SYNTHESIS,CHARACTERIZATION, AND REACTIONS OF MONOMERIC TITANIUM COMPLEXES CONTAINING A CHELATING BIS(PHENOLATE) LIGAND [1, 2]

Abstract

The synthesis of Ti(iso)Cl₂ (iso = the dianion of 2, 2′-ethylidenebis(4, 6-di-rert-butylphenol)) is described. Metathesis reactions of this complex with Grignard reagents, as well as alkali metal salts, yielded Ti(iso)X₂ (X = CH₃, CH, Ph, CH₂SiMe₃, OCMe₃, or NMe₂). Reactions of the Ti-C bond in Ti(iso)(CH₃)₂ toward halogens, active hydrogen compounds, and acetone were studied. In addition. Ti(iso)(X)(Y) (X = CI or CH₃; Y = OC₆H₂-2, 6-^tBu₂-4-Me) could be prepared with the formation of only one coordination isomer. The new complexes have been thoroughly characterized by ¹H and ¹³C NMR spectroscopies. The solid state structure of Ti(iso)Cl₂ was determined via single crystal X-ray diffraction methods. The complex is monomeric, with approximately tetrahedral geometry about the titanium ion. The structure of Ti(iso)Cl₂ is compared to that of Ti(ultra)Cl₂ (ultra = the dianion of 2, 2′-mefhylenebis(6-tert-butyl-4-mefhylphenol)), which was redetermined to greater precision.     

Transport properties of mesoscopic graphene rings

Based on a recursive Green's function method, we investigate the conductance of mesoscopic graphene rings in the presence of disorder, in the limit of phase coherent transport. Two models of disorder are considered: edge disorder and surface disorder. Our simulations show that the conductance decreases exponentially with the edge disorder and the surface disorder. In the presence of flux, a clear Aharonov-Bohm conductance oscillation with the period Φ₀ (Φ₀=h/e) is observed. The edge disorder and the surface disorder have no effect on the period of AB oscillation. The amplitudes of AB oscillations vary with gate voltage and flux, which is consistent with the previous results. Additionally, ballistic rectification and negative differential resistance are observed in I-V curves, with on/off characteristic.     

Complications in the Castagnoli-Cushman reaction: An unusual course of reaction between cyclic anhydrides and sterically hindered indolenines

Attempted reaction of indolenines (which represent rather sterically hindered cyclic imines) with a series of dicarboxylic acid anhydrides yielded no expected product, the Castagnoli-Cushman lactam. Instead, products presumably formed via N-acyliminium species trapping by a carboxylate anion. Among them, hydrolytically labile 2:2 adducts of an indolenine and a cyclic anhydride, containing a 16-membered cyclic core, are particularly intriguing. This result contradicts the recently reported successful Castagnoli-Cushman reaction of indolenines with homophthalic anhydride suggesting a mechanistic switch in the course of the reaction.     

The dual of a constacyclic code,self dual,reversible constacyclic codes and constacyclic codes with complementary duals over finite local Frobenius non-chain rings with nilpotency index 3

Over finite local Frobenius non-chain rings with nilpotency index 3 and when the length of the codes is relatively prime to the characteristic of the residue field of the ring, the structure of the dual of $\gamma$-constacyclic codes is established and the algebraic characterization of self-dual $\gamma$-constacyclic codes, reversible $\gamma$-constacyclic codes and $\gamma$-constacyclic codes with complementary dual are given. Generators for the dual code are obtained from those of the original constacyclic code.     

Synthesis of Seven-Membered Benzolactones by Nickel-Catalyzed C−H Coupling of Benzamides with Oxetanes

A NiCl₂(PEt₃)₂-catalyzed regioselective C−H coupling of 8-aminoquinoline-derived benzamides with oxetanes has been developed. The reaction proceeds with concomitant removal of the 8-aminoquinoline auxiliary to directly form the corresponding seven-membered benzolactones, which frequently occur in natural products and bioactive molecules. Additionally, no stereochemical erosion is observed during the course of the reaction, and the use of enantioenriched and substituted oxetane thus provides a new avenue to the optically active benzolactone.     

On the variety of triangles for a hyper-Kähler fourfold constructed by Debarre and Voisin

We study the similarities between the Fano varieties of lines on a cubic fourfold, a hyper-Kähler fourfold studied by Beauville and Donagi, and the hyper-Kähler fourfold constructed by Debarre and Voisin in [3]. We exhibit an analog of the notion of “triangle” for these varieties and prove that the 6-dimensional variety of “triangles” is a Lagrangian subvariety in the cube of the constructed hyper-Kähler fourfold.     

Modular class primes in the Sundaram sieve

The purpose of this paper is to consider analogues of the twin-prime conjecture in various classes within modular rings.     

Commuting traces of multilinear maps on invertible elements

Let R be a unital simple ring. Under some technical restrictions, we characterize m-linear mappings G:R^m→R satisfying [G(u,…,u),u]?=?0 for all unit u∈R.