Development and applications of the LFDFT: the non-empirical account of ligand field and the simulation of the f–d transitions by density functional theory

Abstract

Ligand field density functional theory (LFDFT) is a methodology consisting of non-standard handling of DFT calculations and post-computation analysis, emulating the ligand field parameters in a non-empirical way. Recently, the procedure was extended for two-open-shell systems, with relevance for inter-shell transitions in lanthanides, of utmost importance in understanding the optical and magnetic properties of rare-earth materials. Here, we expand the model to the calculation of intensities of f → d transitions, enabling the simulation of spectral profiles. We focus on Eu(2+)-based systems: this lanthanide ion undergoes many dipole-allowed transitions from the initial 4f(7)((8)S7/2) state to the final 4f(6)5d(1) ones, considering the free ion and doped materials. The relativistic calculations showed a good agreement with experimental data for a gaseous Eu(2+) ion, producing reliable Slater-Condon and spin-orbit coupling parameters. The Eu(2+) ion-doped fluorite-type lattices, CaF2:Eu(2+) and SrCl2:Eu(2+), in sites with octahedral symmetry, are studied in detail. The related Slater-Condon and spin-orbit coupling parameters from the doped materials are compared to those for the free ion, revealing small changes for the 4f shell side and relatively important shifts for those associated with the 5d shell. The ligand field scheme, in Wybourne parameterization, shows a good agreement with the phenomenological interpretation of the experiment. The non-empirical computed parameters are used to calculate the energy and intensity of the 4f(7)-4f(6)5d(1) transitions, rendering a realistic convoluted spectrum.

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

“…2 by the dashed magenta curve, which complies with the principle of ligand field theory. [16,28]. With this, for the ground electron configurations containing d electrons only, the following Slater-Condon parameters are requested: F 2 (dd) and F 4 (dd).…”

“…This is achieved by AOC occupation schemes, where we insure that five electrons are evenly distributed in the 3d orbitals of Mn 2+ to comply with the ligand field concept [16,28] considering the ground electron configuration, whereas one electron is promoted from the core and semi-core 1s or 2s or 3s orbitals and is evenly distributed in the 4p orbitals considering the excited electron configurations. The molecular orbitals were expanded using triple-zeta plus two polarization Slater-type orbital (STO) functions (TZ2P+) for the manganese atoms and triple-zeta plus one polarization STO function (TZP) for the oxygen and hydrogen atoms.…”

“…Then based on this LDA minimum energy structure, the generalized gradient approximation (GGA) functional (PBE) [52] was used to compute the electronic structure related to the ground 3d 5 and the excited ns 1 3d 5 4p 1 electron configurations of Mn 2+ , with n = 1, 2, 3, in the free ion as well as in the aquacomplex and the related optical properties. Following the LFDFT procedure [16,28], the Slater-Condon integrals, the spin-orbit coupling constants, and the ligand field parameters are obtained from the radial functions and the eigenvalues of the molecular Kohn-Sham orbitals having dominant 1s, 2s, 3s, 3d, and 4p characters.…”

“…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].…”

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

“…The second calculation route will be described later in eqn (14). The term for the ligand-field splitting in eqn (1) represents the contribution of the chemical environment (ligands) to the electronic structure of the transition metal ion.…”