[Wannier] k-gradient implementation

[Nicola Marzari]

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