The Advent of Quantum Crystallography: Form and Structure Factors from Quantum Mechanics for Advanced Structure Refinement and Wavefunction Fitting

Abstract

X-ray diffraction experiments contain much more information than the information usually exploited for structure determination. In quantum crystallography, quantum mechanical wavefunctions are used to extract that information about bonding and properties from the measured X-ray structure factors. Here we show how quantum mechanically derived structure factors and atomic form factors are constructed to allow the improved description of the diffraction experiment. Subsequently, we discuss the basics and the applications of the advanced structure refinement method Hirshfeld Atom Refinement and of the X-ray constrained wavefunction fitting technique.

Hydrogen atoms in bridging positions from quantum crystallographic refinements: influence of hydrogen atom displacement parameters on geometry and electron density

“…Note that in the XCW fitting step no self-consistent field of point charges and dipoles was used since it is expected that the crystal field effects are absorbed by the wavefunction during the fitting procedure. This point is further discussed in Ernst et al 60 and Grabowsky et al 61 The figures of merit after XCW fitting and the maximum value of the manually adjusted perturbation parameter λ determining the degree of influence of the experimental structure factors on the wavefunction are collected in Tables S5 and S6 in the ESI. †…”

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).…”

Different Reactivities of (5-Ph2P-Ace-6-)2MeSiH toward the Rhodium(I) Chlorides [(C2H4)2RhCl]2 and [(CO)2RhCl]2. Hirshfeld Atom Refinement of a Rh–H···Si Interaction

“…78−84 Therefore, we employed Hirshfeld atom refinement (HAR), 85,86 a new technique for single-crystal X-ray structure refinement in the field of quantum crystallography, 87 which uses theoretically calculated nonspherical atomic electron densities to produce the atomic form factors used in the crystallographic least-squares refinement. 88 Therefore, HAR is able to determine the positions of H atoms accurately and precisely. 89 However, so far only transition-metal hydrides of the first-transition-metal period could be successfully refined using the standard HAR procedure.…”