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<H2><A ID="SECTION00058000000000000000">
4.8 Fourier interpolation of phonon potential</A>
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<P>
The potential perturbation caused by the displacement of a single atom is
spatially localized. Hence, the phonon potential can be interpolated from
<I>q</I> points on a coarse grid to other <I>q</I> points using Fourier interpolation.
To use this functionality, first, one shoud run a <TT>ph.x</TT> calculation for <I>q</I>
points on a regular coarse grid.
Then, a <TT>dvscf_q2r.x</TT> run performs an inverse Fourier
transformation of the phonon potentials from a <I>q</I> grid to a real-space
supercell. Finally, by specifying <TT>ldvscf_interpolation=.true.</TT> in
<TT>ph.x</TT>, the phonon potentials are Fourier transformed to given <I>q</I> points.
<P>
For insulators, the nonanalytic long-ranged dipole part of the potential needs
to be subtracted and added before and after the interpolation, respectively.
This treatment is activated by specifying <TT>do_long_range=.true.</TT> in the
input files of <TT>dvscf_q2r.x</TT> and <TT>ph.x</TT>.
<P>
Due to numerical inaccuracies, the calculated Born effective charges may not
add up to zero, violating the charge neutrality condition. This error may lead
to nonphysical polar divergence of the phonon potential for <I>q</I> points close
to <I>Γ</I>, even in IR-inactive materials. To avoid this problem, one can
specify <TT>do_charge_neutral=.true.</TT> in the input files of
<TT>dvscf_q2r.x</TT> and <TT>ph.x</TT>. Then, the phonon potentials and the Born
effective charges are renormalized by enforcing the charge neutrality condition,
following the scheme of S. Ponce et al, J. Chem. Phys. (2015).
<P>
The Fourier interpolation of phonon potential is proposed and described in the
following papers:
<P>
A. Eiguren and C. Ambrosch-Draxl, Phys. Rev. B <B>78</B>, 045124 (2008);
<P>
S. Ponce et al, J. Chem. Phys. <B>143</B>, 102813 (2015);
<P>
X. Gonze et al, Comput. Phys. Commun., <B>248</B>, 107042 (2020).
<P>
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