Statistical analysis of multipole-model-derived structural parameters and charge-density properties from high-resolution X-ray diffraction experiments

A quantum crystallographic protocol for general use

Quantum crystallography has become ever more important in recent years for the accurate determination of molecular and crystal structures. The results of quantum crystallographic refinements of X-ray data are as accurate and precise as from neutron diffraction and they give access to the complete electronic structure of the compound under investigation. Is the method now mature enough and easy enough to use to extend and ultimately supersede standard X-ray crystal structure determination routines? We utilize the world's most common crystal structure-the YLID test crystal that every owner of an X-ray diffractometer receives with their machine-to show under which circumstances routine, low-resolution, and even room-temperature measurements can be subjected to quantum crystallographic refinement. Based on this, we describe a quantum crystallographic protocol step by step that makes application of quantum crystallographic refinement easy to use and reproducible. We encourage that valuable YLID test measurements are not discarded but made available for method development, increasing the availability of repeated measurements from a handful to tens of thousands.

Towards improved accuracy of Hirshfeld atom refinement with an alternative electron density partition

Hirshfeld atom refinement (HAR) is generally the chosen method for obtaining accurate hydrogen atom parameters from X-ray diffraction data. Still, determination can prove challenging, especially in the case of atomic displacement parameters (ADPs). We demonstrate that such a situation can occur when the ADP values of the bonding partner of the hydrogen atom are not determined accurately. Atomic electron densities partially overlap and inaccuracies in the bonding neighbour ADPs can be partially compensated for with modifications to the hydrogen ADPs. We introduce a modified version of the original Hirshfeld partition: the exponential Hirshfeld partition, parameterized with an adjustable parameter (n) to allow control of the overlap level of the atomic electron densities which, for n = 1, is equivalent to the Hirshfeld partition. The accuracy of the HAR-like procedure using the new partition (expHAR) was tested on a set of organic structures using B3LYP and MP2 electron densities. Applying expHAR improved the hydrogen atom parameters in the majority of the structures (compared with HAR), especially in cases with the highest deviations from the reference neutron values. X-H bond lengths and hydrogen ADPs improved for 9/10 of the structures for B3LYP-based refinement and 8/9 for MP2-based refinement when the ADPs were compared with a newly introduced scale-independent similarity measure.

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).

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.

X-ray constrained wavefunctions based on Hirshfeld atoms. II. Reproducibility of electron densities in crystals of α-oxalic acid dihydrate

The Hirshfeld atom-based X-ray constrained wavefunction fitting (HA-XCW) procedure is tested for its reproducibility, and the information content of the fitted wavefunction is critically assessed. Fourteen different α-oxalic acid dihydrate data sets are used for this purpose, and the first joint fitting to 12 of these data sets is reported. There are systematic features in the electron density obtained from all data sets which agree with higher level benchmark calculations, but there are also many other strong systematic features which disagree with the reference calculations, most notably those associated with the electron density near the nuclei. To enhance reproducibility, three new protocols are described and tested to address the halting problem of XCW fitting, namely: an empirical power-function method, which is useful for estimating the accuracy of the structure factor uncertainties; an asymptotic extrapolation method based on ideas from density functional theory; and a `conservative method' whereby the smallest value of the regularization parameter is chosen from a series of data sets, or subsets.

X-ray constrained wavefunctions based on Hirshfeld atoms. I. Method and review

The X-ray constrained wavefunction (XCW) procedure for obtaining an experimentally reconstructed wavefunction from X-ray diffraction data is reviewed. The two-center probability distribution model used to perform nuclear-position averaging in the original paper [Grimwood & Jayatilaka (2001). Acta Cryst. A57, 87-100] is carefully distinguished from the newer one-center probability distribution model. In the one-center model, Hirshfeld atoms are used, and the Hirshfeld atom based X-ray constrained wavefunction (HA-XCW) procedure is described for the first time, as well as its efficient implementation. In this context, the definition of the related X-ray wavefunction refinement (XWR) method is refined. The key halting problem for the XCW method - the procedure by which one determines when overfitting has occurred - is named and work on it reviewed.

