7244 t h a t t h e trans-cis d i c i n n a m a t e , T C , is i n e r t with respect
to the cycloaddition reaction, b u t the c o m p u t a t i o n of t h e a p p a r e n t q u a n t u m efficiency involves p h o t o n s a b s o r b e d b y t r a n s species i n b o t h TT a n d TC c o m p o u n d s . T h e e x t r a p o l a t e d q u a n t u m efficiency, w h e r e t h e r a t i o of c i s / t r a n s = 0, requires n o correction since only TT is present. T h e reason f o r t h e variation in t h e a p p a r e n t q u a n t u m efficiency of t h e t r a n s --t cis isomerization is d u e t o t h e well-known photoreversibility of this reaction. T h e m a i n objective o f t h i s s t u d y w a s t o o b t a i n relative efficiencies of t h e cycloaddition a n d t h e isomerization reactions. T h e values f o r t h e a p p a r e n t q u a n t u m efficiencies of t h e l a t t e r as a f u n c t i o n of cisltrans r a t i o s a r e given i n T a b l e I1 a n d represented i n F i g u r e 3. T h e
at,,,,-,
efficiency of t h e trans --t cis isomerization is t h e intercept, a n d its value is 0.473. T h e e x t r a p o l a t e d value o b t a i n e d f o r t h e photocyclization is 0.086. T h e r a t i o of t h e efficiencies, @'cli@t,,,,.,, I, is r e m a r k a b l y high. T h i s is ascribed t o a n d consistent b i t h t h e c o n c e p t that pairs of c i n n a m o y l g r o u p s h a k e b e e n forced i n t o close proximity. a s i t u a t i o n a n a l o g o u s t o t h a t of t h e solid s t a t e . T h e efficiency of t h e photocyclization reaction is a p p r o x i m a t e l y 18 of t h e value of t h e p h o toisomerization reaction. F o r synthetic purposes, o n e s h o u l d be able t o o b t a i n nearly theoretical yields o f c y c l o b u t a n e p r o d u c t s since t h e trans-trans c o m p o u n d is irre\ ersibly r e m o v e d f r o m t h e reaction mixture, a n d t h e equilibrium is shifted t o w a r d m o r e t r a n s -trans formation.
Radiationless Decay of Singlet Molecular Oxygen in Solution. An Experimental and Theoretical Study of Electronic-to-Vibrational Energy Transfer Paul B. Merkel and David R. Kea" Cotitribittion f r o m the Department of Chemistry, Unicersity of California, Riuerside, California 92502. Receiced January 29, 1972
Abstract: A Q-switched ruby laser has been used to spectroscopically measure the lifetime of singlet ('A) oxygen in solution. The nature of the solvent is found t o have a remarkable effect on the lifetime of singlet oxygen with values ranging from 2 psec in water to 700 gsec in CC1). A simple theory has been developed to account for the quenching of lA by the solvent in terms of intermolecular electronic-to-vibrational energy transfer. According to this theory the quenching efficiency can be quantitatively related to the intensities of infrared overtone and combina3 2transitions and especially near 7880 and tional absorption bands of the solvent in the energy regions of lA 6280 cm-', the respective 0 .--, 0 and 0 -+ 1 oxygen transition energies. Direct calculation of the quenching rates using this theory with no adjustable parameters yields a better than order of magnitude agreement with experimental results. An analysis of gas phase and solution quenching rate constants indicates rate constants obtained in one as phase may be used to compute quenching constants in the other phase. This applies t o the quenching of well as ]A. The apparent lack of a heavy atom effect on the '3. lifetime can be accounted for. Large deuterium effects are predicted and observed. The theory indicates that the quenching involves a second-order indirect mixing of 3 2 and lA states through l Z by interaction with the solvent, in which 3 Zand '3 are mixed cia a n intramolecular spin-orbit