Computational study of singlet and triplet sulfonylnitrenes insertion into 1,3‐butadienes: 1,2‐ or 1,4‐cycloaddition?

The formation of N‐trifluoromethylsulfonyl‐2‐vinylaziridine and N‐trifluoromethylsulfonyl‐3‐pyrroline by the reaction of the singlet and triplet trifluoromethanesulfonylnitrenes with s‐cis‐ and s‐trans‐1,3‐butadienes was studied theoretically at the B3LYP/6‐311++G(d,p) and M06‐2X/6‐311++G(d,p) levels of theory. The singlet trifluoromethanesulfonylnitrene adds to s‐cis‐ and s‐trans‐1,3‐butadiene exothermally in one step to give the product of 1,2‐cycloaddition, N‐trifluoromethylsulfonyl‐2‐vinylaziridine, the energy decreasing by 88.5 and 86.2 kcal/mol at the B3LYP level and by 105.2 and 103.0 kcal/mol at the M06‐2X level, respectively. The formed 2‐vinylaziridine can undergo rotation about the C(2)–C_sp2 bond with the barrier not exceeding 3.5 kcal/mol and to rearrange into N‐trifluoromethylsulfonyl‐3‐pyrroline. The triplet trifluoromethanesulfonylnitrene reacts with s‐cis‐ and s‐trans‐1,3‐butadiene in two steps. The first exothermic step is the formation of the triplet diradical adducts. The second step is the spin inversion with the energy raising by 5.8 and 17.8 kcal/mol at the B3LYP level and by 11.0 and 20.8 kcal/mol at the M06‐2X level for the adducts to s‐cis‐ and s‐trans‐1,3‐butadiene, respectively. Recombination of the radical centers occurs selectively to give N‐trifluoromethylsulfonyl‐2‐vinylaziridine that is exothermally rearranged into N‐trifluoromethylsulfonyl‐3‐pyrroline with the energy barrier of 40 kcal/mol at the B3LYP level and of 50 kcal/mol at the M06‐2X level. Copyright © 2014 John Wiley & Sons, Ltd.     

Characterization of Pinched Ricci Curvature by Functional Inequalities

In this article, functional inequalities for diffusion semigroups on Riemannian manifolds (possibly with boundary) are established, which are equivalent to pinched Ricci curvature, along with gradient estimates, \(L^p\)-inequalities and log-Sobolev inequalities. These results are further extended to differential manifolds carrying geometric flows. As application, it is shown that they can be used in particular to characterize general geometric flow and Ricci flow by functional inequalities.     

On Gradient Solitons of the Ricci–Harmonic Flow

In this paper, we study gradient solitons to the Ricci flow coupled with harmonic map heat flow. We derive new identities on solitons similar to those on gradient solitons of the Ricci flow. When the soliton is compact, we get a classification result. We also discuss the relation with quasi-Einstein manifolds.     

The system Na2CO3–CaCO3–MgCO3 at 6 GPa and 900–1250°C and its relation to the partial melting of carbonated mantle

In order to constrain the Na₂CO₃–CaCO₃–MgCO₃ T–X diagram at 6?GPa in addition to the binary and pseudo-binary systems we conducted experiments along the Na₂CO₃–Ca_0.5Mg_0.5CO₃ join. At 900–1000°C, melting does not occur and isothermal sections are presented by one-, two- and three-phase regions containing Ca-bearing magnesite, aragonite, Na₂CO₃ (Na₂) and Na₂(Ca_1–0.9Mg_0-0.1)_3-4(CO₃)_4-5 (Na₂Ca_3-4), Na₄(Ca_1–0.6Mg_0–0.4)(CO₃)₃ (Na₄Ca), Na₂(Ca_0-0.08Mg_1–0.92)(CO₃)₂ (Na₂Mg) phases with intermediate compositions. The minimum melting point locates between 1000°C and 1100°C. This point would resemble that of three eutectics: Mgs–Na₂Ca₃–Na₂Mg, Na₂Mg–Na₂Ca₃–Na₄Ca or Na₂Mg–Na₄Ca–Na₂, in the compositional interval of [45Na₂CO₃·55(Ca_0.6Mg_0.4)CO₃]–[60Na₂CO₃·40Ca_0.6Mg_0.4CO₃]. The liquidus projection has seven primary solidification phase regions for Mgs, Dol, Arg, Na₂Ca₃, Na₄Ca, Na₂ and Na₂Mg. The results suggest that extraction of Na and Ca from silicate to carbonate components has to decrease minimum melting temperature of carbonated mantle rocks to 1000–1100°C at 6?GPa and yields Na-rich dolomitic melt with a Na# (Na₂O/(Na₂O?+?CaO?+?MgO))?≥?28?mol%.     

Existence of non-trivial harmonic functions on Cartan–Hadamard manifolds of unbounded curvature

The Liouville property of a complete Riemannian manifold M (i.e., the question whether there exist non-trivial bounded harmonic functions on M) attracted a lot of attention. For Cartan–Hadamard manifolds the role of lower curvature bounds is still an open problem. We discuss examples of Cartan–Hadamard manifolds of unbounded curvature where the limiting angle of Brownian motion degenerates to a single point on the sphere at infinity, but where nevertheless the space of bounded harmonic functions is as rich as in the non-degenerate case. To see the full boundary the point at infinity has to be blown up in a non-trivial way. Such examples indicate that the situation concerning the famous conjecture of Greene and Wu about existence of non-trivial bounded harmonic functions on Cartan–Hadamard manifolds is much more complicated than one might have expected.      

Stereoselective synthesis of unnatural α-amino acid derivatives through photoredox catalysis

A protocol for stereoselective C-radical addition to a chiral glyoxylate-derived N-sulfinyl imine was developed through visible light-promoted photoredox catalysis, providing a convenient method for the synthesis of unnatural α-amino acids. The developed protocol allows the use of ubiquitous carboxylic acids as radical precursors without prior derivatization. The protocol utilizes near-stoichiometric amounts of the imine and the acid radical precursor in combination with a catalytic amount of an organic acridinium-based photocatalyst. Alternative mechanisms for the developed transformation are discussed and corroborated by experimental and computational studies.

A protocol for stereoselective C-radical addition to a chiral glyoxylate-derived N-sulfinyl imine was developed through visible light-promoted photoredox catalysis, providing a convenient method for the synthesis of unnatural α-amino acids.     

Mono- and Diamination of 4,6-Dichloropyrimidine, 2,6-Dichloropyrazine and 1,3-Dichloroisoquinoline with Adamantane-Containing Amines

N-heteroaryl substituted adamantane-containing amines are of substantial interest for their perspective antiviral and psychotherapeutic activities. Chlorine atom at alpha-position of N-heterocycles has been substituted by the amino group using convenient nucleophilic substitution reactions with a series of adamantylalkylamines. The prototropic equilibrium in these compounds was studied using NMR spectroscopy. The introduction of the second amino substituent in 4-amino-6-chloropyrimidine, 2-amino-chloropyrazine, and 1-amino-3-chloroisoquinoline was achieved using Pd(0) catalysis.     

17O NMR spectra of some organotin(IV) compounds containing O,C,O-chelating ligands

The 17O chemical shifts of substituted benzyl ethers and a set of organotin(IV) derivatives containing O,C,O-chelating ligands were studied. Measured 17O chemical shifts were correlated with the additivity substituent increments for carbon atoms in the alkyl groups, and intramolecular Sn-O distance was obtained by X-ray diffraction techniques in the solid state.