On the anisotropic energy transfer to random acceptors

We present exact expressions for the ensemble averaged decay of the excitation of a donor molecule, due to the energy transfer via anisotropic dipolar interactions to acceptors distributed randomly on a lattice. We compare in two special cases the approximate, Förster-type expressions, valid for low acceptor concentrations and long times, with the exact results: in the case of a completely random angular distribution and in case of a preferential orientation. The connection to the decay law for isotropic interactions [Blumen and Manz, J. Chem. Phys. 71, 4694 (1979)] is also presented. Whereas the approximate expressions show similar qualitative behavior in all cases, their regions of validity (compared to the exact results) differ considerably; the difference is especially large for the decay due to acceptors which are randomly distributed on the lattice but are orientationally ordered.