Coordination compounds of manganese(II) with 1,10 phenanthroline

TG and DTA of the compounds Mn(phen)₂X₂ (where X=CN^–,CNO^–, NCS^– and NCSe^–), Mn(phen) (NCS)₂, Mn(NCS)₂ and Mn(NCSe)₂ (wherephen=1,10 phenanthroline) are reported and discussed. Decomposition schemes are proposed based on TG and DTA results and, where possible, the analysis and properties of intermediates formed during thermal breakdown. The decomposition of thiocyanate and selenocyanate ligands is observed to lead to an apparent slight increase in sample weight. This phenomenon is discussed in relation to buoyancy changes resulting from the release of sulphur or selenium vapours.

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Zusammenfassung TG und DTA Untersuchungen der Verbindungen Mn(phen)₂X₂ (X=CN^–, CNO^–, NCS^– und NCSe^–), Mn(phen) (NCS)₂, Mn(NCS)₂ und Mn(NCSe)₂ (phen =1.10 Phenantrolin) werden beschrieben. Anhand der TG- und DTA-Ergebnisse werden Zerzetzungsschemata vorgeschlagen und wenn möglich, Analyse und Eigenschaften der im Laufe der thermischen Zersetzung entstandenen Zwischenprodukte angegeben. Es wurde beobachtet, da\ die Zersetzung der Thiocyanat- und Selenocyanatliganden zu einer scheinbaren schwachen Zunahme des Probengewichts führt. Dieses PhÄnomen wird im Zusammenhang mit infolge der Abspaltung von Schwefel- oder SelendÄmpfen auftretenden Änderungen des Auftriebs diskutiert.

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Résumé On décrit et discute la TG et l'ATD des composés Mn(phén)₂X₂ (X=CN^–, CNO^–, NCS^– et NCSe^–), Mn(phén) (NCS)₂, Mn(NCS)₂ et Mn(NCSe)₂ (oùphén=1,10 phénantroline). On propose des schémas de décomposition à partir des résultats de TG et d'ATD et, si possible, on donne l'analyse et les propriétés des produits intermédiaires formés lors de la décomposition thermique. On a observé que la décomposition des ligands de thiocyanate et de sélénocyanate entraine une faible augmentation apparante du poids du prélèvement. On explique ce phénomène par les variations de poussée résultant du dégagement de vapeurs de soufre ou de sélénium.

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()₂₂, () (NCS)₂, Mn(NCS)₂ Mn(NCSe)₂, X=CN^–, CNO^–, NCS^–, NCSe^– =1.10. , , - , . . - , .

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We wish to express our thanks to Professor S. C. Bevan for helpful advice, particularly in connection with the buoyancy effect noted for thiocyanate and selenocyanate complexes.     

Thermal decomposition of Cu(I) phosphine complexes

The thermal decomposition of Cu(I) phosphine complexes of the general types (CuXPPh₃)₄, [CuX(PPh₃)₂] and [CuX(PPh₃)₃] was investigated.The thermal decomposition of (CuXPPh₃)₄, where X denotes Cl^–, Br^–, I^–, NO ₃ ^– and PPh₃=P(C₆H₅)₃, occurs with formation of a phosphine oxide intermediate. For the remaining complexes this intermediate was not proved in the thermal decomposition.

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Zusammenfassung Die thermische Zersetzung der Cu(I)-Phosphinkomplexe vom allgemeinen Typ (CuXPPh₃)₄ und [CuX(PPh₃)₂], wie auch [CuX(PPh₃)₃] wurde untersucht. Die thermische Zersetzung von (CuXPPh₃)₄, wobei X=Cl^–, Br^–, I^– und NO ₃ ^– bedeutet und PPh₃=P(C₆H₅)₃, verläuft unter Bildung eines Phosphinoxid Zwischenproduktes, bei den übrigen Komplexen konnte dieses im Laufe der thermischen Zersetzung nicht nachgewiesen werden.

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Résumé On a étudié la décomposition thermique des complexes phosphine-Cu(I) de formule générale (CuXPPh₃)₄, [CuX(PPh₃)₂], [CuX(PPh₃)₃]. La décomposition thermique de (CuXPPh₃)₄, où X désigne Cl^–, Br^–, I^– et NO ₃ ^– , et PPh₃=P(C₆H₅)₃, s'effectue avec formation d'un oxyde de phosphine intermédiaire; avec les autres complexes, cet intermédiaire n'a pas été mis en évidence au cours de la décomposition thermique.

