Feature: A roadmap to improve the convergence performance of ABACUS

[WHUweiqingzhou]

Background

Current ABACUS sometimes faces convergence challenge for some complicated metal/surface and spin-polarized systems. In order to improve the convergence performance of ABACUS, we will try new algorithms in ABACUS, and a feasible roadmap is as follows:

• Step I: improve the performance of kerker preconditioner, and improve the convergence behavior for general calculations.
  Done.
  Issue Feature: change criterion in kerker dielectric matrix calculations for charge mixing #3094
  PR Feature: improved implementation of kerker preconditioner #3133
  Issue Feature: add a new parameter mixing_gg0_min #3294
  PR Feature: add a new parameter 'mixing_gg0_min' #3305
• Step II: separate the mixture of charge density and magnetic density.
  Currently, ABACUS calculate residual using charge density and magnetic density together. Ref: Journal of the Physical Society of Japan 82 (2013) 114706. This modification is expected to greatly improve the convergence calculation problem of magnetic materials.
  nspin=2 Done.
  Issue Feature: mix charge density and magnetic density separately #3225
  PR Feature: a new mixing method for magnetic calculations #3226
  nspin=2 for metaGGA Done.
  Issue Poor performance of mGGA functional in ABACUS for spin-polarized SCF #3260
  PR Bug: Fix convergence problem of spin-polarized metaGGA calculation for nspin=2 #3328
  nspin=4
  Issue Feature: update mixing method for non-colinear calculation #3285
  PR Feature: mixing density and magnetism {mx,my,mz} separately for non-colinear calculation #3330
  nspin=4 angle mixing
  Issue Feature: more advanced mixing method for non-colinear calculations #3336
  PR Feature: a promising angle mixing method for non-colinear calculations #3356
• Step III: Mixture of density matrix.
  Now, ABACUS only mix charge density instead of density matrix. This modification is expected to greatly improve the convergence calculation problem of several calculations, in which use density matrix as projector, f.e. DFT+U/DeepKS/EXX.
  Issue Feature: mix density matrix by the coefficients of charge density mixing #3535
  PR Feature: mix real-space density matrix for better convergence of DFT+U #3549
• Step IV: (Optional) Increase history dimension in DIIS calculations.
  Current default value is 8 in ABACUS, which is 45 in VASP. Increasing ndim is quite important in some calculations. To this end, we need to reduce the memory cost of residual. We can make this reduction by using a cutoff in G-space, which is effective for PW calculation, but does not work in LCAO calculation.
• Step V: (Optional) Try metric of inner product.
  As mentioned in Ref. Physical review B, 54(16), 11169, the metric of inner product sometimes is even more important than kerker preconditioner, which is worth to try.
• Step VI: Build an automated workflow for Mixing
  During all above development, we will make heavy tests to make sure every modification is meaningful. During this process, we will gradually optimize an automated workflow.
• Step VII: Polish default value of mixing parameter
  Taking advantage of automated workflow, we will delete Charge::auto_set() and polish default value of mixing parameter. Current default value is mixing_beta=0.2, mixing_gg0=1.0 for metals; mixing_beta=0.7, mixing_gg0=1.0 for semimetals.

We just list some practical and promising choice to improve ABACUS's convergence performance, any other suggestion is welcomed to discuss.

Describe the solution you'd like

Realize this roadmap step by step.

[WHUweiqingzhou]

A Chinese handbook about convergence issue is open to the public now:
https://ucoyxk075n.feishu.cn/docx/R0sqdk6T0o2RY4x5IWgcJ3RHnug?from=from_copylink

[WHUweiqingzhou]

I will close this issue now. Maybe reopen if any update of mixing method.