Self-consistent mode-coupling theory of excitation transport with long-range transfer rates in solution

A self-consistent mode-coupling theory for incoherent excitation transport is applied to the calculation of excitation dynamics in solution. The long time transport properties for multipolar, w(r)∼(σ/r)m, exchange, w(r)∼exp[−(r−σ)/R)], and Gaussian, w(r)∼exp[−(r2−σ2)/γ2], transfer rates are compared using the same self-consistent procedure. r is the intermolecular separation, and σ is the molecular hard-sphere diameter. Diffusive behavior is found to hold at long times in all cases. However as the transfer rates become more short range (increasing m and decreasing R and γ), the diffusion coefficient shows an abrupt variation with density, which resembles a percolation transition.