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(CuXPPb₃)₄ [CuX(PPh₃)₂] [CuX(PPh₃)₃]. (CuXPPh₃)₄, X=Cl^–, Br^–, I^–, NO ₃ ^– , PPh₃=(₆₅)₃ . .

     

Zwitterionic [(H3NCH2C≡CC≡CCH2NH3)]Cu2Cl4 π-Complex: Template Synthesis and Crystal Structure

Crystals of the [(H₃NCH₂CCCCCH₂NH₃)]Cu₂Cl₄ -complex, formed in the oxidative dimerization of propargylammonium cations, were obtained by ac electrochemical synthesis from CuCl₂ · 2H₂O and propargylammonium chloride ([CCCH₂NH₃]Cl) and studied by X-ray diffraction analysis (DARCh automated diffractometer, MoK radiation, /2 scan mode; 2275 reflections with F 4(F), R = 0.048). Crystals are monoclinic: space group B2/b, a = 19.591(6) Å, b = 7.299(3) Å, c = 8.636(3) Å, = 106.83(3)°, Z = 4. The structure consists of individual [(H₃NCH₂CCCCCH₂NH₃)]Cu₂Cl₄ moietes united through the elongated Cu···Cl contacts (2.827(5) Å) into chains oriented along the [010] direction. The bond of the centrosymmetric propargylammonium dimer is -coordintated by copper(I) atom and is elongated to 1.227(6) Å.     

Stopped-flow study of the oxidation of ascorbic acid by the oxo-bridged trinuclear ruthenium complex [(NH3)5RuORu(NH3)4 ORu(NH3)5]7+

The kinetics of the oxidation of ascorbic acid by [(NH₃)₅RuORu(NH₃)₄ORu(NH₃)₅]⁷⁺ has been studied by the stopped-flow method. The activation parameters have been calculated and a possible mechanism is suggested.

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[(NH₃)₅RuORu(NH₃)₄ORu·(NH₃)₅]⁷⁺ . .

     

Pitzer Parameters for the Pertechnetate Ion in the System Na+/K+/Mg2+/Ca2+/Cl−/SO 2 4 −/TcO − 4 /H2O at 25°C

Isopiestic vapor pressure experiments are performed at 25°C with aqueous Mg(TcO₄)₂ solutions and with ternary mixtures containing various combinations of NaTcO₄, Mg(TcO₄)₂, NaCl, MgCl₂, Na₂SO₄, and MgSO₄. The osmotic coefficients of the binary solutions are used to evaluate the binary Pitzer parameters ⁽⁰⁾, ⁽¹⁾, and C for Mg(TcO₄)₂. We previously reported these parameters for NaTcO₄. The binary parameters for KTcO₄ and Ca(TcO₄)₂ are evaluated from solubilities of KTcO₄ in KCl and CaCl₂ solutions, respectively. The mixing parameters _{TcO 4} ^– _/Cl ^–, _{M/TcO 4} ^– _/Cl ^–, _{TcO 4} ^– _{/SO 4} ^2– , _{M/TcO 4} ^– _{/SO 4} ^2– , and _Na ⁺ _/Mg ²⁺ _/TcO4 ^2– are calculated from either osmotic coefficients or solubilities in the corresponding ternary mixtures. The evaluated set of Pitzer parameters predicts well the activity coefficients and solubilities of KTcO₄ in multicomponent systems.     

Mechanism of non-catalytic proton exchange in aprotic low-polar solvents

The kinetics of proton exchange for the CD₃OH–(CH₃)₃COH and CD₃OH–CH₃COOH systems in various solvents have been studied by dynamic¹H and²H NMR. The mechanism of the process is discussed.

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¹H ²H CD₃OH–(CH₃)₃COH CD₃OH–CH₃COOH . .

     

Ionic Mobility, Phase Transitions, and Electric Conductivity in Ammonium Tetrafluoroantimonate and Heptafluorodiantimonate(III)

The dynamics of the fluoride and proton sublattices and the electrophysical properties of NH₄SbF₄ (I) and NH₄Sb₂F₇ (II) in the temperature range 210-435 K were studied by ¹⁹F and ¹H NMR and impedance spectroscopy. Types of ionic motion were determined and their activation energies were estimated. The structural phase transitions in I and II form the high-temperature modifications -NH₄SbF₄ and -NH₄Sb₂F₇, having high ionic (superionic) conductivity in the range 425-435 K (1.9-1.5×10^-3 S/cm).     

