[CP2K-user] [CP2K:21944] Re: Real space representation of S and KS matrices with k-points
Dmitry Ryndyk
dmitry.ryndyk at tu-dresden.de
Mon Nov 3 12:11:03 UTC 2025
Hi Fabian,
the NEGF code (not written by me) compares the coordinates of two
FORCE_EVAL: one for the entire system and the other for an electrode
(contact). If I try to shift the electrode coordinates in the input file,
an error appears. I can rewrite it, but I found a better solution: shift
the coordinates inside the code after the point where they are compared.
Best wishes,
Dmtry
Fabian Ducry schrieb am Montag, 3. November 2025 um 12:50:42 UTC+1:
> 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... 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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