"Please follow http://dx.doi.org/10.1016/0010-4655(94)00164-W and
http://dx.doi.org/10.1016/0010-4655(74)90057-5. These are connected to some
programs found in the Computer Physics Communications Program Library
(http://www.cpc.cs.qub.ac.uk ) which are described in the articles:
ACKJ v1.0 Normal coordinate analysis of crystals, J.Th.M. de Hosson.
ACMI v1.0 Group-theoretical analysis of lattice vibrations, T.G. Worlton, J.L. Warren. See erratum Comp. Phys. Commun. 4(1972)382.
ACMM v1.0 Improved version of group-theoretical analysis of lattice
dynamics, J.L. Warren, T.G. Worlton." (Info from Pascal Thibaudeau)
If you have a bulk structure, then imaginary frequencies indicate a lattice instability. However, they can appear also as a result of a non-converged groundstate (Ecut, k-point grid, ...).
Recently I also found that the parameters tr2_ph for the phonons and conv_thr for the groundstate can affect the quality of the phonon calculation, especially the "vanishing" frequencies for molecules." (Info from Katalyn Gaal-Nagy)
An example: large negative phonon frequencies in 1-dimensional chains. "It is because probably some of atoms are sitting on the saddle points of the energy surface. Since QE symmetrizes charge density to avoid small numerical oscillation, the system cannot break the symmetry with the help of numerical noise. Check your system's stability by displacing one or more atoms a little bit along the direction of eigen-vector which has negative frequency. The eigen-vector can be found in the output of dynamical matrices of ph.x. One example here is: for 1d aluminum chain, the LO mode will be negative if you place two atoms at (0.0,0.0,0.0) and (0.0,0.0,0.5) of crystal coordinates. To break the symmetry enforced by QE code, change the second atom coordinate to (0.0,0.0,0.505). Relax the system. You will find the atom will get itself a comfortable place at (0.0,0.0,0.727), showing a typical dimerization effect." (info by Nicola Marzari).