[CP2K-user] [CP2K:19895] Re: Problem with the calculation of the CUBE file and Wannier Centres using the ROKS method?

[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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