Libxc tutorial

Directory for Libxc totorial. For the detaild formalism and notation, please refer

1. https://www.tddft.org/programs/libxc/manual/libxc-5.1.x/
2. https://doi.org/10.1016/j.cpc.2012.05.007

We have following example systems

1. Graphene: metalic system with occupation smearing
2. WS2     : insulating system w/o occupation smearing

For each example system, we have LDA/GGA example directries.

In each directory, we compute

1. Vxc(r) and  <mk|Vxc|nk> from pw2bgw.x ... Ref
2. Vxc(r) and  <mk|Vxc|nk> from pp.x
3. Vxc(r) and  <mk|Vxc|nk> from Libxc

We only consider collinear calculation.

For method 2.

we first do pp.x and print Vxc(r) = Vtot(r) - Vbare(r) - Vhatree(r) in a FFTgrid and then
    
1-1. do FFT Vxc(r) to Vxc(g). Then we can compute <mk|Vxc|nk> in G-space.
1-2. do IFFT unk(g) to unk(r). Then we can compute <mk|Vxc|nk> in R-space.