Ligand field density functional theory for the prediction of future domestic lighting

Abstract

We deal with the computational determination of the electronic structure and properties of lanthanide ions in complexes and extended structures having open-shell f and d configurations. Particularly, we present conceptual and methodological issues based on Density Functional Theory (DFT) enabling the reliable calculation and description of the f -d transitions in lanthanide doped phosphors. We consider here the optical properties of the Pr 3+ ion embedded into various solid state fluoride host lattices, for the prospection and understanding of the so-called quantum cutting process, being important in the further quest of warm-white light source in light emitting diodes (LED). We use the conceptual formulation of the revisited ligand field (LF) theory, fully compatibilized with the quantum chemistry tools: LFDFT. We present methodological advances for the calculations of the Slater-Condon parameters, the ligand field interaction and the spin-orbit coupling constants, important in the non-empirical parameterization of the effective Hamiltonian adjusted from the ligand field theory. The model shows simple procedure using less sophisticated computational tools, which is intended to contribute to the design of modern phosphors and to help to complement the understanding of the 4f n -4f nÀ1 5d 1 transitions in any lanthanide system.

The angular overlap model extended for two-open-shell f and d electrons

“…In cases with more than one electron it cannot be discriminated in the spectral terms from a gap due to the Slater-Condon F 0 (ff) and F 0 (fd) parameters. Thus for the Pr 3+ complexes 19,21 taken as examples in the following, we obtain:…”

“…[16][17][18][19][20] Therefore, we do not aim in this paper to describe the electrostatic interaction part of the Hamiltonian, i.e. the Slater-Condon parameters relevant for the multi-electron problem, for which our theoretical model has been already improved 19 and revised 21 in previous studies. The calculation of the spin-orbit coupling is placed in the growing efforts devoted nowadays to the relativistic quantum chemistry tools.…”

“…21, using the radial functions of the 4f and 5d Kohn-Sham orbitals of Pr 3+ to extract the Slater-Condon parameters. These radial functions are graphically presented in Fig.…”

A non-empirical calculation of 2p core-electron excitation in compounds with 3d transition metal ions using ligand-field and density functional theory (LFDFT)

“…This is the second calculation route pointed out in the Methodology section. The ZORA Hamiltonian is shown in eqn (13). It results from the zeroth-order regular expansion in e/(2c 2 À V) of the Dirac equation 53 which in general gives very accurate results in atomic calculations, i.e.…”

Electronic fine structure calculation of metal complexes with three-open-shell s, d, and p configurations

“…the work of Harry Ramanantoanina et al [23][24][25][26][27][28]), the LFDFT method was extended to handle the electronic structure and properties arising from two-openshell electron configurations for the description of the photophysical properties of lanthanide based phosphors. Presently, the LFDFT is again extended in this work to account for the electronic structure and properties arising from excited three-open-shell electron configurations resulting, in principle, from the excitations of core or semi-core electrons, which are visible in soft or hard regime X-ray absorption fine structure spectroscopy [29][30][31][32][33][34][35] as well as in energy loss spectroscopy [36,37].…”