We report the synthesis of vanadium(V) oxo complex 1 with a pincer-type dianionic mesoionic carbene (MIC) ligand L 1 and the general formula [VOCl(L 1 )]. A comparison of the structural (SC-XRD), electronic (UV–vis), and electrochemical (cyclic voltammetry) properties of 1 with the benzimidazolinylidene congener 2 (general formula [VOCl(L 2 )]) shows that the MIC is a stronger donor also for early transition metals with low d-electron population. Since electrochemical studies revealed both complexes to be reversibly reduced, the stronger donor character of MICs was not only demonstrated for the vanadium(V) but also for the vanadium(IV) oxidation state by isolating the reduced vanadium(IV) complexes [Co(Cp*) 2 ][1] and [Co(Cp*) 2 ][2] ([Co(Cp*) 2 ] = decamethylcobaltocenium). The electronic structures of the compounds were investigated by computational methods. Complex 1 was found to be a moderate precursor for salt metathesis reactions, showing selective reactivity toward phenolates or secondary amides, but not toward primary amides and phosphides, thiophenols, or aryls/alkyls donors. Deoxygenation with electron-rich phosphines failed to give the desired vanadium(III) complex. However, treatment of the deprotonated ligand precursor with vanadium(III) trichloride resulted in the clean formation of the corresponding MIC vanadium(III) complex 6 , which undergoes a clean two-electron oxidation with organic azides yielding the corresponding imido complexes. The reaction with TMS-N 3 did not afford a nitrido complex, but instead the imido complex 10 . This study reveals that, contrary to popular belief, MICs are capable of supporting early transition-metal complexes in a variety of oxidation states, thus making them promising candidates for the activation of small molecules and redox catalysis.

The high-valent molybdenum(VI) N-heterocyclic carbene complexes, (NHC)MoO 2 (1) and (NHC)MoO(N t Bu) (2) (NHC = 1,3bis(3,5-di-tert-butyl-2-phenolato)-benzimidazol-2-ylidene), are investigated toward their catalytic potential in the deoxygenation of nitroarenes. Using pinacol as the sacrificial and green reductant, both complexes are shown to be very active (pre)catalysts for this transformation allowing a reduction of the catalyst loading down to 0.25 mol %. Mechanistic investigations show μ-oxo bridged molybdenum(V) complexes [(NHC)MoO] 2 O (4) and [(NHC)Mo-(N t Bu)] 2 O (5) as well as zwitterionic pinacolate benzimidazolium complex 6, with a doubly protonated NHC ligand, to be potentially active species in the catalytic cycle. Both 4 and 5 can be prepared independently by the deoxygenation of 1 and 2 using triethyl phosphine (PEt 3 ) or triphenyl phosphine (PPh 3 ) and were shown to exhibit an unusual multireferenced ground state with a very small singlet−triplet gap at room temperature. Computational studies show that the spin state plays an unneglectable role in the catalytic process, efficiently lowering the reaction barrier of the deoxygenation step. Mechanistic details, putting special emphasis on the fate of the catalyst will be presented and potential routes how nitroarene reduction is facilitated are evaluated.

The tree of heaven, Ailanthus altissima (MILL.) SWINGLE, is a globally invasive plant known to secrete allelopathic metabolites called quassinoids. Quassinoids are highly modified triterpenoids. So far, nothing has been known about the biochemical basis of quassinoid biosynthesis. Here, based on transcriptome and metabolome data of Ailanthus altissima, we present the first three steps of quassinoid biosynthesis, which are catalysed by an oxidosqualene cyclase and two cytochrome P450 monooxygenases, resulting in the formation of the protolimonoid melianol. Strikingly, these steps are identical to the first steps of the biosynthesis of limonoids, structurally different triterpenoids from sister plant families within the same order Sapindales. Our results are therefore not only important to fully understand the biosynthesis of complex triterpenoids in plants, but also confirm the long-standing hypothesis that quassinoids and limonoids share an evolutionary origin. In addition, our transcriptome data for Ailanthus altissima will be beneficial to other researchers investigating the physiology and ecology of this invasive tree.

We study convergence of nonlinear systems in the presence of an "almost Lyapunov" function which, unlike the classical Lyapunov function, is allowed to be nondecreasing-and even increasing-on a nontrivial subset of the phase space. Under the assumption that the vector field is free of singular points (away from the origin) and that the subset where the Lyapunov function does not decrease is sufficiently small, we prove that solutions approach a small neighborhood of the origin. A nontrivial example where this theorem applies is constructed.

We present a new method for motion planning for control systems. The method aims to provide a natural computational framework in which a broad class of motion planning problems can be cast; including problems with holonomic and non-holonomic constraints, drift dynamics, obstacle constraints and constraints on the magnitudes of the applied controls. The method, which finds its inspiration in recent work on the so-called geometric heat flows and curve shortening flows, relies on a hereby introduced partial differential equation, which we call the affine geometric heat flow, which evolves an arbitrary differentiable path joining initial to final state in configuration space to a path that meets the constraints imposed on the problem. From this path, controls to be applied on the system can be extracted. We provide conditions guaranteeing that the controls extracted will drive the system arbitrarily close to the desired final state, while meeting the imposed constraints and illustrate the method on three canonical examples.