Removing Combinatorial Complexity for Systematic Initialization of Electronic Geometries for Fermi-Löwdin-Orbital Self-Interaction Corrections to Density Functional Approximations

Density functional theory suffers from the self-interaction error due to the approximation of the exchange-correlation energy. The Fermi-Löwdin-Orbital (FLO) self-interaction correction (SIC) [1] employs the Perdew-Zunger (PZ) theory [2] in which the PZ SIC energy is minimized with respect to the Fermi orbital descriptors (FODs). FODs are the positions in space where FLOs are localized and are the ingredients needed to define a unitary transformation that connects localized and canonical orbitals. They can be viewed as describing a quasi-classical electronic geometry. In the FLO-SIC method, a major challenge is the initialization of the FOD geometry for systems containing transition metal ions and for systems having double or resonance bonds. We describe a machine-human learning paradigm that reduces the combinatorial complexity associated with initiating FODs to a hierarchical screening approach that reduces the search to a series of single-atom calculations. Examples of this approach to several difficult systems, including a trianionic molecule with a magnetically active center, will be discussed.

[1] M. R. Pederson, A. Ruzsinszky, and J. P. Perdew J. Chem. Phys. 140, 121103 (2014)
[2] J. P. Perdew and A. Zunger Phys. Rev. B 23, 5048 (1981)