The valence problem of Pd4Br4Te3

Pd(4)Br(4)Te(3) was prepared from Pd, Te, and PdBr(2) at 700 K. Its structure was determined by single-crystal X-ray diffraction to be triclinic, P$\bar 1$, Pearson symbol aP22; a=842.5(2), b=845.0(3), c=864.8(3) pm; alpha=82.55(3), beta=73.36(2), gamma=88.80(2) degrees ; Z=2. The Br and Te atoms are arranged according to the motif of cubic closest-packed spheres in which every 15th position is vacant; the Pd atoms occupy 8/15 of the octahedral voids. The symmetry relations with the packing of spheres are derived. Prominent structural units are hollow cuboctahedral [(PdBrTe)(6)] units, the Pd atoms are positioned near the centers of the square faces of the Br(6)Te(6) cuboctahedra; the cuboctahedra and double-octahedral Pd(2)Br(4)Te(6) units are connected to strands by sharing triangular Te(3) faces. The strands are condensed by common Br atoms into layered assemblies. Conspicuously close Te--Te contacts in the Te(3) triangles indicate attractive Te--Te interactions. The valence puzzle is resolved by the formula Pd(+II)(4)Br(-I)(4)Te(-4/3)(3). Positive Te--Te Mulliken orbital populations and the Pd--K, Br--K, and Te--L(III) XANES spectra of Pd(4)Br(4)Te(3) referenced to the spectra of PdBr(2), K(2)PdBr(6), PdTe, and PdTe(2) are in accord with attractive Te--Te interactions. The measured semiconducting and diamagnetic properties are compatible with the derived picture of chemical bonding in Pd(4)Br(4)Te(3).     

Mercury bis(phenyltellurolate) as a precursor for the synthesis of binary and ternary nanoclusters

The reaction of Hg(TePh)2 with AgX (X = Cl, NO3) in the presence of PPh3 and PMePh2 in dimethylformamide (DMF) affords the cluster [Hg6Ag4(TePh)16] (1) at room temperature or [Hg6Ag4Te(TePh)14]2 (2) with heating. When Hg(TePh)2 is reacted with [Co(PPh3)2Cl2] or [Ni(PPh3)2Cl2], the clusters [Hg8Te(PhTe)12Cl4]Q [3; Q = [Co(DMF)6]2+ (3a), [Ni(DMF)6]2+ (3b)] are formed. The syntheses of 1 and 2 occur with the incorporation of AgI into the cluster, and the single-crystal analyses show that the two ternary clusters consist of Hg, Ag, and Te centers occupying well-defined positions. Compounds 3a and 3b do not show the incorporation of the metal into the cluster, but the CoII and NiII salts provide the Cl atom to generate the anionic cluster 3 stabilized by the [Co(DMF)6]2+ or [Ni(DMF)6]2+ ion.     

Tetrahedral boron chemistry for the preparation of highly efficient "cascatelle" devices

The replacement of the two fluorine atoms on the boron center of the well-known Bodipy fluorophore by functionalized acetylenic groups opens the way to a new family of highly luminescent, redox active, and stable fluorophores termed "E-Bodipy" species. The substitution is effective for ethynyl-lithium reagents incorporating tolyl, naphthyl, pyrenyl, fluorenyl, and terpyridinyl units. The protocol also tolerates the presence of various functional groups in the dipyrromethene meso position such as pyrene, phenylethynylpyrene, 4'-terpyridine, and iodophenyl. The last of these is particularly useful for a further coupling reaction enabling introduction of a flexible arm bearing a succinimidyl unit reactive toward primary amines. X-ray structure determinations of two E-Bodipy compounds confirm the introduction of the ethynyl units and show the boron atoms to have a distorted tetrahedral environment, with B-C(ethynyl) approximately 1.59 A and both boron atoms lying essentially in the mean planes of the dipyrromethene units. All the new compounds show intense electronic absorption bands (epsilon 60,000-70,000 M-1 cm-1), high quantum yields (>80%), and slow rates of nonradiative decay. Absorption by the aromatic substituents results in a "cascatelle" process leading to emission exclusively through the boradiazaindacene entity and thus large virtual Stokes' shift (>10,000 cm-1). The new compounds are also redox active, with the formation of both Bodipy+* and Bodipy-* occurring more readily than for F-Bodipy species. The molecules in their excited states are strong reducing agents.     

Extrapolation methods for approximating arc length and surface area

A well-known method of estimating the length of a parametric curve in is to sample some points from it and compute the length of the polygon passing through them. In this paper we show that for uniform sampling of regular smooth curves, Richardson extrapolation can be applied repeatedly giving a sequence of derivative-free length estimates of arbitrarily high orders of accuracy. A similar result is derived for the approximation of the area of parametric surfaces.      

Injectivity and adjoint extremals

The following investigation deals with injectivity results for general diffeomorphisms as well as for Haar's transformation. We apply these results to adjoint variational problems introduced by Haar [6]. In particular, we prove a generalization of Krust's theorem for two-dimensional adjoint extremals. Received March 20, 1998 / Accepted April 24, 1998     

Polystyrene with Pendant Mixed Functional Ruthenium(II)‐Terpyridine Complexes

A vinyl substituted 2,2′:6′,2″‐terpyridine and a mixed, bifunctional ruthenium(II)‐terpyridine complex bearing a vinyl and a hydroxymethyl group are utilized as comonomers for radical copolymerization with styrene. The resulting polymers are characterized by means of UV‐vis spectroscopy and gel permeation chromatography, coupled with an in‐line diode array spectrophotometer.