Role of gemini surfactants (m‐s‐m type; m = 16, s = 4–6) on the reaction of [Zn(II)‐Gly‐Phe]+ with ninhydrin

In the present paper, reaction of zinc‐glycylphenylalanine ([Zn(II)‐Gly‐Phe]⁺) with ninhydrin has been investigated in gemini (m‐s‐m type; m = 16, s = 4–6) surfactants at temperature (70 °C) and pH (5.0). Monitoring the appearance of product at 400 nm was used to follow the kinetics, spectrophotometrically. The order of the reaction with respect to [Zn(II)‐Gly‐Phe]⁺ was unity while with respect to [ninhydrin] was fractional. The reaction constants involved in the mechanism were obtained. In addition to the rate constant (k_Ψ) increase and leveling‐off regions are observed with the geminis, just like as seen with conventional surfactant hexadecyltrimethylammonium bromide (CTAB), the former produced a third region of increasing k_Ψ at higher concentrations. A close agreement between observed and calculated rate constants was found under varying experimental conditions. A suitable mechanism consistent with the experimental findings has been proposed. Copyright © 2014 John Wiley & Sons, Ltd.     

Alkane oxidation by the system ‘tert‐butyl hydroperoxide–[Mn2L2O3][PF6]2 (L = 1,4,7‐trimethyl‐1,4,7‐triazacyclononane)–carboxylic acid’

The kinetics of cyclohexane (CyH) oxygenation with tert‐butyl hydroperoxide (TBHP) in acetonitrile at 50 °C catalysed by a dinuclear manganese(IV) complex 1 containing 1,4,7‐trimethyl‐1,4,7‐triazacyclononane and co‐catalysed by oxalic acid have been studied. It has been shown that an active form of the catalyst (mixed‐valent dimeric species ‘Mn^IIIMn^IV’) is generated only in the interaction between complex 1 and TBHP and oxalic acid in the presence of water. The formation of this active form is assumed to be due to the hydrolysis of the Mn? O? Mn bonds in starting compound 1 and reduction of one Mn^IV to Mn^III. A species which induces the CyH oxidation is radical tert‐BuO ^. generated by the decomposition of a monoperoxo derivative of the active form. The constants of the equilibrium formation and the decomposition of the intermediate adduct between TBHP and 1 have been measured: K = 7.4 mol^?1 dm³ and k = 8.4 × 10^?2 s^?1, respectively, at [H₂O] = 1.5 mol dm^?3 and [oxalic acid] = 10^?2 mol dm^?3. The constant ratio for reactions of the monomolecular decomposition of tert‐butoxy radical (tert‐BuO ^. → CH₃COCH₃ + CH) and its interaction with the CyH (tert‐BuO ^. + CyH → tert‐BuOH + Cy ^. ) was calculated: 0.26 mol dm^?3. One of the reasons why oxalic acid accelerates the oxidation is due to the formation of an adduct between oxalic acid and 1 (K ≈ 10³ mol^?1 dm³). Copyright © 2007 John Wiley & Sons, Ltd.     

Kinetics of the gas‐phase homogeneous unimolecular elimination of selected ethyl esters of 2‐oxo‐carboxylic acids

The gas‐phase elimination kinetics of selected ethyl esters of 2‐oxo‐carboxylic acid have been studied over the temperature range of 270–415 °C and pressures of 37–114 Torr. The reactions are homogeneous, unimolecular, and follow a first‐order rate law in a seasoned static reaction vessel, with an added free radical suppressor toluene. The observed overall and partial rate coefficients are expressed by the following Arrhenius equations:

