[Pw_forum] Using q2r.x - incorrect IFC symmetries

[Paolo Giannozzi]

On Mon, 2015-02-09 at 15:45 -0800, Navaneetha Krishnan wrote:

> I used ibrav=0 and my lattice vectors are [0 0.5 0.5], [0.5 0 0.5],
> [0.5 0.5 0] in alat units. So if I understand the convention given in
> the faq phonon section of the documentation, the first nearest
> neighbors should have the indices [1 1 1], [5 1 1], [1 5 1] and [1 1
> 5].

The first nearest neighbors of atom 1 = (0,0,0) in cell at (0,0,0) are:
1.) atom 2 = (0.25, 0.25, 0.25) in cell at ( 0.0, 0.0, 0.0);
2.) atom 2 = (0.25, 0.25, 0.25) in cell at ( 0.0,-0.5,-0.5);
3.) atom 2 = (0.25, 0.25, 0.25) in cell at (-0.5, 0.0,-0.5);
4.) atom 2 = (0.25, 0.25, 0.25) in cell at (-0.5,-0.5, 0.0);

You assume that the indices <=> lattice vector correspondence is:
  [1 1 1] == (0, 0, 0), i.e. the two atoms are in the same cell
  [2 1 1] == (0, 0.5, 0.5)
  [5 1 1] == (0,-0.5,-0.5) (i.e. as above, refolded) 
etc, yielding atoms 1 2 + [1 1 1], [5 1 1], [1 5 1], [1 1 5] as
neighbors. This makes sense (I would have made the same assumption), 
but apparently the code uses a different sign convention and thinks 
that the neighbors are either:
  atoms 1 2 + [1 1 1], [2 1 1], [1 2 1], [1 1 2]
or
  atoms 2 1 + [1 1 1], [5 1 1], [1 5 1], [1 1 5]
You may verify that these force constants have a more symmetric look
(I did).

I am not sure where such sign convention comes from, but I am quite 
sure that the interatomic force constants are used in a way that is
consistent with the convention adopted for writing them and that 
results are correct.

Paolo

> From my understanding, the first nearest neighbours for Si have the
> diagonal term in the force constant matrix +/- alpha and off-diagonal
> term in the force constant matrix +/- beta for some alpha and beta. 
> 
> 
> Now, the [1 1 1] force constant seems to have the right symmetries :
> atom pair : 1 2
> 148    1   1   1  -6.40122756000E-02 11
> 652    1   1   1  -4.29620484800E-02 12
> 1156    1   1   1  -4.29620484800E-02 13
> 1660    1   1   1  -4.29620484800E-02 21
> 2164    1   1   1  -6.40122756000E-02 22
> 2668    1   1   1  -4.29620484800E-02 23
> 3172    1   1   1  -4.29620484800E-02 31
> 3676    1   1   1  -4.29620484800E-02 32
> 4180    1   1   1  -6.40122756000E-02 33
> 
> 
> However, the [5 1 1] (and [1 5 1], [1 1 5]) force constants do not
> have the right symmetries 
> atom pair : 1 2
> 152    5   1   1  -3.87971851534E-03 11
> 656    5   1   1   1.05471196450E-03 12
> 1160    5   1   1   1.05471196450E-03 13
> 1664    5   1   1   1.05471196450E-03 21
> 2168    5   1   1  -3.60176689065E-04 22
> 2672    5   1   1  -3.96403112877E-04 23
> 3176    5   1   1   1.05471196450E-03 31
> 3680    5   1   1  -3.96403112877E-04 32
> 4184    5   1   1  -3.60176689065E-04 33
> 
> 
> The first column is the line number in my file, then followed by the
> three indices for the lattice vectors, then the force constant and
> then finally the component (11=xx, 12=xy and so on)
> 
> 
> 
> Does anyone have an idea why this happens?
> 
> 
> P.S. : In the si.scf.in file, I have CELL_PARAMETERS {cubic}. I have
> also tried with CELL_PARAMETERS {alat} and there is no difference.
> 
> 
> Thanks,
> Navaneeth
> -- 
> Navaneetha Krishnan Ravichandran,
> Graduate Student,
> Mechanical Engineering,
> Caltech.
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