Radical Ions of a Bishomobinaphthylene Containing two 1,6-methano[10]annulene moieties: An ESR and ENDOR study

The radical cation and the radical anion of ‘syn’-cyclobuta[1,2-c:3,4-c′]di-1,6-methano[10]annulene (‘syn’-4a,12a:6a, 10a-bishomobinaphthylene; 3 ) have been characterized by their hyperfine data. The highly resolved ESR spectrum of $ 3^{+ \atop \dot{}} $ is dominated by a triplet splitting from the outer pair of methano β-protons (H_o). In contrast, the ESR spectrum of $ 3^{- \atop \dot{}} $ is poorly resolved with the largest coupling constants arising from perimeter α-protons. The different hyperfine features of $ 3^{+ \atop \dot{}} $ and $ 3^{- \atop \dot{}} $ are rationalized by MO models. The SOMO of $ 3^{+ \atop \dot{}} $ ψ_SA(b₁), has substantial LCAO coefficients of the same sign at the bridged atoms C(1), C(6), C(11), and C(16), whereas in the SOMO of $ 3^{- \atop \dot{}} $, ψ_SS(a₁), the four atoms lie in the vertical nodal planes. The large width and the reluctance to saturation of the lines in the ESR spectrum of $ 3^{- \atop \dot{}} $ are attributed to the near-degeneracy of the lowest antibonding MO's. Due to their similar nodal properties, the SOMO's of $ 3^{- \atop \dot{}} $ and the radical anions of binaphthylene ( 4 ), 1,6-methano[10]annulene ( 1 ), and naphthalene ( 2 ) are interrelated. Moreover, because the cyclic π-systems in 3 and 1 deviate in the same way from planarity, the effect of such distortions on the coupling constants, a_Hμ, of the perimeter α-protons in $ 3^{- \atop \dot{}} $ and $ 1^{- \atop \dot{}} $ should be comparable. Indeed, on going from $ 4^{- \atop \dot{}} $ to $ 3^{- \atop \dot{}} $, the |a_Hμ| values are reduced exactaly by half as much as the corresponding values on passing from $ 2^{- \atop \dot{}} $ to $ 3^{- \atop \dot{}} $, of which the cyclic π-systems are twice contained in $ 4^{- \atop \dot{}} $ and $ 3^{- \atop \dot{}} $ respectively.     

The Radical Cations of Bicyclo[2.2.1]hepta-2,5-diene (8,9,10-Trinorborna-2,5-diene) and bicyclo[2.2.2]octa-2,5-diene (2,3-Dihydrobarrelene). An ESR and ENDOR study

The radical cation of bicyclo[2-2.1]hepta-2,5-diene (8,9,10-trinorborna-2,5-diene; 1 ) in CF₂ClCFCl₂, and CF₃CCl₃ matrices and that of bicyclo[2.2.2]octa-2,5-diene (2,3-dihydrobarrelene; 2 ) in CFCl₃ and CF₃CCl₃ matrices have been studied by ESR and ENDOR spectroscopy. For ${\bf 1}^{+ \atop \dot{}}$, the coupling constants of the olefinic, methano-bridge, and bridgehead protons are ?0.780 ±0.005, +0.304±0.002, and ?0.049±0.002 mT, respectively. The hyperfine tensor for the methano-bridge protons is axial, A_x = +0.263 ± 0.002 and A_y = +0.386 ± 0.002 mT, while that for the olefinic protons is orthorhombic, A_x = ?0.594 ± 0.005, A_y= ?0.913 ± 0.005, and A_z = ?0.834 ± 0.005 mT (x parallel to C? H- z parallel to 2p_π axis). For ${\bf 2}^{+ \atop \dot{}}$, the coupling constants of the olefinic, ethano-bridge, and bridgehead protons are ?0.68 ± 0.01, +0.162 ± 0.005, and ?0.108 ± 0.005 mT, respectively. The hyperfine data for ${\bf 1}^{+ \atop \dot{}}$ and ${\bf 2}^{+ \atop \dot{}}$ fully support the presentation of their singly occupied orbitals as antisymmetric combinations, b₂(π), of the two bonding ethene π-MO's.     

