[CP2K-user] [CP2K:22120] Re: The KERKER mixing method may be more suitable than the BROYDEN mixing method for calculations involving magnetic systems.

[Shiyang Wang (W0728)]

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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