Electron–phonon coupling in conjugated polymers: Reference force field and transferable coupling constants for polyacetylene

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Abstract
A Herzberg–Teller expansion for π electrons in the ground state of conjugated polymers identifies quadratic electron–phonon (e–ph) contributions and suggests a σ+π reference force field F 0 based on butadiene. Linear response theory then fixes linear e–ph coupling constants for the Raman shifts in polyacetylene (PA) due to π‐electron fluctuations. The same coupling constants and the known isotopic dependences of the reference accurately give the Raman frequencies of (CD) x and (13CH) x ; with a different susceptibility,F 0 and the coupling constants also account for Raman modes of polyenes and for photo‐ or dopant‐induced infrared modes of PA and its isotopes. We develop a general phenomenological approach for identifying modes coupled to π‐electron fluctuations and show that both CCC and CCH bends are weakly active in PA. Linear and quadratic e–ph coupling constants and various susceptibilities are related to π‐electron Hamiltonians, primarily to Hückel models and to Coulomb interactions in the Pariser–Parr–Pople model. We also relate our approach to previous PA models with linear e–ph coupling or modified force fields.