[Pw_forum] symmetry problem with Si lattice

[Paolo Giannozzi]

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