Boranes: The Boron Subhydride B104.67H3 with a Distorted β-Boron Crystal Structure

A single crystal of the boron subhydride B_104.67(4)H₃ was serendipitously obtained while attempting to synthesize β-boron. An accurate crystal structure analysis revealed a distorted β-boron framework with the noncentrosymmetric space group R3m. We have found one interstitial site occupied by boron. The site related by inversion remains empty. The distortions of the framework result in ideal environments for the interstitial boron atom, and for the three hydrogen atoms at bridging positions between icosahedral B₁₂ groups, they result in ideal B-H distances of 1.33 Å. B_104.67(4)H₃ is a borane with the lowest amount of hydrogen recorded to date, and it is the first compound with a noncentrosymmetrically distorted β-boron framework.

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.

Aspherical scattering factors for SHELXL - model, implementation and application

A new aspherical scattering factor formalism has been implemented in the crystallographic least-squares refinement program SHELXL. The formalism relies on Gaussian functions and can optionally complement the independent atom model to take into account the deformation of electron-density distribution due to chemical bonding and lone pairs. Asphericity contributions were derived from the electron density obtained from quantum-chemical density functional theory computations of suitable model compounds that contain particular chemical environments, as defined by the invariom formalism. Thanks to a new algorithm, invariom assignment for refinement in SHELXL is automated. A suitable parameterization for each chemical environment within the new model was achieved by metaheuristics. Figures of merit, precision and accuracy of crystallographic least-squares refinements improve significantly upon using the new model.

On avoiding negative electron density in Gram-Charlier refinements of anharmonic motion: the example of glutathione

The structure of glutathione, γ-l-Glutamyl-l-cysteinyl-glycine (C10H17N3O6S), 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.

The electrostatic potential of dynamic charge densities

A procedure to derive the electrostatic potential (ESP) for dynamic charge densities obtained from structure models or maximum-entropy densities is introduced. The ESP essentially is obtained by inverse Fourier transform of the dynamic structure factors of the total charge density corresponding to the independent atom model, the multipole model or maximum-entropy densities, employing dedicated software that will be part of the BayMEM software package. Our approach is also discussed with respect to the Ewald summation method. It is argued that a meaningful ESP can only be obtained if identical thermal smearing is applied to the nuclear (positive) and electronic (negative) parts of the dynamic charge densities. The method is applied to structure models of dl-serine at three different temperatures of 20, 100 and 298 K. The ESP at locations near the atomic nuclei exhibits a drastic reduction with increasing temperature, the largest difference between the ESP from the static charge density and the ESP of the dynamic charge density being at T = 20 K. These features demonstrate that zero-point vibrations are sufficient for changing the spiky nature of the ESP at the nuclei into finite values. On 0.5 e Å-3 isosurfaces of the electron densities (taken as the molecular surface relevant to intermolecular interactions), the dynamic ESP is surprisingly similar at all temperatures, while the static ESP of a single molecule has a slightly larger range and is shifted towards positive potential values.

Invariom modeling of disordered structures: case studies on a dipeptide, an amino acid, and cefaclor, a cephalosporin antibiotic

Routines to facilitate the treatment of disorder in invariom modeling have been implemented in the open-source program MolecoolQt, a visualization program for charge-density work, and InvariomTool, a pre-processor program. Two published structures of an amino acid and a dipeptide and the new structure of cefaclor, a cephalosporin antibiotic, provide examples with increasing amounts of disorder, which can now be successfully modeled with invarioms. Like for ordered structures, these non-spherical scattering factors predicted by density functional theory significantly improve the structural model (figures of merit and standard deviations) also in these cases. Furthermore, they allow rapid calculation and comparison of the electrostatic potential and the molecular dipole moment for the different conformers present in the crystal structures.

Charge Density of L-Alanyl-glycyl-L-alanine Based on X-Ray Data Collection Periods from 4 to 130 Hours

The charge density of the tripeptide L-alanyl-glycyl-L-alanine was determined from three X-ray data sets measured at different experimental setups and under different conditions. Two of the data sets were measured with synchrotron radiation (beamline F1 of Hasylab/DESY, Germany and beamline X10SA of SLS, Paul-Scherer-Institute, Switzerland) at temperatures around 100 K while a third data set was measured under home laboratory conditions (MoKα radiation) at a low temperature of 20 K. The multipole refinement strategy to derive the experimental charge density was the same in all cases, so that the obtained charge density properties could directly be compared. While the general analysis of the three data sets suggested a small preference for one of the synchrotron data sets (Hasylab F1), a comparison of topological and atomic properties gave in no case an indication for a preference of any of the three data sets. It follows that even the 4 h data set measured at the SLS performed equally well compared to the data sets of substantially longer exposure time.

