The formal combination of three singlet biradicaloid entities to a singlet hexaradicaloid metalloid Ge14[Si(SiMe3)3]5[Li(THF)2]3 cluster

The reaction of GeBr with LiSi(SiMe(3))(3) leads to the metalloid cluster compound [(THF)(2)Li](3)Ge(14)[Si(SiMe(3))(3)](5) (1). After the introduction of a first cluster of this type, in which 14 germanium atoms form an empty polyhedron, [(THF)(2)Li](3)Ge(14)[Ge(SiMe(3))(3)](5) (2), we present here further investigations on 1 to obtain preliminary insight into its chemical and bonding properties. The molecular structure of 1 is determined via X-ray crystal structure solution using synchrotron radiation. The electronic structure of the Ge(14) polyhedron is further examined by quantum chemical calculations, which indicate that three singlet biradicaloid entities formally combine to yield the singlet hexaradicaloid character of 1. Moreover, the initial reactions of 1 after elimination of the [Li(THF)(2)](+) groups by chelating ligands (e.g., TMEDA or 12-crown-4) are presented. Collision induced dissociation experiments in the gas phase, employing FT-ICR mass spectrometry, lead to the elimination of the singlet biradicaloid Ge(5)H(2)[Si(SiMe(3))(3)](2) cluster. The unique multiradicaloid bonding character of the metalloid cluster 1 might be used as a model for reactions and properties in the field of surface science and nanotechnology.     

Extremely bulky amido-group 14 element chloride complexes: potential synthons for low oxidation state main group chemistry

The preparation of a series of extremely bulky secondary amines, Ar*N(H)SiR(3) (Ar* = C(6)H(2){C(H)Ph(2)}(2)Me-2,6,4; R(3) = Me(3), MePh(2) or Ph(3)) is described. Their deprotonation with either LiBu(n), NaH or KH yields alkali metal amide complexes, several monomeric examples of which, [Li(L){N(SiMe(3))(Ar*)}] (L = OEt(2) or THF), [Na(THF)(3){N(SiMe(3))(Ar*)}] and [K(OEt(2)){N(SiPh(3))(Ar*)], have been crystallographically characterised. Reactions of the lithium amides with germanium, tin or lead dichloride have yielded the first structurally characterised two-coordinate, monomeric amido germanium(II) and tin(II) chloride complexes, [{(SiR(3))(Ar*)N}ECl] (E = Ge or Sn; R = Me or Ph), and a chloride bridged amido-lead(II) dimer, [{[(SiMe(3))(Ar*)N]Pb(μ-Cl)}(2)]. DFT calculations on [{(SiMe(3))(Ar*)N}GeCl] show its HOMO to exhibit Ge lone pair character and its LUMO to encompass its Ge based p-orbital. A series of bulky amido silicon(IV) chloride complexes have also been prepared and several examples, [{(SiR(3))(Ar*)N}SiCl(3)] (R(3) = Me(3), MePh(2)) and [{(SiMe(3))(Ar*)N}SiHCl(2)], were crystallographically characterised. The sterically hindered group 14 complexes reported in this study hold significant potential as precursors for kinetically stabilised low oxidation state and/or low coordination number group 14 complexes.     

Stereoselectivity of the Radical Reductive Alkylation of Enamines: Importance of the Allylic 1,3-Strain Model

Radical addition to enamines using Bu₃SnH as reducing agent are reported (Schemes 2 and 4). The diastereoselectivity of these reactions was examined in different systems (Tables 1 and 2). Enamines derived from cyclic ketones such as cyclohexanone were alkylated with high diastereoselectivity with preferential formation of the cis-disubstituted cycloalkanes. In acyclic systems such as enamines derived from propiophenone and diethyl ketone, moderate to high stereoselectivities were observed in the H-abstraction step. A model based principally on minimization of allylic 1,3-strain (A^1,3 strain) was deduced from the experimental results and semi-empirical (AM1) calculations.     

Diastereoselective proton transfer: a route to enantiomerically pure half-sandwich rhenium complexes

