Chiral induction in quinoline-derived oligoamide foldamers: assignment of helical handedness and role of steric effects

Chiral groups attached to the end of quinoline-derived oligoamide foldamers give rise to chiral helical induction in solution. Using various chiral groups, diastereomeric excesses ranging from 9% to 83% could be measured by NMR and circular dichroism. Despite these relatively weak values and the fact that diastereomeric helices coexist and interconvert in solution, the right-handed or left-handed helical sense favored by the terminal chiral group could be determined unambiguously using X-ray crystallography. Assignment of chiral induction was performed in an original way using the strong tendency of racemates to cocrystallize, and taking advantage of slow helix inversion rates, which allowed one to establish that the stereomers observed in the crystals do correspond to the major stereomers in solution. The sense of chiral helical induction was rationalized on the basis of sterics. Upon assigning an Rs or Ss chirality to the stereogenic center using a nomenclature where the four substituents are ranked according to decreasing sizes, it is observed that Rs chirality always favors left-handed helicity and Ss chirality favors right-handed helicity (P). X-ray structures shed some light on the role of sterics in the mechanism of chiral induction. The preferred conformation at the stereocenter is apparently one where the bulkiest group should preferentially point away from the helix, the second largest group should be aligned with the helix backbone, and the smallest should point to the helix.     

Dichloro and alkylchloro gallium derivatives of dichalcogenoimidodiphosphinate ligands: isolation of a spirogallium cation

Dichloro and chloromethyl Ga(III) complexes of general formulae [XClGa-eta2-{R2P(E)NP(E'R'2-E,E'}](X = Cl, R, R'= Ph, E, E'= O (1), S (2), Se (3); R = Ph, R'= OEt, E = O, E'= S (4); R = Me, R'= Ph, E, E'= S (5) and X = Me, E, E'= O (6), S (7), Se (8)) were synthesised by either metathesis reactions between GaCl3 and the potassium salt of the ligand (X = Cl) or by methane eliminations from in situ prepared GaMe2Cl and the protonated ligands LH (X = Me). Redistribution reaction of (3) in either CDCl3 or THF afforded the solvent-free tetracoordinate gallium spirocycle cation [Ga-{eta2-{Ph2P(Se)NP(Se)Ph2-Se,Se'})2]+ (9+). The molecular structures of complexes 2, 4, 5, 7 and 9(+) show non-planar gallacycle rings.     

Action d'organolithiens sur la méthyl-2 quinoxaline. Etude de la réactivité des adduits

The action of organolithium reagents such as phenyllithium or n-bulyllithium on 2-methylquinoxaline gave lithiation of the methyl group which upon reaction with electtropholesphiles produce side chain alkenyl derivatives. On the other hand organolithium reagents react with the quinoxaline azomethine bond to give I-lithio-2-alkyl)or ary-1)-3 methylquinoxalines which can be further loithiated on the methyl group to give 2-alkyl(or aryl)-3-alkenylquinoxaline derivatives. The adducts can be condensed with clectrophiles such as benzonitrile or methlyl benzoate but only methyl benzoate leads to N condensed derivatives. Furthermore substituted 1,2,3,4-terahydroqinoxalines are available via the above lithio intermediates.     

The Regularity of Optimal Irrigation Patterns

A branched structure is observable in draining and irrigation systems, in electric power supply systems, and in natural objects like blood vessels, the river basins or the trees. Recent approaches of these networks derive their branched structure from an energy functional whose essential feature is to favor wide routes. Given a flow s in a river, a road, a tube or a wire, the transportation cost per unit length is supposed in these models to be proportional to s ^α with 0 < α < 1. The aim of this paper is to prove the regularity of paths (rivers, branches,...) when the irrigated measure is the Lebesgue density on a smooth open set and the irrigating measure is a single source. In that case we prove that all branches of optimal irrigation trees satisfy an elliptic equation and that their curvature is a bounded measure. In consequence all branching points in the network have a tangent cone made of a finite number of segments, and all other points have a tangent. An explicit counterexample disproves these regularity properties for non-Lebesgue irrigated measures.     

