Generation of random bivariate normal deviates and computation of related integrals

A method which transforms two random variables having rectangular distributions into a pair of bivariate normal deviates with prescribed covariance matrix is described. The same transformation is used for integrating the bivariate normal distribution over areas which are the intersection of the domain outside an equiprobability ellipse and a sector determined by two lines through the point of gravity of the normal distribution.     

Dipole moment enhancement in molecular crystals from X-ray diffraction data.

Although reliable determination of the molecular dipole moment from experimental charge density analyses on molecular crystals is a challenging undertaking, these values are becoming increasingly common experimental results. We collate all known experimental determinations and use this database to identify broad trends in the dipole moment enhancements implied by these measurements as well as outliers for which enhancements are pronounced. Compelling evidence emerges that molecular dipole moments from X-ray diffraction data can provide a wealth of information on the change in the molecular charge distribution that results from crystal formation. Most importantly, these experiments are unrivalled in their potential to provide this information in such detail and deserve to be exploited to a much greater extent. The considerable number of experimental determinations now available has enabled us to pinpoint those studies that merit further attention, either because they point unequivocally to a considerable enhancement in the crystal (of 50 % or more), or because the experimental determinations suggest enhancements of 100 % or more--much larger than independent theoretical estimates. In both cases further detailed experimental and theoretical studies are indicated.     

Stabilization of a Two‐Coordinate Mononuclear Cobalt(0) Compound

Compound (Me₂‐cAAC:)₂Co⁰ ( 2 ; Me₂‐cAAC:=cyclic (alkyl) amino carbene; :C(CH₂)(CMe₂)₂N‐2,6‐iPr₂C₆H₃) was synthesized by the reduction of the precursor (Me₂‐cAAC:)₂Co^ICl ( 1 ) with KC₈ in THF. The cyclic voltammogram of 1 exhibited one‐electron reduction, which suggests that synthesis of a bent 2‐metallaallene ( 2 ) from 1 should be possible. Compound 2 contains one cobalt atom in the formal oxidation state zero, which is stabilized by two Me₂‐cAAC: ligands. Bond lengths from X‐ray diffraction are 1.871(2) and 1.877(2) Å with a C‐Co‐C bond angle of 170.12(8)°. The EPR spectrum of 2 exhibited a broad resonance attributed to the unique quasi‐linear structure, which favors near degeneracy and gives rise to very rapid relaxation conditions. The cAAC?Co bond in 2 can be considered as a typical Dewar–Chatt–Duncanson type of bonding, which in turn retains 2.5 electron pairs on the Co atom as nonbonding electrons.     

Polymer-solid contacts described by soft, coarse-grained models

The ability of soft, coarse-grained models to describe the narrow interface of a nearly incompressible polymer melt in contact with a solid is explored by numerical self-consistent field calculations and Monte-Carlo simulations. We investigate the effect of the discreteness of the bead-spring architecture by quantitatively comparing the results of a bead-spring model with different number of beads, N, but identical end-to-end distance, R(e), and a continuous Gaussian-thread model. If the width, ξ, of the narrow polymer-solid contact is smaller or comparable to the length of a statistical segment, b=R(e)/√N-1, strong differences in the interface tension and the density profiles between the two models are observed, and strategies for compensating the discrete nature of the bead-spring model are investigated. Compensating the discretization of the chain contour in the bead-spring model by applying an external segment-solid potential, we simultaneously adjust the interface tension and the density profile to the predictions of the Gaussian-thread model. We suggest that the geometry of the polymer-solid contact and the interface tension are relevant characteristics that a coarse-grained model of polymer-solid contacts must reproduce in order to establish a quantitative relationship to an experimental system.     

From Furan to Molecular Stairs: Syntheses,Structural Properties,and Theoretical Investigations of Oligocyclic Oligoacetals

The synthesis of oligocyclic oligoacetals using five‐membered rings as repetitive unit is described. Furan was used as the starting material, which is converted by a three‐step procedure consisting of twofold cyclopropanation, reduction, and oxidative ring enlargement into a tricyclic bis(enol ether). A repetition of this synthetic procedure leads to the formation of extended oligoacetal systems. Insights into the structures were gained by X‐ray crystallographic investigations and revealed helical arrangements of the subunits in the solid‐state. DFT (B3LYP) calculations have been carried out to elucidate the transition state of the ring enlargement and the flexibility of the annelated oligocyclic systems. Strain energies and topologies of potential cyclically condensed oligoacetals are predicted.     

N-heterocyclic carbene stabilized dichlorosilylene transition-metal complexes of V(I), Co(I), and Fe(0)

Reactions of N-heterocyclic carbene stabilized dichlorosilylene IPr·SiCl(2) (1) (IPr = 1,3-bis(2,6-diisopropylphenyl)imidazol-2-ylidene) with (η(5)-C(5)H(5))V(CO)(4), (η(5)-C(5)H(5))Co(CO)(2), and Fe(2)(CO)(9) afford dichlorosilylene complexes IPr·SiCl(2)·V(CO)(3)(η(5)-C(5)H(5)) (2), IPr·SiCl(2)·Co(CO)(η(5)-C(5)H(5)) (3), and IPr·SiCl(2)·Fe(CO)(4) (4), respectively. Complexes 2-4 are stable under an inert atmosphere, are soluble in common organic solvents, and have been characterized by elemental analysis and multinuclear ((1)H, (13)C, and (29)Si) NMR spectroscopy. Molecular structures of 2-4 have been determined by single crystal X-ray crystallographic studies and refined with nonspherical scattering factors.