Extremal k *-Cycle Resonant Hexagonal Chains

Denote by ^* _n the set of all k ^*-cycle resonant hexagonal chains with n hexagons. For any B _n ^* _n , let m(B _n ) and i(B _n ) be the numbers of matchings (=the Hosoya index) and the number of independent sets (=the Merrifield–Simmons index) of B _n , respectively. In this paper, we give a characterization of the k ^*-cycle resonant hexagonal chains, and show that for any B _n ^* _n , m(H _n )m(B _n ) and i(H _n )i(B _n ), where H _n is the helicene chain. Moreover, equalities hold only if B _n =H _n .     

Unsymmetrical dinuclear cobalt and nickel trimethylacetate complexes

The reaction of the dinuclear complex Co₂(-OOCCMe₃)₂(²-OOCCMe₃)₂bpy₂ (1) with the polymer [Co(OH) _n (OOCCMe₃)_2–n ] _x afforded the unsymmetrical dinuclear complex bpyCo₂(₂-O,²-OOCCMe₃)(₂-O,O"-OOCCMe₃)₂(²-OOCCMe₃) (2). The reaction of 2,2"-dipyridylamine with [Co(OH) _n (OOCCMe₃)_2–n ] _x gave rise to the analogous complex [(C₅H₄N)₂NH]Co₂(₂-O,²-OOCCMe₃)(-OOCCMe₃)₂(²-OOCCMe₃) (3). The reaction of complex 1 with Ni₄(₃-OH)₂(-OOCCMe₃)₄(OOCCMe₃)₂(MeCN)₂[²-o-C₆H₄(NH₂)(NHPh)]₂ (4) produced an isostructural heterometallic analog of complex 2 with composition bpyM₂(₂-O,²-OOCCMe₃)(₂-O,O"-OOCCMe₃)₂(²-OOCCMe₃) (5) (M = Co, Ni; Co : Ni = 1 : 1) and the dinuclear heterometallic complex bpy(HOOCCMe₃)M(-OH₂)(-OOCCMe₃)₂M(OOCCMe₃)₂[o-C₆H₄(NH₂)(NHPh)] (6) (M = Co, Ni; Co : Ni = 0.15 : 1.85). Compounds 2 and 5 exhibit ferromagnetic spin-spin exchange interactions.     

First and second thermodynamic mixing properties of ethylbenzene +n-alkanes: Experimental and theory

Isobaric expansibilities _P and isothermal compressibilities _T have been determined at 25 and 45°C for binary mixtures of ethylbenzene + n-tetradecane and + n-hexadecane and the corresponding excess functions (V ^E /T)_P and (V ^E /P)_T have also been obtained. With these data and supplementary literature values, the following second order mixing properties are also reported at 25°C: _S ^E , (V ^E /P)_T, C_V and (VT). All mixing quantities have been compared with the results obtained at 25°C by using the Prigogine-Flory-Patterson theory of liquid mixtures. The predicted values suggest that the ability of ethylbenzene as a breaker of the pure n-C_n orientations is similar to what we found for toluene and higher than for p-xylene.     

Eigenvalues of the real generalized eigenvalue equation perturbed by a low-rank perturbation

The low-rank perturbation (LRP) method solves the perturbed eigenvalue equation (B +V) _k = _k (C +P) _k , where the eigenvalues and the eigenstates of the related unperturbed eigenvalue equationB _i = _i C _i are known. The method is designed for arbitraryn-by-n matricesB, V, C, andP, with the only restriction that the eigenstates _i of the unperturbed equation should form a complete set. We consider here a real LRP problem where all matrices are Hermitian, and where in addition matricesC and (C +P) are positive definite. These conditions guarantee reality of the eigenvalues _k and _i . In the original formulation of the LRP method, each eigenvalue _k is obtained iteratively, starting from some approximate eigenvalue _k . If this approximate eigenvalue is not well chosen, the iteration may sometimes diverge. It is shown that in the case of a real LRP problem, this danger can be completely eliminated. If the rank of the generalized perturbation {V, P} is small with respect ton, then one can easily bracket and hence locate to any desirable accuracy the eigenvalues _k (k = 1, ...,n) of the perturbed equation. The calculation of alln eigenvalues requiresO(² n ²) operations. In addition, if the perturbation (V, P) is local with the localizabilityl p, then onlyO(² n) operations are required for a derivation of a single eigenvalue.     

