Addition theorem and matrix elements of radiative multipole operators

The addition theorem for radiative multipole operators, i.e., electric-dipole, electric-quadropole, or magnetic-dipole, etc., is derived through a translational transformation. The addition theorem of μth component of the angular momentum operator, L _μ (r), is also derived as a simple expression that represents a general translation of the angular momentum operator along an arbitrary orientation of a displacement vector and when this displacement is along the Z-axis. The addition theorem of the multipole operators is then used to analytically evaluate the matrix elements of the electric and magnetic multipole operators over the basis functions, the spherical Laguerre Gaussian-type function (LGTF), . The explicit and simple formulas obtained for the matrix elements of these operators are in terms of vector-coupling coefficients and LGTFs of the internuclear coordinates. The matrix element of the magnetic multipole operator is shown to be a linear combination of the matrix element of the electric multipole operator     

Recurrence and Differential Relations for Spherical Spinors

We present a comprehensive table of recurrence and differential relations obeyed by spin one-half spherical spinors (spinor spherical harmonics) Ω_{κ μ}(n) used in relativistic atomic, molecular, and solid state physics, as well as in relativistic quantum chemistry. First, we list finite expansions in the spherical spinor basis of the expressions A·B Ω_κμ(n) and A·(B×C) Ω_κμ(n), where A, B, and C are either of the following vectors or vector operators: n=r/r (the radial unit vector), e ₀, e _±1 (the spherical, or cyclic, versors), (the 2×2 Pauli matrix vector), (the dimensionless orbital angular momentum operator; I is the 2×2 unit matrix), (the dimensionless total angular momentum operator). Then, we list finite expansions in the spherical spinor basis of the expressions A·B F(r)Ω_κμ(n) and A·(B×C) F(r)Ω_κμ(n), where at least one of the objects A, B, C is the nabla operator , while the remaining ones are chosen from the set .     

Stable [C2H7O2]+ isomers: Experimental and theoretical evidence for the existence of protonated peroxides and proton-bound dimers in the gas phase

Evidence is presented for the gas phase generation of at least eight stable isomeric [C₂H₇O₂]⁺ ions. These include energy-rich protonated peroxides (ions \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH}_2 {\rm O}\mathop {\rm O}\limits^{\rm + } {\rm H}_{\rm 2} $\end{document} (e), \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH}_{\rm 2} \mathop {\rm O}\limits^{\rm + } {\rm (H)OH} $\end{document} (f) and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm O}\mathop {\rm O}\limits^{\rm + } {\rm (H)CH}_{\rm 3} {\rm (g)),} $\end{document} (g)), proton-bound dimers (ions \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH = O} \cdot \cdot \cdot \mathop {\rm H}\limits^{\rm 3} \cdot \cdot \cdot {\rm OH}_{\rm 2} $\end{document} (h) and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH2 = O} \cdot \cdot \cdot \mathop {\rm H}\limits^{\rm + } \cdot \cdot \cdot {\rm HOCH}_{\rm 3} $\end{document} (i)) and hydroxy-protonated species (ions \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 2} {\rm (OH)CH}_{\rm 2} \mathop {\rm O}\limits^{\rm + } {\rm H}_{\rm 2} (a), $\end{document} \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH(OH)}\mathop {\rm O}\limits^{\rm + } {\rm H}_{\rm 2} $\end{document} (b) and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm OCH}_{\rm 2} \mathop {\rm O}\limits^{\rm + } {\rm H}_{\rm 2} $\end{document} (c)). The important points of the present study are (i) that these ions are prevented by high barriers from facile interconversion and (ii) that both electron-impact- and proton-induced gas phase decompositions seem to proceed via multistep reactions, some of which eventually result in the formation of proton-bound dimers.     

