Some investigations in the theory of open-shell ions

The use of V, W and X coefficients in calculations of matrix elements is shown. General formulae for all two-electron spin-orbit coupling matrices in an octahedral strong-field coupling scheme are deduced. The parametrization of the electrostatic energy in ligand field theory is discussed and the number of parameters required is given in various cases. The configuration f ² in an octahedral strong-field scheme is treated in some detail and reasons for the anomalously low paramagnetism of PuF₆ are exposed, largely in contradiction to earlier views [13, 14]. Finally it is shown that expressions involving recoupling matrix elements, which occur in a scheme for calculating matrix elements of one-electron operators given by Tanabe and Kamimura [3], are proportional to W and X coefficients, thus considerably extending the scope of the latter work.     

Intramolecular Photochemistry and Energy Transfer in Molecular Crystals of [2.2] metacyclophane-1-ene and 1,2-diphenylcyclopentene

The intramolecular photocyclisation reactions of the stilbene analogues [2.2] metacyclophane-1-ene (MCPE) and 1,2-diphenylcyclopentene (DPCP) have been investigated in the solid state. In MCPE there is little or no energy transfer through the crystal prior to photoreaction, which occurs in regions of otherwise perfect crystal. This may in large part be due to a slow energy transfer rate because excited molecules relax to a distorted state which is only weakly coupled to its neighbours. In DPCP in the solid state photocyclisation will not occur, presumably for steric reasons. Energy transfer in DPCP is measurably slower than that expected for a rigid lattice.     

The spatially anisotropic frustrated Heisenberg ferrimagnet on a square lattice

We study the zero temperature properties of the two-dimensional spatially anisotropic ferrimagnet with competing interactions, using the linear spin-wave theory, and consider pairs of mixed-spins in the set (1/2,1,3/2). We find a small region magnetically disordered in the phase diagram for some values of the anisotropy parameter.     

Fimbrolide disulfanes: synthesis and crystal interactions

A series of novel fimbrolide disulfanes is synthesized and a crystal structure analysis reveals interesting inter-molecular halogen-bonding and CO?CO (carbonyl-carbonyl) dipolar interactions. Molecular modelling studies with the target protein display significant halogen-bonding interactions in the ligand -binding site.     

Real-time field measurements of stable isotopes in water and CO2 by Fourier transform infrared spectrometry

Continuous records of isotope behaviour in the environment are invaluable to understanding mass and energy fluxes. Although techniques such as isotope ratio mass spectrometry provide high precision data, they are not well suited to the analysis of a large number of samples and are currently restricted to use in the laboratory. Fourier transform infrared spectrometers are relatively cheap and sufficiently portable and robust to be taken into the field to collect continuous records of gas-phase isotope behaviour. Several examples of the application of this technique will be presented. One data set provides half-hourly determinations of vertical profiles of D/H in water vapour above agricultural fields over a 3-week period; the same infrared spectra can also be used to determine 13C/12C in CO2. The technique has also been applied to the study of CO2 in ambient air and in a limestone cave system. Some of the features and complications associated with the method will also be considered.     

An accurate and efficient method for the incompressible Navier–Stokes equations using the projection method as a preconditioner

The projection method is a widely used fractional-step algorithm for solving the incompressible Navier–Stokes equations. Despite numerous improvements to the methodology, however, imposing physical boundary conditions with projection-based fluid solvers remains difficult, and obtaining high-order accuracy may not be possible for some choices of boundary conditions. In this work, we present an unsplit, linearly-implicit discretization of the incompressible Navier–Stokes equations on a staggered grid along with an efficient solution method for the resulting system of linear equations. Since our scheme is not a fractional-step algorithm, it is straightforward to specify general physical boundary conditions accurately; however, this capability comes at the price of having to solve the time-dependent incompressible Stokes equations at each timestep. To solve this linear system efficiently, we employ a Krylov subspace method preconditioned by the projection method. In our implementation, the subdomain solvers required by the projection preconditioner employ the conjugate gradient method with geometric multigrid preconditioning. The accuracy of the scheme is demonstrated for several problems, including forced and unforced analytic test cases and lid-driven cavity flows. These tests consider a variety of physical boundary conditions with Reynolds numbers ranging from 1 to 30000. The effectiveness of the projection preconditioner is compared to an alternative preconditioning strategy based on an approximation to the Schur complement for the time-dependent incompressible Stokes operator. The projection method is found to be a more efficient preconditioner in most cases considered in the present work.     

The production of slow positron beams from magnesium oxide-coated moderators

Preliminary observations are reported which support the assertion of Canter et al. [1] that the moderation of fast positrons by magnesium oxide is connected with the large amounts of positronium produced by the positrons within the powder.     

Rotational analyses of the A1Π-X1Σ+ and the a3Π-X1Σ+ systems of AlBr

The absorption spectrum of the A¹Π-X¹Σ⁺ system and the emission spectrum of the a³Π-X¹Σ⁺ system of AlBr have been examined at higher resolution than previously used. The present study has produced a significantly improved set of molecular constants for these excited states of AlBr. All data have been fitted in a self-consistent manner for an optimum set of constants. The broadening of features in the A-X system has been attributed to type c⁺ predissociation in the A¹Π state. Also, a comparison is made between the emission and absorption spectra of the A-X system.