# Assessing exchange-correlation functional performance in the chalcogenide lacunar spinels GaM$_4$Q$_8$ (M = Mo, V, Nb, Ta; Q = S, Se)

## TL;DR

This study systematically evaluates various density functional theory exchange-correlation functionals to determine their effectiveness in modeling the structural, electronic, magnetic, and optical properties of chalcogenide lacunar spinels, highlighting the strengths and limitations of each.

## Contribution

It provides a comprehensive comparison of LDA, GGA, meta-GGA, and hybrid functionals in accurately predicting properties of GaM$_4$Q$_8$ lacunar spinels, guiding future computational studies.

## Key findings

- LDA underperforms in predicting lattice constants and magnetism.
- GGA functionals like PBE and PBEsol perform reasonably well.
- Hybrid HSE06 accurately predicts lattice constants but overestimates band gaps.

## Abstract

We perform systematic density functional theory (DFT) calculations to assess the performance of various exchange-correlation potentials $V_{xc}$ in describing the chalcogenide GaM$_4$Q$_8$ lacunar spinels (M=Mo, V, Nb, Ta; Q=S, Se). We examine the dependency of crystal structure (in cubic and rhombohedral symmetries), electronic structure, magnetism, optical conductivity, and lattice dynamics in lacunar spinels at four different levels of $V_{xc}$: the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA, and hybrid with fractional Fock exchange. We find that LDA significantly underperforms GGA and higher level functionals in predicting lattice constants. LDA also fails to properly describe the magnetism in the family, and for some compositions it does not find the ground state distorted crystal structure. The Perdew-Burke-Ernzerhof (PBE) and PBE revised for solids (PBEsol) GGA functionals perform reasonably well in predicting lattice constants as well as the electronic structures. We find that the GGA with an on-site Coulomb interaction (GGA$+U$) is unnecessary to produce a semiconducting state in the distorted polar $R3m$ phase. Plus Hubbard $U$ values ranging from 1$\sim$2 eV, however, improve the quantitative performance of the GGA functionals. The meta-GGA functional SCAN predicts reasonable lattice constants and electronic structures; it exhibits behavior similar to the GGA$+U$ functionals for small $U$ values. The hybrid functional HSE06 is accurate in predicting the lattice constants, but leads to a band gap of $\approx$1 eV in the rhombohedral phase, which is higher than the experimental estimation of 0.2 eV. Our findings suggest that accurate qualitative and quantitative simulations of the lacunar spinel family with DFT requires careful attention to the nuances of the exchange-correlation functional and considered spin structures.