MR detection of mechanical vibrations using a radiofrequency field gradient

A new method for NMR characterization of mechanical waves, based upon radiofrequency field gradient for motion encoding, is proposed. A binomial B1 gradient excitation scheme was used to visualize the mobile spins undergoing a periodic transverse mechanical excitation. A simple model was designed to simulate the NMR signal as a function of the wave frequency excitation and the periodicity of the NMR pulse sequence. The preliminary results were obtained on a gel phantom at low vibration frequencies (0-200 Hz) by using a ladder-shaped coil generating a nearly constant RF field gradient along a specific known direction. For very small displacements and/or B1 gradients, the NMR signal measured on a gel phantom was proportional to the vibration amplitude and the pulse sequence was shown to be selective with respect to the vibration frequency. A good estimation of the direction of vibrations was obtained by varying the angle between the motion direction and the B1 gradient. The method and its use in parallel to more conventional MR elastography techniques are discussed. The presented approach might be of interest for noninvasive investigation of elastic properties of soft tissues and other materials.     

Resin dynamics contributes to the NMR line broadening of organic molecules grafted onto a polystyrene resin

Despite the use of high resolution magic angle spinning NMR, the NMR linewidth of anchored molecules on the commonly used Merrifield solid phase resins remains larger than that of the corresponding molecules in solution. We investigate the different mechanisms that might be at the origin of this line broadening. Experimentally, we use the CPMG method to determine the (15)N relaxation times of a tethered tripeptide and show that the slow resin dynamics significantly contributes to the transverse relaxation.     

The Atiyah-Singer theorems: A probabilistic approach. II. The Lefschetz fixed point formulas

In this paper the Lefschetz fixed point formulas of M. F. Atiyah and I. M. Singer (Ann. of Math.87 (1968), 484–530, 546–604) for classical elliptic complexes are proved by using probabilistic methods.     

Stepwise and concerted electron-transfer/bond breaking reactions. solvent control of the existence of unstable pi ion radicals and of the activation barriers of their heterolytic cleavage

Available data from various sources seem to indicate an important role of solvation in the cleavage rates of intermediate pi ion radicals, in the passage from concerted to stepwise electron-transfer/bond breaking reaction pathways and even in the very existence of pi ion radicals. After preliminary computations treating the solvent as dielectric continuum, these expectations are examined with the help of a simple model system involving the anion radical of ONCH(2)Cl and two molecules of water, which allows the application of advanced computational techniques and a treatment of these solvent effects that emphasizes the role of solvent molecules that sit close to the charge centers of the molecule. A pi ion radical minimum indeed appears upon introduction of the two water molecules, and cleavage is accompanied by their displacement toward the leaving anion, thus offering a qualitative mimicry of the experimental observations.     

Activation barriers in the homolytic cleavage of radicals and ion radicals

As revealed by several experimental examples, radicals and ion radicals may, in contrast with closed-shell molecules, undergo exothermic homolytic cleavages (.A..B --> A: +.B) with substantial activation barriers. A two-state semiclassical model is proposed for explaining the existence of the barrier and estimating its magnitude. It is based on the intersection of the potential energy surfaces characterizing the dissociation of a bonding state, .A..B -->.A. +.B, on one hand, and the approach to bonding distance of a repulsive state, A: +.B --> A therefore B, on the other. After inclusion of the bond cleavage and formation as Morse curves in the normal-mode analysis, a simple activation driving force relationship is obtained, the two main ingredients of the intrinsic barrier being the triplet excitation energy of the A moiety and the pi*--> sigma* excitation energy in .A-B. The model is then tested by quantum chemical calculations, first on a simplified system to evaluate the calculation techniques and then on a real system. A comparison of the model predictions with experiment is finally performed using the rate data recently gathered for the cleavage of 4-cyanophenyl alkyl ether anion radicals, which cover a respectable range of driving forces, showing satisfactory agreement between theoretical predictions and experimental data.