Band 233, Heft 9-10 - Special Issue: Pioneering Experimental Electron Densities – A Celebration of Peter Luger’s Career in Crystallography / Guest Editors: Birger Dittrich, Simon Grabowsky, Christian W. Lehmann

The history of electron density (ED) research is surveyed and its historical highlights in the 20 th century are summarized. The progress, reached at the beginnig of the 21 st century, is described including contributions from the Berlin school. Key experimental advances concern X-ray sources and synchrotron radiation, measuring reflection data at very low temperatures (down to ~10 K), as well as the introduction of area detectors. Methodological progress was reached by new software systems for the refinement and analysis of ED data sets. This allowed to obtain quantitative ED properties, making use of Bader’s Quantum Theory of Atoms in Molecules (QTAIM). More recently methods, which combine experimental X-ray data and quantum-chemically derived wave functions, established the rapidly developing new field of “Quantum Crystallography.”

Six new rare earth metal-rich intermetallic compounds RE 9 CoMg 4 with RE =Y, Dy, Ho, Er, Tm and Lu were synthesized by induction-melting the elements in sealed niobium ampoules followed by annealing in muffle furnaces. The structures of Y 9 CoMg 4 and Tm 8.56 CoMg 4.44 were refined from single-crystal X-ray diffraction data: P 6 3 / mmc , a =965.65(6), c =971.07(5) pm, wR 2=0.0599, 614 F 2 values, 20 variables for Y 9 CoMg 4 and a =945.20(4), c =953.11(5) pm, wR 2=0.0358, 585 F 2 values, 21 variables for Tm 8.56 CoMg 4.44 (a small homogeneity range results from Tm/Mg mixing). The RE 9 CoMg 4 phases crystallize with a coloring variant of the aristotype Co 2 Al 5 . The striking structural motif is a hexagonal rod packing of rows of corner- and face-sharing tetrahedral Mg 4 clusters with Mg–Mg distances ranging from 304 to 317 pm in Y 9 CoMg 4 . These rows are similar to the hexagonal Laves phases RE Mg 2 . The space between the rows is filled with rows of face-sharing Co@Y 6 trigonal prisms (TP) and empty Y 6 octahedra (O) in the sequence –TP–O–O–. The many isopointal coloring variants of the aristotype Co 2 Al 5 are briefly discussed.

Rhodium boryl complexes are valuable catalysts for hydro- or diboration reactions of alkenes, but can also react with ketones (R 2 C=O) and imines (R 2 C=NR′) giving rise to insertion products having formally Rh–R 2 C–O/NR′–B linkages. The resulting molecular structures, however, may show complex metal–ligand and ligand–ligand interaction patterns with often unclear metal–ligand connectivities (hapticities, η n ). In order to assign the correct hapticity in a set of asymmetric rhodium-allyl compounds with molecular structures indicating η 1−5 bonding, a comprehensive DFT study was conducted. The study comprises determination of a variety of real-space bonding indicators derived from computed electron and pair densities according to the AIM, ELI-D, NCI, and DORI topological and surface approaches, which uncover the metal–ligand connectivties and suggest an asymmetric ligand–metal donation/metal–ligand back-donation framework according to the Dewar–Chatt–Duncanson model.

The synthesis of the isomeric compounds 1,8-bis(diphenylphosphino)biphenylene ( 1 ) and 1,5-bis(diphenylphosphino)biphenylene ( 2 ) is reported. Compound 1 was used as bidentate ligand towards late transition metal chlorides giving rise to six complexes 1 ·MCl 2 (M=Ni, Pd, Pt) and 1 ·MCl (M=Cu, Ag, Au), which have been fully characterized. The electronic bond characteristics of the polar-covalent M–P and M–Cl bonds of 1 ·MCl 2 (M=Ni, Pd, Pt) and 1 ·MCl (M=Cu, Ag, Au) were determined by a computational real-space bonding indicator (RSBI) analyses including the atoms-in-molecules, electron localizability indicator, and non-covalent interactions (NCI) index methods based on the molecular structures established by single crystal X-ray diffraction. Consistent with the electronegativity differences, the polarity of the M–Cl bonds is found to be systematically higher compared to the M–P bonds. In addition, there is a tendency for decreasing bond polarities downwards the column (Ag–P is an exception). Consequently, the highest bond polarities are observed for the Ni–Cl and Cu–Cl bonds, whereas the lowest polarities are observed for the Pt–P and Au–P bonds.