coupling. Mixing of ' 2 and l4 is also important in the quenching of ' E , and the matrix elements used to account for the observed quenching rate constants for l4 automatically lead to rate constants for the quenching of ' 2 which are in good agreement with the experimental values. The theory thus appears to be internally consistent. The techniques used t o measure the solvent-controlled decay of singlet oxygen have also been used to evaluate the absolute rate constants for the reaction of singlet oxygen with various acceptors. A quantum yield of 0.9 =k 0.1 was measured for the formation of 1 Afrom quenching of triplet state methylene blue. The quenching of singlet oxygen by &carotene and a polymethene pyrylium dye (I) has been investigated. We confirm the earlier suggestion by Foote that the $-carotene quenching of singlet oxygen is nearly diffusion controlled ( 2 X 10"' M-' sec-l in benzene). The rate constant for Ihe quenching of lA by I i s found to be 3 X 10'" M-' sec-' in acetonitrile. The discrepancy between our observation that the lifetime of !A is extremely solvent sensitive and earlier indications that the lifetime is relatively solvent independent is resolved. Our findings indicate the factors which may permit lA lifetimes of greater than 1 msec in appropriate solvents t o be obtained. +-
R
ecognition o f t h e i m p o r t a n c e o f singlet molecular oxygen as a n i n t e r m e d i a t e i n t h e p h o t o o x i d a t i o n o f u n s a t u r a t e d h y d r o c a r b o n s h a s s t i m u l a t e d m u c h of t h e c u r r e n t interest i n t h e chemical a n d physical p r o p erties of this O n e of t h e m o s t c o m m o n m e t h o d s o f g e n e r a t i n g singlet oxygen is via energy (I) (2) (3) (4)
C . S . Foote and S. Wexler, J . Anier. Cheni. Soc., 86, 3879 11964). E. J. Corey and W. C. Taylor, ibici., 86,3881 (1964). I, 4 4 the Franck-Condon factors decrease extremely rapidly as m increases. For the isolated molecule, as m the values decrease as ~ l : l O - ~ : l O - ~ X :2 increases from 0 to 3. 45 Complete intramolecular conversion of energy from lA into vibration of 3 2 requires excitation to m = 5 . Because of the rapid decrease in F,, the relaxation of 'A oxygen is expected to be most rapid when large amounts of electronic energy can be transferred to vibrational excitation of the solvent. If, for example, all of the lA excitation energy is transferred to the solvent, theory predicts that the lA decay rate will be directly proportional to the solvent ir absorption intensity at -7880 cm-l. If the solvent absorption bands at this energy are not particularly strong, then quenching in which 3L: is formed in its m = 1 vibrational state and the solvent picks up (78801600) cm-' of vibrational excitation will also occur, and solvent absorption in the region of 6280 cm-1 becomes important. Quantitative Test of Theory. It is evident that theory can at least qualitatively account for the dramatic variation of the life-time of singlet oxygen in various solvents and for the fact that there is a good correlation between infrared absorption intensity and quenching rate constants. As a quantitative test of the theory, let us try to compute the lifetime of 'A in a particular solvent. Since experimental values of M , are available, the only quantity that we will actually have to compute at this point is P e l ' . To do this, we choose a coordinate system with an oxygen molecule at its center and the z axis as the molecular axis as illustrated in Figure 8. Noting that R = R , rz or Ri2 = ( R 2 - ri2),where r , is the distance of the ith oxygen electron from the origin, we can write
-
+
(16) A Maclaurin series expansion of [ l - (ri2/R2)]-'yields
Referring to eq 10 we can write Pel'
=
