Expression of theSU(2) rotation matrices D( j ) in terms of normalized irreducible tensorial matrices

TheSU(2) rotation matricesD ^(j), specified in terms of axis and angle of rotation, are expressed as linear combination of normalized irreducible tensorial matricces (NITM) of rankl = 0 to 2j rotated to the polar angles of the axis. The rotated NITM are constructed from spherical harmonics of the same rank. Since this formulation requires no matrix products, it may be computationally more efficient than Euler angle formulas, particularly for largej. Rotated NITM and formulas for theD ^(j) withj = 1/2 andj = 1 are written out explicitly. A formula for the structure constants of the products of conformable NITM is also given in terms of 3-j and 6-j symbols.     

The effect of olefinic terminal chains on the mesomorphic properties of 4,4'-disubstituted diphenyldiacetylenes

New diphenyldiacetylenes of the type with A, B = H and/or F; m = 0, 1; n = 1-4; and X = C n H 2n + 1 , F, CF 3 or CN were synthesized and their mesomorphic properties determined by hot stage polarizing microscopy and DSC. When m = 0, all of these compounds showed only a nematic phase except when X = CF 3 when both nematic and smectic A phases were seen. Both clearing and melting temperatures were higher than those reported for substitution with the corresponding alkyl chains but the much larger increase in clearing temperatures produced considerably wider nematic phases. Eutectic mixtures of a few of these olefins yielded nematic materials also having much wider temperature ranges and higher clearing temperatures than the eutectic mixtures of the alkyl compounds, while retaining their high birefringence and low viscosities. Such materials are of interest for beam-steering devices.

Four of the diacetylenes with m = 1 ( A, B = H) were also prepared ( X = C 6 H 13 , F, n = 2, 3). When X was C 6 H 13 ( n = 2), the nematic range was smaller in the 2- than in the 1-olefin but wider than in the alkyl series. When X = F, either no nematic phase or a monotropic one was observed, whereas the 1-olefins gave a much wider nematic phase. Both transition temperatures were lower than those for the corresponding 1-olefin and alkyl analogues. The compound with X = C 6 H 13 and n = 2 had a melting temperature below room temperature.     

Inertia-preserving secant updates

Corrections to the last two equations of Ref. 1 are given.     

OVERVIEW OF EXPERIENCES WITH PHOTODYNAMIC THERAPY FOR MALIGNANCY IN 192 PATIENTS

Abstract From April 1982 to April 1986 we used photodynamic therapy to treat 192 patients with various malignancies. In all, 172 injections of hematoporphyrin derivative and 135 injections of dihematoporphyrin ether were made intravenously to sensitize the tumors; 684 photodynamic treatments were given using a tunable dye argon laser system for the light source. The technical problems of the light source and delivery systems are presented and the efficacy of therapy is analyzed.     

Structural transformations during the gas chromatography of carbamates

Summary There is no apparent paucity of examples illustrative of the structural changes observed during the gas chromatography of diverse carbamates and thiocarbamates. In many cases the resultat thermal degradation products observed are analogous in some measure to the three possible modes of decomposition reported in nonchromatographic thermal studies for N-phenyl carbamates [4, 35, 36], e.g., Dyer andWright [35] have shown that when R is a primary or secondary alkyl group, all three modes of decomposition can occur when the reaction is carried out in the absence of solvents. If the amine and isocyanate products are allowed to remain in the formation mixture, diphenyl urea is also formed, viz., As has been shown, the thermal and hydrolytic stabilities of carbamates exhibit a marked dependence upon the degree and type of N-substitution. Disubstituted carbamates are quite resistant to thermal decomposition (as well as hydrolysis). Monosubstituted carbamates readily undergo thermal decomposition at elevated temperatures to yield primarily the respective isocyanate while unsubstituted carbamates have been reported to decompose to allophanates, cyanuric acid, and alcohol [37]. The thermal decomposition of unsubstituted carbamates is accelerated appreciably in the presence of eventrace amounts of metal salts, giving rise to the formation of cyamelide. The degradative scheme for the diol dicarbamates (as typified by the medicinal carbamates, meprobamate and soma) is more difficult to interpret.Paquin [38] reported that the pyrolysis of the dicarbamate of 1,3-butylene glycol (I), yielded an oxazolidone (II) and a cyclic urea (III) as follows: The further degradation of compounds II and III under pyrolytic conditions remains a distinct possibility.

