Photoacids, Photoacidity and Forster Cycle

Figure 12.13 Forster cycle of HP and HPTS photoacids in water. Energy levels are for the photoacids A H and their conjugated base (A ). The energy levels of both photoacids are normalized to the energy of the ground state level of the photoacids. The Forster cycle is plotted to scale in the units of pK, pK = AG / log RT.

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],... 

The pK found in this way may be directly compared with Forster-cycle calculations. However, straightforward utilization of the fluorescence titration method is usually limited to moderately strong photoacids due to partial deactivation processes of the photoacid occurring in very concentrated mineral acid solutions. The most accurate method of finding the pK of a photoacid is by direct kinetic measurements of the excited-state proton dissociation and recombination rates °. However, these measurements are not trivial and are limited to a relatively small number of photoacids where accurate measurement of the excited-state reversible dynamics of the proton-transfer reaction is possible. 

Equation 17 may be viewed as an explicit form of the Forster cycle. It depends on both intramolecular and intermolecular factors which determine the extent of the photoacidity. The first factor is the difference between the excited-state and the ground-state proton affinities of the photobase. This difference will be equal to the difference in the intramolecular stabilization of the proton upon the electronic excitation of the acid, and will depend, in general, on the quantum-mechanical properties of the first excited electronic state of the photoacid. The second factor is the difference in the solvation energies of the base and the photoacid upon electronic excitation. The magnitude of the solvation-energy terms will depend in general both on the solvent and the solutes and will depend on the nature of the first electronic state of the photoacid and its conjugate base. 

L where the L is of a greatly rednced charge-transfer natnre than the corresponding L state of 1-naphthol. It follows that in the case of 2-naphthol, one expects a much smaller solvent effect on the Forster-cycle acidity than the corresponding effect on 1-naphthol acidity. This indeed seems to be the case when the photoacidity of 1-naphthol and 2-naphthol was estimated from Forster-cycle calculations in water and methanol (Tables 1 and 2). 

Interestingly, Forster-cycle calculations of the pAla in methanol (Table 2) seem to confirm the substituent effect on the polarity of the emitting state of 1-naphthol as discussed above the less polar the emitting state of the acid compared to the emitting state of its conjugate base, the larger the Forster-cycle acidity of the photoacid. The calculated Forster-cycle difference between the ground-state and excited-state acidities in methanol was 12.3, 11.3, 10.9, 9.3 and 8.8 for the 2-substituted, 3-substituted, unsubstituted 4- and... 

Figure 12.5 Forster cycle of photoacids in solution. Energy levels are for a general photoacid A H and its conjugated base (A ) - S,> is the excited-state of the acid and S, > of the base, g> is the ground-state ofthe acid and g > ofthe anion, respectively, hv, and hv i, are the energy of the absorption transition and hv f, are the energy ofthe fluorescence transition ofthe acid and base, respectively. ACp,c and (the Forster...

The total error in carrying out the Forster cycle with the averaged transition energies of the photoacid and photobase rather than with the thermodynamic AGppG and AG ppQ values may be estimated by the following simple algebraic consideration, Eq. (12.8). 

The difference between the ground-state and excited-state equilibrium constants of the photoacid as defined thermodynamically by the Forster cycle, ApJG (therm), is given by ... 

The two lowest-energy electronic absorption bands of 2-naphthol in various solvents are shown in Fig. 12.6. These are assigned to transitions to the Lj, state (Sj) and to the state (S2). In cases where the vertically accessed excited state level of the photoacid and the relaxed excited state level of the photoacid are both the relatively nonpolar Lj, state the difference between the calculated value and the thermodynamic value of pfTj is expected to be small. It has indeed been found that Forster cycle with average transition frequencies is a very good approximation for calculating ApfC values of photoacids in the Lj, electronic excited state [75]. 

Figure 12.8 Forster cycle of photoacids in solution when two different singlet states are involved in the photon absorption and photon emission processes of the photoacid i.e., the L, and the states. The four possible...

The general validity of the Forster cycle approach is undoubtedly linked first of all with the reality of the assumed microscopic reversibility of exdted-state proton transfer reactions. Secondly, the reliability of the K scale should be checked, when possible, against directly determined K values of well behaved photoacids. Furthermore, for the general validity of the IC scale to hold as defined by the Forster cycle its validity should not depend on the photoacid actually reaching equilibrium conditions or even on observing at all an excited-state proton transfer reaction within the finite lifetime of the excited state. These assertions should be carefully tested and checked before establishing the general applicability of the Forster cycle. 

Arguably, the first evidence for the general validity of the pK scale came from steady-state fluorescence titrations of well behaved photoacids such as 2-naphthol [27]. As already indicated, this method was largely developed by Weller [9] and resulted in IC values which were in general agreement with the Forster cycle predictions (see below). 

Eq. (12.18) for the correlation between the proton transfer rate, kp and (the dependence on enters through the free energy of activation term AG see below) usually result in very good agreement between the observed reactivity of the photoacid and its Forster cycle value. 

As a final example we compare the photoacidities of l-naphthol-5-sulfonate and 1-naphthol 5-tetrabutyl. The Forster cycle of the two photoacids was measured in methanol. The 5-position of the 1-naphthol system is considered the most sensitive to substituents (Table 12.4). As discussed in the HPTS case the sulfonate... 

Below we carry out a survey of the Forster cycle photoacidity of several well known photoacids in order to examine the -iL paradigm. Arguably, the best examples are 1-naphthol which is considered to be a photoacid, 2-naphthol (ifj, acid), 1-hydroxypyrene (ifj,) and HPTS ( Sj). 

Figure 12.20 Forster cycle ofl N and 2N photoacids in DMSO. The energy levels of both photoacids are normalized to the energy of the ground state level.

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