Rearrangement of the Radical Anions of 1,6-Bridged[10]Annulenes to Derivatives of 5H-Benzocycloheptene and Benzotropylium

The rearrangement products obtained upon reduction of 1,6-methano[10]-annulene ( 1 ) and its 11-halogen derivatives have been studied by ESR. and, in part, by ENDOR. spectroscopy. These derivatives comprise 11,11-difluoro- ( 2 ), 11-fluoro- ( 3 ), 11,11-dichloro- ( 4 ) and 11-bromo-1,6-methano[10]annulene ( 5 ), as well as the 2,5,7,10-tetradeuteriated compounds 2 -D₄ and 3 -D₄. The studies of the secondary products in question have been initiated by the finding that the radical anion of 11,11-dimethyltricyclo[4.4.1.0^1,6]undeca-2,4,7,9-tetraene ( 12 ), i.e., the prevailing valence isomer of 11,11-dimethyl-1,6-methano[10]annulene, undergoes above 163 K a rearrangement to the radical anion of 5,5-dimethylbenzocycloheptene ( 14 ). A rearrangement of this kind also occurs for the radical anion of the parent compound 1 , albeit only above 323 K. The lower reactivity of 1 \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document} relative to 12 \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document} is rationalized by the assumption that the first and rate determining step in the case of 1 \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document} is the valence isomerization to the radical anion of tricyclo[4.4.1.0^1,6]undeca-2,4,7,9-tetraene ( 1a ). In the reducing medium used in such reactions (potassium in 1,2-dimethoxyethane), the final paramagnetic product of 1 \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document} is not 5H-benzocycloheptene ( 15 ), but the benzotropylium radical dianion ( ). This product ( ) is also obtained from the radical anions of the halogen-substituted 1,6-methano[10]annulenes, 2 to 5 , in the same medium. The temperatures required for the conversion of 2 \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document} and 3 \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document} into lie above 293 and 243 K, respectively, whereas the short-lived species 4 \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document} and 5 \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document} undergo such a rearrangement already at 163 K. The stability of the four halogen-substituted radical anions thus decreases in the sequence 2 \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document} > 3 \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document} > 4 \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document} ≈ 5 \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document}. Replacement of 2 \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document} and 3 \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document} by 2 -D₄\documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document} and 3 -D₄\documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document}, respectively, leads to 1,4,5,8-tetradeuteriobenzotropylium radical dianion ( ). Experimental evidence and theoretical arguments indicate that the rearrangements in question are initiated by a loss of one ( 3 \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document} and 5 \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document}) or two ( 2 \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document} and 4 \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document}) halogen atoms. Such a reaction step must involve the intermediacy of the radical 19 · (see below) which rapidly isomerizes to the benzotropylium radical 16 :. Support for the transient existence of 19 . is provided by the thermolysis of 1,6-methano [10]annulene-11-t-butylperoxyester (6) which yields 16 . in a temperature dependent equilibrium with a mixture of its dimers ( 16 ₂). In the hitherto unreported ESR. spectra of 2\documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document}. and 3\documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}} $\end{document}, the coupling constants of the ring protons differ considerably from the analogous values for the radical anions of other 1,6-bridged [10]annulenes. These differences strongly suggest that the fluoro-substitution substantially affects the character of the singly occupied orbital.     

