Van der Waals and Polar Intermolecular Contact Distances: Quantifying Supramolecular Synthons

Crystal structures are viewed as being determined by ranges and constraints on interatomic contact distances between neighboring molecules. These distances are considered to arise from environment‐dependent atomic sizes, that is, larger sizes for isotropic, van der Waals type contacts and smaller sizes for more‐polar, possibly ionic contacts. Although the idea of different, or anisotropic, radii for atoms is not new, we developed a method of obtaining atomic sizes that is based on a theoretical framework. Using different atomic sizes for the same atom in different environments, we were able to rationalize some structural observations and anomalies. For example, benzene with the Pbca structure may be described in terms of two types of C???H interactions: a longer contact largely of the van der Waals type, and a shorter, structure‐determining type (C^δ????H^δ+), which we term “n‐polar”. Our approach is illustrated with three examples: 1) the equivalence in crystal packing of fluorobenzene, benzonitrile, pyridine N‐oxide, and pyridine/HF 1:1 molecular complex, all of which take the not‐so‐common tetragonal P4₁2₁2 space group and are practically isomorphous; 2) the similarity of the Pa3 acetylene and Pbca benzene crystal structures; and 3) the equivalence between an increase in pressure and an increase in the “n‐polar” contacts in Pbca benzene; in other words, the equivalence between hydrostatic pressure and chemical pressure. In the context of crystal engineering, we describe a method whereby the topological information conveyed in a supramolecular synthon is recast in a more quantitative manner. A particular synthon, and in turn the crystal structure to which it leads, is viable within small ranges of distances of its constituent atoms, and these distances are determined by chemical factors.     

Gaussian expansions from STOs by the distance between subspaces

Expansions of STO orbitals with GTO s for the first-row atoms have been obtained by the method of the distance between subspaces. The expansion coefficients and exponential parameters were simultaneously varied when the distance between subspaces, which are generated from STO and GTO functions, is minimized. The ζ; exponents (or scale factors) for the atomic orbitals that are optimized for these atoms are also shown to be almost independent of the number of Gaussian functions. Comparisons carried out with Stewart's least-squares method produce equivalent results when exponents for 2s and 2p functions are different. Some examples and applications for several atomic properties of the first-row atoms are included: energies and expectation values of rⁱ and pⁱ for the several expansions. These new minimal basis sets were tested for diatomic and polyatomic molecules containing these atoms. © 1993 John Wiley & Sons, Inc.     

On a new semi‐empirical electrotopological index for QSRR models

A new semi‐empirical electrotopological index, I_SET, for quantitative structure–retention relationships (QSRR) models was developed based on the refinement of the previously published semi‐empirical topological index, I_ET. We demonstrate that the values of C_i fragments that were firstly attributed from the experimental chromatographic retention and theoretical deductions have an excellent relationship with the net atomic charge of the carbon atoms. Thus, the values attributed to the vertices in the hydrogen‐suppressed graph of carbon atoms (C_i) are calculated from the correlation of the net atomic charge in each carbon atom, which is obtained from quantum chemical semi‐empirical calculations, and the C_i fragments for primary, secondary, tertiary and quaternary carbon atoms (1.0, 0.9, 0.8 and 0.7, respectively) obtained from the experimental values. This shows that I_ET encoded this quantum physical reality and that it is possible to calculate a new I_SET (the semi‐empirical electrotopological index) through the net atomic charge values obtained from a Mulliken population analysis using the semi‐empirical AM1 method and their correlation with the values attributed to the different types of carbon atoms. This demonstrates that the I_SET encodes information on the charge distribution of the solute on which dispersive and electrostatic interactions between the solute (alkanes and alkenes) and the stationary phase strongly depend. Thus, this new method can be considered as an initial step towards forthcoming QSRR/QSAR studies. Copyright © 2008 John Wiley & Sons, Ltd.     