Structures and relative energies of gas-phase [C2H7N]+˙ radical cations

Ab initio molecular orbital calculations with split-valence plus polarization basis sets and incorporating electron correlation and zero-point energy corrections have been used to examine possible equilibrium structures on the [C₂H₇N]⁺˙ surface. In addition to the radical cations of ethylamine and dimethylamine, three other isomers were found which have comparable energy, but which have no stable neutral counterparts. These are \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm C}\limits^{\rm .} {\rm H}_{\rm 2} {\rm CH}_{\rm 2} \mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 3} $\end{document}, \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} \mathop {\rm C}\limits^{\rm .} {\rm H}\mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 3} $\end{document}and\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} \mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 2} \mathop {\rm C}\limits^. {\rm H}_{\rm 2} {\rm }, $\end{document} with calculated energies relative to the ethylamine radical cation of ?33, ?28 and 4 kJ mol^?1, respectively. Substantial barriers for rearrangement among the various isomers and significant binding energies with respect to possible fragmentation products are found. The predictions for \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm C}\limits^. {\rm H}_{\rm 2} {\rm CH}_{\rm 2} \mathop {\rm N}\limits^ + {\rm H}_{\rm 3} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} \mathop {\rm C}\limits^{\rm .} {\rm H}\mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 3}$\end{document} are consistent with their recent observation in the gas phase. The remaining isomer, \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} \mathop {\rm N}\limits^{\rm + } {\rm H}_{\rm 2} \mathop {\rm C}\limits^{\rm .} {\rm H}_{\rm 2} {\rm },$\end{document}is also predicted to be experimentally observable.     

Effect of long-chain branching on the relation between steady-flow and dynamic viscosity of polyethylene melts

The steady-state viscosity η, the dynamic viscosity η′, and the storage modulus G′ of several high-density and low-density polyethylene melts were investigated by using the Instron rheometer and the Weissenberg rheogoniometer. The theoretical relation between the two viscosities as proposed earlier is:\documentclass{article}\pagestyle{empty}\begin{document}$ \eta \left( {\dot \gamma } \right){\rm } = {\rm }\int {H\left( {\ln {\rm }\tau } \right)} {\rm }h\left( \theta \right)g\left( \theta \right)^{{\raise0.7ex\hbox{$3$} \!\mathord{\left/ {\vphantom {3 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}} \tau {\rm }d{\rm }\ln {\rm }\tau $\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$ \theta {\rm } = {\rm }{{\dot \gamma \tau } \mathord{\left/ {\vphantom {{\dot \gamma \tau } 2}} \right. \kern-\nulldelimiterspace} 2} $\end{document}; \documentclass{article}\pagestyle{empty}\begin{document}$ {\dot \gamma } $\end{document} is the shear rate, H is the relaxation spectrum, τ is the relaxation time, \documentclass{article}\pagestyle{empty}\begin{document}$ g\left( \theta \right){\rm } = {\rm }\left( {{2 \mathord{\left/ {\vphantom {2 \pi }} \right. \kern-\nulldelimiterspace} \pi }} \right)\left[ {\cot ^{ - 1} \theta {\rm } + {\rm }{\theta \mathord{\left/ {\vphantom {\theta {\left( {1 + \theta ^2 } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {1 + \theta ^2 } \right)}}} \right] $\end{document}, and \documentclass{article}\pagestyle{empty}\begin{document}$ h\left( \theta \right){\rm } = {\rm }\left( {{2 \mathord{\left/ {\vphantom {2 \pi }} \right. \kern-\nulldelimiterspace} \pi }} \right)\left[ {\cot ^{ - 1} \theta {\rm } + {\rm }{{\theta \left( {1{\rm } - {\rm }\theta ^2 } \right)} \mathord{\left/ {\vphantom {{\theta \left( {1{\rm } - {\rm }\theta ^2 } \right)} {\left( {1{\rm } + {\rm }\theta ^2 } \right)^2 }}} \right. \kern-\nulldelimiterspace} {\left( {1{\rm } + {\rm }\theta ^2 } \right)^2 }}} \right] $\end{document}. Good agreement between the experimental and calculated values was obtained, without any coordinate shift, for high-density polyethylenes as well as for a low density sample with low n_w, the weight-average number of branch points per molecule. The correlation, however, was poor with low-density samples with large values of the long-chain branching index n_w. This lack of coordination can be related to n_w. The empirical relation of Cox and Merz failed in a similar way.     

