A novel algorithm for solving quasi penta-diagonal linear systems

In this paper, a novel numerical algorithm for solving quasi penta-diagonal linear systems is presented. The computational costs of the algorithm is less than those of three successful algorithms given by El-Mikkawy and Rahmo (Comput Math Appl 59:1386–1396, 2010), by Lv and Le (Appl Math Comput 204:707–712, 2008), and by Jia et al. (Int J Comput Math 89:851–860, 2012). In addition, a new recursive method for inverting the quasi penta-diagonal matrices is also discussed. The implementation of the algorithm using Computer Algebra Systems (CASs) such as MATLAB and MAPLE is straightforward. Two numerical examples are given in order to demonstrate the performance and efficiency of our algorithm.     

Preorganised effects of a tetramesogenic supermolecule on supramolecular assembly in the liquid crystalline phases

After preparing a homologous series of tetrameric mesogenic compounds in which two U-shaped molecules were connected via a rigid benzene derivative or a flexible alkyl chain, we investigated their phase transition behaviour using optical microscopy, differential scanning calorimetry and X-ray diffraction analysis. The compounds possessing an alkyl spacer as the central group exhibited nematic and smectic A phases just as the corresponding U-shaped molecule did. The compound possessing a 1,2-benzene unit as the connecting group showed nematic and smectic A phases, although the compound possessing a 1,3-benzene unit exhibited only an anticlinic smectic C phase. Structure–property relations of the liquid crystalline tetramers are interpreted in terms of preorganised effects of the four mesogenic units.     

Luminescence Color‐Tuning through Polymorph Doping: Preparation of a White‐Emitting Solid from a Single Gold(I)–Isocyanide Complex by Simple Precipitation

We report the luminescent color tuning of a new complex, 2‐benzothiophenyl(4‐methoxyphenyl isocyanide)gold(I) ( 1 ), by using a new “polymorph doping” approach. The slow crystallization of the complex 1 afforded three different pure polymorphic crystals with blue, green, and orange emission under UV‐light irradiation. The crystal structures of pure polymorphs of 1 were investigated in detail by means of single‐crystal X‐ray analyses. Theoretical calculations based on the single‐crystal structures provided qualitative explanation of the difference in the excited energy‐levels of the three polymorphs of 1 . In sharp contrast, the rapid precipitation of 1 , with the optimized conditions reproducibly afforded homogeneous powder materials showing solid‐state white‐emission with Commission Internationale de l’Éclairage (CIE) 1931 chromaticity coordinates of (0.33, 0.35), which is similar to pure white. New “polymorphic doping” has been revealed to be critical to this white emission through spectroscopic and X‐ray diffraction analyses. The coexistence of the multiple polymorphs of 1 within the homogeneous powder materials and the ideal mixing of multiple luminescent colors gave its white emission accompanied with energy transfer from the predominant green‐emitting polymorph to the minor orange‐emitting polymorph.     

Control of Exchange Interactions in π Dimers of 6‐Oxophenalenoxyl Neutral π Radicals: Spin‐Density Distributions and Multicentered–Two‐Electron Bonding Governed by Topological Symmetry and Substitution at the 8‐Position

