Refractive index dependence of the Forster resonance excitation transfer rate

The rate or yield of resonance electronic excitation transfer is an important tool of biological research, used to estimate distances between chromophores. Besides the interchromophore distance, this rate or yield depends on several other parameters that are clearly important for determining the correct distances. In particular, in a medium characterized by a refractive index n, the expression for the rate contains a factor n(-4). We argue here that the correct value for n is that of the donor-acceptor intervening medium, not that of the overall solvent, as has been argued by some. The choice is clearly important to any quantitative application of the theory since the index of typical relevant materials ranges from 1.3 to 1.6. Incidental to our analysis, a certain expression that connects dipole strengths with radiative lifetimes requires correction. This leads to revisions of estimates of the amounts of exciton delocalization in antenna complexes from purple bacteria (downward by 25%). In our analysis we distinguish three physically distinct ways in which refractive index affects the rate and suggest how they should be handled.