Structural study of alternating copolymerization of aziridines with cyclic imide

The structures of copolymers of aziridines with cyclic imides were determined by means of infrared spectrometry, paper electrophoresis of the hydrolyzate, and NMR spectrometry. The structure of the repeating unit in the copolymer of ethylenimine with succinimide was \documentclass{article}\pagestyle{empty}\begin{document}$\rlap{--} ({\rm CH}_2 {\rm CH}_2 {\rm NHCOCH}_2 {\rm CH}_2 {\rm CONH}\rlap{--} ) $\end{document}. The endgroups of the copolymer were N-acylethylenimine ring, N-substituted succinimide ring, and primary amide group. The copolymer of ethylenimine with N-ethylsuccinimide had the repeating unit of \documentclass{article}\pagestyle{empty}\begin{document}$ \rlap{--} [{\rm CH}_2 {\rm CH}_2 {\rm NHCOCH}_2 {\rm CH}_2 {\rm CON}({\rm C}_2 {\rm H}_5 )\rlap{--} ] $\end{document} and the endgroups of N-acylethylenimine and N-substituted succinimide ring. N-Ethylethylenimine did not copolymerize with succinimide, but in the presence of water, the reaction occurred to give an amorphous polymer. This copolymer had the repeating unit \documentclass{article}\pagestyle{empty}\begin{document}$ \rlap{--} [{\rm CH}_2 {\rm CH}_2 {\rm NHCOCH}_2 {\rm CH}_2 {\rm CON}({\rm C}_2 {\rm H}_5 )\rlap{--} ] $\end{document} and the endgroups were N-substituted succinimide ring and amine group but not N-acylethylenimine ring. On the basis of this structural information, the initiation reaction was discussed.     

Polymerization of σ-bonded organo-transition metal derivatives of styrene

Five new monomers of transition metal complexes containing a styryl group, trans-\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm Pd}({\rm PBu}_{\rm 3})_2 \rlap{--} ({\rm C}_6 {\rm H}_4 {\rm CH} \hbox{=\hskip-2pt=} {\rm CH}_2 ){\rm X\ X \hbox{=\hskip-2pt=} Cl(Ia),\ X \hbox{=\hskip-2pt=} Br(Ib)},\ {\rm X \hbox{=\hskip-2pt=} CN(Ic),\ X \hbox{=\hskip-2pt=} Ph(Id)} $\end{document} and trans-\documentclass{article}\pagestyle{empty}\begin{document}${\rm Pt(PBu}_{\rm 3} {\rm )}_{\rm 2} \rlap{--} ({\rm C}_{\rm 6} {\rm H}_{\rm 4} {\rm CH} \hbox{=\hskip-2pt=} {\rm CH}_2 ){\rm Cl}({\rm II})$\end{document}, were synthesized. The monomers were readily homopolymerized in benzene with the use of AIBN or BBu₃–oxygen as the initiator. Copolymerization of Ia with styrene was carried out by using AIBN. From the Cl content of the copolymers by analysis, monomer reactivity ratios and Q–e values were obtained as follows: r₁ = 1.49, r₂ = 0.45; Q₂ = 0.41, e₂ = ?1.4 (M₁ = styrene, M₂ = Ia). Based on the above data, the σ-bonded palladium moiety at para position of styrene acts as a strongly electron-donating group to the phenyl ring. This is also supported by the olefinic β-carbon chemical shift of ¹³C NMR for Ia.     