Fragmentation and transferability in Hirshfeld atom refinement

Hirshfeld atom refinement (HAR) is one of the most effective methods for obtaining accurate structural parameters for hydrogen atoms from X-ray diffraction data. Unfortunately, it is also relatively computationally expensive, especially for larger molecules due to wavefunction calculations. Here, a fragmentation approach has been tested as a remedy for this problem. It gives an order of magnitude improvement in computation time for larger organic systems and is a few times faster for metal-organic systems at the cost of only minor differences in the calculated structural parameters when compared with the original HAR calculations. Fragmentation was also applied to polymeric and disordered systems where it provides a natural solution to problems that arise when HAR is applied. The concept of fragmentation is closely related to the transferable aspherical atom model (TAAM) and allows insight into possible ways to improve TAAM. Hybrid approaches combining fragmentation with the transfer of atomic densities between chemically similar atoms have been tested. An efficient handling of intermolecular interactions was also introduced for calculations involving fragmentation. When applied in fragHAR (a fragmentation approach for polypeptides) as a replacement for the original approach, it allowed for more efficient calculations. All of the calculations were performed with a locally modified version of Olex2 combined with a development version of discamb2tsc and ORCA. Care was taken to efficiently use the power of multicore processors by simple implementation of load-balancing, which was found to be very important for lowering computational time.

Hirshfeld atom like refinement with alternative electron density partitions

Hirshfeld atom refinement is one of the most successful methods for the accurate determination of structural parameters for hydrogen atoms from X-ray diffraction data. This work introduces a generalization of the method [generalized atom refinement (GAR)], consisting of the application of various methods of partitioning electron density into atomic contributions. These were tested on three organic structures using the following partitions: Hirshfeld, iterative Hirshfeld, iterative stockholder, minimal basis iterative stockholder and Becke. The effects of partition choice were also compared with those caused by other factors such as quantum chemical methodology, basis set, representation of the crystal field and a combination of these factors. The differences between the partitions were small in terms of R factor (e.g. much smaller than for refinements with different quantum chemistry methods, i.e. Hartree-Fock and coupled cluster) and therefore no single partition was clearly the best in terms of experimental data reconstruction. In the case of structural parameters the differences between the partitions are comparable to those related to the choice of other factors. We have observed the systematic effects of the partition choice on bond lengths and ADP values of polar hydrogen atoms. The bond lengths were also systematically influenced by the choice of electron density calculation methodology. This suggests that GAR-derived structural parameters could be systematically improved by selecting an optimal combination of the partition and quantum chemistry method. The results of the refinements were compared with those of neutron diffraction experiments. This allowed a selection of the most promising partition methods for further optimization of GAR settings, namely the Hirshfeld, iterative stockholder and minimal basis iterative stockholder.

On the accuracy and precision of X-ray and neutron diffraction results as a function of resolution and the electron density model

X-ray diffraction is the main source of three-dimensional structural information. In total, more than 1.5 million crystal structures have been refined and deposited in structural databanks (PDB, CSD and ICSD) to date. Almost 99.7% of them were obtained by approximating atoms as spheres within the independent atom model (IAM) introduced over a century ago. In this study, X-ray datasets for single crystals of hydrated α-oxalic acid were refined using several alternative electron density models that abandon the crude spherical approximation: the multipole model (MM), the transferable aspherical atom model (TAAM) and the Hirshfeld atom refinement (HAR) model as a function of the resolution of X-ray data. The aspherical models (MM, TAAM, HAR) give far more accurate and precise single-crystal X-ray results than IAM, sometimes identical to results obtained from neutron diffraction and at low resolution. Hence, aspherical approaches open new routes for improving existing structural information collected over the last century.

