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Dear Espen,
<div class=""><br class="">
</div>
<div class="">thanks for your message.</div>
<div class="">First of all I'd like to remind the policy of this mailing list of signing posts with the official affiliation.</div>
<div class=""><br class="">
</div>
<div class="">Then, to your issue: while having complex values in the Mmn overlaps might seem surprising at first, this is correct.</div>
<div class="">If you are at Gamma only, your 'first-neighbour k-points' in k-space (needed to compute gradients in k-space, a key part of the Wannierisation algorithm), are "Gamma points" in neighbouring (reciprocal) cells.</div>
<div class=""><br class="">
</div>
<div class="">More precisely, the line </div>
<div class=""> 1 1 0 0 1</div>
<div class="">means exactly that the next 4x4 block is the overlap of the (periodic part of the) wave functions at the Gamma point (nk=1, first integer) with the point (k+b) obtained as starting the Gamma point (nk=1, second integer) and shifting it by (0,
0, 1) in units of reciprocal vectors (last three integers). So in this example "b" is the third reciprocal vector "b_3".</div>
<div class=""><br class="">
</div>
<div class="">Now, while at Gamma you can choose an appropriate phase to get real u_nk (which are periodic in real space), this phase can indeed be chosen *locally* in reciprocal space, but not globally.</div>
<div class="">That is to say, there is a non-zero phase between u_Gamma and u_b3.</div>
<div class=""><br class="">
</div>
<div class="">I think it is instructive to read sections IV.C.3 and IV.C.4 of the Marzari-Vanderbilt paper (PRB 1997), which has comments that are much closely related to this (for the related case of functions that can be chosen real under inversion symmetry).</div>
<div class="">This is also commented in footnote 4 of the review of Marzari et al, Rev. Mod. Phys.. 84 (2012) and discussed in detail in section II.F.2 of the same review.</div>
<div class=""><br class="">
</div>
<div class="">If you prefer to look into the code - I don't know about VASP, but for Quantum ESPRESSO you can check search for `zerophase` in the source code of pw2wannier90 (e.g. here
<a href="https://gitlab.com/QEF/q-e/blob/86749ba053539de4785264c98fdc7f3ffdbb2b0d/PP/src/pw2wannier90.f90" class="">
https://gitlab.com/QEF/q-e/blob/86749ba053539de4785264c98fdc7f3ffdbb2b0d/PP/src/pw2wannier90.f90</a>) to see when and how this phase is introduced (indeed, when the at least one of the last three numbers of the line discussed above is non-zero).</div>
<div class=""><br class="">
</div>
<div class="">I hope this explanation clarifies a bit the issue.</div>
<div class=""><br class="">
</div>
<div class="">Best,</div>
<div class=""><br class="">
</div>
<div class="">Giovanni</div>
<div class=""><br class="">
<div class="">
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<div>-- <br class="">
Giovanni Pizzi<br class="">
EPFL and NCCR MARVEL<br class="">
<a href="http://people.epfl.ch/giovanni.pizzi" class="">http://people.epfl.ch/giovanni.pizzi</a><br class="">
http://nccr-marvel.ch/en/people/profile/giovanni-pizzi</div>
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<blockquote type="cite" class="">
<div class="">On 27 Nov 2020, at 13:00, Espen Sagvolden <<a href="mailto:Espen.Sagvolden@sintef.no" class="">Espen.Sagvolden@sintef.no</a>> wrote:</div>
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<div class="">
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<span lang="EN-US" class="">Dear all,<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""><o:p class=""> </o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class="">Seemingly paradoxical values arise in the seedname.mmn files from wannier_setup with VASP: They seem to be complex-valued (alternating between purely real and purely imaginary), even when the underlying VASP wavefunction is real
(gamma-point computation). Since the seedname.mmn entries should only be orbital overlaps, this troubles me, but I'm new to Wannier90 and there may be something I don't know about the overlap integrals.<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""><o:p class=""> </o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class="">Here is an excerpt from the seedname.mmn file for a subspace of the four lowest orbitals from a gamma-point VASP run with real orbitals:<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""><o:p class=""> </o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class="">File generated by VASP: unknown system<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 4 1 4<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 1 1 0 0 1<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.946270648002 -0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.000695821546 0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.000000000000 -0.000000278197<o:p class=""></o:p></span></div>
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<span lang="EN-US" class=""> -0.000000000000 -0.000000195965<o:p class=""></o:p></span></div>
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<span lang="EN-US" class=""> -0.000695821546 0.000000000000<o:p class=""></o:p></span></div>
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<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.000000000000 -0.000000001135<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.000000000000 -0.000000278197<o:p class=""></o:p></span></div>
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<span lang="EN-US" class=""> 0.962394262259 0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
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<span lang="EN-US" class=""> -0.000000000000 -0.000000195965<o:p class=""></o:p></span></div>
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<span lang="EN-US" class=""> -0.000000000000 -0.000000001135<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.000000000265 -0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.962394258975 0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 1 1 1 1 -1<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.810376149699 0.000000000000<o:p class=""></o:p></span></div>
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<span lang="EN-US" class=""> -0.000596328721 0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.000000000000 0.498834776389<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.000000000000 0.103890215607<o:p class=""></o:p></span></div>