Kinetics and Equilibria for Complex Formation between Palladium(II) and Chloroacetate

Kinetics and equilibria for the formation of a 1:1 complex between palladium(II) and chloroacetate were studied by spectrophotometric measurements in 1.00 mol HClO₄ at 298.2 K. The equilibrium constant, K, of the reaction

High temperature polymers. I.—Sulfone ether diamines as intermediates for tractable high temperature polymers

A useful synthesis of a series of new aromatic sulfone ether diamines, H₂NC₆H₄O\documentclass{article}\pagestyle{empty}\begin{document}$\hbox{---}\hskip-5pt[\ {\rm C}_{\rm 2} {\rm H}_{\rm 4} {\rm SO}_{\rm 2} {\rm C}_{\rm 6} {\rm H}_{\rm 4} \hbox{--} {\rm ORO}\hbox{---}\hskip-5pt ]_n {\rm OC}_{\rm 6} {\rm H}_{\rm 4} {\rm SO}_{\rm 2} {\rm C}_{\rm 6} {\rm H}_{\rm 4} \hbox{---} {\rm OC}_{\rm 6} {\rm H}_{\rm 4} {\rm NH}_{\rm 2} $\end{document}, where n = 0, 1, 2…, which increases the tractability of polyimides, polyamide-imides, and polyamides, was developed. These diamines were prepared by condensing various proportions of sodium p-aminophenate, sodium bisphenates, and dichlorodiphenyl sulfone. The synthetic procedures are now refined to the point where simply coagulating these diamines into water yields high purity polymer-grade sulfone ether diamines. The latter have good tractability; and in some cases, it is possible to extrude and injection-mold these high temperature polymers.     

The gas-phase pyrolysis of alkyl nitrites. III. Isopropyl nitrite

The rate of decomposition of isopropyl nitrite (IPN) has been studied in a static system over the temperature range of 130–160°C. For low concentrations of IPN (1–5 × 10^?5M), but with a high total pressure of CF₄ (～0.9 atm) and small extents of reaction (～1%), the first-order rates of acetaldehyde (AcH) formation are a direct measure of reaction (1), since k₃ » k₂(NO): \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ {\rm IPN}\begin{array}{rcl} 1 \\ {\rightleftarrows} \\ 2 \\ \end{array}i - \Pr \mathop {\rm O}\limits^. + {\rm NO},i - \Pr \mathop {\rm O}\limits^. \stackrel{3}{\longrightarrow} {\rm AcH} + {\rm Me}. $\end{document} Addition of large amounts of NO (～0.9 atm) in place of CF₄ almost completely suppressed AcH formation. Addition of large amounts of isobutane – t-BuH – (～0.9 atm) in place of CF₄ at 160°C resulted in decreasing the AcH by 25%. Thus 25% of \documentclass{article}\pagestyle{empty}\begin{document}$ i - \Pr \mathop {\rm O}\limits^{\rm .} $\end{document} were trapped by the t-BuH (4): \documentclass{article}\pagestyle{empty}\begin{document}$ i - \Pr \mathop {\rm O}\limits^. + t - {\rm BuH} \stackrel{4}{\longrightarrow} i - \Pr {\rm OH} + (t - {\rm Bu}). $\end{document} The result of adding either NO or t-BuH shows that reaction (1) is the only route for the production of AcH. The rate constant for reaction (1) is given by k₁ = 10^{16.2±0.4–41.0±0.8}/θ sec^?1. Since (E₁ + RT) and ΔH°₁ are identical, within experimental error, both may be equated with D(i-PrO-NO) = 41.6 ± 0.8 kcal/mol and E₂ = 0 ± 0.8 kcal/mol. The thermochemistry leads to the result that \documentclass{article}\pagestyle{empty}\begin{document}$ \Delta H_f^\circ (i - {\rm Pr}\mathop {\rm O}\limits^{\rm .} ) = - 11.9 \pm 0.8{\rm kcal}/{\rm mol}. $\end{document} From ΔS°₁ and A₁, k₂ is calculated to be 10^10.5±0.4M^?1·sec^?1. From an independent observation that k₆/k₂ = 0.19 ± 0.03 independent of temperature we find E₆ = 0 ± 1 kcal/mol and k₆ = 10^9.8+0.4M^?;1·sec^?1: \documentclass{article}\pagestyle{empty}\begin{document}$ i - \Pr \mathop {\rm O}\limits^. + {\rm NO} \stackrel{6}{\longrightarrow} {\rm M}_2 {\rm K} + {\rm HNO}. $\end{document} In addition to AcH, acetone (M₂K) and isopropyl alcohol (IPA) are produced in approximately equal amounts. The rate of M₂K formation is markedly affected by the ratio S/V of different reaction vessels. It is concluded that the M₂K arises as the result of a heterogeneous elimination of HNO from IPN. In a spherical reaction vessel the first-order rate of M₂K formation is given by k₅ = 10^9.4–27.0/θ sec^?1: \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm IPN} \stackrel{5}{\longrightarrow} {\rm M}_2 {\rm K} + {\rm HNO}. $\end{document} IPA is thought to arise via the hydrolysis of IPN, the water being formed from HNO. This elimination process explains previous erroneous results for IPN.     

