The molecular g values,magnetic susceptibility anisotropies,and the molecular quadrupole moments in ethylene sulphide

The first and second-order Zeeman effect has been observed in the rotational transitions in ethylene sulphide to yield the molecular g values and magnetic susceptibility anisotropies. These data are

and

The a axis bisects the CSC angle and the b axis is also in the molecular plane. Only the relative signs of the molecular g values can be obtained experimentally. However, by comparing the molecular quadrupole moments calculated with both sets of g values, we can assign the signs as shown above.

The molecular quadrupole moments are

and

all in units of 10^-26 e.s.u. cm². These molecular quadrupole moments are compared to other similar molecules. The values of the diagonal elements in the paramagnetic susceptibility tensor are

and

all in units of 10^-6 erg/g ² mole. The anisotropies in the second moment of the electronic charge distributions are

and

all in units of 10^-16 cm².     

Natural embedding of group in NMR spin algebras

NMR aspects of finite group natural-embeddings in higher n-fold spin algebras over Hilbert space are considered in the context of icosahedral cage clusters associated with specific ¹¹B borohydride, -deuteride anions for which n = 12. The focus of the discussion is on the abstract and physical models derived from permutation modules in the form of λ ├ n partitions over , where . Hence, the related Kostka expansion coefficients from the pure abstract spin space of mapping and other -combinatorial aspects, including the nature of inner tensor products arising in the high-n limit, are especially pertinent. Further insight into spin cluster NMR problems is provided by studies of -induced algebras derived from the [λ_SA] self-associated irreps. Motivation for the work comes from its potential physical applications for higher-n bi-cluster NMR problems, e.g., in spin dynamics. The representational properties derived are essential in understanding the structure of Liouville space for both SU(2) and higher spin SU(m) clusters. The Hilbert space aspects presented here impact strongly on the somewhat neglected question of the nature of subduction, i.e., involving a finite group naturally embedded in a higher group, within an implicit dual Racah symmetry chain. The essential mappings presented here include both the λ module-onto-{[λ′]} set and the aspects, where the Kostka integers of the former arise naturally in the realization of λ module mappings over .     

Rotational band contour analysis in the 2760 Å system of p-chlorofluorobenzene

The origin band of the 2760 å system of p-chlorofluorobenzene has been shown to be a type B band of a prolate asymmetric top. The electronic assignment of the system is therefore ¹ B ₂-¹ A ₁.

The excited state rotational constants are:

compared with the estimated ground state constants:

The rotational origin of the band is at 36275·1 ± 0·2 cm^-1.     

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.     

Comment on the determination of the intermolecular potential energy function of neon from spectroscopic,equilibrium and transport data

A quantum-mechanical treatment of the dynamics of relaxation of a twolevel mode coupled to a thermal bath is presented. The Zwanzig-Mori projection-operator formalism is employed to derive exact equations of motion for the correlation function and the excess population , where and are the coordinate and number operators associated with the two-level mode. In the van Hove weak-coupling limit it is shown that |G _ν|² and Δn decay exponentially with time constants τ and τ′, respectively. Explicit expressions for τ and τ′ are determined and the relationship between them clearly established. The application of the model to the specific problem of the effects of vibrational relaxation on isotropic Raman spectral lineshapes in dense media is emphasized.     

The gas-phase electron paramagnetic resonance spectrum of vibrationally excited SO radicals

Gas-phase E.P.R. spectra from the first six vibrational levels in X ³Σ^- SO have been detected and analysed using a Hund's case (b) formalism. The spectra can be fitted using the following molecular constants:

The first and second derivatives of with respect to the normalized internuclear distance ξ were calculated from these constants. A simple analytic formalism is described which enables the variation of with internuclear distance to be separated into contributions from the matrix elements and from the change in energy spacing between interacting states. Both effects are important in the derivatives of , but it is suggested that in SO most of the variation of with rotational and vibrational state is due to the increase in the second-order part of the parameter as the separation between the ground and the dominant perturbing state decreases. This explanation implies that the expression proposed recently by Veseth and Lofthus for the rotational variation of is not accurate, and enables the conflict between the results of their analysis and ab initio calculations to be resolved.     

Spectral intensities of the trivalent lanthanides

The variation of the Judd-Ofelt parameters across the isostructural series of ions, [LnW₁₀O₃₅]^7- is considered. The parameters are shown to vary in the manner predicted by the Judd-Ofelt theory involving only a static intensity—gaining mechanism. parameters are shown to vary randomly. The results are contrasted with those previously published for Ln³⁺ doped in Y₂O₃. The variation of for the lanthanide aquo ions is briefly discussed.     

Nuclear spin relaxation in molecular fluids near the critical point

The Watson version of the molecular vibration-rotation hamiltonian is expanded in terms of the scalar invariants of the inverse of the moment of inertia tensor using the generalized Lucas polynomials. The resultant expansion consists of the matrices Î, , ² with coefficients depending on the normal coordinates. This is in contrast to the usual expansion as a power series in the matrix .     

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.     

Nuclear magnetic spin-lattice relaxation and molecular motion in solid white phosphorus and in liquid phosphorus

The ³¹P spin-lattice relaxation rates have been measured in solid white phosphorus and in liquid phosphorus over the temperature range 110 K to 400 K and at Larmor frequencies of 10 MHz and 30 MHz. The contributions to the measured relaxation rate from the different interactions have been separated. In the low-temperature, crystalline phase there are important contributions to the relaxation rate from the anisotropic chemical shielding and the intramolecular dipole-dipole interactions which are modulated by the reorientational motion of the molecule. Interference effects between these two interactions, which are important in liquids, are demonstrated to be quenched by the strong dipolar interactions in the solid. The reorientational correlation time is given by

and the chemical shielding anisotropy by

In the high-temperature, plastic-crystalline phase the reorientational correlation time is

as obtained from the anisotropic chemical shielding relaxation rate which is separated from the other contributions by its quadratic dependence on the Larmor frequency. Using this τ _R the intramolecular dipole-dipole relaxation rate is calculated. The contribution from the translational diffusion modulated intermolecular dipole-dipole interaction is calculated from the self-diffusion coefficient. When these contributions are subtracted from the observed relaxation rate, there remains a frequency-independent relaxation rate, proportional to 1/δ _R , which is attributed to the spin-rotational interaction. The latter is shown to be quantitatively consistent with large-angle reorientational jumps of the P₄ molecules by 120° about their C _3v axes. The relaxation in the liquid phase is dominated by the spin-rotational interaction and the expression representing the spin-rotational relaxation rate is the same as the one derived in the plastic-crystalline phase. The mechanism of molecular reorientation in the liquid is therefore the same as in the plastic-crystalline phase.