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 .     

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.     

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.     

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 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 .     

Statistical mechanics of solid and liquid mixtures of ortho- and para-hydrogen

It is known from experimental measurements that the configurational free energy of solid and liquid mixtures of p-H₂ and o-H₂ is approximately of the form

where is the mole fraction of o-H₂. Assuming that this dependence of F _conf on is due solely to orientational forces a quantum-mechanical calculation of F _conf is developed which is valid for moderately low temperatures. A simplified statistical model is used consisting of a rigid lattice. The theoretical free energy obtained is however much smaller than the experimental one probably on account of the crudeness of the model. Various refinements are discussed.     

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.     

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.     

On the effective Zeeman Hamiltonian for a linear molecule in an orbitally degenerate state

Values of the dissociation energies and the interaction constants in the long-range potential

for the B ³Π_Ou+ states of Br₂ and Cl₂ have been obtained from least-squares fits to the attractive part of the Rydberg-Klein-Rees potentials. The term in r ^-6 is not negligible even at large internuclear distances corresponding to the last few vibrational levels. The validity of the long-range inverse-power expansion in the internuclear distance r has been investigated. The expansion is valid outside the electron-overlap region given by

in agreement with the result found in the analysis of I₂.     

Thermodynamic parameters for gaseous sulphate ion

Electrostatic energies and Madelung parameters for M ₂SO₄ (M = Li, Na, K, Rb and Cs) and for MSO₄ (M = Ca) are reported. An assessment of the charge distribution within the sulphate ion (q ₀ = -0·80) is made and values:

and

are assigned to the enthalpies of formation and solvation of the gaseous sulphate ion. The total lattice potential energies are found to be

A value of -1267 kJ mol^-1 is assigned for the oxide ion affinity of sulphur trioxide.     

Molecular motions in plastic succinonitrile: correlation times from incoherent neutron scattering

In the plastic phase (233 K < T < 331 K), the succinonitrile molecule N≡C-(CH₂)₂-C≡N undergoes motions of isomerization between two gauche and a trans conformations and, when in its transform, rotational motions of reorientation from a diagonal of the b.c.c. unit cell to another. After an evaluation of the multiple scattering correction using both a Monte Carlo simulation technique and a semianalytical calculation, the experimental quasi-elastic neutron spectra measured at 302 K were corrected and a comparison is made to a model taking into account the two coupled molecular motions.

The correlation times found by fitting this model to the corrected data are: for the rotational motion, and for the reaction of isomerization gauche?trans.