Chemical Bonding in Colossal Thermopower FeSb2

FeSb₂ exhibits a colossal Seebeck coefficient ( S ) and a record-breaking high thermoelectric power factor. It also has an atypical shift from diamagnetism to paramagnetism with increasing temperature, and the fine details of its electron correlation effects have been widely discussed. The extraordinary physical properties must be rooted in the nature of the chemical bonding, and indeed, the chemical bonding in this archetypical marcasite structure has been heavily debated on a theoretical basis since the 1960s. The two prevalent models for describing the bonding interactions in FeSb₂ are based on either ligand-field stabilization of Fe or a network structure of Sb hosting Fe ions. However, neither model can account for the observed properties of FeSb₂ . Herein, an experimental electron density study is reported, which is based on analysis of synchrotron X-ray diffraction data measured at 15 K on a minute single crystal to limit systematic errors. The analysis is supplemented with density functional theory calculations in the experimental geometry. The experimental data are at variance with both the additional single-electron Sb-Sb bond implied by the covalent model, and the large formal charge and expected d-orbital splitting advocated by the ionic model. The structure is best described as an extended covalent network in agreement with expectations based on electronegativity differences.

Charge density of 4-methyl-3-[(tetrahydro-2H-pyran-2-yl)oxy]thiazole-2(3H)-thione. A comprehensive multipole refinement, maximum entropy method and density functional theory study

The structure of 4-methyl-3-[(tetrahydro-2H-pyran-2-yl)oxy]thiazole-2(3H)-thione (MTTOTHP) was investigated using X-ray diffraction and computational chemistry methods for determining properties of the nitrogen-oxygen bond, which is the least stable entity upon photochemical excitation. Experimentally measured structure factors have been used to determine and characterize charge density via the multipole model (MM) and the maximum entropy method (MEM). Theoretical investigation of the electron density and the electronic structure has been performed in the finite basis set density functional theory (DFT) framework. Quantum Theory of Atoms In Molecules (QTAIM), deformation densities and Laplacians maps have been used to compare theoretical and experimental results. MM experimental results and predictions from theory differ with respect to the sign and/or magnitude of the Laplacian at the N-O bond critical point (BCP), depending on the treatment of n values of the MM radial functions. Such Laplacian differences in the N-O bond case are discussed with respect to a lack of flexibility in the MM radial functions also reported by Rykounov et al. [Acta Cryst. (2011), B67, 425-436]. BCP Hessian eigenvalues show qualitatively matching results between MM and DFT. In addition, the theoretical analysis used domain-averaged fermi holes (DAFH), natural bond orbital (NBO) analysis and localized (LOC) orbitals to characterize the N-O bond as a single σ bond with marginal π character. Hirshfeld atom refinement (HAR) has been employed to compare to the MM refinement results and/or neutron dataset C-H bond lengths and to crystal or single molecule geometry optimizations, including considerations of anisotropy of H atoms. Our findings help to understand properties of molecules like MTTOTHP as progenitors of free oxygen radicals.

TAAM: a reliable and user friendly tool for hydrogen-atom location using routine X-ray diffraction data

Hydrogen is present in almost all of the molecules in living things. It is very reactive and forms bonds with most of the elements, terminating their valences and enhancing their chemistry. X-ray diffraction is the most common method for structure determination. It depends on scattering of X-rays from electron density, which means the single electron of hydrogen is difficult to detect. Generally, neutron diffraction data are used to determine the accurate position of hydrogen atoms. However, the requirement for good quality single crystals, costly maintenance and the limited number of neutron diffraction facilities means that these kind of results are rarely available. Here it is shown that the use of Transferable Aspherical Atom Model (TAAM) instead of Independent Atom Model (IAM) in routine structure refinement with X-ray data is another possible solution which largely improves the precision and accuracy of X-H bond lengths and makes them comparable to averaged neutron bond lengths. TAAM, built from a pseudoatom databank, was used to determine the X-H bond lengths on 75 data sets for organic molecule crystals. TAAM parametrizations available in the modified University of Buffalo Databank (UBDB) of pseudoatoms applied through the DiSCaMB software library were used. The averaged bond lengths determined by TAAM refinements with X-ray diffraction data of atomic resolution (d_min ≤ 0.83 Å) showed very good agreement with neutron data, mostly within one single sample standard deviation, much like Hirshfeld atom refinement (HAR). Atomic displacements for both hydrogen and non-hydrogen atoms obtained from the refinements systematically differed from IAM results. Overall TAAM gave better fits to experimental data of standard resolution compared to IAM. The research was accompanied with development of software aimed at providing user-friendly tools to use aspherical atom models in refinement of organic molecules at speeds comparable to routine refinements based on spherical atom model.