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Strukturumwandlungen w?hrend der Gas-Chromatographie von Carbamaten

Zusammenfassung Es besteht offenbar kein Mangel an Beispielen für Strukturumwandlungen w?hrend der Gas-Chromatographie verschiedener Carbamate und Thiocarbamate. In vielen F?llen entsprechen die beobachteten resultierenden thermischen Abbauprodukte in gewissem Ma?e den drei m?glichen Abbauformen, über die in nichtchromatographischen thermischen Untersuchungen von N-Phenylcarbamaten berichtet wird [4, 35, 36], z.B. Dyer Wright [35] haben gezeigt, da?, wenn R eine prim?re oder sekund?re Alkylgruppe ist, alle drei Abbauformen vorkommen k?nnen, wenn die Reaktion in Abwesenheit von L?sungsmitteln stattfindet. Wenn die Amin- und Isocyanat-Produkte in der Mischung belassen werden, bildet sich auch Diphenylharnstoff, n?mlich: Wie gezeigt wurde, besitzt die thermische und hydrolytische Stabilit?t von Carbamaten eine starke Abh?ngigkeit von Grad und Art der N-Substitution. Disubstituierte Carbamate sind ziemlich resistent gegen therm?sche Zersetzung (wie auch gegen Hydrolyse). Monosubstitutierte Carbamate lassen sich bei h?heren Temperaturen leicht thermisch zersetzen, wobei haupts?chlich das entsprechende Isocyanat entsteht, w?hrend sich unsubstituierte Carbamate nach [37] in Allophanate, Cyanurs?ure und Alkohol zersetzen. Der thermische Abbau unsubstituierter Carbamate wird durch Anwesenheit selbst geringer Spuren von Metallsalzen nennenswert beschleunigt, wobei Cyamelid entsteht. Das Abbauschema für die Diol-Dicarbamate (typische Beispiele: medizinische Carbamate, Meprobamat und Soma) ist schwieriger zu interpretieren.Paquin [38] berichtet, da? bei der Pyrolyse des Dicarbamats von 1,3-Butylenglycol (I) ein Oxazolidon (II) und ein cyclischer Harnstoff (III) in der folgenden Weise entstanden: Der weitere Abbau der Verbindungen II und III unter Pyrolysebedingungen ist nicht auszuschlie?en.

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Transformations de structure pendant la chromatographie en phase gazeuse de carbamates

Sommaire On ne manque pas d'exemples qui illustrent les transformations de structure observées pendant la chromatographie en phase gazeuse de divers carbamates et thiocarbamates. Souvent les produits de dégradation thermiques obtenus sont analogues, dans une certaine mesure, a ceux formés par décomposition thermique selon un des schémas probable signalé ci-après, procédés qui furent decrits pour des carbamates N-phényliques [4, 35, 36] dans des études de stabilité thermique non-chromatographiques, par exemple: Dyer etWright [35] ont démontré, si R est un groupe alkyle primaire ou secondaire, les trois modes de décomposition peuvent avoir lieu si la réaction se produit en l'absence de solvants. Si les amines et les isocyanates sont laissés dans le mélange, il y a aussi formation de diphénylurée, c'est-à-dire Il a été montré que la stabilité thermique et hydrolytique de carbamates dépend fortement du degré et type de la N-substitution. Des carbamates disubstitués sont assez résistants à la décomposition thermique (ainsi qu'à l'hydrolyse). Les carbamates monosubstitutés sont facilement sujets à la décomposition thermique à des températures élevées, produisant surtout l'isocyanate correspondant, tandis que, selon la littérature, des carbamates non-substitués sont décomposés en formant des allophanates, acide cyanurique, et alcool [37]. La décomposition thermique de carbamates non-substitués est accélérée sensiblement par la présence de sels métalliques, même à l'état de trace, provoquant la formation de cyamélide. Le schéma de dégradation des diol-dicarbamates (exemples typiques: carbamates médicinaux, méprobamate, soma) est plus difficile à interpréter.Paquin [38] a trouvé que la pyrolyse du dicarbamate de 1,3-butylène glycol (I) produit un oxazolidone (II) et une urée cyclique (III) d'après le schéma suivant: La dégradation ultérieure des composés II et III sous des conditions pyrolytiques n'est pas à exclure.

     

Direct detection of the biradicals generated in the Norrish type II reaction

The biradicals generated in the Norrish type II reaction from the triplet manifold have been observed using laser flash photolysis techniques. The spectra and extinction coefficients closely resemble those of typical ketyl radicals. Typical lifetimes are in the 40–100 ns range depending on the solvent. Their interaction with oxygen is essentially diffusion controlled.     

