Bug: Eigenvalues are too large! in mGGA SCF

[QuantumMisaka]

Describe the bug

When doing ABACUS SCF using mGGA like:

• RTPSS: MGGA_X_RTPSS+MGGA_C_REVTPSS
• RPPSCAN: MGGA_X_RPPSCAN+MGGA_C_RPPSCAN

There will be problem:

 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
                         NOTICE                           
 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
 Eigenvalues are too large!
 CHECK IN FILE : OUT.clean/warning.log
 
 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
                         NOTICE                           
 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

While the ETOT in SCF being a large positive number, showing an unstable SCF process.

RPPSCAN.tar.gz
RTPSS.tar.gz

Expected behavior

mGGA should run properly in these case.
In fact, R2SCAN runs normally.

To Reproduce

Run in example with normal v2.0 or v2.1 LCAO and SG15 PP

Environment

ABACUS: 3.7.1 58126a8
Compiler: Intel Toolchain by oneAPI 2023
ORB: v2.0 and v2.1(dev) can both reproduce this problem

Additional Context

No response

Task list for Issue attackers (only for developers)

• Verify the issue is not a duplicate.
• Describe the bug.
• Steps to reproduce.
• Expected behavior.
• Error message.
• Environment details.
• Additional context.
• Assign a priority level (low, medium, high, urgent).
• Assign the issue to a team member.
• Label the issue with relevant tags.
• Identify possible related issues.
• Create a unit test or automated test to reproduce the bug (if applicable).
• Fix the bug.
• Test the fix.
• Update documentation (if necessary).
• Close the issue and inform the reporter (if applicable).

[QuantumMisaka]

Same problem in oTPSS-D

[jinzx10]

Given that the calculation provided by RPPSCAN.tar.gz runs around 50 steps before erratic behaviors start to occur, it might be a charge mixing issue results from solving a linear equation with unstable algorithm (as discussed under #4058 ). We are investigating this possibility and update will be given shortly.

[QuantumMisaka]

In the newest version now, this problem still exist：

                              ABACUS v3.7.4

               Atomic-orbital Based Ab-initio Computation at UStc                    

                     Website: http://abacus.ustc.edu.cn/                             
               Documentation: https://abacus.deepmodeling.com/                       
                  Repository: https://github.com/abacusmodeling/abacus-develop       
                              https://github.com/deepmodeling/abacus-develop         
                      Commit: 93badfa87 (Wed Aug 28 10:18:22 2024 +0800)

 Fri Aug 30 15:02:36 2024
 MAKE THE DIR         : OUT.clean/
 RUNNING WITH DEVICE  : CPU / Intel(R) Xeon(R) Platinum 8358 CPU @ 2.60GHz
 dft_functional readin is: MGGA_X_RTPSS+MGGA_C_TPSS
 dft_functional in pseudopot file is: PBE
 Please make sure this is what you need
 dft_functional readin is: MGGA_X_RTPSS+MGGA_C_TPSS
 dft_functional in pseudopot file is: PBE
 Please make sure this is what you need

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 Warning: the number of valence electrons in pseudopotential > 8 for Fe: [Ar] 3d6 4s2
 Pseudopotentials with additional electrons can yield (more) accurate outcomes, but may be less efficient.
 If you're confident that your chosen pseudopotential is appropriate, you can safely ignore this warning.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

