Linear MgCp*2 vs Bent CaCp*2: London Dispersion, Ligand-Induced Charge Localizations, and Pseudo-Pregostic C-H···Ca Interactions.

In the family of metallocenes, MgCp*2 (Cp* = pentamethylcyclopentadienyl) exhibits a regular linear sandwich structure, whereas CaCp*2 is bent in both the gas phase and solid state. Bending is typically observed for metal ions which possess a lone pair. Here, we investigate which electronic differences cause the bending in complexes lacking lone pairs at the metal atoms. The bent gas-phase geometry of CaCp*2 suggests that the bending must have an intramolecular origin. Geometry optimizations with and without dispersion effects/d-type polarization functions on MCp2 and MCp*2 gas-phase complexes (M = Ca, Mg) establish that attractive methyl···methyl London dispersion interactions play a decisive role in the bending in CaCp*2. A sufficient polarizability of the metal to produce a shallow bending potential energy curve is a prerequisite but is not the reason for the bending. Concomitant ligand-induced charge concentrations and localizations at the metal atoms are studied in further detail, for which real-space bonding and orbital-based descriptors are used. Low-temperature crystal structures of MgCp*2 and CaCp*2 were determined which facilitated the identification and characterization of intermolecular pseudo-pregostic interactions, C-H···Ca, in the CaCp*2 crystal structure.

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.

Accurate Bond Lengths to Hydrogen Atoms from Single-Crystal X-ray Diffraction by Including Estimated Hydrogen ADPs and Comparison to Neutron and QM/MM Benchmarks.

Amino acid structures are an ideal test set for method-development studies in crystallography. High-resolution X-ray diffraction data for eight previously studied genetically encoding amino acids are provided, complemented by a non-standard amino acid. Structures were re-investigated to study a widely applicable treatment that permits accurate X-H bond lengths to hydrogen atoms to be obtained: this treatment combines refinement of positional hydrogen-atom parameters with aspherical scattering factors with constrained "TLS+INV" estimated hydrogen anisotropic displacement parameters (H-ADPs). Tabulated invariom scattering factors allow rapid modeling without further computations, and unconstrained Hirshfeld atom refinement provides a computationally demanding alternative when database entries are missing. Both should incorporate estimated H-ADPs, as free refinement frequently leads to over-parameterization and non-positive definite H-ADPs irrespective of the aspherical scattering model used. Using estimated H-ADPs, both methods yield accurate and precise X-H distances in best quantitative agreement with neutron diffraction data (available for five of the test-set molecules). This work thus solves the last remaining problem to obtain such results more frequently. Density functional theoretical QM/MM computations are able to play the role of an alternative benchmark to neutron diffraction.

Invariom based electron density studies on the C/Si analogues haloperidol/sila-haloperidol and venlafaxine/sila-venlafaxine.

The subjects of this study are the structures and electron densities of the carbon/silicon analogues haloperidol/sila-haloperidol (1a/1b) and venlafaxine/sila-venlafaxine (2a/2b). The parent carbon compounds 1a (an antipsychotic agent) and 2a (an antidepressant) are both in clinical use. For haloperidol/sila-haloperidol, three published structures were studied in more detail: the structures of haloperidol hydrochloride (1a·HCl), haloperidol hydropicrate (1a·HPic) and sila-haloperidol hydrochloride (1b·HCl). For venlafaxine/sila-venlafaxine, the published structures of venlafaxine (2a), venlafaxine hydrochloride (2a·HCl; as orthorhombic (2a·HCl-ortho) and monoclinic polymorph (2a·HCl-mono)) and sila-venlafaxine hydrochloride (2b·HCl) were investigated. Based on these structures, the molecular electron densities were reconstructed by using the invariom formalism. They were further analysed in terms of Bader's quantum theory of atoms in molecules, electrostatic potentials mapped onto electron density isosurfaces and Hirshfeld surfaces. These studies were performed with a special emphasis on the comparison of the corresponding carbon/silicon analogues.

Oxygen transfer from an intramolecularly coordinated diaryltellurium oxide to acetonitrile. Formation and combined AIM and ELI-D analysis of a novel diaryltellurium acetimidate.

