The optical spectra of the lanthanides doped into single crystal LaF3 have been interpreted in terms of transitions within 4f N configurations. Energy matrices combining free‐ion terms with a crystal field for an approximate model which assumes C2v instead of the actual C2 site symmetry were diagonalized. Excellent correlations were obtained between experimental transition energies and the computed level structures. We also report the results of previously unpublished experimental spectroscopic investigations of Nd3+ and Sm3+:LaF3, as well as predicted energy levels for Pm3+:LaF3. The spectroscopic data for each ion were independently interpreted using an effective‐operator model, then the model parameters were intercompared. Systematic trends have been identified, and a comprehensive energy level diagram is presented.

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A systematic analysis of the spectra of the lanthanides doped into single crystal LaF3

List of contributors Preface Introduction 1 Crystal field splitting mechanisms D J Newman and Betty Ng 2 Empirical crystal fields D J Newman and Betty Ng 3 Fitting crystal field parameters D J Newman and Betty Ng 4 Lanthanide and actinide optical spectra G K Liu 5 Superposition model D J Newman and Betty Ng 6 Effects of electron correlation on crystal field splitting M F Reid and D J Newman 7 Ground state splittings in S-state ions D J Newman and Betty Ng 8 Invariants and moments Y Y Yeung 9 Semiclassical model K S Chan 10 Transition intensities M F Reid Appendix 1 Point symmetry D J Newman and Betty Ng Appendix 2 QBASIC programs D J Newman and Betty Ng Appendix 3 Accessible program packages Y Y Yeung, M F Reid and D J Newman Appendix 4 Computer package CST Cz Rudowicz Bibliography Index

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Crystal Field Handbook

A parametric model for lanthanide and actinide atomic and crystal energy levels is presented that correlates trends in Hartree–Fock calculations with empirically determined atomic parameters in such a way that predictions for unclassified complex cases can be made from the analysis of simpler ones. When appropriate effective operators, including electrostatic operators up to the third rank for fN configurations and magnetic operators up to the second rank for fN and fNd shells, are used in the parametric Hamiltonian, statistical errors of 10–20 cm−1 are typical for the simpler examples presented.

Parametric model for f-shell configurations. I. The effective-opertor Hamiltonian

For pt.I see ibid., vol.17, p.23-75 (1984). As an illustration of the theory developed in the first paper in this series, a set of five orthogonal parameters is used to describe all electrostatic two-particle excitations in the 3dN configurations completely to second order. These parameters represent the term energies of d2 and, consequently, the 3dN configurations are perceived as a collection of 1/2N(N-1)d2 pairs, the total energy of the configuration being the sum of the corresponding pair energies. As regards their effects, the parameters are partitioned into a structural and an additive part; the structural part is found to behave as a linear function of N, whereas the additive part is proportional to the average energy of the configuration. In order to take into account all electrostatic one-particle effects as well, two orthogonalised three-body parameters T1 and T2 are used, the first corresponding to the well known Trees parameter and the second covering the remaining class of one-electron excitations. With a least-squares fitting procedure, both the d2 energies and the three-electron parameters are determined for the dN ground configuration in the III, IV, V and VI spectra of the iron group elements. Surprisingly, the effects of T2 turn out to be important, especially for the lower ionisation stages. Amongst other things, old problems concerning the far-off position with respect to calculations of the 12D term in the 3d6, and parameter irregularities in the 3d7 configurations, seem to be solved with the introduction of T2. As a result, the mean error of the fit in some of these cases is reduced by factors of three to four. Using the above set of parameters, a prediction of the 3d4 ground configuration of Mn IV is made.

https://iopscience.iop.org/article/10.1088/0022-3700/17/20/010/pdf

Energies of N equivalent electrons expressed in terms of two-electron energies and independent three-electron parameters: a new complete set of orthogonal operators. III. Ab initio calculations

Electronic Energy Level Structure

For pt. I see abstr. A25410 of 1971. The usefulness of a 'model building' approach to rare earth configuration interaction is emphasized as an alternative to doing full ab initio calculations. Second order perturbation theory is used to calculate the eleven parameters which characterize the effective two-electron magnetic interaction in both Pr2+ and Pr3+. Good agreement is obtained with the Pr2+ experimental parameters without introducing screening.

https://iopscience.iop.org/article/10.1088/0022-3700/4/10/024/pdf

Configuration interaction in rare earth ions. II. Magnetic interactions

For pt. II see ibid., vol.4, 1388 (1971). Numerical estimates of the Trees parameters alpha , beta , gamma for Pr2+ (4f3) are reported. Configuration interactions through second order excitations to bound states are considered in detail. It is shown that excitations of the type 4d to 4f and 4f to 5d are dominant. The results are compared with recent work on Pr3+. Bound state excitations alone grossly overestimate the parameters for both ions. Introduction of a screening factor of 1/5 for the excitations of two 4f electrons from d states gives reasonable agreement with experiment. Excitations to the continuum are crudely estimated but they do not appear to give sufficiently large corrections to the values of alpha , beta and gamma to lead to good agreement with experimental data.

D J Newman

Papers

Configuration interaction in rare earth ions. II. Magnetic interactions

Configuration interaction in rare earth ions. III. Trees parameters for Pr2+ and Pr3+