Highly Efficient Non-palladium Catalyzed Controlled Synthesis and X-ray Analysis of Functionalized 1,2-Diaryl-, 1,2,3-Triaryl- and 1,2,3,4-Tetraarylbenzene

A general, two-step highly efficient synthesis of 1,2-diaryl-, 1,2,3-triaryl- and 1,2,3,4-tetraarylbenzenes from simple stitching of alpha-oxo-ketene-S,S-acetals and active methylene compounds via a ‘lactone intermediate��� is described. This procedure offers easy access to highly functionalized arylated-benzenes containing sterically demanding groups in good to excellent yields. The novelty of the procedure lies in the fabrication of aromatic compounds with desired conformational flexibility along the molecular axis in a transition metal-free environment through easily accessible precursors. The crystal analysis of these arylated-benzene scaffolds showed that the peripheral aryl rings are arranged in propeller-like fashion with respect to the central benzene rings. Examination of the crystal packing in the structure of a 1,2,3,4-tetraarylbenzene 12c revealed a “N…pi interaction” between molecules related by a two-fold screw axis running in a direction. It is interesting that the repeat of the array of N…pi interaction around the axis of the 1,2,3,4-tetraarylbenzene 12c enforces the molecules in a helical pattern.

Topologically Accurate Dual Isosurfacing Using Ray Intersection

“Dual contouring” approaches provide an alternative to standard Marching Cubes (MC) method to extract and approximate an isosurface from trivariate data given on a volumetric mesh. These dual approaches solve some of the problems encountered by the MC methods. We present a simple method based on the MC method and the ray intersection technique to compute isosurface points in the cell interior. One of the advantages of our method is that it does not require us to use Hermite interpolation scheme, unlike other dual contouring methods. We perform a complete analysis of all possible configurations to generate a look-up table for all configurations. We use the look-up table to optimize the ray-intersection method to obtain minimum number of points necessarily sufficient for defining topologically correct isosurfaces in all possible configurations. Isosurface points are connected using a simple strategy.