Long wave theory of absorption and reflection in molecular crystals

The theory of long waves originally developed by Born and Huang for ionic crystals and then adapted for molecular crystals with one molecule per unit cell by Hall is extended to include molecular crystals with two molecules per unit cell. A study is made of the non-analytic behaviour of the energy bands as the wave vector tends to zero and it is found that the energies of the optically excited levels will be different from the values usually assumed. The dispersion relation is obtained and used to discuss metallic reflectivity. The finite lifetime of the excited states can also be included in the theory and this has the effect of changing the position of maximum absorption as well as reducing the reflectivity. A comparison is made between the long wave theory, the simple form of Davydov theory and experiment.