Experimental determination of core electron deformation in diamond

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).

Novel Ultrahard Extended Hexagonal C10, C14 and C18 Allotropes with Mixed sp2/sp3 Hybridizations: Crystal Chemistry and Ab Initio Investigations

Based on 4H, 6H and 8H diamond polytypes, novel extended lattice allotropes C10, C14 and C18 characterized by mixed sp3/sp2 carbon hybridizations were devised based on crystal chemistry rationale and first-principles calculations of the ground state structures and energy derived properties: mechanical, dynamic (phonons), and electronic band structure. The novel allotropes were found increasingly cohesive along the series, with cohesive energy values approaching those of diamond polytypes. Regarding mechanical properties, C10, C14, and C18 were found ultrahard with Vickers hardness slightly below that of diamond. All of them are dynamically stable, with positive phonon frequencies reaching maxima higher than in diamond due to the stretching modes of C=C=C linear units. The electronic band structures expectedly reveal the insulating character of all three diamond polytypes and the conductive character of the hybrid allotropes. From the analysis of the bands crossing the Fermi level, a nesting Fermi surface was identified, allowing us to predict potential superconductive properties.

Prediction of Novel Ultrahard Phases in the B-C-N System from First Principles: Progress and Problems

The modern synthesis of superhard and, especially, ultrahard phases is a fascinating area of research that could lead to the design of new, industrially important materials. Computational methods built within the well-established quantum mechanics framework of density functional theory (DFT) play an important role in the search for these advanced materials and the prediction of their properties. The close relationship between the physical properties of carbon and boron nitride has led to particular interest in the B-C-N ternary system, characterized by the small radii of the elements, resulting in short interatomic distances and reduced volumes-the parameters being 'recipes' for very high hardness in three-dimensional structures. The purpose of this review is to provide a brief outline of recent developments and problems in predicting novel ultrahard carbon allotropes as well as binary and ternary compounds of the B-C-N system with particular emphasis on the analysis of the models used to evaluate the hardness of the theoretically predicted structures.

Electron density and thermal motion of diamond at elevated temperatures

The electron density and thermal motion of diamond are determined at nine temperatures between 100 K and 1000 K via synchrotron powder X-ray diffraction (PXRD) data collected on a high-accuracy detector system. Decoupling of the thermal motion from the thermally smeared electron density is performed via an iterative Wilson-Hansen-Coppens-Rietveld procedure using theoretical static structure factors from density functional theory (DFT) calculations. The thermal motion is found to be harmonic and isotropic in the explored temperature range, and excellent agreement is observed between experimental atomic displacement parameters (ADPs) and those obtained via theoretical harmonic phonon calculations (HPC), even at 1000 K. The Debye temperature of diamond is determined experimentally to be Θ_D = 1883 (35) K. A topological analysis of the electron density explores the temperature dependency of the electron density at the bond critical point. The properties are found to be constant throughout the temperature range. The robustness of the electron density confirms the validity of the crystallographic convolution approximation for diamond in the explored temperature range.

Interacting Quantum Atoms Method for Crystalline Solids

An implementation of the Interacting Quantum Atoms method for crystals is presented. It provides a real space energy decomposition of the energy of crystals in which all energy components are physically meaningful. The new package ChemInt enables one to compute intra-atomic and inter-atomic energies, as well as electron population measures used for quantitative description of chemical bonds in crystals. The implementation is tested and applied to characteristic molecular and crystalline systems with different types of bonding.

The Effects of Chemical Bonding at Subatomic Resolution: A Case Study on α-Boron

Similar to classical asphericity shifts, aspherical deformations of the electron density in the atomic core region can result in core asphericity shifts in refinements using a Hansen-Coppens multipolar model (HCM), especially when highly precise experimental datasets with resolutions far beyond sin(θ)/λ ≤ 1.0 Å⁻¹ are employed. These shifts are about two orders of magnitude smaller than their counterparts caused by valence shell deformations, and their underlying deformations are mainly of dipolar character for 1st row atoms. Here, we analyze the resolution dependence of core asphericity shifts in α-boron. Based on theoretical structure factors, an appropriate Extended HCM (EHCM) is developed, which is tested against experimental high-resolution (sin(θ)/λ ≤ 1.6 Å⁻¹) single-crystal diffraction data. Bond length deviations due to core asphericity shifts of α-boron in the order of 4–6·10⁻⁴ Å are small but significant at this resolution and can be effectively compensated by an EHCM, although the correlation of the additional model parameters with positional parameters prevented a free refinement of all core model parameters. For high quality, high resolution data, a proper treatment with an EHCM or other equivalent methods is therefore highly recommended.

