  Motivated by recent experimental observation (see e.g., I.V.Rubtsov, Acc.
Chem. Res., v. 42, 1385 (2009)) of vibrational energy transport in CH_2O_N and
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.
