Roman Kalinowski

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.

Charge transfer via the dative N-B bond and dihydrogen contacts. Experimental and theoretical electron density studies of four deltahedral boranes.

In an approach combining high resolution X-ray diffraction at low temperatures with density functional calculations, two closo-borates, B12H12(2-) (1) and B10H10(2-) (2), and two arachno-boranes, B10H12L2 (L = amine (3) or acetonitrile (4)), are studied by means of Atoms In Molecules (AIM) theory and Electron Localizability Indicator (ELI-D). The charge transfer via the dative N-B bonds in the arachno-boranes and via dihydrogen contacts in the closo-borates is quantified. The dative N-B bond in 4 is significantly shorter and stronger than that in 3 and in small N-B Lewis acid base adducts from the literature. It is even shorter in the gas phase than in the crystal environment in contrast to the bond shortening in the crystal generally found for N-B Lewis acid-base adducts. Furthermore, the calculated charge transfer in terms of AIM charges is opposite to the expected N → B direction but still weak as found for all other N-B bonds. The intramolecular charge redistributions due to intermolecular interactions are quantified by the AIM and ELI-D analysis of contact ion pairs. The latter method gives a deeper understanding of delocalization effects in the borane cages as well as in the counterions. Since dihydrogen bonds are rarely found in crystal structures, one focus was directed to the topologies of the large number of 58 experimentally found contacts of this type. The analysis reveals that the electron density at the bond critical point, the corresponding Laplace function, and the curvature along the bond path (λ3) show a behavior that clearly discriminates these interactions from classical hydrogen bonds, confirming earlier theoretical findings.

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.

Real-Space Indicators for Chemical Bonding. Experimental and Theoretical Electron Density Studies of Four Deltahedral Boranes

In an approach combining high-resolution X-ray diffraction at low temperatures with density functional theory calculations, two closo-borates, B(12)H(12)(2-) (1) and B(10)H(10)(2-) (2), and two arachno-boranes, B(10)H(12)L(2) [L = amine (3) or acetonitrile (4)], were analyzed by means of the atoms-in-molecules (AIM) theory and electron localizability indicator (ELI-D). The two-electron three-center (2e3c) bonds of the borane cages are investigated with the focus on real-space indicators for chemical bonding and electron delocalization. In compound 2, only two of the three expected bond critical points (bcps) are found. However, a weakly populated ELI-D basin is found for this pair of adjacent B atoms and the delocalization index and the Source contributions are on the same order of magnitude as those for the other pairs. The opposite situation is found in the arachno-boranes, where no ELI-D basins are found for two types of B-B pairs, which, in turn, exhibit a bcp. However, again the delocalization index is on the same order of magnitude for this bonding interaction. The results show that an unambiguous real-space criterion for chemical bonding is not given yet for this class of compounds. The arachno-boranes carry a special B-B bond, which is the edge of the crown-shaped molecule. This bond is very long and extremely curved inward the B-B-B ring. Nevertheless, the corresponding bond ellipticity is quite small and the ELI-D value at the attractor position of the disynaptic valence basin is remarkably larger than those for all other B-B valence basins. Furthermore, the value of the ED is large in relation to the B-B bond length, so that only this bond type does not follow a linear relationship of the ED value at the bcp versus B-B bond distances, which is found for all other B-B bcps. The results indicate that both 2e2c and 2e3c bonding play a distinct role in borane chemistry.

Transferability and reproducibility in electron-density studies--bond-topological and atomic properties of tripeptides of the type L-alanyl-X-L-alanine.