Experimental charge density of grossular under pressure - a feasibility study

X-ray diffraction studies of crystals under pressure and quantitative experimental charge density analysis are among the most demanding types of crystallographic research. A successful feasibility study of the electron density in the mineral grossular under 1 GPa pressure conducted at the CRISTAL beamline at the SOLEIL synchrotron is presented in this work. A single crystal was placed in a diamond anvil cell, but owing to its special design (wide opening angle), short synchrotron wavelength and the high symmetry of the crystal, data with high completeness and high resolution were collected. This allowed refinement of a full multipole model of experimental electron distribution. Results are consistent with the benchmark measurement conducted without a diamond-anvil cell and also with the literature describing investigations of similar structures. Results of theoretical calculations of electron density distribution on the basis of dynamic structure factors mimic experimental findings very well. Such studies allow for laboratory simulations of processes which take place in the Earth's mantle.

The many flavours of halogen bonds - message from experimental electron density and Raman spectroscopy

Experimental electron-density studies based on high-resolution diffraction experiments allow halogen bonds between heavy halogens to be classified. The topological properties of the electron density in Cl...Cl contacts vary smoothly as a function of the interaction distance. The situation is less straightforward for halogen bonds between iodine and small electronegative nucleophiles, such as nitrogen or oxygen, where the electron density in the bond critical point does not simply increase for shorter distances. The number of successful charge-density studies involving iodine is small, but at least individual examples for three cases have been observed. (a) Very short halogen bonds between electron-rich nucleophiles and heavy halogen atoms resemble three-centre-four-electron bonds, with a rather symmetric heavy halogen and without an appreciable σ hole. (b) For a narrow intermediate range of halogen bonds, the asymmetric electronic situation for the heavy halogen with a pronounced σ hole leads to rather low electron density in the (3,-1) critical point of the halogen bond; the properties of this bond critical point cannot fully describe the nature of the associated interaction. (c) For longer and presumably weaker contacts, the electron density in the halogen bond critical point is only to a minor extent reduced by the presence of the σ hole and hence may be higher than in the aforementioned case. In addition to the electron density and its derived properties, the halogen-carbon bond distance opposite to the σ hole and the Raman frequency for the associated vibration emerge as alternative criteria to gauge the halogen-bond strength. We find exceptionally long C-I distances for tetrafluorodiiodobenzene molecules in cocrystals with short halogen bonds and a significant red shift for their Raman vibrations.

Doxycycline hydrate and doxycycline hydrochloride dihydrate – crystal structure and charge density analysis

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.

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.

A method to estimate statistical errors of properties derived from charge-density modelling

Estimating uncertainties of property values derived from a charge-density model is not straightforward. A methodology, based on calculation of sample standard deviations (SSD) of properties using randomly deviating charge-density models, is proposed with the MoPro software. The parameter shifts applied in the deviating models are generated in order to respect the variance-covariance matrix issued from the least-squares refinement. This `SSD methodology' procedure can be applied to estimate uncertainties of any property related to a charge-density model obtained by least-squares fitting. This includes topological properties such as critical point coordinates, electron density, Laplacian and ellipticity at critical points and charges integrated over atomic basins. Errors on electrostatic potentials and interaction energies are also available now through this procedure. The method is exemplified with the charge density of compound (E)-5-phenylpent-1-enylboronic acid, refined at 0.45 Å resolution. The procedure is implemented in the freely available MoPro program dedicated to charge-density refinement and modelling.

A comparison of the experimental and theoretical charge density distributions in two polymorphic modifications of piroxicam

