  Intramolecular energy transport is generally responsible for chemical energy
balance in molecular systems. The transport is fast and efficient if energy is
transferred by optical phonons in periodic oligomers, but its efficiently is
limited by decoherence emerging due to anharmonic interactions with acoustic
phonons. We show that in the most common case of the optical phonon band being
narrower than the acoustic bands decoherence takes place in two stages. The
faster stage involves optical phonon multiple forward scattering due to
absorption and emission of transverse acoustic phonons, i. e. collective
bending modes with a quadratic spectrum; the transport remains ballistic and
the speed can be altered. The subsequent slower stage involves phonon
backscattering in multiphonon processes involving two or more acostic phonons
resulting is a switch to diffusive transport. If the initially excited optical
phonon possesses a relatively small group velocity, then its equilibration in
the first stage is accompanied by its acceleration due to its transitions to
states propagating faster. This theoretical expectation is consistent with the
recent measurements of optical phonon transport in alkane chains, accelerating
with increasing the chain length.