Computational Chemistry-Guided Syntheses and Crystal Structures of the Heavier Lanthanide Hydride Oxides DyHO, ErHO, and LuHO

Heteroanionic hydrides offer great possibilities in the design of functional materials. For ternary rare earth hydride oxide REHO, several modifications were reported with indications for a significant phase width with respect to H and O of the cubic representatives. We obtained DyHO and ErHO as well as the thus far elusive LuHO from solid-state reactions of RE2O3 and REH3 or LuH3 with CaO and investigated their crystal structures by neutron and X-ray powder diffraction. While DyHO, ErHO, and LuHO adopted the cubic anion-ordered half-Heusler LiAlSi structure type (F4¯3m, a(DyHO) = 5.30945(10) Å, a(ErHO) = 5.24615(7) Å, a(LuHO) = 5.171591(13) Å), LuHO additionally formed the orthorhombic anti-LiMgN structure type (Pnma; LuHO: a = 7.3493(7) Å, b = 3.6747(4) Å, c = 5.1985(3) Å; LuDO: a = 7.3116(16) Å, b = 3.6492(8) Å, c = 5.2021(7) Å). A comparison of the cubic compounds’ lattice parameters enabled a significant distinction between REHO and REH1+2xO1−x (x < 0 or x > 0). Furthermore, a computational chemistry study revealed the formation of REHO compounds of the smallest rare earth elements to be disfavored in comparison to the sesquioxides, which is why they may only be obtained by mild synthesis conditions.

Atomic-Scale Visualization of Ultrafast Bond Breaking in X-Ray-Excited Diamond

Ultrafast changes of charge density distribution in diamond after irradiation with an intense x-ray pulse (photon energy, 7.8 keV; pulse duration, 6 fs; intensity, 3×10^{19}  W/cm^{2}) have been visualized with the x-ray pump-x-ray probe technique. The measurement reveals that covalent bonds in diamond are broken and the electron distribution around each atom becomes almost isotropic within ∼5  fs after the intensity maximum of the x-ray pump pulse. The 15 fs time delay observed between the bond breaking and atomic disordering indicates nonisothermality of electron and lattice subsystems on this timescale. From these observations and simulation results, we interpret that the x-ray-induced change of the interatomic potential drives the ultrafast atomic disordering underway to the following nonthermal melting.

HoHO: A Paramagnetic Air-Resistant Ionic Hydride with Ordered Anions

The substitution of hydrogen for oxygen atoms in metal oxides provides opportunities for influencing the solid-state properties. Such hydride oxides (or oxyhydrides) are potential functional materials and scarce. Here, we present the synthesis and characterization of holmium hydride oxide with the stoichiometric composition HoHO. It was prepared by the reaction of Ho₂O₃ with either HoH₃ or CaH₂ as a powder of light-yellow color in sunlight and pink color in artificial light (Alexandrite effect), which is commonly observed for ionic Ho(III) compounds. HoHO crystallizes with an ordered fluorite superstructure (F4̅3m, a = 5.27550(13) Å, half-Heusler LiAlSi type), as evidenced by powder X-ray and neutron powder diffraction on both hydride and deuteride and supported by quantum-mechanical calculations. HoHO is the first representative with considerable ionic bonding for this structure type. The thermal stability and inertness toward air are remarkably high for a hydride because it reacts only above 540 K to form Ho₂O₃. At 294(1) K and 25(3)% relative humidity, HoHO is stable for at least 3 months. HoHO is paramagnetic with μ_eff(Ho³⁺) = 10.41(2) μ_B without any sign of magnetic ordering down to 2 K.

