Efficient Olefin Epoxidation by Robust Re4 Cluster‐Supported MnIII Complexes with Peracids: Evidence of Simultaneous Operation of Multiple Active Oxidant Species,MnVO,MnIVO,and MnIII?OOC(O)R

Two new tetranuclear chalcocyanide cluster complexes, [{Mn(saloph)H₂O}₄Re₄Q₄(CN)₁₂]?4 CH₃OH? 8 H₂O (saloph=N,N′‐o‐phenylenebis(salicylidenaminato), Q=Se ( 1 ‐Se), Te ( 2 ‐Te)), have been synthesized by the diffusion of a methanolic solution of [PPh₄]₄[Re₄Q₄(CN)₁₂] into a methanolic solution of [Mn(saloph)]⁺. The structure of 2 ‐Te has been determined by X‐ray crystallography. These rhenium cluster‐supported [Mn^III(saloph)] complexes have been found to efficiently catalyze a wide range of olefin epoxidations under mild experimental conditions in the presence of meta‐chloroperbenzoic acid (mCPBA). Olefin epoxidation by these catalysts is proposed to involve the multiple active oxidants Mn^V?O, Mn^IV?O, and Mn^III? OOC(O)R. Evidence in support of this interpretation has been derived from reactivity and Hammett studies, H₂¹⁸O‐exchange experiments, and the use of peroxyphenylacetic acid as a mechanistic probe. Moreover, it has been observed that the participation of Mn^V?O, Mn^IV?O, and Mn^III? OOC(O)R can be controlled by changing the substrate concentration. This mechanism provides the greatest congruity with related oxidation reactions that employ certain Mn complexes as catalysts.     

1,3-phosphorus zwitterions with cyano-group at anion center

This review focuses on synthesis and properties of 1,3-phosphorus-containing zwitterions that have at the anionic center cyano-group and either ester (type one) or carbamate (type two) moieties. Zwitterions belonging to type one possess dual nucleophile reactivity, i.e., depending on the properties of the electrophiles they may form either C- or N-derivatives. Zwitterions belonging to type two possess triple nucleophile reactivity. In their reactions with electrophiles, they may form even three types of derivatives, i.e., at the C-, O- or N-atoms. This nucleophile multiplicity is not just interesting from the theoretical standpoint but may also open the ways to the synthesis of new compounds that can be important from the practical standpoint, such as physiologically active compounds, catalysts, analytical reagents, etc.     

Intermolecular π‐stacking and F...F interactions of fluorine‐substituted meso‐alkynylporphyrin

Two C2‐symmetric meso‐alkynylporphyrins, namely 5,15‐bis[(4‐butyl‐2,3,5,6‐tetrafluorophenyl)ethynyl]‐10,20‐dipropylporphyrin, C₅₀H₄₂F₈N₄, (I), and 5,15‐bis[(4‐butylphenyl)ethynyl]‐10,20‐dipropylporphyrin, C₅₀H₅₀N₄, (II), show remarkable π–π stacking that forms columns of porphyrin centers. The tetrafluorophenylene moieties in (I) show intermolecular interactions with each other through the F atoms, forming one‐dimensional ribbons. No significant π–π interactions are observed in the plane of the phenylene and tetrafluorophenylene moieties in either (I) or (II). The molecules of both compounds lie about inversion centers.     

Yet another proof of Marstrand’s theorem

In a paper from 1954 Marstrand proved that if K ⊂ ℝ² is a Borel set with Hausdorff dimension greater than 1, then its one-dimensional projection has positive Lebesgue measure for almost-all directions. In this article, we give a combinatorial proof of this theorem, extending the techniques developed in our previous paper [9].     

Generation and near-field imaging of Airy surface plasmons

We demonstrate experimentally the generation and near-field imaging of nondiffracting surface waves, plasmonic Airy beams, propagating on the surface of a gold metal film. The Airy plasmons are excited by an engineered nanoscale phase grating, and demonstrate significant beam bending over their propagation. We show that the observed Airy plasmons exhibit self-healing properties, suggesting novel applications in plasmonic circuitry and surface optical manipulation.     

Electromagnetic field with induced massive term: Case with scalar field

We consider an interacting system of massless scalar and electromagnetic fields, with the Lagrangian explicitly depending on the electromagnetic potentials, i.e., interaction with broken gauge invariance. The Lagrangian for interaction is chosen in such a way that the electromagnetic field equation acquires an additional term, which in some cases is proportional to the vector potential of the electromagnetic field. This equation can be interpreted as the equation of motion of photon with induced nonzero rest-mass. This system of interacting fields is considered within the scope of Bianchi type-I (BI) cosmological model. It is shown that, as a result of interaction the isotropization process of the expansion takes place.     

Symmetry breaking in plasmonic waveguides with metal nonlinearities

We studied nonlinear effects in plasmonic metal film waveguides and couplers stimulated by third-order optical response due to ponderomotive metal nonlinearities. We analyzed the structure and dispersion of nonlinear plasmonic guided modes and predicted the bifurcations and symmetry breaking of nonlinear modes for the critical powers, depending on the structure dimensions.     

An interplay between static potential and Reggeon trajectory for QCD string

I consider two cases where QCD string is described by an effective theory of long strings: the static potential and meson scattering amplitudes in the Regge regime. I show how they can be solved in the mean-field approximation, justified by the large number of space–time dimensions, and argue that it turns out to be exact. I compare contributions from QCD string and perturbative QCD and discuss experimental consequences for the scattering amplitudes.