Elimination versus ring opening: a convergent route to alkylidene-cyclobutanes

Functionalized alkylidene-cyclobutanes have been prepared from 2-fluoropyridinyl-6-oxy precursors derived from vinyl cyclobutanols by a radical addition-elimination process. A wide range of functional groups is tolerated, and the alkylidene-cyclobutanes can be further elaborated into cyclopentanones. The limitation of this approach resides in the competition with opening of the cyclobutane ring.     

Quantification of glucuronidated and sulfated steroids in human urine by ultra-high pressure liquid chromatography quadrupole time-of-flight mass spectrometry

The urinary steroid profile is constituted by anabolic androgenic steroids, including testosterone and its relatives, that are extensively metabolized into phase II sulfated or glucuronidated steroids. The use of liquid chromatography coupled to mass spectrometry (LC-MS) is an issue for the direct analysis of conjugated steroids, which can be used as urinary markers of exogenous steroid administration in doping analysis, without hydrolysis of the conjugated moiety. In this study, a sensitive and selective ultra high-pressure liquid chromatography coupled to quadrupole time-of-flight mass spectrometer (UHPLC-QTOF-MS) method was developed to quantify major urinary metabolites simultaneously after testosterone intake. The sample preparation of the urine (1 mL) was performed by solid-phase extraction on Oasis HLB sorbent using a 96-well plate format. The conjugated steroids were analyzed by UHPLC-QTOF-MS^E with a single-gradient elution of 36 min (including re-equilibration time) in the negative electrospray ionization mode. MS^E analysis involved parallel alternating acquisitions of both low- and high-collision energy functions. The method was validated and applied to samples collected from a clinical study performed with a group of healthy human volunteers who had taken testosterone, which were compared with samples from a placebo group. Quantitative results were also compared to GC-MS and LC-MS/MS measurements, and the correlations between data were found appropriate. The acquisition of full mass spectra over the entire mass range with QTOF mass analyzers gives promise of the opportunity to extend the steroid profile to a higher number of conjugated steroids.     

A semi-analytical model for the behavior of saturated viscoplastic materials containing two populations of voids of different sizes

This paper presents a micromechanical model for a porous viscoplastic material containing two populations of pressurized voids of different sizes. Three scales are distinguished: the microscopic scale (corresponding to the size of the small voids), the mesoscopic scale (corresponding to the size of the large voids) and the macroscopic scale. It is assumed that the first homogenization step is performed at the microscopic scale, and, at the mesoscopic scale, the matrix is taken to be homogeneous and compressible. At the mesoscopic scale, the second homogenization step, on which the present study focuses, is based on a simplified representative volume element: a hollow sphere containing a pressurized void surrounded by a nonlinear viscoplastic compressible matrix. The nonlinear behavior of the matrix, which is expressed using the results obtained in the first homogenization step, is approached using a modified secant linearization procedure involving the discretization of the hollow sphere into concentric layers. Each layer has uniform secant moduli. The predictions of the model are compared with the more accurate numerical results obtained using the finite element method. Good agreement is found to exist with all the macroscopic stress triaxialities and all the porosity and nonlinearity values studied.     

A localized Jarník–Besicovitch theorem

Fundamental questions in Diophantine approximation are related to the Hausdorff dimension of sets of the form {x∈R:δx=δ}, where δ?1 and δx is the Diophantine approximation exponent of an irrational number x. We go beyond the classical results by computing the Hausdorff dimension of the sets {x∈R:δx=f(x)}, where f is a continuous function. Our theorem applies to the study of the approximation exponents by various approximation families. It also applies to functions f which are continuous outside a set of prescribed Hausdorff dimension.     

