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(This page is under development, and might be completed Winter 2002).

Consider the formation of molecular orbitals in the bonding between two hydrogen atoms, as shown in Fig. 17. The combination of two equal-energy atomic orbitals, one from each hydrogen atom, leads to two molecular orbitals. One of these, the bonding molecular orbital, has a lower energy, while the other, the antibonding orbital, has a higher energy. The molecular orbitals can accommodate exactly the same number of electrons as the atomic orbitals from which they were formed, namely two per orbital. For the normal bonding distance d between the two atoms, the energies shown in Fig. 17 lead from the two atomic orbitals at A in Fig. 18 to the two molecular orbitals at B.

If, instead of two atoms, we now consider four atoms, we expect to see four molecular orbitals as at C in Fig. 18. Extrapolating this approach to the bonding in a piece of metal containing some 10²³ atoms per cubic centimeter, we could reasonably expect 10²³ molecular orbitals in an "energy band" as at D. There are so many levels in this band that for all practical purposes it may be viewed as being continuous. If the band is 1 eV wide, then the spacing between adjacent levels would be 10^-23 eV, an immeasurably small quantity.

Band theory gives a full explanation of the properties of the metallic elements of the periodic table and of the alloys formed between them. The shape of the energy band depends on the atomic orbitals involved and the geometrical arrangement and spacing between the atoms. The electrons available for bonding, that is, the sum of the valence electrons for all the atoms present, now occupy the band from the bottom upward, as in Fig. 19. This "density-of-states" diagram shows that the capacity to hold electrons varies with the energy within the band. The top of the electron filling is called the Fermi surface, usually designated Ef, and is illustrated for metallic iron in Fig. 19; the changed position for the closely related copper, which has three more bonding electrons per atom, is also indicated. These bonding electrons no longer belong to individual atoms, but to the piece of metal as a whole; they are "delocalized."

The good electrical and thermal properties of metals immediately follow from this description. An electric field raises an electron from below the Fermi surface to a higher energy level in the band, as indicated by the vertical arrows in Fig. 19, thus creating a movable negatively-charged electron above E_f and a movable positively-charged "hole" below E_f. In the applied electric field these two species move in opposite directions, representing an electric current. Heat also produces electrons and holes, both of which diffuse away from the hot region, thus producing a flow of energy and resulting in thermal conductivity without any net charge movement.

When light falls onto a piece of iron, the electrons below the Fermi surface can also become excited into higher energy levels in the band by absorbing the energy from the light, as in Fig. 19, producing electron-hole pairs. The light is so intensely absorbed that it can penetrate to a depth of only a few hundred atoms, typically less than a single wavelength. Since the metal is a conductor of electricity, this absorbed light, which is, after all, an electromagnetic wave, will induce alternating electric currents on the metal surface. These currents immediately re-emit the light out of the metal, thus providing strong reflection of a polished metal surface.

The efficiency of this process depends on the selection rules that apply to the atomic orbitals from which the energy band had formed. If the efficiency of absorption and reemission is approximately equal at all optical energies, then the different colors in white light will be reflected equally well, thus leading to the "silvery" color of polished iron and silver surfaces. However, if the efficiency decreases with increasing energy, as is the case for gold and copper, the reduced reflectivity at the blue end of the spectrum results in yellow and reddish colors, respectively.

The colors of alloys follow a similar pattern, but are difficult to predict a priori. For example, the addition of 25 percent silver to pure gold produces a green alloy while a similar amount of copper produces a red one.

The direct light absorption of a metal in the absence of reflection is observed only in rare instances. Gold is so malleable that it can be beaten into gold leaf less than 100 nm thick, then revealing a bluish-green transmitted-light color. When gold is in metallic colloidal form, however, as in the 10-nm-diameter particles in "ruby glass," the very complex "Mie scattering theory" has to be used to explain the unexpected red color illustrated in Plate VIII; the yellow glass in this figure is colored by Mie scattering from metallic colloidal silver particles.

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FIG. 17. The energy of bonding and antibonding molecular orbitals of the hydrogen molecule H₂

FIG. 18. The conversion of atomic orbitals into molecular orbitals and bands.

FIG. 19. Density-of-states - diagram for the metals iron Fe and copper Cu; vertical arrows indicate transitions produced by electricity, heat, or light.

PLATE VIII. Antique engraved Czechoslovakian glass colored yellow with silver and red with gold (both Mie scattering from colloidal particles).

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