• Ethyl oxalyl chloride
• log k_overall (s^?1) = (13.22 ± 0.45) ? (179.4 ± 4.9) kJ mol^?1 (2.303 RT)^?1
• Ethyl piperidineglyoxylate
• log k_(CO2) (s^?1) = (12.00 ± 0.30) ? (191.2 ± 3.9) kJ mol^?1 (2.303 RT)^?1
• log k_(CO) (s^?1) = (12.60 ± 0.09) ? (210.7 ± 1.2) kJ mol^?1 (2.303 RT)^?1
• log k_t(overall) (s^?1) = (12.22 ± 0.26) ? (193.4 ± 3.4) kJ mol^?1 (2.303 RT)^?1
• Ethyl benzoyl formate
• log k_(CO2) (s^?1) = (12.89 ± 0.72) ? (203.8 ± 9.0) kJ mol^?1 (2.303 RT)^?1
• log k_(CO) (s^?1) = (13.39 ± 0.31) ? (213.3 ± 3.9) kJ mol^?1 (2.303 RT)^?1
• log k_t(overall) (s^?1) = (13.24 ± 0.60) ? (205.8 ± 7.6) kJ mol^?1 (2.303 RT)^?1

The kinetic and thermodynamic parameters of these reactions, together with those reported in the literature, lead to consider three different mechanistic pathways of elimination. Copyright © 2010 John Wiley & Sons, Ltd.     

Dimer radical cation of 4‐thiouracil: a pulse radiolysis and theoretical study

Pulse radiolysis with optical absorption detection has been used to study the reactions of hydroxyl radical (OH^?) with 4‐thiouracil (4TU) in aqueous medium. The transient absorption spectrum for the reaction of OH^? with 4TU is characterized by λ_max 460 nm at pH 7. A second‐order rate constant k_(4TU+OH) of 1.7 × 10¹⁰ M^?1 s^?1 is determined via competition kinetics method. The transient is envisaged as a dimer radical cation [4TU]₂^?+, formed via the reaction of an initially formed radical cation [4TU]^?+ with another 4TU. The formation constant of [4TU]₂^?+ is 1.8 × 10⁴ M^?1. The reactions of dibromine radical ion (Br₂^??) at pH 7, dichlorine radical ion (Cl₂^??) at pH 1, and azide radical (N₃^?) at pH 7 with 4TU have also produced transient with λ_max 460 nm. Density functional theory (DFT) studies at BHandHLYP/6–311 + G(d,p) level in aqueous phase showed that [4TU]₂^?+ is characterized by a two‐centerthree electron (2c‐3e) [?S∴S?] bond. The interaction energy of [?S∴S?] bond in [4TU]₂^?+ is ?13.01 kcal mol^?1. The predicted λ_max 457 nm by using the time‐dependent DFT method for [4TU]₂^?+ is in agreement with experimental λ_max. Theoretical calculations also predicted that compared with [4TU]₂^?+, 4‐thiouridine dimer is more stable, whereas 4‐thiothymine dimer is less stable. Copyright © 2013 John Wiley & Sons, Ltd.     

The kinetics and mechanism of the homogeneous,unimolecular gas‐phase elimination of 2‐(4‐substituted‐phenoxy)tetrahydro‐2H‐pyranes

The gas‐phase elimination kinetics of tetrahydropyranyl phenoxy ethers: 2‐phenoxytetrahydro‐2H‐pyran, 2‐(4‐methoxyphenoxy)tetrahydro‐2H‐pyran, and 2‐(4‐tert‐butylphenoxy)tetrahydro‐2H‐pyran were determined in a static system, with the vessels deactivated with allyl bromide, and in the presence of the free radical inhibitor toluene. The working temperature and pressure were 330 to 390°C and 25 to 89 Torr, respectively. The reactions yielded DHP and the corresponding 4‐substituted phenol. The eliminations are homogeneous, unimolecular, and satisfy a first‐order rate law. The Arrhenius equations for decompositions were found as follows:

