Pariser–Parr–Pople force field for π-electrons: Raman and infrared shifts of trans-polyacetylene

The transfer integrals t(R) and Coulomb potential V(R) of π-electron Hamiltonians He define linear electron–phonon (e–ph) coupling constants t′(R) and V′(R) for the equilibrium structure. We generalize linear response (LR) theory for Raman and ir shifts due to π-electron delocalization in Hamiltonians with arbitrary t(R) and spin independent V(R). π-electron contributions ΔFij to the force field of trans-polyacetylene (PA) are obtained in the symmetry coordinates Si, with i=1–5, for k=0 phonons. We compare ΔFij for Hückel chains with alternating transfer integrals t(1±δ) and for Pariser–Parr–Pople (PPP) models with hydrocarbon parameters derived from π–π* spectra to a phenomenological ΔFij for trans-PA and its isotopes. An exponential rather than linear t(R) is found. The molecular PPP potential V(R) accounts quantitatively for π-electron coupling to CCC bends and for the length dependence of the Raman shifts of finite polyenes. The dominant but not exclusive π-electron coupling remains the dimerization coordinate singled out in previous treatments, with substantially larger t′(R) than V′(R) contributions in the PPP force field. We comment on extensions of LR theory to PA models with interacting π-electrons and several electronic susceptibilities.