Betty Ng

The superposition model of crystal fields

The superposition model was originally developed to separate the geometrical and physical information in crystal field parameters. Its success in the analysis of lanthanide spectra has been paralleled by the success of the related angular overlap model in the analysis of d-electron spectra. The basic ideas, method of application and reliability of the superposition model are discussed and its relationship with the angular overlap model is clarified. Developments described are the application of the superposition model to the ground (L=0) multiplet splittings of d5 and f7 ions, orbit-lattice interactions, transition intensities and correlation crystal fields. Special attention is paid to work which has been claimed to support or disprove the postulates of the model.

Many‐body crystal field calculations. I. Methods of computation and perturbation expansion

The practical implementation of biorthogonal perturbation techniques to calculate one‐ and two‐electron crystal field parameters is described. The systems and basis sets used in the calculations are described in detail, and several crucial aspects of the numerical procedures are discussed. A complete listing of second order perturbation diagrams with associated denominator corrections is given.

Many‐body crystal field calculations. II. Results for the system Pr3+–Cl−

Contributions to the Slater parameters, crystal field and correlation crystal field parameters for the two‐ion system Pr3+–Cl− are calculated using the many‐body diagrammatic expansion technique. Both ligand polarization and covalency are shown not to provide significant contributions to the Slater parameters. Ligand polarization is also eliminated as a major contributor to the correlation crystal field, but this mechanism does produce significant crystal field contributions. New, important, contributions to all three sets of parameters are identified and the overall results are related to experimental data.

Complete second-order calculations of intensity parameters for one-photon and two-photon transitions of rare-earth ions in solids

Biorthogonal perturbation methods originally developed for lanthanide crystal-field calculations are applied to 4f-4f electric dipole transition intensities for the system Pr3+-Cl-. The results confirm earlier suggestions that ligand polarization contributions are crucial to understanding the relative signs of the intensity parameters. They also show that ‘covalent’ or ‘charge transfer’ excitations from occupied ligand states to 4f orbitals give significant contributions. Our calculations are also applied to two-photon absorption and electronic Raman scattering amplitudes. The major second-order contribution to these processes comes from excitations from 4f to 5d orbitals.

Many‐body perturbation theory for effective Hamiltonians using nonorthogonal basis sets

A diagrammatic many‐body perturbation approach using nonorthogonal basis sets is used to derive explicit expressions for an Hermitian effective Hamiltonian matrix. Approximate overcompleteness is shown not to lead to any difficulties provided that an exact inverse of the overlap matrix is obtained. Applications of the formalism to crystal‐field calculations are discussed in detail.

Parametrisation and interpretation of paramagnetic ion spectra

The essential similarity between interaction mechanisms for the 3dn, 4fn and 5fn series of paramagnetic ions in solids is emphasised. Some prevalent views of the relationship between parameter values and interaction mechanisms for 3dn ions are challenged. A unified model of the interaction processes is proposed and optimal parametrisation procedures for correlation crystal-field effects in 3dn ions are discussed.

Crystal field superposition model analyses for tetravalent actinides

Intrinsic, or single ligand parameters, are derived for Cl-, Br- and O2- ligands. These allow the approximate prediction of crystal field parameters for any site where the atomic positions are known. Several instances where published parameters are apparently incorrect have been discovered. Derived parameter ratios support the argument that the simple molecular orbital description of crystal fields breaks down for the tetravalent actinides.

Ab initio calculation of crystal-field correlation effects in Pr3+-Cl-

Many-body perturbation theory, with non-orthogonal basis states, has been used to determine covalency, overlap and ligand polarisation contributions to the intrinsic crystal-field and correlation crystal-field parameters for the system Pr3+-Cl- spaced as in PrCl3. Significant crystal-field contributions are shown to arise from ligand polarisation, but there are no significant contributions to either the Slater parameters or the correlation crystal-field parameters from this mechanism. Calculated values of crystal-field parameters are in reasonable agreement with experiment. A new approach to the phenomenological treatment of crystal-field correlation effects is suggested.

Ab initio lanthanide crystal field calculation for small internuclear separations

Pr3+-Cl- intrinsic crystal field parameters Ak have been calculated for three internuclear separations, between the equilibrium distance (R0=5.5812 au) in PrCl3 and 4.0812 au. The results show that pi -bonding and charge penetration contributions both tend to increase the A4/A6 ratio for interionic separations much smaller than the equilibrium spacing. It follows that mechanisms similar to those which have been successfully employed for crystal field calculations in ionic solids may also be invoked to explain the observed crystal fields in covalently bonded solids, where this ratio is much larger, and metals, where it is negative.

Two-electron tensor operator expressions in crystal-field theory

A relation between two alternative parametrisations describing anisotropic two-electron interactions is obtained. This clarifies the role of the spin-correlated crystal field parametrisation, allowing the authors to express it as a simple truncation of one of the alternative two-electron parametrisations.