[Pw_forum] Symmetry

[Paolo Giannozzi]

On Saturday 10 May 2003 09:09, Sergei Lisenkov wrote:

> It is very strange, but PWscf does not find the any symmetry in fullerene
> C60. Why?

Hi,

part of the answer is already contained in Stefano's message.
The following will appear in the next version of the users' 
guide. I hope this will help.

Paolo

-- 
Paolo Giannozzi             e-mail:  giannozz at nest.sns.it
Scuola Normale Superiore    Phone:   +39/050509412
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\item {\em pw.x does not find all the symmetries you expected.}
      {\tt pw.x} determines first the symmetry operations (rotations)
      of the Bravais lattice; then checks which of these are
      symmetry operations of the system (including if needed
      fractional translations). This is done by rotating
      (and translating if needed) the atoms in the unit cell
      and verifying if the rotated unit cell coincides with
      the original one.

      You may miss symmetry operations because:
      1) The number of significant figures in the atomic positions
         is not big enough. In {\tt PP/checksym.f90}, the variable
         {\tt accep} is used to decide whether a rotation is a
         symmetry operation. Its current value ($10^{-5}$) is quite
         strict: a rotated atom must coincide with another atom to 5
         significant digits. You may change the value of {\tt accep}
         and recompile.
      2) They are not acceptable symmetry operations of the Bravais 
         lattice. This is the case for C$_{60}$, for instance:
         the $I_h$ icosahedral group of C$_{60}$ contains 5-fold
         rotations that are incompatible with translation symmetry
      3) The system is rotated with respect to symmetry axis.
         For instance: a C$_{60}$ molecule in the fcc lattice will
         have 24 symmetry operations ($T_h$ group) only if the double
         bond is aligned  along one of the crystal axis; if C$_{60}$
         is rotated in some arbitrary way, pw.x may not find any
         symmetry, apart from inversion.
      4) They contain a fractional translation that is incompatible
         with the FFT grid. Typical fractional translations are 1/2 or 1/3
         of a lattice vector. If the FFT grid is not divisible 
         respectively by 2 or by 3, the symmetry operation will not
         transform the FFT grid into itself. Such symmetry operations
         are disabled to prevent problems with symmetrization. 
         Note that if you change cutoff or unit cell volume, the
         automatically computed FFT grid changes. and this may explain
         changes in symmetry (and number of k-points as a consequence)
         for no apparent good reason (only if you have fractional
         transations in the system, though).
      5) A fractional translation, without rotation, is a symmetry
         operation of the system (meaning that the cell is actually
         a supercell). In this case, all symmetry operations containing
         fractional translations are disabled. The reason is that in this
         rather exotic case there is no (simple) way to select those
         symmetry operations forming a group (in the strict mathematical
         sense).
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