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

Abstract

The ligand field density functional theory (LFDFT) algorithm is extended to treat the electronic structure and properties of systems with three-open-shell electron configurations, exemplified in this work by the calculation of the core and semi-core 1s, 2s, and 3s one-electron excitations in compounds containing transition metal ions. The work presents a model to non-empirically resolve the multiplet energy levels arising from the three-open-shell systems of non-equivalent ns, 3d, and 4p electrons and to calculate the oscillator strengths corresponding to the electric-dipole 3d m → ns 1 3d-m 4p 1 transitions, with n = 1, 2, 3 and m = 0, 1, 2, …, 10 involved in the s electron excitation process. Using the concept of ligand field, the Slater-Condon integrals, the spin-orbit coupling constants, and the parameters of the ligand field potential are determined from density functional theory (DFT). Therefore, a theoretical procedure using LFDFT is established illustrating the spectroscopic details at the atomic scale that can be valuable in the analysis and characterization of the electronic spectra obtained from X-ray absorption fine structure or electron energy loss spectroscopies. Keywords Ligand field density functional theory (LFDFT) .Three-open-shell electron configuration . Multiplet structure and electric-dipole allowed transitions

Theoretical insight into the magnetic circular dichroism of uranium N6,7‐edge X‐ray absorption

“…We use the LFDFT method, [21][22][23] at the extended level with a three-open-shell electron configuration, [15,26] to calculate the multiplet energies E and multielectronic eigenfunctions ψ. The LFDFT treats near-degeneracy correlation using an ad hoc configuration interaction algorithm within active Kohn-Sham molecular orbitals that are formally identified as having predominant uranium 4f, 5f, and 6d parentage.…”

“…where the Kohn-Sham orbitals that are selectively chosen as active subspace are occupied with fractional electrons. [23][24][25][26][27] The active subspace is selectively identified on the basis of their fractional parentage coefficients for uranium 4f, 5f, and 6d. In ADF, [37][38][39] these fractional parentage coefficients are the portion of molecular orbitals ordered by energy, with the most significant symmetrized fragment orbital gross population.…”

“…It is also noteworthy that the AOC method is, in Slater's sense, well suited to resolve ligand‐field states . The AOC method implies a spin‐restricted SCF, where the Kohn‐Sham orbitals that are selectively chosen as active subspace are occupied with fractional electrons . The active subspace is selectively identified on the basis of their fractional parentage coefficients for uranium 4 f , 5 f , and 6 d .…”

A DFT-based theoretical model for the calculation of spectral profiles of lanthanide M4,5-edge x-ray absorption

“…Equation 12complies with the fundamental concept of ligand-field theory, 34,35 where electrons are moving in a central-field independent of the atomic ml basis functions. 34,35 Although the spin-orbit coupling constants ζ 3d and ζ 4f can also be obtained using the radial functionsR 3d andR 4f , [36][37][38][39] it is more convenient to take advantage of the spin-orbit ZORA method 26,27 in ADF. [11][12][13] The primary advantage of using the ZORA method is that the spin-orbit coupling interaction is self-consistently treated.…”