On the use of symmetry in the ab initio quantum mechanical simulation of nanotubes and related materials

Nanotubes can be characterized by a very high point symmetry, comparable or even larger than the one of the most symmetric crystalline systems (cubic, 48 point symmetry operators). For example, N = 2n rototranslation symmetry operators connect the atoms of the (n,0) nanotubes. This symmetry is fully exploited in the CRYSTAL code. As a result, ab initio quantum mechanical large basis set calculations of carbon nanotubes containing more than 150 atoms in the unit cell become very cheap, because the irreducible part of the unit cell reduces to two atoms only. The nanotube symmetry is exploited at three levels in the present implementation. First, for the automatic generation of the nanotube structure (and then of the input file for the SCF calculation) starting from a two‐dimensional structure (in the specific case, graphene). Second, the nanotube symmetry is used for the calculation of the mono‐ and bi‐electronic integrals that enter into the Fock (Kohn‐Sham) matrix definition. Only the irreducible wedge of the Fock matrix is computed, with a saving factor close to N. Finally, the symmetry is exploited for the diagonalization, where each irreducible representation is separately treated. When M atomic orbitals per carbon atom are used, the diagonalization computing time is close to Nt, where t is the time required for the diagonalization of each 2M × 2M matrix. The efficiency and accuracy of the computational scheme is documented. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Homoleptic Zincate‐Promoted Room‐Temperature Halogen–Metal Exchange of Bromopyridines

Homoleptic lithium tri‐ and tetraalkyl zincates were reacted with a set of bromopyridines. Efficient and chemoselective bromine–metal exchanges were realized at room temperature with a substoichiometric amount of nBu₄ZnLi₂?TMEDA reagent (1/3 equiv; TMEDA=N,N,N′,N′‐tetramethylethylenediamine). This reactivity contrasted with that of tBu₄ZnLi₂?TMEDA, which was inefficient below one equivalent. DFT calculations allowed us to rationalize the formation of N???Li stabilized polypyridyl zincates in the reaction. The one‐pot difunctionalization of dibromopyridines was also realized using the reagent stoichiometrically. The direct creation of C? Zn bonds in bromopyridines enabled us to perform efficient Negishi‐type cross‐couplings.     

A HTS Assay for the Detection of Organophosphorus Nerve Agent Scavengers

A new pro‐fluorescent probe aimed at a HTS assay of scavengers is able to selectively and efficiently cleave the P? S bond of organophosphorus nerve agents and by this provides non‐toxic phosphonic acid has been designed and synthesised. The previously described pro‐fluorescent probes were based on a conventional activated P? Oaryl bond cleavage, whereas our approach uses a self‐immolative linker strategy that allows the detection of phosphonothioase activity with respect to a non‐activated P? Salkyl bond. Further, we have also developed and optimised a high‐throughput screening assay for the selection of decontaminants (chemical or biochemical scavengers) that could efficiently hydrolyse highly toxic V ‐type nerve agents. A preliminary screening, realised on a small α‐nucleophile library, allowed us to identify some preliminary “hits”, among which pyridinealdoximes, α‐oxo oximes, hydroxamic acids and, less active but more original, amidoximes were the most promising. Their selective phosphonothioase activity has been further confirmed by using PhX as the substrate, and thus they offer new perspectives for the synthesis of more potent V nerve agent scavengers.     

Failure of the Ingard-Myers boundary condition for a lined duct: an experimental investigation

This paper deals with experimental investigation of the lined wall boundary condition in flow duct applications such as aircraft engine systems or automobile mufflers. A first experiment, based on a microphone array located in the liner test section, is carried out in order to extract the axial wavenumbers with the help of an "high-accurate" singular value decomposition Prony-like algorithm. The experimental axial wavenumbers are then used to provide the lined wall impedance for both downstream and upstream acoustic propagation by means of a straightforward impedance education method involving the classical Ingard-Myers boundary condition. The results show that the Ingard-Myers boundary condition fails to predict with accuracy the acoustic behavior in a lined duct with flow. An effective lined wall impedance, valid whatever the direction of acoustic propagation, can be suitably found from experimental axial wavenumbers and a modified version of the Ingard-Myers condition with the form inspired from a previous theoretical study [Aure?gan et al., J. Acoust. Soc. Am. 109, 59-64 (2001)]. In a second experiment, the scattering matrix of the liner test section is measured and is then compared to the predicted scattering matrix using the multimodal approach and the lined wall impedances previously deduced. A large discrepancy is observed between the measured and the predicted scattering coefficients that confirms the poor accuracy provided from the Ingard-Myers boundary condition widely used in lined duct applications.     

Monte Carlo simulation and theory of proton NMR transverse relaxation induced by aggregation of magnetic particles used as MRI contrast agents

Superparamagnetic particles are widely used in MRI as R2 contrast agents. In this last decade, different studies have focused on aggregation of superparamagnetic particles for important applications such as multimodal agents. A complete study--via simulations--of the influence of aggregation on the MR efficiency of these particles at high magnetic field is presented here. First, an empirical expression is proposed for R2 in the presence of uniformly distributed nanoparticles, taking into account two regimes at once (motional averaging and slow motion regimes). Three cluster shapes are simulated: Sphere, shell and line. An analytical model is proposed to understand water transverse relaxation induced by spherical and shell aggregates. Simulations lead to the conclusion that, in the motional averaging regime, the most efficient aggregate contrast agent is the densest sphere or shell.     

Comparison of Different Definitions of Traces for a Class of Ramified Domains with Self-Similar Fractal Boundaries

We consider a class of ramified bidimensional domains Ω with a self-similar fractal boundary Γ^?∞?, which is supplied with a probability measure μ called the self-similar measure. Emphasis is put on the case when the domain is not a ε???δ domain as defined by Jones and the fractal set is not totally disconnected. We compare two notions of trace on Γ^?∞? for functions in W ^1,q (Ω): the classical one, see for instance the book by Jonnson and Wallin, 1984, using the strict definition of a function at a point of $\overline{\Omega}$ , and another one proposed in 2007 and heavily relying on self-similarity. We prove that the two traces coincide μ-almost everywhere on Γ^?∞?. As a corollary, we characterize the critical number $\bar q$ for which for all $q<\bar q$ (resp. $q > \bar q$ ) there is a (resp. no) continuous extension operator from W ^1,q (Ω) to W ^1,q (?²).     

A General Way,From L-Ascorbic And D-Isoascorbic Acids,To Homochiral α-Hydroxy, α,β-Dihydroxy And α,β-Epoxy-Aldehydes,Useful Building Blocks For The Synthesis Of Linear Oxygenated Fatty Acids Metabolites

Abstract

Enantiomerically pure α-hydroxy, α,β-dihydroxy and α,β-epoxyaldehydes, useful building blocks for the synthesis of acyclic oxygenated fatty acids metabolites, were synthetized via epoxybutanediol acetonide starting from the commercially available L-ascorbic and D-isoascorbic acids.     

Dimension of asymptotic cones of Lie groups

We compute the covering dimension of the asymptotic cone ofa connected Lie group. For simply connected solvable Lie groups,this is the codimension of the exponential radical. As an application of the proof, we give a characterization ofconnected Lie groups that quasi-isometrically embed into a nonpositivelycurved metric space. Received February 6, 2007.