The generalized invariom database (GID)

Invarioms are aspherical atomic scattering factors that enable structure refinement of more accurate and more precise geometries than refinements with the conventional independent atom model (IAM). The use of single-crystal X-ray diffraction data of a resolution better than sin θ/λ = 0.6 Å(-1) (or d = 0.83 Å) is recommended. The invariom scattering-factor database contains transferable pseudoatom parameters of the Hansen-Coppens multipole model and associated local atomic coordinate systems. Parameters were derived from geometry optimizations of suitable model compounds, whose IUPAC names are also contained in the database. Correct scattering-factor assignment and orientation reproduces molecular electron density to a good approximation. Molecular properties can hence be derived directly from the electron-density model. Coverage of chemical environments in the invariom database has been extended from the original amino acids, proteins and nucleic acid structures to many other environments encountered in organic chemistry. With over 2750 entries it now covers a wide sample of general organic chemistry involving the elements H, C, N and O, and to a lesser extent F, Si, S, P and Cl. With respect to the earlier version of the database, the main modification concerns scattering-factor notation. Modifications improve ease of use and success rates of automatic geometry-based scattering-factor assignment, especially in condensed hetero-aromatic ring systems, making the approach well suited to replace the IAM for structures of organic molecules.

Anharmonic motion in experimental charge density investigations

In the charge density study of 9-diphenylthiophosphinoylanthracene the thermal motion of several atoms needed an anharmonic description via Gram-Charlier coefficients even for data collected at 15 K. As several data sets at different temperatures were measured, this anharmonic model could be proved to be superior to a disorder model. Refinements against theoretical data showed the resemblance of an anharmonic model and a disorder model with two positions very close to each other (~0.2 Å), whereas these two models could be clearly distinguished if the second position is 0.5 Å apart. The refined multipole parameters were distorted when the anharmonic motion was not properly refined. Therefore, this study reveals the importance of detecting and properly handling anharmonic motion. Unrefined anharmonic motion leads to typical shashlik-like residual density patterns. Therefore, careful analysis of the residual density and the derived probability density function after the refinement of the Gram-Charlier coefficients proved to be the most useful tools to indicate the presence of anharmonic motion.

ShelXle: a Qt graphical user interface for SHELXL

ShelXle is a graphical user interface for SHELXL [Sheldrick, G. M. (2008). Acta Cryst. A64, 112-122], currently the most widely used program for small-molecule structure refinement. It combines an editor with syntax highlighting for the SHELXL-associated .ins (input) and .res (output) files with an interactive graphical display for visualization of a three-dimensional structure including the electron density (F(o)) and difference density (F(o)-F(c)) maps. Special features of ShelXle include intuitive atom (re-)naming, a strongly coupled editor, structure visualization in various mono and stereo modes, and a novel way of displaying disorder extending over special positions. ShelXle is completely compatible with all features of SHELXL and is written entirely in C++ using the Qt4 and FFTW libraries. It is available at no cost for Windows, Linux and Mac-OS X and as source code.

ShelXle: a Qt graphical user interface for SHELXL

ShelXle is a user-friendly graphical user interface for SHELXL. It combines an editor with syntax highlighting for SHELXL-associated files with an interactive graphical display for visualization of a three-dimensional structure.

ShelXle is a graphical user interface for SHELXL [Sheldrick, G. M. (2008). Acta Cryst. A64, 112–122], currently the most widely used program for small-molecule structure refinement. It combines an editor with syntax highlighting for the SHELXL-associated .ins (input) and .res (output) files with an interactive graphical display for visualization of a three-dimensional structure including the electron density (F_o) and difference density (F_o–F_c) maps. Special features of ShelXle include intuitive atom (re-)naming, a strongly coupled editor, structure visualization in various mono and stereo modes, and a novel way of displaying disorder extending over special positions. ShelXle is completely compatible with all features of SHELXL and is written entirely in C++ using the Qt4 and FFTW libraries. It is available at no cost for Windows, Linux and Mac-OS X and as source code.

