Synthese und Kristallstrukturen der Phosphaniminato-Komplexe [MCl2(NPPh3)]2 mit M = Al und Ga, [SbCl2(NPMe3)(DMF)]2 sowie des Phosphanimin-Komplexes [Ph3PNH · BF3] · THF

Syntheses and Crystal Structures of the Phosphorane Iminato Complexes [MCl₂(NPPh₃)]₂ with M = Al and Ga, [SbCl₂(NPMe₃)(DMF)]₂, and of the Phosphorane Imine Complex [Ph₃PNH · BF₃] · THF The phosphorane iminato complexes [MCl₂(NPPh₃)]₂ with M = Al and Ga and [SbCl₂(NPMe₃)(DMF)]₂ are formed as colourless crystals by reactions of the anhydrous trichlorides MCl₃ (M = Al, Ga, Sb) with the corresponding silylated phosphorane imines Me₃SiNPR₃ in acetonitrile and in dimethyl formamide, respectively. The phosphorane imine derivative [Ph₃PNH · BF₃] · THF is formed from Me₃SiNPPh₃ and boron trifluoride etherate in boiling tetrahydrofuran. The compounds are characterized by their i. r. spectra and by crystal structure analyses. [AlCl₂(NPPh₃)]₂ : Space group P1 , Z = 1, structure solution with 1 585 observed unique reflections, R = 0.061. Lattice dimensions at ?70°C: a = 917.6, b = 1 053.5, c = 1 145.2 pm, α = 111.72°, β = 100.80°, γ = 109.95°. [GaCl₂(NPPh₃)]₂ : Space group P1 , Z = 1, structure solution with 2 586 observed unique reflections, R = 0.066. Lattice dimensions at ?70°C: a = 917.5, b = 1 058.3, c = 1 153.7 pm, α = 105.52°, β = 107.75°, γ = 109.88°. In both compounds the metal atoms are linked to planar M₂N₂ four-membered rings via the N-atoms of the phosphorane iminato groups. [SbCl₂(NPMe₃)(DMF)]₂ : Space group P2₁/n, Z = 4, structure solution with 3 805 observed unique reflections, R = 0.038. Lattice dimensions at ?70°C: a = 1 913.0, b = 726.8, c = 2 040.7 pm, β = 113.62°. The unit cell contains two symmetry independent dimeric molecules, in which the antimony atoms are centrosymmetricly μ₂ linked via the N-atoms of the phosphorane iminato groups. Along with the oxygen atom of the dimethyl formamide molecule the Sb atoms achieve a ψ-octahedral environment. [Ph₃PNH · BF₃] · THF : Space group C2/c, Z = 8, structure solution with 2 048 observed unique reflections, R = 0.058. Lattice dimensions at ?70°C: a = 2 460.4, b = 869.2, c = 1 978.0 pm, β = 116.35°.     

Targeting Bayes factors with direct-path non-equilibrium thermodynamic integration

Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a comparatively small number of parameters, intrinsic errors from sampling fluctuations may outweigh the differences in the log marginal likelihood estimates. In the present article, we propose a TI scheme that directly targets the log Bayes factor. The method is based on a modified annealing path between the posterior distributions of the two models compared, which systematically avoids the high variance prior regime. We combine this scheme with the concept of non-equilibrium TI to minimise discretisation errors from numerical integration. Results obtained on Bayesian regression models applied to standard benchmark data, and a complex hierarchical model applied to biopathway inference, demonstrate a significant reduction in estimator variance over state-of-the-art TI methods.     

Macromodeling of high-speed interconnects by positive interpolation of vertical segments

In this paper a novel macromodeling scheme is presented to model the per unit of length (p.u.l.) parameters of uniform transmission lines. In particular, it is focused on single on-chip interconnects, because their p.u.l. parameters are influenced by the presence of semiconductor (s) and as such exhibit a strong frequency-dependency, making the modeling process harder. Starting from a set of very accurate tabulated data samples, obtained by two-dimensional electromagnetic modeling, rational models for the four p.u.l. parameters are constructed. The novelty of the approach lies in the fact that the rational models are positive by construction and that a controllable accuracy is obtained. These models can then further be used to construct multivariate models, e.g., for variability analysis. Here, the novel scheme is applied to an on-chip inverted embedded microstrip line, of which the signal integrity behavior is assessed in both the frequency and the time domain, demonstrating the applicability of the macromodels.