Enantiodivergent synthesis of P-chirogenic phosphines

Several approaches for the enantiodivergent synthesis of P-chirogenic mono- and diphosphines are described, using ephedrine methodology and phosphine borane chemistry. Firstly, both enantiomers of a tertiary phosphine can be obtained starting from the same oxazaphospholidine borane complex, prepared from (+)-ephedrine, when changing the order of addition of the organolithium reagents during the synthetic pathway. The second approach is based on the chlorophosphine boranes, which react with an organolithium reagent, to afford the corresponding phosphines with inversion of configuration. In the case where the chlorophosphine borane reacts with the t-butyl lithium reagent, a metal-halogen exchange occurs to afford the corresponding phosphide borane with retention of the configuration. The reaction of the phosphide borane with an alkyl halide leads to the same phosphine, but with the opposite configuration. Another approach depends on the diastereoselective preparation of the starting oxazaphospholidine borane complex from (?)-ephedrine, which leads according the case, to either one or the other enantiomer of a phosphine. Finally, the synthesis of (R,R)- and (S,S)-1,2-bis(methylphenylphosphino)ethane is also demonstrated using both enantiomers of the P-chirogenic diphosphinite diborane, which simultaneously allows the introduction of alkyl- or aryl substituents on the phosphorus atoms. In summary, these approaches show the great efficiency of the “ephedrine methodology” for the enantiodivergent synthesis of P-chirogenic mono- and diphosphines, and bearing alkyl or aryl substituents.     

A formal [3+3]-annulation-based approach to pancratistatins: total synthesis of (±)-7-deoxy-pancratistatin and its 2-epi and 2,4-diepi analogues

A full account is given for the total synthesis and the cytotoxic activity against the human lung tumoral cell line NCI-H460 of (±)-7-deoxy-pancratistatin and its 2-epi- and 2,4-diepi- unnatural analogues.     

Haarlet analysis of Lipschitz regularity in metric measure spaces

In this note we shall give a characterization of Lipschitz spaces on spaces of homogeneous type via Haar coefficients.     

Hybrid functionals and GW approximation in the FLAPW method

We present recent advances in numerical implementations of hybrid functionals and the GW approximation within the full-potential linearized augmented-plane-wave (FLAPW) method. The former is an approximation for the exchange–correlation contribution to the total energy functional in density-functional theory, and the latter is an approximation for the electronic self-energy in the framework of many-body perturbation theory. All implementations employ the mixed product basis, which has evolved into a versatile basis for the products of wave functions, describing the incoming and outgoing states of an electron that is scattered by interacting with another electron. It can thus be used for representing the nonlocal potential in hybrid functionals as well as the screened interaction and related quantities in GW calculations. In particular, the six-dimensional space integrals of the Hamiltonian exchange matrix elements (and exchange self-energy) decompose into sums over vector–matrix–vector products, which can be evaluated easily. The correlation part of the GW self-energy, which contains a time or frequency dependence, is calculated on the imaginary frequency axis with a subsequent analytic continuation to the real axis or, alternatively, by a direct frequency convolution of the Green function G and the dynamically screened Coulomb interaction W along a contour integration path that avoids the poles of the Green function. Hybrid-functional and GW calculations are notoriously computationally expensive. We present a number of tricks that reduce the computational cost considerably, including the use of spatial and time-reversal symmetries, modifications of the mixed product basis with the aim to optimize it for the correlation self-energy and another modification that makes the Coulomb matrix sparse, analytic expansions of the interaction potentials around the point of divergence at k = 0, and a nested density and density-matrix convergence scheme for hybrid-functional calculations. We show CPU timings for prototype semiconductors and illustrative results for GdN and ZnO.     

The self-dual point of the two-dimensional random-cluster model is critical for q?≥ 1

We prove a long-standing conjecture on random-cluster models, namely that the critical point for such models with parameter q?≥?1 on the square lattice is equal to the self-dual point ${p_{sd}(q) = \sqrt{q} / (1+\sqrt{q})}$ . This gives a proof that the critical temperature of the q-state Potts model is equal to ${\log (1+\sqrt q)}$ for all q?≥ 2. We further prove that the transition is sharp, meaning that there is exponential decay of correlations in the sub-critical phase. The techniques of this paper are rigorous and valid for all q?≥ 1, in contrast to earlier methods valid only for certain given q. The proof extends to the triangular and the hexagonal lattices as well.     

ESR and electrochemical study of 5-nitroindazole derivatives with antiprotozoal activity

The electrochemistry of 3-alkoxy- and 3-hydroxy-1-[omega-(dialkylamino)alkyl]-5-nitroindazole derivatives were characterized using cyclic voltammetry in DMSO. The nitro reduction process was studied and this was affected by the acid moieties present in these compounds. A nitro anion self-protonation process was observed. This phenomenon was studied by cyclic voltammetry in presence of increasing amount of NaOH. The reactivity of the nitro anion radical of these derivatives with glutathione was also studied by cyclic voltammetry. The oxidizing effect of glutathione is supported by the parallel decrease of the anodic peak current and increase of the cathodic peak in the cyclic voltammograms, corresponding to the wave of the nitro anion radical from uncharged species with the addition of glutathione. Nitro anion radicals obtained by electrolytic reduction of these derivatives were measured and analyzed in DMSO using electron spin resonance spectroscopy.