Self-interaction Corrected Energy Functional Applied to Molecules and Solids
Hannes Jónsson1,2,3
1Science Institute and Faculty of Physical Sciences, University of Iceland, Reykjavík, Iceland
2Department of Chemistry, Brown University, USA
3Department of Applied Physics, Aalto University, Finland
Localized electronic states and weakly bound electrons extending far from atom nuclei are examples where practical implementations of Kohn-Sham density functional theory (DFT) such as GGA, meta-GGA and hybrid functionals tend to fail. A variational and self-consistent implementation of the Perdew-Zunger self-interaction correction (PZ-SIC) using complex optimal orbitals [1] has been applied to several such systems and found to give good results. Calculations of dipole bound anion [2], Rydberg excited states of molecules and molecular clusters [3], localized charge state in a diamine cation [4] and electronic holes in oxide crystals [5] will be presented. The computational effort of the PZ-SIC calculations scales with system size in the same way as DFT/GGA calculations but the prefactor is large since an effective potential needs to be evaluated for each orbital (calculations that could, however, be carried out in parallel) and optimal orbitals need to be found in terms of the Kohn-Sham orbitals. PZ-SIC is an example of an extended functional form where the energy depends explicitly on the orbital densities, not just the total electron density. While significant improvements are obtained with PZ-SIC compared with practical implementations of Kohn-Sham DFT, problems can also be introduced such as incorrect symmetry breaking [6]. The orbital density dependent functional form could, however, be exploited more generally to develop a self-interaction free functional rather than as a correction to Kohn-Sham functionals, thereby providing a mean field theory for optimal orbitals and orbital energies.
[1] S. Lehtola and H. Jónsson, J. Chem. Theory Comput. 10, 5324 (2014); S. Lehtola, E. Ö. Jónsson, and H. Jónsson, J. Chem. Theory Comput. 12, 4296 (2016).
[2] Y. Zhang, P.M. Weber and H. Jónsson, J. Phys. Chem. Letters 7, 2068 (2016
[3] H. Gudmundsdóttir, Y. Zhang, P.M. Weber and H. Jónsson, J. Chem. Phys. 141, 234308 (2014).
[4] X. Cheng, Y. Zhang, E. Jónsson, H. Jónsson and P.M. Weber, Nature Communications 7, 11013 (2016); 9, 5348 (2018).
[5] H. Gudmundsdóttir, E. Ö. Jónsson and H. Jónsson, New Journal of Physics 17, 083006 (2015).
[6] S. Lehtola, M. Head-Gordon and H. Jónsson, J. Chem. Theory Comput. 12, 3195 (2016).