Bifunctional even-electron ions. II. Fragmentation behaviour of aliphatic ω-hydroxy and ω-methoxy methoxonium ions

Bifunctional methoxonium ions \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm R} -\mathop {\rm C}\limits^ + ({\rm OCH}_3 ) - ({\rm CH}_2 )_{\rm n} - {\rm OH}({\rm b}) $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm R} - \mathop {\rm C}\limits^ + ({\rm OCH}_3 ) - ({\rm CH}_2 )_{\rm n} - {\rm OCH}_3 ({\rm c}) $\end{document} (c) show as the main reactions those caused by functional group interaction, as has already been found for the analogous hydroxonium ions (g). Although there are similarities in the fragmentation behaviour of the isomeric ions b and g, their fragmentation pathways are different, proving b and g as distinct species. The dominant primary fragmentation for b and c is loss of CH₃OH. The hydrogen migrations prior to this reaction have been established by deuterium labelling. The findings on the fragmentation behaviour of the bifunctional methoxonium ions have been extended to the general behaviour of hydroxy and alkoxy substituted alkoxonium ions.     

Pyrolysis of dimethyl peroxide

By using isobutane (t-BuH) as a radical trapit has been possible to study the initial step in the decomposition of dimethyl peroxide (DMP) over the temperature range of 110–140°C in a static system. For low concentrations of DMP (2.5 × 10^?5?10^?4M) and high pressures of t?BuH (～0.9 atm) the first-order homogeneous rate of formation of methanol (MeOH) is a direct measure of reaction (1): \documentclass{article}\pagestyle{empty}\begin{document}${\rm DMP}\mathop \to \limits^1 2{\rm Me}\mathop {\rm O}\limits^{\rm .},{\rm Me}\mathop {\rm O}\limits^{\rm .} + t{\rm - BuH}\mathop \to \limits^4 {\rm MeOH} + t{\rm -}\mathop {\rm B}\limits^{\rm .} {\rm u}$\end{document}. For complete decomposition of DMP in t-BuH, virtually all of the DMP is converted to MeOH. Thus DMP is a clean thermal source of Me\documentclass{article}\pagestyle{empty}\begin{document}$\mathop {\rm O}\limits^{\rm .}$\end{document}. In the decomposition of pure DMP complications arise due to the H-abstraction reactions of Me\documentclass{article}\pagestyle{empty}\begin{document}$\mathop {\rm O}\limits^{\rm .}$\end{document} from DMP and the product CH₂O. The rate constant for reaction (1) is given by k₁ = 10^15.5?37.0/θ sec^?1, very similar to other dialkyl peroxides. The thermochemistry leads to the result D(MeO? OMe) = 37.6 ± 0.2 kcal/mole and /H(Me\documentclass{article}\pagestyle{empty}\begin{document}$\mathop {\rm O}\limits^{\rm .