DFT and phonon calculations
This protocol is extracted from research article:
Polymorphism of bulk boron nitride
Sci Adv, Jan 18, 2019; DOI: 10.1126/sciadv.aau5832

First-principles calculations based on DFT were performed to analyze the energy and structural and vibrational properties of BN polymorphs. We performed these calculations with the VASP (Vienna Ab initio simulation package) code (32) using projector augmented-wave method potentials (33). The electronic states 1s-2s of B and 2s-2p of N atoms were considered as valence. Wave functions were represented in a plane-wave basis truncated at 650 eV. By using these parameters and dense k-point grids for the integration within the first Brillouin zone (IBZ), energies were converged to within 1 meV per formula unit (0.1 kJ/mol; fig. S4). In the geometry relaxations, a tolerance of 0.01 eV Å−1 were imposed in the atomic forces.

Ab initio phonon frequencies were calculated with the direct method to assess the vibrational stability of the analyzed BN polymorphs and estimate their Gibbs free energies as a function of temperature and pressure within the QHA (27). In the direct method, the force-constant matrix was calculated in real space by considering the proportionality between atomic displacements and forces (34). The quantities with respect to which our phonon calculations were converged include the size of the supercell, the size of the atomic displacements, and the numerical accuracy in the sampling of the IBZ. We found the following settings to provide quasi-harmonic free energies converged to within 0.1 kJ/mol: 4 × 4 × 4 supercells (where the figures indicate the number of replicas of the unit cell along the corresponding lattice vectors; fig. S4), atomic displacements of 0.02 Å, and q-point grids of 14 × 14 × 14. The value of the phonon frequencies were obtained with the PHON code developed by Alfè (34). By using this code, we exploited the translational invariance of the system to impose the three acoustic branches to be exactly zero at the center of the Brillouin zone and applied central differences in the atomic forces.

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