Polarization in Kohn-Sham density-functional theory

The modern theory of polarization, based on a Berry phase, is currently implemented in most first-principle electronic structure codes. Many KS-DFT calculations have addressed various phenomena (ferroelectricity, piezoelectricity, lattice dynamics, infrared spectra of liquid and amorphous systems) in several materials. Notwithstanding, the KS polarization does not coincide with the exact one, even when ideally implemented with the exact KS crystalline potential. This is at odds with the fact that the KS electrical dipole of a bounded crystallite coincides by definition with the exact one: we analyze this issue from several viewpoints. According to the modern theory, the polarization of a centrosymmetric crystal does not vanish in general; we show that the polarization of a centrosymmetric quasi-1d systems (stereoregular linear polimer) is a topological invariant: ergo in this case the KS polarization coincides with the exact one.