[CP2K-user] [CP2K:21942] Re: Real space representation of S and KS matrices with k-points
Fabian Ducry
fabianducry at gmail.com
Mon Nov 3 11:50:27 UTC 2025
Hi Dmitry,
I don't understand what does not work with shifting the atoms to between -L/2 and L/2. Even if the atoms are part of a larger structure, a linear shift should not affect the elements.
Cheers,
Fabian
On 30 October 2025 11:08:31 GMT, Dmitry Ryndyk <dmitry.ryndyk at tu-dresden.de> wrote:
>Hi Fabian,
>
>Unfortunately, it does not work if you need to analyse different parts of a
>bigger system and calculate matrix elements for these parts consistently.
>
>Best,
>Dmitry
>Fabian Ducry schrieb am Donnerstag, 30. Oktober 2025 um 11:24:03 UTC+1:
>
>> Hi Dmitry,
>>
>> You can easily do it with
>> https://manual.cp2k.org/trunk/CP2K_INPUT/FORCE_EVAL/SUBSYS/TOPOLOGY/CENTER_COORDINATES.html
>> bo need to manually shift the atoms. But I think it should be better
>> documented. I'll try to find time to do it.
>>
>> Cheers,
>> Fabian
>>
>>
>> On 29 October 2025 23:05:43 GMT+03:00, Dmitry Ryndyk <
>> dmitry... at tu-dresden.de> wrote:
>>
>>> Ah, indeed!
>>> It works and technically solves my problem.
>>> Thank you, Fabian!
>>> Why not do it by default when creating RS image matrices?
>>>
>>> Best wishes,
>>> Dmitry
>>>
>>> Fabian Ducry schrieb am Mittwoch, 29. Oktober 2025 um 17:14:47 UTC+1:
>>>
>>>> Hi Dmitry,
>>>>
>>>> the coordinates need to be in (-L/2, L/2) in each dimension, where L is
>>>> the length of the cell.
>>>>
>>>> Cheers,
>>>> Fabian
>>>>
>>>>
>>>> On 29 October 2025 18:21:43 GMT+03:00, Dmitry Ryndyk <
>>>> dmitry... at tu-dresden.de> wrote:
>>>>
>>>>> Meanwhile, I found a very strange problem with the real space matrix
>>>>> images themselves.
>>>>> As an example, a very simple system of a 1D H array, with 4 atoms in
>>>>> the unit cell (input file in attachment).
>>>>> The coordinates are
>>>>> &CELL
>>>>> ABC 16.0 16.0 6.0
>>>>> PERIODIC xyz
>>>>> &END CELL
>>>>> &COORD
>>>>> H 0.00000000 0.00000000 0.00000000
>>>>> H 0.00000000 0.00000000 1.50000000
>>>>> H 0.00000000 0.00000000 3.00000000
>>>>> H 0.00000000 0.00000000 4.50000000
>>>>> &END COORD
>>>>>
>>>>> The 5 RS image cells are
>>>>> S CSR write| 5 periodic images
>>>>> Number X Y Z
>>>>> 1 0 0 0
>>>>> 2 0 0 -1
>>>>> 3 0 0 1
>>>>> 4 0 0 -2
>>>>> 5 0 0 2
>>>>>
>>>>> and the 0,0,0 image for S overlap is (all other in attachment)
>>>>>
>>>>> 1 1 0.10000000000000E+001
>>>>> 1 2 0.39126534955779E+000
>>>>> 1 3 0.39734112631705E-001
>>>>> 1 4 0.39126534955779E+000
>>>>> 2 1 0.39126534955779E+000
>>>>> 2 2 0.10000000000000E+001
>>>>> 2 3 0.39126534955779E+000
>>>>> 2 4 0.39734112631705E-001
>>>>> 3 1 0.39734112631705E-001
>>>>> 3 2 0.39126534955779E+000
>>>>> 3 3 0.10000000000000E+001
>>>>> 3 4 0.12433452435606E-002
>>>>> 4 1 0.39126534955779E+000
>>>>> 4 2 0.39734112631705E-001
>>>>> 4 3 0.12433452435606E-002
>>>>> 4 4 0.10000000000000E+001
>>>>>
>>>>> As one can see, the values of S correspond to the atom positions in
>>>>> order
>>>>> 4 1 2 3
>>>>> not
>>>>> 1 2 3 4
>>>>> as I assume to be correct.
>>>>>
>>>>> If one makes only one RS image, e.g., taking
>>>>> ABC 16.0 16.0 16.0
>>>>> in the input file, the file looks correct.
