[CP2K-user] [CP2K:22122] 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. 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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