Recently Affleck et al. derived the existence of Friedel oscillations in the presence of a Kondo impurity. They supported their analytic derivation by numerical calculations using Wilson’s renormalization approach (NRG). In this paper the size of the Friedel oscillations is calculated with the FAIR method (Friedel Artificially Inserted Resonance) which has been recently developed. The results o...

We study the density disturbance of a correlated one–dimensional electron liquid in the presence of a scatterer or a barrier. The 2kF – periodic density profile away from the barrier (Friedel oscillation) is computed for arbitrary electron–electron interaction and arbitrary impurity strength. We find that in presence of correlations, the Friedel oscillation decays slower than predicted by Fermi...

The development of efficient Friedel-Crafts alkylations of arenes and heteroarenes using only catalytic amounts of a Lewis acid has gained much attention over the last decade. The new catalytic approaches described in this review are favoured over classical Friedel-Crafts conditions as benzyl-, propargyl- and allyl alcohols, or styrenes, can be used instead of toxic benzyl halides. Additionally...

An efficient diastereo- and enantioselective Friedel-Crafts alkylation of indoles with 3-nitro-2H-chromenes catalyzed by diphenylamine-linked bis(oxazoline) and bis(thiazoline) Zn(II) complexes has been developed. This asymmetric Friedel-Crafts alkylation led to medicinally privileged indolyl(nitro)chromans in good yields with high enantioselectivities (up to 95% ee) and diastereoselectivities ...

An interesting rearrangement of arylvinylidenecyclopropanes having three substituents at the 1- and 2-positions of the corresponding cyclopropane catalyzed by Lewis acids to give 6aH-benzo[c]fluorine derivatives via a double intramolecular Friedel-Crafts reaction or to give an indene derivative via an intramolecular Friedel-Crafts reaction is described.

We consider the Friedel sum rule in the context of the scattering theory for the Schrödinger operator −D2 x + V (x) on graphs made of one-dimensional wires connected to external leads. We generalize the Smith formula for graphs. We give several examples of graphs where the state counting method given by the Friedel sum rule is not working. The reason for the failure of the Friedel sum rule to c...

We consider the Friedel sum rule in the context of the scattering theory for the Schrödinger operator −D2 x + V (x) on graphs made of one-dimensional wires connected to external leads. We generalize the Smith formula for graphs. We give several examples of graphs where the state counting method given by the Friedel sum rule is not working. One of the reasons for the failure of the Friedel sum r...

The first examples of 3,3-diaryloxetanes are prepared in a lithium-catalyzed and substrate dependent divergent Friedel-Crafts reaction. para-Selective Friedel-Crafts reactions of phenols using oxetan-3-ols afford 3,3-diaryloxetanes by displacement of the hydroxy group. These constitute new isosteres for benzophenones and diarylmethanes. Conversely, ortho-selective Friedel-Crafts reactions of ph...

An enantioselective Friedel-Crafts alkylation with alpha,beta-unsaturated 2-acyl imidazoles and electron-rich aromatic nucleophiles catalyzed by bis(oxazolinyl)pyridine-scandium(III) triflate complexes has been accomplished. These alpha,beta-unsaturated 2-acyl imidazoles are effective electrophiles for the Friedel-Crafts reaction. The resulting adduct 2-acyl imidazole is easily converted to ami...