Determine the origin of the Ba3BiSb spillage discrepancy

Determine whether the discrepancy between the fixed-60 Quantum ESPRESSO spillage and the published VASP spillage for semimetallic Ba3BiSb is caused by occupied-band-count ambiguity, by performing mesh-converged calculations and comparing the VASP occupation and degeneracy treatment for the same crystal structure.

Background

For Ba3BiSb, the occupied electronic subspace is ill-defined at Γ because a triply degenerate state lies at the Fermi level and the material has overlapping occupied and empty bands. Changing the assumed occupied-state count by only two bands changes the computed spillage substantially, demonstrating that the numerical result is highly sensitive to the convention used to identify occupied states.

The fixed-60 Quantum ESPRESSO calculation gives a spillage of 2.016, whereas the published VASP reference is 2.267. The paper notes that the discrepancy may be due to occupation-count ambiguity, but the available calculations do not establish this causally; mesh convergence and a direct comparison of VASP’s occupation and degeneracy handling are required.

References

This interpretation is not definitive because none of the occupation counts considered above reproduces the reference value of $2.267$. The closest result is $2.12$ for $56$ electrons. The analysis establishes that occupation-count ambiguity is sufficiently large to account for the observed discrepancy, but it does not necessarily establish causality. A definitive assessment would require mesh-converged calculations and the VASP occupation and degeneracy treatment for the same structure.

— Calculation of DFT Spin-Orbit Spillage with Quantum ESPRESSO  (2609.04517 - Nguyen et al., 3 Sep 2026) in Section 11, “Limitations for semimetals,” paragraph “Implications”