Forster cycle

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... 

Ultrafast ESPT from the neutral form readily explains why excitation into the A and B bands of AvGFP leads to a similar green anionic fluorescence emission [84], Simplistic thermodynamic analysis, by way of the Forster cycle, indicates that the excited state protonation pK.J of the chromophore is lowered by about 9 units as compared to its ground state. However, because the green anionic emission is slightly different when it arises from excitation into band A or band B (Fig. 5) and because these differences are even more pronounced at low temperatures [81, 118], fluorescence after excitation of the neutral A state must occur from an intermediate anionic form I not exactly equivalent to B. State I is usually viewed as an excited anionic chromophore surrounded by an unrelaxed, neutral-like protein conformation. The kinetic and thermodynamic system formed by the respective ground and excited states of A, B, and I is sometimes called the three state model (Fig. 7). 

The Forster cycle method is quite simple, which explains why it has been extensively used. One of the important features of this cycle is that it can be used even in cases where the equilibrium is not established within the excited-state lifetime. However, use of the Forster cycle is difficult or questionable when (i) two absorption bands overlap (ii) the electronic levels invert during the excited-state lifetime (usually in a solvent-assisted relaxation process) (iii) the excited acidic and basic forms are of different orbital origins (electronic configuration or state symmetry) and (iv) the changes in dipole moment upon excitation are different for the acidic and basic forms. 

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)... 

In some cases, data obtained through the Forster cycle show similar inconsistencies, depending on whether absorption or emission is used. It may well be that either the equilibrium structure in the excited state is very different from the unrelaxed Franck-Condon one, or that 0-0 frequencies are too poorly estimated. It seems, therefore, that the most reliable results are those generated by method (3). This method has been applied to the study of carbazole (3) acidity in its S, state (85MI5). 

The Spectroscopy of Proton Transfer and the Forster Cycle. The absorption and emission spectra of the acid and base forms of a molecule are of course different, since these forms represent distinct chemical species. The excitation energies (e.g. S0- St) are however related according to a very simple scheme of energy levels known as the Forster cycle this is shown in Figure 4.47(a). 

The Forster cycle therefore permits the calculation of the excited state pA (from AH ) simply from spectroscopic data (assuming of course that the ground state pK is known, from usual titration measurements). 

The pA value derived from the Forster cycle is however a theoretical5 value, two important assumptions being involved in its derivation ... 

Excited-state proton transfer relates to a class of molecules with one or more ionizable proton, whose proton-transfer efficiency is different in the ground and excited states. The works of Forster [2-4] and Weller [5-7] laid the foundation for this area on which much of the subsequent work was based. Forster s work led to the understanding of the thermodynamics of ESPT. He constructed a thermodynamic cycle (Forster cycle) which, under certain acceptable approximations, provides the excited-state proton-transfer equilibrium constant (pK f,) from the corresponding ground-state value (pKa) and electronic transition energies of the acid (protonated) and base (deprotonated) forms of the ESPT molecule ... 

According to the Forster cycle, if the longest wavelength electronic transition of the deprotonated form is of lower energy compared to that of the protonated form (red-shifted electronic absorption or emission spectrum of the deprotonated form with reference to the protonated-form spectrum), the molecule has enhanced excited-state acidity (i.e., the pK a of the molecule is lower than pKa). Equation (1) provides a quick and effective method for evaluating a molecule for its ESPT behavior. 

Weller s work [5-7] on the kinetics of ESPT brought out the importance of competition between the rates of deactivation of the excited states and the rates of proton transfer. In cases where the deactivation rates are slow enough for a complete establishment of excited-state equilibrium, fluorimetric titrations provide a method for experimental determinations of pK a. However, it has been realized that for a fairly large number of ESPT molecules, there is a frequent mismatch of pA"f, values obtained from Forster cycle and fluorimetric titrations methods. There are also examples of extended fluorimetric titration curves resulting from low proton availability in the mid-pH region (4-10). Various modifications of the Forster cycle and extensions of Weller s original kinetic considerations have been made from time to time and have been reviewed periodically. Some of the earlier important ones include those by Weller [7] in 1961, Vander Donckt [8] in 1970, Schulman [9] in 1974, and Klopffer [10] in 1977. The review by Ireland and Wyatt [11] contains extensive references of experimental results available in the literature until 1976. 

