Overcrowded naphthologs of mono-bridged tetraarylethylenes: analogs of bistricyclic aromatic enes

The naphthalogous mono-bridged tetraarylethylenes 9,9′-di-(1-naphthylmethylene)-9H-fluorene (5) and 9,9′-di-(1-naphthylmethylene)-9H-xanthene (6), analogs of bifluorenylidene (1) and bixanthenylidene (2), have been synthesized and their molecular and crystal structures have been determined. Ene 5 has been prepared by two alternative synthetic routes. The molecular structures of 5 and 6 show that each of these enes has very small twist around the central double bond, but the two naphthalene rings in both 5 and 6 are highly twisted. According to the NMR study, 5 and 6 in solution adopt conformations which are similar to those found by X-ray crystal structure analysis. The notable upfield shifts of H¹ and H⁸ (6.11 and 6.83 ppm, respectively) and H² and H⁷ (6.70 and 6.44 ppm, respectively) in 5 and 6 are due to the shielding caused by the nearly orthogonally twisted naphthalene rings. The B3LYP/6-31G(d) calculations of 5, 6, and their 2-naphthyl and phenyl analogs have been performed. In the 1-naphthyl series, the more efficient conjugation between the naphthyl substituents and the central C=C and the overcrowding due to the peri-hydrogen atoms lead to higher twists of the naphthyl groups and to lower twists of the central C=C. In the 2-naphthyl series, the opposite effects are noted. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

Taming 3-manifolds using scalar curvature

In this paper we address the issue of uniformly positive scalar curvature on noncompact 3-manifolds. In particular we show that the Whitehead manifold lacks such a metric, and in fact that \mathbbR³{\mathbb{R}^3} is the only contractible noncompact 3-manifold with a metric of uniformly positive scalar curvature. We also describe contractible noncompact manifolds of higher dimension exhibiting this curvature phenomenon. Lastly we characterize all connected oriented 3-manifolds with finitely generated fundamental group allowing such a metric.     

Intersystem crossing at singlet conical intersections

The energy of the lowest triplet state of organic molecules is intermediate between the ground state and the first excited singlet. At the S₁/S₀ conical intersection, the two singlet states are degenerate. It is shown that for some molecules (ethylene, benzene, toluene and pyrrole) the T₁ state is also degenerate with the two singlet states. Moreover, the spin orbit coupling matrix element at this structure is necessarily large, so that intersystem crossing can be quite efficient. If the lowest triplet state is repulsive (as in the studied molecules) it may significantly contribute to the dissociation yield under certain experimental conditions.     

Nitrones-III: Reaction of 3,4-dihydroisoquinoline n-oxide with phosphonoylids

Reaction of 3,4-dihydroisoquinoline N-oxide 1 with diethyl cyanomethylphosphonate 2 gave the enaminonitrile 1-cyanomethylene-1,2,3,4-tetrahydroisoquinoline 3. Reaction of 1 with trialkyl phosphonoacetate 4 gave 5, the fused aziridine derivative 7 - exo - carbethoxy -1 - aza - 4,5 - benzo - bicyclo[4.1.0]heptene - 4, and the enaminoester 1-carbalkoxymethylene-1,2,3,4-tetrahydroisoquinoline 6. The ratio of 5:6 depends on the reaction conditions. While using 1,2-dimethoxyethane the aziridine 5 is the major product; using alcoholic solvents the yield of 6 increases at the expense of 5 with increasing acidity of the solvent.     

Radical decomposition of <Emphasis Type="Italic">N,N</Emphasis>-bis-(3-chloro-1,4-naphthoquinon-2-yl) amine in basic conditions followed by EPR

EPR spectroscopy was used to assess the radicals produced upon basic decomposition of N,N-bis-(3-chloro-1,4-naphthoquinon-2-yl) amine (BClNQA). Three radicals have been trapped and identified: N-bis(3-chloro-1,4-naphthoquinone) hydrazine radical (6), 2-hydroxy-3-chloro-1,4-naphthoquinone anion radical (9) and 2-amino-3-chloro-1,4-naphthoquinone radical (8). The probable reaction mechanism, the structure of intermediates as well as the reaction profile are discussed.     

Thermo-XRD-analysis and peptization study of the adsorption of alizarinate by Co-, Ni-, and Cu-montmorillonite

The adsorption of the monovalent anionic dye alizarinate onto Co-, Ni- and Cu-montmorillonite was carried out by adding the dye into aqueous clay suspensions. During the loading of the clay suspension by alizarinate, only some of the added organic anion is adsorbed by the clay forming d-coordination chelate complexes on the clay surface. Maximum adsorption of Co-, Ni- and Cu-clay were 13, 13 and 25 mmol dye per 100 g clay. Since the capacity of the clay for these transition metal cations is 38 mmol per 100 g clay, these saturations indicate that only part of the transition metal cations form positively charged d-coordination chelate complexes with metal:ligand ratio of 1. The complex cations can be located inside the interlayer spaces or on the broken bonds surfaces. Thermo-XRD-analysis and peptization studies of the solids and the clay water systems respectively were used here to identify the sorption sites. The Co and Ni complexes were obtained on the broken bonds surfaces whereas the Cu complexes were obtained in the interlayer space. Co²⁺, Ni²⁺ and Cu²⁺ were extracted from the clay into suspensions containing excess alizarinate.     

An algorithm for selecting a good value for the parameter c in radial basis function interpolation

The accuracy of many schemes for interpolating scattered data with radial basis functions depends on a shape parameter c of the radial basis function. In this paper we study the effect of c on the quality of fit of the multiquadric, inverse multiquadric and Gaussian interpolants. We show, numerically, that the value of the optimal c (the value of c that minimizes the interpolation error) depends on the number and distribution of data points, on the data vector, and on the precision of the computation. We present an algorithm for selecting a good value for c that implicitly takes all the above considerations into account. The algorithm selects c by minimizing a cost function that imitates the error between the radial interpolant and the (unknown) function from which the data vector was sampled. The cost function is defined by taking some norm of the error vector E = (E ₁, ... , E_N)^T where E _k = E_k = f_k - S^k x_k) and S _k is the interpolant to a reduced data set obtained by removing the point x _k and the corresponding data value f _k from the original data set. The cost function can be defined for any radial basis function and any dimension. We present the results of many numerical experiments involving interpolation of two dimensional data sets by the multiquadric, inverse multiquadric and Gaussian interpolants and we show that our algorithm consistently produces good values for the parameter c. This revised version was published online in June 2006 with corrections to the Cover Date.