• 2‐phenoxytetrahydro‐2H‐pyran
• log k₁ (s^?1) = (14.18 ± 0.21) ? (211.6 ± 0.4) kJ mol^?1 (2.303 RT)^?1
• 2‐(4‐methoxyphenoxy)tetrahydro‐2H‐pyran
• log k₁ (s^?1) = (14.11 ± 0.18) ? (203.6 ± 0.3) kJ mol^?1 (2.303 RT)^?1
• 2‐(4‐tert‐butylphenoxy)tetrahydro‐2H‐pyran
• log k₁ (s^?1) = (14.08 ± 0.08) ? (205.9 ± 1.0) kJ mol^?1 (2.303 RT)^?1

The analysis of kinetic and thermodynamic parameters for thermal elimination of 2‐(4‐substituted‐phenoxy)tetrahydro‐2H‐pyranes suggests that the reaction proceeds via 4‐member cyclic transition state. The results obtained confirm a slight increase of rate constant with increasing electron donating ability groups in the phenoxy ring. The pyran hydrogen abstraction by the oxygen of the phenoxy group appears to be the determinant factor in the reaction rate.     

Solid‐phase epitaxy of InOx Ny alloys via thermal oxidation of InN films on yttria‐stabilized zirconia

The characteristics of InO_x N_y alloy films prepared via thermal oxidation of InN epitaxial films with In‐ or N‐polarities grown on nearly lattice‐matched, yttria‐stabilized zirconia (YSZ) substrates are investigated. The InN films were oxidized to InO_x N_y with a gradual change in O/N composition by annealing in air. Structural analysis revealed that the temperature for phase transition from wurtzite structure depends on the polarity of InN, and N‐polar InO_x N_y films can retain their wurtzite structure even at higher temperatures compared with the case of In‐polar films. Furthermore, changes in the valence band structure and optical characteristics of the InO_x N_y alloys take place via thermal oxidation. These results indicate that InO_x N_y grown via thermal oxidation of N‐polar InN on YSZ can be considered as an alloy semiconductor for optoelectronic devices. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lithium solvation and diffusion in the 1‐butyl‐3‐methylimidazolium bis(trifluoromethanesulfonyl)imide ionic liquid

The Raman spectra of (1 − x)(BMITFSI), xLiTFSI ionic liquids, where 1‐butyl‐3‐methylimidazolium cation (BMI⁺) and bis(trifluoromethane‐sulfonyl)imide anion (TFSI⁻) are analyzed for LiTFSI mole fractions x < 0.4. As expected from previous studies on similar TFSI‐based systems, most lithium ions are shown to be coordinated within [Li(TFSI)₂]⁻ anionic clusters. The variation of the self‐diffusion coefficients of the ¹H, ¹⁹F, and ⁷Li nuclei, measured by pulsed‐gradient spin‐echo NMR (PGSE‐NMR) as a function of x, can be rationalized in terms of the weighted contribution of BMI⁺ cations, TFSI⁻ ‘free’ anions, and [Li(TFSI)₂]⁻ anionic clusters. This implies a negative transference number for lithium. Copyright © 2008 John Wiley & Sons, Ltd.     

Room‐temperature scavengers for macromolecular crystallography: increased lifetimes and modified dose dependence of the intensity decay

