Hello all. I have a question about CRYSTAL23 and how it works when it comes to calculating eigenvalues for certain k-points. Let's look at the example of SiO2 cell with 12 ions:
*** K POINTS COORDINATES (OBLIQUE COORDINATES IN UNITS OF IS = 6)
1-R( 0 0 0) 2-C( 1 0 0) 3-C( 2 0 0) 4-R( 3 0 0)
5-C( 1 1 0) 6-C( 2 1 0) 7-C( 2 2 0) 8-C( 0 0 1)
9-C( 1 0 1) 10-C( 2 0 1) 11-C( 3 0 1) 12-C( 1 1 1)
13-C( 2 1 1) 14-C( 2 2 1) 15-C( 0 0 2) 16-C( 1 0 2)
17-C( 2 0 2) 18-C( 3 0 2) 19-C( 1 1 2) 20-C( 2 1 2)
21-C( 2 2 2) 22-R( 0 0 3) 23-C( 1 0 3) 24-C( 2 0 3)
25-R( 3 0 3) 26-C( 1 1 3) 27-C( 2 1 3) 28-C( 2 2 3)
So here it shows 28 k-points for the 6x6x6 Monkhorst-Pack grid, and if I understand correctly, the reason why it's not showing all 216 points is because the program recognizes the crystal symmetry so it knows that the energy at (1 0 0) is the same as at (0 1 0), (0 0 1), (-1 0 0), etc?
If that is the case, then to build a high-symmetry path along Gamma-X-K-Gamma, for example... we could just take the points 4-R( 3 0 0) and 7-C( 2 2 0) and divide them by IS, which in this case is 6 to get the points (0.5, 0, 0) and (1/3, 1/3, 0). Would that be correct? Because that would make the extraction of eigenvalues quite simple for this path.
Thanks in advance,
Chris