Lobedness, complex orbitals, and the self-interaction energies of multiple bonds

A size-extensive formulation of the Perdew-Zunger self-interaction correction (PZ-SIC) [1] can be accomplished using localized Fermi Löwdin orbitals (FLOs) [2]. However, real FLOs are noded and semi-local functionals introduce an error that reflects the incipient division of one electron into fragments of non-integer electron number [3].  With real FLOs, molecules with multiple bonds are under-bound and the FLOs associated with the multiple bonds are strongly noded.  This suggests that the under-binding is directly linked to the nodality.  We explore this link using a method that reduces the lobedness of these orbitals without altering the total electron density. This scheme effectively provides an upper bound on the PZ-SIC energy minimized in the variational space of complex orbitals [4,5] and yields a lower energy solution than with the original orbitals, thereby improving the atomization energies of the molecules.

1. J.P. P. and A. Z., Phys. Rev. B 23, 5048 (1981)

2. M. R. P., A. R., and J. P. P., J. Chem. Phys. 140, 121103 (2014)

3. C. S. et al., J. Chem. Phys. 150, 174102 (2019)

4. M. R. P., R. A. H., and C. C. L., J. Chem. Phys. 80, 1972 (1984)

5. S. K., P. K., and H. J., Phys. Rev. A 84, 050501(R) (2011)