Doklady Chemistry, Vol. 385, Nos. 4–6, 2002, pp. 221–224. Translated from Doklady Akademii Nauk, Vol. 385, No. 6, 2002, pp. 780–783. Original Russian Text Copyright © 2002 by Chesnokov, Abakumov, Cherkasov, Shurygina.

CHEMISTRY

Photoinduced Hydrogen Transfer in Reactions of Photoreduction of Carbonyl-Containing Compounds in the Presence of Hydrogen Donors S. A. Chesnokov, Academician G. A. Abakumov, V. K. Cherkasov, and M. P. Shurygina Received April 10, 2002

The reactions of photoreduction of carbonyl-containing compounds (A) in the presence of hydrogen donors have been well documented [1, 2]. Most works focused on studying the photochemical behavior of individual compounds (benzophenone, fluorenone, 9,10-phenanthrenequinone, etc.) and provided no comparative experimental information for constructing a theoretical reaction model. The kinetics of the photoreduction of a number of o-benzoquinones (o-Q), which have similar structures and different electrochemical characteristics, in the presence of different para-substituted N,N-dimethylanilines (p-X-DMA) was studied in [3]. It was found that the rate constant kH of the photoreduction of o-Q (photoinduced hydrogen transfer) is a function of the free energy of electron transfer ∆Ge with a maximum at ∆Ge ~ 0. A similar extreme dependence kH = f(∆Ge) with a kH maximum at ∆Ge ~ 0 was obtained in [3] by recalculating the kinetic data on the photoreduction of fluorenone in the presence of some p-XDMAs [4]. Rehm and Weller [5, 6] were the first to find a quantitative correlation between the kinetics of quenching through electron transfer from excited states of aromatic hydrocarbons in the presence of amines and the thermodynamic properties of reaction pairs. They also suggested an empirical equation for calculation of ∆Ge. This equation is used to describe the processes associated with photoinduced electron transfer [7–9]:

.–

.+

∆Ge = –∆E00 – E( A /A) + E(DH/ DH ) – T∆Se + const, (1) where ∆E00 is the one-electron potential corresponding to the spectroscopic energy of the 0→0 transition of the lowest lying excited state of the carbonyl-containing .– .+ compound; E( A /A) and E(DH/ DH ) are the redox potentials of the acceptor and donor, respectively; and ∆Se is the entropy change upon the formation of a charge-transfer complex (contact radical-ion pair).

Razuvaev Institute of Organometallic Chemistry, Russian Academy of Sciences ul. Tropinina 49, Niznii Novgorod, 603600 Russia

In this paper, we report on a theoretical model of photoreduction of carbonyl-containing compounds and compare it with available and new experimental data. In constructing the model of hydrogen transfer in the course of photoreduction, we assumed the process to consist of electron transfer followed by proton transfer. The process involves reacting particles in three states: an encounter complex (EC), a triplet radical-ion pair (RIP), and a triplet radical pair (RP). In the encounter complex (3A, DH), the molecules are held together by van der Waals forces. The EC contains the acceptor molecule 3A photoexcited to the lowest triplet state and the hydrogen-donor molecule DH in the ground state. The energy of formation of the EC is several kilocalories per mole [8] and is slightly dependent on the nature of the reacting molecules. Upon electron transfer, the encounter complex transforms to the triplet radical-ion .– .+ pair 3( A , D H ). The energy of the charge-transfer complex ∆Ge can be positive or negative relative to the energy of the initial state (the encounter complex). Within a series of photoacceptors (∆E00 = const) and hydrogen donors with similar structures (∆Se = const), the sign and magnitude of ∆Ge are determined by the redox characteristics of the reagents. The ∆Ge range can constitute tens of kilocalories per mole. The difference in energy between the charge-transfer state (RIP) and the initial state of the system (EC) is ∆Ge. Proton transfer in the RIP leads to the formation of the triplet RP . . 3(A H , D ). The position of the energy level of the triplet RP relative to the EC is unknown. This compels us to make a second assumption: the energies of the initial and final states of the system (of the encounter complex and triplet radical-ion pair) are the same and equal to zero (the energy of the triplet state of the photoacceptor ∆E00 is taken as zero). With allowance for this assumption, the energy diagram of the process involving two successive stages—electron transfer to form the EC and proton transfer to produce the triplet RP— can be presented as in Fig. 1. The energy of the chargetransfer state can be both positive and negative depending on the nature of the reagents. At ∆Ge > 0 (Fig. 1a), the kinetics of the hydrogen-transfer reaction as a whole will be determined by the electron-transfer stage.