}$\end{document}) = 3.8 ± 0.2 kcal/mole. It is concluded that D(RO? OR) and D(RO? H) are unaffected by the nature of R. From ΔS and A₁, k₂ is calculated to be 10^10.3±0.5 M^?1· sec^?1: \documentclass{article}\pagestyle{empty}\begin{document}$2{\rm Me}\mathop {\rm O}\limits^{\rm .} \mathop \to \limits^2 {\rm DMP}$\end{document}. For complete reaction, trace amounts of t-BuOMe lead to the result k₂ ～ 10⁹ M^?1 ·sec^?1: \documentclass{article}\pagestyle{empty}\begin{document}$2t{\rm - Bu}\mathop \to \limits^5$\end{document} products. From the relationship k₆ = 2(k₂k_5a)^1/2 and with k_5a = 10^8.4 M^?1 · sec^?1, we arrive at the result k₆ = 10^9.7 M^?1 · sec^?1: \documentclass{article}\pagestyle{empty}\begin{document}$2t{\rm - u}\mathop {\rm B}\limits^{\rm .} \to (t{\rm - Bu)}_{\rm 2}{\rm,}t{\rm -}\mathop {\rm B}\limits^{\rm .} {\rm u} + {\rm Me}\mathop {\rm O}\limits^{\rm .} \mathop \to \limits^6 t{\rm - BuOMe}$\end{document}.     

An investigation of the decomposition of the intermediate ions produced by electron-impact. II—[C7H7]+ ions from several halogenotoluenes

The structure and decomposition of the [C₇H₇]⁺ ions produced by electron-impact from o-, m- and p-chlorotoluene, o-, m- and p-bromotoluence, and p-iodotoluence, have been investigated. By determining the relative abundance of normal and metastable ions, these [C₇H₇]⁺ ions at electron energy of 20 eV are shown to be so-called ‘tropylium ions’. The amount of the internal energy of the [C₇H₇]⁺ ion estimated by the relative ion abundance ratios, ? [C₅H₅]⁺/[C₇H₇]⁺ and m*/[C₇H₇]⁺ for the decomposition \documentclass{article}\pagestyle{empty}\begin{document}$ [{\rm C}_{\rm 7} {\rm H}_{\rm 7}]^ + \mathop \to \limits^{m^* } [{\rm C}_{\rm 5} {\rm H}_{\rm 5}]^ + + {\rm C}_{\rm 2} {\rm H}_{\rm 2} $\end{document}, is in the order iodotoluene > bromotoluene > chlorotoluene. The heats of formation of the activated complexes for the reaction \documentclass{article}\pagestyle{empty}\begin{document}$ [{\rm C}_{\rm 7} {\rm H}_{\rm 7}]^ + \mathop \to \limits^{m^* } [{\rm C}_{\rm 5} {\rm H}_{\rm 5}]^ + + {\rm C}_{\rm 2} {\rm H}_{\rm 2} $\end{document} were estimated. The values suggest that the decomposing [C₇H₇]⁺ ions from various halogenotoluenes are identical in structure.     