Secondary metabolites of Astragalus danicus Retz. and A. inopinatus Boriss.

The chemical composition of the above-ground parts of Astragalus danicus and A. inopinatus collected in the Baikal region (Eastern Siberia) was studied for the first time. From A. danicus, pentacyclic triterpene saponins were isolated and identified, viz., 3-O-(-glucuronopyranosyl)-3,22,24-trihydroxyolean-12-ene, 3-O-[O-(-d-xylopyranosyl)-(12)-(-glucuronopyranosyl)]-3,22,24-trihydroxyolean-12-ene, 3-O-[O-(-d-glucopyranosyl)-(12)-(-glucuronopyranosyl)]-3,22,24-trihydroxyolean-12-ene, 3-O-[O-(-l-rhamnopyranosyl)-(12)-O-(-d-xylopyranosyl)-(12)-(-glucuronopyranosyl)]-3,22,24-trihydroxyolean-12-ene, 3-O-[O-(-l-rhamnopyranosyl)-(12)-O-(-d-glucopyranosyl)-(12)-(-glucuronopyranosyl)]-3,22,24-trihydroxyolean-12-ene, 3-O-methyl-d-chiro-inositol, and linolenic acid. In A. inopinatus, the same saponins were identified as well as tricosan-1-ol and tetracosan-1-ol, 5,7,4"-trihydroxyflavon (apigenin), and a tetracyclic triterpenoid, 20(R),24(S)-epoxycyclolanost-9(11)-ene-3,6,16,25-tetrol (cycloastragenol). All reported compounds from the both genus of Astragalus were isolated for the first time. Methanolic extracts of A. danicusand A. inopinatus exhibited low inhibitory activity with respect to the growth of HeLa cells. The chloroform fraction of A. danicus showed a strong antimicrobial activity against Staphylococcus aureus and a strong cytotoxic activity against HeLa cells.     

Radical scavenging properties of a flavouring agent–Vanillin

Using pulse radiolysis technique, the one-electron oxidation of vanillin (V-OH) with azide radicals, at pH 6 and 9 resulted in the formation of vanillin phenoxyl radical with k = 6.7 × 10⁷ and 2.5 × 10⁹ dm³ mol^-1 s^-1, respectively. The transient absorption spectra of the vanillin phenoxyl radical (V-O) formed either at pH 6 or 9, showed a _max at 410 nm. At pH 5, the OH radicals seem to form an adduct with vanillin, _max at 430 nm and k(OH + V-OH) = 3.3 × 10⁹ dm³ mol^-1 s^-1, while at pH 9, the OH radical reaction resulted in the formation of vanillin phenoxyl radical with _max at 410 nm and k(OH + V-O-) = 6.6 × 10⁹ dm³ mol^-1 s^-1. The reactivity of NO₂radicals with vanillin is lower by orders of magnitude signifying an incomplete reaction. In general, the rate constants for the reaction of OH, N, NO radicals with vanillin were higher at pH 9 than at the lower pH. Its reactivity with other one-electron oxidants like CCl₃OO, CHCl₂OO and CH radicals and the ability to chemically repair tryptophanyl and guanosyl radicals with k = 1.5 - 4 × 10⁷ dm³ mol^-1 s^-1 indicate its antioxidative behaviour.     

Kinetics and mechanism of the hydrolysis of sodium carboxymethylcellulose (Na-CMC) by a cellulase complex

TheSomogyi-Nelson colorimetric method is applied in a new manner more suitable for evaluating the kinetics of the enzyme hydrolysis of sodium carboxymethylcellulose (Na-CMC) catalyzed by the cellulase complex. By means of selective inhibition of a chosen enzyme from the cellulase complex it became possible to trace the effect of the other enzymes included in its composition.

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Kinetik und Mechanismus der Hydrolyse von Natriumcarboxymethylcellulose (Na-CMC) durch einen Cellulase-Komplex

Zusammenfassung Die kolorimetrische Methode nachSomogyi undNelson wird nach einem neuen Verfahren zur Verfolgung der Kinetik der hydrolytischen Spaltung von Natriumcarboxymethylcellulose (Na-CMC), katalysiert durch den Cellulase-Komplex, angewandt. Durch selektive Inhibierung eines bestimmten Enzyms des Cellulase-Komplexes kann man die Wirkung der anderen zu seiner gesamten Zusammensetzung gehörenden Enzyme verfolgen.

