Rate constant resonance energy transfer

Very large rate constants have been found for near resonant energy transfer between infrared active vibrations in CO2 Such near-resonant transitions and their dependence on temperature have also been studied for collisions between vibrationally excited CO2 and other polyatomic molecules as CH4, C2H4, SF et al. The deactivation cross-sections range from 0.28 for CH3F to 4.3 for SFs at room temperature, and decrease with increasing temperature. 

Harriman and Ziessel recently reported the acetylide bridged bimetallic complex [(mpt)Os(tCCb)Ru(bpy)2]4+ (tCCb shown in Scheme 4) [62]. Excitation of the Ru(II) center resulted in nearly 100% efficient energy transfer to the Os to mpt MLCT state with a rate constant of 7 2 x 10iO s-1. Analysis of the Forster overlap factor led to the prediction of a much lower rate constant for resonant energy transfer and the authors concluded that the process was dominated by an electron exchange transfer mechanism. 

The elucidation of the structure, dynamics and self assembly of biopolymers has been the subject of many experimental, theoretical and computational studies over the last several decades. [1, 2] More recently, powerful singlemolecule (SM) techniques have emerged which make it possible to explore those questions with an unprecedented level of detail. [3-55] SM fluorescence resonance energy transfer (FRET), [56-60] in particular, has been established as a unique probe of conformational structure and dynamics. [26-55] In those SM-FRET experiments, one measures the efficiency of energy transfer between a donor dye molecule and an acceptor dye molecule, which label specific sites of a macromolecule. The rate constant for FRET from donor to acceptor is assumed to be given by the Forster theory, namely [59,61-64]... 

This is due to the uniform initial condition k(t), which starts from its maximal value ki) Wrrd3r and drops with time, approaching the stationary limit from above. Contrary to this famous result, the experimental study of delayed fluorescence of anthracene in viscous solution [262] showed quite the opposite time behavior of k t). As it is initially much less than ko, the rate constant increases with time, approaching the long-time asymptote (3.56) from below. The authors of Ref. 262 called this anomaly the anti-Smoluchowski time behavior of the delayed fluorescence. They properly attributed it to a nonuniform distribution of triplets generated by the intersystem conversion from singlets that are preliminary quenched by the resonant energy transfer. 

They found that Forster s theory of resonance energy transfer was applicable to such systems if the Interchromophoric distance and orientation, the fluorescence efficiency of the donor, the extinction of the acceptor, and the overlap between the emission of the donor and the absorption of the acceptor are of magnitudes which produce a transfer rate constant of less than 10 s and a transfer efficiency which is not too close to 0 or 1. 

As long as r > 3R0, the fluorescence decay is close to exponential, the lifetime of the donor fluorescence decreases linearly with increasing concentration of A and fluorescence quenching obeys Stern Volmer kinetics (Section 3.9.8, Equation 3.36). However, the bimolecular rate constants ket of energy transfer derived from the observed quenching of donor fluorescence often exceed the rate constants of diffusion kd calculated by Equation 2.26, because resonance energy transfer does not require close contact between D and A. Finally, when r < 3R0, at high concentrations and low solvent viscosity, the kinetics of donor fluorescence become complicated, but an analysis is possible,109,110 if required. 

The temperature dependences of the total quenching constants have been measured by Deakin and Husain and by Burde and McFarlane. The rate constants were found to increase with increasing temperature for H2 and HD, but to decrease with increasing temperature for Dj. Butcher et al. have interpreted these temperature variations in terms of near resonant energy transfer of the type... 

The maximum fluorescence quantum yield is 1.0 (100 %) every photon absorbed results in a photon emitted. Compounds with quantum yields of 0.10 are still considered quite fluorescent. The fluorescence lifetime is an instance of exponential decay. Thus, it is similar to a first-order chemical reaction in which the first-order rate constant is the sum of all of the rates (a parallel kinetic model). Thus, the lifetime is related to the facility of the relaxation pathway. If the rate of spontaneous emission or any of the other rates are fast, the lifetime is short (for commonly used fluorescent compounds, typical excited state decay times for fluorescent compounds that emit photons with energies from the UV to near infrared are within the range of 0.5-20 ns). The fluorescence lifetime is an important parameter for practical applications of fluorescence such as fluorescence resonance energy transfer. There are several rules that deal with fluorescence. 

The transfers that take place by mechanism 1 are limited by diffusion of molecules in solution and should be affected by the viscosity of the medium. Transfers by mechanism 2, on the other hand, should be much less sensitive to the viscosity of the medium. It was shown by Foster [86] that the rate constant of resonance-energy transfer (mechanism 1), as a function of distance, is ... 

This breadth of reactivity necessitates understanding and control of selectivity. To this end, Sohn and Ihee have conducted fluorescence resonance energy transfer experiments with a range of catalysts, with specially designed alkenes, allenes, and alkynes that are tethered to a dye (Figure 2.12). When the ruthenium complex coordinates the alkene/allene/alkyne, the fluorescence is quenched. Catalysts studied included Mol, Gl, G2, GHl, and GH2 rate constants and thermodynamic parameters were obtained in each case (Table 2.8). These experiments showed that catalyst systems react... 

Rate constant for Forster resonance energy transfer (FRET)... 

A quantitative theoretical treatment was developed by Forster [39], who applied time-dependent perturbation theory to dipole-dipole interactions. The following is a simplified account. The probability of resonance energy-transfer from D to A at a distance R may be represented by a first-order rate parameter et (often, but inaccurately, called a rate constant), which is proportional to R and to the integral J representing the spectral overlap between the emission spectrum of the donor and the absorption spectrum of the acceptor. Forster s expression is ... 

Let us first consider the case of the dynamic quenching, which means that the interaction between the fluorophore and the quencher occurs in the excited state of the fluorophore, F, either as a collision or a long-range resonance energy transfer between F and Q, both leading to nonradiative deactivation of F. The excited-state lifetime t can be expressed by the sum of the rate constants of individual deactivation processes ... 

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