  Molecular aggregates can under certain conditions transport electronic
excitation energy over large distances due to dipole-dipole interactions. Here,
we explore to what extent thermal motion of entire monomers can guide or
enhance this excitation transport. The motion induces changes of aggregate
geometry and hence modifies exciton states. Under certain conditions,
excitation energy can thus be transported by the aggregate adiabatically,
following a certain exciton eigenstate. While such transport is always slower
than direct migration through dipole-dipole interactions, we show that
transport through motion can yield higher transport efficiencies in the
presence of on-site energy disorder than the static counterpart. For this we
consider two simple models of molecular motion: (i) longitudinal vibrations of
the monomers along the aggregation direction within their inter-molecular
binding potential and (ii) torsional motion of planar monomers in a plane
orthogonal to the aggregation direction. The parameters and potential shapes
used are relevant to dye-molecule aggregates. We employ a quantum-classical
method, in which molecules move through simplified classical molecular
dynamics, while the excitation transport is treated quantum mechanically using
Schr\"odinger's equation. For both models we find parameter regimes in which
the motion enhances excitation transport, however these are more realistic for
the torsional scenario, due to the limited motional range in a typical Morse
type inter-molecular potential. We finally show that the transport enhancement
can be linked to adiabatic quantum dynamics. This transport enhancement through
adiabatic motion appears a useful resource to combat exciton trapping by
disorder.
