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

Abstract

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.

Figures (2)

• Figure 1: SIC energy, $E^{SIC}[n_i]$, from FLO-SCAN calculations for select spectator, participant, and stretched bond orbitals for four representative reactions. The energies are evaluated at several steps along approximate reaction pathways connecting the reactant (R) species to the transition state (TS), and from the TS to the product (P) species. Differences in $E^{SIC}[n_i]$ for a given orbital between the TS and the R (P) reflect the contribution of that orbital to the SIC correction of the forward (reverse) reaction barrier.
• Figure 2: The magnitude of the self-exchange-correlation energy (XC) divided by the self-Hartree energy (H) is presented for FLOs in four representative reactions: (a) $T_{4}$: CH$_4$+OH$\rightarrow$CH$_3$+H$_2$O, (b) $T_{12}$: H+OH$\rightarrow$O+H$_2$, (c) $T_{13}$: H+H$_4$S$\rightarrow$H$_4$+HS, and (d) $T_{9}$: F+H$_2$$\rightarrow$FH+H. The XC/H ratios were obtained from self-consistent FLO-SCAN calculations for each reaction. Red, black, and green dots represent XC/H ratios for FLOs in the reactants (R), transition state (TS), and product (P) species, respectively. The horizontal dashed line signifies the reference point where the magnitude of XC equals H. Vertical dotted lines indicate participant (PO) and stretched bond (SB) orbitals involved in the respective reactions. Data for spin-up (down) FLOs are shown on a beige (gray) background. Changes in XC/H for a given FLO reflect changes in the shape of the FLO between the R, TS, and P states. Further discussion is provided in the text.