The Radical Ions of Naphtho [1,8-cd]-[1,2,6]thiadiazine and Some of Its Derivatives

The radical cations and anions of naphtho [1,8-cd]-[1,2,6]thiadiazine (1) and 6,7-dihydroacenaphtho [5, 6-cd]-[1,2,6]thiadiazine (2) , as well as the radical anion of acenaphtho [5, 6-cd]-[1,2,6]thiadiazine (3) have been characterized by ESR. spectroscopy. The π-spin distributions in the radical cations \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\oplus \atop \dot{}}$\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ 2^{\oplus \atop \dot{}}$\end{document} strongly resemble those in the iso-π-electronic phenalenyl radical. A prominent feature of the radical anions \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}}$\end{document}, \documentclass{article}\pagestyle{empty}\begin{document}$ 2^{\ominus \atop \dot{}}$\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ 3^{\ominus \atop \dot{}}$\end{document} is the substantial localization of the π-spin population on the thiadiazine fragment. These findings are satisfactorily accounted for by HMO models using conventional heteroatom parameters.     

Einelektronen-Redoxreaktionen von 4-(1-Pyridinio)phenolat-Betain: ESR/ENDOR-Charakterisierung seiner Radikalionen und ‘Batterie-Effekt’

One-Electron Redox Reactions of 4-(1-Pyridinio)phenolate Betaine: ESR/ENDOR Characterization of its Radical Ions and ‘Battery Effect’ Blue zwitterionic 2,6-Di(tert-butyl)-4-(2,4,6-triphenyl-1-pyridinio)phenolate 1a can be reduced to its blue-green radical anion ${\bf 1}^{- \atop \dot{}}$ using alkaline metals, and oxidized to its colorless radical cation 1 by Ag(OOCCF₃) or electrochemically. ESR/ENDOR spectra of their aprotic THF solutions indicate predominant spin population either in the pyridinium (${\bf 1a}^{- \atop \dot{}}$) or in the phenolate ring (${\bf 1a}^{+ \atop \dot{}}$). Reduction with other alkaline metals Li, Na, or Cs yields no changes in the ESR/ENDOR signal patterns, i.e. provides no indication of radical ion pair formation. The cyclovoltammetrically determined first reduction and oxidation potentials at ?1.11 V and +0.26 V, respectively, are both reversible and, in principle, allow to construct a molecular battery.     

The Radical Anion of 1,2-Diphenylcyclopentene

ESR. and ENDOR. studies are reported for the radical anions of 1,2-diphenylcyclopentene ( 3 ) and its di(pe+deuteriophenyl)-derivative (3-D₁₀). Comparison of the coupling constants of the phenyl protons in 3 \documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document}. with the analogous values for the radical anions of 1,2-diphenyl substituted cyclopropene ( 1 ) and cyclobutene ( 2 ) reveals regular changes in the sequence 1 \documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document}, 2 \documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document}, 3 \documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document}, which are caused by an increasing twist of the phenyl groups about the C(1), C(1′)- and C(2), C(1″)-bonds linking them to the ethylene fragment. Such a twist is shown to be also responsible for the large difference in the coupling constants of the methylene β-protons in 3 \documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document}. (0.659 and 0.293 mT). It is suggested that - in order to minimize the losses caused by this twist in the π-delocalization energy - the 2 p_z-axes at the centres 1 and 2 deviate from a perpendicular orientation to the mean plane of the cyclopentene ring. A deviation by 19° from such an orientation is required to account for the observed β-proton coupling constants in terms of their conventional cos²-dependence on the dihedral angles θ.     

The Radical Anions of 5,5′- and 6,6′-Biazulenyl

ESR. and, in part, ENDOR. studies are reported on the radical anions of 5,5′-and 6,6′-biazulenyl ( 1 and 2 , resp.), as well as on their 1, 1′, 3, 3′-tetradeuterioderivatives ( 1 -d₄ and 2 -d₄). The reduction processes of 1 and 2 leading to these radical anions (\documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}}$\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ 2^{\ominus \atop \dot{}}$\end{document}) and the dianions ( ) have been investigated by polarography and cyclic voltammetry. The half-wave reduction potential of 1 and the π-spin distribution in \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{\ominus \atop \dot{}}$\end{document} are consistent with the model of two weakly interacting azulene π-systems, whereas the analogous findings for 2 and \documentclass{article}\pagestyle{empty}\begin{document}$ 2^{\ominus \atop \dot{}}$\end{document} point to a strong interaction between two such systems. This difference can be traced to the distinct inequality ∥c₆₅ ∥ « ∥ c₆₆ ∥ in the LCAO coefficients c_6μ at the centres μ=5 and 6 for the LUMO Ψ₆ of azulene.     