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Symbols Used E enzyme (E—cellulase;E—exo-cellobiohydrolase;E—-glucosidase) - [E] _w weight concentration of enzymeE - S substrate (Na-CMC—sodium carboxymethylcellulose) - [S]₀ weight concentration of substrateS - I inhibitor (I—lactose;I—calcium chloride;I—condurrite-B-epoxide) - P product (P—oligosaccharides;P—cellobiose;P—D-glucose) - P end product (K , K , K ) - DP degree of polymerization - DS degree of substitution - ES enzyme-substrate complex (E S, E S, E S) - EP enzyme-product complex (E P, E P) - EI enzyme-inhibitor complex (E I, E I, E I) - M _s molecular mass of substrateS - K _s substrate constant (K _s , K _s , K _s ) - K _I inhibitor constant (K _I , K _I , K _I ) - K _m Michaelis-Menten constant - k ₊₁,k ₊₂ (k ₊₂ ,k ₊₂ ,k ₊₂ ) forward rate constants - k _–1 reverse rate constant - ₀ initial rate of reaction - V maximal reaction rate - A change in absorbance - molar absorption coefficient - wavelength Herrn Prof. Dr.Hans Tuppy zum 60. Geburtstag herzlichst gewidmet.     

Synthesis and X-ray crystal structure of [1,3-bis(η5-cyclopentadienyl)-1,1,3,3-tetramethyldisiloxane]hafnium(IV) dichloride

Summary The tetramethyldisiloxane-bridged hafnocene complex [HfCl₂{-(⁵-C₅H₄)SiMe₂OSiMe₂(²-C₅H₄)}] (1) has been prepared by the reaction of HfCl₄ with the dilithiatedbis(cyclopentadienyl)disiloxane (LiC₅H₄SiMe₂)₂O in a molar ratio of 1:2. The new compound was characterized by spectroscopic and X-ray diffraction methods. The crystals are monoclinic of space groupP2₁/c and isostructural with the corresponding complexes of titanium and zirconium. The unit cell dimensions area=13.51(1) Å,b=8.672(7) Å,c=15.41(1) Å, =97.15(2)°, andZ=4.

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Darstellung und Röntgenkristallstruktur von [1,3-Bis(⁵-cyclopentadienyl)-1,1,3,3-tetramethyldisiloxan]hafnium(IV)dichlorid

Zusammenfassung Der tetramethyldisiloxan-überbrückte Hafnocenkomplex [HfCl₂{-(⁵-C₅H₄)-SiMe₂OSiMe₂(²-C₅H₄)}] (1) wurde durch Umsetzung von HfCl₄ mit dem lithiiertenBis(cyclopentadienyl)disiloxan (LiC₅H₄SiMe₂)₂O im Molverhältnis 1:2 dargestellt. Die neue Verbindung wurde spektroskopisch und röntgenographisch charakterisiert. Sie kristallisiert in der monoklinen RaumgruppeP2₁/c und ist isostrukturell mit den entsprechenden Titan-und Zirkoniumkomplexen. Die Dimensionen der Einheitszelle sinda=13.51(1) Å,b=8.672(7) Å,c=15.41(1) Å, =97.15(2)° undZ=4.

     

Effect of thick fixed-charge layers on electrostatic interaction — a theoretical approach

The electrostatic interaction pressure of charged surface layers is considered qualitatively and quantitatively. In the case of mutual penetration of the surface layers in addition to Maxwell stress and osmotic resp. hydrostatic pressure an isotropic stress on the fixed charges carrying molecules of the surface layers has to be taken into account. The derivation of the pressure-distance equations is given starting from both thermodynamic/electrostatic and hydrostatic/electrostatic principles. A possible biological significance of the additional stress is discussed emphasizing its role in modifying the structure of surface layer molecules.List of symbols e ₀ elementary charge - k Boltzmann constant - n _i concentration of theith ionic species in the bulk solution - P hydrostatic pressure - P hydrostatic pressure in the bulk volume (× ) - P ^h integration constant, independent on ×:P ^h =P(h) - T absolute temperature - Z _i electrovalence of theith ionic species - thickness of the surface layer - , ₀ relative and absolute permittivities - II(×) osmotic pressure at position × - II osmotic pressure in the bulk solution (× ) - osmotic pressure in the symmetry plane of interacting identical surface layers (electric field strength equals zero) - integration constant, independent on ×: - _e ^h electrostatic component of the disjoining pressure _e ^h = _e (h) - (×) mobile charge density profile (cations and anions of the electrolyte) - (×) fixed charge density profile - ^t(x) total charge density profile ( ^t = +) - ¹(x) fixed charge density profile of one of the two surface layers ( ¹(×) 0 for 0×) - (×) electric potential profile     