The advent of highly intense wiggler and undulator beamlines has reintroduced the problem of X‐ray radiation damage in protein crystals even at cryogenic temperatures (100 K). Although cryocrystallography can be utilized for the majority of protein crystals, certain macromolecular crystals (e.g. of viruses) suffer large increases in mosaicity upon flash cooling and data are still collected at room temperature (293 K). An alternative mechanism to cryocooling for prolonging crystal lifetime is the use of radioprotectants. These compounds are able to scavenge the free radical species formed upon X‐ray irradiation which are thought to be responsible for part of the observed damage. Three putative radioprotectants, ascorbate, 1,4‐benzoquinone and 2,2,6,6‐tetramethyl‐4‐piperidone (TEMP), were tested for their ability to prolong lysozyme crystal lifetimes at 293 K. Plots of relative summed intensity against dose were used as a metric to assess radioprotectant ability: ascorbate and 1,4‐benzoquinone appear to be effective, whereas studies on TEMP were inconclusive. Ascorbate, which scavenges OH radicals (k_OH = 8 × 10⁹ M^?1 s^?1) and electrons with a lower rate constant (k_e‐(aq) = 3.0 × 10⁸ M^?1 s^?1), doubled the crystal dose tolerance, whereas 1,4‐benzoquinone, which also scavenges both OH radicals (k_OH = 1.2 × 10⁹ M^?1 s^?1) and electrons (k_e‐(aq) = 1.2 × 10¹⁰ M^?1 s^?1), offered a ninefold increase in dose tolerance at the dose rates used. Pivotally, these preliminary results on a limited number of samples show that the two scavengers also induced a striking change in the dose dependence of the intensity decay from a first‐order to a zeroth‐order process.     

Hydrogen abstraction from H‐donor substrates by the 6‐CF3‐benzotriazol‐N‐oxyl radical (TFNO)

The aminoxyl radical 6‐trifluoromethyl‐benzotriazol‐N‐oxyl (TFNO) has been generated from the parent hydroxylamine 6‐CF₃‐1‐hydroxy‐benzotriazole (TFBT) by one‐electron oxidation with a Ce^IV salt and characterized by spectrophotometry and cyclic voltammetry (CV). Rate constants of H‐abstraction (k_H) by TFNO from a number of H‐donor benzylic substrates have been determined spectrophotometrically in MeCN solution at 25 °C. A radical H‐atom transfer (HAT) route of oxidation is substantiated for TFNO by several pieces of evidence. The kinetic data also testify the relevance of stereoelectronic effects upon the HAT reactivity of TFNO. Copyright © 2010 John Wiley & Sons, Ltd.     

Gas‐phase oxidation of CH2 = C(CH3)CH2Cl initiated by OH radicals and Cl atoms: kinetics and fate of the alcoxy radical formed

Relative kinetics of the reactions of OH radicals and Cl atoms with 3‐chloro‐2‐methyl‐1‐propene has been studied for the first time at 298 K and 1 atm by GC‐FID. Rate coefficients are found to be (in cm³ molecule^?1 s^?1): k₁ (OH + CH₂ = C(CH₃)CH₂Cl) = (3.23 ± 0.35) × 10^?11, k₂ (Cl + CH₂ = C(CH₃)CH₂Cl) = (2.10 ± 0.78) × 10^?10 with uncertainties representing ± 2σ. Product identification under atmospheric conditions was performed by solid phase microextraction/GC‐MS for OH reaction. Chloropropanone was identified as the main degradation product in accordance with the decomposition of the 1,2‐hydroxy alcoxy radical formed. Additionally, reactivity trends and atmospheric implications are discussed. Copyright © 2015 John Wiley & Sons, Ltd.     

Joint theoretical and experimental study of the gas‐phase elimination kinetics of tert‐butyl ester of carbamic,N, N‐dimethylcarbamic,N‐hydroxycarbamic acids and 1‐(tert‐butoxycarbonyl)‐imidazole

