Forster constant

We now focus our attention on the presence of the unperturbed donor quantum yield, Qd, in the definition of R60 [Eq. (12.1)]. We have pointed out previously [1, 2] that xd appears both in the numerator and denominator of kt and, therefore, cancels out. In fact, xo is absent from the more fundamental expression representing the essence of the Forster relationship, namely the ratio of the rate of energy transfer, kt, to the radiative rate constant, kf [Eq. (12.3)]. Thus, this quantity can be expressed in the form of a simplified Forster constant we denote as rc. We propose that ro is better suited to FRET measurements based on acceptor ( donor) properties in that it avoids the arbitrary introduction into the definition of Ra of a quantity (i />) that can vary from one position to another in an unknown and indeterminate manner (for example due to changes in refractive index, [3]), and thereby bypasses the requirement for an estimation of E [Eq. (12.1)]. 

Seminal studies on the dynamics of proton transfer in the triplet manifold have been performed on HBO [109]. It was found that in the triplet states of HBO, the proton transfer between the enol and keto tautomers is reversible because the two (enol and keto) triplet states are accidentally isoenergetic. In addition, the rate constant is as slow as milliseconds at 100 K. The results of much slower proton transfer dynamics in the triplet manifold are consistent with the earlier summarization of ESIPT molecules. Based on the steady-state absorption and emission spectroscopy, the changes of pKa between the ground and excited states, and hence the thermodynamics of ESIPT, can be deduced by a Forster cycle [65]. Accordingly, compared to the pKa in the ground state, the decrease of pKa in the... 

One of the most popular applications of molecular rotors is the quantitative determination of solvent viscosity (for some examples, see references [18, 23-27] and Sect. 5). Viscosity refers to a bulk property, but molecular rotors change their behavior under the influence of the solvent on the molecular scale. Most commonly, the diffusivity of a fluorophore is related to bulk viscosity through the Debye-Stokes-Einstein relationship where the diffusion constant D is inversely proportional to bulk viscosity rj. Established techniques such as fluorescent recovery after photobleaching (FRAP) and fluorescence anisotropy build on the diffusivity of a fluorophore. However, the relationship between diffusivity on a molecular scale and bulk viscosity is always an approximation, because it does not consider molecular-scale effects such as size differences between fluorophore and solvent, electrostatic interactions, hydrogen bond formation, or a possible anisotropy of the environment. Nonetheless, approaches exist to resolve this conflict between bulk viscosity and apparent microviscosity at the molecular scale. Forster and Hoffmann examined some triphenylamine dyes with TICT characteristics. These dyes are characterized by radiationless relaxation from the TICT state. Forster and Hoffmann found a power-law relationship between quantum yield and solvent viscosity both analytically and experimentally [28]. For a quantitative derivation of the power-law relationship, Forster and Hoffmann define the solvent s microfriction k by applying the Debye-Stokes-Einstein diffusion model (2)... 

This is the famous Forster relation that expresses the singlet-singlet transition rate constant in terms of the spectral overlap of the emission spectra of D and absorption spectra of A. 

The proton dissociation constants, of two series of 3,7-bis(arylazo)-2,6-diphenyl-1 //-irnidazo[l,2-7]pyrazoles, in the ground state and the excited state were determined by the spectrophotometric method and utilizing the Forster energy cycle, respectively. These constants were correlated by the Hammett equation and the results of such correlations with spectral data indicated that both series of compounds exist in solution almost exclusively in the l//-bis-(arylazo) tautomeric form A <2002T2875> (Scheme 3). 

Another major energy transfer process, the so-called Forster transfer mechanism is based on a dipole-dipole interaction between the host excited state and the guest ground state (Figure 4.2) [24], It does not include the transfer of electrons and may occur over significantly larger distances. The rate constant of the Forster energy transfer is inversely proportional to the sixth power of the distance R between the molecules ... 

By substituting Eq. (B4.4.5) into Eq. (B4.4.7), we obtain the Forster rate constant kjl (Eq. 4.78 in the text) for energy transfer in the case of long-range dipole-dipole interaction, and substitution of Eq. (B4.4.6) into Eq. (B4.4.7) leads to the Dexter rate constant k fl (Eq. 4.85 in the text) for the short-range exchange interaction. 

Forster s formulation of long-range dipole-dipole transfer (very weak coupling) Forster derived the following expression for the transfer rate constant from classical considerations as well as on quantum-mechanical grounds ... 