Naphthols with electron-withdrawing groups such as cyano sulfonyl and methanesulfonyl at C-5 and C-8 exhibit greatly enhanced photoacidity [48], 5,8-dicyano-1-naphthol shows remarkable photoacidity with a pKa of 7.8 and a Forster cycle pK a of -4.5. The kinetics and mechanism of ESPT of these superphotoacid molecules have been subjected to extensive investigations in recent times [49-53],... 

Figure 2.17 Potential energy diagram illustrating the Forster Cycle, in which the differences between the ground- and excited-state enthalpies, AH0, of the protonated (HA) and deprotonated...

This equilibrium may be treated thermodynamically and the equilibrium constant may be estimated from the Forster Cycle, as shown in Figure 2.17. This cycle illustrates the enthalpy differences between the acid and base forms of the ground-and excited-state species. According to such a scheme, the difference between the ground- and excited-state pJCa values may be estimated from the ground-state... 

Although useful, the Forster Cycle is a theoretical estimate of pfCa, with the validity of its application being limited by the following assumptions ... 

For 2-imino-4-thiazoline the calculated tt4 — nf transition at 210 nm corresponds to the observed band in thanol at 302 nm (e = 15.000). The localization of this transition (Fig. VI-3) suggests a higher pKa in the tt4 — it excited state for these compounds (63). The Forster cycle, which permits the prediction of protomeric equilibrium for excited states, cannot be applied to the present amino-imino equilibrium because the protonation of 2-aminothiazole may occur on different heteroatoms for ground and excited states. Ultraviolet studies of 2-aminothiazole agree, however, with potentiometric measurements (see Section II.2) that in the ground state the amino form greatly predominates (93). This technique gives the same conclusion in the case of 2-acetamidothiazole (92. 94). 

The relationship suggested above between the frequency shift accompanying protonation (or any other chemical reaction) and the change in equilibrium constant upon excitation is formalized in the Forster cycle (Forster, 1950), illustrated in Fig. 2. Proceeding from... 

Excited state pX-values are most easily accessible through the use of the Forster cycle which has been described in the introduction. To perform this calculation for a particular molecule it is necessary to know the ground state equilibrium constant for the reaction in question and to have some measure of the energy difference between the lowest vibrational level of the ground and the excited state in both the B and BH+ forms. Thus to calculate pi Sj) we need the 0-0 energy of the S0-S transition and for pX(Tt) that of the Sq-T transition. 

In practice, handling Sq- transitions is often simpler (though less satisfactory), since absorption spectra are not normally available and the maxima of the B and BH+ phosphorescence bands must then be used in the Forster cycle. However Sq-Tj absorption spectra can sometimes be obtained, especially if perturbation methods can be used to enhance the singlet to triplet transition probability. For example, Grabowska and Pakula (1966) induced Sq-Tj absorption in a series of nitrogen-containing heterocyclic compounds by the oxygen perturbation method of Evans (1957). Hence, for these compounds, by combination of absorption and phosphorescence spectral results, the 0-0 transitions could be located more accurately. 

This method for obtaining p f(T )-values was introduced by Jackson and Porter (1961). It is even more time-consuming compared to the Forster cycle than the fluorescence titration method and relatively few direct determinations have been made of pA (T1). The experimental techniques have recently been described by Chibisov (1970) and Labhartand Heinzelmann (1973). Developments in instrumentation, including the introduction of laser excitation, have been reviewed by Porter and West (1973). 

Molecule Protonation (P) or Deprotonation (D) P (So) Forster cycle calculations Fluorescence intensity measurements pK(Ti) Forster cycle calculations Ref... 

Since the Forster cycle provides the simplest and least time-consuming route to p.K, it is not surprising that most values have been determined in this way, nor that there are many more pi Sx) entries than p-K(Tj). In all cases p.K-values are quoted as they appear in the original papers, although determinations of this kind cannot be reliable to better than 0-2 p/ units (corresponding to an error of... 

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