Overcoming the limitations of cutoffs for defining atomic coordination in multicomponent systems

A common way to understand structure in multimolecular systems is the coordination shell which comprises all the neighbors of an atom. Coordination, however, is nontrivial to determine because there is no obvious way to determine when atoms are neighbors. A common solution is to take all atoms within a cutoff at the first minimum of the radial distribution function, g(r). We show that such an approach cannot be consistently applied to model multicomponent systems, namely mixtures of atoms differing in size or charge. Coordination shells using the total g(r) are found to be too restrictive for atoms of different size while those using pairwise g(r)s are excessive for charged mixtures. The recently introduced relative angular distance algorithm, however, which defines coordination instantaneously from atomic positions, is consistently able to define coordination shells containing the expected neighboring atoms for all these systems. This more robust way to determine coordination should in turn make coordination a more robust way to understand structure. © 2017 Wiley Periodicals, Inc.     

pyMolDyn: Identification,structure, and properties of cavities/vacancies in condensed matter and molecules

pyMolDyn is an interactive viewer of atomic systems defined in a unit cell and is particularly useful for crystalline and amorphous materials. It identifies and visualizes cavities (vacancies, voids) in simulation cells corresponding to all seven 3D Bravais lattices, makes no assumptions about cavity shapes, allows for atoms of different size, and locates the cavity centers (the centers of the largest spheres not including an atom center). We define three types of cavity and develop a method based on the split and merge algorithm to calculate all three. The visualization of the cavities uses the marching cubes algorithm. The program allows one to calculate and export pair distribution functions (between atoms and/or cavities), as well as bonding and dihedral angles, cavity volumes and surface areas, and measures of cavity shapes, including asphericity, acylindricity, and relative shape anisotropy. The open source Python program is based on GR framework and GR3 routines and can be used to generate high resolution graphics and videos. © 2016 Wiley Periodicals, Inc.     

Iron Borohydride Pincer Complexes for the Efficient Hydrogenation of Ketones under Mild,Base‐Free Conditions: Synthesis and Mechanistic Insight

The new, structurally characterized hydrido carbonyl tetrahydridoborate iron pincer complex [(iPr‐PNP)Fe(H)(CO)(η¹‐BH₄)] ( 1 ) catalyzes the base‐free hydrogenation of ketones to their corresponding alcohols employing only 4.1 atm hydrogen pressure. Turnover numbers up to 1980 at complete conversion of ketone were reached with this system. Treatment of 1 with aniline (as a BH₃ scavenger) resulted in a mixture of trans‐[(iPr‐PNP)Fe(H)₂(CO)] ( 4 a ) and cis‐[(iPr‐PNP)Fe(H)₂(CO)] ( 4 b ). The dihydrido complexes 4 a and 4 b do not react with acetophenone or benzaldehyde, indicating that these complexes are not intermediates in the catalytic reduction of ketones. NMR studies indicate that the tetrahydridoborate ligand in 1 dissociates prior to ketone reduction. DFT calculations show that the mechanism of the iron‐catalyzed hydrogenation of ketones involves alcohol‐assisted aromatization of the dearomatized complex [(iPr‐PNP*)Fe(H)(CO)] ( 7 ) to initially give the Fe⁰ complex [(iPr‐PNP)Fe(CO)] ( 21 ) and subsequently [(iPr‐PNP)Fe(CO)(EtOH)] ( 38 ). Concerted coordination of acetophenone and dual hydrogen‐atom transfer from the PNP arm and the coordinated ethanol to, respectively, the carbonyl carbon and oxygen atoms, leads to the dearomatized complex [(iPr‐PNP*)Fe(CO)(EtO)(MeCH(OH)Ph)] ( 32 ). The catalyst is regenerated by release of 1‐phenylethanol, followed by dihydrogen coordination and proton transfer to the coordinated ethoxide ligand.     

