Blinking fluorescence of single donor-acceptor pairs: Important role of ``dark'' states in resonance energy transfer via singlet levels

Abstract

The influence of triplet levels on Förster resonance energy transfer via singlet levels in donor-acceptor (D-A) pairs is studied. Four types of D-A pair are considered: (i) two-level donor and two-level acceptor, (ii) three-level donor and two-level acceptor, (iii) two-level donor and three-level acceptor, and (iv) three-level donor and three-level acceptor. If singlet-triplet transitions in a three-level acceptor molecule are ineffective, the energy transfer efficiency E=I_{A}/(I_{A}+I_{D}), where I_{D} and I_{A} are the average intensities of donor and acceptor fluorescence, can be described by the simple theoretical equation E(F)=FT_{D}/(1+FT_{D}). Here F is the rate of energy transfer, and T_{D} is the donor fluorescence lifetime. In accordance with the last equation, 100% of the donor electronic energy can be transferred to an acceptor molecule at FT_{D}≫1. However, if singlet-triplet transitions in a three-level acceptor molecule are effective, the energy transfer efficiency is described by another theoretical equation, E(F)=F[over ¯](F)T_{D}/[1+F[over ¯](F)T_{D}]. Here F[over ¯](F) is a function of F depending on singlet-triplet transitions in both donor and acceptor molecules. Expressions for the functions F[over ¯](F) are derived. In this case the energy transfer efficiency will be far from 100% even at FT_{D}≫1. The character of the intensity fluctuations of donor and acceptor fluorescence indicates which of the two equations for E(F) should be used to find the value of the rate F. Therefore, random time instants of photon emission in both donor and acceptor fluorescence are calculated by the Monte Carlo method for all four types of D-A pair. Theoretical expressions for start-stop correlators (waiting time distributions) in donor and acceptor fluorescence are derived. The probabilities w_{N}^{D}(t) and w_{N}^{A}(t) of finding N photons of donor and acceptor fluorescence in the time interval t are calculated for various values of the energy transfer rate F and for all four types of D-A pair. Comparison of the calculated D and A fluorescence trajectories with those measured by Weiss and co-workers proves the important role of triplet levels in energy transfer via singlet levels.