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∆Ge > 0 RIP

Energy

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∆Ge < 0

RP

Reaction coordinate

(a)

≠ ∆ Ge

RP

EC EC

of electron-transfer reactions is well elaborated [10] and is applied to the description of bimolecular reac≠ tions of photoinduced electron transfer [7–9]. ∆ G e › will be given by the Marcus equation

Reaction coordinate

Hence, ∆Ge will dictate the activation energy of the hydrogen-transfer reaction Ea(H). With a decrease in ∆Ge, Ea(H) will also decrease and the hydrogen-transfer rate constant (photoreduction of the acceptor) kH will increase. At ∆Ge < 0 (Fig. 1b), the charge-transfer state is more stable than the EC. Hence, the encounter of the molecules is followed by electron transfer to produce .– .+ the most stable species 3( A , D H ). In this case, for proton transfer to take place and for the triplet RP . . 3(A H , D ) to form, the system in the charge-transfer state must have an excess energy roughly equal to ∆Ge. Therefore, variations in ∆Ge toward negative values (due to the enhancement of the donor–acceptor properties of the reagents) lead to an increase in Ea(H) and, correspondingly, to a decrease in kH. This means that, on the whole, the hydrogen-transfer activation energy is proportional to the ∆Ge magnitude. At ∆Ge ~ 0, Ea(H) is a minimum; correspondingly, kH should be maximal. This model implies that the electron and proton transfers exhibit opposite trends with a change in ∆Ge. This can be tentatively explained by the fact that, at ∆Ge > 0, the less stable radical-ion state has a higher probability of being stabilized through the removal of the proton and the formation of the radical pair. The analytical dependence of kH on ∆Ge is generally described by Eq. (2): (2)

To find the form of the f(|∆Ge |) function, let us take into account that, at ∆Ge > 0, the hydrogen transfer activation energy corresponds to the electron transfer acti≠ ≠ vation energy ∆ G e . Let us assume that Ea(H) = ∆ G e › ≠

2

(3)

where λ is the reorganization energy. From the equality ≠ Ea(H) = ∆ G e › at ∆Ge > 0, it follows that 2

Fig. 1. Energy diagrams of photoinduced hydrogen transfer in the course of photoreduction of the carbonyl-containing compound (A) in the presence of the hydrogen donor (DH).

f ( ∆G e ) kH = k0 exp  – -------------------- .  RT 

2

( λ + ∆G e )  kH = k0 exp  – -------------------------.  4λRT 

(b)

RIP

λ ( 1 + ∆G e /λ ) ( λ + ∆G e ) = ----------------------------------= -------------------------, 4 4λ

and find the analytical expression for ∆ G e . The theory

(4)

Let us find the expression for kH at ∆Ge < 0. The hydrogen transfer activation energy will be equal to the activation energy of proton transfer from the chargetransfer state to the triplet RP. Our assumption that the energies of the EC and PR states are the same implies that the activation energy of the reverse electron trans≠ fer from the PIP to the EC (∆ G –e ) is close to the activation energy of proton transfer resulting in the RP (Fig. 1), ≠ i.e., Ea(H) = ∆ G –e . Hence, at ∆Ge < 0, the equation ( λ – ∆G e )  kH = k0 exp  – ------------------------ 4λRT  2

(5)

is valid. Thus, for all ∆Ge values, the general equation containing the sought f(|∆Ge |) function can be written as ( λ + ∆G e )  kH = k0 exp  – ---------------------------- .  4λRT  2

(6)

According to Eq. (6), the equation λ k H ( ∆Ge = 0 ) = k0 exp  – -----------  4RT 

(7)

is valid at ∆Ge = 0. To eliminate k0, we normalize kH to k H ( ∆Ge = 0 ) and obtain the following expression for the normalized photoreduction rate constant kH(N): ( ∆G e + 2λ ∆G e ) kH(N) = kH/ k H ( ∆Ge = 0 ) = exp  – ---------------------------------------- . (8)   4λRT Within the same series of donors and acceptors (λ = const), the expressions for kH and kH(N) have only one variable, ∆Ge, which is calculated based on the data known for each reagent pair by Eq. (1). The kH (kH(N)) = f(∆Ge) function is extreme; for any reagents, kH (kH(N)) is a maximum at ∆Ge = 0. The reorganization energy [10] is additive and consists of two terms, λint (“inner-sphere” interaction) and λout [9, 10]. The λint contribution within a series of reagents of the same type should remain constant and be independent of the solvent. The energy of reorgani2