Structural transformations in silver nanoparticles

A molecular dynamics simulation was performed for silver clusters of 147, 309, and 561 atoms with the initial cuboctahedral habit in the temperature range 0–1000 K with an embedded atom potential for silver. Structural transitions of the silver clusters to complex twins (icosahedral habit) with coherent (111)/(111) boundaries over all edges of icosahedra were found, which started at temperatures of 50 K, 350 K, and 700 K, respectively. To analyze the structural transformations in nanoparticles, an algorithm is proposed based on a simplicial Delaunay decomposition (Delaunay triangulation). It was found that after the transition of silver nanoparticles to complex twins, the atomic motion becomes vibrational; the atoms vibrate around the sites that correspond to the vertices of the regular polyhedra. In the case of the 147-atom silver nanoparticle, the polyhedra are arranged in the following sequence, starting from the center of mass: icosahedron (12 atoms), icosododecahedron (30 atoms), icosahedron (12 atoms), dodecahedron (20 atoms), truncated icosahedron (60 atoms, isostructural with fullerene C₆₀), icosahedron (12 atoms), and one atom at the center of mass.     

Optical response of bimetallic Li x Na8−x (0≦x≦8) and of doped Na8Zn clusters

Total (elastic + inelastic) cross-sections for electron scattering from C, N, O atoms and their simple molecules are studied theoretically. Thee ^–-C, N, O atomic calculations are done in the complex optical potential approach. To study the electron scattering from O₂, N₂, CO, NO, CN, C₂ as well as CO₂, N₂O, NO₂ O₃ targets, we have adopted an additivity rule, wherein the molecular cross-section is an incoherent sum of the cross-sections of the constituent atoms. The cross-sections of C, N & O atoms are presented at incident energiesE _i =10–1000 eV, the molecular cross-sections are presented atE _i =100–1000 eV. The reliability of the additivity rule is discussed against the background of experimental data.     

A new method for predicting conduction anesthesia

A new method for predicting conduction anesthesia has been suggested. The method is based on calculation of theP matrix probabilities of interatomic contacts for each molecule of the compounds considered. TheP matrix enables one to evaluate the main tendencies of atoms and atomic groups to interact in biochemical sorption on the nerve fiber surface. The minimum effective concentrations calculated for 25 compounds are in good agreement with the experimental data. The correlation coefficient between the experimental and calculated values is 0.98 when the standard deviation is 0.1 mmol L⁻¹. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1781–1784, October, 1997.     

Tm2.22Co6Sn20 and TmLi2Co6Sn20 stannides as disordered derivatives of the Cr23C6 structure type

A new ternary dithulium hexacobalt icosastannide, Tm_2.22Co₆Sn₂₀, and a new quaternary thulium dilithium hexacobalt icosastannide, TmLi₂Co₆Sn₂₀, crystallize as disordered variants of the binary cubic Cr₂₃C₆ structure type (cF116). 48 Sn atoms occupy sites of m.m2 symmetry, 32 Sn atoms sites of .3m symmetry, 24 Co atoms sites of 4m.m symmetry, eight Li (or Tm in the case of the ternary phase) atoms sites of symmetry and four Tm atoms sites of symmetry. The environment of one Tm atom is an 18‐vertex polyhedron and that of the second Tm (or Li) atom is a 16‐vertex polyhedron. Tetragonal antiprismatic coordination is observed for the Co atoms. Two Sn atoms are enclosed in a heavily deformed bicapped hexagonal prism and a monocapped hexagonal prism, respectively, and the environment of the third Sn atom is a 12‐vertex polyhedron. The electronic structures of both title compounds were calculated using the tight‐binding linear muffin‐tin orbital method in the atomic spheres approximation (TB–LMTO–ASA). Metallic bonding is dominant in these compounds, but the presence of Sn—Sn covalent dumbbells is also observed.     

Dichloro­[(6R,7S,8S,14S)‐(–)‐sparteine‐κ2N,N′]mercury(II)

In the title compound, [HgCl₂(C₁₅H₂₆N₂)], the chiral alkaloid (6R,7S,8S,14S)‐(−)‐l ‐sparteine acts as a bident­ate ligand, with two Cl⁻ ligands occupying the remaining coordination sites, producing a distorted tetra­hedron. The N—Hg—N plane is twisted by 81.1 (2)° from the Cl—Hg—Cl plane. The mid‐point of the N⋯N line does not lie exactly on the Cl—Hg—Cl plane but is tilted towards one of the N atoms by 0.346 Å. Similarly, the mid‐point of the Cl⋯Cl line is tilted toward one of the Cl atoms by 0.163 Å. The packing structure shows that the complex is stabilized by two inter­atomic Cl⋯H contacts involving both Cl atoms and the methyl­ene or methine H atoms of the (−)‐sparteine ligand.     

