[Pw_forum] Relaxation of Cu100 with PBE pseudopotential

Alcantara Ortigoza, Marisol alcantar at phys.ksu.edu
Thu Feb 10 23:08:08 CET 2005


Hi,

I was trying to relax Cu100 using 9 p(2x2) layers + 9 vacuum by using
PBE pseudopotential provided by pwscf.

First I calculated the lattice constant which turned to be ~ 3.67 A, in
good agreement with experiment (3.61, an error less than 2%). Therefore,
I proceed to relax the surface and I found these results:

> Relaxation of Cu100 with a = 3.67 A
> 
> ATOMIC_POSITIONS (alat)
> Cu       0.500000000   0.500000000  -2.022823825
> Cu       0.000000000   0.000000000  -2.022823918
> Cu       0.000000000   0.500000000  -1.489744169
> Cu       0.500000000   0.000000000  -1.489744169
> Cu       0.500000000   0.500000000  -1.000543208
> Cu       0.000000000   0.000000000  -1.000543383
> Cu       0.000000000   0.500000000  -0.511527906
> Cu       0.500000000   0.000000000  -0.511527906
> Cu       0.000000000   0.000000000   0.000000000
> Cu       0.500000000   0.500000000   0.000000000
> Cu       0.500000000   0.000000000   0.511527906
> Cu       0.000000000   0.500000000   0.511527906
> Cu       0.000000000   0.000000000   1.000543383
> Cu       0.500000000   0.500000000   1.000543208
> Cu       0.500000000   0.000000000   1.489744169
> Cu       0.000000000   0.500000000   1.489744169
> Cu       0.000000000   0.000000000   2.022823918
> Cu       0.500000000   0.500000000   2.022823825
>  
>  Forces acting on atoms (Ry/au):
> 
>      atom   1 type  1   force =     0.00000000    0.00000000
> -0.00067738
>      atom   2 type  1   force =     0.00000000    0.00000000
> -0.00067707
>      atom   3 type  1   force =     0.00000000    0.00000000
> -0.00006941
>      atom   4 type  1   force =     0.00000000    0.00000000
> -0.00006941
>      atom   5 type  1   force =     0.00000000    0.00000000
> -0.00067574
>      atom   6 type  1   force =     0.00000000    0.00000000
> -0.00067565
>      atom   7 type  1   force =     0.00000000    0.00000000
> -0.00063682
>      atom   8 type  1   force =     0.00000000    0.00000000
> -0.00063682
>      atom   9 type  1   force =     0.00000000    0.00000000
> 0.00000000
>      atom  10 type  1   force =     0.00000000    0.00000000
> 0.00000000
>      atom  11 type  1   force =     0.00000000    0.00000000
> 0.00063682
>      atom  12 type  1   force =     0.00000000    0.00000000
> 0.00063682
>      atom  13 type  1   force =     0.00000000    0.00000000
> 0.00067565
>      atom  14 type  1   force =     0.00000000    0.00000000
> 0.00067574
>      atom  15 type  1   force =     0.00000000    0.00000000
> 0.00006941
>      atom  16 type  1   force =     0.00000000    0.00000000
> 0.00006941
>      atom  17 type  1   force =     0.00000000    0.00000000
> 0.00067707
>      atom  18 type  1   force =     0.00000000    0.00000000
> 0.00067738
> 
>    That means that,
> 
> 1st and 2nd layers separated by                        ~    + 6.62%
> completely wrong result!!!
> 2nd and 3rd layers approached by                     ~    - 2.16%
> completely wrong result!!!
> 
Which is clearly wrong according to the experiment, which predicts:

1st and 2nd layers approach by                   ~    -2.4 %   

2nd and 3rd layers separate by                   ~     +1.0 %  

Therefore, I was advised to calculate carefully the lattice constant
using the Murnaghan equation of state and repeat the relaxation. But,
this time I had to be more careful and calculate the stress too while
relaxing the system. 

