Experimental charge-density studies: data reduction and model quality: the more the better?

Comparative study of conventional and synchrotron X-ray electron densities on molecular crystals

Five different electron density datasets obtained from conventional and synchrotron single crystal X-ray diffraction experiments are compared. The general aim of the study is to investigate the quality of data for electron density analysis from current state-of-the-art conventional sources, and to see how the data perform in comparison with high-quality synchrotron data. A molecular crystal of melamine was selected as the test compound due to its ability to form excellent single crystals, the light atom content, and an advantageous suitability factor of 3.6 for electron density modeling. These features make melamine an optimal system for conventional X-ray diffractometers since the inherent advantages of synchrotron sources such as short wavelength and high intensity are less critical in this case. Data were obtained at 100 K from new in-house diffractometers Rigaku Synergy-S (Mo and Ag source, HyPix100 detector) and Stoe Stadivari (Mo source, EIGER2 1M CdTe detector), and an older Oxford Diffraction Supernova (Mo source, Atlas CCD detector). The synchrotron data were obtained at 25 K from BL02B1 beamline at SPring-8 in Japan (λ = 0.2480 Å, Pilatus3 X 1M CdTe detector). The five datasets were compared on general quality parameters such as resolution, ⟨I/σ⟩, redundancy and R factors, as well as the more model specific fractal dimension plot and residual density maps. Comparison of the extracted electron densities reveals that all datasets can provide reliable multipole models, which overall convey similar chemical information. However, the new laboratory X-ray diffractometers with advanced pixel detector technology clearly measure data with significantly less noise and much higher reliability giving densities of higher quality, compared to the older instrument. The synchrotron data have higher resolution and lower measurement temperature, and they allow for finer details to be modeled (e.g. hydrogen κ parameters).

Applicability of transferable multipole pseudo-atoms for restoring inner-crystal electronic force density fields. Chemical bonding and binding features in the crystal and dimer of 1,3-bis(2-hydroxyethyl)-6-methyluracil

We considered it timely to test the applicability of transferable multipole pseudo-atoms for restoring inner-crystal electronic force density fields. The procedure was carried out on the crystal of 1,3-bis(2-hydroxyethyl)-6-methyluracil, and some derived properties of the scalar potential and vector force fields were compared with those obtained from the experimental multipole model and from the aspherical pseudo-atom model with parameters fitted to the calculated structure factors. The procedure was shown to accurately replicate the general vector-field behavior, the peculiarities of the quantum potentials and the characteristics of the force-field pseudoatoms, such as charge, shape and volume, as well as to reproduce the relative arrangement of atomic and pseudoatomic zero-flux surfaces along internuclear regions. It was found that, in addition to the quantum-topological atoms, the force-field pseudoatoms are spatially reproduced within a single structural fragment and similar environment. In addition, the classical and nonclassical hydrogen bonds in the uracil derivative crystal, as well as the H...O, N...O and N...C interactions in the free π-stacked dimer of the uracil derivative molecules, were studied using the potential and force fields within the concepts of interatomic charge transfer and electron lone pair donation-acceptance. Remarkably, the nitrogen atoms in the N...O and N...C interactions behave rather like a Lewis base and an electron contributor. At the same time, the hydrogen atom in the H...O interaction, being a Lewis acid, also participates in the interatomic electron transfer by acting as a contributor. Thus, it has been argued that, when describing polar interatomic interactions within orbital-free considerations, it makes more physical sense to identify electronegative (electron occupier) and electropositive (electron contributor) atoms or subatomic fragments rather than nucleophilic and electrophilic sites.

The advanced treatment of hydrogen bonding in quantum crystallography

Although hydrogen bonding is one of the most important motifs in chemistry and biology, H-atom parameters are especially problematic to refine against X-ray diffraction data. New developments in quantum crystallography offer a remedy. This article reports how hydrogen bonds are treated in three different quantum-crystallographic methods: Hirshfeld atom refinement (HAR), HAR coupled to extremely localized molecular orbitals and X-ray wavefunction refinement. Three different compound classes that form strong intra- or intermolecular hydrogen bonds are used as test cases: hydrogen maleates, the tripeptide l-alanyl-glycyl-l-alanine co-crystallized with water, and xylitol. The differences in the quantum-mechanical electron densities underlying all the used methods are analysed, as well as how these differences impact on the refinement results.

