  The conversion of an absorbed photon from the exciton energy into the
reaction centre in the photosynthetic complex has a near unit efficiency. It is
becoming clear that any classical model, where the exciton hopping is modeled
by a classical stochastic diffusion equation, cannot explain such a high degree
of efficiency. A number of different quantum models have been proposed, ranging
from a purely unitary model with long range exciton interactions to a
noise-aided stochastic resonance models. Here we propose a very simple
spin-boson model that captures all the features of the efficient part of energy
transfer. We show how this model describes a scenario where a donor-acceptor
system can be brought into resonance by a narrow band of vibrational modes so
that the excitation transfer between the two can be made arbitrarily high. This
is then extended to a seven exciton system such as the widely-studied FMO
photosynthetic complex to show that a high efficiency is also achievable
therein. Our model encodes a number of readily testable predictions and we
discuss its generalisations to include the localisation in the reaction centre.