Multipole electron densities and structural parameters from synchrotron powder X-ray diffraction data obtained with a MYTHEN detector system (OHGI)

Powder X-ray diffraction has some inherent advantages over traditional single-crystal X-ray diffraction in accurately determining electron densities and structural parameters due to the lower requirements for sample crystallinity, simpler corrections and measurement simultaneity. For some simple inorganic materials, it has been shown that these advantages can compensate for disadvantages such as peak overlap and error-prone background subtraction. Although it is challenging to extend powder X-ray diffraction-based electron-density studies to organic materials with significant peak overlap, previous results using a dedicated vacuum diffractometer with a large image-plate camera (AVID) demonstrated that it can be done. However, the vacuum setup with the off-line detector system was found to prohibit a widespread use. Fast microstrip detectors, which have been employed at a number of powder diffraction beamlines, have the potential to facilitate electron-density studies. Nevertheless, no electron-density studies even for materials with slight peak overlap have been performed with microstrip detectors. One of the most critical problems has been a difference in sensitivity between microstrip channels, which substantially defines the dynamic range of a detector. Recently, a robust approach to this problem has been developed and applied to a total scattering measurement system (OHGI) with 15 MYTHEN microstrip modules. In the present study, synchrotron powder X-ray diffraction data obtained with OHGI are evaulated in terms of multipole electron densities and structural parameters (atomic positions and displacement parameters). These results show that, even without a dedicated setup and perfect samples, electron-density modelling can be carried out on high-quality powder X-ray diffraction data. However, it was also found that the required prior information about the sample prohibits widespread use of the method. With the presently obtainable data quality, electron densities of molecular crystals in general are not reliably obtained from powder data, but it is an excellent, possibly superior, alternative to single-crystal measurements for small-unit-cell inorganic solids. If aspherical atomic scattering factors can be obtained from other means (multipole databases, theoretical calculations), then atomic positions (including for hydrogen) and anisotropic atomic displacement parameters (non-hydrogen atoms) of excellent accuracy can be refined from synchrotron powder X-ray diffraction data on organic crystals.

YHO, an Air-Stable Ionic Hydride

Metal hydride oxides are an emerging field in solid-state research. While some lanthanide hydride oxides (LnHO) were known, YHO has only been found in thin films so far. Yttrium hydride oxide, YHO, can be synthesized as bulk samples by a reaction of Y₂O₃ with hydrides (YH₃, CaH₂), by a reaction of YH₃ with CaO, or by a metathesis of YOF with LiH or NaH. X-ray and neutron powder diffraction reveal an anti-LiMgN type structure for YHO (Pnma, a = 7.5367(3) Å, b = 3.7578(2) Å, and c = 5.3249(3) Å) and YDO (Pnma, a = 7.5309(3) Å, b = 3.75349(13) Å, and c = 5.3192(2) Å); in other words, a distorted fluorite type with ordered hydride and oxide anions was observed. Bond lengths (average 2.267 Å (Y-O), 2.352 Å (Y-H), 2.363 Å (Y-D), >2.4 Å (H-H and D-D), >2.6 Å (H-O and D-O), and >2.8 Å (O-O)) and quantum-mechanical calculations on density functional theory level (band gap 2.8 eV) suggest yttrium hydride oxide to be a semiconductor and to have considerable ionic bonding character. Nonetheless, YHO exhibits a surprising stability in air. An in situ X-ray diffraction experiment shows that decomposition of YHO to Y₂O₃ starts at only above 500 K and is still not complete after 14 h of heating to a final temperature of 1000 K. YHO hydrolyzes in water very slowly. The inertness of YHO in air is very beneficial for its potential use as a functional material.

Valence-Shell Electron-Pair Repulsion Theory Revisited: An Explanation for Core Polarization

Valence-shell electron-pair repulsion (VSEPR) theory constitutes one of the pillars of theoretical predictive chemistry. It was proposed even before the advent of the concept of "spin", and it is still a very useful tool in chemistry. In this article we propose an extension of VSEPR theory to understand the core structure and predict core polarization in the main-group elements. We show from first principles (Electron Localization Function analysis) how the inner- and outer-core shells are organized. In particular, electrons in these regions are structured following the shape of the dual polyhedron of the valence shell (3^rd period) or the equivalent polyhedron (4^th and 5^th periods). We interpret these results in terms of "hard" and "soft" core character. All the studied systems follow this trend, providing a framework for predicting electron distribution in the core. We also show that lone pairs behave as "standard ligands" in terms of core polarization. The predictive character of the model was tested by proposing the core polarization in different systems not included in the original set (such as XeF₄ and [Fe(CN)₆ ]^3- ) and checking the hypothesis by means of a posteriori calculations. From the experimental point of view, the extension of VSEPR to the core region has consequences for current crystallography research. In particular, it explains the core polarization revealed by high resolution X-ray experiments.

