ISYM-tag and SYMPREC-tag

$$ISYM = 0 \vert 1 \vert 2 \vert 3$$

Default

1

switch symmetry on (1, 2 or 3) or off (0). For ISYM=2 a more efficient, memory conserving symmetrisation of the charge density is used. This reduces memory requirements in particular for the parallel version. ISYM=2 is the default if PAW data sets are used. ISYM=1 is the default if VASP runs with US-PP's.

For ISYM=3, the forces and the stress tensor only are symmetrized, whereas the charge density is left unsymmetrized (VASP.5.1 only). This option might be useful in special cases, where charge/orbital ordering lowers the crystal symmetry, and the user wants to conserve the symmetry of the positions during relaxation. However, the flag must be used with great caution, since a lower symmetry due to charge/orbital ordering, in principle also requires to sample the Brillouin zone using a k-point mesh compatible with the lower symmetry caused by charge/orbital ordering.

The program determines automatically the point group symmetry and the space group according to the POSCAR file and the line MAGMOM in the INCAR file. The SYMPREC-tag (VASP.4.4.4 and newer versions only) determines how accurate the positions in the POSCAR file must be. The default is 10$^{-5}$, which is usually suffiently large even if the POSCAR file has been generated with a single precision program. Increasing the SYMPREC tag means, that the positions in the POSCAR file can be less accurate. During the symmetry analysis, VASP determines

• the Bravais lattice type of the supercell,
• the point group symmetry and the space group of the supercell with basis (static and dynamic) - and prints the names of the group (space group: only 'family'),
• the type of the generating elementary (primitive) cell if the supercell is a non-primitive cell,
• all 'trivial non-trivial' translations (= trivial translations of the generating elementary cell within the supercell) -- needed for symmetrisation of the charge,
• the symmetry-irreducible set of k-points if automatic k-mesh generation was used and additionally the symmetry-irreducible set of tetrahedra if the tetrahedron method was chosen together with the automatic k-mesh generation and of course also the corresponding weights ('symmetry degeneracy'),
• and tables marking and connecting symmetry equivalent ions.

The symmetry analyses is done in four steps:

• First the point group symmetry of the lattice (as supplied by the user) is determined.
• Then tests are performed, whether the basis breaks symmetry. Accordingly these symmetry operations are removed.
• The initial velocities are checked for symmetry breaking.
• Finally, it is checked wheter MAGMOM breaks the symmetry. Correspondingly the magnetic symmetry group is determined (VASP.4.4.4 and newer releases only; if you use older version please also see section 6.12).

The program symmetrises automatically:

• The total charge density according to the determined space group
• The forces on the ions according to the determined space group.
• The stress tensor according to the determined space group

Why is symmetrisation necessary: Within LDA the symmetry of the supercell and the charge density are always the same. This symmetry is broken, because a symmetry-irreducible set of k-points is used for the calculation. To restore the correct charge density and the correct forces it is necessary to symmetrise these quantities.

It must be stressed that VASP does not determine the symmetry elements of the primitive cell. If the supercell has a lower symmetry than the primitive cell only the lower symmetry of the supercell is used in the calculation. In this case one should not expect that forces that should be zero according to symmetry will be precisely zero in actual calculations. The symmetry of the primitive cell is in fact broken in several places in VASP:

• local potential:

  In reciprocal space, the potential $V( {\bf G})$ should be zero, if G is not a reciprocal lattice vector of the primitive cell. For PREC=Med, this is not guaranteed due to "aliasing" or wrap around and the charge density (and therefore the Hatree potential) might violate this point. But even for PREC=High, small errors are introduced, because the exchange correlation potential $V_{xc}$ is calculated in real space.

• k-points:

  In most cases, the automatic k-point grid does not have the symmetry of the primitive cell.