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

[Stefano de Gironcoli]

I beg to differ

wurtzite https://en.wikipedia.org/wiki/Wurtzite in described as having 
Space group  186 P63mc http://img.chem.ucl.ac.uk/sgp/large/186az3.htm 
which is a non symmorphic group

zincblend (the fcc analogue of hcp wurtzite) has symmetry  216. F-43m 
http://img.chem.ucl.ac.uk/sgp/large/216az3.htm

which is symmorphic  ( td x translations )

stefano


On 3/13/26 21:27, Roland Winkler wrote:
> 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
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