Theory of mesoscopic magnetism in photonic crystals

We provide a rigorous theoretical basis for the artificial magnetic activity of metamaterials near resonances. Our approach is a renormalization-based scheme that authorizes a completely general theory. The major result is an explicit expression of the effective permeability, in terms of resonant frequencies. The theoretical results are checked numerically, and we give applications of our theory to left-handed media and to the solution of the Pokrovski-Efros paradox.     

Roughness-Induced Effects on the Quasi-Geostrophic Model

We study in this paper the effect of small-scale irregularities on the quasi-geostrophic model. This study is motivated by some problems related to oceanography, as the Gulf Stream separation, or the impact of the topography on the global circulation. We first consider the role of coastal roughness in the phenomenon of western intensification of boundary currents. We show that the roughness is responsible for a nonlinear dynamics of the boundary layers, governed by a quasilinear elliptic equation. We thus extend substantially the classical derivation of Munk layers [15] and the results of convergence obtained in [10]. We then discuss the effect of a rough topography, by generalizing and justifying some formal computations of [17]. In particular, we derive rigorously a simplified model of oceanic circulation, with a nonlinear and nonlocal dissipative term due to the roughness.Acknowledgement This work has been partially supported by the GDR Amplitude Equations and Qualitative Properties (GDR CNRS 2103: EAQP) and by the IDOPT project in Grenoble.     

Spin-charge separation in two-dimensional frustrated quantum magnets

The dynamics of a mobile hole in two-dimensional frustrated quantum magnets is investigated by exact diagonalization techniques. Our results provide evidence for spin-charge separation upon doping the kagome lattice, a prototype of a spin liquid. In contrast, in the checkerboard lattice, a symmetry broken valence bond crystal, a small quasiparticle peak is seen for some crystal momenta, a finding interpreted as a restoration of weak holon-spinon confinement.     

Amino-aryl-carbenes: alternative ligands for transition metals?

Despite the presence of a single amino substituent, an amino-anthryl-carbene was found to behave as a strong sigma-donor weak pi-acceptor ligand toward rhodium(I) fragments.     

Thiyl radical-mediated cleavage of allylic C-N bonds: scope, limitations, and theoretical support to the mechanism

Thiols mediate the radical isomerization of allylic amines into enamines. The reaction results in the cleavage of the allylic C-N bond, after treatment with aqueous HCl. The mechanism involves the abstraction of an allylic hydrogen alpha to nitrogen by thiyl radical, followed by a return hydrogen transfer from the thiol to the carbon gamma to nitrogen in the intermediate allylic radical. The scope and limitations of the reaction with respect to the nature of the thiol, to the structure of the allylic chain, and to the nature of the substituents at nitrogen were investigated. The experimental results were interpreted on the ground of DFT calculations of the C-Halpha BDE in the starting allylic amines, and of the C-Hgamma BDE in the resulting enamines. The efficiency of the initial hydrogen transfer is the first requirement for the reaction to proceed. A balance must be found between the S-H BDE and the two above-mentioned C-H BDEs. The incidence of stereoelectronic factors was analyzed through NBO calculations performed on the optimized geometries of the starting allylic amines. Additional calculations of the transition structures and subsequent tracing of the reaction profiles were performed for the abstraction of Halpha from both the allyl and the prenyl derivatives by p-TolS(*). The latter allowed us to estimate the rate constant for the abstraction of hydrogen by thiyl radical from an N-prenylamine and an N-allylamine.     

Theoretical study of rhodium(I) carbene complexes: the structural versatility of phosphino- compared with aminocarbenes

Density functional calculations are reported for complexes of general formula [(carbene)RhClL(2)] featuring model phosphino- and aminocarbenes. Both the cis and trans isomers of the rhodium(I) eta(1)-complexes (1-9) were investigated, and the influence of the rhodium co-ligands (L=ethylene, phosphine, or carbon monoxide) was evaluated. In the case of phosphinocarbenes and carbon monoxide as a ligand, a somewhat unusual coordination mode was observed, in which a significant intramolecular Cl-->C(carbene) interaction is present. The propensity of phosphino- and aminocarbenes to behave as four electron donors was also investigated both structurally and energetically on the related eta(2)-complexes 10-18. These results as a whole emphasize the structural versatility of phosphino- compared with aminocarbene complexes.