Consideration of dipole orientation angles yields accurate rate equations for energy transfer in the rapid diffusion limit

Abstract

Dipole-dipole energy transfer between suitable donor and acceptor chromophores is an important luminescence quenching mechanism and has been shown to be useful for distance determination at the molecular level. In the rapid diffusion limit, where the excited-state lifetime of the donor is long enough to allow the donor and acceptor to diffuse many times their average separation before deexcitation, it is usually assumed that the relative dipolar orientation is completely averaged due to rotational Brownian motion. Under this simplifying assumption, analytical expressions have been derived earlier for the energy transfer rate between donor and acceptor characterized by different geometries. Most such expressions, however, are only approximate because complete angular averaging is permitted only in a geometry that possesses spherical symmetry surrounding each chromophore. In this paper analytical expressions that correctly account for incomplete angle averaging due to steric hindrance are presented for several geometries. Each of the equations reveals a dependence of the energy transfer rate on chromophore orientation. It is shown that correctly accounting for this effect can lead to improvements in estimates of the distance of closest approach from measured quenching rates based on energy transfer experiments.