On Genuine Bernstein–Durrmeyer Operators

We continue the studies on the so–called genuine Bernstein–Durrmeyer operators U _n by establishing a recurrence formula for the moments and by investigating the semigroup T(t) approximated by U _n . Moreover, for sufficiently smooth functions the degree of this convergence is estimated. We also determine the eigenstructure of U _n , compute the moments of T(t) and establish asymptotic formulas. Received: January 26, 2007.     

Schwingungs-Raman-Spektren von Hexahalogenokomplexen von OsIV (X = Cl,I) und IrIV (X = Cl,Br) bei 80 K

Vibrational Raman Spectra of Hexahalo Complexes of Os^IV (X = Cl, I) and Ir^IV (X = Cl, Br) at 80 K The Resonance-Raman (RR) spectra of the tetrabutyl- resp. tetraethylammonium salts of [OsCl₆]^2?, [OsI₆]^2?, [IrCl₆]^2?, and [IrBr₆]^2? have been investigated with the excitation-lines of an Ar⁺ and Kr⁺ laser. Devices with a movable sample holder for low-temperature experiments (80 K) are described. The anormal intensities of some of the Ra-active fundamentals are attributed to the RR effect. As a rule the deformation vibration υ₅(T_2g) is RR enhanced if excited within a π—π*(dt_2g)-CT-transition and the stretching vibration υ₂(E_g) is RR-enhanced within a π—σ*(de_g)-CT-transition. The dispersion of the degree of depolarisation of the three Ra-active fundamentals of [IrBr₆]^2? demonstrates, that this rule cannot only be applicated to the symmetrical but also to the antisymmetrical part of the scattering tensor.     

CrIII-Phthalocyaninate: Darstellung,Eigenschaften und Kristallstruktur von l-Bis(triphenylphosphin)iminium-trans-di(nitrito(O))phthalocyaninato(2–)-chromat(III)

Cr^III Phthalocyaninates: Synthesis, Properties, and Crystal Structure of l-Bis(triphenylphosphine)iminium trans-Di(nitrito(O))phthalocyaninato(2–)chromate(III) [Cr(H₂O)₂Pc^2?]I_x reacts with excess (PNP)NO₂ in dimethylformamide to yield less soluble greenblack l-bis(triphenylphosphine)iminium trans-di(nitrito(O))phthalocyaninato(2–)chromate(III), ^l(PNP)^trans[Cr(ONO)₂Pc^2?], which crystallizes in the triclinic space group P1 (No. 2) with Z = 2. The Cr atom is in the center of the Pc^2? ligand and the two nitrite ions are monodentate O-coordinated in a mutually trans arrangement to the Cr atom. The Cr? O and Cr? N_iso bond distances are 1.9898(14) und 1.981(2) Å, respectively. The geometric data of the coordinated nitrite ion are: d(N? O) = 1.307(2) Å; d(N? O) = 1.205(2) Å; ?(O? N? O) = 113.7(2)°; ?(Cr? O? N) = 116.85(12)°. The non-bonding O atoms are trans to the Cr atom. The Pc^2? ligand is slightly saddled. Three weak spin-allowed trip-quartet(TQ) transitions (in 10³ cm^?1): TQ1 (8.20) < TQ2 (11.3) < TQ3 (20.33) and the characteristic π-π* transitions of the Pc^2? ligand: B (14.68) < Q₁ (27.1) < Q₂ (29.0) < N (35.4) are observed in the UV-VIS-NIR spectrum. Prominent luminescence spectra are obtained by excitation within the TQ1 region, in which the spin-forbidden trip-sextet transition at 7376 cm^?1 dominates at low temperatures (T < 50 K). The vibrational spectra are discussed. In coincidence of the excitation lines with TQ3, v_s(Cr? O) at 378 cm^?1 is selectively resonance Raman (RR) enhanced. v_as(Cr? O) is observed in the FIR spectrum at 391 cm^?1. The following internal vibrations (in cm^?1) of the nitrito ligand are in the MIR spectrum: v_as(N? O)/1447 > v_as(N? O)/1018/1029 > δ(O? N? O)/828 and in the RR-spectrum: v_s(N? O)/1410 > v_s(N? O)/952, the last followed by three overtones.     

