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The rise and fall of stretched bond errors: Extending the analysis of Perdew-Zunger self-interaction corrections of reaction barrier heights beyond the LSDA

Incorporating self-interaction corrections (SIC) significantly improves chemical reaction barrier height predictions made using density functional theory methods. We present a detailed, orbital-by-orbital analysis of these corrections for three semi-local density functional approximations (DFAs) situated on the three lowest rungs of the Jacob's Ladder of approximations. The analysis is based on Fermi-Löwdin Orbital Self-Interaction Correction calculations performed at several steps along the reaction pathway from the reactants (R) to the transition state (TS) to the products (P) for four representative reactions selected from the BH76 benchmark set. For all three functionals, the major contribution to self-interaction corrections of the barrier heights can be traced to stretched bond orbitals that develop near the TS configuration. The magnitude of the ratio of the self-exchange-correlation energy to the self-Hartree energy (XC/H) for a given orbital is introduced as an indicator of one-electron self-interaction error. For the exact, but unknown density functional, XC/H = 1.0 for all orbitals, while for the practical DFAs studied here, XC/H spans a range of values. The largest values are obtained for stretched or strongly lobed orbitals. We show that significant differences in XC/H for corresponding orbitals in the R, TS, and P configurations can be used to identify the major contributors to the SIC of barrier heights and reaction energies. Based on such comparisons, we suggest that barrier height predictions made using the SCAN meta-generalized gradient approximation may have attained the best accuracy possible for a semi-local functional using the Perdew-Zunger SIC approach.