[CP2K-user] Overlap matrices for transport

[Rutger Duflou]

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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