[Wien] tetrahedron BZ integration

[Peter Blaha]

> suppose one uses kgen to create a BZ mesh and find irreducible points.  The integral of some quantity f(k) over the full BZ can now be approximated by a sum over the irreducible k-points   integral of f = sum (i=1..N)  weight(i)  * f(ki).
>
> Are the weights which we find in the output of the kgen program these integration weights?  (I know that eg tetra requires something more clever - there the weights will depend of the position of every tetrahedron w.r.t. the fermi surface).  Or are these just numbers that say how many reducible points map onto the irreducible one, while some factors are still missing to get the weight(i) ?

For semiconductors or for the fully occupied bands of a metal the weights of
the individual k-points is just given as listed in case.klist (last column)
and these weights are simply the "multiplicity" of a k-point in the BZ.

For metals some bands may cross EF and for those (and only those) the
tetrahedron method has an effect. Here you divide the BZ into tetrahedra
and each tetrahedra is filled only up to EF. For these weight the "linear"
or the modified Tetrahedra method (by Blöchl) is used. In the latter one
has this non-linear correction (which may lead to negative weights! and to
problems in optic! see UG).

The actual weight of each eigenvalue is printed eg. in the case.help* files!


                                      P.Blaha
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-15671             FAX: +43-1-58801-15698
Email: blaha at theochem.tuwien.ac.at    WWW: http://info.tuwien.ac.at/theochem/
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