Kohn's theory of the insulating state: a quantum-chemistry viewpoint

The qualitative difference between insulators and conductors not only manifests itself in the excitation spectra but also--according to Kohn's theory [Phys. Rev. 133, A171 (1964)]--in a different organization of the electrons in their ground state: the wave function is localized in insulators and delocalized in conductors. Such localization, however, is hidden in a rather subtle way in the many-body wave function. The theory has been substantially revisited and extended in modern times, invariably within a periodic-boundary-condition framework, i.e., ideally addressing an infinite condensed system. Here we show how the localization/delocalization of the many-body wave function shows up when considering either three-dimensional clusters of increasing size or quasi-one-dimensional systems (linear polymers, nanotubes, and nanowires) of increasing length, within the ordinary "open" boundary conditions adopted for finite systems. We also show that the theory, when specialized to uncorrelated wave functions, has a very close relationship with Boy's theory of localization [Rev. Mod. Phys. 32, 296 (1960)]: the Boys orbitals in the bulk of the sample behave in a qualitatively different way in insulating versus conducting cases.