The tri‐tert‐butylphenalenyl (TBPLY) radical exists as a π dimer in the crystal form with perfect overlapping of the singly occupied molecular orbitals (SOMOs) causing strong antiferromagnetic exchange interactions. 2,5‐Di‐tert‐butyl‐6‐oxophenalenoxyl (6OPO) is a phenalenyl‐based air‐stable neutral π radical with extensive spin delocalization and is a counter analogue of phenalenyl in terms of the topological symmetry of the spin density distribution. X‐ray crystal structure analyses showed that 8‐tert‐butyl‐ and 8‐(p‐XC₆H₄)‐6OPOs (X=I, Br) also form π dimers in the crystalline state. The π‐dimeric structure of 8‐tert‐butyl‐6OPO is seemingly similar to that of TBPLY even though its SOMO–SOMO overlap is small compared with that of TBPLY. The 8‐(p‐XC₆H₄) derivatives form slipped stacking π dimers in which the SOMO–SOMO overlaps are greater than in 8‐tert‐butyl‐6OPO, but still smaller than in TBPLY. The solid‐state electronic spectra of the 6OPO derivatives show much weaker intradimer charge‐transfer bands, and SQUID measurements for 8‐(p‐BrC₆H₄)‐6OPO show a weak antiferromagnetic exchange interaction in the π dimer. These results demonstrate that the control of the spin distribution patterns of the phenalenyl skeleton switches the mode of exchange interaction within the phenalenyl‐based π dimer. The formation of the relevant multicenter–two‐electron bonds is discussed.     

2,3,17,18‐Tetrahalohexaphyrins and the First Phlorin‐type Hexaphyrins

1‐(Triisopropylsilyl)‐3,4‐dichloropyrrole and 1‐(triisopropylsilyl)‐3,4‐difluoropyrrole were conveniently prepared from the corresponding 3,4‐dibromopyrrole by lithiation followed by halogenation. 2,3,17,18‐Tetrahalogeno [26]‐ and [28]hexaphyrins have been prepared by condensation of 3,4‐dihalopyrroles and a dipyrromethane‐dicarbinol. 2,3,17,18‐Tetrahalogenated hexaphyrins display variable structural and electronic properties depending upon the halogen atom and the number of π‐electrons. Tetrabromo[28]hexaphyrin and tetrachloro[28]hexaphyrin were further reduced with excess NaBH₄ to furnish meso‐reduced hexaphyrins as the first example of phlorin‐type meso‐aryl‐substituted hexaphyrins.     

Systematic evaluation of the palladium-catalyzed hydrogenation under flow conditions

Four types of heterogeneous Pd catalysts (10% Pd/C, 10% Pd/HP20, 0.5% Pd/MS3A, and 0.3% Pd/BN) were applied to the flow hydrogenation to systematically evaluate the appropriate conditions for the reduction of a wide variety of reducible functionalities. The use of 10% Pd/C and 10% Pd/HP20 allowed the hydrogenation of various reducible functionalities by a single-pass of the substrate–MeOH solution through the catalyst cartridge, while 0.5% Pd/MS3A and 0.3% Pd/BN catalyzed a novel chemoselective hydrogenation; only alkene, alkyne, azide, and nitro functionalities could be reduced with other coexisting reducible functionalities intact.     

Highly stereoselective Michael reduction/intramolecular Michael reaction cascade to synthesize trans-stereodiad comprising an all-carbon quaternary stereogenic center

A highly stereoselective Michael reduction/intramolecular Michael reaction cascade is described. The cascade is initiated by the regioselective Michael reduction of an α-methylidene ester with L-Selectride. This is followed by the highly stereoselective intramolecular Michael reaction which efficiently constructs a six-membered carbocyclic ring with formation of the trans-stereodiad, composed of an all-carbon quaternary center and a tertiary stereogenic center. The stereoselectivity is perfectly controlled by the choice of alkene geometry in the Michael acceptor.     

Palladium‐Catalyzed Amination of Aryl Sulfides with Anilines

A combination of a palladium–NHC catalyst and potassium hexamethyldisilazide enables the amination of aryl sulfides with anilines to afford a wide variety of diarylamines. The reaction conditions are versatile enough for the reaction of even bulky ortho‐substituted aryl sulfides. This amination can be applied to the modular synthesis of N‐aryl carbazoles from the corresponding ortho‐bromothioanisoles. As aryl sulfoxides undergo extended Pummerer reactions to afford ortho‐substituted aryl sulfides, the Pummerer products are thus useful substrates for the amination to culminate in efficient syntheses of a 2‐anilinobenzothiophene and an indole as proof‐of‐principle of the utility of the extended Pummerer reaction/amination cascade.