2164
B. Stevens and J. A. Ors
tramolecular perturbations by comparing the progressions for vapor and for condensed systems (liquid solutions and solid matrices).
Discussion D. S. MCCLURE.Is the intensity of the high overtones you see caused by the electrical anharmonicity of the bonds being stretched?
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B. R. HENRY.We have actually looked on the problem more from the point of view of mechanical anharmonicity than of electrical anharmonicity, but in this region of the spectrum it may be impossible to disentangle one from the other. The detailed intensity problem in normal mode language is one that I think we haven’t solved, and to my knowledge, neither has anyone else.
S. J. STRICKLER.I do not believe you can say the results are all due to electrical anharmonicity. The local mode states are just those for which the mechanical anharmonicity is a maximum. One can think of anharmonicity in terms of a sort of Morse potential-the lower the dissociation energy, the greater the anharmonicity. For a CH2 group, for example, the Morse curve for a symmetric CH stretch would level off a t the energy of breaking two CH bonds. But a localized mode levels off at breaking one bond, so would be much more anharmonic. In terms of normal modes this is a combination of symmetric and antisymmetric modes. The mechanical anharmonicity would therefore favor appearance of the local modes discussed by Dr. Henry. B. R. HENRY.I think the whole analysis in terms of local modes, as a matter of fact, follow the kind of argument that Dr. Strickler has just described. When energy is pumped into a benzene molecule, and in particular, into the C-H stretching modes, six C-H bonds would not break off simultaneously. What would happen, I think, is that one bond is going to break off because that’s a much lower energy process. That’s why eventually, on physical grounds, the vibrational pattern must change to a local mode pattern. And that shows up, I think, in the very large value of the normal mode coupling anharmonicity constants. Because the anharmonic contribution to the energy goes up (quadratically) with vibrational quantum number, it tells us that, as the energy increases, the normal modes are more and more highly coupled. In our language, really what we are producing are local modes.
M. KASHA.In these local mode states is it possible to follow the anharmonic combinations out into the visible and uv? Your experiments and theory offer the interesting possibility for studying in-
B. R. HENRY.I agree
R. KOPELMAN.I would like to go back to the previous problem. How do the spectral-density-of-states and the energy-density-ofstates compare? If they differ, does not this imply electrical anharmonicity considerations in addition to mechanical anharmonicity? B. R. HENRY.I really don’t think that what we have done is that sophisticated. All we are doing is saying that from the evidence of the ir spectrum it appears that selection rules are operating so that the radiation field interacts with the molecule in such a way as to select certain states. Now the interesting question is: Are these states that the radiation field appears to see the same states that we should be using when we calculate photophysical processes, such as radiationless transitions, for instance, or unimolecular reactions? Now it is not necessarily true that they are the same states. Intuitively, one would feel, strictly because of the large values of the off-diagonal terms in a normal mode representation, that local modes might be a better starting point for the calculation of Franck-Condon factors for radiationless transitions or for insertion into the theory of unimolecular reactions, if you are trying to think about energy flow in a unimolecular process. W. T. SIMPSON.I’d like to make a comment. I think what the radiation field sees, in this case, are stationary states. I think, however, that the stationary states are not the normal modes. They involve what you might call configuration interaction among modes that have the same symmetry. B. R. HENRY.I don’t think that these can be true stationary states in the sense that as we saw in one of those last spectra I presented there are couplings between the local modes. My physical picture of what does go on is that if we think of the benzene molecule and consider something like AUCH= 6 excitations, then what’s happening is that the energy is moving around the benzene ring in a kind of a way that one C-H bond is stretching, then the next one, then the next one, and the next one. Then, a t any one time the chances are that the energy is localized in a single C-H oscillator. Do you agree with that?
W. T. SIMPSON. No, this represents a difference in your point of view and mine.
Photoperoxidation of Unsaturated Organic Molecules. 16. Excitation Energy Fission B. Stevens* and J. A. Ors Department of Chemistry, University of South Florida, Tampa, Florida 33620 (Received February 12, 1976)
T h e q u a n t u m yield 7 ~ of0photosensitized ~ addition of molecular oxygen to an organic acceptor M is the product of the q u a n t u m yield of 0z1A formation and the efficiency +MO* of OzlA addition t o the acceptor (process 1)where
M
+ OzlA
-
+
MOz
(1)
SI+ Oz3Z S I + 023Z T1
-+
TI + OzlA
(3)
T I + Oz38
(4)
So + O2lA
(5)
+ Oz32
(6)
+ 0232
T I + Oz3Z
4
-+
So
are spin-allowed and exothermic if both the singlet-triplet splitting AEST (process 3) and triplet energies ET (process 5 ) + M O ~ = hl[M]/(hl[M] k z ) , Measurements of 7 ~ as0a ~ exceed the excitation energy of 0 2 I A at 8000 cm-l. In terms function of dissolved oxygen concentration have been anaof the parameters a = h3/(k3 k . 4 ) and t = k b / ( k 5 h ~the ) lyzedl t o identify the operative oxygen quenching process of overall reaction q u a n t u m yield is given b y and triplet (TI) states of the sensitizer of which singlet (SI) (1) Y M O ~= + M O ~ ~ Y I+S Po2[a+ 41 YIS)~! t h e processes
O z l ~ OZ32
+
(2)
+
+
-
The Journal of Physical Chemistry, Voi. 80, No. 20, 1976
2165
Photoperoxidation of Unsaturated Organic Molecules
TABLE I: Photoperoxidation Parameters a
Sensitizer/acceptor
Tetracene
DMBAb
Rubrene
DMAC
YF YIS YM02(PO? = 0 ) YMOz(P02 = 1)
0.19 f 0.02 0.68d 0.10 0.16 0.61 f 0.07 4.0(-4) 2.4(-3) 0.14f 0.01 1.2 f 0.2 1.2(8) 10 400
0.36f 0.03 60.64f 0.03 0.066 0.10 0.66 f 0.06 1.7(-4) 1.6(-3) 0.096 f 0.01 1.0 f 0.2 2.7(7) -11 000
0.98 f 0.02 60.02 f 0.02 0.02 f 0.02 0.55 0.04f 0.04 4.0(-4) 1.0(-3) 0.29 f 0.03 1.9f 0.4 3.0(6) -9 000
0.90 f 0.04 SO.10 f 0.06 0.02f 0.03 0.50 0.04 f 0.10 4.0(-4) 1.2(-3) 0.25 f 0.03 2.0 f 0.4 1.5(6) -11 000
trrs/(a + t ) e [MI, M P, M-l @MOP
a+t
krs, s-l AEsT, cm-l
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a
Solvent benzene at 25 "C. * 9,10-Dimethyl-1,2-benzanthracene.9,lO-Dimethylanthracene.
where yfs is the sensitizer intersystem crossing yield and the probability that SI is quenched by Oz3Z, Poz = K[Ozl/(l + K [ O z ] )is available from independent measurements of the Stern-Volmer fluorescence quenching constant K . Linear plots of the data Y M O ~(PO,)provide the quotients (Table I) YMOz(P02
= O)/YM02(PO2 = 1) = t?'IS/(R
+ 6)
(11)
which are close to independent measurements of 71s (tetracenez) or to values estimated as 1 - YF (DMBA) indicating that cy 3rf(T1lA)
3rg( T , ~ z ) > 3ri( ~ ~ 3 2 3rr ) (T,~A)
h3 >> h4 h3