If we consider only the outermost pair of oxygen electrons explicitly, then the zero-order electronic wave functions for 'A and ' 2 can be expressed in the form3l 1 { i nd1)Fz(2)l - I nu(1)Fu(2)l1 42
$('A)
=
$('A)
= -{
$('2) =
7
1 lnA1)Fu(2)l - IFdl)nA2)'I d 2 1 { 1 n*(l)?z(2) I+ I n y ( 1 W 2 ) !1 4 2
where n, and nu are antibonding a orbitals occupied by unpaired electrons (1) and (2) and a bar indicates spin p. From the character of these functions it is evident that only interactions involving the unpaired electrons will be effective in mixing, and that a oneelectron perturbation of the form V = V(1) V(2) which destroys axial ( z ) symmetry will suffice, since
+
($(lA>iVl$(lL:>)
=
+
1 j{(rz(l)iV(l)l~z(N
(nz(2)l V(2)I nz(2)) - (.,(1>/ V(l>lr,(lN (ru(2)l V(2)l a,(2)) 1 (20) In the present situation V(1) and V(2) have the same form and we can write Pel'
=
( 4V(l)l n.2) - ( 4W)Inu)
(21)
To make a crude estimate of the magnitude of P e l ' , consider the special situation in which the solvent dipole points along the x axis as in Figure 9. Using only the first term in (22) we have Pel'
=
e R
- - 2 ( ( n , l ~ ~Oil~nz) -
COS 611 nu))
(23)
For an electron in the n, orbital cos O1 'v 1, while in the r uorbital cos el = (1 - sin2 e,)'/z 'v 1 - ( YI2/2R2). Thus Pel' 'v
(44) G . Herzberg, "Spectra of Diatomic Molecules," Van Nostrand, Princeton, N. J., 1950. (45) M. Halmann and I. Laulicht, J . Chem. Phys., 43, 438 (1965).
(19)
e
-2R"nuI
Y121n,)
(24)
Using R = 5 A and (nul Yl21n,) = 1 A2, we obtain P e l ' 'v 4 X I O 3 esu/cm2 and Pel 'v -80 esu/cm2. The contribution to P e l ' from the r12/R2 term in V(1)
Merkel, Kearns 1 Radiationless Decay of Singlet Molecular Oxygen
7252
will be reduced by approximately an order of magnitude. Consequently, our neglect of this term and other higher order terms isjustifiable. The interaction matrix element can now be expressed as
Pmn N 80 (esu/cmz)F,'/'M,
(25) If we assume the 0-0 oxygen transition (for which Fo 1) to be most important, then jM,lZ can be obtained from the solvent infrared absorption intensity in the region of 7880 cm-I through use of the relationship 4 6
-
The molar extinction coefficient for water at 7880 cm-' is Integrating over 200 cm-l (kT) gives iM,I2 'v 2 X e m Zcm2, from which we calculate Po, 'v erg N -5 X cm-l. Finally, assuming TTrlb 1: sec,36we obtain a value for the rate constant for the radiationless decay of singlet oxygen in water of
In view of the approximations, the agreement with the experimental estimate of kz N lo5 sec-' is remarkably good. We have considered a particularly favorable orientation of the solvent dipole relative to the oxygen molecule and the average orientation would not produce as strong an interaction. On the other hand, at the small distances considered the dipole approximation is not strictly valid and leads to an underestimation of P e l ' . A more accurate, but involved treatment would require a consideration of the electrostatic interaction of a system of point charges. In order to properly include the effects of the 0 I, 0 2, and other nonadiabatic transitions, we need the Franck-Condon factors appropriate to each. Isolated molecule Franck-Condon factors are probably not appropriate for oxygen molecules in solution, since there are experimental data which indicate that these may be rather sensitive to solvent perturbations. For example, Evans has observed 0 + 0:O + 1 intensity ratio of -1 :0.3 for the IA + 31:absorption of oxygen at high pressure in 1,1,2-trichlorotrifluoroethane. 47 If we assume that in the present situation Fl N 0.1 (intermediate between the isolated molecule and high pressure cases), then with reference to the data in Tables I and I1 we obtain the following empirical expression relating the lA lifetime to solvent ir absorption.
