How to use linear response method to calculate Hubbard U in CP2K

[Jundi Wang]

Dear CP2K developers,

I am writing to ask how to use linear response method to calculate Hubbard U in CP2K. I find the way to do both the self-consistent calculation and the Non-self-consistent calculation, but I don't know how to apply energy (α) to a specific orbital of a specific atom to obtain the corresponding electron occupation number. I don't know if there is a function that can be implemented in cp2k.

Thank you for your help,

wjd

[Matt Watkins]

I don't belive this is currently implemented in cp2k. You might be able to script something to the effect.

[Cao Yang]

Dear CP2K developers,

I would like to follow up on this topic regarding the calculation of Hubbard U using the linear-response approach in CP2K.

I noticed that in a previous discussion (May 2024), it was mentioned that the linear-response calculation of Hubbard U was not yet implemented in CP2K and that a scripted workflow might be required.

Recently, I came across the work by Liu, Chai, Si, O'Regan and co-workers on the implementation of the Minimum-Tracking Linear Response (MT-LR) Hubbard and Hund corrected DFT method in CP2K. According to the publication, the MT-LR framework for determining Hubbard U and Hund J parameters was implemented within Quickstep.

I am currently using CP2K 2026.1 and would like to know:

1. Has the MT-LR method for calculating Hubbard U (and possibly Hund J) been fully integrated into the current public release of CP2K?

2. If so, could you please point me to the relevant documentation or provide the corresponding input keywords/workflow?

3. If this functionality is not yet available in the public release, what would be the recommended approach for obtaining reliable U values for transition-metal oxides (e.g., TiO₂) within CP2K? Would a manual linear-response procedure or another first-principles approach be recommended?

Any suggestions or references would be greatly appreciated.

Thank you very much for your time and help.

Best regards,

Cao Y.