Aren‐Stapelung in den Kanälen eines dreidimensionalen Koordinationspolymers: Kristallstruktur des Natriumkomplexes [Na{C6H4(SO2)2N}(H2O)] und supramolekulare Verwandtschaft mit dem analogen Silberkomplex

Metal Salts of Benzene‐1,2‐di(sulfonyl)amine. 5. Arene Stacking in the Channels of a Three‐Dimensional Coordination Polymer: Crystal Structure of the Sodium Complex [Na{C₆H₄(SO₂)₂N}(H₂O)] and its Supramolecular Relationship to the Analogous Silver Complex The sodium compound NaZ · H₂O, derived from HZ = ortho‐benzenedisulfonimide, has been characterized by single crystal X‐ray diffraction at –100 °C (orthorhombic, space group Pna2₁, Z = 4). The five‐membered 1,3,2‐dithiazolide heterocycle possesses an envelope conformation, the N atom lying 30.3(1) pm outside the mean plane of the S–C–C–S moiety. The sodium ion attains a severely distorted octahedral coordination via Na⁺…O^δ– interactions with four anions and one water molecule. In contrast to the previously reported lamellar layer structures of CsZ, RbZ · H₂O and KZ · H₂O, the present crystal displays a three‐dimensional coordination assembly consisting of sodium ions, (SO₂)₂N groups and water molecules. This polar framework is pervaded by parallel channels approximately 800 × 800 pm² in profile, into which the lipophilic benzo rings are stacked at intercentroid distances of 402 pm. Re‐examination of AgZ · H₂O (Z. Anorg. Allg. Chem. 1993 , 619, 1441) discloses a striking supramolecular relationship to the sodium congener. In the crystal packing of the silver complex, one‐dimensional strands comprising pentacoordinate cations are associated by O–H…O(S) hydrogen bonds into a three‐dimensional polar framework, which again accommodates stacks of benzo groups within parallel channels.     

Lamellare Schichten auf der Grundlage von Wasserstoffbrücken und π‐Stapelung: Kristallstrukturen der Komplexe [Mg(H2O)6]Z2 und [Be(H2O)4]Z2�2 H2O mit Z‐ = C6H4(SO2)2N‐: Metallsalze des Benzol‐1, 2‐di(sulfonyl)amins. 8 [1, 2]

Metal Salts of Benzene‐1, 2‐di(sulfonyl)amine. 8. Lamellar Layers Based upon Hydrogen Bonding and π‐Stacking: Crystal Structures of the Complexes [Mg(H₂O)₆]Z₂ and [Be(H₂O)₄]Z₂�2 H₂O, where Z^‐ is C₆H₄(SO₂)₂N^‐ The crystal structures of the title complexes (both triclinic, space group P1¯, Z = 1 for M = Mg, Z = 2 for M = Be) have been determined by low‐temperature X‐ray diffraction. They consist of non‐coordinating ortho‐benzenedisulfonimide anions and, respectively, inversion‐symmetric octahedral [Mg(H₂O)₆]²⁺ cations or tetrahedral [Be(H₂O)₄]²⁺ cations and two non‐coordinating water molecules. In both structures, all O—H hydrogen bond donor groups are used to associate the components into two‐dimensional assemblies comprising an internal polar lamella of metal cations, (SO₂)₂N groups and water molecules, and hydrophobic peripheral regions consisting of vertically protruding benzo rings. Carbocycles drawn alternatingly from adjacent layers form π‐stacking arrays, whereby the aromatic rings display intercentroid distances in the range 340—370 pm. Several short C—H ⃜O contacts, which may be viewed as weak hydrogen bonds, occur within and between the layers.     

