An experimental estimate of the relative aromaticity of the cyclooctatetraene dianion by fusion to dimethyldihydropyrene

The synthesis of the cyclooctatetraene dianion (COT(2-)) fused at the [e]-position of trans-10b,10c-dimethyl-10b,10c-dihydropyrene (DHP) is described, and by comparison of (1)H NMR properties and NICSAv to the analogous benzene fused DHP, the relative aromaticity of the dianion is found to be at least as great as that of benzene, and substantially larger than that of the cyclopentadienide anion.     

A novel approach to isoindolo[2,1-a]indol-6-ones

A convenient route to isoindolo[2,1-a]indol-6-ones has been developed starting from the appropriate 2-(N-phthaloyl)benzoic acids. Formation of the acid chlorides with thionyl chloride followed by heating with triethyl phosphite in a suitable solvent resulted in a multistep reaction giving tetracyclic β-ketophosphonates that on reduction with sodium borohydride gave the required indolones in good overall yields. Analogous β-ketophosphonates were also prepared starting with N,N-(1,8-naphthaloyl)-2-aminobenzoic acid and 2-(2,5-dioxo-2,5-dihydro-1H-pyrrol-1-yl)benzoic acids although of these only the naphthaloyl product could be reduced with sodium borohydride without cleaving the amide bond in the ring system.     

Three-dimensional X-ray diffraction in the diamond anvil cell: application to stishovite

Three-dimensional X-ray diffraction can be used for characterizing the orientation, position, and strain tensor of single grains in a polycrystalline aggregate. Here, we show how the method is well suited for diamond anvil cell data with heterogeneous grain sizes, with an application to two samples of stishovite at 15 and 26 GPa. For each grain, we obtain a well-defined orientation matrix and cell parameters. Center of mass position can also be adjusted to the experimental data, with errors in the present experiment. Finally, strain tensors are adjusted for the individual grains. The stress distribution obtained is in agreement with expectations from the diamond anvil cell geometry and previous measurements of stishovite strength. Advantages and potential for improvement of the method are then discussed.     

Subfactors of Index Less Than 5, Part 3: Quadruple Points

One major obstacle in extending the classification of small index subfactors beyond ${3 +\sqrt{3}}$ is the appearance of infinite families of candidate principal graphs with 4-valent vertices (in particular, the ??weeds?? ${\mathcal{Q}}$ and ${\mathcal{Q}'}$ from Part 1 (Morrison and Snyder in Commun. Math. Phys., doi:10.1007/s00220-012-1426-y, 2012). Thus instead of using triple point obstructions to eliminate candidate graphs, we need to develop new quadruple point obstructions. In this paper we prove two quadruple point obstructions. The first uses quadratic tangles techniques and eliminates the weed ${\mathcal{Q}'}$ immediately. The second uses connections, and when combined with an additional number theoretic argument it eliminates both weeds ${\mathcal{Q}}$ and ${\mathcal{Q}'}$ . Finally, we prove the uniqueness (up to taking duals) of the 3311 Goodman-de la Harpe-Jones subfactor using a combination of planar algebra techniques and connections.     

Crystal Structures of a Series of Bis{(2-Aminobenzoyl-)amino}alkanes

Abstract  The crystal structures of 1,2-bis-{(2-aminobenzoyl-)amino}ethane(1), 1,4-bis-{(2-aminobenzoyl-)amino}butane(2) and 2,2-dimethyl-1,3-bis-{(2-aminobenzoyl-)amino}-propane(3) have been determined by single crystal X-ray diffraction analysis. 1 and 2 are centrosymmetric molecules which lie on crystallographic centers of symmetry and adopt extended conformations. On the other hand, owing to the odd number of carbon atoms in the spacer unit, 3 does not show centrosymmetry, but crystallizes in a non-centrosymmetric space group and assumes a folded conformation. The crystal structures of 1, 2 and 3 are compared with the known structures of anthranilamide (7) and the N-alkyl anthranilamide derivative 8. Crystal data: 1 C₁₆H₁₈N₄O₂, monoclinic, space group P2₁/a, a = 9.5262(8) ?, b = 5.4200(5) ?, c = 15.3821(14) ?, β = 105.980(5)° and V = 763.52(12) ?³, for Z = 2. 2 C₁₈H₂₂N₄O₂, monoclinic, space group C2/c, a = 32.0710(17) ?, b = 5.4732(4) ?, c = 9.7326(5) ?, β = 102.570(4)° and V = 1667.42(17) ?³, for Z = 4. 3 C₁₉H₂₄N₄O₂, orthorhombic, space group Pca2₁, a = 16.7676(4) ?, b = 10.1847(2) ?, c = 10.5338(5) ?, and V = 1798.89(7) ?³, for Z = 4. Index Abstract  The crystal structures of 1,2-bis-{(2-aminobenzoyl-)amino}ethane(1), 1,4-bis-{(2-aminobenzoyl-)amino}butane(2) and 2,2-dimethyl-1,3-bis-{(2-aminobenzoyl-)amino}-propane(3) have been determined by single crystal X-ray diffraction analysis. 1 and 2 are centrosymmetric molecules which lie on crystallographic centers of symmetry and adopt extended conformations, whereas 3 does not show centrosymmetry, but crystallizes in a non-centrosymmetric space group and assumes a folded conformation.      

Fully polarizable QM/MM calculations: An application to the nonbonded iodine–oxygen interaction in dimethyl‐2‐iodobenzoylphosphonate

The compound dimethyl‐2‐iodobenzoylphosphonate is unusual in that it forms well‐ordered crystals that clearly show short iodine‐oxygen interactions in which both the iodine and the oxygen are in their normal oxidation states. These interactions were studied using a new hybrid quantum mechanical–molecular mechanical approach that employs a polarizable molecular mechanics component. The electric field at the molecular mechanics atoms was calculated from a distributed multipole expansion of the wave function; this induced dipoles on the molecular mechanics atoms. The electrostatic potential in a spherical shell around the induced dipoles was reproduced through induced charges on the atomic center and those bonded to it using an analytical (rather than numerical) procedure. The new atomic charges (induced charges plus permanent charges) were then able to interact with the quantum mechanical entity and polarize the wave function. The procedure was iterated to convergence. The calculations show that the iodine atom becomes more positive in the crystal environment (modeled by a chain of three molecules of dimethyl‐2‐iodobenzoylphosphonate). Thus, while the cooperative effects of the crystal environment may not be the only feature stabilizing this unusual interaction, they do play a significant role in reducing the otherwise unfavourable iodine–oxygen monopole–monopole interaction. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 478–482, 2000     

An approximate treatment of scattering based on the delta boundary operator

The development of a scheme to treat two-dimensional electromagneticscattering by electrically large, perfectly conducting bodiesis described. It incorporates the effects of surface curvatureand non-local phenomena and has the potential to provide thebasis for a general technique yielding more accurate predictionsthan the widely used physical optics method.