Density functional theory (DFT) has become an essential tool for predicting the stability and properties of materials. In this work, we present a detailed first-principles study of the formation energy of the wurtzite-phase group-III nitrides AlN, GaN, and InN. We evaluate the influence of both the computational method and exchange-correlation functional on the energetic stability of these compounds. Two distinct approaches are employed to solve the Kohn-Sham equations: the Full Potential Linearized Augmented Plane Wave (FP-LAPW) method, implemented in the WIEN2k and ELK codes, and the Pseudopotential + Plane Wave (PP-PW) method, as implemented in Quantum Espresso and VASP, using the Norm-Conserving, Ultrasoft, and Projector Augmented Wave pseudopotentials. Several exchange-correlation (XC) functionals are considered, including GGA-based functionals (PW91, PBE, PBEsol, and WC), and meta-GGA (SCAN). The results demonstrate that formation energies are significantly affected by both the choice of method and the XC functional. To validate the dynamical stability of the InN phase, phonon dispersion and vibrational density of states were calculated. The thermal properties and Raman-active phonon modes are also analyzed and show good agreement with available experimental data. This study provides valuable benchmarks for improving the predictive accuracy of DFT-based simulations and offers insights for the design of nitride-based optoelectronic materials. • Formation energy is affected by the choice of method and XC functional. • FP-LAPW (WIEN2k) best reproduces experimental formation energies of AlN, GaN, InN. • Phonon and Raman analyses confirm WZ-InN dynamical stability and match experiments. • PBEsol improves InN formation energy accuracy over standard PBE.
Arellano-Ramírez et al. (Sun,) studied this question.