Multipole electron densities and atomic displacement parameters in urea from accurate powder X-ray diffraction

Electron density determination based on structure factors obtained through powder X-ray diffraction has so far been limited to high-symmetry inorganic solids. This limit is challenged by determining high-quality structure factors for crystalline urea using a bespoke vacuum diffractometer with imaging plates. This allows the collection of data of sufficient quality to model the electron density of a molecular system using the multipole method. The structure factors, refined parameters as well as chemical bonding features are compared with results from the high-quality synchrotron single-crystal study by Birkedal et al. [Acta Cryst. (2004), A60, 371-381] demonstrating that powder X-ray diffraction potentially provides a viable alternative for electron density determination in simple molecular crystals where high-quality single crystals are not available.

QTAIM Assessment of the Intra- and Intermolecular Bonding in a Bis(nitramido-oxadiazolate) Energetic Ionic Salt at 20 K

Accurate experimental determination of the electron density distribution for the energetic ionic salt bis(ammonium) 2,2'-dinitramido-5,5'-bis(1-oxa-3,4-diazolate) dihydrate (1) is obtained from multipole modeling of single-crystal X-ray diffraction data collected at 20 K. The intra- and intermolecular bonding is assessed in terms of the quantum theory of atoms in molecules (QTAIM) with a view to better understanding the physicochemical properties in relation to chemical bonding. Topological analysis reveals stronger bonding for the N-NO₂ bond relative to energetic nitramines RDX and HMX and the indication of a trend between this and impact sensitivity of nitro-containing energetic materials is noted. The intermolecular bonding of 1 is dominated by classical H-bonds but includes multiple π-bonding interactions and interactions between H-bond donor and acceptor atoms where bond paths are deflected by H atoms. There also exists a weak O···O interaction between end-on nitro groups, as well as an intramolecular ring-forming 1,5-type interaction. An anharmonic description of thermal motion was required to obtain the best fitting model, despite the low temperature of the study. The experimental study was complemented by periodic boundary DFT calculations at the experimental geometry as well as gas phase calculations on the isolated dianion.

On the error in the nucleus-centered multipolar expansion of molecular electron density and its topology: A direct-space computational study

The convergence of nucleus-centered multipolar expansion of the quantum-chemical electron density (QC-ED), gradient, and Laplacian is investigated in terms of numerical radial functions derived by projecting stockholder atoms onto real spherical harmonics at each center. The partial sums of this exact one-center expansion are compared with the corresponding Hansen-Coppens pseudoatom (HC-PA) formalism [Hansen, N. K. and Coppens, P., "Testing aspherical atom refinements on small-molecule data sets," Acta Crystallogr., Sect. A 34, 909-921 (1978)] commonly utilized in experimental electron density studies. It is found that the latter model, due to its inadequate radial part, lacks pointwise convergence and fails to reproduce the local topology of the target QC-ED even at a high-order expansion. The significance of the quantitative agreement often found between HC-PA-based (quadrupolar-level) experimental and extended-basis QC-EDs can thus be challenged.

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.

Experimental Charge-Density Study of the Intra- and Intermolecular Bonding in TKX-50

The intra- and intermolecular bonding in the known phase of dihydroxylammonium 5,5'-bistetrazole-1,1'-diolate, TKX-50, has been analyzed on the basis of the experimentally determined charge density distribution from high-resolution X-ray diffraction data obtained at 20 K. This was compared to the charge density obtained from DFT calculations with periodic boundary conditions using both direct calculations and derived structure factors. Results of topological analysis of the electron density corroborate that TKX-50 is best described as a layered structure linked primarily by a number of hydrogen bonds as well as by a variety of other interactions. Additional bonding interactions were identified, including a pair of equivalent 1,5-type intramolecular closed-shell interactions in the dianion. Refinement of anharmonic motion was shown to be essential for obtaining an adequate model, despite the low temperature of the study. Although generally unusual, the implementation of anharmonic refinement provided a significant improvement compared to harmonic refinement of both traditional and split-core multipole models.