Heterovalent trinuclear Co(III)-Co(II)-Co(III) complexes with N-(2-Carboxyethyl)salicylaldimines

The heterovalent trinuclear cobalt complexes [Co₂^IIIL₄ ⁱ · Co^II(H₂O)₄] · nXmY (L ⁱ are deprotonated Schiff bases derived from substituted salicylaldehydes and β-alanine; i = 1–3) were obtained and characterized. An X-ray diffraction study of the trinuclear cobalt complex with N-(2-carboxyethyl)salicylaldimine showed that the central Co(II) ion and the terminal Co(III) ions are linked by bridging carboxylate groups. Either terminal Co(III) atom is coordinated to two ligand molecules. They form an octahedral environment consisting of two azomethine N atoms, two phenolate O atoms, and two O atoms of two carboxylate groups. The central Co(II) atom is coordinated to four water molecules and to two O atoms of two bridging carboxylate ligands involved in the coordination sphere of the terminal Co(III) atoms.     

DBD Surface Modification of Polymers in Relation to the Spatial Distribution of Reactive Oxygen Species

The homogeneity of a helium dielectric barrier discharge, working at atmospheric pressure and containing oxygen as contaminant, is assessed by mapping the spatial distribution of oxygen metastable atoms in relation to the uniformity of surface properties. Tunable diode laser absorption spectroscopy is used to monitor the time evolution of the absorption coefficient corresponding to the oxygen metastable atoms on the 3⁵S₂ level, as a function of the laser absorbing path, whereas bi-dimensional Abel transform is used to obtain local information on the space distribution of the metastable atoms in the discharge. The radial distribution of the surface properties is investigated using atomic force microscopy, contact angle measurement and X-ray photoelectron spectroscopy. The results show that the oxygen metastables density has complex space–time behavior, and the spatial distribution of the reactive species yields specific radial profile of the surface properties of a polymer film depending on the treatment time.     

Random walks and their diagnostic value for characterization of atomic environment

A characterization of atomic environments based on counting random walks in a molecular skeleton is outlined. To each atom in a molecule a sequence of integers w₁, w₂, w₃,…, w_n is assigned, where w_i represents the number of self-returning walks of length k, the length being defined by the number of bonds traversed. Properties of the derived atom codes are discussed. The codes display an impressive diversity and are superior to atomic codes based on enumeration of self-avoiding walks (or paths) in discriminating atomic environments. In certain cases the codes of individual atoms are not unique and the same codes appear in different molecules or even within the same molecule. The occurrence of the nonunique codes can be related to special structural situations, associated with the occurrence of isospectral graphs. These isospectral graphs which have atoms with identical codes can generate additional isospectral structures by attaching any arbitrary group to such points. If nonequivalent atoms of a single molecule have identical random walk codes, substitution at the singular points alternatively will produce isospectral graphs. Examples of such situations are given.     

Coexistence of menisci and the influence of neighboring pores on capillary displacement curvatures in sphere packings

The methods of calculating meniscus curvatures given by Mayer and Stowe and also independently by Princen are essentially the same. The method is exact for pores defined by rods. From comparison with experimental results, the method provides, for zero contact angle at least, a close approximation for pores defined by spheres. The application of the method to model pores defined by rods and spheres is discussed with particular attention being paid to the effects of neighboring pores. The merits of defining the neighbors of a particular pore as mirror images are discussed together with the effect of neighboring pores on the determination of pore sizes from capillary displacement curvatures. Meniscus curvatures of a family of pore shapes defined by three equal rods and mirror image neighbors are tabulated. A simple correlation was found between these values and estimates of the curvature given by the Haines incircle approximation.     

