# 103-Compound Band Structure Benchmark of Post-SCF Spin-Orbit Coupling Treatments in Density-Functional Theory

## TL;DR

This paper benchmarks various spin-orbit coupling treatments in density-functional theory across 103 inorganic compounds, providing a comprehensive dataset to evaluate accuracy and guide future computational methods.

## Contribution

It introduces a large, high-quality band structure benchmark set for SOC treatments in DFT, including comparisons between self-consistent and non-self-consistent approaches.

## Key findings

- High agreement for elements up to Z≈50 between treatments
- Deviations up to 11% for heavy elements like Tl, Pb, Bi, Po
- SOC effects are similar across PBE and HSE06 functionals when scalar-relativistic structures agree

## Abstract

We quantify the accuracy of different non-self-consistent and self-consistent spin-orbit coupling (SOC) treatments in Kohn-Sham and hybrid density-functional theory by providing a band structure benchmark set for the valence and low-lying conduction energy bands of 103 inorganic compounds, covering chemical elements up to Po. Reference energy band structures for the PBE density functional are obtained using the full-potential (linearized) augmented plane wave code Wien2k, employing its self-consistent treatment of SOC including Dirac-like p$^{1/2}$ orbitals in the basis set. We use this benchmark set to benchmark a computationally simpler, non-self-consistent all-electron treatment of SOC based on scalar-relativistic orbitals and numeric atom-centered orbital basis functions. For elements up to Z$\approx$50, both treatments agree virtually exactly. For the heaviest elements considered (Tl, Pb, Bi, Po), the band structure changes due to SOC are captured with a relative deviation of 11% or less. For different density functionals (PBE vs. the hybrid HSE06), we show that the effect of spin-orbit coupling is usually similar but can be dissimilar if the qualitative features of the predicted underlying scalar-relativistic band structures do not agree. All band structures considered in this work are available online via the NOMAD Repository to aid in future benchmark studies and methods development.