The Radical Anions of 1,2-diphenylcyclohexene and Structurally Related Compounds. Conformational ESR and ENDOR studies

ESR, ENDOR, and TRIPLE resonance studies have been performed on the radical anions of 1,2-diphenylcyclohex-1-ene ( 4 ), 1,2-di(perdeuteriophenyl)cyclohex-1-ene ((D₁₀) 4 ) the trans-configurated 3,4-diphenyl-8-oxabicyclo[4.3.0]non-3-ene ( 5 ) and its 2,2,5,5-tetradeuterio derivative (D₄) 5 , and 2,3-diphenyl-8,9,10-trinorborn-2-ene ( 6 ). The spectra of \documentclass{article}\pagestyle{empty}\begin{document}$ 4^{- \atop \dot{}} $\end{document} exhibit strong temperature dependence along with a specific broadening of ESR hyperfine lines and proton ENDOR signals. The coupling constant, which bears the main responsibility for these features, is that of the β-protons in the quasi-equatorial positions of the cyclohexene ring, and the experimental findings are readily rationlized in terms of relatively modest conformational changes without invoking the inversion of the half-chair form. The hyperfine data for the β-protons in \documentclass{article}\pagestyle{empty}\begin{document}$ 5^{- \atop \dot{}} $\end{document} closely resemble the corresponding low-temperature values for \documentclass{article}\pagestyle{empty}\begin{document}$ 4^{- \atop \dot{}} $\end{document}, However, the ‘unusual’ features observed for \documentclass{article}\pagestyle{empty}\begin{document}$ 4^{- \atop \dot{}} $\end{document} are absent in the ESR and ENDOR spectra of \documentclass{article}\pagestyle{empty}\begin{document}$ 5^{- \atop \dot{}} $\end{document}, because the half-chair conformation of the cyclohexene ring in \documentclass{article}\pagestyle{empty}\begin{document}$ 5^{- \atop \dot{}} $\end{document} is deprived of its flexibility. Although the boat form of this ring in \documentclass{article}\pagestyle{empty}\begin{document}$ 6^{- \atop \dot{}} $\end{document} is also rigid, the spectra of \documentclass{article}\pagestyle{empty}\begin{document}$ 6^{- \atop \dot{}} $\end{document} are temperature-dependent, due to an interconversion between two propeller-like conformations of the phenyl groups. The pertinent barrier is 30 ± 5 kJ ·mol^?1. An analogous interconversion presumably takes place in \documentclass{article}\pagestyle{empty}\begin{document}$ 4^{- \atop \dot{}} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ 5^{- \atop \dot{}} $\end{document} as well, but, unlike \documentclass{article}\pagestyle{empty}\begin{document}$ 6^{- \atop \dot{}} $\end{document}, it is not amenable to experimental study.     

The ESR. Spectrum of the Diphenylcyclopropenone Radical Anion

The ESR. spectrum of the relatively unstable radical anion of diphenylcyclo-propenone (II) has been observed upon electrolytic reduction of II in N,N-di-methylformamide and 1,2-dimethoxyethane. Simple MO models account well for the π-spin distribution and for the restricted rotation of the phenyl substituents in II\documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document}. A rather facile loss of a CO molecule by II\documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document} results in formation of the radical anion of tolane (diphenylacetylene; III). No ESR. spectra could be obtained for the radical anions of dialkylcyclopropenones which are even shorter-lived than II\documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document}, although decay by decarbonylation seems to be less favoured with them than with II\documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document}. In presence of air, electrolytic reduction of either II or its dimethyl and di-t-butyl analogues yields the correspondingly disubstituted semidione anions.     

