[CP2K-user] [CP2K:22127] Re: The KERKER mixing method may be more suitable than the BROYDEN mixing method for calculations involving magnetic systems.

[yis...@163.com]

Thank you for your reply.

在2026年2月28日星期六 UTC+8 03:40:12<Shiyang Wang (W0728)> 写道：

> Based on my experience, at least for the Broyden scheme, setting ALPHA too 
> small (below 0.1 or even 0.05) or too large (above the default value of 
> 0.4) is generally detrimental to convergence.
>
> In your tests, the reduction of the convergence metric with 
> smaller ALPHA values can indeed be seen as a positive sign. However, the 
> convergence remains rather slow, and it is unclear whether oscillations may 
> occur near the convergence threshold — something that CP2K frequently 
> exhibits for this type of system.
>
> In my view, the difficulty of achieving SCF convergence for such systems 
> in CP2K is primarily related to the underlying algorithms and 
> characteristics of the basis functions, while the choice of density mixing 
> scheme plays a secondary role. If you look into it, you will find that VASP 
> also employs a Broyden-type mixing scheme for charge density.
>
> Perhaps further improvements in this direction should become a focus for 
> future development.
>
> 在2026年2月27日星期五 UTC+8 23:31:42<yis... at 163.com> 写道：
>
>> Sorry, I might have lost my cool just now. You understand that when 
>> computational time is relatively limited, encountering non-convergence is 
>> always a bit of a hair-pulling experience. Thank you very much for your 
>> selfless help. I will retest the similarities and differences between 
>> KERKER and BROYDEN for convergence in magnetic systems. CP2K is indeed a 
>> very powerful piece of software. Here, I would like to ask a question: when 
>> I use KERKER and encounter non-convergence, I usually lower the ALPHA 
>> parameter to 0.001. While running CP2K, I observe that the Convergence 
>> parameter always decreases as the number of iterations increases. However, 
>> with BROYDEN, it feels like it oscillates. Could this be a numerical 
>> artifact caused by ALPHA being too low?
>>
>> 在2026年2月27日星期五 UTC+8 21:28:30<yis... at 163.com> 写道：
>>
>>> Thank you for your reply. However, based on the test results, it is 
>>> still difficult to converge.
>>>
>>> 在2026年2月26日星期四 UTC+8 18:43:32<Shiyang Wang (W0728)> 写道：
>>>
>>>> Dear yisichi-design,
>>>>
>>>> For BROYDEN_MIXING, you should use NBROYDEN instead of BETA to help 
>>>> convergence. Default NBROYDEN is 4, which often hinders convergence. You 
>>>> can increase it to 8 or even 12. BETA is used for KERKER_MIXING.
>>>>
>>>> For such systems, reducing the ALPHA value does indeed help with 
>>>> convergence (the default is 0.4), and this is often done in practice (we 
>>>> often use 0.3 or even 0.15). However, setting ALPHA too small may lead to 
>>>> numerical issues.
>>>>
>>>> To understand what *“Spin contamination estimate not implemented for 
>>>> k‑points”* means, you may need to look up what *spin contamination* 
>>>> refers to. In CP2K, in most cases this warning can be safely ignored.
>>>>
>>>> If there’s anything else that needs to be discussed, feel free to add 
>>>> it at any time.
>>>>
>>>> 在2026年2月26日星期四 UTC+8 12:37:55<yis... at 163.com> 写道：
>>>>
>>>>> Hello CP2K developers,
>>>>>             A few days ago on GitHub, we discussed whether the KERKER 
>>>>> or BROYDEN mixing method is more suitable for magnetic system calculations. 
>>>>> Following up on that, I have done some tests and found that the KERKER 
>>>>> mixing method may be more appropriate for magnetic systems than BROYDEN. 
>>>>> Below is my testing procedure.
>>>>>              I used two test models: a unit cell model of NiFe(OH)₂ 
>>>>> and the (010) surface of gamma-NiOOH. For the NiFe(OH)₂ unit cell, the test 
>>>>> procedure was as follows. First, with SMEAR enabled, the number of 
>>>>> iterations for the SCF calculation was set to 100. I then tested the 
>>>>> effects of different mixing methods, ALPHA, and BETA on convergence. The 
>>>>> test results are shown in Table 1. Figure 1 shows a screenshot of the SCF 
>>>>> results for the first 50 steps of Test1, which used the KERKER mixing 
>>>>> method with ALPHA = 0.2 and BETA at its default value. Both Table 1 and 
>>>>> Figure 1 indicate that under these parameters, SCF does not converge and 
>>>>> shows no trend toward convergence. In Test2, ALPHA was reduced to 0.03 
>>>>> while keeping other parameters the same as in Test1. Figure 1 and Table 1 
>>>>> show that a convergence trend appears, albeit slowly. After 100 iterations, 
>>>>> the convergence value reached 0.00041471. Although it has not yet met the 
>>>>> convergence criterion, I believe that increasing the number of iterations 
