Probing the accuracy and precision of Hirshfeld atom refinement with HARt interfaced with Olex2

Hirshfeld atom refinement (HAR) is a novel X-ray structure refinement technique that employs aspherical atomic scattering factors obtained from stockholder partitioning of a theoretically determined tailor-made static electron density. HAR overcomes many of the known limitations of independent atom modelling (IAM), such as too short element-hydrogen distances, r(X-H), or too large atomic displacement parameters (ADPs). This study probes the accuracy and precision of anisotropic hydrogen and non-hydrogen ADPs and of r(X-H) values obtained from HAR. These quantities are compared and found to agree with those obtained from (i) accurate neutron diffraction data measured at the same temperatures as the X-ray data and (ii) multipole modelling (MM), an established alternative method for interpreting X-ray diffraction data with the help of aspherical atomic scattering factors. Results are presented for three chemically different systems: the aromatic hydro-carbon rubrene (orthorhombic 5,6,11,12-tetra-phenyl-tetracene), a co-crystal of zwitterionic betaine, imidazolium cations and picrate anions (BIPa), and the salt potassium hydrogen oxalate (KHOx). The non-hydrogen HAR-ADPs are as accurate and precise as the MM-ADPs. Both show excellent agreement with the neutron-based values and are superior to IAM-ADPs. The anisotropic hydrogen HAR-ADPs show a somewhat larger deviation from neutron-based values than the hydrogen SHADE-ADPs used in MM. Element-hydrogen bond lengths from HAR are in excellent agreement with those obtained from neutron diffraction experiments, although they are somewhat less precise. The residual density contour maps after HAR show fewer features than those after MM. Calculating the static electron density with the def2-TZVP basis set instead of the simpler def2-SVP one does not improve the refinement results significantly. All HARs were performed within the recently introduced HARt option implemented in the Olex2 program. They are easily launched inside its graphical user interface following a conventional IAM.

Validation of X-ray Wavefunction Refinement

In this work, the quality of the electron density in crystals reconstructed by the multipolar model (MM) and by X-ray wavefunction refinement (XWR) is tested on a set of high-resolution X-ray diffraction data sets of four amino acids and six tripeptides. It results in the first thorough validation of XWR. Agreement statistics, figures of merit, residual- and deformation-density maps, as well as atomic displacement parameters are used to measure the quality of the reconstruction relative to the measured structure factors. Topological analysis of the reconstructed density is carried out to obtain atomic and bond-topological properties, which are subsequently compared to the values derived from benchmarking periodic DFT geometry optimizations. XWR is simultaneously in better agreement than the MM with both benchmarking theory and the measured diffraction pattern. In particular, the obvious problems with the description of polar bonds in the MM are significantly reduced by using XWR. Similarly, modeling of electron density in the vicinity of hydrogen atoms with XWR is visibly improved.

Quantum crystallography

Approximate wavefunctions can be improved by constraining them to reproduce observations derived from diffraction and scattering experiments. Conversely, charge density models, incorporating electron-density distributions, atomic positions and atomic motion, can be improved by supplementing diffraction experiments with quantum chemically calculated, tailor-made electron densities (form factors). In both cases quantum chemistry and diffraction/scattering experiments are combined into a single, integrated tool. The development of quantum crystallographic research is reviewed. Some results obtained by quantum crystallography illustrate the potential and limitations of this field.

Superelectrophilic Behavior of an Anion Demonstrated by the Spontaneous Binding of Noble Gases to [B12 Cl11 ]<sup/>

It is common and chemically intuitive to assign cations electrophilic and anions nucleophilic reactivity, respectively. Herein, we demonstrate a striking violation of this concept: The anion [B₁₂ Cl₁₁ ]^- spontaneously binds to the noble gases (Ngs) xenon and krypton at room temperature in a reaction that is typical of "superelectrophilic" dications. [B₁₂ Cl₁₁ Ng]^- adducts, with Ng binding energies of 80 to 100 kJ mol^-1 , contain B-Ng bonds with a substantial degree of covalent interaction. The electrophilic nature of the [B₁₂ Cl₁₁ ]^- anion is confirmed spectroscopically by the observation of a blue shift of the CO stretching mode in the IR spectrum of [B₁₂ Cl₁₁ CO]^- and theoretically by investigation of its electronic structure. The orientation of the electric field at the reactive site of [B₁₂ Cl₁₁ ]^- results in an energy barrier for the approach of polar molecules and facilitates the formation of Ng adducts that are not detected with reactive cations such as [C₆ H₅ ]⁺ . This introduces the new chemical concept of "dipole-discriminating electrophilic anions."

