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.marz...@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 >> _______________________________________________ >> Wannier mailing list >> Wannier@lists.quantum-espresso.org >> https://lists.quantum-espresso.org/mailman/listinfo/wannier > > -- > ---------------------------------------------------------------------- > 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 > > _______________________________________________ > Wannier mailing list > Wannier@lists.quantum-espresso.org > https://lists.quantum-espresso.org/mailman/listinfo/wannier _______________________________________________ Wannier mailing list Wannier@lists.quantum-espresso.org https://lists.quantum-espresso.org/mailman/listinfo/wannier