The Taming of Redox-Labile Phosphidotitanocene Cations

Tame d⁰ phosphidotitanocene cations stabilized with a pendant tertiary phosphane arm are reported. These compounds were obtained by one-electron oxidation of d¹ precursors with [Cp₂Fe][BPh₄]. The electronic structure of these compounds was studied experimentally (EPR, UV/Vis, and NMR spectroscopy, X-ray diffraction analysis) and through DFT calculations. The theoretical analysis of the bonding situation by using the electron localization function (ELF) shows the presence of π-interactions between the phosphido ligand and Ti in the d⁰ complexes, whereas dπ–pπ repulsion prevents such interactions in the d¹ complexes. In addition, CH–π interactions were observed in several complexes, both in solution and in the solid state, between the phosphido ligand and the phosphane arm. The d⁰ complexes were found to be light sensitive, and decompose through Ti−P bond homolysis to give Ti^III species. A naked d⁰ phosphidotitanocene cation has been trapped by reaction with diphenylacetylene, yielding a Ti/P frustrated Lewis pair (FLP), which was found to be less reactive than a previously reported Zr analog.     

Insights into the Two-Electron Reductive Process of [FeFe]H2ase Biomimetics: Cyclic Voltammetry and DFT Investigation on Chelate Control of Redox Properties of [Fe2(CO)4(κ2-Chelate)(μ-Dithiolate)]

The electrochemical reduction of complexes [Fe₂(CO)₄(κ²-phen)(μ-xdt)] (phen=1,10-phenanthroline; xdt=pdt ( 1 ), adt^iPr ( 2 )) in MeCN-[Bu₄N][PF₆] 0.2 m is described as a two-reduction process. DFT calculations show that 1 and its monoreduced form 1⁻ display metal- and phenanthroline-centered frontier orbitals (LUMO and SOMO) indicating the non-innocence of the phenanthroline ligand. Two energetically close geometries were found for the doubly reduced species suggesting an intriguing influence of the phenanthroline ligand leading to the cleavage of a Fe−S bond as proposed generally for this type of complex or retaining the electron density and avoiding Fe−S cleavage. Extension of calculations to other complexes with edt, adt^iPr bridge and even virtual species [Fe₂(CO)₄(κ²-phen)(μ-adt^R)] (R=CH(CF₃)₂, H) or [Fe₂(CO)₄(κ²-phen)(μ-pdt^R)] (R=CH(CF₃)₂, iPr) showed that the relative stability between both two-electron-reduced isomers depends on the nature of the bridge and the possibility to establish a remote anagostic interaction between the iron center {Fe(CO)₃} and the group carried by the bridged-head atom of the dithiolate group.     

Real-Time Analysis of Polyphenol–Protein Interactions by Surface Plasmon Resonance Using Surface-Bound Polyphenols

A selection of bioactive polyphenols of different structural classes, such as the ellagitannins vescalagin and vescalin, the flavanoids catechin, epicatechin, epigallocatechin gallate (EGCG), and procyanidin B2, and the stilbenoids resveratrol and piceatannol, were chemically modified to bear a biotin unit for enabling their immobilization on streptavidin-coated sensor chips. These sensor chips were used to evaluate in real time by surface plasmon resonance (SPR) the interactions of three different surface-bound polyphenolic ligands per sensor chip with various protein analytes, including human DNA topoisomerase IIα, flavonoid leucoanthocyanidin dioxygenase, B-cell lymphoma 2 apoptosis regulator protein, and bovine serum albumin. The types and levels of SPR responses unveiled major differences in the association, or lack thereof, and dissociation between a given protein analyte and different polyphenolic ligands. Thus, this multi-analysis SPR technique is a valuable methodology to rapidly screen and qualitatively compare various polyphenol–protein interactions.     

On the Supra-LUMO Interaction: Case Study of a Sudden Change of Electronic Structure as a Functional Emergence

The synergistic functioning of redox-active components that emerges from prototypical 2,2′-di(N-methylpyrid-4-ylium)-1,1′-biphenyl is described. Interestingly, even if a trans conformation of the native assembly is expected, due to electrostatic repulsion between cationic pyridinium units, we demonstrate that cis conformation is equally energy-stabilized on account of a peculiar LUMO (SupLUMO) that develops through space, encompassing the two pyridiniums in a single, made-in-one-piece, electronic entity (superelectrophoric behavior). This SupLUMO emergence, with the cis species as superelectrophore embodiment, originates in a sudden change of electronic structure. This finding is substantiated by insights from solid state (single-crystal X-ray diffraction) and solution (NOE NMR and UV-vis-NIR spectroelectrochemistry) studies, combined with electronic structure computations. Electrochemistry shows that electron transfers are so strongly correlated that two-electron reduction manifests itself as a single-step process with a large potential inversion consistent with inner creation of a carbon-carbon bond (digital simulation). Besides, absence of reductive formation of dimers is a further indication of a preferential intramolecular reactivity determined by the SupLUMO interaction (cis isomer pre-organization). The redox-gated covalent bond, serving as electron reservoir, was studied via atropisomerism of the reduction product (VT NMR study). The overall picture derived from this in-depth study of 2,2′-di(N-methylpyrid-4-ylium)-1,1′-biphenyl proves that trans and cis species are worth considered as intrinsically sharply different, that is, as doubly-electrophoric and singly-superelectrophoric switchable assemblies, beyond conformational isomerism. Most importantly, the through-space-mediated SupLUMO may come in complement of other weak interactions encountered in Supramolecular Chemistry as a tool for the design of electroactive architectures.     

Riemannian foliations on manifolds with non-negative curvature

1980Mathematics Subject Classification (1985Revision): 53C12, 57R30     

Dissipative periodic systems and symmetric interpolation in Schur classes

Matrix-valued functions analytic and contractive in the open unit disk (Schur functions) play an important role in system theory. They represent transfer functions of causal time-invariant dissipative systems. In this paper we show how a Schur function can still be associated to a k-periodic system. This function satisfies a certain symmetry condition (conditions (1.7) for k=2 and (4.4) for general k). We study a general bitangential interpolation problem for the Schur functions satisfying this symmetry condition.     

A classification of thin shell theories

This paper gives a modern mathematical analysis of the relationships between several, different linear shell theories. It also discusses the asymptotic role played by membrane theory. It presents theorems on the existence and uniqueness of solutions of membrane equations depending on the concavity of the surface.