The gas‐phase elimination kinetics of the title compounds were carried out in a static reaction system and seasoned with allyl bromide. The working temperature and pressure ranges were 200–280 °C and 22–201.5 Torr, respectively. The reactions are homogeneous, unimolecular, and follow a first‐order rate law. These substrates produce isobutene and corresponding carbamic acid in the rate‐determining step. The unstable carbamic acid intermediate rapidly decarboxylates through a four‐membered cyclic transition state (TS) to give the corresponding organic nitrogen compound. The temperature dependence of the rate coefficients is expressed by the following Arrhenius equations: for tert‐butyl carbamate logk₁ (s^?1) = (13.02 ± 0.46) – (161.6 ± 4.7) kJ/mol(2.303 RT)^?1, for tert‐butyl N‐hydroxycarbamate logk₁ (s^?1) = (12.52 ± 0.11) – (147.8 ± 1.1) kJ/mol(2.303 RT)^?1, and for 1‐(tert‐butoxycarbonyl)‐imidazole logk₁ (s^?1) = (11.63 ± 0.21)–(134.9 ± 2.0) kJ/mol(2.303 RT)^?1. Theoretical studies of these elimination were performed at Møller–Plesset MP2/6‐31G and DFT B3LYP/6‐31G(d), B3LYP/6‐31G(d,p) levels of theory. The calculated bond orders, NBO charges, and synchronicity (Sy) indicate that these reactions are concerted, slightly asynchronous, and proceed through a six‐membered cyclic TS type. Results for estimated kinetic and thermodynamic parameters are discussed in terms of the proposed reaction mechanism and TS structure. Copyright © 2007 John Wiley & Sons, Ltd.     

Catalysis by hydrogen chloride in the gas‐phase elimination kinetics of 2‐phenyl‐2‐propanol and 3‐methyl‐1‐buten‐3‐ol

A homogeneous, molecular, gas‐phase elimination kinetics of 2‐phenyl‐2‐propanol and 3‐methyl‐1‐ buten‐3‐ol catalyzed by hydrogen chloride in the temperature range 325–386 °C and pressure range 34–149 torr are described. The rate coefficients are given by the following Arrhenius equations: for 2‐phenyl‐2‐propanol log k₁ (s^?1) = (11.01 ± 0.31) ? (109.5 ± 2.8) kJ mol^?1 (2.303 RT)^?1 and for 3‐methyl‐1‐buten‐3‐ol log k₁ (s^?1) = (11.50 ± 0.18) ? (116.5 ± 1.4) kJ mol^?1 (2.303 RT)^?1. Electron delocalization of the CH₂?CH and C₆H₅ appears to be an important effect in the rate enhancement of acid catalyzed tertiary alcohols in the gas phase. A concerted six‐member cyclic transition state type of mechanism appears to be, as described before, a rational interpretation for the dehydration process of these substrates. Copyright © 2007 John Wiley & Sons, Ltd.     

Electrochemical Studies on Substituted Iron-Hexacyanoiron(III) Bi-Layered Thin Films at Glassy Carbon Electrode/Electrolyte Interface

Thin films (30–50 nm) of bilayered HCM (hexacyanometalates) were prepared using direct electrodeposition or electrochemically driven insertion-substitution of PB (Prussian Blue) or InHCF (Indium Hexacyanoferrate) or K..In _x [Fe{CN}₆] _y , as starting material. The redox behavior of the immobilized counter/central ions at GCE/electrolyte interface have been investigated in aqueous KCl (pH 1) electrolytes using dynamic voltammetric techniques. Studies show that when the counter Fe or In ion is replaced by expandable partially filled d orbits elements such as Ru³⁺ a redox wave of the inserted counter ion is observed. Furthermore, the substitution of Fe as a counter ion with other poly-valent cations was found to be reversible if PB was the starting material. Studies were extended to include the EC (electrochemical) behavior of related HCM compounds such as K...Al _x [Fe{CN}₆] _y K, Ni _x [Fe{CN}₆] _y Cu _x [Fe{CN}₆] _y , K..Zn _x [Fe{CN}₆] _y and, K..Ru[Fe{CN}₆]₃. Unlike studied 3d cations, GCE modified with thin films of copper-hexacyanoiron (III) KCu _x [Fe{CN}₆] _y or CHF showed two redox waves with E^o _f 0.6, 0.9 V vs Ag/AgCl. Studies showed that even immobilized Cu ions were capable of catalyzing the oxidation of hydrazine and sulfite. The mechanism for electro-oxidation is also included.     

