Very Large Cyclic Compounds

Very large ring systems, containing more than 50 ring members, are becoming increasingly important in different topics in natural sciences. These so-called gigantocycles differ from smaller macrocycles in physical properties, special structural features and chemical behaviour. This article is meant to be the first summary of such ring systems and a synopsis of the most remarkable examples with their fascinating nano-scaled structures and ingenious synthesis. To restrict the scope of the article, only isolated and completely characterized, monodisperse compounds are presented. Furthermore, attention is mainly directed at organic gigantocycles. Some ultracycles with more than 100 ring members, mainly occurring in polymer chemistry and nature, will also be described.     

Strained Ammonium Precursors for Radiofluorinations

The increasing application of positron emission tomography (PET) in nuclear medicine has stimulated the extensive development of a multitude of novel and versatile techniques to introduce fluorine-18, especially for the radiolabelling of biologically or pharmacologically active molecules. Taking into consideration that the introduction of fluorine-18 (t_1/2=109.8 min) mostly proceeds under harsh conditions, radiolabelling of such molecules represents a challenge and is of enormous interest. Ideally, it should proceed in a regioselective manner under mild physiological conditions, in an acceptable time span, with high yields and high specific activities. Special attention has been drawn to 2-fluoroethyl and 3-fluoropropyl groups, which are often the active sites of radiofluorinated compounds. Precursors containing an ammonium leaving group – such as a strained azetidinium or aziridinium moiety – can help to overcome these obstacles leading to a convenient and mild introduction of [¹⁸F]fluoride with high radiochemical yields.     

Polybenzimidazole dendrimer containing triazine rings-based high-temperature proton exchange membranes with high performances over a wide humidity range

A high-temperature proton exchange membrane with high proton conductivity over a wide humidity range still remains a challenge. PBI dendrimer containing triazine rings (TPBI) was synthesized to approach this aim considering its high content of hygroscopic terminal groups and of larger free volume. A novel proton conductor previously synthesized (zirconium 3-sulfopropyl phosphonate, ZrSP) was doped due to its good proton conductivity over a wide humidity range. TPBI was post-crosslinked with a tetrafunctional epoxy resin (N,N,N′,N′-tetraglycidyl-4,4′-diaminodiphenylmethane, TGDDM) to enhance the mechanical stability at low cross-linking degrees, which allowed high doping levels of ZrSP, and thus, high conductivity. The prepared membranes (TPBI-TGDDM/ZrSP) showed good thermal stability, high proton conductivity over wide humidity range, and good dimensional stability. At suitable degrees of branching, TPBI-TGDDM/ZrSP exhibited superior mechanical property, oxidative stability, methanol barrier property, and membrane selectivity than its linear analog (mPBI-TGDDM/ZrSP). As ZrSP instead of PA was applied as the proton conductor, TPBI-TGDDM/ZrSP showed good durability of proton conductivity, especially in comparison with TPBI-TGDDM/PA, which highly retarded decline in conductivity caused by PA leaking. The proton conductivity at 180 °C of TPBI(20)-TGDDM(10)/ZrSP(50) achieved 142, 84.2 and 23.6 mS cm^?1 at 100%, 50%, and 0 RH, respectively.     

The ring opening of cyclopropylidene to allene: global features of the reaction surface

Summary The global features of the groundstate ring opening of cyclopropylidene to allene are studied by means ofab-initio FORS MCSCF calculations based on a minimal AO basis set. The energy surface is completely mapped out in terms of three reaction coordinates, namely the CCC ring-opening angle and two angles describing the rotations of the CH₂ groups. For each choice of these three variables, the twelve remaining internal coordinates are optimized by energy minimization. In the initial phase of the reaction, as the CCC angle opens, the CH₂ groups rotate in a disrotatory manner, maintainingC _s symmetry. This uphill reaction path leads to a transition region which occurs early, for a CCC angle of about 84°. In this transition region the reaction path branches into two pathways which are each others' mirror images. The system exhibits thus abifurcating transition region. Passed this region, the two pathways are overall conrotatory in character. However, these downhill reaction paths to the products are poorly defined because, from a CCC opening angle of about 90° on,the CH ₂ groups can rotate freely and isoenergetically in a synchronized, cogwheel-like manner and this disrotatory motion can mix unpredictably with the conrotatory downhill motion. There is no preference for any one of the two reaction pathways yielding the two stereoisomers of allene and the reaction is thereforenonstereospecific with respect to the numbered hydrogen atoms. The global surface is documented by means of contour maps representing slices corresponding to constant CCC angles. The bifurcating transition region is mapped in detail.Operated for the U.S. Department of Energy by Iowa State University under Contract No. 7405-ENG-82. This work was supported by the office of Basic Energy Sciences     

Practical synthesis of bicyclic pyrazol-5-one derivatives

This communication describes a convenient synthesis of fused bicyclic pyrazolones in a one-pot reaction procedure. Modified protocols are also developed to access 5,5-bicyclic and bulky pyrazolones in good yields. The method reported herein represents a practical approach to structurally diversified bicyclic pyrazolones.     

