High resolution nuclear-magnetic-resonance spectra of hydrocarbon groupings

The interpretation of ABC-type spectra is discussed in relation to several series of calculated spectra; some frequency and intensity sum rules are indicated.

The hydrogen spectra of some vinyl derivatives, X. CH = CH₂ (X = F, Cl, Br, O and C) have been analysed. It is shown that

and that a modified correlation holds between the J^gem coupling constants of CH₂ groups and the H-C-H angle in a range of molecules. All three coupling constants of the vinyl compounds decrease approximately linearly with the electronegativity of X; these effects are probably transmitted through the sigma bonds. By contrast the difference between the chemical shift of the = CH₂ group and that of the XHC = group is approximately linearly dependent on Taft's resonance parameter, σ_R , suggesting that the pi-electron distribution is principally concerned in this case.     

On the kinetics of a two-level system with a diffusion-modulated interaction

For a two-level system corresponding to a particle of spin ½ in a random field in the Z direction, the relaxation function

has been estimated, the magnitude Ω(t) being the sum of the isotropic interactions of the particle in question with particles j executing diffusional motion. Specifically Ω(t)=ω₀ + Σ ω(Mj, rj), where ω₀ = constant, M_j is a random time-independent parameter, ω(M, r) decreases with r faster than r ^-3 and r _j = r _j (t) is a diffusional, random function. From the expression for <σ⁺(t)>, we establish general features of the relaxation phenomenon for diffusional processes, and calculate the relaxation rate 1/T ₂ and relaxation shift Δω to be 1/T ₂-iΔω = 4π CAv_M λ _M , where C is the concentration of particles and λ _M is the scattering length for an equation of the Schrödinger type with an imaginary potential -iω(M, r) instead of U/?, and diffusion coefficient instead of ?/2m. We also found that for the case of ‘external’ relaxation, the Redfield approach proved valid only under the simultaneous restrictions of low concentration and weak interaction.     

Spin density distribution and stereochemistry of triphenylmethyl radical in solution

¹³C-E.S.R. coupling constants of triphenylmethyl radical are readily obtained from the model compound tris-(3,5-di-t-butylphenyl)-methyl. Twisting of the phenyl substituents in solution is proven for the first time by the observation of a considerable contribution from hyperconjugation to ac_ortho ^C. This twisting causes the unusually large a _meta ^H by π-σ interaction as proposed by Pople for twisted benzyl radicals. Two different sets of spin densities are obtained for C₁ and C₂ by employing ac₂ ^C, coupling constants of the ring protons and , depending on whether the σ-π parameters of Karplus and Fraenkel or those recently proposed by Strom, Underwood and Jurkowitz are used. The comparison of ac₁ ^C calculated from these spin densities with the experimental carbon-13 splitting at C₁ indicates some deviation from trigonal planarity at C₁ in solution when the σ-π-parameters of Karplus and Fraenkel are used. Use of the Strom, Underwood and Jurkowitz parameters, on the other hand, lead to pure sp² hybridization at C₁. The latter result is in contrast to the deviations from trigonal planarity observed previously for the central carbon atoms of triphenylmethyl radical in the gas phase and of tris-(p-nitrophenyl)-methyl in the solid state.     

Estimation of hyperfine coupling constants of 29Si nuclei in the radical anions of trimethylsilyl-substituted π-electron systems

An attempt has been made to relate the coupling constant a _Si of a ²⁹Si nucleus in the radical anions of nine trimethylsilyl derivatives of π-electron systems to the spin populations ρ _Si and of the silicon and the substituted carbon centre , respectively. For the parameter Q _CSi of the relation an absolute value of circa 20 gauss is found, whereas Q _Si appears not to be significantly different from zero. The coupling constants a _Si calculated by means of this relation agree moderately well with the experimental values (standard error circa 0·6 gauss). An HMO model in which the trimethylsilyl substituents are treated as pseudo-π-centres, with the parameters h _Si = -1·5 and k _CSi = 0·55, reproduces satisfactorily the spin distribution in the corresponding radical anions.     

Hyperfine coupling constants and their dependence on charge densities

In paramagnetic aromatic systems the relation between the hyperfine coupling constants a _H for the protons and the spin density ρ on the adjacent carbon atom is usually given by the relation a _H = -Qρ (McConnell) in which Q is a constant characteristic for the C-H bond. In the paramagnetic ions of aromatic molecules the carbon atoms have in general besides a non-zero spin density also a non-zero excess charge density.

If one takes into account both the effect of the spin density ρ and the excess charge density ε on the C-H bond, the following formula is obtained for the proton hyperfine coupling constant:

in which Q and K are predicted to be positive constants of the same order of magnitude.

Comparison with experimental data gives Q = 31·2 gauss; K = 17 gauss.     

Origin of the E.S.R. hyperfine anisotropy and the cos2 θ rule of the β-fluorine couplings

The origin of the hyperfine couplings of β-fluorine nuclei in free radicals has been studied using the hyperfine tensors determined for and in single crystals. The direction of the maximum principal element of the β-fluorine coupling tensor in was found to be very close to the direction of the maximum overlap of the fluorine 2p π orbital with the half-filled carbon 2p π orbital. This means that the spin density in the fluorine 2p π orbital is mainly due to the direct overlap with the carbon 2p π orbital and the contributions from the hyperconjugation and the spin polarization mechanisms are less important. The cos²θ rule, B ₀ + B cos²θ, for the β-fluorine coupling tensor was also derived from the conformational dependence of the overlap integral. Using the ratio of B/B ₀ calculated from the overlap integral together with the observed hyperfine tensor for , the absolute values of B ₂ and B were determined and results were applied to the β-fluorine coupling tensor of the rotating CF₃ group in . The calculated tensor is in very good agreement with the one observed.     

