[Pw_forum] Convergence of imaginary modes

[Brad Malone]

Hello QE users,

I am calculating the lattice dynamical properties of a high-pressure phase.
As has been documented in this forum, phonon frequencies can be quite
sensitive to the various other parameter of the calculation (wavefunction
cutoff, BZ sampling, etc.) and it's important to test this explicitly and
not rely on the parameters one finds converged for say, a total-energy SCF
calculation.

In the testing of my phonon frequencies with respect to the density of the
k-point sampling in the SCF calculation prior to the phonon calculation, I
decided to test a uniform grid of q-points rather than simply the Gamma
phonon since I don't know of any a priori reason to expect that all phonon
frequencies converge identically (although in my prior experience this is
approximately true). I found that almost all frequencies are converged to
within about 1% or so at a "small" kgrid sampling of about 40x40x40.
However, one mode is wildly unconverged at this point, and differences on
the order of 100s of cm^1 can be found by going to a kgrid sampling of
80x80x80. So I just kept increasing the kpoint sampling until I converged
this mode. The mode didn't fully converge until 200x200x200, although it is
pretty close at 160x160x160.The mode finally converged to a negative value
(although was positive until the kpoint sampling was in the triple digits in
each direction).

This negative mode signals an instability of the structure along the path
corresponding to the phonon displacement pattern. That's all well and good.
I know that this structure is thermodynamically unstable at pressures in the
ballpark of the calculation, and so if it's dynamically unstable too no
problem. Since the structure becomes more thermodynamically stable at higher
presures, I increased the pressure and tested the phonon frequencies again.
I found that the negative mode goes positive, and increases in frequency as
the pressure is increased (as one might guess). However, this mode still
depends very sensitively on the kpoint sampling and doesn't get close to
full convergence until about 160x160x160 similarly to the calculation at
lower pressures.

In previous lattice dynamical calculations, I've always been blessed with
positive frequencies (at least those that can't be ASRed away) and I'm
curious as to whether the more sensitive convergence of imaginary modes (and
those that are close to being unstable) is a property that others have found
in their calculations or whether it is something unusual with the system
that I am studying.

Thanks,
Brad Malone
UC Berkeley
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