Conformally invariant tensors of an almost Hermitian manifold associated with the holomorphic curvature tensor

We consider an almost Hermitian manifold and apply the conformal change of metric to its holomorphic curvature tensor. In such a way we find that the generalized Bochner curvature tensor can be expressed as a linear combination of B ₁, B ₂, and B ₃ such that (6.4) holds. Each of the tensors B ₁, B ₂, B ₃ is conformally invariant and satisfies the condition (1.2) of K?hler type.     

Scalar mesons moving in a finite volume and the role of partial wave mixing

Phase shifts and resonance parameters can be obtained from finite-volume lattice spectra for interacting pairs of particles, moving with non-zero total momentum. We present a simple derivation of the method that is subsequently applied to obtain the ?Ц? and ??K phase shifts in the sectors with total isospin I = 0 and I = 1/2 , respectively. Considering different total momenta, one obtains extra data points for a given volume that allow for a very efficient extraction of the resonance parameters in the infinite-volume limit. Corrections due to the mixing of partial waves are provided. We expect that our results will help to optimize the strategies in lattice simulations, which aim at an accurate determination of the scattering and resonance properties.     

The highly stereoselective decarboxylation of (+)-1-bromo-1-chloro-2,2,2-trifluoropropanoic acid to give (+)-1-bromo-1-chloro-2,2,2-trifluoroethane [(+)-halothane] with retention of configuration

The absolute configuration of the title acid 2 has been determined to be S by X-ray crystallography. Thus, decarboxylation of 2 produces (S)-(+)-halothane with 99% retention of configuration. This behavior is compared to other stereoselective decarboxylation reactions of α-haloacids from the literature that also gave high degrees of retention of configuration when in the form of their quaternary ammonium salts, which contain one proton. The proton of the ammonium salt is necessary in order to protonate the anionic intermediate formed from decarboxylation. In the absence of this relatively acidic proton, we had previously found that using triethylene glycol (TEG) as both the solvent and proton source for the decarboxylation reaction of acid 2 caused poor stereoselectivity. This was in contrast to 1,2,2,2-tetrafluoro-1-methoxypropionic acid 6, which showed a high degree of retention of configuration in TEG. In order to rationalize this differing behavior, we report DFT studies at PCM-B3LYP/6-31++G⁷ level of theory (the results were additionally confirmed with 6-311++G⁷ and aug-cc-pVDZ basis sets). The energy barrier to inversion of configuration of the anionic reaction intermediate 11 of acid 2 is 10.23 kcal/mol. However, we find that the anionic intermediate 10 from acid 6 would rather undergo β-elimination instead of inversion of configuration. Thus the planar transition state required for inversion of configuration is never reached, regardless of the rate of proton transfer to the anion.     

From data to knowledge—Use of the Cambridge Structural Database for studying molecular interactions

Abstract

The ordered arrangement of molecules and ions in crystal structures is the result of non-bonded interactions, albeit modulated in the crystalline state by random crystal packing forces. Each individual crystal structure gives but a snapshot of these interactions. It is only by examining a large number of structures containing similar molecules or functional groups that we can gain any generalized knowledge about the rules governing molecular interactions. Indeed if we knew these rules it should be possible to predict crystal structures likely to be formed by specific molecules, whereas at present each new crystal structure requires a de novo experimental solution. We would also be able to evaluate the relative contribution of non-bonded and crystal packing forces and extrapolate to the interactive behaviour of molecules in solution and, most importantly, in the environments encountered in biological systems. A key to these studies is the Cambridge Structural Database (CSD) system where experimental results from over 100,000 individual structure determinations are stored in computer readable form. The system also provides the computational tools needed to locate the relevant structures and analyse the numerical data using a variety of statistical techniques. This paper describes the latest Version of the CSD system (Version 5) released Autumn 1992. The use of the system is illustrated by several examples, such as the preferential interaction of certain functional groups, the study of the C—H…O bond and drug-DNA interactions.