Why soft modes can be a sign of incorrect result ?

Many soft modes in the phonon dispersion curves may suggest technical mistakes in calculating the Hellmann-Feynman forces. Some reasons are listed below:

• A necessary displacement(s), hence the Hellmann-Feynman list(s) is missing by mistake.
• The supercell optimization process was done with not sufficient care. It is required that the largest absolute value of the HF force is less, or much less then 0.000100 eV/Å. If this condition is not fullfil the HF forces, computed for plus and minus displacements, stay much different. The interactomic potential, even for well optimized supercell, and for as small displacements as 0.03Å, could lead to different HF forces between plus and minus variants. Calculating both displacements on well optimized supercell, one takes the average force, and hence derives average force constants.
• One may check how the derived force constants diminish with increasing distance between relevant atoms, plotting them at Create/Hellmann-Feynman Forces/Plot Force Constants. The decay should be two, or better three orders of magnitude smaller in any direction of the supercell. When this condition is unsatisfied, the missing force constants beyond the supercell do not enter into the dynamical matrix, and the phonon modes may appear soft. Enlargement of the supercell (if possible) may help in this case. Small decay of force constants with distance between atoms occurs is strongly ionic crystals.
• If optimization of supercell was sufficient, and the decay of force constans is three order of magnitudes within the supercell, then fake soft modes can be caused (i) by neglecting the magnetic interaction, i.e. by neglecting to treat of spin-up, spin-down separatelly, or (ii) by neglecting the strong electron coupling interaction, i.e. not treating the crystal in LDA+U, or GGA+U approximation.