Electron density based analysis of N–H⋯OC hydrogen bonds and electrostatic interaction energies in high-resolution secondary protein structures: insights from quantum crystallographic approaches

Limiting values of the topological parameters and the electrostatic interaction energies to establish the presence of true N–H⋯OC H-bonds in protein main-chain have been identified using quantitative and qualitative analyses of electron densities.

The role of multiple observations in small-molecule single-crystal service X-ray structure determination

In order to gain a better understanding of how to improve the quality of small-molecule single-crystal X-ray diffraction data achievable in a finite time, a study was carried out to investigate the effect of varying the multiplicity, acquisition time, detector binning, maximum resolution and completeness. The results suggest that, unless there are strong arguments for a different strategy, a good routine procedure might be to optimize the conditions necessary to get the best data from single scans, and then choose a multiplicity of observations (MoO) to utilize the available time fully. Different strategies may be required if the crystal is highly absorbing, is larger than the incident beam, is enclosed in a capillary tube or is unusual in some other way. The signal-to-noise ratio should be used with care, as collecting data for longer or at higher multiplicity appears to give a systematic underestimate of the intensity uncertainties. Further, the results demonstrate that including poor-quality data in a refinement may degrade the result and, in the general case, the accidental omission of reflections has a very small impact on the refinement as long as they are omitted at random. Systematic omission of reflections needs a convincing procedural justification.

Quantum pressure focusing in solids: a reconstruction from experimental electron density

Here an approach is presented for reconstructing the distribution of electronic internal quantum pressure in the electronic continuum of solids from the experimental electron density. Using the formalism of the density functional theory, the spatial inner-crystal map of the quantum pressure is obtained. The results are visualized via the indicator of quantum pressure focusing (IQPF) which reveals the regions where the pressure is concentrated or depleted due to quantum effects. IQPF contains all quantum electron-shell structure-forming contributions resulting from kinetic, exchange and correlation effects, and presents a clear picture of the chemical bond features in crystals with different type of bonding mechanisms.

Experimental charge density study on FLPs and a FLP reaction product

The charge density distribution of the intramolecular frustrated Lewis pair (FLP) Mes2PCH2CH2B(C6F5)2 (1), the phosphinimine HNPMes2CH2CH2B(C6F5)2 (2), as well as a FLP homologue with nitrogen NEt2CHPhCH2B(C6F5)2 (3) were investigated with Bader’s quantum theory of atoms in molecules (QTAIM). The charge densities were derived from both experimental high-resolution X-ray diffraction data (2, 3) and theoretical calculations (1, 3). The QTAIM analysis for the FLPs 1 and 3 showed the prominent B-pnictogen interaction to be weak dative bonds without significant charge-transfer. This holds also true for the B–N–bond of 2. The nitrogen atom is negatively charged, due to a charge transfer from phosphorous and shows features of a sp2-hybridization. The bond is therefore best described as a non-hypervalent Pδ+–Nδ− moiety.

Ground-State Charge-Density Distribution in a Crystal of the Luminescent ortho-Phenylenediboronic Acid Complex with 8-Hydroxyquinoline

This contribution is devoted to the first electron density studies of a luminescent oxyquinolinato boron complex in the solid state. ortho-Phenylenediboronic acid mixed with 8-hydroxyquinoline in dioxane forms high-quality single crystals via slow solvent evaporation, which allows successful high resolution data collection (sin θ/λ = 1.2 Å^-1) and charge density distribution modeling. Particular attention has been paid to the boron-oxygen fragment connecting the two parts of the complex, and to the solvent species exhibiting anharmonic thermal motion. The experiment and theory compared rather well in terms of atomic charges and volumes, except for the boron centers. Boron atoms, as expected, constitute the most electron-deficient species in the complex molecule, whereas the neighboring oxygen and carbon atoms are the most significantly negatively charged ones. This part of the molecule appears to be very much involved in the charge transfer occurring between the acid fragment and oxyquinoline moiety leading to the observed fluorescence, as supported by the time-dependent density functional theory (TDDFT) results and the generated transition density maps. TDDFT calculations indicated that p-type atomic orbitals contributing to the HOMO-1, HOMO, and LUMO play the major role in the lowest energy transitions, and enabled further comparison with the charge density features, which is discussed in details. Furthermore, the results confirmed the known fact the Q ligand character is most important for the spectroscopic properties of this class of complexes.