The reaction of the intramolecularly coordinated diaryltellurium(IV) oxide (8-Me2NC10H6)2TeO with acetonitrile proceeds with oxygen transfer and gives rise to the formation of the novel zwitterionic diaryltelluronium(IV) acetimidate (8-Me2NC10H6)2TeNC(O)CH3 (1) in 57% yield. Hydrolysis of 1 with hydrochloric acid affords acetamide and the previously known diarylhydroxytelluronium(IV) chloride [(8-Me2NC10H6)2Te(OH)]Cl.

Electron densities of bexarotene and disila-bexarotene from invariom application: a comparative study.

By the application of the invariom formalism, which provides aspherical atomic scattering factors, the electron densities of the RXR-selective retinoid agonists bexarotene (1a) and disila-bexarotene (1b) were derived from their known low resolution (d = 0.76 Å) crystal structures. The density distributions allowed us to make a comparison of the electronic properties of these pharmacologically relevant compounds. Differences were found to be restricted to relatively small regions in the terminal six-membered rings of the tetrahydronaphthalene and tetrahydrodisilanaphthalene fragments. In total, the replacement of two carbon atoms in 1a by silicon atoms (→1b) does neither influence the electronic structures nor the pharmacological properties (RXR receptor activation) significantly. It should be noted that the almost completely software supported invariom formalism can yield electronic information for biologically interacting systems with moderate effort. This offers interesting possibilities for drug research, in that steric and electronic information can be combined for the analysis of intermolecular recognition and interaction on an atomic scale. This approach is also valuable for the design and development of silicon-containing drugs using the carbon/silicon switch strategy.

Electron density study of the anti-Alzheimer's disease drug donepezil from conventional x-ray data and invariom database application.

BACKGROUND: The crystal structures of a very large number of compounds with biological relevance are known. Application of the invariom formalism provides the aspherical electron density distribution. RESULTS AND DISCUSSION: The electron density distribution of the anti-Alzheimer's disease drug donepezil was derived from its x-ray structure reported in the literature, using the invariom database. The electrostatic potential mapped on the electron density isosurface shows how the positive charge of the donepezilium cation is distributed over a wide surface range. The presence of intermolecular contacts can be illustrated by the Hirshfeld surface. Comparable interactions are found in both the small-molecule structure and an acetylcholinesterase complex with donezepil from the literature. CONCLUSION: The electron density of donepezil in the small-molecule crystal structure mimics the intermolecular interactions within the receptor site. Complementing steric properties with electronic information can be a valuable procedure in the examination of molecular recognition of systems with biological activity.

Experimental electron density of sumanene, a bowl-shaped fullerene fragment; comparison with the related corannulene hydrocarbon.

The experimental electron density of sumanene, C(21)H(12), was extracted from a high resolution X-ray data set measured at 100 K and topologically analyzed. In addition to bond topological and atomic properties, information about the density distribution between adjacent molecules, which show close C···C approaches of ~3.4 Å within the columnar π-stacks in the crystal lattice, are discussed. A comparison is made with the electron density of the related corannulene molecule based also on the analysis of Electron Localizability Indicator (ELI-D) calculations.

Experimental and theoretical electron-density study of three isoindole derivatives: topological and Hirshfeld surface analysis of weak intermolecular interactions.

A combined experimental and theoretical study of three isoindole derivatives was made on the basis of a topological analysis of their electron-density distributions. Experimental electron densities were determined from high-resolution X-ray diffraction data sets measured with synchrotron radiation at 100 K, whereas theoretical calculations were performed using DFT methods at the B3LYP\6-311++G(3df,3pd) level of approximation. Both experimental and theoretical models are in good agreement with each other. Since the analysed structures possess a variety of hydrogen-bonding interactions, weak intermolecular contacts of C-H···C(π), C,N(π)···C,N(π) and H···H types were subject to our special interest and are discussed in detail. They were characterized quantitatively and qualitatively by topological properties using Bader's Atoms in Molecules theory and by mapping the electron-density distribution, electrostatic potential and a geometric function on the Hirshfeld surface. This way the forces and directions of intermolecular interactions as present on the molecular surfaces were depicted and described. These interactions not only guide crystal packing, but are likewise important for recognition processes involving (aza)isoindole fragments in a biological environment.

Reactivity differences between α,ß-unsaturated carbonyls and hydrazones investigated by experimental and theoretical electron density and electron localizability analyses.

