  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 [J. P.
Perdew and A. Zunger, Phys. Rev. B, {\bf 23}, 5048 (1981)]
self-interaction-correction (PZSIC), as well as two variations of the recently
developed, locally scaled self-interaction correction (LSIC) [R. R. Zope
\textit{et al.}, J. Chem. Phys. {\bf 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.
