Dear Nicola and Jonathan,

Thank you for the expedient reply! This has been very helpful!

I have a followup question: in the output ".bvec" file, is there any particular reason why the set of b-vectors are written out for each k-point? Are there situations where the set of b-vectors differs from k-point to k-point?

Best regards,


Louisiana State University

On 11/4/23 6:04 AM, Jonathan Yates wrote:
Dear Yue,

  In support of Nicola’s comments: a long time I did some comparisons of the B1 
approach from MV97, and the simpler 6 neighbour approach. I didn’t look at the 
resulting MLWF - rather I looked at the form of the position operator they lead 
to. Indeed, for the same k-point mesh the B1 approach gives a more accurate 
position operator - and also a more symmetric representation. See

Prof. Jonathan Yates
Professor of Materials Modelling, Dept of Materials, University of Oxford
Tutor for Materials Science, St Edmund Hall, Oxford.

On 4 Nov 2023, at 02:55, Nicola Marzari <> wrote:

Dear Yue,

admittedly both are easy - but think e.g. at a fcc lattice - its reciprocal 
lattice is bcc, 8 neighbours, and calculating the gradient using those 8 b_k 
vectors will be more accurate, at a given sampling, than just using 3.


On 03/11/2023 23:55, Lun Yue wrote:
Dear all,
I have a question regarding the implementation of the k-gradient.
1) In Wannier90, it is implemented by constructing the weights such that the 
completeness relation is fully satisfied [Eq. (B1), PRB 56, 12847 (1997)].
2) Another approach would be to calculate the numerical derivatives along the 
reciprocal lattice vectors (which is easy as the quantities are given in a 
Monkhorst-Pack grid), and then transform to the Cartesian coordinates using the 
metric tensor and the reciprocal lattice vectors.
I am wondering why approach 1) was implemented over approach 2) in Wannier90. 
The second approach seems to be easier, or does approach 2) fail in some cases?
Best regards,
Lun Yue
Louisiana State University
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Prof Nicola Marzari, Chair of Theory and Simulation of Materials, EPFL
Director, National Centre for Competence in Research NCCR MARVEL, SNSF
Head, Laboratory for Materials Simulations, Paul Scherrer Institut
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