Solutions of the Multiconfiguration Equations in Quantum Chemistry

The multiconfiguration methods are the natural generalization of the well-known Hartree-Fock theory for atoms and molecules. By a variational method, we prove the existence of a minimum of the energy and of infinitely many solutions of the multiconfiguration equations, a finite number of them being interpreted as excited states of the molecule. Our results are valid when the total nuclear charge Z exceeds N–1 (N is the number of electrons) and cover most of the methods used by chemists. The saddle points are obtained with a min-max principle; we use a Palais-Smale condition with Morse-type information and a new and simple form of the Euler-Lagrange equations.     

Optical sectioning in wide-field microscopy obtained by dynamic structured light illumination and detection based on a smart pixel detector array

Optical sectioning in wide-field microscopy is achieved by illumination of the object with a continuously moving single-spatial-frequency pattern and detecting the image with a smart pixel detector array. This detector performs an on-chip electronic signal processing that extracts the optically sectioned image. The optically sectioned image is directly observed in real time without any additional postprocessing.     

Jack Polynomials in Superspace

This work initiates the study of orthogonal symmetric polynomials in superspace. Here we present two approaches leading to a family of orthogonal polynomials in superspace that generalize the Jack polynomials. The first approach relies on previous work by the authors in which eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland Hamiltonian were constructed. Orthogonal eigenfunctions are now obtained by diagonalizing the first nontrivial element of a bosonic tower of commuting conserved charges not containing this Hamiltonian. Quite remarkably, the expansion coefficients of these orthogonal eigenfunctions in the supermonomial basis are stable with respect to the number of variables. The second and more direct approach amounts to symmetrize products of non-symmetric Jack polynomials with monomials in the fermionic variables. This time, the orthogonality is inherited from the orthogonality of the non-symmetric Jack polynomials, and the value of the norm is given explicitly.     

Re-based heterogeneous catalysts for olefin metathesis prepared by surface organometallic chemistry: reactivity and selectivity

Herein we describe the catalytic activity of 1, a well-defined Re alkylidene complex supported silica, in the reaction of olefin metathesis. This system is highly active for terminal and internal olefins with initial rates up to 0.7 mol per mol Re per s. It also catalyses the self-metathesis of methyl oleate (MO) without the need of co-catalysts. The turnover numbers can reach up to 900 for MO, which is unprecedented for a heterogeneous Re-based catalyst. Moreover the use of silica as a support can bring major advantages, such as the possibility to use branched olefins like isobutene, which are usually incompatible with alumina-based supports; therefore, the formation of isoamylene from the cross-metathesis of propene and isobutene can be performed. All these results are in sharp contrast to what has been found for other silica- or alumina-supported rhenium oxide systems, which are either completely inactive (silica system) or typically need co-catalysts when functionalised olefins are used. Finally the initiation step corresponds to a cross-metathesis reaction to give a 3:1 mixture of 3,3-dimethylbutene and trans-4,4-dimethylpent-2-ene, and make this catalyst the first generation of well-defined Re-based heterogeneous catalysts.     

A supramolecular cup-and-ball C60-porphyrin conjugate system

In addition to the ammonium-crown ether recognition, pi-stacking interactions between the C60 sphere and the porphyrin moiety have been evidenced in a supramolecular complex obtained from a porphyrin-crown ether conjugate and a fullerene derivative bearing an ammonium unit.     

On the structure of weight modules

Given any simple Lie superalgebra , we investigate the structure of an arbitrary simple weight -module. We introduce two invariants of simple weight modules: the shadow and the small Weyl group. Generalizing results of Fernando and Futorny we show that any simple module is obtained by parabolic induction from a cuspidal module of a Levi subsuperalgebra. Then we classify the cuspidal Levi subsuperalgebras of all simple classical Lie superalgebras and of the Lie superalgebra W. Most of them are simply Levi subalgebras of , in which case the classification of all finite cuspidal representations has recently been carried out by one of us (Mathieu). Our results reduce the classification of the finite simple weight modules over all classical simple Lie superalgebras to classifying the finite cuspidal modules over certain Lie superalgebras which we list explicitly.

     

Ultrashort microwave pulses generated due to three magnon interactions

Density-functional theory is applied to the interaction site model to study gas-liquid nucleation in a partially immiscible binary system consisting of spherical Lennard-Jones atoms (monomers) and dumbbell molecules of two Lennard-Jones atoms (dimers). Increased interaction anisotropy between the dimer sites and monomers is shown to result in mutual enhancement of nucleation. Critical nuclei with a lamellar structure are observed at high dimer activities.     

Retardation effects in the rotating string model

A new method to study the retardation effects in mesons is presented. It is based on a generalized rotating string model, in which a nonzero value of the relative time between the quark and the antiquark is allowed. This approach leads to a retardation term in the Hamiltonian which behaves as a perturbation of the nonretarded Hamiltonian and preserves the Regge trajectories for light mesons. The straight-line ansatz is used to describe the string, and the relevance of this approximation is tested. It is shown that the string is actually curved because of retardation, but this bending does not bring a relevant contribution to the energy spectrum of the model.     

Electrochemical reduction of oxygen catalyzed by a wide range of bacteria including Gram-positive

Most bacteria known to be electrochemically active have been harvested in the anodic compartments of microbial fuel cells (MFCs) and are able to use electrodes as electron acceptors. The reverse phenomenon, i.e. using solid electrodes as electron donors, is not so widely studied. To our knowledge, most of the electrochemically active bacteria are Gram-negative. The present study implements a transitory electrochemical technique (cyclic voltammetry) to study the microbial catalysis of the electrochemical reduction of oxygen. It is demonstrated that a wide range of aerobic and facultative anaerobic bacteria are able to catalyze oxygen reduction. Among these electroactive bacteria, several were Gram-positive. The transfer of electrons was direct since no activity was obtained with the filtrate. These findings, showing a widespread property among bacteria including Gram-positive ones, open new and interesting routes in the field of electroactive bacteria research.