Density functional theory (DFT) suffers from self-interaction errors (SIE) that generally result in the underestimation of chemical reaction barrier heights. This is commonly attributed to delocalization of electrons over stretched bonds found in transition state structures. The Perdew-Zunger self-interaction correction (PZ-SIC) and locally scaled self-interaction correction (LSIC) improve the barrier heights for many reactions, with LSIC giving higher accuracy than PZ-SIC on average. These methods employ an orbital-by-orbital correction scheme to remove the one-electron SIE using Fermi-Löwdin orbitals (FLOs).

The self-interaction correction (SIC) can be divided into a term due to the changes in the density when SIE is removed (density-driven errors) and a term due to energy corrections from each of the FLOs. In many cases the density-driven error is small. Furthermore, we hypothesize that the FLO energy contribution comes mainly from a limited number of orbitals that are directly involved in bond-breaking and bond-making events. We call these “participant” FLOs, in contrast to “spectator” FLOs that are not directly involved in changes to the bonding structure. Hence our hypothesis is that △E^SIC≈ △E_part^SICand △E_spect^SIC ≈ 0.

We test this hypothesis by examining the reaction barriers for the BH76 dataset. We categorize the reactions roughly as “early”, “middle” or “late” transition states (TS). The participant and spectator FLOs in the transition state were picked and mapped to the reactant and the product FLOs to get △E_part^SICand △E_spect^SICfor forward and reverse reactions. The hypothesis is followed for middle TS, but not by early and late TS reactions. Early TS reactions fail the hypothesis when △E^SICis small or negative, while late TS reactions fail due to a change in the hybridization of the spectator FLOs. LSIC does not follow the hypothesis any better than PZ-SIC. The hypothesis is not justified by including only the participant FLOs. Spectator FLOs contribute significantly and cannot be excluded from the analysis.

Prakash Mishra

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