[CP2K-user] Overlap matrices for transport

[fa...@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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