[Pw_forum] k point convergence of dielectric properties

[Nicola Marzari]

Dario,


great detective work - and more remarkable than I would have
guessed (although I've been a fan for years of the shifted grids).

What Stefano said so clearly is related to the original idea of Alfonso
Baldereschi (PRB 7, 5121 (1973)) and generalized by Chadi and Cohen (PRB
8, 5747 (1973) - interestingly written in Paris VI Jussieu) - i.e. how 
to choose a single, special k-point (Baldereschi) or meshes of them
(Chadi and Cohen) in order to get the most accurate average. Basically,
a function f(k) that has the symmetry f the crystal, fourier expanded in
plane waves exp (i k.R) (R lattice vectors), can be rewritten as a
linear combination of symmetrized stars of plane waves (you bunch
together all the plane waves that have the same modulus for R, paying
some attention to degenerate shells that have different symmetry). By
choosing k's such that the largest number of those symmetrized stars
(sum exp (i k.R), sum over the R of a star) are zero, you have a recipe
that gives accurate integrals

Stefano de Gironcoli wrote:
> ... this annoying fact is the origin of the infamous 
> nosym=.true. options that much confusion generates in most users until 
> they realize what its meaning and purpose really is ... there are many 
> threads on that in the archive....

A god-blessing ! Try it - instead of using a 2x2x2 shifted mesh (4 
k-points, if no symmetry is present beside time reversal) use only 1
point, and stop the code from symmetrizing it using nosym=true.

The results will be very close to the full mesh, at 1/4 of the cost.

				nicola

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Prof Nicola Marzari   Department of Materials Science and Engineering
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