Vibrational analysis of trans-polyacetylene : (CH)x and (CD)x

Abstract
We have calculated the normal modes « in the plane » of a trans-polyacetylene chain (CH)x, using a model with twelve force constants. When x is infinite, the Born cyclic condition allows us to determine both the dispersion and the density of states curves by using Fourier's dynamical, Hermitian matrix technique. It is shown that the peaks of the density of states correspond well to the normal mode frequencies of a chain of finite length (starting from x = 20) observable from IR and Raman scattering