Phonon dispersions: Performance of the generalized gradient approximation

By computing the phonon dispersions of a few selected solids (Si, C, Al, and Cu), within density-functional perturbation theory, we compare the performance of the local density approximation (LDA) with that of the generalized gradient approximations (GGA’s) in the form recently proposed by Perdew, Burke, and Ernzerhof [Phys. Rev. Lett. 77, 3865 (1996)]. We find that GGA systematically lowers the frequencies of phonon branches with positive Grüneisen parameters. This effect is correlated with the GGA’s expansion of the lattice constant, since GGA phonon frequencies computed at the experimental lattice constants are higher than the corresponding LDA ones. In C, Al, and Cu, LDA and GGA phonon dispersions have similar accuracy with respect to the experimental data. Si is an exception since the LDA phonon dispersions are already in very good agreement with experiment and GGA worsens the comparison.