-
-
1 ~
7
(psec)-'
1 :
+
0.5(OD7860) 0.05(0D6280)
+
higher terms
(28)
where OD7860and OD6280 are optical densities of 1 cm of solvent at 7880 and 6280 cm- l , respectively. 48 Examination of the data in Tables I and I1 indicates that for most solvents higher terms in expression 28 (46) J. N. Murrell, "The Theory of the Electronic Spectra of Organic Molecules," Wiley, Nea York, N. Y . , 1963, p 9. (47) D. F. Evans, Chem. Commun., 367 (1969). (48) The previous theoretical treatment indicates that k , i will be proportional to oscillator strength multiplied by the number of coupled solvent oscillators or roughly to optical density.
Journal of the American Chemical Society
can be neglected. Lifetimes in benzene, chloroform, carbon disulfide, and carbon tetrachloride, however, are substantially shorter than those calculated using only the 0-0 and 0-1 terms, but the correlation can be improved by inclusion of terms involving transitions 2 IA + to higher vibrational levels of 5?. The 0 3 2 transition energy is e 4 7 0 0 cm-I. Benzene has a very strong absorption in this region (OD of 1 cm ~ 7 . 0 ) . A Franck-Condon factor of F2 'v 5 X (us. for an isolated oxygen molecule) would bring the predicted and observed 'A lifetimes in benzene into good agreement. Chloroform and carbon disulfide exhibit moderate absorption within ' v k T of 4700 cm- I, and thus radiationless decay of lA to the m = 2 level of 3 2 is expected to be important in these solvents also. Of the remaining solvents studied only acetone shows an absorption at 4700 cm-1 which is strong (OD N 3.0 in a 1-cm cell) relative to that at 7880 and the value of 7 6280 cm-I. With an Fz of 5 X in acetone calculated from expression 28 is closer to the measured lifetime. Transitions further into the infrared evidently must be included to account for the lA lifetime in carbon tetrachloride. When oxygen Franck-Condon factors in various solvents become available, more accurate calculations of radiationless decay rates will be permitted. Singlet oxygen lifetimes are expected to be longest in solvents such as nitrogen and argon which lack infrared intensity. It is worth noting that for a particularly strong solvent-oxygen interaction, transitions to the m = 5 vibrational level of 32: may become more allowed. Hence transfer of excitation energy to the solvent would be less important, and the static dipole moment of the solvent could become significant in radiationless decay. Deuterium Effects. Since the infrared overtone bands of common solvents in the regions of interest are usually due to C-H or 0-H vibrations, the theory predicts that there can be large solvent deuterium effects on the lifetime of singlet oxygen. The lifetime of 'A in water is 2 psec, and a comparison of the infrared absorption intensities of H 2 0 and D 2 0 (Table 11) suggests that the lifetime in the latter solvent should increase by approximately a factor of 9. Our experimental studies of the photooxidation efficiencies in H 2 0 and D 2 0 indicate that there is actually a tenfold change.IG A similar tenfold increase in the singlet oxygen lifetime is predicted, and observed, in going from a 1 : 1 mixture of HZO CH30H to DzO :CD3OD. Solvent deuteration will not necessarily lead to an increase in the lifetime of singlet oxygen as the case of acetone illustrates. The reduction in absorption intensity at 7880 cm-I upon deuteration of acetone is almost completely compensated for by the intensity increase at 6280 cm-'. Although deuteration will in general lead to a decrease in near-ir absorption intensities, it is possible that a situation might arise in which deuteration shifts would create resonances that would actually enhance lA relaxation. Because deuteration involves a very minor perturbation of the solvent, the deuterium effect on the lifetime of singlet oxygen can be used as a powerful diagnostic tool for investigating the role of singlet oxygen in various chemical and physical processes. Recently, for example, we have used the deuterium effect to dem-
94:2I / October 18, I972
-
7253