Spectral properties and temperature-dependence of semiconductivity of various doped bismuth trioxide polycrystals

Several samples of Nb₂O₅-doped Bi₂O₃ and Y₂O₃-doped Bi₂O₃ were carefully prepared and sintered at 700° for 3 hours. Extensive measurements were carried out on these samples, including X-ray diffraction spectra, infrared absorption spectra and the temperature-dependence of the DC-electrical conductivity in the solid state. The results obtained were discussed, correlated and interpreted. Finally, the optimum compositions were established and recommended for doped-Bi₂O₃ in the electronics industry.

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Zusammenfassung Einige Proben von mit Nb₂O₅ und Y₂O₃ gedopten Bi₂O₃ wurden hergestellt und bei 700 °C 3 Stunden gesintert. Von den Proben wurden Röntgendiffraktogramme und IR-Absorptionsspektren aufgenommen und die Temperaturabhängigkeit der elektrischen Gleichstromleitfähigkeit im festen Zustand gemessen. Die erhaltenen Ergebnisse werden diskutiert, zueinander in Beziehung gesetzt und interpretiert. Optimale Zusammensetzungen werden ermittelt und für gedoptes Bi₂O₃ in der Elektronikindustrie empfohlen.

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Bi₂O₃, Nb₂O₅ Y₂O₃, 3 700°. , . . , .

     

Stereospecific coordination ofl-hydroxyproline esters with triosmium clusters

The reactions of cluster (-H)Os₃(CO)₁₀(-OH) with ethyl and isopropyl esters ofl-oxyproline were studied. In the presence of Me₃NO intermediate complex (-H)Os₃(CO)₉(-OH)L (L — isopropyl ester ofl-oxyproline) is formed, which slowly converts to the more stable cluster (-H)Os₃(CO)₉ . Cluster complexes containing chelate-bridging heterocycles were also obtained by heating (-H)Os₃(CO)₁₀(-OH) with esters ofl-oxyproline. In both cases, only one of the possible diastereomeric complexes (-H)Os₃(CO)₉ (R = Et, Prⁱ) is formed, which indicates that the reactions are stereospecific. Based on analysis of Dreiding's models, an attempt to determine the absolute configuration of the obtained clusters was made.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2021–2025, October, 1995.     

Detector quantum efficiency: An important parameter for FT-IR spectroscopy

Spectral detectivities (D ^*()) are commonly used to characterize the sensitivity of infrared detectors, but for most spectroscopic purposes they are very misleading.For photon detectorsspectral detector quantum efficiencies ( _q ()) are needed in order to calculate the (S/N) ratio for the photon-noise limited situation. An equation to calculate _q(#x03C3;) fromD ^*() values is presented. The results for some common IR-detectors are surprising.As an application for the use of _q () values theS/N ratio of an FT-IR spectrum from an optimized FTS instrument under photon-limited conditions is given.     

On the Interaction of Two Finite-Dimensional Quantum Systems

Interaction of quantum system S ^a described by the generalised × eigenvalue equation A| _s =E _s S ^a | _s (s=1,...,) with quantum system S ^b described by the generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) is considered. With the system S ^a is associated -dimensional space X ^a and with the system S ^b is associated an n-dimensional space X _n ^b that is orthogonal to X ^a . Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]| _k = _k [S ^a +S ^b +P]| _k (k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S ^a ,S ^b and S=S ^a +S ^b +P are, in addition, positive definite. It is shown that each eigenvalue _{k i} of the combined system is the eigenvalue of the × eigenvalue equation . Operator in this equation is expressed in terms of the eigenvalues _i of the system S ^b and in terms of matrix elements _s |V| _i and _s |P| _i where vectors | _s form a base in X ^a . Eigenstate | _k ^a of this equation is the projection of the eigenstate | _k of the combined system on the space X ^a . Projection | _k ^b of | _k on the space X _n ^b is given by | _k ^b =( _k S ^b –B)^–1(V– _k P})| _k ^a where ( _k S ^b –B)^–1 is inverse of ( _k S ^b –B) in X _n ^b . Hence, if the solution to the system S ^b is known, one can obtain all eigenvalues _{k i} } and all the corresponding eigenstates | _k of the combined system as a solution of the above × eigenvalue equation that refers to the system S ^a alone. Slightly more complicated expressions are obtained for the eigenvalues _{k i} } and the corresponding eigenstates, provided such eigenvalues and eigenstates exist.     

