Following the previous discussion on DFT in strong fields, I would like to ask about the difference between those two alternatives (BDFT and CDFT). By CDFT I do not mean (constrained DFT, but current DFT). The mathematical background of these two can be found in:
- Vignale, et al., Density-functional theory in strong magnetic fields, Phys. Rev. Lett. 1987, 59, 2360.
- Grayce, et al., Magnetic-field density functional theory, Phys. Rev. A, 1994, 50, 3089.
- Tellgren, et al., Choice of basic variables in current-density functional theory, Phys. Rev. A 2012, 86, 062506.
- Bates, et al., Harnessing the meta-generalised gradient approximation for time-dependent density functional theory, J. Chem. Phys. 2012, 137, 164105.
- Furness, et al., Current density functional theory using meta-generalised gradient exchange-correlation functionals, J. Comp. Theory Comput. 2015, 11, 4169.
- Reimann, et al., Magnetic-field density functional theory (BDFT): Lessons from the adiabatic connection, J. Comp. Theory Comput. 2017, 13, 4089.
- Reimann, et al., Kohn-Sham energy decomposition for molecules in a magnetic field, Mol. Phys. 2018.
To summarise, Kohn-Sham CDFT has the advantages that it is universal (can be applied for any magnetic field / vector potential A), a non-perturbative implementation can be applied to arbitrary field strengths, and functionals can be generated from existing meta-GGAs. However, functional dependence on the physical current, j_p is not widely studied, hence, new functionals are required.
What about the advantages (and differences) of BDFT?