Niederkoordinierte Phosphor-Verbindungen. 42. Trennung und röntgenographische Strukturbestimmung der E,Z-Isomeren des 2,4,6-Tri(tert.butyl)phenyl-phenylmethylenphosphans

Low-Coordinated Phosphorus Compounds. 42. Separation and Structure Determination by X-Ray of the E,Z-Isomers of 2,4,6-Tri(tert.butyl)phenyl-phenylmethylenphosphaalkene The E,Z-isomers of phosphaalkenes can be separated by fractional crystallisation and HPLC. The structures of the E,Z-forms of the phosphaalkene 2a have been proved by X-ray determination.     

Zur Kenntnis des RbNiCrF6-Typs. V. Neue Fluoride CsBMF6 mit B = MnII bzw. NiII und M = Ga,Fe, Rh bzw. Sc,In, Tl,Rh

On the RbNiCrF₆ Type. V. New Fluorides of the Type CsBMF₆ with B = Mn^II or Ni^II and M = Ga, Fe, Rh or Sc, In, Tl, Rh New prepared are the cubic compounds CsNiScF₆ (light yellow, a = 10.60 Å); CsNiInF₆ (lightyellow, a = 10.64 Å); CsNiTlF₆ (light yellow, a = 10.60 Å); CsNiRhF₆ (light redbrown, a = 10.37 Å); CsMnGaF₆ (pink, a = 10.42 Å); CsMnFeF₆ (light green, a = 10.55 Å) and CsMnRhF₆ (redbrown, a = 10.58 Å), all RbNiCrF₆ type of structure. The Madelung part of lattice energy, MAPLE, is calculated and discussed.     

Quantification of Ion‐Pairing Effects on the Nucleophilic Reactivities of Benzoyl‐ and Phenyl‐Substituted Carbanions in Dimethylsulfoxide

Second‐order rate constants for the reactions of acceptor‐substituted phenacyl (PhCO?CH^??Acc) and benzyl anions (Ph?CH^??Acc) with diarylcarbenium ions and quinone methides (reference electrophiles) have been determined in dimethylsulfoxide (DMSO) solution at 20 °C. By studying the kinetics in the presence of variable concentrations of potassium, sodium and lithium salts (up to 10^?2 mol L^?1), the influence of ion‐pairing on the reaction rates was examined. As the concentration of K⁺ did not have any influence on the rate constants at carbanion concentrations in the range of 10^?4–10^?3 mol L^?1, the acquired rate constants could be assigned to the reactivities of the free carbanions. The counter ion effects increase, however, in the series K⁺<Na⁺<Li⁺, and the sensitivity of the carbanion reactivities toward variation of the counter ion strongly depends on the structure of the carbanions. The reactivity parameters N and s_N of the free carbanions were derived from the linear plots of log k₂ against the electrophilicity parameters E of the reference electrophiles, according to the linear‐free energy relationship log k₂(20 °C)=s_N(N+E). These reactivity parameters can be used to predict absolute rate constants for the reactions of these carbanions with other electrophiles of known E parameters.     

Equiangular tight frames with centroidal symmetry

An equiangular tight frame (ETF) is a set of unit vectors whose coherence achieves the Welch bound, and so is as incoherent as possible. Though they arise in many applications, only a few methods for constructing them are known. Motivated by the connection between real ETFs and graph theory, we introduce the notion of ETFs that are symmetric about their centroid. We then discuss how well-known constructions, such as harmonic ETFs and Steiner ETFs, can have centroidal symmetry. Finally, we establish a new equivalence between centroid-symmetric real ETFs and certain types of strongly regular graphs (SRGs). Together, these results give the first proof of the existence of certain SRGs, as well as the disproofs of the existence of others.     

On the flexibility of the design of multiple try Metropolis schemes

The multiple try Metropolis (MTM) method is a generalization of the classical Metropolis–Hastings algorithm in which the next state of the chain is chosen among a set of samples, according to normalized weights. In the literature, several extensions have been proposed. In this work, we show and remark upon the flexibility of the design of MTM-type methods, fulfilling the detailed balance condition. We discuss several possibilities, show different numerical simulations and discuss the implications of the results.     

Synthesis of Air‐Stable,Volatile Uranium(IV) and (VI) Compounds and Their Gas‐Phase Conversion To Uranium Oxide Films

Four air‐stable, volatile uranium heteroarylalkenolates have been synthesized and characterized by three synthetic approaches and their gas phase deposition to uranium oxide films has been examined.