It is still a challenge to predict a compound's reactivity from its ground-state electronic nature although Bader-type topological analyses of the electron density (ED) and electron localizability indicator (ELI) give detailed and useful information on electron concentration and electron-pair localization, respectively. Both ED and ELI can be obtained from theoretical calculations as well as high-resolution X-ray diffraction experiments. Besides ED and ELI descriptors, the delocalization index is used here; it is likewise derived from theoretical calculations as well as from experimental X-ray results, but in the latter case, demonstrated here for the first time. We investigate α,ß-unsaturated carbonyl and hydrazone compounds because resonance exhibited by these compounds in the electronic ground-state determines their reactive behavior. The degree of resonance as well as the reactivity contrast are quantified with the electronic descriptors. Moreover, competitive mesomeric substituent effects are studied using the two biologically important compounds acrolein and acrylamide. The reactivity differences predicted from the analyses are in line with the known reactivity of these compounds in organic synthesis. Hence, the capability of the ED and ELI for rationalizing and predicting different and competing substituent effects with respect to reactivity is demonstrated.

Electron density of two bioactive oligocyclic indole and oxindole derivatives obtained from low-order X-ray data and invariom application.

For two indole and oxindole bioactive molecules, low-order room-temperature X-ray data were used to generate aspherical electron density (ED) distributions by application of the invariom formalism. An analysis of the ED using the quantum theory of atoms in molecules (QTAIM) was carried out, which allowed for quantitatively examining bond orders and charge separations in various parts of the molecules. The inspection of electrostatic potentials (ESPs) and Hirshfeld surfaces provided additional information on the intermolecular interactions. Thus, reactive regions of the molecules could be identified, covalent and electrostatic contributions to interactions could be visualized, and the forces causing the crystal packing scheme could be rationalized. As the used invariom formalism needs no extra experimental effort compared to routine X-ray analysis, its wide application is recommended because it delivers information far beyond the normally obtained steric properties. In this way, complementary contributions to drug design can be given as is demonstrated for indoles in this study, which are involved in the metabolism of plants and animals as well as in cancer therapy.

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.

Effect of electron-withdrawing substituents on the epoxide ring: an experimental and theoretical electron density analysis of a series of epoxide derivatives.

A series of acceptor-substituted epoxide derivatives is scrutinized by means of experimental and theoretical electron-density investigations. Due to the possibility of nucleophilic ring-opening, the epoxide ring is not only a very useful functional group in organic synthesis, but acceptor-substituted epoxides are valuable building blocks for the design of protease inhibitors. Therefore, the electron-density analysis in this work focuses on two main aspects that can contribute to rational drug design: (i) the quantification of the electron-withdrawing substituent effects on the epoxide ring and (ii) the intermolecular interactions involving the epoxide ring in combination with different substituents. It can be shown that the electron-withdrawing properties of the substituents cause an elongation of the C-C bonds in the epoxide rings and the loss of electron density can be measured by an analysis of critical points, atomic charges, and the source function. The different strengths of the substituents are reflected in these properties. Covalent and electrostatic contributions to the intermolecular interactions and thus the lattice energies are depicted on different molecular surfaces.

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 (bcp's) 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 bcp's. The results indicate that both 2e2c and 2e3c bonding play a distinct role in borane chemistry.

Charge transfer via the dative N-B bond and dihydrogen contacts. Experimental and theoretical electron density studies of small Lewis acid-base adducts.