INTERACTION OF VIOLOGEN DYES WITH CHROMATOPHORES AND REACTION-CENTER PREPARATIONS FROM RHODOSPIRILLUM RUBRUM

Abstract —Various low-potential viologen dyes enhance light-induced absorption changes in the near-infrared region (ΔA870) in chromatophore preparations from Rhodospirillum rubrum in the presence of dichlorophenol indophenol and a high concentration of ascorbate (DCPIP + asc). An increase in ΔA870 was also observed in large reaction-center preparations from R. rubrum with viologens in the presence of ascorbate. Our results indicate that E'₀, of the primary electron acceptor X may be as low as -0.37 V, as suggested recently by P. A. Loach (1973, personal communication).     

PHYCOBILIPROTEINS: COMPARISON OF SOLUTION AND SINGLE CRYSTAL FLUORESCENCE FOR C-PHYCOCYANIN AND B-PHYCOERYTHRIN*

Abstract— Trimeric and hexameric solution forms of C-phycocyanin (CPC) from the cyanophyte Agme-nellum quadruplicatum have been isolated and their spectral properties compared to those obtained from single crystals. Although the absorbance peak of a suspension of small C-phycocyanin crystals is red-shifted only 7 nm relative to the solution forms, the single crystal fluorescence is red-shifted 60 nm relative to the solution forms. The crystal fluorescence spectrum exhibits a single peak at LD_max= 708 nm when excited at 514.5 or 530.9 nm and two peaks (LD_max= 661 and 708 nm) when excitation occurs at 568.2 nm. Fluorescence depolarization measurements indicate that extensive energy transfer could occur for both solution and crystal forms with the latter being dependent upon the relative orientation of the crystal with respect to the excitation dipole. Similar results were obtained with B-phycoerythrin (BPE) from the red alga Porphyridium cruentum where the single crystal fluorescence is red-shifted =50nm relative to the solution spectra with two peaks (LD_max= 583 and 617 nm) observed whose relative intensities are dependent on the excitation wavelength (LD_max– 514.5 and 530.9 nm). Single crystal fluorescent lifetimes exhibited considerable shortening relative to that observed for the solution forms. The implications of these results are discussed with respect to the possible relationships of the crystalline structures to the assembly forms present within phycobilisomes.     

A study of thermal decomposition of the solid-layered fluorocarbon,poly(carbon monofluoride)

Isothermal-thermogravimetric analyses were used to obtain kinetic data on the CF_x decomposition. Weight of samplevs. time curves were obtained for compounds having stoichiometries CF_0,61, CF_0.96, CF_1.08, and CF_1.12 for several different temperatures over the range 450–650° and in both a nitrogen atmosphere and in vacuum. A small percentage of fluorine in the atmosphere was shown to strongly inhibit thermal decomposition.These experimental results were fit to various theoretical models and it was found that a satisfactory fit was obtained by use of the Avrami equation, -In(1–)=(kt)ⁿ, where is the extent of reaction,k is an apparent rate constant, andn is an apparent reaction order. The valuen=2.0 was indicated which corresponds to planar growth of the decomposed phase.This information was combined with analytical data for the gaseous and solid products of decomposition to formulate a detailed mechanism.

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Zusammenfassung Isotherm-thermogravimetrische Analysen wurden durchgeführt um kinetische Daten über die Zersetzung von CF_x zu erhalten. Probengewicht-Zeit-Kurven wurden für Verbindungen mit stöchiometrischen Verhältnissen von CF_0.61, CF_0.96, CF_1.08 und CF_1.12 bei verschiedenen Temperaturen im Bereich von 450° bis 650°, in Stickstoff sowie im Vakuum aufgenommen. Ein geringer Prozentsatz an Fluor in der Atmosphäre wirkte stark inhibierend auf die thermische Zersetzung.Diese Versuchsergebnisse wurden verschiedenen theoretischen Modellen angepasst und es wurde gezeigt, dass mit Hilfe der Avrami-Gleichung -In (1–)=(kt)ⁿ eine befriedigende Anpassung möglich ist, wobei =Ausmaß der Reaktion, k=scheinbare Geschwindigkeitskonstante undn=scheinbare Reaktionsordnung ist. Der angedeutete Wertn=2.0 entspricht einer planaren Zunahme der zersetzten Phasen.Diese Information wurde mit analytischen Daten der gasförmungen und festen Zersetzungsprodukte kombiniert um einen Mechanismus in allen Einzelheiten zu formulieren.