>>>>>
>>>>> 1 1 0.10000000000000E+001
>>>>> 1 2 0.39126534955779E+000
>>>>> 1 3 0.39734112631705E-001
>>>>> 1 4 0.12433452435606E-002
>>>>> 2 1 0.39126534955779E+000
>>>>> 2 2 0.10000000000000E+001
>>>>> 2 3 0.39126534955779E+000
>>>>> 2 4 0.39734112631705E-001
>>>>> 3 1 0.39734112631705E-001
>>>>> 3 2 0.39126534955779E+000
>>>>> 3 3 0.10000000000000E+001
>>>>> 3 4 0.39126534955779E+000
>>>>> 4 1 0.12433452435606E-002
>>>>> 4 2 0.39734112631705E-001
>>>>> 4 3 0.39126534955779E+000
>>>>> 4 4 0.10000000000000E+001
>>>>>
>>>>> Here (1,4) and (4,1) matrix elements are the smallest.
>>>>>
>>>>> Besides, this "cyclic shift" depends on k-points and the linear shift
>>>>> of atom coordinates.
>>>>> Even if it does not change k-point calculations itself, it can be
>>>>> important in other problems.
>>>>> Actually, I found this problem in "NEGF" transport systems, where it is
>>>>> important.
>>>>> At the moment, I have not found the origin of this problem.
>>>>>
>>>>>
>>>>> Dmitry Ryndyk schrieb am Dienstag, 28. Oktober 2025 um 11:13:35 UTC+1:
>>>>>
>>>>> Dear Augustin,
>>>>>
>>>>> thank you for the fast answer. It helps me to understand what is going
>>>>> on!
>>>>>
>>>>> Best wishes,
>>>>> Dmitry
>>>>>
>>>>> Augustin Bussy schrieb am Dienstag, 28. Oktober 2025 um 11:11:38 UTC+1:
>>>>>
>>>>> For clarity: Both the S and KS matrices are Hermitian in *k-space*,
>>>>> but in real space, we have: S_ij^*b* = S_ji^-*b*
>>>>>
>>>>> On Tuesday, 28 October 2025 at 10:57:55 UTC+1 Augustin Bussy wrote:
>>>>>
>>>>> Dear Dimitry,
>>>>>
>>>>> Dealing with CP2K's real space matrices in k-point calculations can be
>>>>> quite challenging. In principle, it follows equations (10) and (11) of
>>>>> https://arxiv.org/pdf/2508.15559. Elements i of the
>>>>> qs_env%ks_env%matrix_s_kp array contains real space overlap matrix elements
>>>>> between AOs in the main cell, and AOs in periodic image with index i. The
>>>>> indexing of periodic images is that imposed by the neighbor lists.
>>>>>
>>>>> For historical reasons, the KP overlap and KS matrices are stored as
>>>>> DBCSR *symmetric* types, even though they are not symmetric. That's
>>>>> where it gets complicated. Both the S and KS matrices are Hermitian, and
>>>>> they have the following symmetry: S_ij^*b* = S_ji^-*b*, where *b*
>>>>> denotes the translation from the main cell to a given periodic image.
>>>>> If you have access to the upper diagonal of a real space matrix with
>>>>> one AO in a periodic cell shifted by *b*, and that of a real space
>>>>> matrix with an AO shifted by -*b*, then you can reconstruct the full,
>>>>> asymmetric, real space matrix at *b*.
>>>>>
>>>>> In the code, this operation is done when performing Fourier transforms
>>>>> real space to k-space. For example here:
>>>>> https://github.com/cp2k/cp2k/blob/5f3bc36082e75c975caee6a92073f395a2af7674/src/kpoint_methods.F#L855-L864
>>>>> .
>>>>>
>>>>> I hope that helps.
>>>>> Best,
>>>>> Augustin
>>>>> On Tuesday, 28 October 2025 at 01:38:16 UTC+1 Dmitry Ryndyk wrote:
>>>>>
>>>>> Dear developers,
>>>>>
>>>>> I would greatly appreciate it if you could provide me with the
>>>>> reference to the exact description of the real space S and KS matrices,
>>>>> stored in qs_env%ks_env%matrix_ks_kp and qs_env%ks_env%matrix_s_kp.
>>>>> I mean not the details of DBCSR matrices, but the way the matrix
>>>>> elements are placed inside the matrices.
>>>>> My test calculations, as well as some code investigation, show that
>>>>> these matrix elements are mixed between space replicas ("images") used at
>>>>> k-point calculations, and some rearrangement is required to get normal
>>>>> symmetrical matrices, which depend on the atomic indices.
>>>>>
>>>>> Thank you,
>>>>> Dmitry
>>>>>
>>>>>
>
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