On QM/MM and MO/MO cluster calculations of all-atom anisotropic displacement parameters for molecules in crystal structures

The practical aspects of ab initio calculation of anisotropic displacement parameters (ADPs) for molecules in crystal structures are investigated. Computationally efficient approaches to calculate ADPs are QM/MM or MO/MO methods, where quantum chemical calculations are split into a high-level and a low-level part. Such calculations allow geometry optimizations and subsequent frequency calculations of a central molecule in a cluster of surrounding molecules as found in the crystal lattice. The frequencies and associated displacements are then converted into ADPs. A series of such calculations were performed with different quantum chemical methods and basis sets on the three zwitterionic amino-acid structures of L-alanine, L-cysteine and L-threonine, where high-quality low-temperature X-ray data are available. To scale and compare calculated ADPs, X-ray ADPs from invariom refinement were used. The future use of calculated ADPs will include the investigation of systematic errors in experimental X-ray diffraction data. Completion of an isotropic structural model is already possible. Calculated ADPs might also make it possible to perform charge-density studies on data sets of limited resolution/coverage as obtained from weak scatterers, high-pressure measurements or to deconvolute electron density obtained from the maximum-entropy method.

MoleCoolQt - a molecule viewer for charge-density research

MoleCoolQt is a molecule viewer designed for experimental charge density studies with a user-friendly graphical user interface.

MoleCoolQt is a molecule viewer for charge-density research. Features include the visualization of local atomic coordinate systems in multipole refinements based on the Hansen and Coppens formalism as implemented, for example, in the XD suite. Residual peaks and holes from XDfft are translated so that they appear close to the nearest atom of the asymmetric unit. Critical points from a topological analysis of the charge density can also be visualized. As in the program MolIso, color-mapped isosurfaces can be generated with a simple interface. Apart from its visualization features the program interactively helps in assigning local atomic coordinate systems and local symmetry, which can be automatically detected and altered. Dummy atoms – as sometimes required for local atomic coordinate systems – are calculated on demand; XD system files are updated after changes. When using the invariom database, potential scattering factor assignment problems can be resolved by the use of an interactive dialog. The following file formats are supported: XD, MoPro, SHELX, GAUSSIAN (com, FChk, cube), CIF and PDB. MoleCoolQt is written in C++ using the Qt4 library, has a user-friendly graphical user interface, and is available for several flavors of Linux, Windows and MacOS.

How to easily replace the independent atom model - the example of bergenin, a potential anti-HIV agent of traditional Asian medicine

Bergenin, which has been isolated from a variety of tropical plants, has several pharmacological applications in traditional Asian medicine. Its electron-density distribution was obtained from a room-temperature low-resolution X-ray data set measured with point detection making use of multipole populations from the invariom library. Two refinement models were considered. In a first step, positional parameters and ADPs were refined with fixed library multipoles (model E1). This model was suitable to be input into a second refinement of multipoles (model E2), which converged smoothly although based on Cu Kalpha room-temperature data. Quantitative results of a topological analysis of the electron density from both models were compared with Hartree-Fock and density-functional calculations. With respect to the independent atom model (IAM) more information can be extracted from invariom modelling, including the electrostatic potential and hydrogen-bond energies, which are highly useful, especially for biologically active compounds. The reliability of the applied invariom formalism was assessed by a comparison of bond-topological properties of sucrose, for which high-resolution multipole and invariom densities were available. Since a conventional X-ray diffraction experiment using basic equipment was combined with the easy-to-use invariom formalism, the procedure described here for bergenin illustrates how it can be routinely applied in pharmacological research.

Comparative experimental electron density and electron localization function study of thymidine based on 20 K X-ray diffraction data

From a high-resolution X-ray data set (sin θ/λ = 1.1 Å−1) measured at 20 K the electron-density distribution of the nucleoside thymidine was derived by a classical multipole refinement and by application of the invariom formalism. Owing to the presence of the heteroaromatic thymine ring system two invariom models were compared which considered the nearest and next-nearest neighbors for the invariom assignments. Differences between the two invariom models were small for the bond topological and atomic properties – about five times smaller than differences with the classical multipole refinement. Even the latter differences are in the uncertainty ranges which are commonly observed in experimental charge-density work and were found in molecular regions involved in intermolecular contacts. The application of the constrained wavefunction-fitting approach allowed the electron localization function (ELF) to be obtained from the experimental X-ray data, which was graphically represented and topologically analyzed. ELF basin populations were derived from experiment for the first time. The electron populations in the disynaptic valence basins were related quantitatively to bond orders.