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Résumé La TG isotherme a été utilisée pour obtenir des données cinétiques sur la décomposition de CF_x. Les courbes donnant le poids de l'échantillon en fonction du temps ont été energistrées à différentes températures, entre 450 et 650°, en atmosphère d'azote et sous vide, sur des composés de composition CF_0.61, CF_0.96 et CF_1.08. Un faible pourcentage de fluor dans l'atmosphèere s'est avéré inhiber considérablement la décomposition thermique.Ces résultats expérimentaux ont été confrontés à divers modèles mathématiques. On a trouvé un ajustement satisfaisant à l'aide de l'équation d'Avrami, -In (1–)=(kt)ⁿ, où es l'avancement de la réaction,k une constante de vitesse apparente etn un ordre de réaction apparent. La valeurn=2.0 correspond à une croissance dans le plan de la phase décomposée.Cette information a été combinée avec des données analytiques sur les produits de décomposition gazeux et solides, afin de formuler un mécanisme détaillé.

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- CF_x. — CF_0.61, CF_0.96, CF_1.08 F_1.12 450°–650°, , . . , -1(1–)= (kt)ⁿ, — , k — , n — . n=2, . , .

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Abstracted in part from the Ph. D. thesis of Peter Kamarchik, Jr. Rice University, Houston, Texas, May, 1976.

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This work was supported financially by the National Science Foundation, the U.S. Army Research Office (Durham), the National Aeronautics and Space Administration, and the Robert A. Welch Foundation. Liquid helium was provided under a grant from the Office of Naval Research.     

The use of Hückel theory charge densities and localization energies for the prediction of kinetic and thermodynamic factors involved in an assumed model for the hydrohalogenation of 1,3-butadiene,isoprene and chloroprene

It is assumed that the first step in the hydrohalogenation of a diene under conditions such that an ionic mechanism is operative involves the formation of a linear carbonium ion via attachment of a proton to the 1-position and that the second step involves addition of the halide ion to either the 2- or 4-positions. If it is also assumed that hyperconjugation plays some non-negligible role in the carbonium ion intermediate, then it turns out that the use of Hückel theory charge densities and localization energies predict (1) that the 1,2-product is kinetically favored in the cases of butadiene and isoprene, (2) that the 1,4-product is kinetically favored in the case of chloroprene, and (3) that the 1,4-product is thermodynamically favored in all of the above systems. All of these predictions appear to be in agreement with available experimental results.

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Zusammenfassung Bei der Addition von Halogenwasserstoffen an die hier untersuchten Diene wird im Reaktions-ablauf ein lineares Carbeniumion angenommen. Das Proton wird in 1-Stellung addiert und in einem zweiten Schritt wird das Halogenion in 2- oder 4-Stellung angelagert. Weiter wird angenommen, daß Hyperkonjugation beim intermediären Carbeniumion eine Rolle spielt. Aus den mit der Hückel-theorie ermittelten Ladungsverteilungen und Lokalisierungsenergien läßt sich dann voraussagen, daß (1) das 1,2-Produkt bei Butadien und Isopren, (2) das 1,4-Produkt bei Chloropren kinetisch und (3) das 1,4-Produkt in allen Fällen thermodynamisch bevorzugt ist. Diese Voraussagen scheinen mit den bekannten experimentellen Resultaten übereinzustimmen.

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Résumé On admet que l'hydrohalogénation d'un diène dans des conditions où prévaut un mécanisme ionique comporte comme première étape la formation d'un ion carbonium linéaire par addition d'un proton à la position 1 et comme seconde étape l'addition de l'ion halogène à l'une des positions 2 ou 4. Si l'on admet par ailleurs que l'hyperconjuguaison joue un rôle non négligeable dans l'intermédiaire carbonium, l'emploi de la théorie de Hückel permet de prédire à l'aide des densités de charge et des énergies de localisation (1) que le produit 1,2 est favorable du point de vue cinétique dans les cas du butadiène et de l'isoprène (2) que le produit 1,4 est favorable du point de vue cinétique dans le cas du chloroprène et (3) que le produit 1,4 est favorable du point de vue thermodynamique dans tous ces systèmes. Toutes ces prédictions sont apparemment en accord avec les résultats expérimentaux disponibles.