onstrate that the methylene blue sensitized photooxidation of tryptophan occurs via reaction with singlet oxygen, 1 6 ~ 4 9 This technique should have widespread application in areas such as photodynamic action. Order of magnitude increases in the lA lifetime upon deuteration are predicted for methanol and chloroform and are consistent with some preliminary experimental observations. Thus, these will also be useful solvents for characterizing singlet oxygen reactions. Heavy Atom Effects. Since the lA + transition is formally spin forbidden, one might have expected to observe large external heavy atom solvent effects on the relaxation rate. Our theoretical analysis indicates that this may not be the case, however, in the relaxation of lA for the following reason. There is a large spinorbit mixing of the '2 state with the 3 2 ground state, and mixing of lA with 3 2 is indirectly achieved by an electrostatically induced mixing of lA with '2. In order for there to be a specific heavy atom solvent effect on the relaxation, the heavy atoms would have to provide some new route for mixing lA and 32. An entirely similar process is responsible for the external heavy atom enhancement of the radiationless relaxation of an excited triplet-state molecule to its ground state, and we can use triplet data to place an upper limit on the importance of this mechanism in the oxygen case. For many of the aromatic hydrocarbons in a bromine-containing solvent (tetrabromozene), the radiative lifetimes are on the order of 50 msec and nonradiative transition rates are estimated to be much smaller than 102/sec.50 If we assume that similar electronic matrix elements will be obtained in the case of oxygen, then heavy atom solvents are not expected to enhance the relaxation of lA, since nonheavy atom solvents already give relaxation rates of -105/sec. Amine Quenchers. The amines and other molecules with low ionization potentials may introduce new mixing routes involving charge-transfer states. As developed, our theory does not include this effect, but it could be extended to treat such cases. (49) R . Nilsson, P. B. Merkel, and D. R. Kearns, Photochem. Photobiol., 16, 117 (1972). (50) G. G. Giachino and D. R. Kearns, J . Chem. P h y s . , 52, 2964 (1970).
Relation between Quenching of ' 2 and 'A. In spite of the large spin-orbit coupling of '2 and 32,direct relaxation of 12 to 3 Z is expected to be small because of the extremely unfavorable oxygen Franck-Condon factors for those l2 + 32 transitions which coincide with solvent infrared bands of measurable intensity. The Pel' used in our treatment of lA relaxation is precisely (without reduction by &,,/A,) the quantity which determines relaxation of '2 to 'A, and thus it can be used to compute the rate constants for quenching of '2 by various solvents. As in the relaxation of lA to 3 2 , we expect relaxation of l2 to lA without energy transfer to the solvent to be hindered by the small Franck-Condon factors. For the adiabatic ' 2 to 3 2 transition the solvent will have to take up approximately 5200 cm-l of vibrational excitation. For water the molar extinction coefficient in this region is -1.0 from which we calculate a value of Po, N 0.4 cm-l. Substitution of this value into eq 27 gives a value of kif N 3 X 1Olo sec-l for the quenching rate constant of water which should be compared with our earlier estimate from experimental data of k, N 2 X 10'O sec-l. Application to Other Systems. Radiationless decay of other simple molecules may also fall within the scope of the present theoretical treatment. Molecules with low-lying excited states for which 1 M,I for the solvent is large in regions of favorable F, would be the most likely candidates. Cases intermediate between the small molecule limit and the primarily intramolecular relaxation characteristic of large molecules may also exist. The solvent dependence of radiationless decay of 'A is similar to that for europium(II1) which was recently characterized in detail by Hass and Stein.s1 Preliminary studies5 suggest that radiationless transitions in rare earth ions are another system to which the above theory might be applied. Acknowledgments. The support of the U. S. Public Health Service (Grant G M 10449) is most gratefully acknowledged. We thank Dr. J. Williams for the gift of compound I.
,
(51) Y . Hass and G. Stein, J . Phys. Chem., 7 5 , 3668, 3677 (1971). (52) C. Long and D. R. Kearns, unpublished results.
Merkel, Kearns
Radiationless Decay of Singlet Molecular Oxygen
