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

[Roland Winkler]

Dear Paolo,

now that Stefano corrected my embarrassing mistake regarding the space
group symmetry of wurtzite (that explains everything I am seeing),
I kindly would like to ask one more technical question that you may be
able to answer, as you said you wrote the code for the charge
symmetrization.

I want to understand the generic approach implemented in the code for
charge symmetrization.  It seems to me that the initialization performed
by sym_rho_init_shells is conceptually very similar to the actual
symmetrization performed by sym_rho_serial.  Both routines map
reciprocal lattice vectors onto their images under the crystallographic
point group.  (The phase factors associated with nonsymmorphic
symmetries only affect the images of the charge density and
magnetization.)

Was there a reason why you implemented the rotations of the reciprocal
lattice vectors in sym_rho_init_shells via integer arithmetic, but
sym_rho_serial uses floating point arithmetic for this task?  It would
seem to me that integer arithmetic should work in both cases and it
would be better suited for this task than floating point arithmetic.

Thank you,

Roland


On Sat, Mar 14 2026, Paolo Giannozzi wrote:
> I wrote many years ago the code that symmetrizes the charge density
> in reciprocal space. Unfortunately I have no time right now to delve
> into your question, but please note that the code is generic, uses
> the available crystal symmetry and knows nothing about your specific
> case.
>
> In the first versions of QE symmetry operations were stored as
> matrices of integer numbers, acting on crystal axis. This is
> practical to deal with transformation of real-space grid
> indices. For all other cases, symmetry operations are transformed to
> real matrices, acting on cartesian coordinates.
>
> PG
>
>
> On 3/12/2026 7:20 PM, Roland Winkler wrote:
>> Dear Users
>> I am trying to understand how quantum espresso (pw) is
>> symmetrizing
>> the charge density rhog in reciprocal space.  My understanding is
>> that for a nonmagnetic symmorphic crystal structure all components
>> of rhog in a star should be equal [Streitwolf, Group Theory in
>> Physics, Eq. (6.8)].
>> For systems with zincblende structure this is, indeed, what I get.
>> However, for systems with wurtzite structure half of the components
>> in some stars have opposite signs.
>> More specifically, I have checked that sym_rho_init_shells
>> identifies the stars as expected.  However, sym_rho_serial then
>> gives opposite signs for half of the components in some stars.
>> The code in sym_rho_init_shells is quite straightforward, using
>> integer arithmetic for the transformations of the reciprocal lattice
>> vectors.  This code is doing what I expect, and it gives the results
>> I expect.  However, I have not yet got the same level of
>> understanding for sym_rho_serial.  The latter routine is doing
>> something more complicated, implementing the transformations of the
>> reciprocal lattice vectors via floating point arithmetic where I do
>> not understand the reason for this different approach.  I can merely
>> say that I have instrumented sym_rho_serial to write out the density
>> after symmetrization and I do not get what I expect as described
>> above.  [For example, for the job attached below, the components
>> 12,14,16,18,20,22 and 13,15,17,19,21,23 of rhog form two stars
>> (according to sym_rho_init_shells), but the corresponding values of
>> rhog in each of these stars are not equal.]
>> Am I missing something?  Any help is appreciated.
>> My input file for pw.x is attached.  I am using version 7.5.
>> Roland Winkler
>> &CONTROL
>>    calculation='scf'
>>    verbosity='high'
>>    prefix='zns' ! Output files are named according to prefix
>> /
>> &SYSTEM
>>    space_group=186 ! Space group number
>>    a=3.811  ! Lattice parameter a in angstroms
>>    c=6.234  ! Lattice parameter c in angstroms
>>    nat=2    ! Number of atoms in the asymmetric unit
>>    ntyp=2   ! Number of different atom types. Here, Zn and S.
>>    ecutwfc=40  ! Kinetic energy cutoff for wavefunctions (Ry)
>>    ecutrho=200 ! Kinetic energy cutoff for charge density and potential (Ry)
>> /
>> &ELECTRONS
>> /
>> &IONS
>> /
>> &CELL
>> /
>> ATOMIC_SPECIES
>>    Zn 65.38 zn_pbe_v1.uspp.F.UPF
>>    S  32.065 s_pbe_v1.4.uspp.F.UPF
>> ATOMIC_POSITIONS crystal_sg
>> Zn 1/3 2/3 0.00000
>> S  1/3 2/3 0.38500
>> K_POINTS automatic
>> 2 2 2  0 0 0
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