Calculating atomic force in noncolliear and/or SOC case are needed

[hongriTianqi]

Background

Calculating atomic force in noncolliear and/or SOC case are needed in calculation of DeepSpin.

Describe the solution you'd like

Implement atomic force calculation in noncolliear and/or SOC calculations.

Task list only for developers

• Notice possible changes of behavior
• Explain the changes of codes in core modules of ESolver, HSolver, ElecState, Hamilt, Operator or Psi

Notice Possible Changes of Behavior (Reminder only for developers)

No response

Notice any changes of core modules (Reminder only for developers)

No response

Notice Possible Changes of Core Modules (Reminder only for developers)

No response

Additional Context

No response

Task list for Issue attackers (only for developers)

• Review and understand the proposed feature and its importance.
• Research on the existing solutions and relevant research articles/resources.
• Discuss with the team to evaluate the feasibility of implementing the feature.
• Create a design document outlining the proposed solution and implementation details.
• Get feedback from the team on the design document.
• Develop the feature following the agreed design.
• Write unit tests and integration tests for the feature.
• Update the documentation to include the new feature.
• Perform code review and address any issues.
• Merge the feature into the main branch.
• Monitor for any issues or bugs reported by users after the feature is released.
• Address any issues or bugs reported by users and continuously improve the feature.

[hongriTianqi]

This is related to #3130

[hongriTianqi]

Todos:

• add test links on Force and Stress finite difference tests.
• add case test for the functionality of new codes.

[hongriTianqi]

Finite difference test for noncollinear force with soc:

BCC Fe with mag in (111) direction:

https://app.bohrium.dp.tech/abacustest/?request=GET%3A%2Fapplications%2Fabacustest%2Fjobs%2Fjob-abacustest-v0.3.108-538675

Finite difference test for stress:
(1) collinear calculation:
https://app.bohrium.dp.tech/abacustest/?request=GET%3A%2Fapplications%2Fabacustest%2Fjobs%2Fjob-abacustest-v0.3.109-acc605
(2) noncollinear with soc_lambda = 0:
https://app.bohrium.dp.tech/abacustest/?request=GET%3A%2Fapplications%2Fabacustest%2Fjobs%2Fjob-abacustest-v0.3.109-eb2364
(3) noncollinear with soc_lambda = 1:
https://app.bohrium.dp.tech/abacustest/?request=GET%3A%2Fapplications%2Fabacustest%2Fjobs%2Fjob-abacustest-v0.3.109-3236a6 (all difference < 1 kBar)