Influence of electron-electron interaction on the vibrational frequency in one-dimensional dimerized conjugated systems

We apply the correlated-basis-function approach to study the vibrational stretching mode in a one-dimensional dimerized conjugated system modeled as a Kronig-Penney square-well lattice. Poly- acetylene is taken as prototypical example. Various potential parameters are considered in the one-dimensional energy-band calculations. We find that the one-electron theory is unable to afford simultaneously reasonable descriptions of the electronic and vibrational properties, which indicates the importance of electron-electron interaction in the vibrational modes (and lattice relaxation). Our parameters are selected according to the ionization potential value in polyacetylene. Electron-electron interaction is taken as a screened Coulomb potential. The correlated wave function is evaluated through the Chakravarty-Woo equation within the convolution approximation. We find that electron-electron interaction generally increases the stretching-mode frequency; however, in systems with very large spring constants, the vibrational frequency first decreases as the electron-electron interaction strength increases, then levels off and begins to increase.