  Defect physics is at the heart of microelectronics. By keeping track of the
reference energy in total energy calculations, we explicitly show that the
"potential alignment" correction vanishes, and the classic Markov-Payne
correction yields accurate results. From linear response theory, we further
formulate an accurate expression for the quadrupole correction. Application to
numerous defects including anisotropic material yields accurate formation
energies in small supercells and the historically slow convergence of the 2+
diamond vacancy is shown to be a result of slow varying gap levels of the
defect leading to a size dependent dielectric constant.
