Minimal kernels of Dirac operators along maps

Let M be a closed spin manifold and let N be a closed manifold. For maps and Riemannian metrics g on M and h on N, we consider the Dirac operator of the twisted Dirac bundle . To this Dirac operator one can associate an index in . If M is 2‐dimensional, one gets a lower bound for the dimension of the kernel of out of this index. We investigate the question whether this lower bound is obtained for generic tupels .     

A Thioxanthone Sensitizer with a Chiral Phosphoric Acid Binding Site: Properties and Applications in Visible Light-Mediated Cycloadditions

A chiral phosphoric acid with a 2,2’-binaphthol core was prepared that displays two thioxanthone moieties at the 3,3’-position as light-harvesting antennas. Despite its relatively low triplet energy, the phosphoric acid was found to be an efficient catalyst for the enantioselective intermolecular [2+2] photocycloaddition of β-carboxyl-substituted cyclic enones (e.r. up to 93:7). Binding of the carboxylic acid to the sensitizer is suggested by NMR studies and by DFT calculations to occur by means of two hydrogen bonds. The binding event not only enables an enantioface differentiation but also modulates the triplet energy of the substrates.     

Generalized sensitivity analysis of nonlinear programs using a sequence of quadratic programs

ABSTRACT

Local sensitivity information is obtained for KKT points of parametric NLPs that may exhibit active set changes under parametric perturbations; under appropriate regularity conditions, computationally relevant generalized derivatives of primal and dual variable solutions of parametric NLPs are calculated. Ralph and Dempe obtained directional derivatives of solutions of parametric NLPs exhibiting active set changes from the unique solution of an auxiliary quadratic program. This article uses lexicographic directional derivatives, a newly developed tool in nonsmooth analysis, to generalize the classical NLP sensitivity analysis theory of Ralph and Dempe. By viewing said auxiliary quadratic program as a parametric NLP, the results of Ralph and Dempe are applied to furnish a sequence of coupled QPs, whose unique solutions yield generalized derivative information for the NLP. A practically implementable algorithm is provided. The theory developed here is motivated by widespread applications of nonlinear programming sensitivity analysis, such as in dynamic control and optimization problems.     

Asymmetric Carboxycyanation of Aldehydes by Cooperative AlF/Onium Salt Catalysts: from Cyanoformate to KCN as Cyanide Source

Asymmetric 1,2-additions of cyanide yield enantioenriched cyanohydrins as versatile chiral building blocks. Next to HCN, volatile organic cyanide sources are usually used. Among them, cyanoformates are more attractive on technical scale than TMSCN for cost reasons, but catalytic productivity is usually lower. Here, the development of a new strategy for cyanations is described, in which this activity disadvantage is overcome. A Lewis acidic Al center cooperates with an aprotic onium moiety within a remarkably robust bifunctional Al–F–salen complex. This allowed for unprecedented turnover numbers of up to 10⁴. DFT studies suggest an unexpected unique trimolecular pathway in which the ammonium bound cyanide attacks the aldehyde, which itself is activated by the carbonyl group of the cyanoformate binding to the Al center. In addition, a novel practical carboxycyanation method was developed that makes use of KCN as the sole cyanide source. The use of a pyrocarbonate as carboxylating reagent provided the best results.     

First Bis(σ)-borane Complexes of Group 6 Transition Metals: Experimental and Theoretical Studies

A series of bis(σ)-borane complexes of Group 6 transition metals were prepared by direct dihydroborane coordination to the metal center. Reaction of [M(CO)₃(PCy₃)₂] and two dihydroboranes [DurBH₂] and [(Me₃Si)₂NBH₂] (Dur=2,3,5,6-Me₄C₆H) yielded bis(σ)-borane complexes fac-[M(CO)₃(PCy₃){η²-(H₂BR)}] (R=Dur; 1 : M=Cr, 2 : M=W; R=N(SiMe₃)₂; 3 : M=Cr, 4 : M=W). In the case of molybdenum, we have isolated an arene complex ( 5 ) with [DurBH₂] in which the Dur group acts as a η⁶-bound ligand, and with [(Me₃Si)₂NBH₂] a similar bis(σ)-borane complex was isolated, cis,trans-[Mo(CO)₂(PCy₃)₂{η²-(H₂BN(SiMe₃)₂}] ( 6 ), with a different pattern of auxiliary ligands. The complexes were investigated by multinuclear NMR spectroscopy, mass spectrometry, X-ray diffraction analysis, and computational methods. Quantum theory of atoms in molecules (QTAIM) calculations demonstrated that the borane complexes may be described as pure bis(σ)-borane complexes rather than elongated or stretched examples given that the calculations do not show the presence of a ring-critical point (RCP) at the ring formed by the interactions of the B−H with metal center.     

Top-down synthesis of polyoxometalate-like sub-nanometer molybdenum-oxo clusters as high-performance electrocatalysts

The top-down fabrication of catalytically active molecular metal oxide anions, or polyoxometalates, is virtually unexplored, although these materials offer unique possibilities, for catalysis, energy conversion and storage. Here, we report a novel top-down route, which enables the scalable synthesis and deposition of sub-nanometer molybdenum-oxo clusters on electrically conductive mesoporous carbon. The new approach uses a unique redox-cycling process to convert crystalline Mo^IVO₂ particles into sub-nanometer molecular molybdenum-oxo clusters with a nuclearity of ∼1–20. The resulting molybdenum-oxo cluster/carbon composite shows outstanding, stable electrocatalytic performance for the oxygen reduction reaction with catalyst characteristics comparable to those of commercial Pt/C. This new material design could give access to a new class of highly reactive polyoxometalate-like metal oxo clusters as high-performance, earth abundant (electro-)catalysts.

The top-down synthesis and deposition of polyoxometalate-like clusters on porous carbon is reported together with the high electrocatalytic oxygen reduction reactivity of the composite.     

DFT Study of the Molybdenum‐Catalyzed Deoxydehydration of Vicinal Diols

The mechanism of the molybdenum‐catalyzed deoxydehydration (DODH) of vicinal diols has been investigated using density functional theory. The proposed catalytic cycle involves condensation of the diol with an Mo^VI oxo complex, oxidative cleavage of the diol resulting in an Mo^IV complex, and extrusion of the alkene. We have compared the proposed pathway with several alternatives, and the results have been corroborated by comparison with the molybdenum‐catalyzed sulfoxide reduction recently published by Sanz et al. and with experimental observations for the DODH itself. Improved understanding of the mechanism should expedite future optimization of molybdenum‐catalyzed biomass transformations.     

Definitive Structural Assessment of Enterococcal Diheteroglycan

Enterococcus faecalis is one of most important nosocomial and often multi‐antibiotic resistant pathogens responsible for infections that are difficult to treat. Previously, a cell‐wall polysaccharide termed diheteroglycan (DHG) was isolated and characterized as a promising vaccine candidate. However, the configuration of its lactic acid (LA) residue attached to the galactofuranoside unit was not assessed, although it influences conformation of DHG chain in terms of biological recognition and immune evasion. This study proves the R configuration of the LA residue by means of chemical analysis, investigation of intramolecular NMR nuclear Overhauser effects and molecular dynamics simulations of native DHG and corresponding R and S models, which were obtained by using pyranoside‐into‐furanoside rearrangement. As alternative treatment and prevention strategies for E. faecalis are desperately needed, this discovery may offer the prospect of a synthetic vaccine to actively immunize patients at risk.