Accurate charge densities from powder X-ray diffraction - a new version of the Aarhus vacuum imaging-plate diffractometer

In recent years powder X-ray diffraction has proven to be a valuable alternative to single-crystal X-ray diffraction for determining electron-density distributions in high-symmetry inorganic materials, including subtle deformation in the core electron density. This was made possible by performing diffraction measurements in vacuum using high-energy X-rays at a synchrotron-radiation facility. Here we present a new version of our custom-built in-vacuum powder diffractometer with the sample-to-detector distance increased by a factor of four. In practice this is found to give a reduction in instrumental peak broadening by approximately a factor of three and a large improvement in signal-to-background ratio compared to the previous instrument. Structure factors of silicon at room temperature are extracted using a combined multipole-Rietveld procedure and compared with ab initio calculations and the results from the previous diffractometer. Despite some remaining issues regarding peak asymmetry, the new diffractometer yields structure factors of comparable accuracy to the previous diffractometer at low angles and improved accuracy at high angles. The high quality of the structure factors is further assessed by modelling of core electron deformation with results in good agreement with previous investigations.

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

In this review, recent developments concerning data and model quality in experimental charge-density investigations from a personal view-point are described. Data quality is not only achieved by the high resolution, high I/σ(I) values, low merging R values and high multiplicity. The quality of the innermost reflections especially is crucial for mapping the density distribution of the outermost valence electrons and can be monitored by (I/σ)^asymptotic. New detector technologies seem to be promising improvements. Empirical corrections to correct for low-energy contamination of mirror-focused X-ray data and for resolution- and temperature-dependent errors caused by factors such as thermal diffuse scattering are described. Shashlik-like residual density patterns can indicate the need for an anharmonic description of the thermal motion of individual atoms. The physical reliability of the derived model must be thoroughly analysed. The derived probability density functions for the mean-squared atomic vibrational displacements especially should have only small negative values. The treatment of H atoms has been improved by methods to estimate anisotropic thermal motion. For very high resolution data, the polarization of the core density cannot be neglected. Several tools to detect systematic errors are described. A validation tool is presented that easily detects when the refinement of additional parameters yields a real improvement in the model or simply overfits the given data. In all investigated structures, it is proved that the multipole parameters of atoms with a comparable chemical environment should be constrained to be identical. The use of restraints could be a promising alternative.

Multi-temperature study of potassium uridine-5'-monophosphate: electron density distribution and anharmonic motion modelling

Uridine, a nucleoside formed of a uracil fragment attached to a ribose ring via a β-N1-glycosidic bond, is one of the four basic components of ribonucleic acid. Here a new anhydrous structure and experimental charge density distribution analysis of a uridine-5'-monophosphate potassium salt, K(UMPH), is reported. The studied case constitutes the very first structure of a 5'-nucleotide potassium salt according to the Cambridge Structural Database. The excellent crystal quality allowed the collection of charge density data at various temperatures, i.e. 10, 100, 200 and 300 K on one single crystal. Crystal structure and charge density data were analysed thoroughly in the context of related literature-reported examples. Detailed analysis of the charge density distribution revealed elevated anharmonic motion of part of the uracil ring moiety relatively weakly interacting with the neighbouring species. The effect was manifested by alternate positive and negative residual density patterns observed for these atoms, which `disappear' at low temperature. It also occurred that the potassium cation, quite uniformly coordinated by seven O atoms from all molecular fragments of the UMPH^- anion, including the O atom from the ribofuranose ring, can be treated as spherical in the charge density model which was supported by theoretical calculations. Apart from the predominant electrostatic interactions, four relatively strong hydrogen bond types further support the stability of the crystal structure. This results in a compact and quite uniform structure (in all directions) of the studied crystal, as opposed to similar cases with layered architecture reported in the literature.

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.

