Local modes in the theory of lattice vibrations: derivation and application

Abstract

For the construction of local modes in the harmonic theory of lattice vibrations the authors take over the method developed by des Cloizeaux for generalized Wannier functions complex electronic energy bands. A modification of this method is described showing that the construction of local modes with well defined symmetry is comparatively easy once the vibrational band structure is known. Reconsidering some examples of local coordinates used in earlier work, it is shown that some of the difficulties met there can be avoided by a thorough investigation of the relation between the normal and local modes. The authors indicate what profit is to be expected from the use of local modes in the theory of the cooperative Jahn-Teller effect.