Study of self-interaction-errors in barrier heights using locally scaled and Perdew–Zunger self-interaction methods

Abstract

We study the effect of self-interaction errors on the barrier heights of chemical reactions. For this purpose, we use the well-known Perdew–Zunger self-interaction-correction (PZSIC) [J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981)] as well as two variations of the recently developed, locally scaled self-interaction correction (LSIC) [Zope et al., J. Chem. Phys. 151, 214108 (2019)] to study the barrier heights of the BH76 benchmark dataset. Our results show that both PZSIC and especially the LSIC methods improve the barrier heights relative to the local density approximation (LDA). The version of LSIC that uses the iso-orbital indicator z as a scaling factor gives a more consistent improvement than an alternative version that uses an orbital-dependent factor w based on the ratio of orbital densities to the total electron density. We show that LDA energies evaluated using the self-consistent and self-interaction-free PZSIC densities can be used to assess density-driven errors. The LDA reaction barrier errors for the BH76 set are found to contain significant density-driven errors for all types of reactions contained in the set, but the corrections due to adding SIC to the functional are much larger than those stemming from the density for the hydrogen transfer reactions and of roughly equal size for the non-hydrogen transfer reactions.

Understanding Density-Driven Errors for Reaction Barrier Heights

“…Applying PZSIC to a semilocal DFA can reduce the density- and functional-driven errors in abnormal systems and thus improve, e.g., reaction barrier heights. , However, it has long been known − that applying semilocal DFAs to the Hartree–Fock density tends to produce highly accurate reaction barrier heights and other quantum chemical quantities . This methodology, variously called DFA@HF to indicate a DFA evaluated at the HF density, or HF-DFT, is relatively inexpensive but loses the benefits of self-consistency, like computation of forces from the Hellman–Feynman theorem .…”

How Do Self-Interaction Errors Associated with Stretched Bonds Affect Barrier Height Predictions?

“…LSDA (24.9 kcal/mol) underestimates the barrier by nearly 15 kcal/mol, while both PZSIC (61 kcal/mol) and LSIC (63.7 kcal/mol) overestimate the barrier by more than 20 kcal/mol. The contribution of the DFA part of the PZSIC and LSIC total energy to the barrier height error is −5.2 kcal/mol . For this reaction the contribution of the POs to the barrier height is nearly identical in PZSIC and LSIC, 0.049 hartree or 30.7 kcal/mol, while the contribution of the SOs is much smaller in both methods, −4.6 kcal/mol for PZSIC and 1.3 kcal/mol for LSIC.…”

“…In a FLOSIC calculation, the FODs are optimized to produce FLOs corresponding to the minimum FLOSIC total energy. More details on obtaining FLOs can be found in previous publications , and in the work of Mishra et al…”

“…By doing so, LSIC provides improved predictions of properties such as electron affinities, ionization energies, atomization energies, and polarizabilities − compared to the uncorrected DFA, whereas PZSIC can overcorrect. Recently, Mishra et al studied the performance of PZSIC and LSIC (with two different scaling schemes LSIC­( z ) and LSIC­( w ) , ) for barrier heights of chemical reactions using the large BH76 benchmark set originally developed by Truhlar and co-workers , and updated in a recent database . BH76 contains reference values of forward and reverse barriers for 19 hydrogen transfer (HT) reactions and 19 non-hydrogen transfer (NHT) reactions.…”

“…The focus of this paper is to test the stretched-bond hypothesis using the results obtained by Mishra et al 19 for BH76. The analysis consists of identifying the POs and SOs in the transition state and the corresponding orbitals in the reactant or product states and comparing the SIC energies of these orbitals to determine their contributions to the overall reaction barrier correction.…”