Hydrolytic reactions of cyclic bis(3′‐5′)diadenylic acid (c‐di‐AMP)

Hydrolytic reactions of cyclic bis(3′‐5′)diadenylic acid (c‐di‐AMP) have been followed by Reversed phase high performance liquid chromatography (RP‐HPLC) over a wide pH range at 90 °C. Under neutral and basic conditions (pH ≥ 7), disappearance of the starting material (first‐order in [OH^?]) was accompanied by formation of a mixture of adenosine 2′‐monophosphate and 3′‐monophosphate (2′‐AMP and 3′‐AMP). Under very acidic conditions (from H₀ = ?0.7 to 0.2), c‐di‐AMP undergoes two parallel reactions (first‐order in [H⁺]): the starting material is cleaved to 2′‐AMP and 3′‐AMP and depurinated to adenine (i.e., cleavage of the N‐glycosidic bond), the former reaction being slightly faster than the latter one. At pH 1–3, isomerization to cyclic bis(2′‐5′)diadenylic acid competes with the depurination. Copyright © 2012 John Wiley & Sons, Ltd.     

Micellar effects on aromatic nucleophilic substitution by the ANRORC mechanism. Hydrolysis of 2‐chloro‐3,5‐dinitropyridine

The hydrolysis of 2‐chloro‐3,5‐dinitropyridine by sodium hydroxide in the presence of micelles of cetyltrimethylammonium bromide (CTABr), cetyltrimethylammonium chloride (CTACl) and sodium dodecyl sulfate (SDS) has been studied. The reaction follows a consecutive reaction path involving the formation of a long‐lived intermediate 3 and finally giving the product, 3,5‐dinitro 2‐pyridone 2 . The mechanism follows an addition of the nucleophile, ring opening and ring closure (ANRORC) reaction path. The rate constant was observed to be first‐order dependent on [OH^?]. The rate of reaction increased on increasing [CTABr] and, after reaching to the maxima, it started decreasing. The anionic SDS micelles inhibited the rate of hydrolysis. The results of the kinetic experiments were treated with the help of the pseudophase ion exchange model and the Menger–Portnoy model. The added salts, viz. NaBr, Na‐toluene‐4‐sulphonate, and (CH₃)₄NBr on varying [CTACl] and [SDS] inhibited the rate of reaction. The various kinetic parameters in the presence and absence of salts were determined and are reported herewith. Copyright © 2011 John Wiley & Sons, Ltd.     

Lithium solvation in a PMMA membrane plasticized by a lithium‐conducting ionic liquid based on 1‐butyl‐3‐methylimidazolium bis(trifluoromethanesulfonyl)imide

The Raman and Infrared (IR) spectra of poly(methyl methacrylate) (PMMA) membranes plasticized by ionic liquids of the (1 − x)[1‐butyl‐3‐methylimidazolium bis(trifluoromethanesulfonyl)imide (BMITFSI)],xLiTFSI type, where BMI⁺ is the 1‐butyl‐3‐methylimidazolium cation and TFSI⁻ the bis(trifluoromethanesulfonyl)imide anion, are analyzed for a lithium bis(trifluoromethane sulfone)imide (LiTFSI) mole fraction x = 0.23 and PMMA contents from 0 to 50 wt%. The lithium is found to have an average coordination of about three CO groups and less than one TFSI⁻ anion. It plays the role of a cross‐linker between the ester groups of PMMA and the nonvolatile ionic liquid. Addition of PMMA to the (1 − x)(BMITFSI),xLiTFSI ionic liquid lowers the conductivity but might improve the lithium transference number by transforming the [Li(TFSI)₂]⁻ anionic clusters present in the pure ionic liquid into a mixed coordination by ester groups and TFSI⁻ anions. Copyright © 2008 John Wiley & Sons, Ltd.     

