Molecular dynamic structure and dimerization of polyacetylene

The vibronic interaction in an ( A ) 2 N chain (e.g., polyacetylene) has been studied within the Hückel framework. A Hückel framework scheme for calculating the parameters of molecular dynamic structure, i.e., the linear and quadratic orbital vibronic constants ( OVC s), has been presented. Selection rules for the OVC s in this scheme have been obtained and discussed by using graph theory and group theory, under various boundary conditions. A Hückel noncoupling rule has been concluded and discussed. The dimerization of polyacetylene has then been discussed based on the molecular dynamic structure. It has been shown that for a finite undoped ( A ) 2 N chain the occupied orbital energy ε n at the unified configuration has a negative slope in direction of Q 2 n . As a result, there exists a net Hellmann–Feynman force leading to dimerization. When the chain length goes to infinity, the slopes and forces tend to zero. However, a significant negative curvature in potential surface may occur in the direction of Q 2 n , due to the two‐phonon coupling of the π‐electrons, which could also induce the dimerization. These can be interpreted as the results of the hidden C 4 N +2 symmetry and the imaginary degeneracy in an ( A ) 2 N chain, according to the graph theory for molecular orbitals. Thus, the dimerization of an ( A ) 2 N chain actually destroys its hidden symmetry of C 4 N +2 and reduces its imaginary degeneracy.