Imaginary/negative frequencies can have several reasons, generally mean that the system can gain energy by displacement along this mode. Possible reasons for this can be:
- The structure is not at a local minimum. In this case an accurate geometry optimization will remove the negative frequencies.
- The structure is at a saddle point. In this case, try small random displacements, followed by a geometry optimization to break the symmetry.
- Although phonon calculations are in general possible for strained cells, in some cases, especially for 1D- or 2D-materials, an additional cell optimization might help to remove saddle points and the resulting imaginary frequencies.
If you encounter negative frequencies (or non-negative frequencies in general) in the accoustic branches at the gamma point, then the translational invariance is violated, as the system energy would change by a translation of the entire system. This is typically caused by a problem with the accuracy of the calculation.
If you are using classical potentials then you might try increasing the "Maximum interaction range" parameter in case you have long-ranged potentials (especially for atk2014).
For DFT you may try to increase the accuracy parameters, such as mesh cutoff, tolerance, etc.
As it is not always possible to increase the accuracy until all these non-zero frequencies have vanished, you can enforce the acoustic sum rule, by checking the ASR box in the DynamicalMatrix parameters. Then the dynamical matrix is shifted to correct the ASR at the gamma point.
Note that this doesn't correct negative frequencies at finite q-points.
You may also take a look at the Phonon tutorials
http://www.quantumwise.com/publications/tutorials/itemlist/category/94-phonons-and-thermal-properties .