 UNIFORM GRID DIM        : 180 * 360 * 216
 UNIFORM GRID DIM(BIG)   : 36 * 72 * 108
func,idMGGA_X_RTPSS 299
func,idMGGA_C_TPSS 231
 DONE(0.365311   SEC) : SETUP UNITCELL
 DONE(0.411652   SEC) : INIT K-POINTS
 ---------------------------------------------------------
 Ion relaxation calculations
 ---------------------------------------------------------
 SPIN    KPOINTS         PROCESSORS  NBASE       
 2       8               16          2628        
 ---------------------------------------------------------
 Use Systematically Improvable Atomic bases
 ---------------------------------------------------------
 ELEMENT ORBITALS        NBASE       NATOM       XC          
 C       2s2p1d-7au      13          36          
 Fe      4s2p2d1f-8au    27          80          
 ---------------------------------------------------------
 Initial plane wave basis and FFT box
 ---------------------------------------------------------
 DONE(0.504626   SEC) : INIT PLANEWAVE
 -------------------------------------------
 STEP OF ION RELAXATION : 1
 -------------------------------------------
 START CHARGE      : atomic
 DONE(5.28225    SEC) : INIT SCF
 * * * * * *
 << Start SCF iteration.
 ITER      TMAG       AMAG        ETOT/eV          EDIFF/eV         DRHO         DKIN     TIME/s
 GE1      1.47e+02   1.54e+02  -2.63132111e+05   0.00000000e+00   6.7507e-02   2.3461e+00  56.51
 GE2      1.39e+02   1.57e+02  -2.62999735e+05   1.32375754e+02   6.4177e-02   6.1782e-01  54.85
 GE3      1.17e+02   1.34e+02  -2.62858783e+05   1.40951379e+02   1.0275e-01   1.2878e+00  54.79
 GE4      1.46e+02   1.62e+02  -2.63078512e+05  -2.19728510e+02   3.4275e-02   8.6949e-01  54.80
 GE5      1.48e+02   1.64e+02  -2.63095484e+05  -1.69716843e+01   2.2098e-02   2.5757e-01  54.72
 GE6      1.41e+02   1.57e+02  -2.63037482e+05   5.80012154e+01   5.2049e-02   4.9301e-01  54.68
 GE7      1.51e+02   1.68e+02  -2.63098253e+05  -6.07701864e+01   2.1762e-02   5.2176e-01  54.66
 GE8      1.52e+02   1.69e+02  -2.63107411e+05  -9.15877692e+00   1.8035e-02   1.6656e-01  54.77
 GE9      1.55e+02   1.72e+02  -2.63109843e+05  -2.43204159e+00   1.2635e-02   1.2203e-01  54.85
 GE10     1.55e+02   1.73e+02  -2.63111425e+05  -1.58117706e+00   9.3641e-03   7.7238e-02  54.85
 GE11     1.57e+02   1.75e+02  -2.63111951e+05  -5.26607242e-01   8.1753e-03   3.2073e-02  54.82
 GE12     1.57e+02   1.76e+02  -2.63111343e+05   6.07726581e-01   7.7625e-03   3.9416e-02  54.82
 GE13     1.59e+02   1.77e+02  -2.63112052e+05  -7.08921590e-01   4.5871e-03   4.4232e-02  54.80
 GE14     1.59e+02   1.78e+02  -2.63112071e+05  -1.86084529e-02   4.0026e-03   2.3528e-02  55.02
 GE15     1.60e+02   1.79e+02  -2.63112104e+05  -3.29766090e-02   3.0567e-03   2.0787e-02  54.87
 GE16     1.61e+02   1.80e+02  -2.63112029e+05   7.50034183e-02   3.2748e-03   2.6059e-02  55.00
 GE17     1.61e+02   1.80e+02  -2.63112142e+05  -1.13071642e-01   1.7069e-03   2.2985e-02  54.94
 GE18     1.61e+02   1.80e+02  -2.63112131e+05   1.10184084e-02   2.1800e-03   1.5453e-02  54.89
 GE19     1.61e+02   1.81e+02  -2.63112143e+05  -1.16691293e-02   1.5962e-03   1.1765e-02  54.99
 GE20     1.61e+02   1.80e+02  -2.63112111e+05   3.20015620e-02   1.2060e-03   9.1233e-03  54.97
 GE21     1.61e+02   1.80e+02  -2.63112146e+05  -3.49796522e-02   5.2065e-04   7.8473e-03  55.00
 GE22     1.61e+02   1.81e+02  -2.63112146e+05   8.13117411e-05   4.9286e-04   2.7088e-03  55.06
 GE23     1.61e+02   1.81e+02  -2.63112145e+05   6.42496957e-04   4.3771e-04   1.4791e-03  54.89
 GE24     1.61e+02   1.81e+02  -2.63112153e+05  -7.82306893e-03   3.4688e-04   1.4543e-03  54.93
 GE25     1.61e+02   1.81e+02  -2.63112146e+05   6.80857145e-03   3.0768e-04   1.8449e-03  54.93
 GE26     1.61e+02   1.81e+02  -2.63112139e+05   7.00631372e-03   2.0978e-04   1.5888e-03  55.02
 GE27     1.61e+02   1.81e+02  -2.63112142e+05  -3.50405150e-03   1.8559e-04   1.1907e-03  55.00
 GE28     1.61e+02   1.81e+02  -2.63112144e+05  -1.85452238e-03   1.6274e-04   7.4459e-04  54.99
 GE29     1.61e+02   1.81e+02  -2.63112145e+05  -7.11373555e-04   1.3757e-04   6.8482e-04  55.00
 GE30     1.61e+02   1.81e+02  -2.63112145e+05   2.20153927e-04   8.8167e-05   6.3719e-04  55.04
 GE31     1.61e+02   1.81e+02  -2.63112145e+05   2.15611566e-04   8.6758e-05   3.7442e-04  55.05
 GE32     1.61e+02   1.81e+02  -2.63112145e+05  -9.13095502e-04   6.9037e-05   3.4249e-04  55.01
 GE33     1.61e+02   1.81e+02  -2.63112144e+05   1.66991465e-03   6.0219e-05   2.4125e-04  54.98
 GE34     1.61e+02   1.81e+02  -2.63112145e+05  -1.22293566e-03   5.5723e-05   2.1863e-04  54.96
 GE35     1.61e+02   1.81e+02  -2.63112145e+05   3.60141925e-06   4.4790e-05   1.5367e-04  55.05
 GE36     1.61e+02   1.81e+02  -4.78181344e+05  -2.15069199e+05   3.5952e-05   1.2971e-04  55.00
 GE37    -2.00e+00   4.93e+01  -9.38198360e+04   3.84361508e+05   7.8009e-01   4.6572e+00  54.96
 GE38     1.51e+02   1.66e+02  -2.63042992e+05  -1.69223156e+05   2.3929e-02   4.5400e+00  54.96
 GE39     1.61e+02   1.81e+02  -2.63128169e+05  -8.51771222e+01   6.7728e-04   1.5385e-01  55.00
 GE40     1.61e+02   1.81e+02  -2.63090014e+05   3.81546203e+01   7.2779e-05   5.2969e-03  54.91
 GE41     8.22e+00   3.87e+01  -2.19670332e+05   4.34196822e+04   3.3180e-01   2.6296e+00  55.00
 GE42     1.56e+02   1.73e+02   9.63995117e+08   9.64214787e+08   1.2455e-02   2.5839e+00  54.90
 
 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
                         NOTICE                           
 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
 Eigenvalues are too large!
 CHECK IN FILE : OUT.clean/warning.log
 
 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!