Synthesis of polyamides by the polyaddition of bissuccinimides with diamines

Polyamides which contain succinamide units, ? NHCO? (CH₂)₂? CONH? were prepared by the ring-opening polyaddition of bissuccinimides with diamines at 200°C. in bulk. Nylon 24 and nylon 64 were prepared by the reaction of N,N′-ethylenedisuccinimide with ethylenediamine and of N,N′-hexamethylenedisuccinimide with hexamethylenediamine, respectively. It was suggested that the transamidation reaction by aminolysis influenced the detailed structures of the polymers prepared from N,N′-ethylenedisuccinimide and hexamethylenediamine and from N,N′-hexamethylenedisuccinimide and ethylenediamine. The detailed structures of the polymers are discussed on the basis of their melting points and x-ray diagrams. It is concluded that the polymers contain a crystalline portion of \documentclass{article}\pagestyle{empty}\begin{document}$ \rlap{--}[{\rm NH \hbox{--} (CH}_2 {\rm)}_{\rm 2} {\rm \hbox{--} NHCO \hbox{--}}({\rm CH}_2)_2 {\rm \hbox{--} CONH \hbox{--}}({\rm CH}_2)_6 {\rm \hbox{--} NHCO \hbox{--}}({\rm CH}_2)_2 {\rm \hbox{--} CO\rlap{---}]} $\end{document} sequences.     

The vinyloxonium cation, \documentclass{article}\pagestyle{empty}\begin{document}${\rm CH}_{\rm 2} = {\rm CH - }\mathop {\rm O}\limits^{\rm + } {\rm H}_{\rm 2}$\end{document}, a stable [C2H5O]+ species in the gas phase

The charge stripping mass spectra of [C₂H₅O]⁺ ions permit the clear identification of four distinct species: \documentclass{article}\pagestyle{empty}\begin{document}${\rm CH}_{\rm 3} - {\rm O - }\mathop {\rm C}\limits^{\rm + } {\rm H}_{\rm 2}$\end{document}, \documentclass{article}\pagestyle{empty}\begin{document}${\rm CH}_{\rm 3} - \mathop {\rm C}\limits^{\rm + } {\rm H - OH}$\end{document}, and \documentclass{article}\pagestyle{empty}\begin{document}${\rm CH}_{\rm 2} = {\rm CH - }\mathop {\rm O}\limits^{\rm + } {\rm H}_{\rm 2}$\end{document}. The latter, the vinyloxonium ion, has not been identified before. It is generated from ionized n-butanol and 1,3-propanediol. Its heat of formation is estimated to be 623±12 kJ mol^?1. The charge stripping method is more sensitive to these ion structures than conventional collisional activation, which focuses attention on singly charged fragment ions.     

Gas phase ion chemistry of methyl acetate,methyl propanoate and their enolic tautomers. An experimental approach

From a combination of isotopic substitution, time-resolved measurements and sequential collision experiments, it was proposed that whereas ionized methyl acetate prior to fragmentation rearranges largely into \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_3 \mathop {\rm C}\limits^ + ({\rm OH}){\rm O}\mathop {\rm C}\limits^{\rm .} {\rm H}_2 $\end{document}, in contrast, methyl propanoate molecular ions isomerize into \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm C}\limits^. {\rm H}_2 {\rm CH}_2 \mathop {\rm C}\limits^ + ({\rm OH}){\rm OCH}_3 $\end{document}. Metastably fragmenting methyl acetate molecular ions are known predominantly to form H₂?OH together with \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_3 - \mathop {\rm C}\limits^ + = {\rm O} $\end{document}, whereas ionized methyl propanoate largely yields H₃CO˙ together with \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_3 {\rm CH}_2 - \mathop {\rm C}\limits^ + = {\rm O} $\end{document}. The observations were explained in terms of the participation of different distonic molecular ions. The enol form of ionized methyl acetate generates substantially more H₃CO˙ in admixture with H₂?OH than the keto tautomer. This is ascribed to the rearrangement of the enol ion to the keto form being partially rate determining, which results in a wider range of internal energies among metastably fragmenting enol ions. Extensive ab initio calculations at a high level of theory would be required to establish detailed reaction mechanisms.     

