1172 28 The Structure of Solids, Liquids, and Polymers
as an example. A gold atom in its ground state has filled subshells except for one
electron in the 6ssubshell. We use the orbitals in filled shells as nonbonding orbitals
and constructNdelocalized LCAOMOs using the 6sorbitals from theNatoms of the
crystal as basis functions. The system is modeled as a collection of ions (“cores”) and a
“sea” of mobile electrons occupying the delocalized LCAOMOs. TheseNLCAOMOs
will have slightly different energies, constituting abandof closely spaced energy levels,
analogous to the four delocalized pi energy levels of a benzene molecule, but with many
more members and larger degeneracies. As with these benzene LCAOMOs, the lower-
energy LCAOMOs have more bonding character and the higher-energy LCAOMOs
have more antibonding character.
At low temperatureN/2 orbitals will be occupied by pairs of electrons with opposite
spins. The occupied orbitals have more bonding character than antibonding character,
like the occupied pi orbitals in benzene. The crystal is therefore held together very
strongly, as illustrated by the fact that gold melts at a high temperature (1063◦C).Exercise 28.9
Explain in simple terms why mercury, which has two 6selectrons, melts at a low temperature
(− 38. 4 ◦C). A more complete discussion of the low melting temperature of mercury involves
relativistic quantum mechanics.^7The Band Theory of the Electronic Structure of Solid
In our crude description of the gold crystal, we used the atomic orbitals in filled shells
as nonbonding orbitals and constructed a band of delocalized LCAOMOs from the 6s
orbitals. We can also make delocalized LCAOMOs from all of the orbitals. There is a
band made from the 1sorbitals, another band from the 2sorbitals, a third band from
the 2porbitals, and so on. Figure 28.10 shows the X-ray photoelectron spectrum of a
gold foil, in which the energies of several bands can be seen, as well as the 1sband
from a carbon impurity. The subscript on each band label is the value ofj, the quantum
number for the total angular momentum of one electron.Electrical Conductors and Insulators
If a band is created from orbitals that are partly filled in the separated atoms, as in the 6s
band of gold, the resulting band is only partly filled. There will be a number of vacant
orbitals in the band for electrons to move into. The electrons can easily move from
one orbital to another, and the crystal will be an electricalconductor. If the highest
occupied band in a crystal is completely filled, an electron can move from one orbital
to another in the band only if another electron vacates the second orbital. If there is no
way to create a vacancy the crystal will not conduct electricity, and is aninsulator.Semiconductors
In a semiconductor there is generally a band that is completely filled in the ground
state and aband gapbetween the highest energy of this band and the lowest energy(^7) P. Pyykkö,Chem. Rev., 88 , 563 (1988).