J. Photochem. Photobiol. A: Chem., 56 (1991) 25-34

Application of the collision-complex model to the photophysical processes of singlet oxygen in liquids

S. H. Lin, J. Lewis and T. A. Moore

Department of Chemistry and Center for the Study of Early Events in Photosynthesis, Arizona State Universiv, Tempe, AZ 85287-1604 (U.S.A.)

(Received January 3, 1990)

Abstract

In this paper we propose a collision-complex model for the quenching of singlet oxygen by solvents. Using this model, it is possible to explain the diffusion-controlled quenching rate constants observed for quenchers such as carotenes and the group additivity rules observed for quenchers such as ordinary organic molecules by Hurst, Schuster and Rodgers.

We also present a theoretical treatment of the spectral shift of singlet oxygen in various solvents. It is applied to interpret the experimental data reported by Bromberg and Foote. It is shown that the agreement between experiment and theory is reasonable.

The emission intensity and radiative rate constant of singlet oxygen in liquids are discussed from the viewpoint of the collision-complex model. Both of these properties are shown to be enhanced by solvents and the addition of other quenchers.

We also report the experimental data of the quenching of singlet oxygen by 4-amino- TEMPO in methylene chloride solution. The data are analyzed by the collision-complex model. We show that, from the analysis of the experimental decay curves, both relative radiative and non-radiative rate constants can be determined.

1. Introduction

The photochemistry and photophysics of singlet molecular oxygen (‘A,) have attracted considerable attention [l, 21. A strong dependence of singlet oxygen lifetime on the structure of the solvent has been found [3-101. Theories have been proposed to account for the quenching relaxation by the solvent in terms of intermolecular electronic-to-vibrational energy transfer [3, 10-121. According to the theory of Merkel and Kearns [3, 10-121, the quenching rate constant of singlet oxygen in a solvent can be related to the IR intensities of the solvent in the energy regions of ‘A,(v) --* ‘&(v’) transitions and the Franck-Condon factors of ‘As(v) + 3Xs(~‘) transitions. Hurst and Schuster [6] found that the lifetimes of singlet oxygen in solvents are proportional to the concentration of C-H bonds, C-D bonds, etc. At the same time Rodgers [5] showed that there are linear relationships between the bimolecular quenching rate constant and the number of methylene groups in the carbon skeleton of normal alkanes and normal alcohols, and that the bimolecular quenching rate constant can be built up additively from the various atomic groupings in the quencher molecule, e.g. CHs, CH2, OH, etc. In a previous paper [ll], we have extended the above theories 13, 121 to treat the quenching of singlet oxygen by solvents. This includes introducing the off-resonance factor, which can be related to the emission bandwidth of singlet oxygen

lOlO-6030/91/$3.50 6 Elsetier Sequoia/Printed in The Netherlands

26

in the expression for the rate constant, and involves relating the IR absorption intensities of the solvent to the additivity relationship of the solvent for the quenching rate constant. This treatment takes into account the effect of temperature on singlet oxygen quenching and provides a theoretical foundation for the additivity relationship discovered by Hurst and Schuster [6] and Rodgers [5]. We have shown that the bimolecular quenching constant can be expressed in terms of the electronic transition moment and the Franck-Condon factors of the ‘Ag(v) ---, 3Z?,:,(~‘) transition, the IR absorption intensities of the solvent and the off-resonance factors.

It has been found that, for a number of quenchers such as carotenes, the bimolecular quenching rate constants are diffusion controlled [2, 131. This cannot be explained by the previous theories. In this paper we propose another theory based on the collision- complex model. The collision-complex model was originally proposed to treat collision- induced intersystem crossing (ISC) of intermediate size molecules in the gas phase [14]. Using this theory we can explain the diffusion-controlled case and the case where the group additivity relations of quenching rate constants hold.

2. Theory

We are concerned with the collision-induced ISC, S +T, i.e. ‘02 *302. The quenching process is assumed to take place in two stages. A quencher molecule A colliding with an S molecule is assumed to be captured by it to form a complex whose lifetime is at least a few vibrational periods, Eventually this collision complex, after rapidly redistributing its energy among its various degrees of freedom of internal motion, has its energy concentrated again in a decay and dissociative mode which leads to ISC and dissociation to A and T. We can express the collision-induced ISC by the collision-complex model as follows

kz

S+AISA- w TtA kl

Sk-T (1)

where k represents the total decay rate (i.e. including both radiative and non-radiative decay rates) of S.

