Complexes of a gallium heterocycle with transition metal dicyclopentadienyl and cyclopentadienylcarbonyl fragments, and with a dialkylmanganese compound

The reactivity of several transition metal half sandwich complexes towards an anionic gallium(I) heterocyclic complex, [K(tmeda)][Ga{[N(Ar)C(H)]2}](Ar = C6H3Pri2-2,6), has been investigated. This has led to the anionic half sandwich complexes, [K(tmeda)][(C5H4R)M(CO)n[Ga{[N(Ar)C(H)]2}]](M = V, R = H, n= 3; M = Mn, R = Me, n= 2; M = Co, R = H, n= 1), which crystallographic studies show to form dimers (M = Mn and Co) or a polymer (M = V) through bridging potassium cations. The metal-gallium bond lengths in all complexes are very short which, combined with some spectroscopic evidence, is suggestive of M-Ga pi-bonding. Density functional theory studies of models of all complexes indicate that the level of back-bonding in these complexes is, however, minimal and of a similar order to that seen in analogous complexes incorporating neutral N-heterocyclic carbene ligands. Reactions of the metallocenes, [M(C5H4Me)2](M = V or Cr), with the digallane4, [Ga{[N(Ar)C(H)]2}]2, have afforded the neutral complexes, [M(C5H4Me)2[Ga{[N(Ar)C(H)]2}]], which are thought to be formed via an initial oxidative insertion of the transition metal centre into the Ga-Ga bond of the digallane. X-Ray crystallography shows the complexes to be monomeric. One (M = V) reacts with one equivalent of [K(tmeda)][Ga{[N(Ar)C(H)]2}] to give the crystallographically characterised, anionic bis(gallyl)-complex, [K(tmeda)][V(C5H4Me)2[Ga{[N(Ar)C(H)]2}]2]. For comparison, the reaction of [K(tmeda)][Ga{[N(Ar)C(H)]2}] with [Mn{CH(SiMe3)2}2] was carried out and gave the monomeric, anionic complex, [K(tmeda)][Mn{CH(SiMe3)2}2[Ga{[N(Ar)C(H)]2}]].     

Functionalized nanodiamonds: triamantane and [121]tetramantane

The selective functionalizations of the fundamental hydrogen-terminated nanodiamonds triamantane 1, as well as the most symmetrical representative of the tetramantanes (C(2h)-[121]tetramantane 2) were elaborated. Electrophilic reagents (Br2, HNO3) predominantly attack the medial C-H positions of the cages; bromination of 2 gave the medial 2-bromo derivative almost exclusively. Highly selective apical substitution in 1 and 2 is possible either under single-electron-transfer oxidations via hydrocarbon radical cations or through photoacetylation with diacetyl. The mono- and the bis-acetyl derivatives of 1 and 2 were converted through Bayer-Villiger oxidation and subsequent hydrolysis to the respective apical mono- and dihydroxy derivatives. This exceptional synthetic specificity facilitates the transformation of 2, and perhaps larger nanodiamond molecules, into functionalized building blocks needed for a wide range of applications such as nanotechnology.     

Phospha(III)guanidinate complexes of titanium(IV) and zirconium(IV) amides

Two procedures for the synthesis of group 4 phosphaguanidine compounds M(R₂PC{NR′}₂)(NR″₂)₃ (M = Ti, Zr; R = Ph, Cy; R′ = ⁱPr, Cy; R″ = Me, Et) are described. Spectroscopic characterization indicated symmetrical bonding of the phosphaguanidinate ligand in solution for the P-diphenyl derivatives whereas the P-dicyclohexyl analogs adopt a more rigid geometry with inequivalent N_amidine substituents within the phosphaguanidinate ligand. X-ray diffraction studies show exclusively monomeric tbp metal centers for a series of derivatives, with a chelating phosphaguanidinate ligand that spans an axial and an equatorial position. Two different conformers have been identified in the solid-state that differ in the relative orientation of the phosphorus R₂P–C substituents with respect to the equatorial plane of the tbp metal. The synthetic protocol was extended to the bimetallic complex, [PhP(C{NⁱPr}₂Ti{NMe₂}₃)CH₂–]₂, which was characterized by crystallography as the meso-form.     

Testing independence in nonparametric regression

We propose a new test for independence of error and covariate in a nonparametric regression model. The test statistic is based on a kernel estimator for the L₂-distance between the conditional distribution and the unconditional distribution of the covariates. In contrast to tests so far available in literature, the test can be applied in the important case of multivariate covariates. It can also be adjusted for models with heteroscedastic variance. Asymptotic normality of the test statistic is shown. Simulation results and a real data example are presented.     

Total-variation-diminishing implicit–explicit Runge–Kutta methods for the simulation of double-diffusive convection in astrophysics

We put forward the use of total-variation-diminishing (or more generally, strong stability preserving) implicit–explicit Runge–Kutta methods for the time integration of the equations of motion associated with the semiconvection problem in the simulation of stellar convection. The fully compressible Navier–Stokes equation, augmented by continuity and total energy equations, and an equation of state describing the relation between the thermodynamic quantities, is semi-discretized in space by essentially non-oscillatory schemes and dissipative finite difference methods. It is subsequently integrated in time by Runge–Kutta methods which are constructed such as to preserve the total variation diminishing (or strong stability) property satisfied by the spatial discretization coupled with the forward Euler method. We analyse the stability, accuracy and dissipativity of the time integrators and demonstrate that the most successful methods yield a substantial gain in computational efficiency as compared to classical explicit Runge–Kutta methods.