Benchmarking Density Functional Theory for Accurate Calculation of Nitride Band Gaps

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 <i>GW</i> 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.