Silicon example

[jahidhasansagor]

Hi,

I am trying to follow the example of Silicon (https://docs.epw-code.org/doc/TutorialZG.html). At one point I am confused. Can you explain how the following things happen?

In the example it is mentioned that
"Can you find the k-coordinates of the valence band maximum (VBM) and conduction band minimum (CBM)? Inspecting file bands.dat, those are:"

Code: Select all

0.000000  0.000000  0.000000
-5.811    6.253    6.253    6.253    8.817
...
0.000000  0.840000  0.000000
-2.783   -0.278    3.440    3.440    6.743

Later, in the preparation of equil-nscf_333.in file, following K_POINTS has been used.

Code: Select all

    K_POINTS crystal
    2
    0.000000 0.000000 0.000000 1
    0.000000 1.260000 1.260000 1

After that, it is mentioned that "Since the coordinates are given in units of the reciprocal lattice parameters, we obtain the K-coordinates by multiplying the k-coordinates of VBM and CBM states with the dimensions of the supercell, i.e. if k = [ x y z] then K = [ m×x n×y p×z], where integers m,n,p define an m×n×p supercell.

I am thinking that if 0.84 is multiplied by 3, we get 2.52. Then the K_POINTS should be
0.000000 0.0000000 0.0000000
0.000000 2.5200000 0.0000000

Would someone please clear my confusion?

Best
Md Jahid Hasan
Mechanical Engineering
University of Maine