The proof of the Lane-Emden conjecture in four space dimensions

We partially solve a well-known conjecture about the nonexistence of positive entire solutions to elliptic systems of Lane-Emden type when the pair of exponents lies below the critical Sobolev hyperbola. Up to now, the conjecture had been proved for radial solutions, or in n?3 space dimensions, or in certain subregions below the critical hyperbola for n?4. We here establish the conjecture in four space dimensions and we obtain a new region of nonexistence for n?5. Our proof is based on a delicate combination involving Rellich-Pohozaev type identities, a comparison property between components via the maximum principle, Sobolev and interpolation inequalities on Sn−1, and feedback and measure arguments. Such Liouville-type nonexistence results have many applications in the study of nonvariational elliptic systems.     

Conformation of N(alpha)-substituted hydrazino acetamides in CDCl3, the precious help of the analysis of Deltadelta between amidic hydrogens, and correlation to the conformation of aza-beta3-peptides

[structures: see text] We studied the conformation of a series of primary amides in a solution of chloroform. Classical NMR tools such as dilution experiments, influence of DMSO, and 2D-NOESY, together with X-ray diffraction, were combined with an analysis of the difference of the chemical shift Deltadelta between the geminal amidic protons. This study was addressed in order to understand the conformation adopted by hydrazino acetamides 1a and 1b as model compounds for aza-beta3-peptides. In this manner, it was possible to show that the amidic group of these compounds acts as a H-bond donor and interacts with two different H-bond acceptors. We concluded that the hydrazinoturn, a specific bifurcated H-bond system observed in the solid state, is also the preferred conformation of hydrazino acetamides 1a and 1b in solution. Our results show that the short-range interaction with the N(alpha)-nitrogen lone pair not only stabilizes the C8 pseudocycle but could also contribute to the folding process of aza-beta3-peptides. In light of this, it could explain why aza-beta3-peptides develop a different H-bond network in comparison to their isosteric beta3-peptides analogues. Our work is in keeping with the recent interest of hydrazino peptides as an extension of the beta-peptide concept.     

Far-infrared spectroscopy of small polycyclic aromatic hydrocarbons

Both experimental and theoretical spectroscopic studies on small gas phase polycyclic aromatic hydrocarbons in the far-infrared spectral region are reported. The experimental set-up based on thermal emission and Fourier transform far infrared analysis led to the detection of relatively broad vibrational bands, unresolved in rotation, representative of each molecule. Detailed theoretical investigations were performed, including both ab initio calculations and spectral simulations. For the majority of the samples, this study provides the first detection of the vibrational modes associated with the skeleton motions.     

Rapid access to amino-substituted quinoline, (di)benzofuran, and carbazole heterocycles through an aminobenzannulation reaction

The use of a powerful aminobenzannulation reaction has been applied for the synthesis of amino-substituted quinolines, dibenzofurans, and carbazoles. The precursors are heterocycles bearing a methyl ketone group ortho to an internal alkyne. They are commercially available or can be obtained in three to four classical and efficient reactions: Vilsmeier-Haack, Sonogashira (diversity point), Grignard, and Ley's oxidation. Upon aminobenzannulation reaction-classical conditions being pyrrolidine neat or in a solvent and 4 A MS-an interesting range of disubstituted quinolines, dibenzofurans, and carbazoles are obtained along with enamine formation in some cases. The reaction is useful since meta-substituted heterocycles are produced and also differs from classical heterocyclic methods which go through closure at the heteroatom-containing ring instead of benzene ring formation.     

Diastereoselective Pictet-Spengler approach for the synthesis of pyrrolo[3,2-e][1,4]diazepin-2-one peptide turn mimics

Sixteen pyrrolo[3,2- e][1,4]diazepin-2-ones 1 were synthesized in 4-5 steps and 5-48% overall yields from 4-oxoproline 8 by a route featuring a diastereoselective Pictet-Spengler reaction to close the seven-membered diazepinone ring. Crystallographic analysis of pyrrolo[3,2- e][1,4]diazepin-2-one 1b by X-ray diffraction demonstrated that the alpha-amino acid residue adopted dihedral angle geometry similar to an ideal gamma-turn, illustrating the potential for employing these novel heterocycles as peptide turn mimics.     

Identity SN2 reactions X- + CH3X --> XCH3 + X- (X=F, Cl, Br, and I) in vacuum and in aqueous solution: a valence bond study

The recently developed (L. Song, W. Wu, Q. Zhang, S. Shaik, J. Phys. Chem. A 2004, 108, 6017) valence bond method coupled with a polarized continuum model (VBPCM) has been applied to the identity SN2 reaction of halides in the gas phase and in aqueous solution. The barriers computed at the level of the breathing orbital VB method (P. C. Hiberty, J. P. Flament, E. Noizet, Chem. Phys. Lett. 1992, 189, 259), BOVB and VBPCM//BOVB, are comparable to CCSD(T) and CCSD(T)//PCM results and to experimentally derived barriers in solution (W. J. Albery, M. M. Kreevoy, Adv. Phys. Org. Chem. 1978, 16, 85). The reactivity parameters needed to apply the valence bond state correlation diagram (VBSCD) method (S. Shaik, J. Am. Chem. Soc. 1984, 106, 1227), were also determined by VB calculations. It has been shown that the reactivity parameters along with their semiempirical derivations provide a satisfactory qualitative and quantitative account of the barriers.     

Electrochemical insights into the mechanisms of proton reduction by [Fe2(CO)6{micro-SCH2N(R)CH2S}] complexes related to the [2Fe](H) subsite of [FeFe]hydrogenase

Electrochemical investigations on a structural analogue of the [2Fe](H) subsite of [FeFe]H(2)ases, namely, [Fe(2)(CO)(6){micro-SCH(2)N(CH(2)CH(2)- OCH(3))CH(2)S}] (1), were conducted in MeCN/NBu(4)PF(6) in the presence of HBF(4)/Et(2)O or HOTs. Two different catalytic proton reduction processes operate, depending on the strength and the concentration of the acid used. The first process, which takes place around -1.2 V for both HBF(4)/Et(2)O and HOTs, is limited by the slow release of H(2) from the product of the {2 H(+)/2 e} pathway, 1-2H. The second catalytic process, which occurs at higher acid concentrations, takes place at different potentials depending on the acid present. We propose that this second mechanism is initiated by protonation of 1-2H when HBF(4)/Et(2)O is used, whereas the reduction of 1-2H is the initial step in the presence of the weaker acid HOTs. The potential of the second process, which occurs around -1.4 V (reduction potential of 1-3H(+)) or around -1.6 V (the reduction potential of 1-2H) is thus dependent on the strength of the available proton source.     

A microfluidic device based on droplet storage for screening solubility diagrams

This work describes a new microfluidic device developed for the rapid screening of solubility diagrams. In several parallel channels, hundreds of nanolitre volume droplets of a given solution are first stored with a gradual variation in the solute concentration. Then, the application of a temperature gradient along these channels enables us to read directly and quantitatively phase diagrams, concentration vs. temperature. We show, using a solution of adipic acid, that we can measure ten points of the solubility curve in less than 1 hr and with only 250 microL of solution.