Large anomalies due to insufficiency of Madelung embedding inab initiocalculations of4f−5dand4f−6sexcitations

Abstract

Ab initio embedded-cluster calculations are performed on the ͑CeF 8 ͒ 5− cluster embedded in BaF 2 . The local structure around the Ce 3+ impurity and the transition energies are calculated in the states of main character 4f 1 , 5d 1 , and 6s 1 , without and with spin-orbit coupling. When Madelung embedding is used, large anomalies are observed in the 5d 1 and 6s 1 manifolds. They are shown to be due to an artificial electron leak out of the cluster, at a regime of short Ce-F distances, when it occupies diffuse orbitals like the molecular orbitals of main character 5d and 6s. The main reason for the leak is the lack of linear-independency conditions between the wave functions of the cluster and its environment in Madelung embedding. When these conditions are added by means of ab initio model potential embedding ͑AIMP͒, the anomalies disappear. The 4f-5d absorption transitions calculated with spin-orbit coupling, AIMP embedding, and correlating the electrons with main character F-2s2p and Ce-4d5s5p4f5d, show good agreement with experiment. The present results support previous claims that state-of-the-art ab initio methods of quantum chemistry as the ones used here are nowadays in a position to reliably calculate 4f-5d transitions of lanthanide-doped solids. A proper embedding is crucial for this.

Spectroscopy of High‐Energy States of Lanthanide Ions

“…These transitions should be sharp, whereas those for which the 5d electron changes to a different orbital will be broad. If the bond lengths when the 5d electron is in the lowest 5d orbitals are more contracted than when it is in a 4f orbital and the bond lengths when the electron is in a higher 5d orbital are more expanded, as indicated by the calculations of Seijo and co-workers [21,22,23], then some of the transitions within the 4f N −1 5d configuration will have even broader vibronic bands than the 4f N to 4f N −1 5d transitions.…”

“…This has many shortcomings, as discussed in Refs. [21,22,23]. However, our purpose here is to illustrate the method, and this code is quite suitable for that.…”

“…The ab-initio calculations by Seijo and co-workers [21,22,23] have challenged some common assumptions. It is often assumed that the bond lengths always increase when a lanthanide ion is excited from 4f N to 4f N −1 5d.…”

“…Seijo and co-workers [21,22,23] have concentrated on a smaller number of systems and have used a sophisticated quantum-mechanical embedding scheme to calculate realistic excited-state geometries and potential-energy surfaces.…”

“…It is now possible to make reasonably accurate ab-initio calculations for the 4f N and 4f N −1 5d configurations of lanthanide ions in crystals [20,21,22,23,24,25]. This raises the possibility of determining crystal-field and other parameters from such calculations.…”