Resonances with the complex rotation method: a study of an exactly soluble two-channel model

The complex rotation method is applied to the determination of widths and shifts of an harmonic oscillator predissociated by a linear potential, for when exact analytical formulas are available in the limit of small interchannel coupling. Excellent agreement is obtained.     

Synthesis of dendritic polyamide with protected amino functional groups in the periphery

A homologous series of first-to third-generation dendritic polyamides 2a, 3, and 5 with tris(aminoethyl) amine (TREA) as the core and the protected amino functional groups at the periphery were synthesized via active ester route from “Schlüter” type dendron 1a. Their structures were characterized by ¹H-NMR and mass spectra. Based on the efficient synthesis of the first generation dendrimer 2a (yield 75%), the synthesis of second-generation dendrimer 3 was found to be more efficient via the convergent method (yield 69%), while the mixed strategy was applied efficiently for the synthesis of the higher generation dendrimer 5 (yield 37%). The overall yield for the third generation dendrimer 5 from Schlüter dendron is 12%. __________ Translated from Huaxue Tongbao (Chemistry), 2005, 68(12) (in Chinese)     

5T2-1A1 Spin transition and residual paramagnetism in bis(2,4-bis(2-pyridyl)thiazole)iron(II) complexes: mössbauer effect and magnetism

The ⁵⁷Fe Mössbauer effect in [Fe(pythiaz)₂] (BF₄)₂ (I) and [Fe(pythiaz)₂] (C&O₄)₂ (II) has been studied between 298 and 4.2°K (pythiaz = 2,4-bis(2-pyridyl)thiazole). At 298°K compound I shows a doublet with ΔE_Q(⁵T₂) = 1.29 mm sec^?1 and δ^1S(⁵T₂) = +0.93 mm sec^?1 characteristic of a ⁵T₂ ground state. At 236°K, a second doublet, typical for a ¹A₁ ground state appears. The transition ⁵T₂ å ¹A₁ progresses as the temperature is lowered but levels off below ≈ 120°K. At 4.2°K, 59% of the intensity is due to the ¹A₁ state, and ΔE_Q(¹A₁) = 1.59 mm sec^?1 and δ^1S(¹A₁) = +0.26 mm sec^?1. In an applied magnetic field, V_zz(¹A₁) < 0 has been determined Similar results have been obtained with compound II.Debye-Waller factors f5_T2 and f1_A1. were determined from the Mössbauer spectra under the assumption of Curie-Weiss dependence of the magnetism for the ⁵T₂ and constant μ_eff for the ¹A₁ ground state. The resulting temperature dependence of f1_A1 is highly unusual thus suggesting complicated magnetic behaviour of both ground states in the transition region. Two mechanisms for the nature of the transition are discussed, a “spin-flip” mechanism being the physically more reasonable one. The assumption of a simple Boltzmann distribution (“spin equilibrium”) may be ruled out for the solid but could be encountered in solutions.     

A Boat-Shaped Tetracationic Macrocycle with a Semiconducting Organic Framework

We report the synthesis of a tetracationic macrocycle which contains two N,N′-bis(methylene)naphthalenediimide units inserted in between the pyridinium rings of the bipyridinium units in cyclobis(paraquat-p-phenylene) (CBPQT⁴⁺ or “blue box”) and describe the investigation of its potential use in materials for organic electronics. The incorporation of the two naphthalenediimide (NDI) units into the constitution of CBPQT⁴⁺, not only changes the supramolecular properties of the tetracation in the solid state, but also has a profound influence on the electrochemical and electronic behavior of the resulting tetracationic macrocycle. In particular, the solid-state (super)structure, investigated by single-crystal X-ray diffraction, reveals the formation of a three-dimensional (3D) supramolecular framework with ca. 2.8 nm diameter one-dimensional (1D) hexagonal channels. Electrochemical studies on solid-state thin films of the macrocycle show that they exhibit semiconducting properties with a redox-conductivity of up to 7.6×10⁻⁴ S m⁻¹. Moreover, EPR and ENDOR spectroscopies show that charge is equally shared between the NDIs within the one-electron reduced state of the NDI-based macrocycle on the time scale of these techniques.     

Conjugate points at infinity in infinite dimensional teichmüller spaces

We show in this article that there exists conjugate points at infinity in infinite dimensional Teichmüller spaces.     

Electrochemical Vicinal Difluorination of Alkenes: Scalable and Amenable to Electron-Rich Substrates

Fluorinated alkyl groups are important motifs in bioactive compounds, positively influencing pharmacokinetics, potency and conformation. The oxidative difluorination of alkenes represents an important strategy for their preparation, yet current methods are limited in their alkene-types and tolerance of electron-rich, readily oxidized functionalities, as well as in their safety and scalability. Herein, we report a method for the difluorination of a number of unactivated alkene-types that is tolerant of electron-rich functionality, giving products that are otherwise unattainable. Key to success is the electrochemical generation of a hypervalent iodine mediator using an “ex-cell” approach, which avoids oxidative substrate decomposition. The more sustainable conditions give good to excellent yields in up to decagram scales.     

Groups with many subgroups having polycyclic-by-finite layers or derived subgroup

A group is called (PF)L if the subgroups generated by its elements having same order (finite or infinite) are polycyclic-by-finite. In the present paper we prove that a group is locally graded minimal non-((PF)L∪(𝔓𝔉)𝔄) if, and only if, it is non-perfect minimal non-FC, where (𝔓𝔉)𝔄 denotes the class of (polycyclic-by-finite)-by-abelian groups. We prove also that a group of infinite rank whose proper subgroups of infinite rank are in ((PF)L∪(𝔓𝔉)𝔄) is itself in ((PF)L∪(𝔓𝔉)𝔄) provided that it is locally (soluble-by-finite) without simple homomorphic images of infinite rank. Our last result concerns groups that satisfy the minimal condition on non-((PF)L∪(𝔓𝔉)𝔄)-subgroups.