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

Abstract

Methodological advents for the calculation of the multiplet energy levels arising from multiple-open-shell 2p⁵3dⁿ⁺¹ electron configurations, with n = 0, 1, 2,… and 9, are presented. We use the Ligand-Field Density Functional Theory (LFDFT) program, which has been recently implemented in the Amsterdam Density Functional (ADF) program package. The methodology consists of calculating the electronic structure of a central metal ion together with its ligand coordination by means of the Density Functional Theory code. Besides, the core-hole effects are treated by incorporating many body effects and corrections via the configuration interaction algorithm within the active space of Kohn–Sham orbitals with dominant 2p and 3d characters of the transition metal ions, using an effective ligand-field Hamiltonian. The Slater–Condon integrals (F²(3d,3d), F⁴(3d,3d), G¹(2p,3d), G³(2p,3d) and F²(2p,3d)), spin–orbit coupling constants (ζ_2p and ζ_3d) and parameters of the ligand-field potential (represented within the Wybourne formalism) are therefore determined giving rise to the multiplet structures of systems with 3dⁿ and 2p⁵3dⁿ⁺¹ configurations. The oscillator strengths of the electric-dipole allowed 3dⁿ → 2p⁵3dⁿ⁺¹ transitions are also calculated allowing the theoretical simulation of the absorption spectra of the 2p core-electron excitation. This methodology is applied to transition metal ions in the series Sc²⁺, Ti²⁺,…, Ni²⁺ and Cu²⁺ but also to selective compounds, namely SrTiO₃ and MnF₂. The comparison with available experimental data is good. Therefore, a non-empirical ligand-field treatment of the 2p⁵3dⁿ⁺¹ configurations is established and available in the ADF program package illustrating the spectroscopic details of the 2p core-electron excitation that can be valuable in the further understanding and interpretation of the transition metal L_2,3-edge X-ray absorption spectra.