>>>>> would lead to successful convergence. Test3 further reduced BETA to 0.8 
>>>>> based on Test2. After 100 iterations, the convergence value was 0.00159217, 
>>>>> which is slower than Test2. However, based on my previous experience, if 
>>>>> the parameters in Test2 struggle to converge, trying the parameters in 
>>>>> Test3 can be a useful alternative.
>>>>> [image: 图片2.jpg]
>>>>>        [image: 图片3.jpg]  
>>>>>                                    Fingure 1 Convergence results for 
>>>>> unit cell
>>>>>           I further tested BROYDEN as the wavefunction mixing method, 
>>>>> as shown in Figure 1 and Table 1. Compared to KERKER, its convergence 
>>>>> performance is noticeably worse. The SCF results show persistent 
>>>>> oscillations without a clear trend of convergence. Additionally, compared 
>>>>> to Test4, reducing both ALPHA and BETA to 0.01 still resulted in a 
>>>>> convergence value of 0.07070099 after 100 iterations, but without a 
>>>>> distinct convergence trend. Subsequently, I disabled SMEAR and reran the 
>>>>> same tests. The results are shown in the lower half of Table 1. Compared to 
>>>>> the cases with SMEAR enabled, convergence did not improve. For the same 
>>>>> wavefunction mixing method, ALPHA, and BETA, convergence actually worsened. 
>>>>> For example, with SMEAR disabled, using the KERKER method with ALPHA = 0.03 
>>>>> gave a convergence value of 0.00082845 after 100 iterations, which is 
>>>>> higher than the case with SMEAR enabled. For the BROYDEN method with ALPHA 
>>>>> = 0.2 and default BETA, the convergence value increased to 0.07480723, 
>>>>> still worse than KERKER. Moreover, as shown in Figure 1, when appropriate 
>>>>> ALPHA and BETA values are used with the KERKER method, convergence steadily 
>>>>> improves with increasing iterations rather than oscillating continuously.
>>>>>         Based on these results, I draw the following conclusions:
>>>>>         1. The KERKER mixing method may be more suitable for magnetic 
>>>>> systems than BROYDEN.
>>>>>         2. Default parameters for KERKER generally struggle to 
>>>>> achieve convergence; ALPHA needs to be reduced to 0.03 or even lower.
>>>>>            Further, I selected the (010) surface of gamma-NiOOH to 
>>>>> test SCF convergence. The results are shown in Table 2 and Figure 2. First, 
>>>>> I tested convergence with SMEAR enabled and ADDED_MOS set to 20. Similar to 
>>>>> the unit cell calculations, when ALPHA = 0.2, KERKER failed to converge and 
>>>>> showed no trend toward convergence. For TEST3 and TEST4, after lowering 
>>>>> ALPHA, an interesting phenomenon was observed. In both cases, a clear 
>>>>> convergence trend initially appeared, but after reaching a certain value, 
>>>>> the convergence residual began to increase again. For TEST3 (ALPHA reduced 
>>>>> to 0.03), the residual gradually decreased to 0.0350084 within the first 50 
>>>>> iterations, but then it started to diverge. For TEST4 (BETA reduced to 0.8 
>>>>> and ALPHA reduced to 0.01), the residual decreased to 0.00089041 within the 
>>>>> first 75 steps, then gradually increased to 0.02504273.
>>>>> [image: 图片4.jpg]
>>>>>           [image: 图片5.jpg]  
>>>>>                        Figure 2 Convergence results for slab
>>>>>           For BROYDEN, the convergence behavior was more complex. With 
>>>>> ALPHA = 0.2 and BETA = 0.8, the residual reached 0.05432726 after 200 
>>>>> iterations. However, when ALPHA and BETA were both reduced to 0.01, the 
>>>>> convergence worsened, and the SCF residual oscillated continuously without 
>>>>> a clear trend.
>>>>>              Considering that unoccupied orbitals might affect 
>>>>> convergence, I set ADDED_MOS to -1 -1 and reran the tests. The results in 
>>>>> the lower half of Table 2 show no significant differences.
>>>>> In summary, I conclude:
>>>>>            1. KERKER may be more suitable than BROYDEN for 
>>>>> convergence in magnetic systems.
>>>>>              2. Default parameters for KERKER generally struggle to 
>>>>> achieve convergence; ALPHA needs to be reduced to 0.03 or even lower.
>>>>>             The difficulty of achieving SCF convergence for magnetic 
>>>>> systems in CP2K has been a longstanding issue. I would like to ask the CP2K 
>>>>> developers to review my testing procedure and input files and provide 
>>>>> suggestions for optimizing the input. Additionally, I have a question:
>>>>>           1. What does the warning "WARNING in qs_scf_post_gpw.F:1841 
>>>>> :: Spin contamination estimate not implemented for k-points" mean, and how 
>>>>> can it be resolved?
>>>>>         The input files and results have been compressed into a ZIP 
>>>>> file and are provided as an attachment.
>>>>> Thank you very much
>>>>>
>>>>>
>>>>>

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