Abinit and anaddb dielectric tensor and effective charges outputs incoherences

Hi all,

I am running DFPT calculations for a tetragonal bulk perovskite structure (BTO) using the abinit executable. I obtain second and third order derivatives of the energy, as well as the dielectric tensor, Born effective charges, phonon frequencies and non-linear optical susceptibilities. All of the afore-mentionned quantities are finite.

However, when I post-process the derivative-database issued from the abinit executable with anaddb, I get infinity values for the same dielectric tensor and Born effective charges. The associated log file says:

src_file: m_ddb_diel.F90
src_line: 184
mpi_rank: 0
message: |
The lowest mode appears to be a “true” negative mode,
and not an acoustic mode. This precludes the computation
of the frequency-dependent dielectric tensor.
Action : likely there is no action to be taken, although you,
could try to raise your convergence parameters (ecut and k-points).
For your information, here are the four lowest frequencies :
-5.61982526E-04 -5.61982526E-04 0.00000000E+00 0.00000000E+00
…” (frequencies in Hartree)

In summary, I get negative phonon frequencies (soft modes) for what seems to be the first 2 acoustic modes. I did increase ecut, the number of k-points and relaxed the structure even more but the two lowest frequencies remain negative regardless.

Why do the abinit and anaddb codes yield different results for the same quantities? I assume that the abinit output is more reliable than the anaddb output. How are the dielectric tensor and Born effective charges calculated from anaddb?

As a new user, I am not allowed to attach input/output files but I would be happy to do so if requested.

Many thanks

Master student at EPFL/ETH


Did you check the variables asr and chneut?



chneut has different default value for anaddb and abinit. In the asr variable description also says:
" So, if asr is non-zero, the correction to the self-force will be determined, and the self-force will be imposed to be consistent with the ASR. This correction will work if IFCs are computed (ifcflag/=0), as well as if the IFCs are not computed (ifcflag==0). In both cases, the phonon frequencies will not be the same as the ones determined by the output of abinit, RF case. If you want to check that the DDB is correct, by comparing phonon frequencies from abinit and anaddb, you should turn off both asr and chneut."

Joao Abreu

It could be a bit vicious if the ASR imposition leads to negative phonon modes, but the ASR has to be corrected, certainly. You can also run the DFPT with “rfasr 1” to impose ASR from the onset.

Have you plotted the phonon band structure? Which xc functional and volume (expt vs relaxed …) are you using? For these materials the polar mode is a bit sensitive.

Dear Joao and mverstra,

Thank you for your replies

I was not aware that the asr and chneut default values were different for abinit and anaddb. I used asr = 2 and chneut = 2 using anaddb whereas the abinit default values are asr = 1 and chneut = 1. I will correct this, thanks for spotting it out!

I further checked the eigendisplacements and could see that the 2 negative modes are actually optical (modes 3, 4 and 5 are acoustic and were corrected by the asr). Can imaginary optical modes be corrected at all or exempted from the calculation of the dielectric tensor? Since tetragonal BaTiO3 is stable at RT (the rhombohedral phase is energetically most favorable at 0K) and a ferroelectric, I assume that both thermal and ferroelectric instabilities could be the origin of the negative optical phonon modes. For info, I used the LDA xc functional, the experimental volume is 4.3404983E+02 bohr^3 and becomes 4.1587683E+02 bohr^3 after relaxation using toldff = 1E-12. I also used the PBEsol xc functional, which gave me better structural properties (in particular a less cubic tetragonality). Preliminary results (using a less restrictive toldff = 1E-6) yielded 2 to 3 negative phonon frequencies as well.

I did not plot the full phonon band structure since I am only interested in the homogeneous electric field perturbation at q = 0 0 0. I only have the frequencies for each of the 15 modes down below if this can help:

ABINIT generated phonon band structure file. All in Ha atomic units

number_of_qpoints 1

number_of_phonon_modes 15

1   -0.5619825262E-03   -0.5619825262E-03    0.0000000000E+00    0.0000000000E+00    0.0000000000E+00    0.8078087701E-03    0.8290171799E-03    0.8290171799E-03    0.1315530667E-02    0.1315530667E-02    0.1346330721E-02    0.1418493506E-02    0.2190823795E-02    0.2190823795E-02    0.2384567998E-02


The optical mode is really unstable, and in this case it’s physical. To get to room T BaTiO3 you need to renormalize the phonons quite a bit: anharmonicity makes the frequencies real in practice. This can be done with the a-TDEP executable

there is no tutorial on this yet (should be coming), but it’s very powerful.

Just removing the mode from the dielectric constant calculation is not really correct - the sum rules will be broken.

Dear mverstra,

Thank you for your reply, this is very helpful.

Looking forward to the a-TDEP tutorial !