inputting k- points

[Saranyanarayanan]

When I went through the program for the calculation of photonic band gap of diamond structure (data analysis tutorial of MPB) I noticed that the k- points that are used:
(vector3 0 0.5 0.5) ; X
(vector3 0 0.625 0.375) ; U
(vector3 0 0.5 0) ; L
(vector3 0 0 0) ; Gamma
(vector3 0 0.5 0.5) ; X
(vector3 0.25 0.75 0.5) ; W
(vector3 0.375 0.75 0.375) ; K
But when I searched in literature found that there is a small difference in the k-points:
(vector3 0.5 0 0.5) ; X
(vector3 0.625 0.25 0.625) ; U
(vector3 0.5 0.5 0.5) ; L
(vector3 0 0 0) ; Gamma
(vector3 0.5 0 0.5) ; X
(vector3 0.5 0.25 0.75) ; W
(vector3 0.375 0.375 0.75) ; K
[High-throughput electronic band structure calculations:
challenges and tools, Wahyu Setyawan and Stefano Curtarolo]
I run the program with both the set of k-points and the gap i obtained is 10.869% and 11.0109% respectively.
Why is it so?

[stevengj]

You have to be careful of the basis; the k points in MPB are specified in the basis of the primitive reciprocal lattice vectors, not in the Cartesian basis (i.e. not in the basis of the reciprocal lattice vectors of the cubic supercell).

See also the reciprocal->cartesian and cartesian->reciprocal conversion functions

[stevengj]

For example, if we look at the L point:

mpb> (set! geometry-lattice (make lattice 
                         (basis-size (sqrt 0.5) (sqrt 0.5) (sqrt 0.5))
                         (basis1 0 1 1)
                         (basis2 1 0 1)
                         (basis3 1 1 0)))
mpb> (reciprocal->cartesian (vector3 0 0.5 0))
$1 = #(0.5 -0.5 0.5)

we see that in Cartesian coordinates MPB's L point is (0.5,-0.5,0.5), which is the same as the one you quote above (up to a reflection).