The paper by Perdew and Zunger addresses the issue of self-interaction in density-functional theory (DFT) for many-electron systems. They present two methods for correcting the self-interaction in density functionals, which are sanctioned by the Hohenberg-Kohn theorem. The first method introduces an orbital-dependent single-particle potential, while the second involves a local potential similar to the Kohn-Sham scheme. The authors apply these methods to the local-spin-density (LSD) approximation and demonstrate that the first method properly conserves the number content of the exchange-correlation hole while improving its shape. They find that the corrections improve the accuracy of various physical problems where the uncorrected LSD approach produces systematic errors. The benefits of the self-interaction correction (SIC) include improved total energy values, accurate binding energies of negative ions, more accurate electron densities, and better representation of orbital eigenvalues and long-range behavior of the potential and density. The SIC also addresses issues such as underestimated band gaps in insulators and overestimated cohesive energies in transition metals. The authors discuss the implications of the SIC for the LSD approximation and provide a parametrization of the electron-gas correlation energy at any density.The paper by Perdew and Zunger addresses the issue of self-interaction in density-functional theory (DFT) for many-electron systems. They present two methods for correcting the self-interaction in density functionals, which are sanctioned by the Hohenberg-Kohn theorem. The first method introduces an orbital-dependent single-particle potential, while the second involves a local potential similar to the Kohn-Sham scheme. The authors apply these methods to the local-spin-density (LSD) approximation and demonstrate that the first method properly conserves the number content of the exchange-correlation hole while improving its shape. They find that the corrections improve the accuracy of various physical problems where the uncorrected LSD approach produces systematic errors. The benefits of the self-interaction correction (SIC) include improved total energy values, accurate binding energies of negative ions, more accurate electron densities, and better representation of orbital eigenvalues and long-range behavior of the potential and density. The SIC also addresses issues such as underestimated band gaps in insulators and overestimated cohesive energies in transition metals. The authors discuss the implications of the SIC for the LSD approximation and provide a parametrization of the electron-gas correlation energy at any density.