CE-B3LYP model energies are used to investigate intermolecular interactions in crystals of the relatively weakly bound cyclic ethers, as well as a number of substituted epoxides that have been the focus of high-quality experimental electron density studies. This approach readily provides a complete picture of all intermolecular interactions in these molecular crystals, and CE-B3LYP lattice energies for the unsubstituted cyclic ethers are in excellent agreement with available thermodynamic data. When compared with the outcomes of multipole modelling of X-ray diffraction data, these results suggest that experimental interaction energies are typically underestimated and, contrarily, experimental lattice energies are typically overestimated. These observations deserve careful investigation.

High-resolution low-temperature X-ray diffraction experiments for doxycycline monohydrate and hydrochloride dihydrate have been performed. Translation-Libration-Screw (TLS) analysis for both crystal forms as well as the data from neutron diffraction experiment for hydrochloride combined with the Hansen-Coppens formalism resulted in precise charge density distribution models for both the zwitterionic monohydrate and a protonated hydrochloride crystal forms. Their detailed topological analysis suggested that the electron structure of doxycycline’s amide moiety undergoes significant changes during protonation due to formation of a very strong resonance-assisted hydrogen bond. A notably increased participation of amide nitrogen atom and hydrogen-accepting oxygen atom in the resonance upon doxycycline protonation was observed. A comparison of TLS- and neutron data-derived hydrogen parameters confirmed the experimental neutron data to be vital for proper description of intra- and inter-molecular interactions in this compound. Finally, calculated lattice and interaction energies quantified repulsive Dox-Dox interactions in the protonated crystal form of the antibiotic, relating with a good solubility of doxycycline hydrochloride relative to its hydrate.

An overview is given of the recently proposed method for computation of the electrostatic potential (ESP) of dynamic charge densities derived from multipole models [C. B. Hubschle, S. van Smaalen, J. Appl. Crystallogr. 2017 , 50 , 1627]. The dynamic ESP is presented for the multipole models of the boron polymorphs α -B 12 and γ -B 28 , and stoichiometric boron carbide B 13 C 2 . Minimum values of the ESP are conspiciously equal at approximately −1 electron/Å. Regions with the ESP close to its minimum value form an extended network throughout the crystal structures at locations far away from atoms and bonds. Boron and boron carbide are extended solids containing an infinite network of strong chemical bonds. We have shown that for such solids, the ESP can usefully considered on Hirshfeld surfaces encompassing groups of atoms. Accordingly, we discuss bonding in boron and boron carbide with aid of the ESP on the Hirsfeld surface encompassing a B 12 icosahedral cluster. The structure of the ESP corroborates the interpretation of the bonding characteristics previously proposed for α -B 12 , γ -B 28 and B 13 C 2 .

The aim of the study was to examine noncovalent interactions in considerably different crystal packings of three isoindole compounds. Their structures were compared to three other closely-related derivatives described earlier in the literature. Here we discuss the crystal structures in the context of the hydrogen-bonded motifs and other weak interactions. The hierarchy of investigated intermolecular interactions was examined in a quantitative manner through pairwise interaction energies and energy framework analysis.

For the evaluation of data sets from dynamic structure crystallography, it may be helpful to predict expected R=IONIOFF$R = {{{I_{ON}}} \over {{I_{OFF}}}}$-based agreement factors from the observed intensities and their corresponding standard uncertainties with laser ON and with laser OFF. The predicted R factors serve three purposes: (i) they indicate, which data sets are suitable and promising for further evaluation, (ii) they give a reference R value for the case of absence of systematic errors in the data and (iii) they can be compared to the corresponding predicted F 2 -based R factors. For point (ii) it is inevitable, that the standard uncertainties from the experiment are adequate, i.e. they should adequately describe the noise in the observed intensities and must not be systematically over- or under estimated for a part of the data or the whole data set. It may be this requirement, which is currently the largest obstacle for further progress in the field of dynamic structure crystallography.