Verfolgung der Verbrennungsreaktionen Exothermer Massen auf Basis von Aluminium,Fluoriden und Natriumverbindungen mit Differenzialthermoanalyse

Zusammenfassung Das Verbrennen von Mischungen der exothermen Systeme Al-NaF-NaNO₃ und Al-CaF₂-NaNO₃ wurde durch Röntgenanalyse ergänzte DTA untersucht. Um den Einfluß des durch Dissoziation von NaNO₃ gebildeten Sauerstoffs zu bestimmen wurden auch Mischungen, welche anstatt NaNO₃ NaNO₂ oder Na₂O₂ enthielten, geprüft.Zwei, bei 310° bzw. 850° einsetzende exotherme Reaktionen wurden in den Gemischen vom Typ Al-NaF-NaNO₃ gefunden. Die erste ist der Dissoziation von NaNO₃ zuzuschreiben, die zweite ist der Anwesenheit von Luft zuzuordnen.Beide exothermen Reaktionen wurden im System Al-CaF₂-NaNO₃ in Richtung höherer Temperaturen verschoben. Die Untersuchung der NaNO₂- oder Na₂O₂-haltigen Gemische anstatt NaNO₃ zeigte, daß die Dissoziation von NaNO₃ den zum Verbrennen benötigten Sauerstoff liefert, andererseits würde letztere Reaktion sonst nur in begrenztem Ausmaß stattfinden.

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Combustion of exothermic mixtures belonging to the system Al-NaF-NaNO₃ and Al-CaF₂-NaNO₃ was investigated by DTA and X-ray analysis. In order to determine the influence of the oxygen generated by dissociation of NaNO₃, the mixtures containing NaNO₂ or Na₂O₂ instead of NaNO₃ were also examined.Two exothermic reactions starting at 310° and 850° rsp. were found in the mixtures of the Al-NaF-NaNO₃ type. The first is due to the dissociation of NaNO₃ and the second proceeds independence of the availability of air.Both exothermic reactions were shifted to higher temperatures in the system Al-CaF₂-NaNO₃. Investigation of the mixtures containing NaNO₂ or Na₂O₂ instead of NaNO₃ has proved that the dissociation of NaNO₃ supplies the oxygen required for combustion which should otherwise proceed only in a limited extent.

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Résumé On a étudié, par ATD et par analyse aux rayons X, la combustion des mélanges exothermiques appartenant aux systèmes Al-NaF-NaNO₃ et Al-CaF₂-NaNO₃. Afin de déterminer l'influence de l'oxygène engendré par la dissociation de NaNO₃, on a étudié de même des mélanges contenant NaNO₂ ou Na₂O₂ au lieu de NaNO₃.On a trouvé, dans les mélanges du type Al-NaF-NaNO₃, des réactions exothermiques à partir des temperatures respectives de 310° et 850°. La première est due à la dissociation de NaNO₃ et la seconde dépend de l'air disponible.Dans le système Al-CaF₂-NaNO₃ les deux réactions sont déplacées vers les températures plus élevées. L'examen de mélanges contenant NaNO₂ ou Na₂O₂ au lieu de NaNO₃ à montré que c'est la dissociation de NaNO₃ qui fournit l'oxygène nécessaire pour la combustion. Celleci n'aurait lieu, autrement, que d'une manière limitée.

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, l-NaF-NaNO₃ Al-CaF₂-NaNO₃. , NaNO₃, , NaNO₃, , NaNO₂ Na₂. , Al-NaF-NaNO₃ , 310° 850°. , . Al-CaF₂-NaNO₃ . , NaNO₂ Na₂O₂, , , , , .

