Growth and homogeneity of matchbox manifolds

A matchbox manifold with one-dimensional leaves which has equicontinuous holonomy dynamics must be a homogeneous space, and so must be homeomorphic to a classical Vietoris solenoid. In this work, we consider the problem, what can be said about a matchbox manifold with equicontinuous holonomy dynamics, and all of whose leaves have at most polynomial growth type? We show that such a space must have a finite covering for which the global holonomy group of its foliation is nilpotent. As a consequence, we show that if the growth type of the leaves is polynomial of degree at most 3, then there exists a finite covering which is homogeneous. If the growth type of the leaves is polynomial of degree at least 4, then there are additional obstructions to homogeneity, which arise from the structure of nilpotent groups.     

Weak π-rings

In this paper we establish some characterizations for weak π-rings.     

Electronic structure and thermochemistry for monocarbides MC,MC+ and MC− (M=Zn,Cd, Hg): CCSD(T) and DFT works

In this work, the ab-initio coupled cluster CCSD(T) method and the B3LYP, BP91W and CAM-B3LYP functional of DFT method in conjunction with the aug-cc-pVTZ-PP basis have been applied to study the group 12 monocarbides MC, MC⁺ and MC^?. The potential energy curves (PECs) for the three electronic states ³Σ^?, ⁵Σ^? and ¹Δ of the MC and the two states ²∑^- and ⁴∑^- for the MC⁺ cations and MC^? anions have been investigated. In addition, Bond distance Re, transition energy Te, vibrational frequency ω_e, ionization energy IE, electron affinity EA, dipole moment μ, dissociation energy D₀ and heat formation ΔH°f₀/ΔH°f₂₉₈, were determined for each species. The analysis of the dissociation energy for ZnC, CdC and HgC shows the decrease in the stability of the monocarbides from Zn to Hg. For ΔH°f₀/ΔH°f₂₉₈ values of MC, which are not known experimentally or theoretically, we recommend the following CCSD(T) predictions of ZnC, CdC and HgC: 181.3/178.54, 180.65/178.4 and 175.35/174.71 kcal/mol respectively. Comparing the three functionals with the CCSD(T) results, the CAM-B3LYP functional shows excellent predictive agreement for the various properties of the group 12 monocarbides.     

The Surface Analysis Working Group at the Consultative Committee for Amount of Substance,Metrology in Chemistry and Biology: A successful initiative by Martin Seah

Dr Martin Seah, NPL, was the initiator, founder, and first chairman of the Surface Analysis Working Group (SAWG) at the Consultative Committee for Amount of Substance, Metrology in Chemistry and Biology (CCQM) at the Bureau International des Poids et Mesures (BIPM), the international organization established by the Metre Convention. This tribute letter summarizes his achievements during his chairmanship and his long-running impact on the successful work of the group after his retirement.     

SYNTHESIS AND PROPERTIES OF COPOLYMERS FROM 1-[3,5-BIS(TRIMETHYLSILYL)PHENYL]-2-PHENYLACETYLENE

Copolymerization of 1-[3,5-bis(trimethylsilyl)phenyl]-2-phenylacetylene (m,m-(Me₃Si)₂DPA) with other diphenylacetylene derivatives and their copolymer properties were investigated. Homopolymerization of m,m-(Me₃Si)₂DPA by TaCl₅─n-Bu₄Sn (1:2) did not give the polymer due to steric hindrance. However, m,m-(Me₃Si)2DPA copolymerized with diphenylacetylene (DPA), 1-phenyl-2-[p-(trimethylsilyl)phenyl]acetylene (p-Me₃Si DPA), and 1-phenyl-2-[m-(trimethylsilyl)phenyl]acety-lene (m-Me₃SiDPA) in the presence of TaCl₅─n-Bu₄Sn at various feed ratios to give copolymers in moderate yields. The formed copolymers were yellow to orange solids, which were soluble in common organic solvents such as toluene and CHCl₃. The highest weight-average molecular weights (M_w) of these copolymers reached ca. 6 × 105 and tough films could be obtained by solution casting. Their onset temperatures of weight loss in air were observed around 400°C, indicating high thermal stability. The oxygen permeability coefficients at 25°C of copoly(m,m-(Me₃Si)₂ DPA/DPA) (feed ratio 1:1) and copoly(m,m-(Me₃Si)₂DPA/p-Me₃SiDPA) (feed ratio 1:2) were 21 and 100 barrers, respectively, medium in magnitude among polymers from substituted acetylenes.     

Primary Studies on Variation in Position of Trifluoromethyl Groups in Several Aromatic Group‐14 Derivatives by 19F‐NMR Spectroscopy

Variation in the position of CF₃ groups in several aromatic Group‐14 compounds was studied by ¹⁹F‐NMR spectroscopy. In these compounds R_nECl_4?n (n=1 or 2; E=Si, Ge, or Sn; R=2,4,6‐(CF₃)₃C₆H₂ (=Ar), 2,6‐(CF₃)₂C₆H₃ (=Ar′), or 2,4‐(CF₃)₂C₆H₃ (=Ar″)), Ar, Ar′, and Ar″ are all bulky, strongly electron‐withdrawing ligands. The ¹⁹F‐NMR studies of the variation in position of the CF₃ substituents in these compounds as revealed by chemical shifts could be correlated with the electronegativities of the central elements E, and with intramolecular E–F interactions derived from single‐crystal X‐ray diffraction data. These interactions are considered to play an important role in the stabilization of these compounds.     

A Germylene Supported by Two 2-Pyrrolylphosphane Groups as Precursor to PGeP Pincer Square-Planar Group 10 Metal(II) and T-Shaped Gold(I) Complexes

An efficient synthesis of 2-di-tert-butylphosphanylmethylpyrrole (HpyrmPtBu₂), by treating 2-dimethylaminomethylpyrrole (HpyrmNMe₂) with tBu₂PH at 135 °C in the absence of any solvent, has allowed the preparation of the new PGeP germylene Ge(pyrmPtBu₂)₂ ( 1 ), by treating [GeCl₂(dioxane)] with LipyrmPtBu₂, in which the Ge atom is stabilized by intramolecular interactions with one (solid state) or both (solution) of its phosphane groups. Reactions of germylene 1 with Group 10 metal dichlorido complexes containing easily displaceable ligands have led to [MCl{κ³P,Ge,P-GeCl(pyrmPtBu₂)₂}] [M=Ni ( 2 ), Pd ( 3 ), Pt ( 4 )], which have an unflawed square-planar metal environment. Treatment of germylene 1 with [AuCl(tht)] (tht=tetrahydrothiophene) rendered [Au{κ³P,Ge,P-GeCl(pyrmPtBu₂)₂}] ( 5 ), which is a rare case of a T-shaped gold(I) complex. The hydrolysis of 5 gave the linear gold(I) derivative [Au(κP-HpyrmPtBu₂)₂]Cl ( 6 ). Complexes 2 – 5 contain a PGeP pincer chloridogermyl ligand that arises from the insertion of the Ge atom of germylene 1 into a M−Cl bond of the corresponding metal reagent. The bonding in these molecules has been studied by DFT/NBO/QTAIM calculations. These results demonstrate that the great flexibility of germylene 1 makes it a better precursor to PGeP pincer complexes than the previously known germylenes of this type.