Investigation of the π–π stacking interactions without direct electrostatic effects of substituents: the aromatic∥aromatic and aromatic∥anti-aromatic complexes

Stability of the π–π stacking interactions in the ben∥substituted-ben and ben∥substituted-COT complexes was studied using the computational quantum chemistry methods (where ben and COT are benzene and cyclooctatetraene, ∥ denotes π–π stacking interaction, substituted-ben and substituted-COT are benzene and cyclooctatetraene which substituted with four ethynyl-X groups, respectively, and X = OH, CH₃, H, F, CF₃, CN and NO₂). In these complexes electron-withdrawing substituents lead to larger binding energies and electron-donating ones lead to weaker interactions compared to X = H. There are meaningful correlations between the Hammett constants and binding energies. The atoms in molecules (AIM) analysis shows that formation of these complexes is accompanied by increase in the electron charge densities at the ring critical points of the substituted-ben and substituted-COT rings which leads to increase/decrease of the π–π stacking interactions in the ben∥substituted-ben/ben∥substituted-COT complexes. The charge transfer occurs from benzene to substituted-ben in the ben∥substituted-ben complexes and from substituted-COT to benzene (with the exception of X = CN) in the ben∥substituted-COT ones. Nuclear magnetic resonance calculations demonstrate that interactions of the more aromatic substituted-ben/less anti-aromatic substituted-COT rings with benzene in the ben∥substituted-ben/ben∥substituted-COT complexes can be helpful to enhance strength of the π–π stacking interactions. Thus, regardless of ring size, the π–π stacking interaction is an aromatic–aromatic interaction and π electron cloud properties of interacting rings affect on the strength of this interaction.     

Synthesis of aliphatic polyesters containing tetracyanoquinodimethane units by low-temperature polycondensation reactions

The low-temperature solution polycondensation reaction between 1,4-bis-(2′-hydroxy-ethoxy)benzene and adipyl chloride has been studied in N,N-dimethylacetamide. The effect of temperature, concentration, and reaction time on the percent yield and product viscosity has been determined. Optimum conditions were established for the preparation of high molecular weight products and then applied to the synthesis of novel tetracyanoquinodimethane polyesters. Products were characterized by gel permeation chromatography.     

On the chlorenium source in the asymmetric chlorolactonization reaction

N-Acylated N-chlorohydantoins are shown to be competent chlorenium sources in the (DHQD)(2)PHAL-mediated asymmetric chlorolactonization. The derivatives demonstrate the exact role of the N1 and N3 chlorine atoms in the parent dichlorohydantoins with the N1 chlorine serving as an inductive activator and the N3 chlorine being delivered to the substrate. The putative associated catalyst/chlorine source complex was experimentally demonstrated through a series of matched/mismatched experiments employing chiral N-chlorinated hydantoins.     

Almost homomorphisms between unital <Emphasis Type="Italic">C</Emphasis>*-algebras: A fixed point approach

Let A , B be two unital C*-algebras. By using fixed pint methods, we prove that every almost unital almost linear mapping h : A → B which satisfies h(2 n uy) = h(2 n u)h(y) for all u ∈ U(A), all y ∈ A, and all n = 0, 1, 2, … , is a homomorphism. Also, we establish the generalized Hyers-Ulam-Rassias stability of *-homomorphisms on unital C*-algebras.     

Continuous ant colony system and tabu search algorithms hybridized for global minimization of continuous multi-minima functions

A new hybrid optimization method, combining Continuous Ant Colony System (CACS) and Tabu Search (TS) is proposed for minimization of continuous multi-minima functions. The new algorithm incorporates the concepts of promising list, tabu list and tabu balls from TS into the framework of CACS. This enables the resultant algorithm to avoid bad regions and to be guided toward the areas more likely to contain the global minimum. New strategies are proposed to dynamically tune the radius of the tabu balls during the execution and also to handle the variable correlations. The promising list is also used to update the pheromone distribution over the search space. The parameters of the new method are tuned based on the results obtained for a set of standard test functions. The results of the proposed scheme are also compared with those of some recent ant based and non-ant based meta-heuristics, showing improvements in terms of accuracy and efficiency.     

Killing vector fields on Riemannian and Lorentzian 3-manifolds

We give a complete local classification of all Riemannian 3-manifolds $(M,g)$ admitting a nonvanishing Killing vector field T. We then extend this classification to timelike Killing vector fields on Lorentzian 3-manifolds, which are automatically nonvanishing. The two key ingredients needed in our classification are the scalar curvature S of g and the function $\text{Ric}(T,T)$, where Ric is the Ricci tensor; in fact their sum appears as the Gaussian curvature of the quotient metric obtained from the action of T. Our classification generalizes that of Sasakian structures, which is the special case when $\text{Ric}(T,T)=2$. We also give necessary, and separately, sufficient conditions, both expressed in terms of $\text{Ric}(T,T)$, for g to be locally conformally flat. We then move from the local to the global setting, and prove two results: in the event that T has unit length and the coordinates derived in our classification are globally defined on ${\mathbb{R}}^3$, we give conditions under which S completely determines when the metric will be geodesically complete. In the event that the 3-manifold M is compact, we give a condition stating when it admits a metric of constant positive sectional curvature.