We present a self-consistent linear response calculation of phonon dis
persion relations in LiH and LiD. Our calculations are performed withi
n density-functional perturbation theory using the local-density appro
ximation and the plane-wave pseudopotential method with the inclusion
of the non-linear core correction for exchange and correlation. We acc
urately estimate zero-point effects on the structural properties at ze
ro temperature. The calculated lattice parameter is a little too small
with respect to experiment. The non linear core correction and the in
clusion of zero-point effects reduce the discrepancy from 5.1% to 2.5%
. Good agreement is obtained between calculated and observed phonon di
spersions.