K point & Brillouin zone

[chenmy]

I have a question about the k-point that is given by vasp.
I found some k-points would not include the Brillouin zone.
For example, a hexagonal crystal system, kpoints 4x4x4, and the reciprocal crystal length (b1, b2, b3), got 20 kpoints(obtained in OUTCAR) through symmetry operator.
{this crystal character: b1=b2, angle between b1 and b2 is 60 degree}
Regardless of z axis , this k-points on x-y plane spread in a parallelogram b1xb2 (only consider xy plane), but BZ of this crystal shows hexagon shape. (3/8,3/8, 1/8) is one of this case that don't locate in Brullouin zone.
I want to confirm whether these kpoints out of BZ would fold into BZ during vasp calculation or not.
If they fold into BZ, the k+G numbers will be wrong. that would results in the mistake result in my calculation.
If not, they keep the same value, and proceed the calculation, k+G number will be right.
Does anyone know the answer of this question?
Thanks a lot.

[forsdan]

I'm not sure I understand your question. Nevertheless, please notice that an even mesh breaks the full symmetry of a hexagonal cell. The subsequent symmetrization and reduction to the irreducible Brillouin zone then provides the k-point grid that is used in the calculation. Please compare with page 30 in

http://cms.mpi.univie.ac.at/vasp-worksh ... points.pdf

A gamma centered grid however preserves the full symmetry of the cell and also converges significantly faster than the even grid.

http://cms.mpi.univie.ac.at/vasp/vasp/h ... tices.html

The recommendation is therefore to use a gamma centered grid for a hexagonal cell.

Cheers,
/Dan
<span class='smallblacktext'>[ Edited Thu May 27 2010, 10:48PM ]</span>

[oamnehc]

I'd like to re-state the question raised by chenmy, for I have the similar problem.

Indeed it is natural and correct that by using a 4x4x4 k-mesh input (which is already a gamma-centered grid) for a hexagonal cell (the angle between a1 and a2 is pi/3), one gets 20 k points after symmetrization.

The problem is, why, among the 20 k points, are there 2 points described in VASP OUTCAR as (3/8,3/8,1/8) and (3/8,3/8,3/8)? These two points are OUT OF the conventionally defined Brillouin zone, and actually SHOULD be described by (3/8,-5/8,1/8) and (3/8,-5/8,3/8) instead. They should sit on the BZ boundary.

This is not just a matter of different descriptions. When it comes to any follow-up calculations using k+G, one would wonder if the confusing description of the k points is on purpose or not.

Best,
oamnehc