The electronic characteristics of the dative N−B bond in three Lewis acid−base adducts, hydrazine borane, hydrazine bisborane, and ammonia trifluoroborane, are analyzed by an approach combining experimental electron density determination with a broad variety of theoretical calculations. Special focus is directed to the weak dihydrogen contacts in hydrazine borane. The Atoms In Molecules partitioning scheme is complemented by additional methods like the Source Function, and the Electron Localizability Indicator. For the multipole-free theoretical models of hydrazine borane and hydrazine bisborane, a weak charge donation from Lewis base to acid of about 0.05 e is found, whereas multipole refinement of theoretical and experimental structure factors resulted in opposite signs for the Lewis acid and base fragments. For ammonia trifluoroborane, the donation from Lewis base to acid is slightly larger (about 0.13 e) in the multipole-free models, and the charges obtained by multipole refinement retain the direction of the charge donation but show quite large variations. The natural population analysis charges predict larger charge donations (0.35 e) from the Lewis bases to the acids for the three title complexes. Although the three compounds exhibit intermolecular interactions of different types and strengths, including classical hydrogen bonds, F···H contacts and the already mentioned dihydrogen bonds, almost no charge transfer is detected between different molecules within the crystal environment. The main electronic effect of the formation of the Lewis acid-base adducts and of the crystallization is an increase in the charge separation within the ammonia/hydrazine fragments, which is supported by all investigated bond and atomic properties. The nature of the dative N-B bond is found to be mainly electrostatic, but with a substantial contribution of covalency. The F-B bonds show similarities and differences from the N-B bonds, which makes a distinction of coordinative (or dative) bonds from polar covalent interactions possible.

A simple procedure for the derivation of electron density based surfaces of drug-receptor complexes from a combination of X-ray data and theoretical calculations.

To contribute to an understanding of biological recognition and interaction, an easy-to-use procedure was developed to generate and display molecular surfaces and selected electron density based surface properties. To overcome the present limitations to derive electron densities of macromolecules, the considered systems were reduced to appropriate substructures around the active centers. The combination of experimental X-ray structural information and aspherical atomic electron density data from theoretical calculations resulted in properties like the electrostatic potential and the Hirshfeld surface which allowed a study of electronic complementarity and the identification of sites and strengths of drug-receptor interactions. Applications were examined for three examples. The anilinoquinazoline gefitinib (Iressa(R)) belongs to a new class of anticancer drugs that inhibit the tyrosine kinase activity of the epidermal growth factor receptor (EGFR). In the second example, the interaction of epoxide inhibitors with the main protease of the SARS coronavirus was investigated. Furthermore, the progesterone receptor complex was examined. The quantitative analysis of hydrogen bonding in the chosen substructure systems follows a progression elaborated earlier on the basis of accurate small molecule crystal structures. This finding and results from modified substructures suggest that also the surface properties seem robust enough to provide stable information about the recognition of interacting biomolecular species although they are obtained from medium molecular weighted subfragments of macromolecular complexes, which consist of no more than approximately 40 residues.

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.

Electron densities of three B12 vitamins.

The electron densities of the three natural B(12)-vitamins, two of them being essential cofactors for animal life, were determined in a procedure combining high-order X-ray data collection at low to very low temperatures with high-level density functional calculations. In a series of extensive experimental attempts, a high-order data set of adenosylcobalamin (AdoCbl) could be collected to a resolution of sin theta/lambda = 1.00 A(-1) at 25 K. This modification contains only minor disorder at the solvent bulk. For methylcobalamin (MeCbl), only a severely disordered modification was found (sin theta/lambda = 1.00 A(-1), 100 K, measured with synchrotron radiation). The already published data set of cyanocobalamin (CNCbl) (sin theta/lambda = 1.25 A(-1), 100 K) was reintegrated to guarantee similar treatment of the three compounds and cut to sin theta/lambda = 1.11 A(-1) to obtain a higher degree of completeness and redundancy. On the basis of these accurate experimental geometries of AdoCbl, MeCbl, and CNCbl, state-of-the-art density functional calculations, single-point calculations, and geometry optimizations were performed on model compounds at the BP86/TZVP level of theory to evaluate the electronic differences of the three compounds. AdoCbl and MeCbl are known to undergo different reaction paths in the body. Thus, the focus was directed toward the characterization of the dative Co-C(ax) and Co-N(ax) bonds, which were quantifed by topological parameters, including energy densities; the source function including local source; and the electron localizability indicator (ELI-D), respectively. The source function reveals the existence of delocalized interactions between the corrin macrocycle and the axial ligands. The ELI-D indicates unsaturated Co-C(ax) bonding basins for the two biochemically active cofactors, but not for CNCbl, where a population of 2.2e is found. This may be related to significant pi-backbonding, which is supported by the delocalization index, delta, of 0.15 between the Co atom and the N atom of the cyano ligand. Considering all results, the inherent electronic differences between AdoCbl and MeCbl are found to be small thus, supporting earlier findings that the interaction with the protein site mainly controls the type of Co-C(ax) bond cleavage.