Catalyst‐Free Reductive Coupling of Aromatic and Aliphatic Nitro Compounds with Organohalides

A rare reductive coupling of nitro compounds with organohalides has been realized. The reaction is initiated by a partial reduction of the nitro group to a nitrenoid intermediate. Therefore, not only aromatic but also aliphatic nitro compounds are efficiently transformed into monoalkylated amines, with organohalides as the alkylating agent. Given the innate reactivity of the nitrenoid, a catalyst is not required, resulting in a high tolerance for aryl halide substituents in both starting materials.     

Transient Phosphenium and Arsenium Ions versus Stable Stibenium and Bismuthenium Ions

Fluoride abstraction from bis-m-terphenylelement fluorides (2,6-Mes₂C₆H₃)₂EF (E=P, As) generated the highly reactive phosphenium ion [(2,6-Mes₂C₆H₃)₂P]⁺ and the arsenium ion [(2,6-Mes₂C₆H₃)₂As]⁺, which immediately underwent intramolecular electrophilic substitution and formation of an 1,2,4-trimethyl-6-mesityl-5-m-terphenyl-benzo[b]phospholium ion and an 1,2,4-trimethyl-6-mesityl-5-m-terphenyl-benzo[b]arsolium ion, respectively. The formation of the latter involved a methyl group migration from the ortho-position of a flanking mesityl group to the meta-position. This reactivity of [(2,6-Mes₂C₆H₃)₂E]⁺ (E=P, As) is in sharp contrast to the related stibenium ion [(2,6-Mes₂C₆H₃)₂Sb]⁺ and bismuthenium ion [(2,6-Mes₂C₆H₃)₂Bi]⁺, which have been recently isolated and fully characterized (Angew. Chem. Int. Ed. 2018, 57 , 10080–10084). On the basis of DFT calculations, a mechanism for the rearrangement of the phosphenium and arsenium ions into the phospholium and arsolium ions is proposed, which is not feasible for the stibenium and bismuthenium ions.     

Chloro­bis­[4,4‐bis(hydroxy­methyl)‐2‐(2‐pyridyl)‐4,5‐di­hydro­oxazole‐N,N′]copper(II) chloride hemi­hydrate

The title compound, [CuCl(C₁₀H₁₂N₂O₃)₂]Cl·0.5H₂O, is composed of discrete complex cations, Cl^? anions and water mol­ecules. The O atom of the water mol­ecule lies on a twofold rotation axis. The [CuN₄Cl] coordination polyhedron is intermediate between square pyramidal and trigonal bipy­ramidal.     

Some results for a class of generalized polynomials

A class of generalized polynomials is considered consisting of the null spaces of certain differential operators with constant coefficients. This class strictly contains ordinary polynomials and appropriately scaled trigonometric polynomials. An analog of the classical Bernstein operator is introduced and it is shown that generalized Bernstein polynomials of a continuous function converge to this function. A convergence result is also proved for degree elevation of the generalized polynomials. Moreover, the geometric nature of these functions is discussed and a connection with certain rational parametric curves is established. This revised version was published online in June 2006 with corrections to the Cover Date.     

Electronically excited states of tryptamine and its microhydrated complex

The lowest electronically excited singlet states of tryptamine and the tryptamine (H2O)1 cluster have been studied, using time dependent density functional theory for determination of the geometries and multireference configuration interaction for the vertical and adiabatic excitation energies, the permanent dipole moments, and the transition dipole moment orientations. All molecular properties of the seven experimentally observed conformers of tryptamine could be reproduced with high accuracy. A strong solvent reorientation has been found upon electronic excitation of the 1:1 water cluster of tryptamine to the L(a) and L(b) states. The adiabatically lowest excited singlet state in case of the tryptamine monomer is the L(b) state, while for the 1:1 water complex, the L(a) is calculated below the L(b) state.     

On the restabilization of protein-covered latex colloids at high ionic strengths

Recent experiments on restabilization of protein-covered latex colloids at high ionic strengths reported by Lopez-Leon et al.(1) revealed strong specific anion effects. The same authors also emphasized that a recent polarization model, which involves both hydration and double layer forces, can account only for some of their experimental results but are in disagreement with other experimental results. The aim of the present paper is to show that most experimental results of ref 1 can be described, more than qualitatively, when the association equilibria for all the ions (with both the acidic and basic sites of the protein) are taken into account. As the traditional Poisson-Boltzmann approach, the polarization model neglects additional interactions between ions, and ions and surfaces, not included in the "mean field" electrical potential; therefore, a complete quantitative agreement should not be expected. While many of the discrepancies between calculations and experiment occur at low ionic strengths (10(-)(4)-10(-)(2) M), in the range of validity of the traditional DLVO theory, the latter can neither explain them. It is suggested that the structural modifications of the protein configuration induced by the electrolyte are responsible for some of the disagreements between experiment and calculations.     

Distinct gaps between fractional parts of sequences

Let be a real number, a positive integer and a subset of . We give an upper bound for the number of distinct lengths of gaps between the fractional parts .

     

Quantifying nonclassicality of one-mode Gaussian states of the radiation field

We define the degree of nonclassicality of a one-mode Gaussian state of the quantum electromagnetic field in terms of the Bures distance between the state and the set of all classical one-mode Gaussian states. We find the closest classical Gaussian state and the degree of nonclassicality using a recently established expression for the Uhlmann fidelity of two single-mode Gaussian states. The decrease of nonclassicality under thermal mapping is carefully analyzed. Along the same lines, we finally present the evolution of nonclassicality during linear amplification.     

What is an observable?

The concept of generalized observable in the scheme of Hilbert quantum mechanics is discussed. We give an example of a possible ambiguity of this notion. The role of interpretation and the strong connection with concrete experimental procedures in the discussion of generalized observables are stressed to explain the above ambiguity.Dedicated to Professor Peter Mittelstaedt on the occasion of his 60th birthday.Humboldt fellow, on leave from the Institute of Physics, Nicholas Copernicus University, Torun, Poland.