  A correction method for vertical transition levels (VTLs) involving defect
states calculated with a supercell technique is formulated and its
effectiveness is systematically verified with ten defects in prototypical
materials: cubic-BN, GaN, MgO, and 3C-SiC. Without any corrections, the
absolute errors are around 1 eV with moderate size supercells in most cases. In
contrast, when our correction method is adopted, the absolute errors are
reduced and become less than 0.12 eV in all the cases. Our correction scheme is
general and will have the potential for wide application as it is adaptive for
evaluating various quantities at fixed geometry, as represented by those
relevant to the generalized Koopmans' theorem.
