  We formulate a spin-polarized van Leeuwen and Baerends (vLB) correction to
the local density approximation (LDA) exchange potential [Phys. Rev. A 49, 2421
(1994)] that enforces the ionization potential (IP) theorem following Stein et
al. [Phys. Rev. Lett. 105, 266802 (2010)]. For electronic-structure problems,
the vLB-correction replicates the behavior of exact-exchange potentials, with
improved scaling and well-behaved asymptotics, but with the computational cost
of semi-local functionals. The vLB+IP corrections produces large improvement in
the eigenvalues over that from LDA due to correct asympotic behavior and atomic
shell structures, as shown on rare-gas, alkaline-earth, zinc-based oxides,
alkali-halides, sulphides, and nitrides. In half-Heusler alloys, this
asymptotically-corrected LDA reproduces the spin-polarized properties
correctly, including magnetism and half-metallicity. We also considered
finite-sized systems [e.g., ringed boron-nitirde (B$_{12}$N$_{12}$) and
graphene (C$_{24}$)] to emphasize the wide applicability of the method.