Because this chapter will be mainly concerned with the Forster mechanism of transfer, the results of the Forster theory, given in Section 4.6.3, are recalled here for convenience. The rate constant for transfer between a donor and an acceptor at... 

The Forster resonance energy transfer can be used as a spectroscopic ruler in the range of 10-100 A. The distance between the donor and acceptor molecules should be constant during the donor lifetime, and greater than about 10 A in order to avoid the effect of short-range interactions. The validity of such a spectroscopic ruler has been confirmed by studies on model systems in which the donor and acceptor are separated by well-defined rigid spacers. Several precautions must be taken to ensure correct use of the spectroscopic ruler, which is based on the use of Eqs (9.1) to (9.3) ... 

The survival probability Gs(t) of the donor molecule (i.e. the probability that when excited at t = 0, it is still excited at time t) is obtained by summation over all possible rate constants kT (given by Eq. 9.1), each corresponding to a given donor-acceptor distance r. For a donor molecule surrounded with n acceptor molecules distributed at random in a spherical volume whose radius is much larger than the Forster critical radius R0, Gs(t) is given by... 

Butler P. R. and Pilling M. J. (1979) The Breakdown of Forster Kinetics in Low Viscosity Liquids. An Approximate Analytical Form for the Time-Dependent Rate Constant Chem. Phys. 41, 239-243. 

Conventional absorptiometric and fluorimetric pH indicators show a shift of band positions in absorption and emission spectra between the protonated and deprotonated forms. This feature allows the spectroscopic measurement of the acid dissociation constant in the ground state, Ka, and also the evaluation of the dissociation constant in the excited state, Ka (Eq. (5.5)), from the Forster cycle under the assumption of equivalent entropies of reaction in the two states.<109 112)... 

For the determination of the dissociation constant in the excited state, several methods have been used the Forster cycle,(109 m) the fluorescence titration curve/113 the triplet-triplet absorbance titration curve,014 but all involve the assumption that the acid-base equilibrium may be established during the lifetime of the excited state, which is by no means a common occurrence. A dynamic analysis using nanosecond or picosecond time-resolved spectroscopy is therefore often needed to obtain the correct pK a values.1(n5)... 

The theory of resonance transfer of electronic excitation energy between donor and acceptor molecules of suitable spectroscopic properties was first presented by Forster.(7) According to this theory, the rate constant for singlet energy transfer from an excited donor to a chromophore acceptor which may or may not be fluorescent is proportional to r 6, where r is the distance... 

More convincing proof for a particle-enhanced energy transfer mechanism comes from a study of the concentration dependence of the transfer. Bulk Forster transfer leads to a linear dependence on acceptor concentration with constant donor-to-acceptor ratio. The resonance mechanism would be expected to saturate at (relatively) high concentrations and fall off linearly at very low concentrations. 

Triplet decay in the [Mg, Fe " (H20)] and [Zn, Fe (H20)] hybrids monitored at 415 nm, the Fe " / P isosbestic point, or at 475 nm, where contributions from the charge-separated intermediate are minimal, remains exponential, but the decay rate is increased to kp = 55(5) s for M = Mg and kp = 138(7) s for M = Zn. Two quenching processes in addition to the intrinsic decay process (k ) can contribute to deactivation of MP when the iron containing-chain of the hybrid is oxidized to the Fe P state electron transfer quenching as in Eq. (1) (rate constant kj, and Forster energy transfer (rate constant kj. The triplet decay in oxidized hybrids thus is characterized by kp, the net rate of triplet disappearance (kp = k -I- ki -I- kj. The difference in triplet decay rate constants for the oxidized and reduced hybrids gives the quenching rate constant, k = kp — kj, = k, -I- k , which is thus an upper bound to k(. 

The original work by Monsanto identified [Rh(CO)2l2] as the major Rh spedes under their process conditions and reaction of Mel with this complex as rate controlling for the process [3]. However, the proposed primary product of oxidative addition of Mel to [Rh(CO)2l2r, [RhMe(CO)2l3] , was not observed in early work. Forster [10] studied the reaction of Mel with [Rh(CO)2l2] by IR and found that it gave the acyl complex [Rh(C(0)Me)(C0)l3] , which was also isolated and characterized in the solid state as a dimer. The reaction could be followed quantitatively but the observed rate constant would be antidpated to be a composite of the rate constants for the formation of the intermediate [RhMe(CO)2l3r and its further reaction to [Rh(C(0)Me)(C0)l3] (Eq. (15)) and (Eq. (16)). 

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