Harmonic Calculus on Fractals - A Measure Geometric Approach I

Differentiation of functions w.r.t. finite atomless measures with compact support on the real line is introduced. The related harmonic calculus is similar to that of the classical Lebesgue case. As an application we obtain the Weyl exponent for the spectral asymptotics of the Laplacians w.r.t. linear Cantor-type measures with arbitrary weights.     

Pentaazadienido-Komplexe von Zink,Cadmium und Quecksilber Die Kristallstruktur von [Cd(EtOC6H4-N5-C6H4OEt)2(py)2] und [Hg(tol-N5-tol)2(py)]

Pentaazadienido Complexes of Zinc, Cadmium, and Mercury. The Crystal Structure of [Cd(EtOC₆H₄-N₅-C₆H₄OEt)₂(py)₂] and [Hg(tol-N₅-tol)₂(py)] The pentaazadienido complexes [M(EtOC₆H₄N₅C₆H₄OEt)₂] (M = Zn ( 1 ), Cd ( 2 )) are formed by the reaction of [M(NH₃)₄]²⁺ with [EtOC₆H₄N₅C₆H₄OEt]^? in aqueous ammonia. 2 crystallizes from pyridine as [Cd(EtOC₆H₄N₅C₆H₄OEt)₂py₂] ( 3 ) with the triclinic space group P1 and a = 937.2(2); b = 1422.7(2); c = 2085.5(2) pm; α = 75.28(1)°; β = 94.74(1)°; γ = 99.75(1)°; Z = 2. The central Cd²⁺ ion of 3 exhibits an octahedral coordination by two pyridine ligands in cis arrangement and two (N1, N3)-²⁺ chelating pentaazadienide ions. The reaction of [HgI₄]² with the 1,5-di(tolyl)pentaazadienide anion in aqueous ammonia affords [Hg(p-tol-N₅-tol)₂] ( 4 ), which crystallizes from pyridine in form of [Hg(tol-N₅-tol)₂py] ( 5 ) with the space group P1 and a = 1176.2(4); b = 1203.1(3); c = 1295.6(5) pm; α = 100.77(3)°; β = 110.08(3)°; γ = 94.29(2)°; Z = 2. In 5 the Hg²⁺ cation is threefold coordinated by two monodentate (N3)-η¹ pentaazadienid anions and one pyridine ligand. Within the N₅ chains of the pentaazadienid anions of 3 and 5 localized N? N double bonds are found in the positions N1? N2 and N4? N5 with distances between 125 and 129 pm.     

Second-order nonlinear optical properties of the Ag(111)/electrolyte interface in the presence of self-assembled monolayers containing conjugated pi systems. I. Alpha-functionalized terthiophene films on Ag(111)

The nonlinear optical properties of self-assembled monolayers obtained from bonding two different alpha-functionalized terthiophenes (alpha-T3) to (111) silver electrode surfaces have been investigated using second harmonic generation (SHG). The two (alpha-T3) compounds used were functionalized with alkane chains of different lengths (C8 and C4), and each was terminated with a thiol anchoring group. A nitrile group was attached to the terminal thiophene ring of the (alpha-T3) compound with the C4 chain. The orientation of the polarization of the incident beam was changed systematically and gradually between "p" and "s" orientation and the SH signal (isotropic and anisotropic contributions) analyzed in both directions ("P" and "S"). The symmetry of the system was reduced by the presence of the adlayers from C3v to C3. The dependence on the applied potential and the incident wavelength has also been studied. The relative magnitudes and phases of the various second-order tensor elements have been estimated and compared with the values for a bare surface. A resonance process in the (alpha-T3) pi moiety has been investigated, and from this, the effective "band-gap" energies of the organic semiconductor SAMs (i.e., the energy difference between the pi-pi bands) have been estimated.     

