Parameterized effective Hamiltonians as a diagnostic tool for ab initio analyses of lanthanide crystal field effects (2016)
AuthorsSalkeld, Alexander J.show all
Parameterised effective Hamiltonians are fitted to ab initio energy level calculations of a number of lanthanide materials, in order to extract the equivalent spectroscopic parameters from the ab initio models, particularly from the 4fn-15d excited configurations. By studying parameter variations as a function of impurity-ligand separation in SrCl2:Yb2+, CsCaBr3:Yb2+, and CaF2:Yb2+, a number of trends are observed. The Coulomb and d spin-orbit parameters exhibit variation with impurity-ligand separation which is attributed to the nephelauxetic effect. The crystal field parameters can be shown to vary with power-law dependence in many of the calculations. In SrCl2:Yb2+, this power-law variation is observed to exactly match the point-charge model for the crystal field. An inaccuracy is also identified at the spin-free level of calculation for this material, where the crystal field influence described by the ab initio model decreases with increased ligand proximity, rather than increasing as is expected physically. Effective Hamiltonian parameters are fitted to an experimental excitation spectrum for CaF2:Yb2+. These values are compared to the extracted ab initio parameters. The ab initio parameters are observed to overstate the strengths of the Coulomb interaction, and the d crystal field. Parameters for 4fn+4fn-15d effective Hamiltonians are fitted to the ab initio energy levels of several lanthanide systems of greater complexity: Lu2O3:Pr3+, CaF2:Pr3+, BaF2:Tb3+, and CaF2:Eu2+. The Coulomb parameters, and in particular the F2 Coulomb parameter, tend towards large values in most of these systems, indicating that further corrections due to the missing electron correlation effects from the Hartree-Fock calculations are required. The ff electron correlation parameter extracted from the ab initio calculations is typically 2-3 times the size of those fitted to experimental levels. This is suggested to be the result of the ab initio calculation potentially overlooking important contributions to the electron correlation from continuum states.