Feature: Calculate and output electron localization function (ELF) with KSDFT and OFDFT

[sunliang98]

Reminder

• Have you linked an issue with this pull request?
• Have you added adequate unit tests and/or case tests for your pull request?
• Have you noticed possible changes of behavior below or in the linked issue?
• Have you explained the changes of codes in core modules of ESolver, HSolver, ElecState, Hamilt, Operator or Psi? (ignore if not applicable)

Linked Issue

Fix #...

Unit Tests and/or Case Tests for my changes

• Three integrate tests are added: 119_PW_out_elf, 219_NO_out_elf, 919_OF_out_elf

What's changed?

Calculate and output electron localization function (ELF) with KSDFT and OFDFT.

In order to verify the correctness of the ELF obtained by ABACUS, I have writed another script as reference, which is verified by calculating the Pauli potential. Following are some examples.

1. fcc Al with BLPS

• PW
  

• LCAO
  

• OFDFT with WT KEDF
  

2. CD Si with NC

• PW
  

• LCAO
  

Any changes of core modules? (ignore if not applicable)

• Example: I have added a new virtual function in the esolver base class in order to ...

[kirk0830]

Hi, do you have some model systems tests proving the correctness of implementation? you can calculate ELF of, for example a water molecule and make qualitative comparison with the result from CP2K, like #4937

[sunliang98]

Hi, do you have some model systems tests proving the correctness of implementation? you can calculate ELF of, for example a water molecule and make qualitative comparison with the result from CP2K, like #4937

Thanks for your suggestions, I have uploaded several examples comparing the ELF obtained by ABACUS and another script. Besides, could you please send me the example of water molecule and the output files from CP2K? This will help me further verify the correctness of the ELF calculations.

[sunliang98]

I have calculated the ELF of water molecular (tools/molden/water) using ABACUS with PW basis, the results are nearly identical to those obtained from CP2K. The CP2K results were taken from pr4937 .

However, the ELF obtained using LCAO basis is not as smooth as the one from the PW basis. Since both calculations were performed using the same code, I suspect that the oscillations may be due to the LCAO basis.

[kirk0830]

@sunliang98 hi, you can try with these orbitals:
water_orbs.zip

[sunliang98]

@sunliang98 hi, you can try with these orbitals: water_orbs.zip

Thanks, the results obtained by these orbitals ((left figure)) are much better than previous one. Besides, I have added a small number (1e-5) onto the numerator of chi to suppress the numerical instability caused by LCAO basis, as suggested by 卢天, 陈飞武. 电子定域化函数的含义与函数形式[J]. 物理化学学报, 2011, 27(12): 2786-2792, and the results were significantly improved (right figure).

[kirk0830]

Thanks for your effort. I hope this PR can be an example illustrating how to get the kinetic density even if not with metaGGA functional. Present kernel function for calculating the tau is named as meta_op, hope it will have another more general and appropriate name soon.

[1041176461]

@sunliang98 Hello, I use v3.8.0 with out_elf 1 to calculate ELF, however, "ELF.cube" file is not output. The job is finished successfully. Here is my INPUT file, do I set something wrong?