4f fine-structure levels as the dominant error in the electronic structures of binary lanthanide oxides

TL;DR

This paper investigates the dominant errors in electronic structure calculations of lanthanide oxides, revealing that inaccuracies in 4f levels significantly affect band gap predictions and proposing a refined DFT+U method for better accuracy.

Contribution

It introduces a reformulated linear response DFT+U approach that better predicts 4f levels and optical gaps in lanthanide sesquioxides, improving upon previous methods.

Findings

Optical transition gaps are consistently 5.3-5.5 eV across lanthanide oxides.

Errors in band structure are mainly due to inaccuracies in 4f level predictions.

The new method simplifies understanding of lanthanide electronic structures.

Abstract

The ground-state 4f fine-structure levels in the intrinsic optical transition gaps between the 2p and 5d orbitals of lanthanide sesquioxides (Ln2O3, Ln=La...Lu) were calculated by a two-way crossover search for the U parameters for DFT+U calculations. The original 4f-shell potential perturbation in the linear response method were reformulated within the constraint volume of thegiven solids. The band structures were also calculated. This method yields nearly constant optical transition gaps between Ln-5d and O-2p orbitals, with magnitudes of 5.3~5.5 eV. This result verifies that the error in the band structure calculations for Ln2O3 is dominated by the inaccuracies in the predicted 4f levels in the 2p-5d transition gaps, which strongly and nonlinearly depend on the on-site Hubbard U. The relationship between the 4f occupancies and Hubbard U is non-monotonic and is entirely different from that for materials with 3d or 4d orbitals, such as transition metal oxides. This new linear response DFT+U method can provide a simpler understanding of the electronic structure of Ln2O3 and enables a quick examination of the electronic structures of lanthanide solids prior to hybrid functional or GW calculations.