Bond alternation in infinite periodic polyacetylene: Dynamical treatment of the anharmonic potential

The potential energy of the infinite periodic chain model of polyacetylene (pPA) is symmetric with two equivalent minima separated by the Peierls’ stabilization barrier. In this work it is shown how an energy scale and vibrational energy levels for this highly anharmonic Peierls’ degree of freedom can be estimated. Particular attention is given to the potential energy increase for large deformations. Two empirical methods and direct periodic boundary condition (PBC) density functional theory (DFT) calculations are in semi-quantitative agreement with each other. Each lead to the conclusion that pPA has a zero-point level that is above the Peierls’ barrier. The argument does not depend critically on the barrier height or the other parameters of the model or the computation method. It is concluded that pPA will not exhibit bond alternation since two stable structures are not possible due primarily to the stiffness of the underlying CC sigma bond system.