Experimental charge density distribution studies of two polymorphic forms of piroxicam, β-piroxicam (1) and piroxicam monohydrate (2), were carried out via high-resolution single crystal X-ray diffraction experiments and multipole refinement. The asymmetric unit of (2) consists of two discrete piroxicam molecules, (2a) and (2b), and two water molecules. Geometry differs between (1) and (2) due to the zwitterionic nature of (2) which results in the rotation of the pyridine ring around the C(10)-N(2) bond by approximately 180°. Consequently, the pyridine and amide are no longer co-planar and (2) forms two exclusive, strong hydrogen bonds, H(3)O(4) and H(2)O(3), with bond energies of 66.14 kJ mol^-1 and 112.82 kJ mol^-1 for (2a), and 58.35 kJ mol^-1 and 159.51 kJ mol^-1 for (2b), respectively. Proton transfer between O(3) and N(3) in (2) results in significant differences in surface electrostatic potentials. This is clarified by the calculation of atomic charges in the zwitterion that shows the formally positive charge of the pyridyl nitrogen which is redistributed over the whole of the pyridine ring instead of concentrating at N-H. Similarly, the negative charge of the oxygen is distributed across the benzothiazine carboxamide moiety. The multipole derived lattice energy for (1) is -304 kJ mol^-1 and that for (2) is -571 kJ mol^-1, which is in agreement with the experimentally determined observations of higher solubility and dissolution rates of (1) compared to (2).

Implications of X-ray thermal diffuse scattering in integrated Bragg intensities of silicon and cubic boron nitride

This article describes a theoretical quantification of the thermal diffuse scattering (TDS) contribution to the integrated intensities of single-crystal diffraction from silicon and cubic boron nitride. The TDS intensity is calculatedab initioand the intensity contribution to the Bragg peak determined by integration of a volume of appropriate size. The effect of including TDS in the structure factors is assessed in a subsequent refinement, where the effect on the atomic displacement parameters and the residual Fourier maps is inspected. In both compounds changes caused solely by the TDS inclusion are observed. Particularly, adding TDS to the structure factors of silicon produces significant features in the residual Fourier maps and a change in the atomic displacement parameter. Significant effects are also present at low temperatures. Thus, it is important to address the effect of TDS when pursuing high-accuracy charge densities or if analyzing the atomic displacement parameters.

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.

Validation of experimental charge-density refinement strategies: when do we overfit?

A cross-validation method is supplied to judge between various strategies in multipole refinement procedures. Its application enables straightforward detection of whether the refinement of additional parameters leads to an improvement in the model or an overfitting of the given data. For all tested data sets it was possible to prove that the multipole parameters of atoms in comparable chemical environments should be constrained to be identical. In an automated approach, this method additionally delivers parameter distributions of k different refinements. These distributions can be used for further error diagnostics, e.g. to detect erroneously defined parameters or incorrectly determined reflections. Visualization tools show the variation in the parameters. These different refinements also provide rough estimates for the standard deviation of topological parameters.

An alternative to the goodness of fit

An alternative measure to the goodness of fit (GoF) is developed and applied to experimental data. The alternative goodness of fit squared (aGoFs) demonstrates that the GoF regularly fails to provide evidence for the presence of systematic errors, because certain requirements are not met. These requirements are briefly discussed. It is shown that in many experimental data sets a correlation between the squared residuals and the variance of observed intensities exists. These correlations corrupt the GoF and lead to artificially reduced values in the GoF and in the numerical value of thewR(F2). Remaining systematic errors in the data sets are veiled by this mechanism. In data sets where these correlations do not appear for the entire data set, they often appear for the decile of largest variances of observed intensities. Additionally, statistical errors for the squared goodness of fit, GoFs, and the aGoFs are developed and applied to experimental data. This measure shows how significantly the GoFs and aGoFs deviate from the ideal value one.

Transferable aspherical atom model refinement of protein and DNA structures against ultrahigh-resolution X-ray data

In contrast to the independent-atom model (IAM), in which all atoms are assumed to be spherical and neutral, the transferable aspherical atom model (TAAM) takes into account the deformed valence charge density resulting from chemical bond formation and the presence of lone electron pairs. Both models can be used to refine small and large molecules, e.g. proteins and nucleic acids, against ultrahigh-resolution X-ray diffraction data. The University at Buffalo theoretical databank of aspherical pseudo-atoms has been used in the refinement of an oligopeptide, of Z-DNA hexamer and dodecamer duplexes, and of bovine trypsin. The application of the TAAM to these data improves the quality of the electron-density maps and the visibility of H atoms. It also lowers the conventional R factors and improves the atomic displacement parameters and the results of the Hirshfeld rigid-bond test. An additional advantage is that the transferred charge density allows the estimation of Coulombic interaction energy and electrostatic potential.