Isomerization of the Radical Anions of 6a-Thiathiophthenes

The radical anions of 6a-thiathiophthenes ([1,2]dithiolo[1,5-b] [1,2]dithioles), I(R), convert into those of 4H-thiapyran-4-thiones, III(R), via cis-trans isomerization. The reaction is slowed down when the size of the substituent R in the 2,5-positions of 6a-thiathiophthene increases, and it is prevented by the introduction of a 3,4-polymethylene bridge. The primary and the secondary radical anions, I(R)\documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document} and III(R)\documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document}, respectively, exhibit very similar hyperfine splitting patterns. E.g., in the case of the unsubstituted 6a-thiathiophthene, I(H), and 4H-thiapyran-4-thione, III(H), the proton coupling constants are a_H2,5=6.72 and a_H3,4=1.73 Gauss for I(H)\documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document}, and a_H2,6=6.35 and a_H3,5=2.07 Gauss for III(H)\documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document}. In contrast to I(H)\documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document}, cis-trans isomerization could not thus far be proved to occur with its 1,6-dioxa-analogue, IV(H)\documentclass{article}\pagestyle{empty}\begin{document}$ ^{\ominus \atop \dot{}} $\end{document}, since no ESR. spectrum of the radical anion of 4H-pyran-4-thione, V(H), was detected upon reduction of IV(H).     

The Radical Anions of Some Substituted [2.2]Paracyclophanes

The radical anions of the following substituted [2.2]paracyclophanes have been characterized by ESR. and ENDOR. spectroscopy: 4, 16-dicyano- ( o - 2 ), 4, 12-dicyano- ( p - 2 ), 4,5,12,13-tetracyano- ( 3 ) and 4,5,12,13-tetrakis (alkoxycarbonyl)- [2.2]paracyclophanes ( 4-R , where R = Me, Et, iPr or tBu is the ester alkyl group); 4,5-bis(methoxycarbonyl)[2.2]paracyclophane-12, 13-dicarboxylic anhydride ( 5 ); [2.2]paracyclophane-4,5:12, 13-tetracarboxylic bisanhydride ( 6 ) and bisimides ( 7-R , where R = H, D, Me or Ph is the substituent at the imide N-atom). Comparison of the hyperfine data for these radical anions with those for analogously substituted derivatives of benzene indicates that the most prominent coupling constants are approximately halved on passing from the latter to the former. Lowering of the symmetry, as a consequence of ion pairing, has been observed for the radical anions 4- i Pr \documentclass{article}\pagestyle{empty}\begin{document}$^{\ominus \atop \dot{}}$\end{document} and 4- t Bu \documentclass{article}\pagestyle{empty}\begin{document}$^{\ominus \atop \dot{}}$\end{document} associated with the counterion K ⊕ in 1,2-dimethoxyethane at 183 K, but not for 4-Me \documentclass{article}\pagestyle{empty}\begin{document}$^{\ominus \atop \dot{}}$\end{document} and 4-Et \documentclass{article}\pagestyle{empty}\begin{document}$^{\ominus \atop \dot{}}$\end{document} under the same conditions. This result suggests that the migration of K ⊕ between the preferred sited in two equivalent ion pairs is slowed down by the steric hindrance arising from the bulky iPr and tBu ester groups.     

Theoretical study on peroxyl radical additions to methyl‐substituted ethenes

The electrophilic additions of hydroperoxyl (HO$_{2}^{\mbox{\mathversion{bold}$\cdot$}}$) and alkylperoxyl (RO$_{2}^{\mbox{\mathversion{bold}$\cdot$}}$) radicals to substituted ethenes were studied using the AM1 semiempirical molecular orbital (MO) methods at the self‐consistent field/unrestricted Hartree–Fock (SCF/UHF) level. Reactantlike transition states were predicted for the title additions. The reactivity of an alkylperoxyl radical toward ethenes was found to be decreased as the degree of methyl (Me) substitution on the alkyl group of the radical increased. The relative reactivity and regioselectivity in HO$_{2}^{\mbox{\mathversion{bold}$\cdot$}}$ additions to substituted ethenes was suggested to be SOMO (singly occupied)‐HOMO controlled. A good correlation was established between the activation enthalpy $(\Delta H_{f}^{\ast})$ for the studied additions and the Taft polar substituent constants (σ*) of RO$_{2}^{\mbox{\mathversion{bold}$\cdot$}}$. The Evans–Polanyi correlation between $\Delta H^{\mbox{\mathversion{bold}$\cdot$}}_{f}$ and $\Delta H^{\circ}_{r}$ was justified and the validity of the Hammond postulate was indicated. The calculated results were compared with the available experimental data. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 761–771, 2000     

