  We present a microscopic picture rationalizing the surprisingly steep
decrease of the band gap with temperature in insulators, crystalline or
otherwise. The gap narrowing largely results from fluctuations of
long-wavelength optical phonons---when the latter are present---or their
disordered analogs, if the material is amorphous. We elaborate on this notion
to show that possibly with the exception of weakly bound solids made of
closed-shell atoms, the existence of an insulating gap or pseudo-gap in a
periodic solid implies that optical phonons must be present, too. This means
that in an insulating solid, the primitive cell must have at least two atoms
and/or that a charge density wave is present. As a corollary, a (periodic)
elemental solid whose primitive unit contains only one atom will ordinarily be
a metal, possibly unless the element belongs to group 18 of the periodic table,
consistent with observation. Some implications of the present results for
quantum solids are briefly discussed, such as that the ground state of the
Wigner crystal must be anti-ferromagnetic. A simple field theory of the
metal-insulator transition is constructed that ties long-wavelength optical
vibrations with fluctuations of an order parameter for the metal-insulator
transition; symmetry-breaking aspects of the latter transition are thereby
highlighted.
