Infrared activity of peierls systems and application to polyacetylene

The conductivity of added charge (e.g. solitons) to a dimerized Peierls condensate with N coupled phonon bands is considered. If the phonon frequencies are low compared with the Peierls gap and the charge extends over several atoms then: (a) The infra-red frequencies ω^φ_n(n = 1, 2,..., N) and their relative weights are independent of the charge configuration. (b) The product P{cyrillic}^N_n = 1 ( ω^φ_n ω^R_n), where ω ^R_n are the Raman frequencies, isotope independent. The results are valid even if electron-electron interactions are present and a pinning effect is included. The product rule (b) is in good agreement with data on trans (CH)_x and (CD)_x. This data also yields the coupling constants and the pinning force.