By applying the steady state approximation to SA, the rate of change of concentration of S is given by

d(S) - = -{k+&(A)}(S) dt

where k, is the collision-induced ISC rate constant

k,= W

- k2 W+k,

(3)

Here the radiative and other non-radiative processes of the SA complex have been ignored.

Equation (3) shows that the probability of the ISC of the collision complex is given by

W p= ~

W+k, Gl (4)

27

and the collision-induced ISC rate constant can be expressed as k,=Pkz, where k2 represents the collisional rate constant for complex formation. In liquids, k2 may be approximated by the diffusion-controlled rate constant.

From eqn. (2) we obtain

(S) = (S), e-t”obS

where 700bs represents the observed lifetime of singlet oxygen

(5)

1 - =k+k,(A)=k+ Tabs

j&+9

From eqn. (4) we can see that W can be a result of the ordinary radiationless transition (ISC in this case) [15] or the intermolecular electronic-to-vibrational energy transfer. For k, we can use the transition state theory.

It should be noted that if WB- kl, then

k,=k> (7)

In this case the observed quenching rate constant k, is equal to the diffusion-controlled rate constant. On the other hand, if W-ckl, then

k,= pki @> 1

In this case the observed quenching rate constant is much smaller than the diffusion- controlled rate constant.

We classify the singlet oxygen quenching into three classes. Class 1 refers to the case in which kl ST=- W, in this case we have k,= U&/k, (see eqn. (8)). In the next section, we show that, in this case, the group additivity relations observed by Hurst and Schuster [6] and Rodgers [5] hold. Class 2 refers to the case in which kl a W, in this case we have k, = k2, i.e. the quenching is diffusion controlled, and the quenching constants are relatively independent of the quenchers used and dependent only on the solvent. Class 3 refers to the intermediate case, i.e. kl = W; kl and W are of the same order of magnitude.

3. Group additivity relations of quenching rate constants

As mentioned in Section 1, Hurst and Schuster [6] and Rodgers [5] discovered the additive rule of atomic groupings in the quencher molecule for a number of quenchers. This is only true for kl > W, in this case k,, is given by eqn. (8). We will show that this group additive rule mainly results from W. As mentioned in Section 2, W can be a result of the intramolecular electronic relaxation by regarding the collision complex as a supermolecule or the intermolecufar electronic-to-vibrational energy transfer between the oxygen molecule and the quencher molecule in the complex. Since the second case has been treated by Merkel and Kearns [3] and Lin et al. [lO-121, only the first case will be discussed in this paper.

According to the theory of radiationless transitions, using the adiabatic approx- imation lav} = sP,O,, and (bv’) = @b@,vs (where @= and G6 represent the electronic wavefunctions and O,, and O,,. denote the vibrational wavefunctions), W can be expressed as [15]

28

Here, for simplicity, it is assumed that A’ is independent of vibrational coordinates. The overall Franck-Condon factor can be written as a product of the Franck-Condon factors of accepting modes

The accepting modes are divided into the major (or high frequency) accepting modes denoted by i and the minor (or low frequency) accepting modes denoted by i. It follows that

(11)

where wi denotes the rate constant for the electronic relaxation where the ith accepting mode receives the vi vibrational quanta and

sy: e-

v; ! si (12)

Here S; denotes the coupling constant (or Huang-Rhys factor) of the ith mode and v: represents the number of phonons accepted by this mode.

For the quenching of singlet oxygen, V; is generally unity, i.e. vf= 1 because of the weak coupling in the complex. In this case we can rewrite eqn. (11) as

(13) i i

where LY~=A~?V~, Ai =Si e-” and ni denotes the number of equivalent major accepting modes. The relation given by eqn. (13) was first proposed by Rodgers.

As mentioned above, the non-radiative rate constant W can also be a result of the intermolecular electronic-to-vibrational energy transfer. In this case, the Fiirster theory can be used; this has been performed by Merkel and Kearns [3] and Lin et al. [lO-121. Lin ef al. have shown that, in this case, W can be built up additively from various atomic groupings in the quencher as reported by Hurst and Schuster [6] and Rodgers [S].

4. Spectral shifts

Recently Bromberg and Foote [16] have measured the luminescence spectra of singlet oxygen in several solvents and have observed a small but significant spectral shift (in the range 30-60 cm-l) in these solvents. In this section, we discuss this solvent-induced spectral shift. In a previous paper 1171, we have generalized the theory of solvent effect on electronic spectra developed by Longuet-Higgins and Pople [18] to derive the spectral shift expressions of van der Waals complexes (i.e. a given solute molecule interacting with a group of solvent atoms or molecules of fixed orientations). We have shown that the spectral (red) shift for the electronic transition 0 +i can be expressed as [17]

29

where &a and cy, represent the polarizabilities of the solvent molecule and solute molecule respectively, /&i denotes the transition moment and R, is the distance between the solute molecule and the /?th solvent molecule.