Polysulfonylamine. CLII [1] Kristallstrukturen von Metall‐di(methansulfonyl)amiden. 6 [2] Drei Schichtstrukturen: Die isotypen binären Verbindungen M[(MeSO2)2N]2 (M = Sr,Pb) und das Ethanol‐Solvat Pb[(MeSO2)2N]2 · EtOH

Polysulfonylamines. CLII. Crystal Structures of Metal Di(methanesulfonyl) amides. 6. Three Layer Structures: The Isotypic Binary Compounds M[(MeSO₂)₂N]₂ (M = Sr, Pb) and the Ethanol Solvate Pb[(MeSO₂)₂N]₂ · EtOH Low‐temperature X‐ray crystal structures are reported for the layer compounds SrA₂ (monoclinic, space group P2₁/n, Z′ = 1), PbA₂ (isotypic and isostructural with SrA₂), and PbA₂·EtOH (triclinic, P1¯, Z′ = 1), where A^— denotes the anion obtained by deprotonation of the strong NH acid (MeSO₂)₂NH. The ternary compound appears to be the first crystallographically established ethanol solvate of a lead(II) complex. In the two‐dimensional coordination networks, the cations adopt either a distorted cubic or, in the solvate, an irregular (O₆N₂)‐octacoordination, the metal centres of the isotypic structures forming close contacts to two (O, N)‐chelating and four κ¹O‐bonding anions, whereas in the solvate one of the latter ligands is displaced by an EtOH molecule. In the isotypic structures, the Pb—O distances are systematically longer than the Sr—O distances and the Pb—N bonds shorter than the Sr—N bonds, which correlates with the softer character of Pb²⁺ as compared to Sr²⁺. The 6s lone pair on Pb²⁺ is stereochemically inactive in both lead compounds. Analogies and discrepancies between the layer architectures are discussed in detail, including an evaluation of short C—H···O contacts in terms of weak hydrogen bonding. Two complexes of composition PbA₂·2 L, where L is pyridine or 1, 10‐phenanthroline, have been synthesized and characterized by analytical methods.     

Polysulfonylamine. CLVIII [1] Kristallstrukturen von Metall‐di(methansulfonyl)amiden. 9 [2] Erhöhung der Kristallsymmetrie durch Kokristallisation: Monoklines Na[(CH3SO2)2N]·H2O und tetragonales NaK[(CH3SO2)2N]2·2H2O

Polysulfonylamines. CLVIII. Crystal Structures of Metal Di(methanesulfonyl)amides. 9. Enhancing Crystal Symmetry by Co‐crystallization: Monoclinic Na[(CH₃SO₂)₂N]·H₂O and Tetragonal NaK[(CH₃SO₂)₂N]₂·2H₂O The three‐dimensional coordination polymers NaA·H₂O ( 1 ) and NaKA₂·2H₂O ( 2 ), derived from the strong NH acid (MeSO₂)₂NH = HA, have been characterized by single crystal X‐ray diffraction at —95 °C ( 1 : monoclinic, space group C2/c, Z′ = 2; 2 : tetragonal, P4₃2₁2, Z′ = 1). The results suggest that structures with Z′ > 1 are good candidates for co‐crystallization experiments. Both packings display layer substructures built up from the multidentately coordinating anions, the aquo ligands and two kinds of chemically and/or crystallographically distinct cations, whereas cations of a third type are intercalated between the layers. All anions have the extended standard conformation of this species; 1 contains two pseudo‐C₂ symmetric A^—, 2 one pseudo‐C₂ and two crystallographically C₂ symmetric A^—. Details for structure 1 : a) The layer‐forming Na(1) and Na(3) cations are distributed over three distinctly separated planes, Na(1) occupies general positions and has a non‐octahedral O₅N environment, Na(3) resides on inversion centres that generate an octahedral O₆ coordination; b) one independent A^— is oriented vertically, the other parallel to the layer plane; c) the intercalated Na(2) ions occupy twofold rotation axes within a single plane and possess a non‐octahedral O₆ environment. Details for structure 2 : a) The layer‐forming K(1) and K(2) cations occupy twofold rotation axes within a unique plane and have chemically identically O₆N₂ coordination polyhedra approximating to hexagonal bipyramids; b) all A^— are oriented vertically to the layer plane; c) the intercalated sodium ions reside on pseudo‐inversion centres, have an octahedral O₆ environment and are distributed over two closely adjacent planes. Owing to the enhanced packing efficiency of the bimetal complex, the vertical layer repeat‐distance is reduced from 1140 pm for 1 to 720 pm for 2 . Each structure exhibits an infinite cation‐water chain that propagates in the direction of the layer stacking and contains the three independent cations.     

