[CP2K-user] Overlap matrices for transport

[Rutger Duflou]

Dear Fabian (and other devs),

I experimented a bit further with the toy problems and came to the 
following conclusion:
- my atoms should have fractional coordinates (relative to the bravais 
vectors) between -0.5 and 0.5. Otherwise, the periodic image of them will 
be taken as the main cell atom such that they are in between -0.5 and 0.5. 
This explains the weird phenomenon I had with cnt.
- For the overlaps with periodic image cells, you should interchange the 
lower or upper triangular parts of S_(x,y,z) and S_(-x,-y,-z) depending on 
whether the sum of the atom indices of the atoms to which the orbitals 
belong are odd or even.
With this I managed to build a script that performs these switches and I 
now get the correct band structure. I think it could still definitely be 
worthwhile for other people (and to have something more robust than my 
script) to have the correct matrices directly from cp2k, but for now I have 
a workaround for my own projects.

Kind regards and many thanks for the help,

Rutger Duflou

Op vrijdag 16 april 2021 om 16:15:48 UTC+2 schreef Rutger Duflou:

> Deer Fabian,
>
> Ah, that explains indeed how cp2k still gets the right result. I had been 
> wondering about that.
> Implementing the right printing would be very helpful. I should mention 
> that it is only a problem when doing a kpoint calculation (which is 
> unfortunately required for real systems as the supercell approach quickly 
> becomes too large), which combined with a comment in the file I mentioned: 
> "! FIXME for non-periodic systems, the whole subcell trick is skipped
>                       ! yielding a Natom**2 pair list build."
> leads me to believe that it is a sort of optimization artifact that could 
> be skipped altogether. I unfortunately do not know how to skip it, so I'm 
> just bringing it to your attention.
>
> Kind regards,
>
> Rutger
>
> Op vrijdag 16 april 2021 om 15:46:28 UTC+2 schreef fa... at gmail.com:
>
>> Dear Rutger,
>>
>> I think it's true that the printed overlap matrices are not entirely 
>> correct. I think the printing of the AO matrices is intended only for 
>> debugging purposes. You can find the relevant code to perform the real 
>> space to k-space transformation in kpoint_methods.F in the rskp_transform 
>> subroutine. At line 733 of the current trunk cp2k uses certain symmetries:
>>
>>          IF (do_symmetric .AND. (iatom > jatom)) THEN
>>             irow = jatom
>>             icol = iatom
>>             fsym = -1.0_dp
>>          END IF
>>
>> I can try to implement the printing of the real space Hamiltonian and 
>> overlap matrices in the csr format if that's something usefull to you.
>>
>> Cheers,
>> Fabian
>> On Friday, 16 April 2021 at 14:07:10 UTC+2 rut... at gmail.com wrote:
>>
>>> Dear developers,
>>>
>>> Apologies beforehand as this is going to be a long question.
>>> I'm using CP2K to extract Hamiltonians and overlap matrices to then use 
>>> them in transport calculations. The band structures that I obtain with the 
>>> Hamiltonians and overlap matrices from CP2K are, however, off. I did quite 
>>> a few tests on 2 toy-problems: two-dimensional WS2 (with 3 atoms) and 
>>> one-dimensional cnt (with 64 atoms). For both systems I calculated the 
>>> overlap matrix from a supercell (without periodic images) and a kpoint 
>>> calculation with periodic images and compared the corresponding overlap 
>>> entries.
>>>
>>> For WS2 the overlap of orbitals both in the main unit cell are equal for 
>>> the supercell and kpoint approach. For periodic images, however, the kpoint 
>>> approach gives symmetrical matrices (which to me does not make sense, the 
>>> overlap between a 1s orbital on W in (0,0,0) and a 1s orbital on S in 
>>> (1,0,0) is not equal to the overlap between a 1s orbital on S in (0,0,0) 
>>> and a 1s orbital on W in (1,0,0)).
>>>     _____
>>>   /         \
>>> /   W-S   \_____            (ASCII art to demonstrate what I mean.) 
>>> \ (0,0,0) /         \                      (I hope the format is 
>>> preserved in this mail).
>>>   \_____/    W-S  \
>>>              \ (1,0,0) /
>>>                \_____/
>>> After comparison with the supercell approach I found that I can 
>>> reproduce the correct matrices if I interchange the upper triangular part 
>>> of the overlap matrix (and KS matrix) with the (x,y,z) and (-x,-y,-z) cell 
>>> when exactly one of the two orbitals resides on W. If no orbital or both 
>>> orbitals reside on W, then I have to interchange the lower-triangular 
>>> elements of the (x,y,z) and (-x,-y,-z) overlap matrices. Looking into the 
>>> source code indeed shows that these periodic image matrices are printed as 
>>> symmetric matrices even though they aren't... I, however, do not understand 
>>> why it is sometimes the upper triangular element and sometimes the 
>>> lower-triangular element that is correct and when it is which for other 
>>> systems.
>>>
>>> For cnt, even the overlap matrices of the main unit cell differ between 
>>> kpoint approach and supercell approach. It seems that in the kpoint 
>>> approach, for the overlap matrix entries it sometimes takes atoms from 
>>> periodic images instead of the main unit cell. I verified this by changing 
>>> the unit cell dimensions and noticing that some overlap matrix entries of 
>>> the main unit cell change, which, as far as I can see, should not be 
>>> possible if they are actually both in the main unit cell.
>>>
>>> I have looked into the source code and think I found some clue on line 
>>> 1263 of qs_neighbour_lists.F (version 7.1), but at that point the code 
>>> becomes a bit too obscure, so I was wondering whether I could get some 
>>> insight into this matter.
>>>
>>> Kind regards,
>>>
>>> Rutger Duflou
>>>
>>>
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