The Kauffman skein algebra of a surface at $${\sqrt{-1}}$$

We study the structure of the Kauffman algebra of a surface with parameter equal to \({\sqrt{-1}}\). We obtain an interpretation of this algebra as an algebra of parallel transport operators acting on sections of a line bundle over the moduli space of flat SU(2)-connections over the surface. We analyse the asymptotics of traces of curve-operators in TQFT in non standard regimes where the root of unity parametrizing the TQFT accumulates to a root of unity. We interpret the case of \({\sqrt{-1}}\) in terms of parallel transport operators.     

New insights in quantum chemical topology studies using numerical grid-based analyses

New insights in Quantum Chemical Topology of one-electron density functions have been proposed here by using a recent grid-based algorithm (Tang et al., J Phys Condens Matter 2009, 21, 084204), initially designed for the decomposition of the electron density. Beyond the charge analysis, we show that this algorithm is suitable for different scalar functions showing a more complex topology, that is, the Laplacian of the electron density, the electron localization function (ELF), and the molecular electrostatic potential (MEP). This algorithm makes use of a robust methodology enabling to numerically assign the data points of three-dimensional grids to basin volumes, and it has the advantage of requiring only the values of the scalar function without details on the wave function used to build the grid. Our implementation is briefly outlined (program named TopChem), its capabilities are examined, and technical aspects in terms of CPU requirement and accuracy of the results are discussed. Illustrative examples for individual molecules and crystalline solids obtained with gaussian and plane-wave-based density functional theory calculations are presented. Special attention was given to the MEP because its topological analysis is complex and scarce.     

Double-hybrid density-functional theory made rigorous

We provide a rigorous derivation of a class of double-hybrid approximations, combining Hartree-Fock exchange and second-order M?ller-Plesset correlation with a semilocal exchange-correlation density functional. These double-hybrid approximations contain only one empirical parameter and use a density-scaled correlation energy functional. Neglecting density scaling leads to a one-parameter version of the standard double-hybrid approximations. We assess the performance of these double-hybrid schemes on representative test sets of atomization energies and reaction barrier heights, and we compare to other hybrid approximations, including range-separated hybrids. Our best one-parameter double-hybrid approximation, called 1DH-BLYP, roughly reproduces the two parameters of the standard B2-PLYP or B2GP-PLYP double-hybrid approximations, which shows that these methods are not only empirically close to an optimum for general chemical applications but are also theoretically supported.     

Synthesis of peptide alkylthioesters using the intramolecular N,S-acyl shift properties of bis(2-sulfanylethyl)amido peptides

The design of novel methods giving access to peptide alkylthioesters, the key building blocks for protein synthesis using Native Chemical Ligation, is an important area of research. Bis(2-sulfanylethyl)amido peptides (SEA peptides) 1 equilibrate in aqueous solution with S-2-(2-mercaptoethylamino)ethyl thioester peptides 2 through an N,S-acyl shift mechanism. HPLC was used to study the rate of equilibration for different C-terminal amino acids and the position of equilibrium as a function of pH. We show also that thioester form 2 can participate efficiently in a thiol-thioester exchange reaction with 5% aqueous 3-mercaptopropionic acid. The highest reaction rate was obtained at pH 4. These experimental conditions are significantly less acidic than those reported in the past for related systems. The method was validated with the synthesis of a 24-mer peptide thioester. Consequently, SEA peptides 1 constitute a powerful platform for access to native chemical ligation methodologies.     

Towards an accurate description of anharmonic infrared spectra in solution within the polarizable continuum model: reaction field, cavity field and nonequilibrium effects

We present a newly developed and implemented methodology to perturbatively evaluate anharmonic vibrational frequencies and infrared (IR) intensities of solvated systems described by means of the polarizable continuum model (PCM). The essential aspects of the theoretical model and of the implementation are described and some numerical tests are shown, with special emphasis towards the evaluation of IR intensities, for which the quality of the present method is compared to other methodologies widely used in the literature. Proper account of an incomplete solvation regime in the treatment of the molecular vibration is also considered, as well as inclusion of the coupling between the solvent and the probing field (cavity field effects). In order to assess the quality of our approach, comparison with experimental findings is reported for selected cases.