Multiplet ligand-field theory using Wannier orbitals

Abstract

We demonstrate how ab initio cluster calculations including the full Coulomb vertex can be done in the basis of the localized, generalized Wannier orbitals which describe the low-energy density functional (LDA) band structure of the infinite crystal, e.g. the transition metal 3d and oxygen 2p orbitals. The spatial extend of our 3d Wannier orbitals (orthonormalized Nth order muffin-tin orbitals) is close to that found for atomic Hartree-Fock orbitals. We define Ligand orbitals as those linear combinations of the O 2p Wannier orbitals which couple to the 3d orbitals for the chosen cluster. The use of ligand orbitals allows for a minimal Hilbert space in multiplet ligand-field theory calculations, thus reducing the computational costs substantially. The result is a fast and simple ab initio theory, which can provide useful information about local properties of correlated insulators. We compare results for NiO, MnO and SrTiO3 with x-ray absorption, inelastic x-ray scattering, and photoemission experiments. The multiplet ligand field theory parameters found by our ab initio method agree within ~10% to known experimental values

1s2p RIXS Calculations for 3d Transition Metal Ions in Octahedral Symmetry

“…More details on the method can be found elsewhere [13,[30][31][32]34] and the references therein. The calculations are performed for a temperature of T = 300 K as described in the following.…”

“…This method enables to avoid the explicit calculation of the intermediate and final states, which are only defined with their respective Hamiltonian. Each of these many-body states is described by a linear combination of Slater determinants [31]. The atomic electronic interactions are parametrised by the Slater integrals, which are reduced to 80% of the Hartree-Fock values.…”

“…It takes into 6 Journal of Spectroscopy account all the 3d-3d, 1s-3d, and 2p-3d electronic Coulomb interactions, as well as the spin-orbit coupling ζ on every open shell of the absorbing atom (e.g., 2p SOC ζ 2p and 3d SOC ζ 3d in 1s2p RIXS). The 2p XAS and 1s2p RIXS spectra were calculated using Quanty which uses second quantisation and the Lanczos recursion method for the exact diagonalisation and Green functions to calculate the spectra [30][31][32]. This method enables to avoid the explicit calculation of the intermediate and final states, which are only defined with their respective Hamiltonian.…”

“…The possible 2p XES final state symmetries are all even symmetries as given in expressions (28), (29), (30), (31), and (32).…”

From Ligand Fields to Molecular Orbitals: Probing the Local Valence Electronic Structure of Ni2+ in Aqueous Solution with Resonant Inelastic X-ray Scattering

“…42,43 The CFM model is an implementation of the ligand-field theory and is thus semiempirical. Recently a number of theoretical developments have emerged looking for a more general and ab initio way to simulate L-edge XAS and RIXS spectra of TM compounds: hybrids of DFT and ligand-field theory, 44 The X-ray absorption (XA) spectrum was measured at the dipole beamline PM3 at the synchrotron radiation source BESSYII of the Helmholtz-Zentrum Berlin in Germany. The spectrum was recorded in transmission mode with a liquid transmission cell setup.…”