Moreover, equilibrium bond lengths for all cases can be estimated from the bond type and the sum of the classical turning radii of the free atoms or ions.
Nonetheless, a strong correlation with insulating behavior can still be inferred. Surprisingly, many semiconductors have no CFR at equilibrium, a key finding for density functional construction. A classical picture of conduction suggests that CARs should be connected in metals, and disconnected in wide-gap insulators, and is confirmed in the limits of extreme compression and expansion.
Calculations with several approximate density functionals and codes confirm these behaviors. They can also appear at a monovacancy in a metal. In all materials, CFRs appear or grow as the internuclear distances are uniformly expanded. At equilibrium geometries, we find that CFRs are absent in perfect metals, rare in covalent semiconductors at equilibrium, but common in ionic and molecular crystals. They are useful for understanding many chemical properties of molecules but need not exist in solids, where the density never decays to zero.
Classical turning surfaces of Kohn–Sham potentials separate classically allowed regions (CARs) from classically forbidden regions (CFRs).