In the last decade three different data bank approaches have been developed that are intended to make electron-density examinations of large biologically important molecules possible. They rely on Baders concept of transferability of submolecular fragments with retention of their electronic properties. Therefore, elaborate studies on the quantification of transferability in experiment and theory are still very important. Tripeptides of the type L-alanyl-X-L-alanine (X being any of the 20 naturally encoded amino acids) serve as a model case between amino acids and proteins. The two experimental electron-density determinations (L-alanyl-L-histidinyl-L-alanine and L-alanyl-L-phenylalanyl-L-alanine, highly resolved synchrotron X-ray diffraction data sets) performed in this study and theoretical calculations on all 20 different L-alanyl-X-L-alanine molecules contribute to a better estimation of transferability in the peptide case. As a measure of reproducibility and transferability, standard deviations from averaging over bond-topological and atomic properties of atoms or bonds that are considered equal in their chemical environments were calculated. This way, transferability and reproducibility indices were introduced. It can be shown that experimental transferability indices generally slightly exceed experimental reproducibility indices and that these larger deviations can be attributed to chemical effects such as changes in the geometry (bond lengths and angles), the polarization pattern and the neighboring sphere due to crystal packing. These effects can partly be separated from each other and quantified with the help of gas-phase calculations at optimized and experimental geometries. Thus, the degree of transferability can be quantified in very narrow limits taking into account experimental errors and chemical effects.

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.

Accurate charge density of the tripeptide Ala-Pro-Ala with the maximum entropy method (MEM): influence of data resolution.

The accurate electron density of Ala-Pro-Ala is determined by the maximum entropy method (MEM), employing the same reflection data measured at 100 K which was used for a multipole refinement by Kalinowski et al. [(2007), Acta Cryst. Accepted for publication]. Properties of the electron density are compared with the corresponding properties of the static electron density from the multipole model and to the dynamic MEM electron density of trialanine at 20 K. It is thus shown that the increased thermal smearing at 100 K leads to lower electron densities in the bond critical points and atomic charges closer to zero for Ala-Pro-Ala than has been obtained for trialanine at 20 K. The influence of the resolution of the data is investigated by a series of MEM calculations. Atomic charges and atomic volumes are found not to depend on the resolution, but the charge density in the BCPs decreases with decreasing resolution of the dataset. The origin of this dependence is found to lie mostly in the more accurate estimate of the atomic displacement parameters (ADPs) for the higher-resolution datasets. If these effects are taken into account, meaningful information on chemical bonding can be obtained with data at a resolution better than d(min) = 0.63 A. Alternatively, low-resolution X-ray diffraction data can be used in accurate electron-density studies by the MEM, if another source of accurate values of the ADPs is available, e.g. from refinements with multipole parameters from a database of transferable multipole parameters.

A First Experimental Electron Density Study on a C70 Fullerene: (C70C2F5)10

The electron density of the C70 fullerene C70(C2F5)10 was determined from a high-resolution X-ray data set measured with synchrotron radiation (beamline F1 of Hasylab/DESY, Germany) at a temperature of 100 K. With 140 atoms in the asymmetric unit this fullerene belongs to the largest problems examined until now by electron density methods. Using the QTAIM formalism quantitative bond topological and atomic properties have been derived and compared with the results of theoretical calculations on the title compound and on free C70 Graphical Abstract A First Experimental Electron Density Study on a C70 Fullerene: (C70C2F5)10

Revised electrostatics from invariom refinement of the 18-residue peptaibol antibiotic trichotoxin A50E

Detailed functional understanding of the action of biological macromolecules is reliant on high-quality, accurate data describing their atomic and electrostatic structural properties. We present the application of cutting-edge modeling techniques to the 18-residue peptaibol antibiotic trichotoxin A50E [J. K. Chugh, H. Bruckner and B. A. Wallace, Biochemistry, 2002, 41, 12934] for which low temperature X-ray data (T = 150 K) at subatomic resolution were retrieved from the Protein Databank. Use of aspherical scattering factors (invarioms) enables refinement of individual coordinates and anisotropic displacement parameters unconstrained and standard uncertainties can be estimated by inversion of the full least-square matrix. However, application of the invariom method to model the electron density of trichotoxin A50E has not only improved the structural model in terms of geometry, figures of merit and anisotropic displacement parameters, but also results in the direct calculation of an ab initio quality electrostatic potential and associated dipole moment. Disagreement with previously published electrostatics and possible functional implications are discussed.