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

[yis...@163.com]

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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