Abstract
The study of dispersion relations for external modes in molecular and complex ionic crystals is reviewed. The concept of external modes is introduced, so that the formal theory may be developed along the lines of standard Born-von K\'arm\'an formalism. The studies reported thus far in the literature are then surveyed against the background of the formal theory. The role of macroscopic electric fields in relation to external modes is next discussed, and the work of Kellermann is generalized to obtain Coulomb coefficients connected with external modes in complex ionic crystals. Finally, the group-theoretical aspects are considered, and the recent work of Maradudin and Vosko is extended to cover the external modes. A detailed illustrative example is also provided.
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