# [Pw_forum] Symmetry

Paolo Giannozzi giannozz at nest.sns.it
Mon May 12 10:28:39 CEST 2003

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,

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
Piazza dei Cavalieri 7      Fax:     +39/050509417, 050563513
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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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