Synthese und Struktur der Platin(O)-Verbindungen [(dipb)Pt]2(COD) und (dipb)3Pt2 sowie des clusters Hg6[Pt(dipb)]4 (dipb = (i-Pr)2P(CH2)4P(i-Pr)2)

Synthesis and Structure of the Platinum(0) Compounds [(dipb)Pt]₂(COD) and (dipb)₃Pt₂ and of the Cluster Hg₆[Pt(dipb)]₄ (dipb = (i-Pr)₂P(CH₂)₄P(i-Pr)₂) The reduction of (dipb)PtCl₂ with Na/Hg yields (dipb)Pt as an intermediate which reacts with the amalgam to form the cluster Hg₆[Pt(dipb)]₄ ( 3 ) or decomposes to (dipb)₃Pt₂ ( 2 ) and Pt. In the presence of COD [(dipb)Pt]₂(COD) ( 1 ) is obtained. 1 crystallizes monoclinicly in the space group P2₁/c with a = 1596.1(4), b = 996.5(2), c = 1550.4(3) pm, β = 113.65(2)°, Z = 2. In the dinuclear complex two (dipb)Pt units are bridged by a 1,2-η²-5,6-η² bonded COD ligand. Whereby the C = C double bonds are lengthened to 145 pm. 2 forms triclinic crystals with the space group P1 and a = 1002.0(2), b = 1635.9(3), c = 868.2(2) pm, α = 94.70(2)°, β = 94.45(2)°, σ = 87.95(1)°, Z = 1. In 2 two (dipb)Pt moieties are connected by a μ-dipb ligand in a centrosymmetrical arrangement. 3 is monoclinic with the space group C2/c and a = 1273.8(3), b = 4869.2(6), c = 1660.2(3) pm, β = 95.16(2)°, Z = 4. The clusters Hg₆[Pt(dipb)]₄ have the symmetry C₂. Central unit is a Hg₆ octahedron of which four faces are occupied by Pt(dipb) groups. The bonding in the cluster is discussed on the basis of eight Pt? Hg two center bonds of 267.6 pm and two Pt? Hg? Pt three center bonds with Pt? Hg = 288.0 pm.     

Literatur

Ohne Zusammenfassung     

Struktur und Koordinationsverhalten des sterisch anspruchsvollen Phenylcycloarsoxans

Structure and Coordination Chemistry of Sterically Demanding Phenylcycloarsoxane Tetrameric phenylcycloarsoxane (C₆H₅AsO)₄ 1 exhibits a boat‐chair‐conformation in the solid state. Its reaction with CuI in benzonitrile leads to the formation of coordination polymers. [(CuI · C₆H₅CN){cyclo‐(C₆H₅AsO)₄}] ( 2 ) underlines the structure‐directing steric requirements of the phenyl side chains. Treatment of 1 with M(CO)₆ (M = Cr, Mo) confirms its capability to undergo metal‐mediated ring expansion. In [{M(CO)₃}₂{cyclo‐(C₆H₅AsO)₆}] with M = Cr ( 3 ) and M = Mo ( 4 ), twelve membered As–O‐rings are stabilised by the participation of alternating As atoms in the coordination spheres of opposite facial transition metal carbonyl fragments M(CO)₃.     

Über Cyanatverbindungen und deren reaktives Verhalten. X. 14N-NMR-Untersuchungen an einigen diamagnetischen Metall- und Triphenylzinnthiocyanatverbindungen sowie Kaliumselenocyanat

Chemical shifts and line-widths of the following soluble diamagnetic ¹⁴N-compounds are given: (NH₄)₂[Hg(SCN)₄], Sr(SCN)₂, K₂[Zn(NCS)₄] · 2 CH₃COCH₃, K₂[Zn(NCS)₄], K₄[Cd(NCS)₆], (C₆H₅)₃SnNCS, C₇H₇NH₃[(C₆H₅)₃Sn(NCS)₂], K[(C₆H₅)₃Sn(NCSe)₂] und KSeCN. Types of bonding of the NCY group (Y = S, Se) in these compounds are discussed and correlated to the measurements. Dependences of the line-widths upon different concentrations and temperatures are given for aqueous KSCN solutions.     

Chloracylierung und Bromacylierung von Carbonylverbindungen: Eine in Vergessenheit geratene Carbonylreaktion. I. Präparative Anwendungsbreite

Chloroacylation and bromoacylation of carbonyl compounds: A forgotten carbonyl reaction. I. Scope of the reaction Aliphatic, α,β-unsaturated and aromatic aldehydes as well as aliphatic ketones react with acyl halides to (α-haloalkyl)esters. These bifunctional derivates contain two leaving groups of different reactivity. The scope of this scarcely of this scarcely known carbonyl reaction is discussed.