For the case of singlet oxygen, & refers to the forbidden transition ‘A-,% and hence is negligible, Thus we have for singlet oxygen

According to eqn. (15), the spectral shift is determined by the polarizability a6 of the solvent molecule and the distribution of the solvent molecules surrounding the oxygen molecule.

Next, we apply eqn. (15) to estimate the spectral shifts of singlet oxygen in various solvents. The polarizabilities of oxygen, benzene and methanol are LY(O*) = 1.60 _k3, a(benzene) = 10.4 A3 and cr(CH30H) = 3.23 A3 [19]. From eqn. (15), to estimate AIV,, it is also necessary to know the distance between the solvent molecules and the solute molecule. For benzene as solvent, we use the van der Waals distance 3.6 %, for R, [17]. We obtain AWoi=50 cm-’ which should be compared with the experimental value [16] of 58 cm-‘. With CH,OH as solvent, we use R, =3.2 A since the CHsOH molecule is polar and smaller than C,Hs. In this case, we obtain AI+‘&=28 cm-’ which should be compared with the experimental value of 33 cm-‘. From these estimates we can see that the agreement between experiment and theory is reasonable.

5. Radiative transitions

In Sections 2 and 3 we presented the collision-complex model of the quenching of singlet oxygen and in Section 4 we discussed the theoretical treatment of the spectral shifts of singlet oxygen induced by solvent. We now discuss the radiative processes of singlet oxygen in liquids.

According to the collision-complex model, the emission intensity 1 of singlet oxygen is contributed by S and SA

I=k,(S) +k:(SA) (16)

which can be rewritten as

I=(S) I k,+ f$$k; 1

(17)

where k, and k: represent the emission rate constants of S and SA respectively. From eqn. (17), we can see that the emission intensity of singlet oxygen can be

enhanced by the solvent effect.. Due to complex formation, the spin-orbit coupling required for the spin-forbidden transition ‘A + ‘Z will also be enhanced, i.e. k:> k,. From the above discussion, we can see that the observed radiative rate constant krvobs for singlet oxygen can be expressed as

k k,(A) k, r,obs=kr+ -

k,+W ’ (18)

30

From eqn. (17), we can see that the emission intensity of singlet oxygen in liquids will, in general, be stronger than that in the collision-free condition by several orders of magnitude. This is indeed experimentally observed.

To understand quantitatively the reason for K,>k,, we consider the spin-orbit coupling A:, in the O2 molecule [20]. For the pure O2 molecule, it can easily be shown that the spin-orbit coupling between the ‘A state and the 31T state is zero, i.e.

w&kolJI3,,GK= 1)) = ((~T2p)lEi:,(1>1(~*2p)) =o (1% where I?:,( 1) denotes the one-electron spin-orbit coupling operator.

For the case in which the O2 molecule forms a complex with a solvent molecule (or. molecules) or a quencher, an interaction will exist, denoted by V, due to the solvent molecule (or molecules) or the quencher which will introduce the mixing of the molecular orbitals, i.e.

(7ep) = (&q3)” + cr4~12p)o (a*2p) = (~*2p)“+c,.,(a2p)o (20)

where

c {(~~2P)“lvl(~2P)o) Tr*lr=

E&-E,

C ((~2P)“l~(6*2P)o>

da= E,* -E,

(21)

Using eqns. (20) and (21), the spin-orbit coupling between ‘A and ‘II now becomes

(@~]&J&(:,(MS= 1)) =C,T~(~12P)“IA:o(1)l(~2P)o~ cC,,~(~T2P)“lA:,(l)l(~2P)0)

(22) which is non-zero. It follows that

and that the transition moment for ‘A-,

which is non-zero. Of course, the 3c state in the same manner as discussed above. contribution has been ignored.