Spatial distribution of electrons near the Fermi level in the metallic LaB6 through accurate X-ray charge density study

Charge densities of iso-structural metal hexaborides, a transparent metal LaB₆ and a semiconductor BaB₆, have been determined using the d > 0.22 Å ultra-high resolution synchrotron radiation X-ray diffraction data by a multipole refinement and a maximum entropy method (MEM). The quality of the experimental charge densities was evaluated by comparison with theoretical charge densities. The strong inter-octahedral and relatively weak intra-octahedral boron-boron bonds were observed in the charge densities. A difference of valence charge densities between LaB₆ and BaB₆ was calculated to reveal a small difference between isostructural metal and semiconductor. The weak electron lobes distributed around the inter B₆ octahedral bond were observed in the difference density. We found the electron lobes are the conductive π-electrons in LaB₆ from the comparison with the theoretical valence charge density. We successfully observed a spatial distribution of electrons near the Fermi level from the X-ray charge density study of the series of iso-structural solids.

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.

Experimental and theoretical charge-density analysis of 1,4-bis(5-hexyl-2-thienyl)butane-1,4-dione: applications of a virtual-atom model

The experimental and theoretical charge densities of 1,4-bis(5-hexyl-2-thienyl)butane-1,4-dione, a precursor in the synthesis of thiophene-based semiconductors and organic solar cells, are presented. A dummy bond charges spherical atom model is applied besides the multipolar atom model. The results show that the dummy bond charges model is accurate enough to calculate electrostatic-derived properties which are comparable with those obtained by the multipolar atom model. The refinement statistics and the residual electron density values are found to be intermediate between the independent atom and the multipolar formalisms.

Low-temperature powder X-ray diffraction measurements in vacuum: analysis of the thermal displacement of copper

A serious limitation of the all-in-vacuum diffractometer reported by Straasø, Dippel, Becker & Als-Nielsen [J. Synchrotron Rad.(2014),21, 119–126] has so far been the inability to cool samples to near-cryogenic temperatures during measurement. The problem is solved by placing the sample in a jet of helium gas cooled by liquid nitrogen. The resulting temperature change is quantified by determining the change in unit-cell parameter and atomic displacement parameter of copper. The cooling proved successful, with a resulting temperature of ∼95 (3) K. The measured powder X-ray diffraction data are of superb quality and high resolution [up to sinθ/λ = 2.2 Å−1], permitting an extensive modelling of the thermal displacement. The anharmonic displacement of copper was modelled by a Gram–Charlier expansion of the temperature factor. As expected, the corresponding probability distribution function shows an increased probability away from neighbouring atoms and a decreased probability towards them.

Synchrotron powder diffraction of silicon: high-quality structure factors and electron density

Crystalline silicon is an ideal compound to test the current state of experimental structure factors and corresponding electron densities. High-quality structure factors have been measured on crystalline silicon with synchrotron powder X-ray diffraction. They are in excellent agreement with benchmark Pendellösung data having comparable accuracy and precision, but acquired in far less time and to a much higher resolution (sin θ/λ < 1.7 Å(-1)). The extended data range permits an experimental modelling of not only the valence electron density but also the core deformation in silicon, establishing an increase of the core density upon bond formation in crystalline silicon. Furthermore, a physically sound procedure for evaluating the standard deviation of powder-derived structure factors has been applied. Sampling statistics inherently account for contributions from photon counts as well as the limited number of diffracting particles, where especially the latter are particularly difficult to handle.

Raman spectroscopic features of the neutral vacancy in diamond from ab initio quantum-mechanical calculations

Ab initio calculations of the Raman spectrum of the neutral vacancy in diamond reproduce observed spectral features of irradiated diamond up to the first-order peak.

Modelling the experimental electron density: only the synergy of various approaches can tackle the new challenges

Electron density is a fundamental quantity that enables understanding of the chemical bonding in a molecule or in a solid and the chemical/physical property of a material. Because electrons have a charge and a spin, two kinds of electron densities are available. Moreover, because electron distribution can be described in momentum or in position space, charge and spin density have two definitions and they can be observed through Bragg (for the position space) or Compton (for the momentum space) diffraction experiments, using X-rays (charge density) or polarized neutrons (spin density). In recent years, we have witnessed many advances in this field, stimulated by the increased power of experimental techniques. However, an accurate modelling is still necessary to determine the desired functions from the acquired data. The improved accuracy of measurements and the possibility to combine information from different experimental techniques require even more flexibility of the models. In this short review, we analyse some of the most important topics that have emerged in the recent literature, especially the most thought-provoking at the recent IUCr general meeting in Montreal.