A potential Cu/V-organophosphonate platform for tailored void spacesviaterpyridine mold casting

The reaction of appropriate copper and vanadium salts with tetratopic methane tetra-p-phenylphosphonic acid (MTPPA) in the presence of 2,2′:6′:2′′-terpyridine (terpy) yielded the three-dimensional bimetallic copper vanadium phosphonate framework [{Cu(terpy)}4Cu(VO2)4(MTPPA-H)2]·4H2O (1). Terpy has no net contribution to the three-dimensional structure providing a potential platform for void space formationviamold-casting. The structure was characterized by single-crystal X-ray diffraction and thermogravimetric analysis (TGA). Magnetic measurements were performed using a SQUID magnetometer. The crystal structure of the methanol solvate of the free ligand, MTPPA·MeOH, was analysed using Hirshfeld surfaces and fingerprint plots.

Importance of Relativistic Effects and Electron Correlation in Structure Factors and Electron Density of Diphenyl Mercury and Triphenyl Bismuth

This study investigates the possibility of detecting relativistic effects and electron correlation in single-crystal X-ray diffraction experiments using the examples of diphenyl mercury (HgPh2) and triphenyl bismuth (BiPh3). In detail, the importance of electron correlation (ECORR), relativistic effects (REL) [distinguishing between total, scalar and spin-orbit (SO) coupling relativistic effects] and picture change error (PCE) on the theoretical electron density, its topology and its Laplacian using infinite order two component (IOTC) wave functions is discussed. This is to develop an understanding of the order of magnitude and shape of these different effects as they manifest in the electron density. Subsequently, the same effects are considered for the theoretical structure factors. It becomes clear that SO and PCE are negligible, but ECORR and scalar REL are important in low- and medium-order reflections on absolute and relative scales-not in the high-order region. As a further step, Hirshfeld atom refinement (HAR) and subsequent X-ray constrained wavefunction (XCW) fitting have been performed for the compound HgPh2 with various relativistic and nonrelativistic wave functions against the experimental structure factors. IOTC calculations of theoretical structure factors and relativistic HAR as well as relativistic XCW fitting are presented for the first time, accounting for both scalar and spin-orbit relativistic effects.

SF5-Enolates in Ti(IV)-Mediated Aldol Reactions

The F···Ti bonding in the transition structures determines high trans- and syn-diastereoselectivities for aldol reactions of SF5-acetates with aldehydes in the presence of TiCl4 in the non-nucleophilic solvent CH2Cl2. Such bonding is canceled in nucleophilic solvents where opposite cis-stereochemistry is observed. The potential of thus obtained stereoisomeric SF5-aryl acrylates as dipolarophiles in the preparation of SF5-containing heterocycles is demonstrated.

Hydrogen atoms can be located accurately and precisely by x-ray crystallography

Precise and accurate structural information on hydrogen atoms is crucial to the study of energies of interactions important for crystal engineering, materials science, medicine, and pharmacy, and to the estimation of physical and chemical properties in solids. However, hydrogen atoms only scatter x-radiation weakly, so x-rays have not been used routinely to locate them accurately. Textbooks and teaching classes still emphasize that hydrogen atoms cannot be located with x-rays close to heavy elements; instead, neutron diffraction is needed. We show that, contrary to widespread expectation, hydrogen atoms can be located very accurately using x-ray diffraction, yielding bond lengths involving hydrogen atoms (A-H) that are in agreement with results from neutron diffraction mostly within a single standard deviation. The precision of the determination is also comparable between x-ray and neutron diffraction results. This has been achieved at resolutions as low as 0.8 Å using Hirshfeld atom refinement (HAR). We have applied HAR to 81 crystal structures of organic molecules and compared the A-H bond lengths with those from neutron measurements for A-H bonds sorted into bonds of the same class. We further show in a selection of inorganic compounds that hydrogen atoms can be located in bridging positions and close to heavy transition metals accurately and precisely. We anticipate that, in the future, conventional x-radiation sources at in-house diffractometers can be used routinely for locating hydrogen atoms in small molecules accurately instead of large-scale facilities such as spallation sources or nuclear reactors.