Cohesive properties of group-III nitrides: A comparative study of all-electron and pseudopotential calculations using the generalized gradient approximation

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We compare the performance of generalized gradient approximations (GGA's) and the local-density approximation (LDA) in density-functional calculations of the cohesive properties of cubic AlN, GaN, and InN. Employing the widely adopted pseudopotential approach, the calculated data are found to depend significantly on the treatment of the core states of the group-III ions, hampering a conclusive assessment of the GGA and LDA. Here we perform all-electron full-potential linearized-augmented plane-wave calculation, which we use to (i) scrutinize the results of pseudopotential calculations, and (ii) provide a proper distinction between the GGA and LDA functionals. We show that the accuracy of pseudopotential calculations is comparable to that of all-electron calculations only if the Ga and In semicore d states are treated as valence rather than core states. We also show that the use of an f-like local component can further improve the transferability of the Ga and In pseudopotentials. Regarding the PBE- (Perdew-Burke-Enzerhof-) GGA [Phys. Rev. Lett. $77,$ 3865 (1996)] we find that the cohesive energies of the group-III nitride crystals (and those of the elemental metals) agree closely with experimental data whereas they are overestimated within the LDA. Lattice parameters are described with similar accuracy within the PBE-GGA and LDA. On the other hand we find that the heats of formation of the group-III nitrides are underestimated by the PBE-GGA and given more accurately by the LDA. For the PBE-GGA, the underestimate is mainly due to the fact that it still overestimates the bond strength of the ${\mathrm{N}}_{2}$ molecule. For the LDA, the heat of formation turns out only slightly too large, because of a fortuitous cancellation of the (larger) errors in the ${\mathrm{N}}_{2}$ molecule and the bulk crystals. Several other GGA functionals are able to improve over the PBE-GGA for molecules like ${\mathrm{N}}_{2}$ due to stronger gradient corrections. Here we find that such more nonlocal GGA's significantly underestimate the cohesive energies of the group-III nitride (and metal) crystals and even further underestimate their heats of formation.