An analytical Hückel-type approach to the relationship between Peierls instability in polyenes and interchain interaction

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Abstract
We propose a convenient method to estimate the magnitude of Peierls instability in finite one- and two-dimensional (1D and 2D) polyenes from the view point of orbital symmetry. The formulas are derived in terms of in-phase and out-of-phase interactions between adjacent carbon atoms on the basis of the analytical Hückel orbitals for polyene with an arbitrary length. The stabilization energies due to bond alternation are defined for the individual energy levels. It is visually shown that bond alternation gives rise to stabilizing the occupied orbitals and destabilizing the vacant orbitals without using the k space based on periodic boundary condition in infinite polymer. This treatment is further extended to the Peierls instability in 2D polyene on the basis of the analytical Hückel orbitals derived for its regular structure. Total π and σ energies are provided as functions of bond alternation and interchain interaction. It is demonstrated that bond alternation is strongly suppressed under the existence of interchain interaction, in which interchange between occupied and unoccupied orbitals plays a crucial role. This treatment would provide a first step to investigate the relationship between crystal structure of more complicated polymer and its electronic property in connection with interchain interaction.