  A relation between the energy of an elementary `insulating' excitation
corresponding to the metal-insulator transition and the bandgap width in a
semiconductor is obtained. An effect of atomic relaxation on the temperature
and pressure dependence of the bandgap width is considered. It is shown that
the metal-insulator transition in a semiconductor causes a weak rhombohedral or
monoclinic distortion in the case of a diamond and zincblende structure and a
weak tetragonal or orthorhombic distortion in the case of a rocksalt structure.
A change in the bandgap associated with a ferroelectric (antiferroelectric)
transition in a semiconductor is also obtained.
