Vibrational energy transport in molecular wires
V. A. Benderskii+, A. S. Kotkin+, I. V. Rubtsov*, E. I. Kats×
+Institute of Problems of Chemical Physics of the RAS, 142432 Chernogolovka, Russia
*Department of Chemistry, Tulane University, LA 70118 New Orleans, USA
× Landau Institute for Theoretical Physics of the RAS, 142432 Chernogolovka, Russia
Motivated by recent experimental observation (see, e.g., I.V. Rubtsov, Acc. Chem. Res.
42, 1385 (2009)) of vibrational energy transport in
(CH2O)N and (CF2)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 σ 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 Tm
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=Tm is dramatically decreased when σ 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
above experimental data) but also of relevance to
design optimal molecular wires providing fast energy transport in various chemical
and biological reactions.