[gpaw-users] Why does usesym=True/False/None give different total energies and magnetic moments?

[jensj at fysik.dtu.dk]

> Dear GPAW users,
>
>  I'm testing GPAW on bulk Nickel (fcc) and have noticed that changing
> usesymm=True to False or None changes the result.
>
>  The total energy and magnetic moment changes on the order of 0.1 eV and
> 0.01 el/unit cell for the unphysical settings gpts=(8,8,8), kpts=(2,2,2).
> Going to gpts=(16,16,16), kpts=(10,10,10) the difference decreases by one
> order of magnitude. (Try attached example scripts.)
>
> Energies (E) and magnetic moments (m):
>     gpts=(8,8,8), kpts=(2,2,2)
>     usesym =   True -- E = -10.6508 -- m =   0.4906
>     usesym =   None -- E = -10.5793 -- m =   0.4987
>     usesym =  False -- E = -10.5793 -- m =   0.4987
>
>  I don't understand why there is any discrepancy at all between using the
> weighted irreducible k-point sum and the full sum over all k-points. I was
> expecting to get numerically the exact same answer even for the
> gpts=(8,8,8), kpts=(2,2,2) settings.
>
>  Does anyone of you understand why this happens?

If you use an orthorhombic cell, you get the same energy with and without
using symmetry.  Try to compare these:

  gpaw -x fcc Ni -O -M 0.5 --kpts=2,2,2

and

  gpaw -x fcc Ni -O -M 0.5 --kpts=2,2,2 --usesymm=False -i F

So, I think the error comes from some of the operations we do on the
real-space grid not fulfilling all the symmetries present.  2-d example: 
evaluate a px type projector function on an orthogonal grid and you will
get the same values as for a py projector - this is not the case for a
hexagonal grid.  With usesymm=True, the density and atomic density
matrices are symmetrized and forced to be symmetric.

JJ

> Cheers / Hugo
>
> p.s. I'm confused by the mail list addresses. I tried to send this to
> gpaw-users at servfys.fysik.dtu.dk but it bounced. d.s.
>
> --
> Hugo Strand, PhD student
>
> Materials and Surface Physics Group
> Department of Physics
> University of Gothenburg
> Origovägen 6B, Rum S3041
> SE-412 96 Gothenburg, Sweden
>
> mail: hugo.strand at physics.gu.se
> tel: +46 31 772 32 01
> fax: +46 31 772 20 92
> _______________________________________________
> gpaw-users mailing list
> gpaw-users at listserv.fysik.dtu.dk
> https://listserv.fysik.dtu.dk/mailman/listinfo/gpaw-users