Influence of substituents on rate constants for recombination of tertiary peroxy radicals

A linear correlation between the logarithm of rate constant (2k_t) for recombination of tertiary peroxy radicals (ROO)^* and ^* constants of substituents R was found to be 1g 2k_t=lg 2k _t ^° . The calculated values are 1g 2k _t ^° =4.59±0.08 and ^*=5.56±0.35.

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I (2k_t) (ROO) R: 1g 2k_t=lg 2k _t ^° . , 1g 1g 2k _t ^° =4,59±0,08 =5,56±0,35

     

Décomposition thermique du sulfite de fer(II) anhydre

Résumé Sous azote ou sous vide, le sulfite ferreux anhydre se décompose vers 210° en magnétite, pyrite et dioxyde de soufre. Concurremment une réaction de dismutation intervient avec formation de FeSO₄, Fe₃O₄ et FeS₂. Lorsque la température atteint 320°, la pyrite et le sulfate réagissent ensemble pour donner Fe_1–xS, Fe₃O₄ et SO₂. Au-delà de 370° le sulfure ferreux non-stchiométrique commence à réagir à son tour avec le sulfate restant pour former de la magnetite et du dioxyde de soufre.

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In nitrogen or under vacuum, anhydrous iron(II) sulfite decomposes near 210° to magnetite, pyrite and sulfur dioxide. A parallel disproportionation reaction occurs with formation of FeSO₄, Fe₃O₄ and FeS₂. When the temperature reaches 320°, pyrite and sulfate react together to give Fe_1–xS, Fe₃O₄ and SO₂. Above 370° the non-stoichiometric ferrous sulfide begins to react with the remaining sulfate to give magnetite and sulfur dioxide.

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Zusammenfassung Unter Stickstoff oder im Vakuum zersetzt sich das wasserfreie Eisen(II)-sulfit in der Nähe von 210 °C zu Magnetit, Pyrit und Schwefeldioxid. Parallel hierzu findet eine Disproportionierung unter Bildung von FeSO₄, Fe₃O₄ und FeS₂ statt. Wenn die Temperatur 320 °C erreicht, reagieren Pyrit und Sulfat unter Bildung von Fe_1–xS, Fe₃O₄ und SO₂ Oberhalb von 370 °C beginnt das nichtstöchiometrische Eisensulfit seinerseits mit dem restlichen Sulfat zu reagieren um Magnetit und Schwefeldioxid zu ergeben.

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(II) 210° , . FeSO₄, Fe₃O₄ FeS₂. 320°, , Fe_1–xS, Fe₃O₄ SO₂. 370° .

     

Thermal and some other properties of the complexes crystallizing from the system Ni(II)-en-[Ni(CN)4]2−-H2O

Seven complex compounds exhibiting the compositions Ni(en)₃Ni(CN)₄·H₂O (I), Ni(en)₃Ni(CN)₄ (II),-Ni(en)₂Ni(CN)₄ (III), Ni(en)Ni(CN)₄·2H₂O (IV), Ni(en)Ni(CN)₄ (V), Ni(en)₂Ni(CN)₄ · 2.5H₂O (VI) and-Ni(en)₂Ni(CN)₄ (VII) were prepared from the system Ni-en-[Ni(CN)₄]^2–-H₂O. These compounds were examined by the methods of infrared spectroscopy, X-ray powder diffractometry, UV-VIS reflectance spectroscopy, and also by the measurement of magnetic moments. The thermal stability, the stoichiometry of thermal decomposition and the mutual transformations were investigated with a derivatograph. The reactions proceeding according to the following schemes were observed if the system was heated to appropriate temperature: (I)(II)(III)(V)(IV) and (VI)(VII)(III)(V)(IV) Process (VII)(III) represents isomerization. The reversibility of the process (V)(IV) is due to the high hygroscopicity of the anhydrous complex. The changes in structure in the course of the individual processes are discussed.