A re-interpretation of the E.P.R. spectrum of the 1,2,3,6,7,8-hexahydropyrene anion radical

The γ radiolysis of carbon tetrachloride at 77 K results in the formation of free radicals which are stable at 185 K and have been identified as ?Cl₃. These radicals trapped in crystallites of CCl₄ or at ‘boundaries’ give very different E.S.R. spectra. Their a _13C coupling constants are practically identical (117 G et 114 G). The structure of ?Cl₃ radicals has been determined: it is nonplanar and the angle has a value of 116°. The action of O₂ on the ?Cl₃ radicals leads to the CCl_{3 2} peroxide radicals whose a _13C coupling at 200 K is 6·15 G.

Après irradiation γ à 77 K du tétrachlorure de carbone, le seul radical stable à 185 K est le radical ?Cl₃. Le radical ?Cl₃, suivant qu'il est piégé au sein des cristallites de CCl₄ ou aux joints de grains, donne un spectre R.P.E. très différent.

Pour les deux types de radicaux, les constantes de couplage a _13C sont voisines (117 G et 114 G). On peut ainsi en déduire que le radical CCl₃ est non plan avec une valeur de 116° pour l'angle . Par action de l'oxygène sur le radical ?Cl₃, on a observé à 200 K le radical CCl_{3 2} dont la constante de couplage a _13C est 6,15 G.     

Molecular orientation correlations and reorientational motions in liquids carbon monoxide,nitrogen and oxygen at 77 K; A Raman and Rayleigh light-scattering study

Reorientational autocorrelation functions have been determined from measurements of depolarized vibrational Raman scattering for liquid carbon monoxide, nitrogen and oxygen at 77 K and atmospheric pressure. The autocorrelation functions, which for these liquids are not significantly affected by vibration-rotation interaction, reveal that free rotation is an important feature of the molecular motion in liquid nitrogen but is less important for carbon monoxide and oxygen. The differences in behaviour are discussed in terms of intermolecular forces.

New values for the depolarized Rayleigh scattering cross section have been determined from intensity measurements made relative to the 992 cm^-1 Raman line of benzene. These values are compared to those reported previously by the authors using a different intensity standard (Chem. Phys. Lett., 31, 355 (1975)). The scattering cross sections yield the following values , where ?_ij is the angle between the major axes of molecules i and j (i≠j) and P ₂ indicates the second Legendre polynomial: -0·15 ± 0·2 for CO, +0·30 ± 0·2 for N₂ and +0·40 ± 0·2 for O₂. The large errors result from uncertainties in the local field correction factor. The negative value for CO can be explained as a result of strong quadrupole interactions which tend to align neighbouring molecules perpendicular to one another. The forms of the reorientational cross-correlation functions determined from the current Raman data and previous Rayleigh data are briefly discussed.     

The Thermo-Field Emission of Electrons in Arc Discharges

Starting from the conventional theory of thermo-field emission of electrons from metal surfaces, the range of validity and the errors of several approximate emission formulae are examined that are additive or harmonic combinations of the limiting thermionic (Richardson) and field emission (Fowler—Nordheim) equations. An optimization of such kinds of equations results in the simple dependence (for example) (iTF electron current density, T temperature, F field strength, k, A, B etc. are constants), or (dependent on only one variable Y = T + β′F β′ = const.). If the emission equations are applied to arc cathodes, both T and F must be expressed as functions of the ion current (I_i) and the ion current density (j_i); a simple interpolating formula of the electron current density j_e adapted to numerical results in the case of Cu cathodes becomes (ā, B?, C?: constants).     

Anharmonic corrections for linear triatomic molecules subject to the Rennet-Teller effect

The effects of vibrational anharmonic terms and of the g_K -correction on the energy levels of a triatomic molecule in a degenerate electronic state are considered. The electronic wavefunctions are described using the approach first suggested in the original paper of Renner. Formulae for the anharmonic corrections in a number of different situations are derived. For an electronic Π state the corrections are given in the form where i runs over the various contributions and x ₁, x ₂, … depend on the anharmonic force constants. The functions F_i can be determined numerically (see equations (4.3) and 4.7)). For the case without spin-orbit interaction the F_i s are given explicitly to first order in ∈ in table 1. Further-more, the same results apply for levels with |K|=v ₂+1 even if the spinorbit interaction is not negligible. Explicit results for levels with |K|<v ₂ including spin-orbit interaction are given in tables 2 and 3. The cases with larger values for Λ (2, 3, …) are also considered. The energy level formulae for a Δ state differ from those derived earlier by Merer and Travis. In particular, the small separation between the vibronic Φ and Π levels with v ₂=1 is now found to be 4g_K . The additional terms that arise from end-over-end rotation of the molecule are discussed in § 6.     

The elastic stiffness constants of β-NH4LiSO4 around its phase transition at 460 K

The complete tensor of the elastic stiffness constantsC _ij (i,j=1 to 6) of -NH₄LiSO₄ has been measured in the temperature range 290 K to 540 K including the ferroelectric phase transition at 460 K, by the ultrasonic pulse echo overlap method.Some ultrasonic attenuation coefficients were determined.The elastic stiffness constants were calculated using Landau Theory. The elastic stiffness constants are all well described within this theory with the exception ofC ₆₆, which can not be reproduced with coupling terms allowed by group theoretical arguments. This together with double peaks observed in the specific heat and in sound attenuation in some directions leads one to suspect an intermediate phase between the paraelectric and the ferroelectric phases.