Evidence of Polaron Excitations in Low Temperature Raman Spectra of Oxalic Acid Dihydrate

Low temperature Raman spectra of oxalic acid dihydrate (8-300 K) for both the polycrystalline and single crystal phase show strong variation with temperature in the interval from 1200 to 2000 cm(-1). Previous low temperature diffraction studies all confirmed the stability of the crystal P21/n phase with no indications of any phase transition, reporting the existence of a strong hydrogen bond between the oxalic acid and a water molecule. A new group of Raman bands in the 1200-1300 cm(-1) interval below 90 K is observed, caused by possible loss of the center of inversion. This in turn could originate either due to disorder in hydroxyl proton positions or due to proton transfer from carboxylic group to water molecule. The hypothesis of proton transfer is further supported by the emergence of new bands centered at 1600 and 1813 cm(-1), which can be explained with vibrations of H3O(+) ions. The broad band at 1600 cm(-1) looses intensity, while the band at 1813 cm(-1) gains intensity on cooling. The agreement between quantum calculations of vibrational spectra and experimentally observed Raman bands of hydronium ions in oxalic acid sesquihydrate crystal corroborates this hypothesis.

First experimental charge density study using a Bruker CMOS-type PHOTON 100 detector: the case of ammonium tetraoxalate dihydrate. Addendum

Addendum to Jarzembskaet al.[Acta Cryst.(2014), B70, 847–855].

New methods in time-resolved Laue pump-probe crystallography at synchrotron sources

Newly developed methods for time-resolved studies using the polychromatic and in particular the pink-Laue technique, suitable for medium and small-size unit cells typical in chemical crystallography, are reviewed. The order of the sections follows that of a typical study, starting with a description of the pink-Laue technique, followed by the strategy of data collection for analysis with the RATIO method. Novel procedures are described for spot integration, orientation matrix determination for relatively sparse diffraction patterns, scaling of multi-crystal data sets, use of Fourier maps for initial assessment and analysis of results, and least-squares refinement of photo-induced structural and thermal changes. In the calculation of Fourier maps a ground-state structure model, typically based on monochromatic results, is employed as reference, and the laser-ON structure factors for the Fourier summations are obtained by multiplying the reference ground-state structure factors by the square root of the experimental ON/OFF ratios. A schematic of the procedure followed is included in the conclusion section.

Charge density investigations on [2,2]-paracyclophane – in data we trust

Four datasets on [2,2]-paracyclophane were collected in-house and at the Advanced Photon Source at two different temperatures for charge density investigation. Global data quality indicators such as high resolution, high I/σ(I) values, low merging R values and high multiplicity were matched for all four datasets. The structural parameters did not show significant differences, but the synchrotron data depicted deficiencies in the topological analysis. In retrospect these deficiencies could be assigned to the low quality of the innermost data, which could have been identified by e.g. merging R values for only these reflections. In the multipole refinement these deficiencies could be monitored using DRK-plot and residual density analysis. In this particular example the differences in the topological parameters were relatively small but significant.

First experimental charge density study using a Bruker CMOS-type PHOTON 100 detector: the case of ammonium tetraoxalate dihydrate

The aim of this study was to test the applicability of a Bruker AXS CMOS-type PHOTON 100 detector for the purpose of a fine charge density quality data collection. A complex crystal containing oxalic acid, ammonium oxalate and two water molecules was chosen as a test case. The data was collected up to a resolution of 1.31 Å−1with high completeness (89.1%;Rmrg= 0.0274). The multipolar refinement and subsequent quantum theory of atoms in molecules (QTAIM) analysis resulted in a comprehensive description of the charge density distribution in the crystal studied. The residual density maps are flat and almost featureless. It was possible to derive reliable information on intermolecular interactions to model the anharmonic motion of a water molecule, and also to observe the fine details of the charge density distribution, such as polarization on O and H atoms involved in the strongest hydrogen bonds. When compared with our previous statistical study on oxalic acid data collected with the aid of CCD cameras, the complementary metal-oxide semiconductor (CMOS) detector can certainly be classified as a promising alternative in advanced X-ray diffraction studies.