     

Formation of cobalt(iii) cations with semiquinonediimine ligands

The reactions of polynuclear cobalt(ii) trimethylacetates [Co(OH) _n (OOCCMe₃)_2–n ] _x , Co₆(₃-OH)₂(OOCCMe₃)₁₀(HOOCCMe₃)₄, or Co₄(₃-OH)₂(OOCCMe₃)₆(HOEt)₆ with an excess of N-phenyl-o-phenylenediamine (1) in toluene followed by treatment with atmospheric oxygen afforded the diamagnetic complex [Co{²-(NPh)(NH)C₆H₄}₂{¹-(NH₂)C₆H₄(NPhH)}]⁺(Me₃CCOO...H...OOCCMe₃)^– (3), whose cation contains the Co^III atom. The reaction of Co₄(₃-OH)₂(OOCCMe₃)₆(HOEt)₆ with a deficient amount of diamine 1 in acetonitrile under an argon atmosphere gave rise to the antiferromagnetic ionic complex [Co{²-(NPh)(NH)C₆H₄}₂MeCN]⁺[Co₂(₂,²-OOCCMe₃)(₂-OOCCMe₃)₂(²-OOCCMe₃)₂]^–·2MeCN (4), whose cation is an isoelectronic analog of the cation in complex 3. The structures of the new compounds were established by X-ray diffraction analysis.     

Systemes eau/surfactant ionique/alcool/hydrocarbure Influence de la nature de l'alcool sur la configuration du domaine de microémulsion et les propriétés de transport des microémulsions

The realms-of existence of water/sodium dodecylsulfate/C₄ to C₇ n-alkanols/n- dodecane monophasic, stable, fluid, transparent and isotropic media, (so-called microemulsions), were determined, atT=25 C, for different values of the surfactant/ alcohol mass ratiok _m. It was found that the configuration of the microemulsion domain in the system phase tetrahedron depends tightly upon that of the mutual solubility area of water, surfactant and alcohol. It has been possible to establish a general correlation between microemulsion domain configuration and microemulsion transport properties such as viscosity and electrical conductivity.

     

Dampfdruckmessungen und Protonenresonanzuntersuchung an Hydriden der intermetallischen Phasen Ti2(Ni,Co) und Ti2(Ni,Fe)

NMR and hydrogen equilibrium pressure measurements were performed on hydrides of the intermetallic compounds Ti₂(Ni, Co) and Ti₂(Ni, Fe). The following values of enthalpy H and entropy S for the formation of the hydrides of the intermetallic phases Ti₂Co and Ti₂Ni were found: H(Ti₂CoH _y )=–47.6 kJ/mol H₂, H(Ti₂NiH _y )=–53.7 kJ/mol H₂; S(Ti₂CoH _y )=–119.8 J/(K·mol H₂), S(Ti₂NiH _y )=–127.5 J/(K·mol H₂). By substitution of Ni or Co by Fe, the values of H and S of the corresponding quaternary hydrides become less negative. An interpretation of the experimental results is tried by the model ofShaltiel and coworkers.Proton diffusion was investigated in a series of the intermetallic hydrides Ti₂(Ni, Co)H _x and Ti₂(Ni, Fe)H _x . The diffusion rate is lowered by increased Ni/Fe substitution. Substitution of Ni by Co scarcely effects the hopping process. The activation energies were found to be smaller for the Ti₂Ni-hydrides compared with the Ti₂Co-hydrides.

Herrn Prof. Dr.H. Nowotny zum 70. Geburtstag gewidmet.     

The Molecular Structure and the Puckering Potential Function of Octamethylcyclotetrasilane,Si4Me8, Determined by Gas Electron Diffraction and Relaxation Constraints from Ab Initio Calculations

Gas electron diffraction data are applied to determine the geometrical parameters of the octamethylcyclotetrasilane molecule using a dynamic model in which the ring puckering is treated as a large amplitude motion. The structural parameters and parameters of the potential function were refined, taking into account the relaxation of the molecular geometry estimated from ab initio calculations at the Hartree–Fock level of theory using a 6-311G** basis set. The potential function has been described as V() = V ₀[(/ _e )² – 1]² with V ₀ = 1.0 ± 0.5 kcal/mol and _e = 28.3 ± 1.9°, where is the puckering angle of the ring. The geometric parameters at the minimum of V() (r _a in Å, in degrees and errors given as three times the standard deviations including a scale error) are as follows: r(Si—C)_av = 1.894(3), r(Si—Si) = 2.363(3), r(C—H) = 1.104(3), CSiC = 109.5(6), SiSiSi = 88.2(2), SiCH = 111.7(6), C = 4.1, where the tilt C was estimated from ab initio constraints. The structural parameters are compared with those obtained for related compounds.     

