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

[Paolo Giannozzi]

I guess the reason is that the conversion from cartesian to crystal axis 
for G-vectors is done in-place using a routine unsurprisingly called 
"cryst_to_cart". The output is in the same real variable "g0". It is not 
wise to compare real numbers with "if (a == b)", as one would do with 
integers, even if in practice they are integers.

Paolo

On 3/14/2026 2:21 PM, Roland Winkler wrote:
> 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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-- 
Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,
Univ. Udine, via delle Scienze 206, 33100 Udine Italy, +39-0432-558216