Experimental charge density of L-alanyl-L-prolyl-L-alanine hydrate: classical multipole and invariom approach, analysis of intra- and intermolecular topological properties

A high-resolution dataset of the tripeptide L-alanyl-L-prolyl-L-alanine hydrate was measured at 100 K using synchrotron radiation and CCD area detection. Electron densities were obtained from a full multipole refinement of the X-ray experimental data, from an invariom transfer and from a theoretical calculation. Topological and atomic properties were derived via an AIM analysis [Atoms in Molecules; see Bader (1990). Atoms in Molecules: A Quantum Theory, No. 22 in International Series of Monographs on Chemistry, 1st ed. Oxford: Clarendon Press] of these densities and compared with each other, as well as with results from the literature of other oligopeptides and amino acids. By application of the invariom formalism to a dataset of limited resolution, its performance was compared with a conventional spherical refinement, highlighting the possibility of aspherically modelling routine structure-determination experiments. The hydrogen-bonding scheme was subject to a detailed analysis according to the criteria of Koch & Popelier [(1995), J. Phys. Chem. 99, 9747–9754] as well as to the characterization of Espinosa et al. [(1998), Chem. Phys. Lett. 285, 170–173; (1999), Acta Cryst. B55, 563–572; (2002), J. Chem. Phys. 117, 5529–5542] using the results from the refined and invariom multipole densities as well as the spherical-density model, which are critically compared.

Bond Orders and Atomic Properties of the Highly Deformed Halogenated Fullerenes C60F18 and C60Cl30 Derived from their Charge Densities

The experimental charge densities of the halogenated C(60) fullerenes C(60)F(18) and C(60)Cl(30) were determined from high-resolution X-ray data sets measured with conventional Mo(Kalpha) radiation at 20 K for C(60)Cl(30) and with synchrotron radiation at 92 K for the fluorine compound. Bond topological and atomic properties were analyzed by using Bader's AIM theory. For the different C--C bonds, which vary in lengths between 1.35 and 1.70 A bond orders n between n=2 and significantly below n=1 were calculated from the bond topological properties at the bond critical points (BCP's). The low bond orders are seen for 5/6 bonds with each contributing carbon carrying a halogen atom. By integration over Bader's zero flux basins in the electron density gradient vector field atomic properties were also obtained. In contrast to free C(60), in which all carbon atoms have a uniform volume of 11 A(3) and zero charge, atomic volumes vary roughly between 5 and 10 A(3) in the halogenated compounds. Almost zero atomic charges are also found in the Cl derivative but a charge separation up to +/-0.8 e exists between C and F in C(60)F(18) due to the higher fluorine electronegativity, which is also seen in the electrostatic potential for which the electronegativity difference between carbon and fluorine, and the addition to one hemisphere of the fullerene cage leads to a strong potential gradient along the C(60)F(18) molecule. From the summation over all atomic volumes it follows that the halogen addition does not only lead to a dramatic distortion of the C(60) cage but also to a significant shrinkage of its volume.

Examination of intermolecular electronic interactions in the crystal structure of C60(CF3)12 by experimental electron density determination

From a high resolution X-ray data set measured at 20 K the experimental electron density of the fullerene C(60)(CF(3))(12) was derived and topologically analyzed to yield, in addition to bond topological and atomic properties, information about the density distribution in the region where hexagons of adjacent molecules approach closely at only 3.3 A.

Introduction and validation of an invariom database for amino-acid, peptide and protein molecules

A database of invarioms for structural refinement of amino-acid, oligopeptide and protein molecules is presented. The spherical scattering factors of the independent atom or promolecule model are replaced by ;individual' aspherical scattering factors that take into account the chemical environment of a bonded atom. All amino acids were analysed in terms of their invariom fragments. In order to generate 73 database entries that cover this class of compounds, 37 model compounds were geometry-optimized and theoretical structure factors were calculated. Multipole refinements were then performed on these theoretical structure factors to yield the invariom database. Validation of this database on an extensive number of experimental small-molecule crystal structures of varying quality and resolution shows that invariom modelling improves various figures of merit. Differences in figures of merit between invariom and promolecule models give insight into the importance of disorder for future protein-invariom refinements. The suitability of structural data for application of invarioms can be predicted by Cruickshank's diffraction-component precision index [Cruickshank (1999), Acta Cryst. D55, 583-601].