6. Quenching by 4-amino-TEMPO

‘IS becomes

(23)

(24)

will also mix with ‘II by spin-orbit coupling Here, for simplicity of demonstration, this

We have experimentally studied the quenching of singlet oxygen by 4-amino- TEMPO in methylene chloride solution. The experimental details will be reported in a separate paper. The concentration of 4-amino-TEMPO varies from 0 to 0.04 mol 1-l. The experimental decay curves can be fitted by the following expression

(25)

31

TABLE 1

Experimental results

Concentration (mol 1-l)

Lifetime (W)

Pre-exponential factor

Cl 81.5 28.8 0.00118 83.0 34.2 0.00718 69.1 35.6 0.0270 44.2 42.8 0.0488 31.4 46.9

Both the pre-exponential factor Ia and the observed lifetime r&s are functions of the quencher (4-amino-TEMPO) concentration C,.

Table 1 lists our experimental results of Ia and r&s as a function of C,. As can be seen from eqn. (17), we have

b=(S), k264) k,+ k+Wk:

1

and

1 - =k,,,=k+k,(A) robs

(26)

(27)

Figure 1 shows the plot of the pre-exponential factor vs. C, and Fig. 2 shows the plot of l/r& vs. cg.

An excellent linear relation is shown in Fig. 2 and from the slope of this straight line we obtain

w k,= ___

k, + W k,=4.2x 16 1 mol-’ s-l

t I 4 I

0.00 0.01 0.02 0.03 0.04

4-Amino-TEMPO Concentration (moles/l)

Fig. 1. Pre-exponential factor vs. quencher concentration.

(28)

32

.035

.030 -

z .025- 9 / 0 l

y .020-

I 0.00 0.01 0.02 0.03 0.04

4-Amino-TEMPO Concentration (moles/l)

Fig. 2. Effect of the quencher concentration on t’he observed lifetimes.

This quencher (4-amino-TEMPO) belongs to class 1, i.e. k,= Wz/kl. It should be noted that l/~,,~ at C, = 0 is mainly due to the quenching by solvent. Using the density of methylene chloride of 1.335 g cme3, we obtain

k;= w’ k;=0_77x ld 1 mol-1 s-l k;

From k, and k;, we can see that 4-amino-TEMPO is a much better quencher than methylene chloride: k,/kk =5.5X lo*. If we assume that kl =ki and k,=k;, then k,,/kA = W/W’ = 5.5 x lo’, i.e. we can determine the relative non-radiative transition rate constant.

From Fig_ 1 we can see that a reasonably good linear relation is also obtained for the plot of I,, vs. C, as is predicted by eqns. (17) and (18). From the slope and intercept of Fig. 1, if we assume that kl =k; and k,=k$, we obtain the relative radiative rate constant as

kXT=-Q) = 13 x 102

k;(CH,Cl$ * (30)

This shows that the quencher 4-amino-TEMPO can also effectively enhance the radiative process of singlet oxygen.

It is important to note that, in this section, we have shown that it is possible to determine experimentally the relative radiative and non-radiative constants from the measurements of I, (the pre-exponential factor) and rObS (the observed lifetimes) as a function of quencher concentration in a given solvent.

7. Conclusions

In this paper we have used the collision-complex model to interpret the quenching, spectral shifts and radiative and non-radiative processes of singlet oxygen. It has been shown that this model can explain most of the existing experimental observations. It should be noted that, for W> kl and k, = kZ, k2 represents the diffusion-controlled rate

33

constant k2 =4wR,D, where D denotes the mutual diffusion coefficient of quencher and singlet oxygen and R, is the critical radius [21]. However, if the quencher molecule is very large, k2 may also contain the probability factor describing how the oxygen molecule finds the appropriate position after its encounter with the quencher molecule. The effect of temperature on the lifetime of singlet oxygen in various solvents has been reported [22]. The collision-complex model can also be used to treat this effect of temperature.

Although the model proposed in this paper is intended for the quenching of singlet oxygen, it may also be used as a mechanism for the product of singlet oxygen 1231. In this case we have

k:

T+3A &T~A =s+r& ‘4

(31)

where T represents the ground state O2 molecule and 3A denotes the excited triplet dye molecule. In this case the rate constant for the production of singlet oxygen can be expressed as

w” k,= - k;

k;+W’

Here IV” represents the unimolecular rate constant of the channel for producing singlet oxygen, and IV’ represents the total decay rate constant of T3A. IV’ and IV’ may be

(32)

different attributed to the multiplicity of the complex T3A.

Acknowledgments

This is publication 048 from the Arizona State University Center for the Study of Early Events in Photosynthesis. The Center is funded by the U.S. Department of Energy grant DE-FG02-88ER1969 as part of the USDA/DOE/NSF Plant Science Center Program. This work was supported in part by NSF. The authors wish to thank Professor P. R. Ogilby and Mr. R. Belford for helpful discussions.

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