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Zusammenfassung Aus einem System Ni-en-[Ni(CN)₄]^2–-H₂O wurden sieben Komplexe der Formeln Ni(en)₃Ni(CN)₄·H₂O (I), Ni(en)₃Ni(CN)₄ (II),-Ni(en)₂Ni(CN)₄ (III), Ni(en)Ni(CN)₄·2H₂O (IV), Ni(en)Ni(CN)₄ (V), Ni(en)₂Ni(CN)₄ · 2.5H₂O (VI) und-Ni(en)₂Ni(CN)₄ (VII) hergestellt. Diese Verbindungen wurden mittels IR-Spektroskopie, Röntgenpulverdiffraktometrie, UV-Reflexionsspektroskopie und durch Messungen des magnetischen Momentes untersucht. Die Wärmestabilität, die Stöchiometrie des thermischen Zerfalles und die gegenseitigen Umwandlungen wurden mittels eines Derivatographen untersucht. Wird das System auf geeignete Temperaturen erhitzt, kann der Reaktionsverlauf durch folgendes Schema dargestellt werden: (I)(II)(III)(V)(IV) und (VI)(VII)(III)(V)(IV).Der Prozeß (VII)(III) verkörpert eine Isomerisierung. Die Umkehrbarkeit von Prozeß (V)(IV) ist auf die ausgeprägten Hygroskopieeigenschaften des wasserfreien Komplexes zurückzuführen. Es werden die im Ablaufe der einzelnen Prozesse vorgehenden Strukturveränderungen besprochen.

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Ni- -[No(N)]² -₂ Ni(en)₃Ni(CN)₄ · ₂ (I), Ni(en)₃Ni(CN)₄ (II),-Ni(en)₂Ni(CN)₄ (III), Ni(en)Ni(CN)₄-2H₂O (IV), Ni(en)Ni(CN)₄ (V), Ni(en)₂Ni(CN)₄ · 2,5H₂O (VI) -Ni(en)₂Ni(CN)₄ (VII). , , - , . , . (I)(II)(III)(V)(IV) (VI)(VII)(III)(V)(IV). (VII)(III) . (V)(IV) . .

     

Kinetics and mechanism of acetylene hydromethylation on organonickel catalysts

Kinetics of methane interaction with acetylene on Ziegler-Natta type organonickel catalysts has been studied. The reaction is first order with respect to methane. The kinetic isotope effect amounts to K_{CH 4}/K_{CD 4}=1.5 and K_{C 2}H₂,CH₄,H₂/K_{C 2}D₂,CD₄,D₂=2.0.

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-. -. K_{CH 4}/K_{CD 4}, K_{C 2}H₂,CH₄,H₂/K_{C 2}D₂,CD₄,D₂ 1,5; 2,0. .

     

Electron structure of the V2 molecule derived from DV-Xα data

Conclusions The electron structure of the V₂ molecule has been calculated by means of the DV-X method. The configuration 3_u ⁴6_g ²7_g ²(l_g)² has been obtained for the ground state, which corresponds to a quintuple bond, and the equilibrium state 1.78 Å. The term of the ground state³_g ^– and the bond length are in agreement with the experimental data.Translated from Izvestiya Akadeinii Nauk SSSR, Seriya Khimicheskaya, No. 9, pp. 232–235, September, 1985.The authors wish to express their gratitude to A. N. Ivanov and V. K. Gryaznov for the provision of the program for the calculation of the atomic Hartree-Fock functions.     

Crystallization of iron phosphate glasses

Differential thermal analysis (DTA), thermogravimetric analysis (TG), X-ray diffraction and Mössbauer spectroscopy were employed in the investigation of crystalline products of FeO_x-P₂O₅ glasses generated by various heat treatments. In glasses with a high value of =Fe²⁺/(Fe²⁺ + Fe³⁺), absorption of oxygen occurs in a broad temperature range identified by TG. Depending on the value of , two exotherms appear in the DTA curves, the low-temperature one corresponding to crystallization of the Fe₃(PO₄)₂ type regions, and the high-temperature one being related to various phases with dominating FePO₄. Each exotherm has its own transformation region, identical in absolute value. The Mössbauer spectra of glasses which underwent thermal treatment at higher temperatures exhibit some indication of phases of the types Fe₃(PO₄)₂ · xH₂O and FePO₄ · xH₂O.

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Zusammenfassung Differentialthermoanalyse (DTA), thermogravimetrische Analyse (TG), Röntgendiffraktion und Mössbauerspektroskopie wurden bei der Untersuchung (von kristalliner Produkte) durch verschiedene thermische Behandlungen hergestellten FeO_x-P₂O₅ Gläsern eingesetzt. In den Glasarten mit einem hohen Wert von =Fe²⁺/(Fe²⁺ + Fe³⁺) erfolgt die Sauerstoffabsorption in einem durch TG [nachgewiesenen breiten Temperaturbereich. In Abhängigkeit von dem -Wert erscheinen zwei Exothermen in den DTA-Kurven, von denen der bei niedriger Temperatur die Kristallisation des Fe₃(PO₄)₂ entspricht, und jener bei höheren Temperaturen in verschiedenen Phasen dem FePO₄. Jede Exotherme hat ihr eigenes Umwandlungsgebiet, das in absolutem Wert identisch ist. Die Mössbauer-Spektren der Gläser welche einer Wärmebehandlung bei höheren Temperaturen unterzogen worden sind, weisen einige Indikationsphasen der Typen Fe₃(PO₄)₂ · xH₂O und FePO₄ · xH₂O auf.

