  We examine the role of self-interaction errors (SIE) removal on the
evaluation of magnetic exchange coupling constants. In particular we analyze
the effect of scaling down the self-interaction-correction (SIC) for three {\em
non-empirical} density functional approximations (DFAs) namely, the local spin
density approximation, the Perdew-Burke-Ernzerhof generalized gradient
approximation, and recent SCAN family of meta-GGA functionals. To this end, we
employ three one-electron SIC methods: Perdew-Zunger [Perdew, J. P.; Zunger, A.
\textit{Phys. Rev. B}, {\bf 1981}, \textit{23}, 5048] SIC, the orbitalwise
scaled SIC method [Vydrov, O. A. \textit{et al.}, \textit{J. Chem. Phys.} {\bf
2006,} \textit{124}, 094108], and the recent {local} scaling method [Zope, R.
R. \textit{et al.}, \textit{J. Chem. Phys.} {\bf 2019}, \textit{151}, 214108].
We compute the magnetic exchange coupling constants using the spin projection
and non projection approaches for sets of molecules composed of dinuclear and
polynuclear H--He models, organic radical molecules, and chlorocuprate, and
compare these results against accurate theories and experiment. Our results
show that for the systems that mainly consist of single electron regions, PZSIC
performs well but for more complex organic systems and the chlorcuprates, an
overcorrecting tendency of PZSIC combined with the DFAs utilized in this work
is more pronounced, and in such cases LSIC with kinetic energy density ratio
performs better than PZSIC. Analysis of the results in terms of SIC corrections
to the density and to the total energy shows that both density and energy
correction are required to obtain an improved prediction of magnetic exchange
couplings.