Composition dependent self‐regenerative property of perovskite‐type oxides

The self‐regenerative property of LaCo_{1–x –y}Pd_x Zn_y O_3±δ and LaFe_{1–x –y}Pd_x Zn_y O_3±δ solid solutions with monometallic Pd or bimetallic Pd/Zn substituents for Co or Fe is studied under a redox cycle by high angular annular dark‐field scanning transmission electron microscopy (STEM‐HAADF) and energy dispersive X‐ray spectroscopy (EDX) and X‐ray diffraction (XRD). These results reveal that the composition of perovskites determines the self‐regenerative property that occurs largely in LaCo_{1–x –y}Pd_x Zn_y O_3±δ but is limited greatly in LaFe_{1–x –y}Pd_x Zn_y O_3±δ. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Homo‐Diels–Alder reaction of a very inactive diene,bicyclo[2,2,1]hepta‐2,5‐diene,with the most active dienophile, 4‐phenyl‐1,2,4‐triazolin‐3,5‐dione. Solvent,temperature, and high pressure influence on the reaction rate

Solvent, temperature, and high pressure influence on the rate constant of homo‐Diels–Alder cycloaddition reactions of the very active hetero‐dienophile, 4‐phenyl‐1,2,4‐triazolin‐3,5‐dione (1), with the very inactive unconjugated diene, bicyclo[2,2,1]hepta‐2,5‐diene (2), and of 1 with some substituted anthracenes have been studied. The rate constants change amounts to about seven orders of magnitude: from 3.95^.10^?3 for reaction (1+2) to 12200 L mol^?1 s^?1 for reaction of 1 with 9,10‐dimethylanthracene (4e) in toluene solution at 298 K. A comparison of the reactivity (ln k₂) and the heat of reactions (?_r‐nH) of maleic anhydride, tetracyanoethylene and of 1 with several dienes has been performed. The heat of reaction (1+2) is ?218 ± 2 kJ mol^?1, of 1 with 9,10‐dimethylanthracene ?117.8 ± 0.7 kJ mol^?1, and of 1 with 9,10‐dimethoxyanthracene ?91.6 ±0.2 kJ mol^?1. From these data, it follows that the exothermicity of reaction (1+2) is higher than that with 1,3‐butadiene. However, the heat of reaction of 9,10‐dimethylanthracene with 1 (?117.8 kJ mol^?1) is nearly the same as that found for the reaction with the structural C=C counterpart, N‐phenylmaleimide (?117.0 kJ mol^?1). Since the energy of the N=N bond is considerably lower (418 kJ/bond) than that of the C=C bond (611 kJ/bond), it was proposed that this difference in the bond energy can generate a lower barrier of activation in the Diels–Alder cycloaddition reaction with 1. Linear correlation (R = 0.94) of the solvent effect on the rate constants of reaction (1+2) and on the heat of solution of 1 has been observed. The ratio of the volume of activation (?V^≠) and the volume of reaction (?V_r‐n) of the homo‐Diels–Alder reaction (1+2) is considered as “normal”: ?V^≠/?V_r‐n = ?25.1/?30.95 = 0.81. Copyright © 2012 John Wiley & Sons, Ltd.     

The self‐energy of the uniform electron gas in the second order of exchange

The on‐shell self‐energy of the homogeneous electron gas in second order of exchange, Σ_2x = Re Σ_2x (k_F, k² _F/2), is given by a certain integral. This integral is treated here in a similar way as Onsager, Mittag, and Stephen [Ann. Physik (Leipzig) 18 , 71 (1966)] have obtained their famous analytical expression e_2x = (in atomic units) for the correlation energy in second order of exchange. Here it is shown that the result for the corresponding on‐shell self‐energy is Σ_2x = e_2x. The off‐shell self‐energy Σ_2x (k, o) correctly yields 2e_2x (the potential component of e_2x) through the Galitskii‐Migdal formula. The quantities e_2x and Σ_2x appear in the high‐density limit of the Hugenholtz‐van Hove (Luttinger‐Ward) theorem.