The vibration spectra of helical molecules: infra-red and Raman selection rules, intensities and approximate frequencies

The infra-red and Raman selection rules for an infinite long-chain molecule having helical symmetry are discussed, and the normal modes of vibration are classified by the use of group theory. A weak-coupling approximation is used to derive relations between the intensities of the variously polarized spectral components arising from a single vibration frequency of the unit out of which the helix is built. A form of matrix perturbation theory is used to obtain some approximate relations between the frequencies of these components; these relations involve the angle ψ relative to the screw axis which separates successive units of the helix and provide, in principle, a method by which this angle may be measured. It is suggested that the methods discussed here may serve as a basis for the interpretation of the spectra of fibrous proteins.