Radical Anions of Cyclic Azoalkanes: An ESR,ENDOR, and TRIPLE-Resonance Study

Radical anions of ten monocyclic and bicyclic azoalkanes containing the azo group in (Z)-conformation, have been fully characterized by their hyperfine data with the use of ESR, ENDOR, and general-TRIPLE-resonance spectroscopy. These azoalkanes are represented by 3,3,5,5-tetramethyl-1-pyrazline ( 1 ), 2,3-diazabicyclo[2.2.1]hept-2-ene ( 4 ), and 2,3-diazabicyclo[2.2.2]oct-2-ene ( 9 ), as well as by their derivatives 2, 3, 5–8 , and 10. For all radical anions $1^{- \atop \dot{}}-10^{- \atop \dot{}}$, the ¹⁴N-coupling constant, a_N, is in the range of +0.83 to +0.97 mT; this finding indicates that the spin population is essentially restricted to the π system of the azo group. The ¹⁴N-hyperfine anisotropy largely affects the width of ESR lines, particularly at low temperatures. Substantial coupling constants of ⁷Li-, ²³K-, and ¹³³Cs-nuclei point to a close association of the radical anions with their alkakimetal counterions. With the exception of ³⁹K, these nuclei give rise to readily observable ENDOR signals which appear along with those stemming from protons. The prominent hyperfine features of $1^{- \atop \dot{}}-10^{- \atop \dot{}}$ are discussed.     

Shear thinning and polymer deformation in large flow fields

We theoretically investigate polymer deformation and shear thinning, i.e., a decrease of intrinsic viscosity, in a dilute polymer solution as a function of the applied shear rate $ \dot \gamma $. We use a bead-and-spring model with hydrodynamic interaction in the Rouse-Zimm framework, approximately accounting also for excluded-volume effects, and impose a constraint on the average mean-square spring length to prevent its stretching at large $ \dot \gamma $. When suitably normalized, both the intrinsic viscosity [η] and the components of the mean gyration tensor 〈SS〉 depend on the single variable $ \xi = {{\dot \gamma \tau _1^{\left( 0 \right)} } \mathord{\left/ {\vphantom {{\dot \gamma \tau _1^{\left( 0 \right)} } {N^{1 - v} }}} \right. \kern-\nulldelimiterspace} {N^{1 - v} }} $ where τ is the longest relaxation time for $ \dot \gamma = 0 $, N is the number of chain springs and v is the Flory exponent. The full shear-rate dependence is obtained numerically, and compared with analytical results obtained under free-draining conditions both for low and for very large shear rates. The shortcomings of the theory are also discussed, in particular a substantial stretching under shear of the central springs, where the intramolecular tension is largest, with a corresponding strong contraction of the end springs due to the average character of the constraint.     

Laserflash-photolysis of the p-Chloranil/naphthalene system: Characterization of the naphthalene radical cation in a fluid medium,

