# Benchmarking Density Functional Theory for Accurate Calculation of Nitride Band Gaps

## TL;DR

This paper evaluates various computational methods for predicting the electronic properties of nitride materials, finding that some advanced functionals significantly outperform traditional ones.

## Contribution

The study introduces a new benchmark dataset of nitride materials and evaluates the accuracy of multiple exchange-correlation functionals for band gap calculations.

## Key findings

- Conventional LDA/PBE functionals significantly underestimate band gaps with large errors.
- Advanced functionals like mBJ and HSE06 show high accuracy with low mean absolute errors.
- The dataset includes diverse nitrides to support future large-scale material screening.

## Abstract

We benchmark exchange-correlation functionals for the
calculation
of fundamental band gaps of inorganic nitrides. These include conventional
functionals such as the local density approximation (LDA), the generalized-gradient
(Perdew–Burke–Ernzerhof) approximation (PBE), simple
Slater exchange functionals (SLOC), specialized LDA/GGA-derived high
local exchange (HLE16) and Armiento–Kümmel semilocal
(AK13) functionals, meta-GGA functionals including TASK, the modified
Becke–Johnson functional (mBJ), and Heyd–Scuseria–Ernzerhof
(HSE06) hybrid functional, as well as quasiparticle GW theory. Since inorganic nitrides remain strongly under-represented
in previous extensive benchmark studies, the current subdatabase contributes
towards building a future large-scale balanced materials compilation
of band gaps to benchmark theory. From a literature survey, we carefully
collect 25 binary and 11 ternary nitrides with a focus on semiconductors
spanning the periodic table, including ionic Li3N, antibixbyite-structured
X3N2 (X = Be, Mg, Ca), early transition metals
and lanthanides (e.g., ScN, YN, and LaN), ultrahard Th3P4-type structured M3N4 (M = Zr,
Hf) compounds, promising photocatalysts Ta3N5, different polymorphs of III–V reference covalent nitrides
(BN, AlN, GaN), and many M3N4 polymorphs (M
= C, Si, and Ge) such as spinel-structured phases. Consistent with
previous extensive benchmark tests, conventional LDA/PBE unsystematically
largely underestimate band gaps with mean absolute errors (MAE) of
>1.0 eV and mean absolute percentage errors (MAPE) of about 50%.
Simple
Slater exchange functional, SLOC, the GGA-derived AK13LDA and HLE16
functionals show improvement over LDA/PBE with MAE of 0.5–0.6
eV (MAPE ∼ 20–25%) with mBJ and HSE06 being the most
accurate, with MAE = 0.30 and 0.28 eV (MAPE 12.1% and 11.1%), respectively.
Strategies for the development of machine learning and the choice
of appropriate exchange-correlation functionals for high-throughput
large-scale material screening are discussed in light of these results.