Darstellung und spektroskopische Charakterisierung von Di(halogeno)phthalocyaninato(1–)rhodium(III), [RhX2Pc1−] (X = Cl,Br, I)

Synthesis and Spectroscopical Characterization of Di(halo)phthalocyaninato(1–)rhodium(III), [RhX₂Pc^1?] (X = Cl, Br, I) Bronze-coloured di(halo)phthalocyaninato(1–)-rhodium(III), [RhX₂Pc^1?] (X = Cl, Br) and [RhI₂Pc^1?] · I₂ is prepared by oxidation of (ⁿBu₄N)[RhX₂Pc^2?] with the corresponding halogene. Irrespective of the halo ligands, two irreversible electrode reactions due to the first ringreduction (E_R = ?0,90 V) and ringoxidation (E_O = 0,82 V) are present in the cyclovoltammogram of (ⁿBu₄N)[RhX₂Pc^2?]. The optical spectra show typical absorptions of the Pc^1?-ligand at 14.0 kK and 19.1 kK. Characteristic vibrational bands are at 1 366/1 449 cm^?1 (i. r.) and 569/1 132/1 180/1 600 cm^?1 (resonance Raman (r. r.)). The antisym. (Rh? X)-stretching vibration is observed at 294 cm^?1 (X = Cl), 240 cm^?4 (Br) and 200 cm^?1 (I). Only the sym. (Rh? I)-stretching vibration at 133 cm^?1 is r. r. enhanced together with a strong line at 170 cm^?1, which is assigned to the (I? I)-stretching vibration of the incorporated iodine molecule. Both modes show overtones and combinationbands.     

Spektroskopische Eigenschaften von Di(phthalocyaninato)metallaten(III) der Seltenen Erden. Teil 2: Die Multikern(1H-, 13C-, 15N-, 17O- und 31P)-NMR-Spektren und Nachweis komplexgebundenen Wassers

Spectroscopical Properties of Di(phthalocyaninato)metalates(III) of the Rare Earth Elements. Part 2: The Multinuclear (¹H, ¹³C, ¹⁵N, ¹⁷O, and ³¹P) NMR Spectra and Determination of Complex Bound Water The ¹H, ¹³C, ¹⁵N, ¹⁷O and ³¹P NMR spectra of (PNP)[Ln(Pc^2?)₂] and (TDOA)[Ln(Pc^2?)₂] (Ln = La …? (—Pm) …? Lu); PNP: di(triphenylphosphine)-iminium; TDOA: Tri(n-dodecyl)n-octylammonium dissolved in CD₂Cl₂ are reported. With the exception of the nitrogen atoms of the cations all light atoms of both homologues complex salt rows have been detected and assigned. Proof of the presence of additional water contained in the (solid) complex salts has been given unambigously. The otherwise strong Fermi contact interactions diminuish rapidly with growing distance from the paramagnetic centre favouring dipolar (pseudo-contact) interactions. As a consequence the mostly element independent paramagnetic shifts of the atoms situated on the periphery of the anion as well as those of the cations and water are determined by the distance factor. Therefore a first glance of the structure of the ion-pair present in solution emerges, in which the water molecule seems to play an important role.     

Zirconiumphthalocyanine: Darstellung und Eigenschaften chloridhaltiger Phthalocyanine des drei- und vierwertigen Zirconiums; Kristallstruktur von cis-Di(triphenylphosphin)iminium-tri(chloro)phthalocyaninato(2–)zirconat(IV)-di(dichlormethan)

