[CP2K-user] [CP2K:19923] Re: Problem with the calculation of the CUBE file and Wannier Centres using the ROKS method?

[Ilya Fedorov]

Dear colleagues,

I found a bug and I have not corrected all issues with the implementation 
of orbitals printing with ROKS. I have now added make_mo_eig(), which 
returns orbitals from OT space. I have limited it to nspin=1 and everything 
now works consistently with CPMD. (https://github.com/cp2k/cp2k/pull/3274)

If you do not mind, may I replace the regtest with oxygen with 
formaldehyde, since it is a simpler example and has a larger dE in ROKS?

Best regards,
Ilya
понедельник, 12 февраля 2024 г. в 19:09:44 UTC+3, Ilya Fedorov: 

> Dear Matthias,
>
> I apologise for such a long reply. The problem turned out to be not so 
> simple.
>
> At this moment it seems that ROKS does not work properly in CP2K.
>
> An oxygen molecule turned out to be a poor example to use with ROKS. I 
> just copied it from an existing regtest for ROKS, but CPMD and CP2K gave 
> the S1 energies lower than the S0 energies.
>
> A better example would be a formaldehyde molecule or a hydrogen molecule.The 
> advantages of formaldehyde are that it has SOMO-1 and SOMO-2 separated in 
> space, which, as will be discussed below, allows for better manifestation of the 
> differences between CP2K and CPMD could be traced. I used a formaldehyde 
> example from the original ROKS paper [Frank, I., Hutter, J., Marx, D., & 
> Parrinello, M. (1998). JPC, 108, 4060]. 
>
> *Here are the main observations:* 
>
>
>    1. The excitation energy E(S1) - E(S0) *in both CPMD and CP2K packages 
>    is about 3.5 eV*, which is in agreement with the paper of Frank et al.
>    2. The *Wannier centres* of all orbitals are almost the *same* between 
>    CPMD and CP2K (see Picture 1), but their *order is different*. This is 
>    important for SOMO-1 and SOMO-2, since we have the rotations turned off for 
>    these orbitals and their centres should have coincided.
>    3. *The most important difference* is in the visualisation of the 
>    orbitals. In the attached pdf-file (S0_S1_CP2K_CPMD.pdf) I visualise the 
>    orbitals for the ground state S0 and of the excited state S1. The 
>    isosurfaces are shown in red (+0.07) and in blue (-0.07). You can see that 
>    for the ground state the orbitals from CPMD and from CP2K coincide. For the 
>    excited state CPMD shows some change of order (with respect to S0) and the 
>    general picture remains close (*the resemblance HOMO ~ SOMO-1 takes 
>    place*). *But for the S1 state in CP2K all orbitals look different, 
>    except last two (SOMO-1 and SOMO-2)*, and the last two orbitals seem 
>    to have switched places (*the resemblance HOMO ~ SOMO-2 takes place*) 
>    (the same pattern as with Wannier centres.).
>
> I attach the codes for calculating the S0 and S1 states in CPMD and CP2K 
> for formaldehyde. 
>
>
>    - The standard cpmd2cube.x script (
>    https://github.com/CPMD-code/Addons/tree/main/cpmd2cube) should be 
>    used to convert the CPMD orbitals to .cube files (cmd: ./cpmd2cube.x 
>    WAVEFUNCTION.*)
>    - To calculate Wannier centres in CPMD, a separate code 
>    (cpmd_s1_wannier.inp) should be used which takes 1 MD step, this is because 
>    a separate case of calculating Wannier centres for ROKS is only implemented 
>    in MD. At the same time, in CPMD the calculation of Wannier centres itself 
>    affects the final output of orbitals
>
> Best regards,
>
> Ilya
>
> P.S. 
> Although the energies of SOMO-1 and SOMO-2 judging by dE ~3.5 eV should be 
> significantly different and could not simply get mixed up. In addition, it 
> is worth noting that despite the complete difference in orbitals 1-5 in 
> CP2K and CPMD, the final Wannier centres are the same, so we can talk about 
> the influence of the difference of the basis or something else? 
>
> Could it be that the OT method does not handle single occupied orbitals 
> correctly or the ROKS method in CP2K does not handle double occupied 
> orbitals correctly? Because in the case of CPMD we see that the shape of 
> the double occupied orbitals has not changed, the order has changed and one 
> new SOMO-2 orbital has been added. In CP2K, the new single occupied 
> orbitals look correct, but the double occupied ones have coordinately 
> changed in ROKS.
>
>  
>
