[QE-users] symmetrization of charge density (pw)

[Roland Winkler]

Hi Pietro,

No, the wurtzite structure (space group #186) is symmorphic, and I
deliberately picked it for that reason.  Ultimately, I am interested,
in particular, in nonsymmorphic structures.  But I wanted to get started
with the simpler symmorphic case.  Yet right now I am stuck.

What physics am I interested in?  This is our recent preprint
arxiv:2509.17278: I want to project the charge and magnetization density
on the irreducible representations (IRs) _not_ of the crystallographic
point group of the respective system where these quantities by
definition must be fully invariant (like the charge density that is
symmetrized by quantum espresso to make it invariant under the point
group of the system), i.e, these quantities transform according to the
identity IR of the symmetry group.  But I want to project these
densities onto the IRs of the extended point (super) group that also
contains space inversion and time inversion as symmetry elements.  In
this case, the magnetization density and parts of the charge density
will transform according to some nontrivial IRs of the larger point
group.  Conceptually, what we are after, is closely related to
"symmetrized plane waves" that you find discussed in (mostly old) books
on group theory in solid state physics.

I was happy to see that most of the infrastructure needed for this is
already present in quantum espresso.  This is the code for the
symmetrization of the charge density as well as the code in bands.x for
identifying the symmetry of Bloch functions (the switch lsym for
bands.x).

And yes, I believe this would be a cool extension for quantum espresso.
There is a lot of physics that one can learn from these nontrivial
projections.

But right now I find that some part of the symmetrized charge density in
a wurtzite structure like wurtzite ZnS (point group C6v) transforms
according to a nontrivial IR of C6v (Gamma_3 in Koster's notation), as
if the actual symmetry of wurtzite was C3v.  This does not make sense.

Roland



On Fri, Mar 13 2026, Pietro Davide Delugas wrote:
> Might it be that the operation is not symmorphic? If  I understand
> well the coefficients differ for a PI phase 
>
> Il 13 mar 2026 12:26 PM, Roland Winkler <rwinkler at niu.edu> ha
> scritto:
> Thank you Pietro for the quick reply.
>
> Sure, the wurtzite structure I am looking at belongs to the hexagonal
> crystal system.  So the lattice has point group symmetry D_6h (which
> includes space inversion).  But the wurtzite structure (space group
> 186) has point group symmetry C_6v (it lacks space invesion).  It is
> the latter group that I am refering to and that is correctly used by
> sym_rho_init_shells and sym_rho_serial.  The stars are defined for
> point group C_6v.  However, after symmetrization, the charge density
> has point group symmetry C_3v, i.e., it is not invariant under C_6v.
>
> What am I missing?
>
> Roland