Resonance Raman scattering from finite and infinite polymer chains

Abstract

Three models for interpreting resonance Raman (RR) spectra of conjugated polymers are compared for the example of a strictly one-dimensional infinite or finite bond-alternating chain: the amplitude-mode model (AMM), the effective-conjugation-coordinate model (ECCM), and the conjugation-length model (CLM). The most characteristic behavior for the RR spectra of conjugated polymers is the change of line shape and line position of Raman modes with laser excitation energy, which is called a dispersion effect. This effect is considered to originate from inhomogeneities in the effective electron-phonon coupling constant λ̃ (AMM), in the effective force constant ${\mathit{f}}_{\mathit{J}\mathit{a}}$ (ECCM), or in the effective conjugation length N (CLM). Generalizing the CLM, we give a unifying picture for the three models mentioned above. The π-electron system is described by the Longuet-Higgins–Salem Hamiltonian, which includes the σ compressibility; and the RR cross section is evaluated with Albrecht’s theory. By calculating λ̃(N) and ${\mathit{f}}_{\mathit{J}\mathit{a}}$(N), it is shown that all inhomogeneities originate from a distribution in N. For correct calculations, no cyclic boundary conditions should be used. Extending Albrecht’s theory to an infinite linear chain, we show the connection between the molecular-physics approximation (CLM) and the solid-state-physics approximation (AMM) for the RR intensity. There are two peaks in the excitation profile: one for the incoming and another for the outgoing resonance. Finally, we show that the usual Franck-Condon analysis is not appropriate for medium-long linear chains because of the dramatic difference in the shape of the total-energy hypersurface for ground and excited states.