[Wannier] Questions encounted in MV97 paper

[spshu at mail.ustc.edu.cn]

Dear all,
 
Hello, everyone. We are two senior students in USTC, China. 
 
We encounted some problems in derivation of formula(34) in "Maximally localized generalized 
Wannier functions for composite energy bands", written by N.Marzari and D.Vanderbilt,
 1997. In this paper, it says that formula (34) was derived partly using formula(32), however, 
we could not get rid of the last term "ImlnM_{nn}^{k,b}" originally in formula (32). 
 
The second question is that it is difficult for me to obtain formula (26). It seems using Taylor 
expansion to expand M_{nn}^{k,b} in orders of b. However, I find it not so straightforward. 
 
The third question comes from "APPENDIX B: FINITE-DIFFERENCE FORMULAS FOR k-SPACE GRIDS". We want to know where can I find the original theory of finitre-difference that would leads to the "B1 condition". Where did the concept of using 
weight factor "w_{b}" come from? What is the role it plays in 
finite-difference for k grids?
 
Thanks a lot.
 
Shipeng Shu, Chen Liao
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