<i>Ab initio</i> derivation of the crystal field parameters for lanthanide ions: The f1 case

Abstract

The crystal field theory as explained by Abragam and Bleaney in their landmark 1970 book on transition-ion electron paramagnetic resonance remains a cornerstone in the development of luminescence applications and molecular magnets based on the f-elements. The modern numerical derivation of the 27 Bkq Stevens crystal field parameters (CFPs), which describe the splitting of the energy levels of a central ion, is traditionally achieved through the effective Hamiltonian theory and multiconfiguration wave function theory calculations, insofar as the lowest J level fully captures the targeted low-energy physics. In this study, we present a novel theoretical approach for determining the CFPs. The procedure resembles the traditional extraction path but crucially accounts for the full |J, MJ⟩ space of an ion configuration with L = 3 and S = 1/2. By demonstrating the extraction procedure using the simplest case of a CeIII 4f1 ion with a crystal-field split J ∈ {5/2, 7/2} manifold, it is shown for the first time that a unique set of CFPs describes the splitting and mixing of both the J manifolds. In fact, this J/J′ mixing is analogous to the “spin mixing” in binuclear transition metal complexes. At the employed level of calculation, we demonstrate that there is no spin–orbit coupling influence on the CFP values. Moreover, for the 4f1 case, the present extraction yields crystal-field and spin–orbit parameters similar to those obtained from ab initio ligand field theory. This study represents the first step of a larger effort in reviewing the theory and extraction procedures of CFPs in f-element complexes.