support for printing soc matrix in LR-TDDFT calculation #7283

Background

Dear,
Does LR-TDDFT allow printing the SOC matrix? I have noticed that CP2K can output the SOC matrix in LR-TDDFT calculations. This matrix serves as a useful tool for analyzing singlet and triplet states, in particular the oscillator strengths of spin-flip transitions.

Describe the solution you'd like

https://manual.cp2k.org/trunk/CP2K_INPUT/FORCE_EVAL/PROPERTIES/TDDFPT/PRINT/SOC_PRINT.html
https://manual.cp2k.org/trunk/CP2K_INPUT/FORCE_EVAL/PROPERTIES/TDDFPT/SOC.html
Like CP2K, provide a tag to control whether the SOC matrix is printed. Here, SOC is treated as a perturbation.
Including this feature would allow a comparison between the perturbative SOC treatment and the full SOC effects in LR-TDDFT 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

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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.