Vibrational energy transport in molecular wires

Motivated by recent experimental observation (see, e.g., I.V. Rubtsov, Acc. Chem. Res. 42, 1385 (2009)) of vibrational energy transport in $(\mathrm{CH}_2\mathrm{O})_N$ and $(\mathrm{CF}_2)_N$ molecular chains ($N=4$–$12$), in this paper we present and solve analytically a simple one dimensional model to describe theoretically these data. To mimic multiple conformations of the molecular chains, our model includes random off-diagonal couplings between neighboring sites. For the sake of simplicity we assume Gaussian distribution with dispersion $\sigma $ for these coupling matrix elements. Within the model we find that initially locally excited vibrational state can propagate along the chain. However the propagation is neither ballistic nor diffusion like. The time $T_m$ for the first passage of the excitation along the chain, scales linearly with $N$ in the agreement with the experimental data. Distribution of the excitation energies over the chain fragments (sites in the model) remains random, and the vibrational energy, transported to the chain end at $t=T_m$ is dramatically decreased when $\sigma $ is larger than characteristic interlevel spacing in the chain vibrational spectrum. We do believe that the problem we have solved is not only of intellectual interest (or to rationalize mentioned above experimental data) but also of relevance to design optimal molecular wires providing fast energy transport in various chemical and biological reactions.