[Wannier] k-gradient implementation

[Lun Yue]

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,

Lun

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
> http://www.tcm.phy.cam.ac.uk/~jry20/wannier/pos_op.html
>
>   Jonathan
>   
> —
> 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 <nicola.marzari at epfl.ch> 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.
>>
>> nicola
>>
>>
>>
>> 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
>> Contact info and websites at http://theossrv1.epfl.ch/Main/Contact
>>
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