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<div class="moz-text-flowed" style="font-family: -moz-fixed;
font-size: 12px;" lang="x-unicode">Dear Wannier Experts,
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<br>
I would like to raise a question, if it makes any sense to
construct Wannier functions and perform Wannier interpolation
starting from an ab initio grid that does not contain Gamma point.
For example if the k-points along direction z are kz=-1/2,
kz=-1/6, kz=1/6 . Such grids are frequently used in ab initio
calculations, but all Wannier90 examples include Gamma point.
However I did not find a statement that such shifted grids are
forbidden, neither in the literature not in the Wannier90 manual.
<br>
<br>
In my view the problem is that Wannier functions are considered
periodic in the real-space (R-vectors) with the period equal to
the size of the ab initio grid. In particular, the
minimal-distance replica selection method (see sec 4.2 <a
class="moz-txt-link-freetext"
href="https://iopscience.iop.org/article/10.1088/1361-648X/ab51ff/meta#cmab51ffs4">https://iopscience.iop.org/article/10.1088/1361-648X/ab51ff/meta#cmab51ffs4</a>
) explicitly assumes
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H(R+T) = H(R)
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however, if one uses a shifted k-grid, it becomes
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H(R+T) = - H(R)
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So, many things may go wrong with such assumption.
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Therefore my question - am I right? If so, should we explicitly
disallow the use of shifted grids, by stopping the calculation if
Gamma point is not on the grid? Or at least show a warning, and
mention this in the user manual? What is your opinion?
<br>
<br>
Or does someone of you regularly use shifted grids and that makes
no practical problems? What is your experience?
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Best Regards,
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<br>
Stepan Tsirkin,
<br>
University of Zurich.
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