Destruktive Komplexierung des dimeren Diorganylzinn(IV)‐hydroxids [Me2Sn(A)(μ‐OH)]2 (HA = Benzol‐1,2‐disulfonsäureimid): Bildung und Strukturen der Einkernkomplexe [Me2Sn(A)2(OPPh3)2] und [Me2Sn(phen)2]2⊕ · 2 A⊖ · MeCN

Polysulfonylamines. CXVI. Destructive Complexation of the Dimeric Diorganyltin(IV) Hydroxide [Me₂Sn(A)(μ‐OH)]₂ (HA = Benzene‐1,2‐disulfonimide): Formation and Structures of the Mononuclear Complexes [Me₂Sn(A)₂(OPPh₃)₂] and [Me₂Sn(phen)₂]^2⊕ · 2 A^⊖ · MeCN Destructive complexation of the dimeric hydroxide [Me₂Sn(A)(μ‐OH)]₂, where A^⊖ is deprotonated benzene‐1,2‐disulfonimide, with two equivalents of triphenylphosphine oxide or 1,10‐phenanthroline in hot MeCN produced, along with Me₂SnO and water, the novel coordination compounds [Me₂Sn(A)₂(OPPh₃)₂] ( 3 , triclinic, space group P 1) and [Me₂Sn(phen)₂]^2⊕ · 2 A^⊖ · MeCN ( 4 , monoclinic, P2₁/c). In the uncharged all‐trans octahedral complex 3 , the heteroligands are unidentally O‐bonded to the tin atom, which resides on a crystallographic centre of inversion [Sn–O(S) 227.4(2), Sn–O(P) 219.6(2) pm, cis‐angles in the range 87–93°; anionic ligand partially disordered over two equally populated sites for N, two S and non‐coordinating O atoms]. The cation occurring in the crystal of 4 has a severely distorted cis‐octahedral C₂N₄ coordination geometry around tin and represents the first authenticated example of a dicationic tin(IV) dichelate [R₂Sn(L–L′)₂]^2⊕ to adopt a cis‐structure [C–Sn–C 108.44(11)°]. The five‐membered chelate rings are nearly planar, with similar bite angles of the bidentate ligands, but unsymmetric Sn–N bond lengths, each of the longer bonds being trans to a methyl group [ring 1: N–Sn–N 71.24(7)°, Sn–N 226.81(19) and 237.5(2) pm; ring 2: 71.63(7)°, 228.0(2) and 232.20(19) pm]. In both structures, the bicyclic and effectively C_S symmetric A^⊖ ions have their five‐membered rings distorted into an envelope conformation, with N atoms displaced by 28–43 pm from the corresponding C₆S₂ mean plane.     

Silber(I)‐di(arensulfonyl)amide und ein Silber(I)‐(arensulfonyl)(alkansulfonyl)amid: Von Bändern zu lamellaren Schichten mit kurzen Zwischenschichtkontakten C–H…Hal–C oder C–Br…Br–C

Structures of Ionic Di(arenesulfonyl)amides. 2. Silver(I) Di(arenesulfonyl)amides and a Silver(I) (Arenesulfonyl)(alkanesulfonyl)amide: From Ribbons to Lamellar Layers Exhibiting Short C–H…Hal–C or C–Br…Br–C Interlayer Contacts Low‐temperature X‐ray crystal structures are reported for AgN(SO₂C₆H₄‐4‐X)₂ · H₂O, where X is Cl ( 4 ) or Br ( 5 ), and for AgN(SO₂Ph)(SO₂Me) ( 6 ). Compounds 4 and 5 and the previously described F analogue ( 3 ) are isotypic, though not strictly isostructural (monoclinic, space group P2₁/c, Z = 4, but egregiously large discrepancies of x and z coordinates for corresponding atoms). Throughout this triad, glide‐plane related formula units are linked along the z axis to form infinite ribbons [(ArSO₂)₂N–Ag(μ‐H₂O)]_∞, in which Ag extends its coordination number to five by accepting one Ag–O bond from each of the (ArSO₂)₂N^⊖ ligands in the adjacent units. By means of O–H…O(S) hydrogen bonds, the ribbons are associated into lamellar layers parallel to the xz plane. Owing to the folded conformation of the anions, the layers display an inner polar region of Ag atoms, H₂O molecules and N(SO₂)₂ groups, outer apolar regions of stacked pairs of aryl rings, and interlayer regions hosting the halogen atoms. Inspection of the latter areas provides sound evidence that the distinct juxtapositions of adjacent layers arise from specific interlamellar attractions and repulsions ( 3 : two C–H…F, all F…F beyond the van der Waals limit d_W; 4 : one C–H…Cl, close packing of Cl atoms at Cl…Cl ≈ d_W; 5 : one C–H…Br, one short Br…Br contact < d_W, all other Br…Br > d_W). Structure 6 (monoclinic, P2₁/n, Z = 4) consists of a lamellar coordination polymer, in which the cation accepts one Ag–N and three Ag–O bonds drawn from four different anions. On account of crystal symmetry, the extended ligand has its Ph and Me groups distributed on both sides of the sheet, the phenyl rings forming the apolar regions of the lamella, whereas the smaller methyl groups are integrated into the corrugated inorganic region by means of weak C–H…O hydrogen bonds.     

