[Wannier] k-gradient implementation

[Jonathan Yates]

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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