Beamline P02.1 at PETRA III for high-resolution and high-energy powder diffraction

Powder X-ray diffraction techniques largely benefit from the superior beam quality provided by high-brilliance synchrotron light sources in terms of photon flux and angular resolution. The High Resolution Powder Diffraction Beamline P02.1 at the storage ring PETRA III (DESY, Hamburg, Germany) combines these strengths with the power of high-energy X-rays for materials research. The beamline is operated at a fixed photon energy of 60 keV (0.207 Å wavelength). A high-resolution monochromator generates the highly collimated X-ray beam of narrow energy bandwidth. Classic crystal structure determination in reciprocal space at standard and non-ambient conditions are an essential part of the scientific scope as well as total scattering analysis using the real space information of the pair distribution function. Both methods are complemented by in situ capabilities with time-resolution in the sub-second regime owing to the high beam intensity and the advanced detector technology for high-energy X-rays. P02.1's efficiency in solving chemical and crystallographic problems is illustrated by presenting key experiments that were carried out within these fields during the early stage of beamline operation.

Contemporary X-ray electron-density studies using synchrotron radiation

Synchrotron radiation has many compelling advantages over conventional radiation sources in the measurement of accurate Bragg diffraction data. The variable photon energy and much higher flux may help to minimize critical systematic effects such as absorption, extinction and anomalous scattering. Based on a survey of selected published results from the last decade, the benefits of using synchrotron radiation in the determination of X-ray electron densities are discussed, and possible future directions of this field are examined.

Hirshfeld atom refinement for modelling strong hydrogen bonds

High-resolution low-temperature synchrotron X-ray diffraction data of the salt L-phenylalaninium hydrogen maleate are used to test the new automated iterative Hirshfeld atom refinement (HAR) procedure for the modelling of strong hydrogen bonds. The HAR models used present the first examples of Z' > 1 treatments in the framework of wavefunction-based refinement methods. L-Phenylalaninium hydrogen maleate exhibits several hydrogen bonds in its crystal structure, of which the shortest and the most challenging to model is the O-H...O intramolecular hydrogen bond present in the hydrogen maleate anion (O...O distance is about 2.41 Å). In particular, the reconstruction of the electron density in the hydrogen maleate moiety and the determination of hydrogen-atom properties [positions, bond distances and anisotropic displacement parameters (ADPs)] are the focus of the study. For comparison to the HAR results, different spherical (independent atom model, IAM) and aspherical (free multipole model, MM; transferable aspherical atom model, TAAM) X-ray refinement techniques as well as results from a low-temperature neutron-diffraction experiment are employed. Hydrogen-atom ADPs are furthermore compared to those derived from a TLS/rigid-body (SHADE) treatment of the X-ray structures. The reference neutron-diffraction experiment reveals a truly symmetric hydrogen bond in the hydrogen maleate anion. Only with HAR is it possible to freely refine hydrogen-atom positions and ADPs from the X-ray data, which leads to the best electron-density model and the closest agreement with the structural parameters derived from the neutron-diffraction experiment, e.g. the symmetric hydrogen position can be reproduced. The multipole-based refinement techniques (MM and TAAM) yield slightly asymmetric positions, whereas the IAM yields a significantly asymmetric position.

Model-independent structure factors from powder X-ray diffraction: a novel approach

Under the experimental condition that all Bragg peaks in a powder X-ray diffraction (PXRD) pattern have the same shape, one can readily obtain the Bragg intensities without fitting any parameters. This condition is fulfilled at the P02.1 beamline at PETRA III using the seventh harmonic from a 23 mm-period undulator (60 keV) at a distance of 65 m. For grain sizes of the order of 1 µm, the Bragg peak shape in the PXRD is entirely determined by the diameter of the capillary containing the powder sample and the pixel size of the image plate detector, and consequently it is independent of the scattering angle. As an example, a diamond powder has been chosen and structure factors derived which are in accordance with those calculated from density functional theory methods of the WIEN2k package to within an accuracy that allows a detailed electron density analysis.