Density functional perturbation theory with spin-orbit coupling: Phonon band structure of lead

The effect of spin-orbit coupling on phonon band structures can be profound for materials containing heavy elements. We describe our implementation of density functional perturbation theory with the spin-orbit interaction for norm-conserving pseudopotentials. We show that the spin-orbit effect on the phonon frequency at the X point in face-centered-cubic Pb is very large; it explains the discrepancy between calculated and experimental frequencies previously observed by Liu and Quong [Phys. Rev. B 53, R7575 (1996)]. Several technical issues (the exchange-correlation functional, the presence of semicore states, the pseudization scheme, and the real-space range of interatomic force constants) are also investigated.