The structure of glutathione, γ - l -Glutamyl- l -cysteinyl-glycine (C 10 H 17 N 3 O 6 S), was studied by multi-temperature single-crystal X-ray diffraction. Residual density maps from conventional independent atom model refinement gave indication of anharmonic motion in the molecule. This was further investigated by invariom refinement with anisotropic displacement parameters for all atoms, which described asphericity due to chemical bonding and lone pairs; afterwards only the residual-density signal of anharmonic motion remained. Treating anharmonicity with third-order Gram-Charlier displacement parameters led to regions with unphysical negative electron density. In contrast, a maximum entropy method (MEM) determination of the electron density successfully takes the features into account. Respective difference electron density plots (MEM minus prior and [Invariom+GC] minus invariom) agree well with each other. Challenges in treating and understanding the phenomenon are discussed. A procedure is proposed how unphysical negative electron density can be avoided. It is closely related to the free lunch algorithm.

Besides the previously known α-form (monoclinic, P 2 1 /c, Z=4) of bis(2,6-dimesitylphenyl)ditelluride, two new polymorphic modifications, namely the β-form (monoclinic, P 2 1 / c , Z=8) and the γ-form (triclinic, P 1̅, Z=2), were obtained serendipitously during chemical reactions. In all three modifications, the individual molecules possess significantly different conformations and bond parameters, such as Te–Te bond lengths, C–Te–Te bond angles, C–Te–Te–C torsion angles and intramolecular Menshutkin interactions, which is also reflected in their non-covalent interactions with adjacent molecules in the crystal lattice via London dispersion and electrostatic forces. The interplay between intermolecular and intramolecular forces in these conformational polymorphs was investigated using quantum chemical calculations, which reveal that the β-form should be thermodynamically stable at absolute zero. In contrast, crystallization experiments and thermoanalytical investigations indicate that the α-form is stable at high temperatures and therefore, both forms might be related by enantiotropism.

The charge density distribution of the intramolecular frustrated Lewis pair (FLP) Mes 2 PCH 2 CH 2 B(C 6 F 5 ) 2 ( 1 ), the phosphinimine HNPMes 2 CH 2 CH 2 B(C 6 F 5 ) 2 ( 2 ), as well as a FLP homologue with nitrogen NEt 2 CHPhCH 2 B(C 6 F 5 ) 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 sp 2 -hybridization. The bond is therefore best described as a non-hypervalent P δ+ –N δ− moiety.

2,3,5,6-Tetrafluoro-1,4-diiodobenzene and 4-(dimethylamino)pyridine co-crystallize in 1:2 stoichiometry. A diffraction experiment at standard resolution was already conducted in 2010 and revealed one of the shortest N···I contacts ever reported. We collected X-ray intensities at 100 K up to a very high resolution of 1.23 Å −1 . These experimental data allowed to refine a structure model based on atom-centered multipoles according to the Hansen-Coppens approach and provided an experimental electron density. A subsequent analysis with the help of Bader’s atoms in molecules theory showed a strong interaction between the pyridine N atom and the σ hole of its closest iodine neighbor on the halogenated benzene. This contact is characterized by a distance of 2.6622(4) Å and associated with a remarkably large electron density of 0.359(5) e ⋅Å −3 in the (3, −1) critical point, unprecedented for a secondary interaction. This bona fide shortest halogen bond ever investigated by an experimental charge density study is associated with a significantly negative total energy density in the bond critical point and thus can reliably be classified as strong. Both the electron density and the position of the bond critical point suggest to compare the short N···I contact to coordinative or covalent bonds rather than to σ hole interactions.

An experimental electronic structure of bis(clonixato)bis(ethanol) bis(imidazole)copper(II) complex, [Cu(cln) 2 (im) 2 (EtOH) 2 ] (cln=clonixato, im=imidazole) (1) has been obtained from single-crystal X-ray diffraction data collected at 100 K using an Incoatec IμS Ag microfocus source. Metal-ligand (ML) bonds and hydrogen bonds (HBs) have been analysed using topological analysis of the experimental electron density with the atoms in molecules (AIM) approach. The central copper atom is octahedrally coordinated by two oxygen atoms from two clonixato anions and two nitrogen atoms from two imidazole ligands in equatorial plane. In axial positions are two oxygen atoms from two ethanol molecules. AIM analysis establishes that the central copper atom is bonded more strongly to the clonixato anion that to the imidazole or ethanol molecules. AIM analysis of two intramolecular and one intermolecular hydrogen bonds permits to estimate their strength. We show that the hydrogen bonds are strong enough to protect the molecule from decomposition in solvent media and to disable the more reactive imidazole-Cu-clonixato complex from interacting with e.g. a macromolecule. The electrostatic potential of the complex shows a highly positive value on the central atom, so the complex is highly reactive in an interaction with negative ligands.