Kinetics of the reaction Cl + NO2 + M

The termolecular rate constant for the reaction Cl + NO₂ + M has been measured over the temperature range 264 to 417 K and at pressure 1 to 7 torr in a discharge flow system using atomic chlorine resonance fluorescence at 140 nm to monitor the decay of Cl in an excess of NO₂. The results are\documentclass{article}\pagestyle{empty}\begin{document}$k_1^{{\rm He}} = 9.4{\rm } \times {\rm }10^{ - 31} \left({\frac{T}{{300}}} \right)^{ - 2.0 \pm 0.05} {\rm cm}^6 {\rm s}^{ - {\rm 1}}$\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$k_1^{{\rm N}2} = (14.8{\rm } \pm {\rm }1.4){\rm } \times {\rm 10}^{ - 31} {\rm cm}^6 {\rm s}^{ - 1}$\end{document} at 296 K where error limits represent one standard deviation. The systematic error of k₁ measurements is estimated to be about 15%. Using a static photolysis system coupled with the FTIR spectrophotometer the branching ratio for the formation of the two possible isomers was found to be ClONO(?75%) and CINO₂(?25%) in good agreement with previous measurements.     

An entanglement model for the dependence of fracture surface energy on molecular weight

Over the last decade, empirical evidence has indicated that the effective surface energy γ associated with the fracture of noncrystalline is a linear function of the reciprocal of the viscosity–average molecular weight: \documentclass{article}\pagestyle{empty}\begin{document}$ \gamma = \gamma _\infty - b\bar M_v ^{ - 1} $\end{document}. For poly(methyl methacrylate), data of J. P. Berry, G. C. Berry and Fox show that gamma; ～ 0 at about the same value of M?_v that corresponds to the polymer chain-entanglement length. From this fact, we have developed an entanglement network model for fracture, that bears a resemblance to F. Bueche's entanglement model for the melt viscosity of bulk polymers. Our model allows for the expression of the previously empirical constants, γ_∞ and b, in terms of molecular parameters: \documentclass{article}\pagestyle{empty}\begin{document}$ {{\gamma _\infty = \gamma _{\rm s} A_{\rm s} Z_{\rm c} \rho _{\rm c} N_A } \mathord{\left/ {\vphantom {{\gamma _\infty = \gamma _{\rm s} A_{\rm s} Z_{\rm c} \rho _{\rm c} N_A } {\bar M_{\rm s} }}} \right. \kern-\nulldelimiterspace} {\bar M_{\rm s} }} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ b = 2({{\bar M_v } \mathord{\left/ {\vphantom {{\bar M_v } {\bar M_n }}} \right. \kern-\nulldelimiterspace} {\bar M_n }})\gamma _\infty M_{\rm f} $\end{document} where M?_n and M?_f are the number-average molecular weights of the polymer and of the free chain ends, M?_v is the viscosity-average molecular weight, γ_s is the average fracture-energy per entanglement in the craze volume, A_s is the average cross-sectional area of the polymer chain, Z_c and ρ_c are the thickness and density of crazed material on the fracture surface, respectively; M?_s is the average strand molecular weight between entanglements, and N_A is AvogadrO's number.     

Kinetics and mechanism of the reactions of the superoxide ion in solutions. I. Absorption spectra and interaction with solvents and cations

Absorption spectra of the superoxide ion have been studied in dimethylformamide (DMF) and acetonitrile (AN). It was found that the superoxide ion existed in equilibrium with an ion pair in AN (K_eq = 20M^?1, Bu₄N⁺ is the cation) and as “free” (solvated) ion in DMF. The addition of DMF caused the destruction of an ion pair in AN. The addition of the proton donors HX (water or ethanol) to the \documentclass{article}\pagestyle{empty}\begin{document}${\rm O}_{\rm 2}^{\overline {\rm .} }$\end{document} solutions in DMF and AN caused the formation of new ion pairs (Bu₄N⁺\documentclass{article}\pagestyle{empty}\begin{document}${\rm O}_{\rm 2}^{\overline {\rm .} }$\end{document})₂HX. The equilibrium constants of these ion pairs were determined in DMF and AN.