Theoretical Study of Pd11Si6 Nanosheet Compounds Including Seven‐Coordinated Si Species and Its Ge Analogues

Nanosheet compounds Pd₁₁(SiiPr)₂(SiiPr₂)₄(CNtBu)₁₀ ( 1 ) and Pd₁₁(SiiPr)₂(SiiPr₂)₄(CNMes)₁₀ ( 2 ), containing two Pd₇(SiiPr)(SiiPr₂)₂(CNR)₄ plates (R=tBu or Mes) connected with three common Pd atoms, were investigated with DFT method. All Pd atoms are somewhat positively charged and the electron density is accumulated between the Pd and Si atoms, indicating that a charge transfer (CT) occurs from the Pd to the Si atoms of the SiMe₂ and SiMe groups. Negative regions of the Laplacian of the electron density were found between the Pd and Si atoms. A model of a seven‐coordinated Si species, that is, Pd₅(Pd?SiMe), is predicted to be a stable pentagonal bipyramidal molecule. Five Pd atoms in the equatorial plane form bonding overlaps with two 3p orbitals of the Si atom. This is a new type of hypervalency. The Ge analogues have geometry and an electronic structure similar to those of the Si compounds. But their formation energies are smaller than those of the Si analogues. The use of the element Si is crucial to synthesize these nanoplate compounds.     

The Ce2Li0.39Ni1.61Si2 structure as a new derivative of the AlB2 family

A new quaternary dicerium lithium/nickel disilicide, Ce₂Li_0.39Ni_1.61Si₂, crystallizes as a new structure type of intermetallic compounds closely related to the AlB₂ family. The crystal–chemical interrelationships between parent AlB₂‐type, BaLiSi, ZrBeSi and the title compound are discussed using the Bärnighausen formalism. Two Ce atoms occupy sites of 3m. symmetry. The remainder, i.e. Ni, mixed Ni/Li and Si atoms, occupy sites of m2 symmetry. The environment of the Ce atom is an 18‐vertex polyhedron and the Ni, Ni/Li and Si atoms are enclosed in tricapped trigonal prisms. The title structure can be assigned to class No. 10 (trigonal prism and its derivatives) according to the Krypyakevich classification scheme [Krypyakevich (1977). In Structure Types of Intermetallic Compounds. Moscow: Nauka]. The electronic structure of the title compound was calculated using the tight‐binding linear muffin‐tin orbital method in the atomic spheres approximation (TB‐LMTO‐ASA). Metallic bonding is dominant in this compound. The strongest interactions are Ni—Si and Ce—Si.     

Li12Cu12.60Al14.37: a new ternary derivative of the binary Laves phases

New ternary dodecalithium dodecacopper tetradecaaluminium, Li₁₂Cu_12.60Al_14.37 (trigonal, Rm, hR39), crystallizes as a new structure type and belongs to the structural family that derives from binary Laves phases. The Li atoms are enclosed in 15‐ and 16‐vertex and the Al3 atom in 14‐vertex pseudo‐Frank–Kasper polyhedra. The polyhedra around the statistical mixtures of (Cu,Al)1 and (Al,Cu)2 are distorted icosahedra. The electronic structure was calculated by the TB–LMTO–ASA (tight‐binding linear muffin‐tin orbital atomic spheres approximation) method. The electron localization function, which indicates bond formation, is mostly located at the Al atoms. Thus, Al—Al bonding is much stronger than Li—Al or Cu—Al bonding. This indicates that, besides metallic bonding which is dominant in this compound, weak covalent Al—Al interactions also exist.     

Calculation of molecular and atomic volumes and surfaces

A method for calculating the molecular volume and surface as the sum of increments of atomic volumes and surfaces is proposed. The calculation of volume and surface increments is performed in three stages: analysis of the intersection picture of interpenetrating spheres; calculation of increments by the exact formulas for atoms with the environment suitable to apply the formulas; and estimation of increments for the remaining atoms by the Monte-Carlo method. At the last stage, the atomic volume increment is estimated using the network of elementary spheric volumes which are cone-shaped and have a vertex in the center of the sphere. The atomic surface increment is estimated simultoneously. Volumes and surfaces of some molecules are given in Table 1.Institute of Organoelement Chemistry, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 34, No. 4, pp. 98–106, July–August, 1993.Translated by T. Yudanova.