Tackling the one-electron self-interaction error within the semilocal density functional framework

One-electron self-interaction errors (SIE), caused by incomplete cancellation of the electron's spurious self-Coulomb interaction, pose a persistent challenge in density functional approximations, as illustrated by the prototypical one-electron system ${\mathrm{H}}_{2}^{+}$. While significant efforts have been made to eliminate SIE through the development of computationally expensive nonlocal density functionals, it is equally important to explore whether SIE can be mitigated within the framework of more efficient semilocal density functionals. In this Letter, we present a nonempirical exchange-only meta-generalized gradient approximation (meta-GGA) that incorporates the Laplacian of the electron density. Our results demonstrate that this meta-GGA significantly reduces SIE, yielding a binding energy curve for ${\mathrm{H}}_{2}^{+}$ that matches the exact solution at equilibrium and improves across a broad range of bond lengths over those of the Perdew-Burke-Ernzerhof and strongly constrained and appropriately normed semilocal density functionals. This advancement paves the way for further development within the realm of semilocal approximations.