Exciton transfer rate between two neutral \textit{trans}-polyacetylene chains

We use the perturbation theory to compute the exciton transfer rate between two neutral \textit{trans}-polyacetylene chains described by the Su-Schrieffer-Heeger (SSH) Hamiltonian. Considering the highly polarizable nature of \textit{trans}-polyacetylene, we compute Coulomb interactions directly without the point dipole approximation as introduced in the conventional Forster approach. We find a much softer chain separation dependence of the energy transfer rate between two \textit{trans}-polyacetylene chains, scaling as 1/r$^{n}$ where n $\sim $ 4 which is different from the well-known n= 6 in the Forster formula or n= 5 in the Hamaker formula for one-dimensional pairwise interactions. At a typical separating distance of 3.5 {\AA}, the $\pi -\pi $ interaction density is 0.21 eV/ {\AA} and the exciton transfer time is 72.6 ps. We are extending our calculations for poly-($p$-phenylenevinylene) (PPV) and the complex porphyrin assembly using our recently developed adapted SSH Hamiltonian.