Excitation of p-Chloranil ( CA ) in propylcyanide (PrCN) at room temperature leads to rapid production of ³ CA * which decays predominantly to CA H· with k = 1.6 · 10⁵ s^?1. Observation of a photoinduced current suggests simultaneous production of CA ^? formed by electron transfer quenching of ³ CA * by the medium. Added naphthalene ( NP ) quenches ³ CA * with k_q = 7.0 · 10⁹M ^?1S ^?1; NP ⁺ is unambigously identified as product (besides CA ^?) of the electron transfer process. Dissociation of the ion pair occurs with essentially unit probability. Higher concentrations of NP lead to the formation of ( NP )⁺₂. Pertinent spectroscopic parameters established for NP ⁺ under the conditions used are λ_max = 685 nm (? = 2970) using the known parameters of CA \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{+ \atop \dot{}} $\end{document} as reference. NP ⁺ and CA \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{+ \atop \dot{}} $\end{document} decay by charge annihilation with k_r = 4.5 · 10⁹ M ^?1S ^?1. The deviation from the diffusion controlled rate constant expected for ionic species, is discussed in view of the spin characteristics of the process. Comparison with two other ion recombination reactions leads to the conclusion that ‘inverted behaviour’ as expected from Marcus' theory does also not show up for backward e^?-transfer between two ions (produced by forward e^?-transfer between two neutrals). Residual absorptions in the system are ascribed to CA H·, tentatively proposed to originate from H⁺-abstraction by CA \documentclass{article}\pagestyle{empty}\begin{document}$ 1^{+ \atop \dot{}} $\end{document} from the solvent. NP ⁺ appears to be a rather stable species with respect to the medium if the latter is meticulously purified.     

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.     

The Radicals and Radical Dianions of Bridged [11]- and [15]Annulenyls as Compared with Those of Benzotropyl and 2,3-Naphthotropyl

The 1,6-methano[11]annulenyl ( 1 ·), 1,6:8, 14-propane-1,3-diylidene[15]annulenyl ( 2 ·), benzotropyl ( 3 ·) and 2,3-naphthotropyl ( 4 ·) radicals have been characterized by their ESR. spectra. The corresponding radical dianions, , , and , have also been studied both by ESR. and ENDOR. spectroscopy. Assignment of the coupling constants a_Hμ to protons in the individual positions μ of these radicals and radical dianions is to a large extent based on investigations of specifically deuteriated derivatives. The radicals 1· , 2· , 3· and 4· exist in temperature-dependent equilibria with ( 1 )₂, ( 2 )₂, ( 3 )₂ and ( 4 )₂, respectively, where ( 1 )₂ to ( 4 )₂ denote mixtures of dimers of 1 · to 4 ·. The dissociation enthalpies, ΔH°, of ( 1 )₂ (102 kJ/mol) and ( 2 )₂ (88 kJ/mol) are considerably smaller than those of ( 3 )₂ and ( 4 )₂ which do not significantly differ from the ΔH° value of bitropyl (139 ± 6 kJ/mol). This finding indicates that the gain in π-electron delocalization energies, Δ(DE)_π, upon dissociation markedly increases on going from bitropyl, ( 3 )₂ and ( 4 )₂ to ( 1 )₂ and ( 2 )₂, and thus points to an additional ‘resonance stabilization’ of 1 · and 2 ·, as compared with 3 · and 4 ·. A more pronounced π-spin localization on the 7-membered ring is observed in 3 ·, 4 ·, and relative to the corresponding species, 1 ·, 2 ·, and . It can be interpreted in terms of simple π-perimeter models without explicitly invoking substantial homoconjugative interactions between the bridged centres in 1 ·, 2 ·, and . However, the shortcomings of these crude models do not allow one to make a clear-cut statement about the contributions of the homotropyl structures to the π-systems of these paramagnetic species. The radical dianions and exhibit considerable hyperfine splittings from one ²³Na or ³⁹K nucleus of the counter-ion, whereas for and such splittings stem from two equivalent alkali metal nuclei. This finding is readily rationalized by different geometries of the bridged annulenyls and their benzo- and naphthotropyl analogues. Hyperfine data are also given for the radical anions of 7 H-benzocycloheptene, ( 3-H )\documentclass{article}\pagestyle{empty}\begin{document}$2^{\ominus \atop \dot{}}$\end{document}, and 6 H-(2,3-naphtho)cycloheptene, ( 4-H )\documentclass{article}\pagestyle{empty}\begin{document}$2^{\ominus \atop \dot{}}$\end{document}, as well as for the radical dianion of 1,6:8,14-bismethano[15]annulenyl, 5 \documentclass{article}\pagestyle{empty}\begin{document}$2^{\ominus \atop \dot{}}$\end{document}.     