Zirconiumphthalocyanines: Synthesis and Properties of Chloride Ligated Phthalocyanines of Ter- and Quadrivalent Zirconium; Crystal Structure of cis-Di(triphenylphosphine)iminium-tri(chloro)phthalocyaninato(2–)zirconate(IV)-di(dichloromethane) cis-Di(chloro)phthalocyaninato(2–)zirconium(IV) is obtained by the reaction of ZrCl₄ with phthalodinitrile in 1-chloronaphthaline at 230°C. It reacts with molten di(triphenylphosphine)iminiumchloride ((PNP)Cl) yielding cis-di(triphenylphosphine)iminium-tri(chloro)phthalocyaninato(2-)zirconate(IV), cis-(PNP)[ZrCl₃Pc^2?]. This crystallizes with two molecules of dichloromethane in the monoclinic space group P2₁/n with the lattice constants a = 15.219(4) Å, b = 20.262(10) Å, c = 20.719(4) Å, b? = 93.46(2)°, Z = 4. The seven coordinated Zr atom is situated in a “square base-trigonal cap” polyhedron. The plane of the three chlorine atoms runs parallel to the plane of the four isoindole nitrogen atoms N_iso. The Zr–Cl distances range from 2.49 to 2.55 Å, the Zr? N_iso distances from 2.26 to 2.29 Å. Due to ion packing effects the Pc^2? ligand shows an asymmetrical convex distortion. The PNP cation adopts the bent conformation. The P? N? P angle is 139°, the P? N distance 1.58 Å. As confirmed by the cyclovoltammograms cis-(PNP)[ZrCl₃Pc^2?] is oxidized (anodically or chemically by Cl₂) to yield cis-tri(chloro)phthalocyaninato(1–)zirconium(IV) and reduced (cathodically or chemically by [BH₄]^?) yielding chlorophthalocyaninato(2–)zirconium(III) and cis-di(triphenylphosphine)iminium-di(chloro)phthalocyaninato(2–)zirconate(III). The optical spectra show the typical π–π*-transitions of the Pc^2? resp. Pc^? ligand not much affected by the different states of oxidation and coordination of zirconium. The same is true for the vibrational spectra of the Pc^2? resp. Pc^? ligand. In the f.i.r. spectra between 350 and 150 cm^?1 the asym. and sym. Zr? Cl stretching and Cl? Zr? Cl deformation vibration as well as the asym. Zr? N stretching vibration of the [ZrCl_xN₄] skeleton (x = 1–3) is assigned.     

Osmium(II)-Phthalocyanine: Darstellung und Eigenschaften von Di(acido)phthalocyaninatoosmaten(II)

Osmium(II) Phthalocyanines: Preparation and Properties of Di(acido)phthalocyaninatoosmates(II) “H[Os(X)₂Pc^2?]” (X = Br, Cl) reacts in basic medium or in the melt with (ⁿBu₄N)X forming less stable, diamagnetic, darkgreen (ⁿBu₄N)₂[Os(X)₂Pc^2?]. Similar dicyano and diimidazolido(Im) complexes are formed by the reaction of “H[Os(Cl)₂Pc^2?]” with excess ligand in the presence of [BH₄]^?. The cyclic voltammograms show up to three quasireversible redoxprocesses: E_1/2(I) = 0.13 V (X = CN), ?0.03 V (Im), ?0.13 V (Br) resp. ?0.18 V (Cl) is metal directed (Os^II/III), E_1/2(II) = 0.69 V (Cl), 0.71 V (Br), 0.83 V (CN), 1.02 V (Im) is ligand directed (Pc^2?/?) and E_1/2(III) = 1.17 V (Cl) resp. 1.23 V (Br) is again metal directed (Os^III/IV). Between the typical “B” (～16.2 kK) and “Q” (～29.4 kK), “N regions” (～34.1 kK) up to seven strong “extra bands” of the phthalocyanine dianion (Pc^2?) are observed in the uv-vis spectrum. Within the row CN > Im > Br > Cl, most of the bands are shifted slightly, the “extra bands” considerably more to lower energy in correlation with E_1/2(I). The vibrational spectra are typical for the Pc^2? ligand with D_4h symmetry. M.i.r. bands at 514, 909, 1 173 and 1 331 cm^?1 are specific for hexa-coordinated low spin Os^II phthalocyanines. In the resonance Raman (r.r.) spectra polarized, depolarized or anomalously polarized deformation and stretching vibrations of the Pc^2? ligand will be selectively enhanced, if the excitation frequency coincides with “extra bands”. With excitation at ～19.5 kK the intensity of the symmetrical Os? X stretching vibration at 295 cm^?1 (X = Cl), 252 cm^?1 (X = Im) and 181 cm^?1 (X = Br) is r.r. enhanced, too. The asymmetrical Os? X stretching vibration is observed in the f.i.r. spectrum at 345 cm^?1 (X = CN), 274 cm^?1 (X = Cl), 261 cm^?1 (X = Im) and 200 cm^?1 (X = Br).