Negative phonon frequencies are always a clear sign of unphysical results which becomes clear immediately when you consider that phonons are the quantization of atomic lattice vibrations.

Consider the root RMS amplitude of acoustic modes which present the (macroscopic) temperature T of the solid. Negative frequencies would mean we would have an abolute T which is negative, so *below* 0 K.

Another point is that negative phonon frequencies can only exist if the their wave vector has a complex argument arg*i due to i^2 = -1 (leading to negative frequencies/energies). A complex wave vector always localizes a particle by attenuating the corresponding wave function, see e.g. to a quantized particle in a box where its wavefunction becomes complex in the forbidden range = barrier. With a complex argument, the particle wavefunction decays rapidly in real space when moving away from the position of the particle -- hence its localization with a complex k argument. Such particles are described by Wannier wavefunctions. For phonons, this means that they *cannot* propagate since this would require a Bloch-like wavefunction (wavefunction of free particle, modulated by the periodic crystal potential) and hence have zero propagation speed (group velocity of phonon). As a consequence, the first derivative of the phonon frequency in k-space is 2pi*df/dk = 0, again due to the correspondence principle in QM (momentum of particle = group velocity of particle multiplied by its mass). Since 2pi*df/dk = 0 stands as per above, there is no physical sound way you get negative phonon frequencies since phonons would have to propagate with a wave vector k not allowing any propagation to change their frequency. If you need an illustration of the above, then please refer to https://doi.org/10.1088/1361-6641/ab8171 or to

https://www.researchgate.net/publication/342261898_Semiconductor_Science_and_Technology_Non-equilibrium_dynamics_materials_and_structures_for_hot_carrier_solar_cells_a_detailed_review_Topical_Review_Non-equilibrium_dynamics_materials_and_structures_fo

There, see to p. 38 (footnote 34) and to p. 6 (equation 6) for the analytic formula of 2pi*df/dk.

This issue was also taken up by the Zunger group, see

https://doi.org/10.1016/j.mattod.2019.08.003 , pp. 4 & 5.

You can avoid negative phonon frequencies by tweaking two parameters:

1) increasing the number of k points (increases the frequency limit for the Fourier transform of the wavefunctions without violating the Shannon theorem; look it up, it's worth it).

2) increase the cutoff energy which has basically the same effect.

until such artefacts are gone. Unlike in electronic structure calculations, the energy of phonons (vs. electrons) is much smaller when seen relative to kT, so the cutoff energy has to be accordingly high to account for a minimal change in phonon frequency to keep the k value from getting complex (unphysical). With VASP, we used cutoff energies of 1.6 to 2 keV when calculating SLs with compounds such as GaSb, BSb, InN, or GaN (few or even one k-point will do due to SL having a mini-BZ vs. full BZ for bulk solids). For bulk approximants, the cutoff energy is usually lower such as 450 eV, but the k-mesh must be much denser; we used 10x10x10 generated with Monkhorst-Pack rules, see http://dx.doi.org/10.1016/j.solmat.2012.12.029

So yes, you need as many dyn files in QE as you have k-points to make sure you get realistic results. Please not that this is a necessary, though not sufficient condition for accuracy; I do not have any info about the approximant you are using.

I hope I could help;

have a good one,

Dirk

thank you Dr. D. König for the detailed answer and taking so much time to respond. Sure it will take a while to go through the references given by you and digest. However, i basically understand the logic of phonon energy is much smaller compared to electrons, so the need of very high cut-off energy and / or dense grid K-grid to optimize the cell. [Is my understanding correct? is it either high cut-off or dense grid, or can i mix both options?]

i tried VASP with Phonopy : failed with negative frequency.

Tried with QE with Phonopy: failed with negative frequency.

tried with only QE, through .dyn file creation using pw.x for SCF step and then tried to create dynamical matrices step with ph.x this always stopped with famous Error in routine cdiaghg (100):

problems computing cholesky . each time with different cdiaghg codes.

However, to sort out the issue kindly let me know the following so that i make another attempt.

my system is a 2D monolayer with vacuum slab above. and a total of 12 atoms. Orthorhombic Pbam space group.

1. as you suggested, i will try with very high ENCUT and also dense KPOINTS in vasp for geometry relaxation and apply Phonopy, and see.

2. with same values i try with QE/Phonopy, if the step-1 above with VASP fails.

May kindly give any suggestions on the above trial.

Regards

D. König Thanks again for your detailed reply.

After many other trail and errors. I found the following and FINALLY success in removing the negative frequencies. If this procedure helps others, may follow.

1. The VASP geometry relaxation with very strict convergence criteria was always failed at the end, as it not converging and going into perpetual calculation with fluctuations, or it asking to change EDIFF value or copy CONTCAR and restart, or over converging to energy but not forces etc. [whatever it may be the strict criteria was a fail in my calculation. Not sure if i am doing anything wrong]

2. Then as per some suggestion, i did vc-relax with QE with high convergence criteria and it converged.

3. took the geometry from there and then with Phonopy/ finite displacement method with VASP finally successful in removing the negative frequency.

So, Can i conclude here, that VERY STRICT CONVERGENCE CRITERIA is the KEY?

Readers may offer opinion, please.

Regards