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.     

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.     

Isometric groups of non-rigid molecules: homomorphisms and reformulation of a theorem on semi-direct product factorization

The structure of isometric groups of semi-rigid molecules is considered from the point of view of homomorphisms relating various representations defining isometric groups. From the kernels of the group homomorphisms the existence of a number of invariant subgroups (, , etc.) is demonstrated.

One of these homomorphisms is shown to relate the problem of the decomposition of isometric groups into semi-direct products to the analogous problem of molecular covering groups. Based on this relation a theorem reported earlier is reformulated by stating explicitly general conditions under which proper semi-factorization is possible or impossible respectively. The latter situation exists only for certain normal cyclic subgroups of cyclic and dihedral groups, whose order is a product of powers of primes.     

Convergence of valence bond and molecular orbital theories

A comparison of the rate of convergence of valence bond (VB), symmetrically orthogonalized-orbital valence bond (), and configuration-interaction molecular orbital (SCF) calculations has been made for model π-electron systems in the minimum basis set approximation; the allyl radical, trans-butadiene, and the methylene cyclobutadienyl radical were studied. For excited states, as well as for the ground state, it is found that VB provides the best convergence in most cases and yields the worst results, with SCF typically falling in between. Properties examined include energy eigenvalues, charge and spin densities, transition energies, and transition dipole moments. Charge-density convergence is in opposite directions for the VB and SCF methods, with VB (and ) overemphasizing the charge on the atoms and SCF overemphasizing the charge in the bonding regions.     

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.     

A radio-tracer study of self-diffusion in the smectic phases iso-butyl 4-(4′-phenylbenzylideneamino) cinnamate [IBPBAC]

Average translational self-diffusion coefficients, , have been determined in the smectic E, B and A phases of unaligned samples of iso-butyl 4-(4′-phenylbenzylideneamino) cinnamate. A radiotracer technique was employed which was based on the serial sectioning method used in the study of diffusion in solids. In the smectic E phase is about 1 × 10^-14 m² s^-1. The self-diffusion in the smectic B phase fits reasonably well to an Arrhenius law with an activation enthalpy of 82 kJ mol^-1. The transition from the smectic B to A phase results in a dramatic rise in . In the smectic A phase the results fit an activation enthalpy for self-diffusion of about 168 kJ mol^-1. Similarities between the diffusion in the smectic E and B phases and in plastic solids are observed.     

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.     

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.     

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 .     

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.     

On the Taylor expansion of the expression for the transition probability for normal absorption processes

Molecular reorientation of 2-chloropyrimidine dissolved in CS₂ (0·1 M) has been investigated by means of ¹³C and proton relaxation. Although weakly coupled, the proton system subjected to non-selective 180-τ-90 pulse sequences allows the determination of one autocorrelation and one cross-correlation dipolar spectral density. The proton and carbon-13 relaxation data allow the complete determination of the rotational diffusional tensor:

and

It is shown that scalar relaxation due to nitrogen-14, has no effect on proton longitudinal relaxation time, because of a cross term due to the symmetry of the molecule, although this mechanism could, a priori, have been thought to be important. Finally, the nitrogen relaxation time recalculated with D_xx , D_yy , D_zz and the quadrupolar coupling tensor is in agreement with the observed linewidth.