in case of two-center electron density functions. [27] Nowadays, Jayatilaka's X-ray constrained wavefunction (XCW) fittinga pproach [28][29][30][31][32] and its later developments [33][34][35][36][37][38][39][40] are the most popular modernv ersions of theo riginal quantum crystallographic methods based on X-ray diffraction. [19] The radial decay of the pseudo-atomsa nd the core and valence scattering factors in multipole modelsa re directly calculated from wavefunctions and hence the analytical shape of the refined electron density is significantly influenced by quantum chemistry.I ti si mportant to mention that, to ag ood approximation, the set of multipolar orbitals may be relatedt oa tomic hybridization states [20] and even to some individual orbital occupancies, for example that of d-orbitals in transition metals, [21] and more recently that of f-orbitals in lanthanides.…”

“…[24] The first discussion about the perspective of obtaining wavefunctions from X-ray scattering (here:C ompton scattering) goes back to 1964 and the first Sagamore conference, [25,26] whereas the first quantum crystallographic method according to the original definition [24] and based on X-ray diffraction was proposed by Clinton and Massa in 1972. [27] Nowadays, Jayatilaka's X-ray constrained wavefunction (XCW) fittinga pproach [28][29][30][31][32] and its later developments [33][34][35][36][37][38][39][40] are the most popular modernv ersions of theo riginal quantum crystallographic methods based on X-ray diffraction. They practically aim at determining wavefunctions that minimize the energy, while reproducing, within the limit of experimental errors, X-ray structure factor amplitudes collected experimentally.A sa na lternative, joint refinement methods for the complete reconstruction of N-representable one-electron density matrices exploit both X-ray diffraction and inelastic Compton scattering data.…”