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PHOTOINDUCED HYDROGEN TRANSFER IN REACTIONS kH(N)

kH(N) 1.0

kH(N)

kH(N)

1.0

1.0

1.0 2

1

223

3

1 2

0.2

0.2 –0.4

–0.2

0 0.2 ∆Ge, eV

–0.2

0 ∆Ge, eV

0.2

–0.2

Fig. 2. Normalized rate constant vs. ∆Ge for the photoreduction of (1) fluorenone and (2) o-benzoquinones in the presence of p-DMA. The theoretical curve calculated by Eq. (8) (λ = 0.6 eV) is shown by the dashed line.

( λ 2 – λ 1 ) ( λ 1 λ 2 – ∆G e ) - . kH(S1)/kH(S2) = exp  ----------------------------------------------------  4λ 1 λ 2 RT 2

(9)

It follows from Eq. (9) that if an increase in solvent polarity is accompanied by an increase in λ (due to the “outer-sphere” contribution), the photoreduction rate constant should decrease. Corollaries of the Theoretical Model (1) The rate constant kH of the photoreduction of hydrogen photoacceptors in the presence of hydrogen donors is a function of the free energy of electron transfer ∆Ge, which can be calculated from the known data by Eq. (1). (2) The kH(∆Ge) function is extreme with a maximum at ∆Ge = 0 irrespective of the nature of the solvent. (3) An increase in the solvent polarity accompanied by an increase in the reorganization energy leads to a decrease in kH. To assess the efficiency of the model suggested, let us compare the calculated dependences kH = f(∆Ge) to experimental data on the kinetics of photoreduction of photoacceptors, such as fluorenone [3, 4] and Ó-benzoquinones (a series of 8 compounds) [3], in the presence of p-X-DMA. Comparison of the theoretical curves and experimental results (Figs. 2, 3) makes it possible to draw the following conclusions. The rate constant of photoreduction of fluorenone and Ó-benzoquinones in the presence of a series of p-X-DMA is a function of the free energy of electron transfer ∆Ge. Both the theoretical and experimental curves pass through a maximum Vol. 385

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0 0.2 ∆Ge, eV

–0.2

0 ∆Ge, eV

0.2

Fig. 3. Simulation of the behavior of kH(N) vs. ∆Ge on increasing the solvent polarity, which causes an increase in λ by 0.1 eV: (1) λ = 0.6 eV and (2) λ1 = 0.6 eV and λ2 = 0.7 eV. The experimental curves of kH(N) vs. ∆Ge for the photoreduction of Ó-benzoquinones in the presence of p–XDMA [3] in (3) toluene and (4) acetonitrile.

zation of the solvation shell beyond the coordination sphere of the reagents (λout) is related to the change in the atomic and orientational polarization of the medium and increases with an increase in solvent polarity [10]. Variation in λ in going from one solvent to another leads to a change in kH. The ratio between the photoreduction rate constants in two different solvents kH(S1)/kH(S2) is described by the equation

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at ∆Ge ~ 0. The increase in the polarity of a solvent, which corresponds to the increase in λ in the model used (Fig. 3, curves 1, 2), leads to a decrease in the kH magnitude, the extreme character of kH = f(∆Ge) with a maximum at ∆Ge ~ 0 (Fig. 3, curves 3, 4) being retained. Therefore, the basic kinetic regularities of photoreduction reactions predicted by theory and obtained in the experiment coincide. The displacement of the kH = f(∆Ge) maximum for a series of Ó-benzoquinone–p-XDMA (Fig. 3, curve 2) is presumably associated with the error in calculation of ∆Ge (uncertainty in ∆E00 and ∆Se). It should be noted that, at ∆Ge < 0, the experimental curves lie above the calculated one. This is caused by the assumption that the activation energies of proton ≠ transfer and reverse electron transfer (∆ G –e ) are equal to each other; actually, these energies are related to each other through a more complicated dependence. To verify the theoretical model suggested, we also studied the photoreduction reaction in a system composed of other reagents, namely, 2,3,5,6-tetrachloro1,4-benzoquinone (p-chloranil) (n-Q1) and 2,6dichloro-1,4-benzoquinone (n-Q2) as hydrogen photoacceptors and polymethylbenzenes (ArH) with the general formula (CH3)nC6H6 – n (n = 1–4, 6) as hydrogen donors. The choice of the system was determined by the preliminary calculation of ∆Ge by Eq. (1) for each pQ1–ArH and p-Q2–ArH pair. To calculate ∆Ge, the following values were taken: ∆E00 = 2.13 eV [1], ∆S = –18 cal mol–1 K–1, const = 3 kcal/mol [6], and .– .– E( A /A)= –0.01 eV for p-Q1 and E( A /A) = –0.18 eV for p-Q2 [1]; the oxidation potentials of ArH