Photoreduction of Thiosulfate in Semiconductor Dispersions

Conduction band electrons produced by band gap excitation of TiO₂-particles reduce efficiently thiosulfate to sulfide and sulfite. \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm 2e}_{{\rm cb}}^ - ({\rm TiO}_{\rm 2}) + {\rm S}_{\rm 2} {\rm O}_3^{2 - } \longrightarrow {\rm S}^{2 - } + {\rm SO}_3^{2 - } $\end{document} This reaction is confirmed by electrochemical investigations with polycrystalline TiO₂-electrodes. The valence band process in alkaline TiO₂-dispersions involves oxidation of S₂O to tetrathionate which quantitatively dismutates into sulfite and thiosulfate, the net reaction being: \documentclass{article}\pagestyle{empty}\begin{document}$ 2{\rm h}^{\rm + } ({\rm TiO}_{\rm 2}) + 0.5{\rm S}_{\rm 2} {\rm O}_{\rm 3}^{{\rm 2} - } + 1.5{\rm H}_{\rm 2} {\rm O} \longrightarrow {\rm SO}_3^{2 - } + 3{\rm H}^{\rm + } $\end{document} This photodriven disproportionation of thiosulfate into sulfide and sulfite: \documentclass{article}\pagestyle{empty}\begin{document}$ 1.5{\rm H}_{\rm 2} {\rm O } + 1.5{\rm S}_{\rm 2} {\rm O}_{\rm 3}^{{\rm 2} - } \mathop \to \limits^{h\nu} 2{\rm SO}_3^{2 - } + {\rm S}^{{\rm 2} - } + 3{\rm H}^{\rm + } $\end{document} should be of great interest for systems that photochemically split hydrogen sulfide into hydrogen and sulfur.     

Exact solution of the relativistic dynamics of a spin‐½ particle moving in a homogeneous magnetic field

The relativistic dynamics of one spin‐½ particle moving in a uniform magnetic field is described by the Hamiltonian $\mathbf{h}^{0}_{D}(\pi)=c\alpha\cdot\pi+\beta mc^{2}$. The discrete (and semidiscrete) eigenvalues and the corresponding eigenspinors are in principle known from the work of Dirac, Rabi, and Bloch. These are extensively reviewed here. Next, exact solutions are worked out for the recoil dynamics in relative coordinates, which involves the Hamiltonian $\mathbf{h}^{0}_{D}(-\mathbf{k})=-c\alpha\cdot\mathbf{k}+\beta mc^{2}$. Exact solutions are also explicitly calculated in the case where the spin‐½ particle has an anomalous magnetic moment such that its Hamiltonian is given by $\mathbf{h}_{D}(\pi)=\mathbf{h}^{0}_{D}(\pi)-\beta\mu_{\mathrm{ano}}\sigma\cdot\mathbf{B}$. Similar exact solutions are derived here when the recoiling particle has an anomalous magnetic moment, that is, the eigenvalues and eigenspinors of the Hamiltonian $\mathbf{h}_{D}(-\mathbf{k})=\mathbf{h}^{0}_{D}(-\mathbf{k})-\beta\mu_{\mathrm{ano}}\sigma\cdot\mathbf{B}$ are explicitly obtained. The diagonalized and separable form of the Hamiltonian h _D(π), written as $\tilde{\mathbf{h}}_{D}(\pi)$, has exceedingly simple forms of eigenspinors. Similarly, the diagonalized and separable form of the operator h _D(? k ), written as $\tilde{\mathbf{h}}_{D}(-\mathbf{k})$, has very simple eigenspinors. The importance of these exact solutions is that the eigenspinors can be used as bases in a calculation involving many spin‐½ particles placed in a uniform magnetic field. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 209–217, 2001