Raman Scattering in Carbon Nanosystems: Solving Polyacetylene

Polyacetylene has been a paradigm conjugated organic conductor since well before other conjugated carbon systems such as nanotubes and graphene became front and center. It is widely acknowledged that Raman spectroscopy of these systems is extremely important to characterize them and understand their internal quantum behavior. Here we show, for the first time, what information the Raman spectrum of polyacetylene contains, by solving the 35-year-old mystery of its spectrum. Our methods have immediate and clear implications for other conjugated carbon systems. By relaxing the nearly universal approximation of ignoring the nuclear coordinate dependence of the transition moment (Condon approximation), we find the reasons for its unusual spectroscopic features. When the Kramers-Heisenberg-Dirac Raman scattering theory is fully applied, incorporating this nuclear coordinate dependence, and also the energy and momentum dependence of the electronic and phonon band structure, then unusual line shapes, growth, and dispersion of the bands are explained and very well matched by theory.