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Physical chemistry 288

In a metal, at least one band is partially filled, caused either by a
deficit of electrons or by band overlap. In an insulator, the highest
occupied band is filled, and there is a significant energy gap
(‘band gap’) between this and the lowest unoccupied band. In a
semiconductor, thermal excitation across the band gap is possible
at ambient temperatures which enables conduction to take place.

Ionic solids are held together by electrostatic forces. For regular
crystals, the molar potential energy of an ion is given by

The Madelung constant, A, depends only upon the symmetry of
the ions in the structure, and hence on the structure type. The
scaling distance d varies in proportion to the size of the unit cell.
Related topics The wave nature of matter (G4) Molecular orbital theory of
diatomic molecules II (H4)
Statistical thermodynamics (G8)
Molecular orbital theory of
diatomic molecules I (H3)

Bonding in solids: band theory

Bonding in solids involves orbital contributions from far more atoms than are
encountered in most molecular systems. Far from complicating the bonding theory, this
very large number enables the bonding to be treated by averaging of all the possible
bonding patterns. Experiments demonstrate that the bonding in solids does not yield
discrete energy levels, but leads to the formation of energy bands within which a given
electron may hold any energy within a continuous range. The model of these bands is
referred to as band theory. Two complementary theories form the basis of band theory.
The tightly bound electron model (also known as the tight binding approximation)
and the free electron model.

Tightly bound electron model
The tightly bound electron model is an extension of the LCAO approach to molecular
orbitals. The energy bands in a solid are treated as a linear combination of the atomic
orbitals of its consituent elements.