# [Pw_forum] improper symmetry analysis

Lorenzo Paulatto paulatto at sissa.it
Wed Apr 22 11:41:33 CEST 2009

In data 22 aprile 2009 alle ore 10:17:02, Kun Yin <kyin.cn at gmail.com> ha
scritto:
> I don't quite understand this sentence. Just try to increase and decrease
> default nr and nrs values as suggested. There are total 9 calculations,
> 1-3 and 8-0 find symmetry right, 4-7 find symmetry wrong.

There is no symmetry "right" and "wrong", in calculations 4-7 pw.x does
not use certain symmetry operations because they are not compatible with
the FFT grid, this will make the calculation a more expensive (as the
reduced number of k-points is higher), but not wrong.

Let's do some number theory:
> temp-1.out:     G cutoff =  744.8786  ( 170271 G-vectors)     FFT grid:
> ( 80, 80, 80)
> temp-2.out:     G cutoff =  722.7847  ( 162825 G-vectors)     FFT grid:
> ( 80, 80, 80)
> temp-3.out:     G cutoff =  704.6276  ( 156325 G-vectors)     FFT grid:
> ( 80, 80, 80)
> temp-4.out:     G cutoff =  689.2743  ( 151669 G-vectors)     FFT grid:
> ( 75, 75, 75)
> temp-5.out:     G cutoff =  676.0151  ( 147349 G-vectors)     FFT grid:
> ( 75, 75, 75)
> temp-6.out:     G cutoff =  664.3728  ( 143471 G-vectors)     FFT grid:
> ( 75, 75, 75)
> temp-7.out:     G cutoff =  654.0170  ( 140255 G-vectors)     FFT grid:
> ( 75, 75, 75)
> temp-8.out:     G cutoff =  644.7053  ( 136787 G-vectors)     FFT grid:
> ( 72, 72, 72)
> temp-9.out:     G cutoff =  636.2575  ( 134435 G-vectors)     FFT grid:
> ( 72, 72, 72)

80 = 2^4       * 5
75 =       3   * 5^2
72 = 2^3 * 3^2
In other words, when the size of you FFT grid is not a multiple of 2 a
certain symmetry operation canot be represented properly. You should be
able to guess which operation it is from your atomic positions
configuration.

If I remember correctly symmetry is applied only on the FFT grid, the
dimensions of the smooth grid should not matter.

> For No. 5 calculation, defulat value is 75 and 48. I set nr1=nr2=nr3=80,
> nr1s=nr2s=nr3s=50. It finds symmetry right!

As consequence of what said above. Setting nrX=80 and leaving nrXs to
their default values should also work.

> when I decrease to nr1=nr2=nr3=72, nr1s=nr2s=nr3s=45. It reports error
> and crash.

Likely they are too small with respect to what your cutoffs requires!

regards

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Lorenzo Paulatto
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