Vibrational energy transport in molecular wires

TL;DR

This paper presents an analytical model for vibrational energy transport in molecular chains, explaining experimental observations and revealing how disorder affects energy propagation and efficiency.

Contribution

It introduces a simple one-dimensional model with random couplings to describe vibrational energy transport in molecular wires, aligning with experimental data and highlighting disorder effects.

Findings

Excitation propagates along the chain but not ballistically or diffusively.

First passage time scales linearly with chain length, matching experiments.

Energy transport efficiency decreases with increased disorder sigma.

Abstract

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.