Theory of ring formation in a reversible system: general solutions

The enumeration theory is extended in this work into a more general theory, taking back-reactions into consideration. The solutions may faithfully reproduce real processes from arbitrary starting points to a steady-state. Therefore, the presented theory includes the equilibrium theory by Jacobson-Stockmayer, the numerical solution by Gordon-Temple, and the irreversible theory by the present authors. The solutions are described first in general forms of transition probabilities {P}, and then explicitly with the aid of rate equations; simple proofs are given. The presented theory was applied to an experimental data: the distribution of cyclic species in poly(ethylene terephthalate). We shall show that agreement between theory and experiment is nearly perfect.AB model N ₀ Total number of units - V System volume - C ₀=N ₀/N _A ·V Initial concentration (N _A : Avogadro's number) - L _x AB type chain x-mer; (AB)_x - N _x Number of AB type x-mers - R _x Ring x-mer - N _Rx Number of ring x-mers - E Small molecule eliminated by bond-formation - N _E Number of small molecules eliminated by bond-formation - h _k Number of reacted functional units (f.u.) in statek - _k Number of reacted functional units (f.u.) in chains in statek - _k Total number of units in chains in statek - D=h _k /N ₀ Extent of reaction in statek - D ^*= _k / _k Extent of reaction in chains in statek - k _L Chain-propagation rate constant - k _Rx Cyclization rate constant of chain x-mers - k _B Bond breakage rate constant of chains - k _B,Rx Bond breakage rate constant of cyclic x-mers - <k _Rx > _k Mean cyclization rate constant in statek - g(x)=k _B,Rx /k _B Ring-opening factor of cyclic x-mers - P _Lx,k Probability that a chain x-mer will be formed in statek - {P} Set of transition probabilities per single jump in forward direction or reverse direction (see the text on individual transition probabilities) AB model M _A Total AA monomer unit number - M _B Total BB monomer unit number - M ₀=M _A +M _B Total particle number - _A,i =2M _A –h _i Unreacted A functional unit (f.u.) number in statei - _B,i =2M _B –h _i Unreacted B f.u. number in statei - _Ax Unreacted A f.u. number on x-mers - h _i Number of reacted A (or B) f.u. in statei - _i Number of reacted A (or B) f.u. in chains in statei - _A,i =2M _A –h _i + _i A f.u. number in chains in statei - _B,i =2M _B –h _i + _i B f.u. number in chains in statei - _i =2(M ₀–h _i + _i ) Total f.u. number in chains in statei - D=h _i /M ₀ Extent of reaction in statei - D _A ^* = _i / _A,i Extent of reaction of A f.u. in chains in statei - D _B ^* = _i / _B,i Extent of reaction of B f.u. in chains in statei - D ^*=2 _i / _i Extent of reaction in chains in statei - L _x (AA-BB)_x-1-AA type chain x-mer;x=1,2,3,... - L _x BB-(AA-BB)_x type chain x-mer;x=0,1,2,... - L _x (AA-BB)_x type chain x-mer;x=1,2,3,... - N _x Number of type x-mers - N _x Number of type x-mers - N _x Number of type x-mers     

Synthesis of Co3(CO)7(μ-η3-Allyl)(μ3-X) Complexes (X=S, Se) and Structure of the Selenium Derivative

The complexes Co₃(CO)₉( ₃-X) (X=S, Se) can be reduced to the corresponding anionic species [Co₃(CO)₉( ₃-X)]^–, which react with allyl bromide to give Co₃(CO)₇(- ³-C₃H₅)( ₃-X) (X=S, Se). These are the first two cobalt complexes containing the bridging - ³-allyl ligand. The structure of the selenium complex was determined by X-ray crystallography. Crystal data for Co₃(CO)₇(- ³-C₃H₅)( ₃-Se) are as follows: space group P2₁/c, a=9.051(2) Å, b=8.102(2) Å, c=21.27(4) Å, =93.82(3)°, Z=4, and R=0.0565 for 2491 observed reflections.