[Pw_forum] symmetry problem with Si lattice
Paolo Giannozzi
giannozz at nest.sns.it
Tue Nov 27 14:42:18 CET 2007
On Nov 27, 2007, at 13:43 , Ezad Shojaee wrote:
> i have a silly problem about Si lattice. I defined it as an SC
> (simple cubic)
> with 8 atoms per basis:
>
> ATOMIC_POSITIONS
> Si 0.00 0.00 0.00
> Si 0.50 0.50 0.00
> Si 0.00 0.50 0.50
> Si 0.50 0.00 0.50
> Si 0.25 0.25 0.25
> Si 0.75 0.75 0.25
> Si 0.25 0.75 0.75
> Si 0.75 0.25 0.75
>
> K_POINTS
> 4
> 0.1250000 0.1250000 0.1250000 1.00
> 0.3750000 0.3750000 0.3750000 1.00
> 0.3750000 0.1250000 0.1250000 3.00
> 0.3750000 0.3750000 0.1250000 3.00
>
> the Total Energy is 4-times as great as the Fcc structure
> total energy (till the 5-th digit), but the code has detected
> 24 symmetries, with no inversion for the SC one. What's
> the problem(if there is any)? Should'nt be 48 symmetries?
there isn't any problem, but there is a subtlety. The 24
symmetries that have no associated fractional translation
are found; the remaining 24 have an associated fractional
translation (1/4 1/4 1/4) and are also found, but not accepted.
The reason is that in a supercell the choice of fractional
translations is not unique and you have no (simple) way
to be sure that the set of all symmetry operations is actually
a group, in the mathematical sense.
Paolo
---
Paolo Giannozzi, Dept of Physics, University of Udine
via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222
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