Diastereoselective preparation and characterization of ruthenium bis(bipyridine) sulfoxide complexes

A new concept in the synthesis of optically active octahedral ruthenium complexes was realized for the first time when cis- or trans-Ru(bpy)2Cl, (cis- or trans-1) was reacted with either (R)-(+)- or (S)-(-)-methyl p-tolyl sulfoxide (2 or 3); this novel asymmetric synthesis leads to the diastereoselective formation of the ruthenium bis(bipyridine) complex cis-delta-[Ru(bpy)2(2)Cl]Cl (4) (49.6% de) or cis-lambda-[Ru(bpy)2(3)Cl]Cl (5) (48.4% de), respectively. cis- or trans-Ru(dmbpy)2Cl2 (cis- or trans-6) (dmbpy = 4,4'-dimethyl-2,2'-bipyridine) also reacts with 2 or 3, leading to the diastereoselective formation of cis-delta-[Ru(dmbpy)2(2)Cl]Cl (7) (59.5% de) or cis-lambda-[Ru(dmbpy)2(3)Cl]Cl (8) (57.2% de), respectively. The diastereoselectivity of these reactions is governed solely by the chirality of the sulfoxide nucleophile. This represents the first process by which a sigma-bonded ligand occupying only a single coordination site has had such an important influence on the stereochemical outcome of a ruthenium bis(bipyridine) complex formation. These novel complexes were fully characterized by elemental analysis and IR, UV/vis, and 1H, 13C, and 2D NMR spectroscopy. An investigation into the chiroptical properties of these novel ruthenium bis(bipyridine) sulfoxide complexes has been carried out, and circular dichroism spectra are used to assign absolute stereochemistry.     

The left-definite Legendre type boundary problem

The left-definite Legendre type boundary problem concerns the study of a fourth-order singular differential expressionM _k [–] in a weighted Sobolev spaceH generated by a Dirichlet inner product. The fourth-order differential equation

Right-angled Coxeter polytopes, hyperbolic six-manifolds, and a problem of Siegel

By gluing together the sides of eight copies of an all-right angled hyperbolic six-dimensional polytope, two orientable hyperbolic six-manifolds with Euler characteristic ?1 are constructed. They are the first known examples of orientable hyperbolic six-manifolds having the smallest possible volume.     

A note on the analytic form of the Kramer sampling theorem

This paper discusses the extension of the Kramer sampling theorem to the case when the kernel is Cauchy analytic in the sampling parameter.     

Efficient importance sampling in low dimensions using affine arithmetic

Despite the development of sophisticated techniques such as sequential Monte Carlo (Del Moral et al. in J R Stat Soc Ser B 68(3):411–436, 2006), importance sampling (IS) remains an important Monte Carlo method for low dimensional target distributions (Chopin and Ridgway in Leave Pima Indians alone: binary regression as a benchmark for Bayesian computation, 32:64–87, 2017). This paper describes a new technique for constructing proposal distributions for IS, using affine arithmetic (de Figueiredo and Stolfi in Numer Algorithms 37(1–4):147–158, 2004). This work builds on the Moore rejection sampler (Sainudiin in Machine interval experiments, Cornell University, Ithaca, 2005; Sainudiin and York in Algorithms Mol Biol 4(1):1, 2009) to which we provide a comparison.