> вторник, 21 ноября 2023 г. в 13:27:51 UTC+3, Ilya Fedorov: 
>
>> Dear Matthias,
>>
>> I am sorry for the delay in answering your question.
>>
>> Indeed, sometimes I observed poor convergence of OT with ROKS, but 
>> sometimes the convergence is much better than diagonalization in СPMD. But 
>> at the moment I do not have a systematic understanding of the roots of this 
>> problem.
>>
>> I made various comparisons between CPMD and CP2K in terms of calculations 
>> with ROKS: comparing forces, trajectories, orbitals and Wannier centers, in 
>> general I got a fairly close agreement.
>>
>> In the near future I plan to collect these results into one report and 
>> post it here.
>>
>> Best
>>
>> Ilya
>>
>> четверг, 16 ноября 2023 г. в 15:31:03 UTC+3, Krack Matthias: 
>>
>>> Hi Ilya
>>>
>>>  
>>>
>>> Thanks for contributing and fixing the print issue.
>>>
>>>  
>>>
>>> Indeed, ROKS produces only one set of orbitals, since there is also only 
>>> one Hamiltonian, i.e. Kohn-Sham matrix, but different orbital occupations 
>>> are applied for spin-up (alpha) and spin-down (beta) electrons which 
>>> results in an alpha and beta electronic density matrix.
>>>
>>>  
>>>
>>> The LOW-SPIN ROKS implementation in CP2K based on OT plus ROTATION is 
>>> experimental as indicated by a warning printed in the output. That 
>>> implementation has not been maintained since a long time. Therefore, I am 
>>> wondering, if the implementation works properly, e.g. for the new test case 
>>> O2_mo_cubes.inp. I tried tighter thresholds and a larger cutoff and box 
>>> size, but the SCF did not converge. What’s your experience and how do the 
>>> results compare to ROKS in CPMD?
>>>
>>>  
>>>
>>> Best
>>>
>>>  
>>>
>>> Matthias
>>>
>>>  
>>>
>>> *From: *cp... at googlegroups.com <cp... at googlegroups.com> on behalf of 
>>> Ilya Fedorov <ilyafe... at gmail.com>
>>> *Date: *Thursday, 16 November 2023 at 10:59
>>> *To: *cp2k <cp... at googlegroups.com>
>>> *Subject: *[CP2K:19518] Re: Problem with the calculation of the CUBE 
>>> file and Wannier Centres using the ROKS method?
>>>
>>> I solved the problem and it was accepted into the code.
>>>
>>> 1.       As I understand it, for ROKS the UKS base is used, and 
>>> different spins of the same orbital have the same density. This allows to 
>>> rely on the UKS codes, while you can use MO_CUBES only for spin-1. 
>>> (regtest: QS/regtest-lsroks/O2_mo_cubes.inp)
>>>
>>> 2.       I added such an implementation in the code. Only two method 
>>> supports:
>>>
>>> o    NONE: No rotation, just print the orbital centers.
>>>
>>> o    JACOBI: Only doubly occupied orbitals rotate; for singly occupied 
>>> orbitals, no rotation occurs (like the NONE method). (regtest: 
>>> QS/regtest-lsroks/O2_loc_wan_jac.inp)
>>>
>>> It is possible to use only NONE and JACOBI. Other methods can be added 
>>> in the future, but ROKS calculates quite slowly, and speeding up the 
>>> Wannier calculation does not make a big contribution here.
>>>
>>>  
>>>
>>> Commits: https://github.com/cp2k/cp2k/pull/3108
>>>
>>> четверг, 24 августа 2023 г. в 15:19:45 UTC+3, Ilya Fedorov: 
>>>
>>> Dear colleagues, 
>>>
>>>  Could you please help me to understand the CP2K implementation of ROKS 
>>> and the Wannier Centers.
>>>
>>> I am facing the following two problems. I can't find an answer in the 
>>> documentation. And, unfortunately, I don't really understand in the code.
>>>
>>> 1) The ROKS implementation in CP2K uses a spin-restricted calculation 
>>> with multiple density matrices. As I understand it, this leads to some 
>>> problems with printing CUBE files (for example, for each orbital it prints 
>>> two cube files for spin_1 and spin_2). Which one is correct? Maybe the sum 
>>> of them gives a correct density? 
>>>
>>> (in log it print “Unclear how we define MOs in the restricted case ... 
>>> skipping”)
>>>
>>>  
>>>
>>> 2) I’m trying to use Wannier Centres with ROKS, but it doesn’t work in 
>>> CP2K. As I understand this is also a multiple density matrix problem. I 
>>> need Wannier Centres only (Many-body Position operator, no Jacobi 
>>> rotation). Right now I use Wannier + ROKS in CPMD, and in CPMD the rotation 
>>> is just switched off for the last two orbitals (diag(1,1)). 
>>>
>>> Best regards
>>>
>>> Ilya
>>>
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>>> .
>>>
>>

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