A new hexaferrocene complex with a [M3(mu3-O)]7+ core

The new hexaferrocene complex 1 has been synthesized and characterized by X-ray diffraction. Its magnetization data were fitted to a detailed theoretical model that considers nonequivalent exchange parameters between Fe ions to yield the magnetic exchange coupling values of J1/kB = -31.5 K and J2/kB = -25.8 K. Moreover, the cyclic voltammogram of complex 1 confirmed its redox activity associated with the presence of ferrocene units, with very small or negligible electronic interactions between them.     

Convex functions and Fourier coefficients

Positivity - The aim of this paper is to prove that the cosine Fourier coefficients $$a_{mn}$$ (with $$m,n\ge 1)$$ of a Popoviciu convex function of two variables are nonnegative.     

The traceless Staudinger ligation with fluorine-18: a novel and versatile labeling technique for the synthesis of PET-radiotracers

The development of rapid radiolabeling techniques under mild reaction conditions involving the short-lived positron emitter fluorine-18 remains a special challenge in organic PET chemistry. This work describes a novel and facile application of the traceless Staudinger ligation as a mild and versatile labeling method for preparation of various radiotracers labeled with fluorine-18.     

Rapid Dihydrogen Cleavage by Persistent Nitroxide Radicals under Frustrated Lewis Pair Conditions

Persistent radicals undergo hydrogen atom abstraction reactions with a great variety of substrates, but not with dihydrogen. It has now been found that the TEMPO radical splits dihydrogen under mild conditions in the presence of the strong bulky B(C₆F₅)₃ boron Lewis acid. The reaction is thought to proceed by a typical frustrated Lewis pair mechanism with the TEMPO radical acting as the active Lewis base. The reaction was analyzed by DFT, which indicates that no significant spin density on the hydrogen atoms is accumulated along the H₂ splitting reaction path.     

Oxidative Addition to Gold(I) by Photoredox Catalysis: Straightforward Access to Diverse (C,N)‐Cyclometalated Gold(III) Complexes

Herein, we report the oxidative addition of aryldiazonium salts to ligand‐supported gold(I) complexes under visible light photoredox conditions. This method provides experimental evidence for the involvement of such a process in dual gold/photoredox‐catalyzed reactions and delivers well‐defined (C,N)‐cyclometalated gold(III) species. The remarkably mild reaction conditions and the ability to widely vary the ancillary ligand make this method a potentially powerful synthetic tool to access diverse gold(III) complexes for systematic studies into their properties and reactivity. Initial studies show that these species can undergo chloride abstraction to afford Lewis acidic dicationic gold(III) species.     

A note on longitudinal oscillations of a generalized Burgers fluid in cylindrical domains

The starting solutions for the oscillating motion of a generalized Burgers fluid due to longitudinal oscillations of an infinite circular cylinder, as well as those corresponding to an oscillating pressure gradient, are established as Fourier–Bessel series in terms of some suitable eigenfunctions. These solutions, presented as sum of steady-state and transient solutions, describe the motion of the fluid for some time after its initiation. After that time, when the transients disappear, the motion of the fluid is described by the steady-state solutions which are periodic in time and independent of the initial conditions. These solutions are also presented in simpler but equivalent forms in terms of modified Bessel functions of first and second kind. In both forms, the steady-state solutions can be specialized to give the similar solutions for Burgers, Oldroyd-B, Maxwell, second grade and Newtonian fluids performing the same motions. Finally, the required time to reach the steady-state for cosine and sine oscillations of the boundary is obtained by graphical illustrations.     

Continuity of Usual Operations and Variational Convergences

Given convergent sequences of functions (f _n ) and (g _n ), we look for conditions ensuring that the sequences (f _n +g _n ), (max(f _n ,g _n )) and (f _n g _n ) converge, being the infimal convolution. The convergences we use are variational convergences. This study is motivated by applications to Hamilton–Jacobi equations.     

Oligomerization and hydroamination of terminal alkynes promoted by the cationic organoactinide compound [(Et2N)3U][BPh4

The three ancillary amido moieties in the cationic complex [(Et2N)3U][BPh4] are highly reactive and are easily replaced when the complex is treated with primary amines. The reaction of [(Et2N)3U][BPh4] with excess tBuNH2 allows the formation of the cationic complex [(tBuNH2)3(tBuNH)3U][BPh4]. X-ray diffraction studies on the complex indicate that three amido and three amine ligands are arranged around the cationic metal center in a slightly distorted octahedral mer geometry. The cationic complex reacts with primary alkynes in the presence of external primary amines to primarily afford the unexpected cis dimer and, in some cases, the hydroamination products are obtained concomitantly. The formation of the cis dimer is the result of an envelope isomerization through a metal-cyclopropyl cationic complex. In the reaction of the bulkier alkyne tBuC identical to CH with the cationic uranium complex in the presence of various primary amines, the cis dimer, one trimer, and one tetramer are obtained regioselectively, as confirmed by deuterium labeling experiments. The trimer and the tetramer correspond to consecutive insertions of an alkyne molecule into the vinylic CH bond trans to the bulky tert-butyl group. The reaction of (TMS) C identical to CH with the uranium catalyst in the presence of EtNH2 followed a different course and produced the gem dimer along with the hydroamination imine as the major product. However, when other bulkier amines were used (iPrNH2 or tBuNH2) both hydroamination isomeric imines Z and E were obtained. During the catalytic reaction, the E (kinetic) isomer is transformed into the most stable Z (thermodynamic) isomer. The unique reactivity of the alkyne (TMS) C identical to CH with the secondary amine Et2NH is remarkable because it afforded the trans dimer and the corresponding hydroamination enamine. The latter probably results from the insertion of the alkyne into a secondary metal-amide bond, followed by protonolysis.     

Two-photon state selection and angular momentum polarization probed by velocity map imaging: application to H atom photofragment angular distributions from the photodissociation of two-photon state selected HCl and HBr

A formalism for calculating the angular momentum polarization of an atom or a molecule following two-photon excitation of a J-selected state is presented. This formalism is used to interpret the H atom photofragment angular distributions from single-photon dissociation of two-photon rovibronically state selected HCl and HBr prepared via a Q-branch transition. By comparison of the angular distributions measured using the velocity map imaging technique with the theoretical model it is shown that single-photon dissociation of two-photon prepared states can be used for pathway identification, allowing for the identification of the virtual state symmetry in the two-photon absorption and/or the symmetry of the dissociative state. It is also shown that under conditions of excitation with circularly polarized light, or for excitation via non-Q-branch transitions with linearly polarized light the angular momentum polarization is independent of the dynamics of the two-photon transition and analytically computable.