The diastereomeric methyl rhenium complex [CpRe(NO){P(Me)(Ph)(2-C6H4NMe2)}(CH3)] was prepared in two steps from chiral racemic [CpRe(NO)(CO)(NCMe)]BF4 and the chiral racemic phosphine P(Me)(Ph)(2-C6H4NMe2). The unlike diastereomer reacts preferentially with MeSO3H to give the ring-closed ionic complex unlike-[CpRe(NO){P(Me)(Ph)(2-C6H4NMe2)}]MeSO3 along with unreacted like-[CpRe(NO){P(Me)(Ph)(2-C6H4NMe2)}(CH3)], which is easily separated and converted to like-[CpRe(NO){P(Me)(Ph)(2-C6H4NMe2)}]MeSO3. Starting from (R)-P(Me)(Ph)(2-C6H4NMe2), the diastereomerically and enantiomerically pure complexes (RRe,SP)-[CpRe(NO){P(Me)(Ph)(2-C6H4NMe2)}]MeSO3 and (SRe,SP)-[CpRe(NO){P(Me)(Ph)(2-C6H4NMe2)}]MeSO3 were obtained. Thus, this reaction sequence demonstrates a highly diastereoselective proton transfer from a functionalized chiral phosphine to a transition metal. Furthermore, it provides efficient access to enantiomerically pure half-sandwich rhenium complexes.     

Finite-size effects in the self-organized critical forest-fire model

We study finite-size effects in the self-organized critical forest-fire model by numerically evaluating the tree density and the fire size distribution. The results show that this model does not display the finite-size scaling seen in conventional critical systems. Rather, the system is composed of relatively homogeneous patches of different tree densities, leading to two qualitatively different types of fires: those that span an entire patch and those that do not. As the system size becomes smaller, the system contains less patches, and finally becomes homogeneous, with large density fluctuations in time. Received 24 April 1999 and Received in final form 26 October 1999     

Monte Carlo simulation and measurement of nanoscale n-MOSFETs

The output characteristics of state-of-the-art n-MOSFETs with effective channel lengths of 40 and 60 nm have been measured and compared with full-band Monte Carlo simulations. The device structures are obtained by process simulation based on comprehensive secondary ion mass spectroscopy and capacitance-voltage measurements. Good agreement between the measured output characteristics and the full-band Monte Carlo simulations is found without any fitting of parameters and the on-currents are reproduced within 4%. The analysis of the velocity profiles along the channel confirms that the on-current is determined by the drift velocity in the source side of the channel. Analytic-band Monte Carlo simulations are found to involve an overestimation of the drain current in the nonlinear regime which becomes larger for increasing drain voltage and decreasing gate length. The discrepancy originates from a higher nonlinear drift velocity and a higher overshoot peak in bulk silicon which is due to differences in the band structures above 100 meV. The comparison between analytic-band and full-band Monte Carlo simulation therefore shows that the source-side velocity in the on-state is influenced by nonlinear and quasiballistic transport.     

Thermal free convection from a solid sphere

Summary Thermal free convection from a sphere has been studied by melting solid benzene spheres in excess liquid benzene (Pr=8,3; 10⁸<Gr<10⁹). Overall heat transfer as well as local heat transfer were investigated. For the effect of cold liquid produced by the melting a correction has been applied. Results are compared with those obtained by other workers who used alternative experimental methods.Nomenclature coefficient of heat transfer - d characteristic length, here diameter of sphere - thermal conductivity - g acceleration of free fall - cubic expansion coefficient - T temperature difference between wall and fluid at infinity - kinematic viscosity - density - c specific heat capacity - a thermal diffusivity (=/c) - D diffusion coefficient - Nu dimensionless Nusselt number (=d/) - Nu* the analogous number for mass transfer (=kd/D) - mean value of Nusselt number - Gr dimensionless Grashof number (=gd ³T/ ²) - Gr* the analogous number for mass transfer (=gd ³x/ ²) - Pr dimensionless Prandtl number (=/a) - Sc dimensionless Schmidt number (=/D)     

Two Novel Characterizations of Self-Decomposability on the Half-Line

Two novel characterizations of self-decomposable Bernstein functions are provided. The first one is purely analytic, stating that a function \(\varPsi \) is the Bernstein function of a self-decomposable probability law \(\pi \) on the positive half-axis if and only if alternating sums of \(\varPsi \) satisfy certain monotonicity conditions. The second characterization is of probabilistic nature, showing that \(\varPsi \) is a self-decomposable Bernstein function if and only if a related d-variate function \(C_{\psi ,d}\), \(\psi :=\exp (-\varPsi )\), is a d-variate copula for each \(d \ge 2\). A canonical stochastic construction is presented, in which \(\pi \) (respectively \(\varPsi \)) determines the probability law of an exchangeable sequence of random variables \(\{U_k\}_{k\in {\mathbb {N}}}\) such that \((U_1,\ldots ,U_d) \sim C_{\psi ,d}\) for each \(d \ge 2\). The random variables \(\{U_k\}_{k\in {\mathbb {N}}},\) are i.i.d. conditioned on an increasing Sato process whose law is characterized by \(\varPsi \). The probability law of \(\{U_k\}_{k \in {\mathbb {N}}}\) is studied in quite some detail.