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, , FeO_x-P₂O₅, . , =Fe²⁺/(Fe²⁺+Fe³⁺) . , - : Fe₃(PO₄)₂, – FePO₄. , . , , Fe₃(PO₄)₂ · ₂ FePO₄ · ₂.

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The authors thank Mrs. Simonyiová for assistance in the experimental part of these investigations, and Dr. Horváth and Dr. Vondrovic for performing the X-ray and TG analyses.     

Telomerization of butadiene with diethylamine catalyzed by Ni, Pd and Pt allyl halide complexes

The telomerization of butadiene with diethylamine with the formation of the tertiary amine (C₂H₅)₂NC₈H₁₃ is catalyzed by Ni, Pd and Pt allyl halide complexes. Triphenylphosphine increases the activity of such catalysts. The rate of telomerization depends strongly on the [PPh₃]/[M] ratio (M=Pd and Pt) and increases in the series of metals: Ni3H₅PdCl)₂ exceeds that of (-C₃H₅)₂ Pd by more than two orders of magnitude.

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Ni, Pd Pt (C₂H₅)₂NC₈H₁₃. . [PPh₃]/[M], M=Pd Pt, : Ni3H₅PdCl)₂ (-C₃H₅)₂Pd.

     

Electronic influence of water adsorbed on ZnO in H2 and Co oxidation

In this paper we calculate the effect of surface OH/OH^– on the simultaneous adsorption of H₂ and O₂ on ZnO. A quantitative comparison between H₂ and CO oxidation rates shows that the two mechanisms are similar for the same water recovery on ZnO.

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OH/OH^– H₂ O₂ ZnO. H₂ CO , ZnO.

     

1A1⇔5T2 Spin Transition in Heterometallic Solid Phases FexNi1-x(Htrz)3(NO3)2 · H2O (Htrz = 1,2,4‐Triazole)

Solid phases Fe_xNi_1-x(Htrz)₃(NO₃)₂ · H₂O (0.4 x 0.8$) and Ni(Htrz)₃(NO₃)₂ · H₂O were synthesized and studied. The phases were studied by means of magnetochemistry, powder Xray difraction analysis, and electronic and IR spectroscopy. The heterometallic phases are described by the stoichiographic method of differentiating dissolution (DD). The values of x were determined by two methods — atomic absorption and DD. Magnetochemical data showed that the solid phases exhibit a hightemperature ¹A₁ ⁵T₂ 0.5 x 0.8 and disappears at x = 0.4. The spin transition is accompanied by thermochromism (color changed from pink to white at 0.6 x 1 and from pink to light lilac at x = 0.5). A decrease in x leads to a decrease in the temperature of the forward (under heating T_c ) and reverse (under cooling T_c ) transitions, a decrease in hysteresis value ( T_c), and a smearing of the spin transition.     

Thermal behaviour of transition metal complexes of dithiocarbazic esters. II

A thermal study (simultaneous TG and DTA measurements) was carried out on the dithiocarbazic ester complexes M[N³CH₂R₁N²C¹(S)SCH₃]₂, where M=Ni, Pt; R₁=C₆H₅. The following disproportionation reaction occurs in the solid state: II is formed through deprotonation of the CH₂ group bound to N³, whereas III is formed through protonation of N³.The influence of inductive and/or steric effects on the mechanism of this reaction is discussed, taking into account the electrochemical and X-ray data on the complexes Pt[NRNC(S)SR']₂ with differentR substituents: R=H, Ph, CH₂Ph, CH₂C₅H₁₁, CH(CH₃)₂, C(CH₃)₃; R=CH₃, CH₂Ph.These results accord with the behaviour of the same complexes in solution.

