Osad'ko I S, Shchukina A L
Institute for Spectroscopy, RAS, Troitsk, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 1):061907. doi: 10.1103/PhysRevE.85.061907. Epub 2012 Jun 8.
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)=Fover ¯T_{D}/[1+Fover ¯T_{D}]. Here Fover ¯ is a function of F depending on singlet-triplet transitions in both donor and acceptor molecules. Expressions for the functions Fover ¯ 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.
研究了三重态能级对供体 - 受体（D - A）对中通过单重态能级的福斯特共振能量转移的影响。考虑了四种类型的D - A对：（i）双能级供体和双能级受体，（ii）三能级供体和双能级受体，（iii）双能级供体和三能级受体，以及（iv）三能级供体和三能级受体。如果三能级受体分子中的单重态 - 三重态跃迁无效，则能量转移效率(E = I_{A}/(I_{A}+I_{D}))（其中(I_{D})和(I_{A})分别是供体和受体荧光的平均强度）可以由简单的理论方程(E(F)=FT_{D}/(1 + FT_{D}))描述。这里(F)是能量转移速率，(T_{D})是供体荧光寿命。根据最后一个方程，当(FT_{D}≫1)时，供体电子能量的100%可以转移到受体分子。然而，如果三能级受体分子中的单重态 - 三重态跃迁有效，则能量转移效率由另一个理论方程(E(F)=F\overline{(F)}T_{D}/[1 + F\overline{(F)}T_{D}])描述。这里(F\overline{(F)})是(F)的函数，取决于供体和受体分子中的单重态 - 三重态跃迁。推导了函数(F\overline{(F)})的表达式。在这种情况下，即使(FT_{D}≫1)，能量转移效率也将远低于100%。供体和受体荧光强度波动的特征表明应该使用两个(E(F))方程中的哪一个来确定速率(F)的值。因此，通过蒙特卡罗方法计算了所有四种类型D - A对在供体和受体荧光中光子发射的随机时刻。推导了供体和受体荧光中起止关联器（等待时间分布）的理论表达式。针对能量转移速率(F)的各种值以及所有四种类型的D - A对，计算了在时间间隔(t)内找到(N)个供体和受体荧光光子的概率(w_{N}^{D}(t))和(w_{N}^{A}(t))。将计算得到的供体和受体荧光轨迹与韦斯及其同事测量的轨迹进行比较，证明了三重态能级在通过单重态能级的能量转移中的重要作用。