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<span lang="EN-US" class=""> -0.000000000000 0.000042846592<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.000000000000 0.498834776389<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.000000000000 0.000205733055<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.648824351005 -0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.046098789574 -0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.000000000000 0.103890215607<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.000000000000 0.000042846592<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.046098789574 -0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.860569485467 -0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 1 1 1 0 -1<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.810376181990 -0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.000596328947 -0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.000000000000 0.159445743764<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.000000000000 0.483948506733<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.000596328947 -0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.811164196521 -0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.000000000000 0.000065759196<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.000000000000 0.000199593417<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.000000000000 0.159445743764<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.000000000000 0.000065759196<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.847555958915 -0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.068638884681 -0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.000000000000 0.483948506733<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.000000000000 0.000199593417<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.068638884681 -0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.661838058801 -0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 1 1 0 1 1<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.810376169686 -0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.000596328168 0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.000000000000 0.339388794748<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.000000000000 -0.380058459416<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
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<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
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<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.000000000000 0.339388794748<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.000000000000 0.000139974419<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.767710591576 -0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.114737676141 0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.000000000000 -0.380058459416<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.000000000000 -0.000156748296<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.114737676141 0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.741683353736 -0.000000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""><o:p class=""> </o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class="">Yet, when seedname.mmn is used in a subsequent wannierization run with gamma_only = T, the resulting seedname_u.mat file seems to be OK (i.e., no imaginary components).<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""><o:p class=""> </o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class="">written on 25Nov2020 at 10:27:40<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 1 4 4<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""><o:p class=""> </o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.0000000000 +0.0000000000 +0.0000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> 0.5773502345 +0.0000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.0002035071 +0.0000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> +0.4419431296 +0.0000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> +0.6865514806 +0.0000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> +0.0003524826 +0.0000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> +0.9999999379 +0.0000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> +0.0000000032 +0.0000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.0000000003 +0.0000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.5773502553 +0.0000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> +0.0002035033 +0.0000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> +0.8155425747 +0.0000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.0394582080 +0.0000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.5773502102 +0.0000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> +0.0002035074 +0.0000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> -0.3735994902 +0.0000000000<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class=""> +0.7260097205 +0.0000000000<o:p class=""></o:p></span></div>
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<span lang="EN-US" class=""><o:p class=""> </o:p></span></div>
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<span lang="EN-US" class=""><o:p class=""> </o:p></span></div>
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<span lang="EN-US" class="">Is this because everything straightens itself out when the MLWF algorithm is run,<o:p class=""></o:p></span></div>
<div style="margin: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;" class="">
<span lang="EN-US" class="">or are imaginary components stripped away at some point because of the keyword gamma_only = T?<o:p class=""></o:p></span></div>
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<span lang="EN-US" class=""><o:p class=""> </o:p></span></div>
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<span lang="EN-US" class="">Best regards,<o:p class=""></o:p></span></div>
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<span lang="EN-US" class=""><o:p class=""> </o:p></span></div>
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<span lang="EN-US" class="">Espen<o:p class=""></o:p></span></div>
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<span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">_______________________________________________</span><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class="">
<span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">Wannier
mailing list</span><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class="">
<a href="mailto:Wannier@lists.quantum-espresso.org" style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px;" class="">Wannier@lists.quantum-espresso.org</a><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class="">
<a href="https://lists.quantum-espresso.org/mailman/listinfo/wannier" style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px;" class="">https://lists.quantum-espresso.org/mailman/listinfo/wannier</a></div>
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