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 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.     

Electron spin resonance spectrum of trapped in a single crystal matrix

The radical , labelled with ¹³C in the position shown, has been prepared by X-irradiation of single crystals of . The ¹³C hyperfine coupling tensor of this radical confirms previous conclusions from a study of the corresponding unlabelled species that the electron is essentially localized on the carbon atom. At room temperature the methylene group undergoes rapid reorientation about the P-C bond while comparison of the ¹³C tensors at 300 K and 77 K suggests that the barrier to rotation has a strong two-fold component but contains intermediate minima.     

On the determination of the intermolecular potential between a tetrahedral molecule and an atom or a linear or a tetrahedral molecule—application to CH4 molecule

A brief summary of the general theory of the long-range potential energy between two molecules, previously developed by Buckingham, is first presented. Then the first detailed expressions of this potential energy are given for the three following molecular pairs : tetrahedral molecule-atom, tetrahedral molecule-linear molecule and tetrahedral molecule-tetrahedral molecule. These expressions are applied to the calculation of the spectral moments of the far infra-red pressure induced absorption band, the second virial coefficient and the intermolecular mean square torque. This allows a discussion of the magnitude of the various terms contributing to this potential energy and leads to a determination, for CH₄, of the octupole and hexadecapole moments, and of the hyperpolarizability:

     

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.     

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.     

Padé approximant for lennard-jones 6–12 fluid

A solution for the time-dependent Schrödinger equation is given for an N-level system interacting with a sinusoidal field of arbitrary amplitude , frequency v and phase δ, in the presence of an applied static field of arbitrary strength . The solution is obtained by a modification of a previous exact method of solution for and retains the essential analytic features of the exact wavefunction for the problem. The Floquet form of the solution yields (a) the location and the widths of allowed transitions and the location of forbidden transitions, by use of characteristic exponent plots, but without evaluating the spectrum, and (b) convenient expressions for the steady-state induced transition probabilities, including the effects of a uniform relaxation mechanism, that only require the solution of the wave equation over the initial period of the hamiltonian. The approach is equally applicable to Stark (or Zeeman) frequency sweep or tuning problems. The ability to incorporate the effects of static fields in the solution is important since a variety of problems (e.g. anti-crossing spectroscopy) involve the application of such fields to a level configuration interacting with a sinusoidal field. As a detailed specific example, the multi-photon steady-state induced transition probabilities and characteristic exponents are studied, as a function of frequency v, for the unperturbed and the perturbed two-level system under saturating conditions. It is also demonstrated, for the coupling strengths of interest in multi-photon calculations, that the method of solution discussed here is a viable unified alternative to dressed-atom techniques.