.+

E1/2(DH/ DH ) were taken from [11]. The theoretical model predicts that the function kH = f(∆Ge) for the p-Q1–ArH system should be extreme with a maximum kH value for the p-Q1–mesitylene pair. Figure 4 shows the plots of the rate constants of photoreduction of p-Q1 and p-Q2 in the presence of ArH in CCl4 versus ∆Ge. As

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kH × 104, s–1

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4

0.75

3

2

the presence of para-substituted N,N-dimethylanilines and the kinetics of photoreduction of p-chloranil and 2,6-dichloro-1,4-benzoquinone in the presence of polymethylbenzenes. ACKNOWLEDGMENTS

2

0.50

This work was supported by the Russian Foundation for Basic Research, project nos. 01–03–33040 and 0015–97336-l.

1

0.25

REFERENCES

–0.2

0

0.2

0.4

∆Ge, eV

Fig. 4. Rate constant vs. ∆Ge for the photoreduction of (1) 2, 3, 5, 6,-tetrachloro-1,4-benzoquinone and (2) 2,6dichloro-1,4-benzoquinone in the presence of polymethylbenzenes in CCl4.

predicted, the experimental kH = f(∆Ge) plot for the pQ1–ArH system is extreme. That the photoreduction curves for p-Q1 and p-Q2 are depicted in the same figure makes it possible to refine the inflection point (at ∆Ge ~ +0.3 eV) in curve 1 (Fig. 4). A small sample of polymethylbenzenes (7 compounds) gives no way of precisely determining the peak position; however, as follows from the data in Fig. 4, it is located at about ∆Ge ~ 0 eV. The maximum kH value is found for the p-Q1– mesitylene pair. With the increase in the solvent polarity in going from CCl4 to CHCl3 and to CH2Cl2, the observable kH value decreases: for the p-Q1—mesitylene pair, it is equal 3.2 × 10–4, 1.48 × 10–4, and 0.12 × 10–4 s–1, respectively. Therefore, the suggested theoretical model of photoreduction describes the available kinetic data on the photoreduction of Ó-benzoquinones and fluorenone in

1. Patai Saul, The Chemistry of the Quinoid Compounds, London: Wiley, 1974. 2. Cohen, S.G., Parola, A., and Parsons, G.H., Chem. Rev., 1973, vol. 73, no. 2, pp. 141–162. 3. Chesnokov, S.A., Cherkasov, V.K., Chechet, Yu.V., et al., Izv. Ross. Akad. Nauk, Ser. Khim., 2000, no. 9, pp. 1515–1520. 4. Cohen, S.G. and Parsons, G., J. Am. Chem. Soc., 1970, vol. 92, pp. 7603–7605. 5. Leonhardt, H. and Weller, A., Ber. Bunsen-Ges. Phys. Chem., 1963, vol. 67, no. 8, pp. 791–795. 6. Knibbe, H., Réhm, D., and Weller, A., Ber. Bunsen-Ges. Phys. Chem., 1969, vol. 73, no. 8/9, pp. 839–845. 7. Levin, P.P. and Kuz’min, V.A., Usp. Khim., 1987, vol. 56, no. 4, pp. 527–557. 8. Rathore, R., Hubig, S.M., and Kochi, J.K., J. Am. Chem. Soc., 1997, vol. 119, pp. 11468–11480. 9. Energy Resources through Photochemistry and Cataslysis, Gratzel, M., Ed., New York: Academic, 1983. Translated under the title Energeticheskie resursy skvoz’ prizmu fotokhimii i kataliza, Moscow: Mir, 1986. 10. Marcus, R.A., J. Chem. Phys., 1956, vol. 24, no. 5, pp. 966–978. 11. Mann, C.K. and Barnes, K.K., Electrochemical Reactions in Nonaqueous Systems, New York: Marcel Dekker, 1970.

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