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Zusammenfassung Dithiokarbamidsäureesterkomplexe M[N³CH₂R₁N²C¹(S)SCH₃]₂ mit M=Ni, Pt und R₁=C₆H₅ wurden thermisch untersucht. Im festen Zustand spielt sich folgende Disproportionierungsreaktion ab: II wird durch Deprotonierung der an N³ gebundenen CH₂ Gruppe und III durch Protonierung des Atoms N² gebildet. Unter Zuhilfenahme der elektrochemischen und Röntgendaten der Komplexe Pt[NRNC(S)SR']₂ mit verschiedenen Substituenten R: R=H, Ph, CH₂Ph, CH₂C₅H₁₁, CH(CH₃)₂, C(CH₃)₃ und R=CH₃ bzw. CH₂Ph wurde der Einfluß von induktiven und/or sterischen Effekten auf den Reaktionsmechanismus diskutiert. Diese Ergebnisse stehen in Übereinstimmung mit dem Verhalten der Komplexe in Lösung.

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M[N³CH₂R₁N²C¹(S)SCH₃]₂, M= Ni, Pt,R ₁=C₆H₅. : II CH₂ , N³, III N². () , Pt[NRNC(S)SR]₂, R= , aR= . .

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We thank prof. A. La Ginestra for many helpful discussions on the various aspects of this work.     

NMR Spectral Assignment of Per-substituted Key-Intermediates of β-Cyclodextrin and Implications in the Structures of the Derivatives

The compounds, 6-per-O-(t-butyldimethylsilyl)--cyclodextrin(1), 2,3-per-O-benzyl-6-per-O-(t-butyldimethylsilyl)--cyclodextrin(2), 2,3-per-O-benzyl--cyclodextrin (3),2,3,6-per-O-benzyl--cyclodextrin (4),2,3,6-per-O-benzoyl--cyclodextrin (5), are used as keyintermediates in the synthesis of selectively substituted -CD derivatives. Simple and assignable ¹H and ¹³C NMR spectra (chemical shifts and coupling constants) were obtained for compounds1–4 indicating C₇ symmetry, ⁴C₁ glucose conformation and major arrangement of H6, H6' atoms at the primary side. The derivative 5, however, gave very broad peaksat room temperature. The peaks could partially be assigned at 270 K, but the broadening was still present at 220 K. This implies that there exist several conformers of similar energyand C₁ symmetry that continuously interchange, since there is not a single type of stabilizing interaction thatpredominates. We attributed this phenomenon to the presence of the carbonyl group, which probablydisfavors - stacking and induces random arrangements of the aromatic rings.     

Liquid-phase oxidation of propylene to propylene glycol acetates over Pd/C and Pt?Pd/C: Effect of platinum on catalyst activity and metal dispersity

Kinetics of oxidation of propylene to propylene glycol and its acetates in acetic acid solutions of lithium nitrate over Pd/C and Pd–Pt/C catalysts has been studied. Catalysts were investigated using X-ray phase analysis and electron microscopy. Platinum introduction into catalyst increases the metal dispersity and the catalyst stability but produces no effect on the nature of surface sites active in propylene oxidation.

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Pd/C Pd–Pt/C. . , , , .

     

Vibrational isotope effect of linear and planar molecules: Deuterated bromoethenes

Linear (planar) molecules A and B which are identical except for isotopic substitutions at the atomic sites are considered. Stretching (bending, out-of-plane) frequencies _k and normal modes _k of the isotopically perturbed molecule B are expressed in terms of stretching (bending, out-of-plane) frequencies _i and the corresponding normal modes _i of the unperturbed molecule A. Complete specification of the unperturbed normal modes is not required. All that is needed are stretching (bending, out-of-plane) amplitudes | _i of the normal modes _i at those sites that are affected by isotopic substitution. The rule which interlaces frequencies _k of molecule A with frequencies _i of molecule B is derived. Given two isotopic molecules A and B that differ by a single isotopic substitution at site , the inversion relation is derived. This relation expresses unperturbed stretching (bending, out-of-plane) amplitudes at the site in terms of stretching (bending, out-of-plane) frequencies of molecules A and B . As an example, out-of-plane vibrations of deuterated bromoethene were considered. In the simplest method 12 out-of-plane frequencies of four polydeuterated bromoethenes were calculated from 12 out-of-plane frequencies of bromoethene and three monodeuterated bromoethenes. Standard deviation of thus calculated frequencies from experimental frequencies is =2.74 cm^–1. In another method, 15 out-of-plane frequencies of four polydeuterated bromoethenes and selected monodeuterated bromoethene are calculated from 9 out-of-plane frequencies of bromoethene and the remaining two monodeuterated bromoethenes. Depending on which monodeuterated bromoethene is selected (1-, cis- or trans-), standard deviation of thus obtained frequencies from experimental frequencies is 1=2.84 cm^–1, c=2.96 cm^–1 and t=2.72 cm^–1.