I found a lattice constant just 0.1% larger than the one I had been
using before:

a = 3.6737 A 

And these were the results I found after relaxing the system:

> Relaxation of Cu100 with a = 3.6737 A  (Murnaghan fitting)
> 
> ATOMIC_POSITIONS (alat)
> Cu       0.500000000   0.500000000  -1.996326571
> Cu       0.000000000   0.000000000  -1.996326572
> Cu       0.000000000   0.500000000  -1.511684867
> Cu       0.500000000   0.000000000  -1.511684867
> Cu       0.500000000   0.500000000  -1.009845482
> Cu       0.000000000   0.000000000  -1.009845452
> Cu       0.000000000   0.500000000  -0.505544119
> Cu       0.500000000   0.000000000  -0.505544119
> Cu       0.000000000   0.000000000   0.000000000
> Cu       0.500000000   0.500000000   0.000000000
> Cu       0.500000000   0.000000000   0.505544119
> Cu       0.000000000   0.500000000   0.505544119
> Cu       0.000000000   0.000000000   1.009845452
> Cu       0.500000000   0.500000000   1.009845482
> Cu       0.500000000   0.000000000   1.511684867
> Cu       0.000000000   0.500000000   1.511684867
> Cu       0.000000000   0.000000000   1.996326572
> Cu       0.500000000   0.500000000   1.996326571
> 
> Forces acting on atoms (Ry/au):
> 
>      atom   1 type  1   force =     0.00000000    0.00000000
> 0.00023390
>      atom   2 type  1   force =     0.00000000    0.00000000
> 0.00023392
>      atom   3 type  1   force =     0.00000000    0.00000000
> -0.00011805
>      atom   4 type  1   force =     0.00000000    0.00000000
> -0.00011805
>      atom   5 type  1   force =     0.00000000    0.00000000
> 0.00087029
>      atom   6 type  1   force =     0.00000000    0.00000000
> 0.00087025
>      atom   7 type  1   force =     0.00000000    0.00000000
> -0.00009007
>      atom   8 type  1   force =     0.00000000    0.00000000
> -0.00009007
>      atom   9 type  1   force =     0.00000000    0.00000000
> 0.00000000
>      atom  10 type  1   force =     0.00000000    0.00000000
> 0.00000000
>      atom  11 type  1   force =     0.00000000    0.00000000
> 0.00009007
>      atom  12 type  1   force =     0.00000000    0.00000000
> 0.00009007
>      atom  13 type  1   force =     0.00000000    0.00000000
> -0.00087025
>      atom  14 type  1   force =     0.00000000    0.00000000
> -0.00087029
>      atom  15 type  1   force =     0.00000000    0.00000000
> 0.00011805
>      atom  16 type  1   force =     0.00000000    0.00000000
> 0.00011805
>      atom  17 type  1   force =     0.00000000    0.00000000
> -0.00023392
>      atom  18 type  1   force =     0.00000000    0.00000000
> -0.00023390
> 
>           total   stress  (ryd/bohr**3)                  (kbar)     P=
> -8.85
>   -0.00008010   0.00000000   0.00000000        -11.78      0.00
> 0.00
>    0.00000000  -0.00008010   0.00000000          0.00    -11.78
> 0.00
>    0.00000000   0.00000000  -0.00002029          0.00      0.00
> -2.99
> 
> 1st and 2nd layers approached by                     ~    -3.07 %
> good agreement with exp.!!! 
> 
> 2nd and 3rd layers separated by                        ~    +0.37 %
> not too bad ...
> 
We were intrigued by these opposite and inconsistent results under a
negligible change in the lattice parameter so, I was advised to repeat
the calculation with the old lattice constant value but, now also
calculating the stress, since maybe I had been doing something wrong... 

Well, fortunately, I got the same relaxed positions, same small final
forces, but what was really amazing was the stress I found:

      total   stress  (ryd/bohr**3)                  (kbar)     P=
231.63
   0.00160923   0.00000000   0.00000000        236.73      0.00
0.00
   0.00000000   0.00160923   0.00000000          0.00    236.73
0.00
   0.00000000   0.00000000   0.00150533          0.00      0.00
221.44

That's it, everything is consistent now, the systems wants to expand
because we imposed a little bit smaller lattice constant. Our question
is, how is it possible that the stress increases so much under such a
small change of the lattice constant?, how can we explain that we find
completely opposite results under such a small change of the lattice
constant?

We definitely conclude that either I'm missing something or Cu PBE
pseudopotentail is dangerously oversensitive so that we cannot trust.

Please let me know your comments.

Thank you very much.

Best regards.

Marisol Alcantara Ortigoza.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: /pipermail/attachments/20050210/b3207c3d/attachment.htm 


More information about the Pw_forum mailing list