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.     

Estimation of diffusion coefficient of Ba++ ions in silica gel from periodic precipitation of BaMoO4

Formation of Liesegang rings on the growth of BaMoO₄ crystals in silica gel by single diffusion is discussed. The rhythmic precipitation is found to be influenced profoundly by (a) the molarity of inner and outerelectrolytes (b) the age of gel and (c) the pH of the gel medium. The time law, spacing law and the law relating diffusion depth and width are verified. A method to estimate the diffusion coefficient of the outer electrolyte in the gel medium is developed and calculated for Ba⁺⁺ions.     

Dieudonné rings associated with

We use Dieudonné theory for periodically graded Hopf rings to determine the Dieudonné ring structure of the -graded Morava -theory , with an odd prime, when applied to the -spectrum (and to ). We also expand these results in order to accomodate the case of the full Morava -theory .

     

Pairs of Semisimple Lie Algebras and their Maximal Reductive Subalgebras

Let \(\mathfrak g\) be a semisimple Lie algebra over a field \(\mathbb K\), \(\text{char}\left( \mathbb{K} \right)=0\), and \(\mathfrak g_1\) a subalgebra reductive in \(\mathfrak g\). Suppose that the restriction of the Killing form B of \(\mathfrak g\) to \(\mathfrak g_1 \times \mathfrak g_1\) is nondegenerate. Consider the following statements: ( 1) For any Cartan subalgebra \(\mathfrak h_1\) of \(\mathfrak g_1\) there is a unique Cartan subalgebra \(\mathfrak h\) of \(\mathfrak g\) containing \(\mathfrak h_1\); ( 2) \(\mathfrak g_1\) is self-normalizing in \(\mathfrak g\); ( 3) The B-orthogonal \(\mathfrak p\) of \(\mathfrak g_1\) in \(\mathfrak g\) is simple as a \(\mathfrak g_1\)-module for the adjoint representation. We give some answers to this natural question: For which pairs \((\mathfrak g,\mathfrak g_1)\) do ( 1), ( 2) or ( 3) hold? We also study how \(\mathfrak p\) in general decomposes as a \(\mathfrak g_1\)-module, and when \(\mathfrak g_1\) is a maximal subalgebra of \(\mathfrak g\). In particular suppose \((\mathfrak g,\sigma )\) is a pair with \(\mathfrak g\) as above and σ its automorphism of order m. Assume that \(\mathbb K\) contains a primitive m-th root of unity. Define \(\mathfrak g_1:=\mathfrak g^{\sigma}\), the fixed point algebra for σ. We prove the following generalization of a well known result for symmetric Lie algebras, i.e., for m=2: (a) \((\mathfrak g,\mathfrak g_1)\) satisfies ( 1); (b) For m prime, \((\mathfrak g,\mathfrak g_1)\) satisfies ( 2).     

Rigid complexes via DG algebras

Let be a commutative ring, a commutative -algebra and a complex of -modules. We begin by constructing the square , which is also a complex of -modules. The squaring operation is a quadratic functor, and its construction requires differential graded (DG) algebras. If there exists an isomorphism , then the pair is called a rigid complex over relative to (there are some finiteness conditions). There is an obvious notion of rigid morphism between rigid complexes.

We establish several properties of rigid complexes, including their uniqueness, existence (under some extra hypothesis), and formation of pullbacks (resp. ) along a finite (resp. essentially smooth) ring homomorphism .

In the subsequent paper, Rigid Dualizing Complexes over Commutative Rings, we consider rigid dualizing complexes over commutative rings, building on the results of the present paper. The project culminates in our paper Rigid Dualizing Complexes and Perverse Sheaves on Schemes, where we give a comprehensive version of Grothendieck duality for schemes.

The idea of rigid complexes originates in noncommutative algebraic geometry, and is due to Van den Bergh (1997).