[Wannier] k-gradient implementation

[Lun Yue]

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