The origins of avoided crossings in polymer dispersion curves

A purely mathematical heuristic model is examined in order to explain the existence of an avoided crossing between two dispersion curves calculated for a certain potential energy surface designed to simulate the dynamics of a linear polyethylene chain. The model shows that a third mode coupled to a two‐mode Fermi‐resonant system is able to create a marked instability in a vibrational spectrum. It is noted that such an explanation would require a fourth‐order coupling term, which is the reason given for the failure of normal mode analysis to properly identify this dynamical effect.