Ein neuartiges Diorganylzinn(IV)-Komplexkation als Gastspezies in einer ionischen Harnstoff-Einschlußverbindung: Bildung und Struktur von [trans-Me2Sn{OC(NH2)2}4]2+ · 2 (MeSO2)2N7 · 6 (NH2)2CO

Polysulfonylamines. CVIII. A Novel Diorganyltin(IV) Complex Cation as Guest Species in an Ionic Urea Inclusion Compound: Formation and Structure of [ trans -Me₂Sn{OC(NH₂)₂}₄]²⁺ · 2 (MeSO₂)₂N⁷ · 6 (NH₂)₂CO The title compound (triclinic, space group P 1, Z = 1, X-ray analysis at –130 °C) was fortuitously obtained during an attempt to complex the known dimeric hydroxide [Me₂Sn(A)(μ-OH)]₂, where A⁷ = (MeSO₂)₂N⁷, with four equivalents of urea. The trans-octahedral and crystallographically centrosymmetric [Me₂Sn(urea)₄]²⁺ cation (Sn–O 221.6 and 223.7 pm, cis-angles in the range 90 ± 1.5°) is the first structurally authenticated [R₂Sn(L)₄]²⁺ complex featuring a urea-type ligand L. In the crystal, these cations are sandwiched between and hydrogen-bonded to puckered layers corresponding to the [011] family of planes. Each layer is constructed from rows of A⁷ anions, which extend parallel to the x axis and are alternatingly cross-linked by a planar zig-zag tape of urea molecules or by a pair of inversion-related urea zig-zag tapes displaying a non-planar roof profile. The structure contains 23 crystallographically independent hydrogen bonds N–H…O/N, comprising two intracationic N–H…O bonds, two and four N–H…O bonds leading to the two respective types of urea tapes, eight N–H…O bonds and one N–H…N⁷ bond connecting the urea tapes to the electronegative atoms of the anions, and six N–H…O interactions between the ligands of the complex guest cation and C=O or S=O acceptors within the layers of the host lattice. The anion A⁷ accepts a total of twelve H bonds and adopts a previously unreported conformation.     

Determination of the polymer tacticity from calculation of infrared spectra based on classical molecular simulations

The infrared absorption spectra of poly(tetrafluoroethylene), PTFE, and poly(chlorotrifluoroethylene), PCTFE, are simulated using a method based on a combination of classical molecular simulations of the amorphous polymer phase with Kramers-Kronig relations. The differences and the analogies between experimental and calculated spectra of the non-stereoregular fluoride polymer, PTFE, are first reported. The isotactic and syndiotactic configurations of PCTFE are then investigated. The comparison between experimental and simulated spectra is established on a vibrational analysis. It reveals the preferred syndiotactic configuration adopted by the PCTFE chain.     

Finding all maximal efficient faces in multiobjective linear programming

An algorithm for finding the whole efficient set of a multiobjective linear program is proposed. From the set of efficient edges incident to a vertex, a characterization of maximal efficient faces containing the vertex is given. By means of the lexicographic selection rule of Dantzig, Orden and Wolfe, a connectedness property of the set of dual optimal bases associated to a degenerate vertex is proved. An application of this to the problem of enumerating all the efficient edges incident to a degenerate vertex is proposed. Our method is illustrated with numerical examples and comparisons with Armand—Malivert's algorithm show that this new algorithm uses less computer time.