corrections to VASP manual and wiki k-point pages

[ymantz]

Dear VASP developers,

I would like to point out a few small corrections that need to be made to one of the VASP manual and wiki pages. In the VASP manual, under "Automatic k-mesh generation" (http://cms.mpi.univie.ac.at/vasp/vasp/A ... ation.html) and at the VASP wiki, under "Automatic k-mesh generation" (http://cms.mpi.univie.ac.at/wiki/index. ... generation), the coefficient

(n1+1/2)/N1 should be [(n1+1/2)/N1]-1/2

and similarly for the coefficients (n2+1/2)/N2 and (n3+1/2)/N3.

In addition, the coefficient

(n1+s1+1/2)/N1 should be [(n1+s1+1/2)/N1]-1/2

and similarly for the coefficients (n2+s2+1/2)/N2 and (n3+s3+1/2)/N3.

These changes are needed to make the coefficients (ni+1/2)/Ni, i = 1-3 equivalent to those in HJ Monkhorst and JD Pack, Phys. Rev. B 13, 5188 (1976) and to make a Monkhorst-Pack mesh without a shift equivalent to a Gamma-centered mesh with a shift of 0.5 0.5 0.5, and vice versa.

Thank you,

Yves

[admin]

Will be considered. Thank you.

[ymantz]

Dear Administrator,

Thanks for your reply. As a follow up to my previous post, I would like to say that the proposed corrections to the VASP manual and wiki pages may not be needed.

In the manual and wiki pages, two sets of expressions are given for the Monkhorst-Pack coefficients. The expressions for Ni odd

(1) ni/Ni

and Ni even

(2) (ni+1/2)/Ni

are different from the expression given in HJ Monkhorst and JD Pack, Phys. Rev. B 13, 5188 (1976)

(2r-q-1)/2q, where r = 1, 2, 3, ..., q and q = number of points

which can be expressed as Eq. (3) using the notation of the manual and wiki pages

(3) [(ni+1/2)/Ni]-1/2

Although Eqs. (1) and (2) are different from Eq. (3), the sets of values given by Eqs. (1) and (3) are equivalent, at least for small, odd values of Ni. Also, the sets of values given by Eqs. (2) and (3) are equivalent, at least for small, even values of Ni.

For example, if Ni = 3, the results are

ni Eq. (1) Eq. (3)
0 0 -1/3
1 1/3 0
2 2/3 1/3

If Ni = 4, the results are

ni Eq. (2) Eq. (3)
0 1/8 -3/8
1 3/8 -1/8
2 5/8 1/8
3 7/8 3/8

The only question is whether or not the sets of values given by Eqs. (1) and (3) and by Eqs. (2) and (3) are equivalent for all odd and even values of Ni, respectively. If they are, then the expressions in the manual and wiki pages do not need to be changed.

On a different note, the statement that a Monkhorst-Pack mesh without a shift is equivalent to a Gamma-centered mesh with a shift of 0.5 0.5 0.5 and vice versa is made in regards to the expressions for the Gamma-centered coefficients

(ni+Si)/Ni

and Monkhorst-Pack coefficients

(ni+Si+1/2)/Ni

The above statement is true for these expressions.

Thanks,

Yves