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interacting Dynamic Electrons Approach
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[WIP] Add Kohn-Sham Strictly Correlated Electrons method #8

Closed DerkKooi closed 1 year ago

DerkKooi commented 1 year ago

Adds the Kohn-Sham Strictly Correlated Electrons method as an alternative. See refs. [1-5] and the notebook example_kssce.ipynb for details. The method works well for strongly correlated systems.

Some issues/points:

  1. For cases in which the gap closes (e.g. $N=2$ singlet, where the density separates into two peaks) the convergence fails. In our work [5] we could achieve convergence using DIIS + dampening + level shifting. Do note that this happens for these systems with any functional that correctly describes them.
  2. There are some choices in the method for using different interpolation methods, which are being pushed around using a dictionary method_params, but this is not very elegant.
  3. Not entirely clear to me yet which interpolation methods are best.

References

  1. F. Malet and P. Gori-Giorgi, Strong correlation in Kohn-Sham density functional theory, Phys. Rev. Lett. 109, 246402 (2012). DOI: 10.1103/PhysRevLett.109.246402
  2. F. Malet, A. Mirtschink, J. C. Cremon, S. M. Reimann, and P. Gori-Giorgi. Kohn-Sham density functional theory for quantum wires in arbitrary correlation regimes. Phys. Rev. B 87, 115146 (2013) DOI: 10.1103/PhysRevB.87.115146
  3. A. Mirtschink, M. Seidl, and P. Gori-Giorgi. Derivative discontinuity in the strong-interaction limit of density functional theory. Phys. Rev. Lett. 111, 126402 (2013) DOI: 10.1103/PhysRevLett.111.126402
  4. F. Malet, A. Mirtschink, K. J. H. Giesbertz, L. O. Wagner, and P. Gori-Giorgi. Exchange-correlation functionals from the strongly-interacting limit of DFT: Applications to model chemical systems. Phys. Chem. Chem. Phys. 16, 14551 (2014) DOI: 10.1039/c4cp00407h
  5. A. Marie, D. P. Kooi, J. Grossi, M. Seidl, Z. Musslimani, K.J.H. Giesbertz, P. Gori-Giorgi. Real space Mott-Anderson electron localization with long-range interactions. Physical Review Research 4, 043192 (2022) DOI: 10.1103/PhysRevResearch.4.043192
JackWetherell commented 1 year ago

Thank you @DerkKooi !!