Invariom structure refinement, electrostatic potential and toxicity of 4-O-methylalpinumisoflavone, O,O-dimethylalpinumisoflavone and 5-O-methyl-4-O-(3-methylbut-2-en-1-yl)alpinumisoflavone

The accurate X-ray single-crystal structures of the isoflavone compounds 4-O-methylalpinumisoflavone, O,O-dimethylalpinumisoflavone and 5-O-methyl-4-O-(3-methylbut-2-en-1-yl)alpinumisoflavone {alpinumisoflavone = 5-hydroxy-7-(4-hydroxyphenyl)-2,2-dimethyl-2H,6H-benzo[1,2-b:5,4-b']dipyran-6-one} from data sets measured at cryogenic temperature have been obtained from invariom modelling using theoretically predicted Hansen and Coppens multipole-model form factors, which describe the aspherical electron density distribution. Molecular dipole moments and electrostatic potentials obtained from invariom modelling are discussed and compared with results from ab initio theoretical calculations. All three studied compounds are solvent extracts of root bark or seed powder of Millettia thonningii (leguminosae), a plant molluscicide and cercaricide used in Franco West Africa as medication against various diseases. The compounds' toxicities to brine shrimp have been determined and their different potencies tentatively related to conformation differences, intramolecular contacts, dipole moments and electrostatic potential features.

Reproducibility and transferability of topological data: experimental charge density study of two modifications ofl-alanyl-l-tyrosyl-l-alanine

Two crystalline modifications of the tripeptide L-Ala-L-Tyr-L-Ala, which have different solvent molecules in the crystal structure (water and ethanol for modifications 1 and 2), were the subject of experimental charge density studies based on high resolution X-ray data collected at ultra-low temperatures of 9 K (1) and 20 K (2), respectively. The molecular structures and the intermolecular interactions were found to be rather similar in the two crystal lattices, so that this study allowed the reproducibility of the charge density of a given molecule in different (but widely comparable) crystalline environments to be examined. With respect to bond topological and atomic properties, the agreement between the two modifications of the title tripeptide was in the same range as found from the comparison with the previously reported results of tri-L-alanine. It follows that the reproducibility and transferability of quantitative topological data are comparable and that within the accuracy of experimental charge density work the replacement of the central amino acid residue L-Ala by L-Tyr has no significant influence, neither on bond nor on the atomic properties of the oligopeptide main chain. Intermolecular interactions in the form of hydrogen bonds were characterized quantitatively and qualitatively by topological criteria and by mapping the charge density distribution on the Hirshfeld surface.

Experimental Advances for High-Speed Evaluation of Electron Densities

Evaluating electron densities of entire classes of chemically or biologically related compounds is within reach thanks to advances in high-speed high-resolution synchrotron diffraction: a 12 h sequence of diffraction experiments has been conducted at the beamline X10SA of the Swiss Light Source (SLS). It resulted in four high-resolution X-ray data sets used for experimental electron density determinations of the two halogenated fullerenes C60F18 and C60Cl30, the Watson and Crick base pair adenine-thymine and the tripeptide L-Ala-Gly-L-Ala. Application is considered relevant for life sciences where the study of structure-guided biological recognition processes can now be completed by electronic information of entire series of molecules.

The invariom model and its application: refinement of D,L-serine at different temperatures and resolution

Three X-ray data sets of the same D,L-serine crystal were measured at temperatures of 298, 100 and 20 K. These data were then evaluated using invarioms and the Hansen & Coppens aspherical-atom model. Multipole populations for invarioms, which are pseudoatoms that remain approximately invariant in an intermolecular transfer, were theoretically predicted using different density functional theorem (DFT) basis sets. The invariom parameters were kept fixed and positional and thermal parameters were refined to compare the fitting against the multi-temperature data at different resolutions. The deconvolution of thermal motion and electron density with respect to data resolution was studied by application of the Hirshfeld test. Above a resolution of sin theta/lambda approximately 0.55 A-1, or d approximately 0.9 A, this test was fulfilled. When the Hirshfeld test is fulfilled, a successful modeling of the aspherical electron density with invarioms is achieved, which was proven by Fourier methods. Molecular geometry improves, especially for H atoms, when using the invariom method compared to the independent-atom model, as a comparison with neutron data shows. Based on this example, the general applicability of the invariom concept to organic molecules is proven and the aspherical density modeling of a larger biomacromolecule is within reach.

L-Tryptophan formic acid solvate at 183 K

In the title compound, C(11)H(12)N(2)O(2).CH(2)O(2), at 183 K. L-tryptophan appears in the zwitterionic form, while the formic acid molecule is neutral. The formic acid molecule is the donor in a strong O-H.O hydrogen bond to the carboxylate group of the tryptophan molecule, with a short O.O contact of 2.487 (2) A.