  More than 30 years ago, polyacetylene was very much in the limelight, an
early example of a conducting polymer and source of many unusual spectroscopic
features spawning disparate ideas as to their origin. Several versions of the
polyacetylene spectrum story emerged, with contradictory conclusions. In this
paper both ordinary and peculiar polyacetylene spectral features are explained
in terms of standard (if disused) spectroscopic concepts, including the
dependence of electronic transition moments on phonon coordinates,
Born-Oppenheimer energy surface properties, and (much more familiarly) electron
and phonon band structure. Raman sideband dispersion and line shapes are very
well matched by theory in a fundamental way. Most importantly, clear
ramifications emerge for the Raman spectroscopy of a wide range of extended
systems, including graphene and beyond, suggesting changes to some common
practice in condensed matter spectroscopy.
