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tion directly and it seems doubtful whether any selection rules hold even approximately for collisions in which the relative kinetic energy is many times the spacing between vibrational energy levels. I n conclusion, shock waves have become im-
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portant in the study of intermolecular energy exchange because they provide a convenient source of high temperatures and because they afford a means of changing temperature and flow velocity in gases at a rate which is comparable to or faster than the energy exchange processes.
INTERMOLECULAR TRANSFER OF ELECTRONIC EXCITATION BY ROBERT LIVINGSTON Department of Chemistry, University of Minnesota, Minneapolis, Minnesota Received January 81, 1067
The transfer of the energy of electronic excitation can occur between atoms or molecules, without the intermediate emission and reabsorption of radiation. Although in some cases this transfer occurs only when the molecules collide, under favorable conditions it may take place (by a process of “inductive resonance”) at separations much greater than the usual kinetic theory collision diameters. Such an exchange of excitation between like molecules leads to depolarization and self-quenching of fluorescence. Between unlike molecules, it can result in sensitized fluorescence and the concurrent quenching of the fluorescence of the sensitizer. These effects have been observed in vapors, liquid solutions and crystals. Some sensitized photochemical reactions appear to be the consequence of the transfer of electronic excitation between unlike molecules.
The transfer of the energy of electronic excitation between molecules or atoms can be demonstrated and studied experimentally by a number of methods. The present discussion is limited to those cases where the exchange of excitation is not accompanied by the transfer of an electron or an atom. This limitation excludes the consideration of inorganic phosphors, where the dominant transfer mechanism involves the excitation of an electron to a conductance band of the crystal. For convenience, the mechanisms of energy transfer may be divided into four groups. Exchange of excitation by the emission and reabsorption of a photon is commonly referred to as the “trivial process,” presumably, since its explanation does not require a new hypothesis, not because it is unimportant in nature or the laboratory. The probability of such transfer is determined by the Beer-Lambert law (involving the transition probabilities of individual molecules) and the geometry of the system. The life time of the excited state of any particular molecule is, of course, unaffected. However, the persistence of excitation in a finite system, composed of many molecules, may be increased by the “imprisonment of radiation.”’ The absorption and emission spectra are normal. A collision which is otherwise normal but involves the transfer of energy from an electronically excited molecule is called a “collision of the second kind.”2 Since the collision partners approach closely in such an act, it is possible for their energy levels to be significantly perturbed. The probability of the occurence of a collision of the second kind is the same type of function of concentration as of any bimolecular reaction involving an excited molecule. (1) P. Pringsheim, “Fluorescence and Phosphorescence,” Interscience Publishers, Inc., New York, N. Y.,1549, pp. 60-63. (2) (a) 0.Klien and S. Rosseland, 2. Physik., 4, 48 (1921); (b) J. Franck, ibid., 9,252 (1922). This term is not always used in the present restricted sense. Sometimes i t is employed so as to include (resonance) transfer of energy across distances much greater than ordinary collision diameters, and also all chemical steps which involve an excited molecule (sr atom).
It leads t o the quenching of fluorescence. Accordingly the life time of the excited fluorescent state is reduced by a factor equal to the ratio of the observed fluorescent yield t o its maximum value. If only a fraction of the energy of excitation is removed by a collision of the second kind, the excited atom may be brought into a metastable state of relatively long half life.3 Intermolecular (or interatomic) transfer of the energy of electronic excitation can occur across distances much greater than kinetic-theory collision diameters by a non-radiative process, variously called “inductive resonance,” “classical resonance” or “sensitized fluore~cence.”4-~ The probability of such exchange of excitation is a complex function of concentration, increasing more rapidly than linearly. For atomic systems, the transfer is most probable when there is exact, or nearly exact, energy resonance between the donor and acceptor; between molecules, it is greatest when there is a large overlap of the emission spectrum of the donor and the absorption spectrum of the acceptor and when both radiative transitions have high probabilities of occurrence. If only one kind of molecule is present, inductive resonance does not alter the mean life of the excited state, except at high concentrations when self-quenching occurs. In mixtures of compounds, resonance transfer of excitation may lead to a decrease in the life of the excited states if the “sink” is a short-lived non-fluorescent molecule, or to an increase, if it is a metastable molecule. In general, the absorption and emission spectra, of the several components, will not be changed. A rapid transfer of excitation in crystals can occur by the .migration of “excitons.”7 Such migra(3) Ref. 1, pp. 99-100. (4) K. Kallinann and F. London, Z. physilc. Chem., B2,207 (1928). (5) (a) T. Forster, Ann. P h y s i k , 2, 55 (1948); (b) 8. Vavilov, J . Phys. U R S S . , 7, 141 (1943). (6) T. Fdrster, “Fluoressenz Organischer Verbindungen,” Vandenhoeck and Ruprecht, Gbttingen, 1951. (7) (a) J. Frenkel, Phys. Reu., 37, 17, 1278 (1931); Phvsik. 2. Sowjettunion, 9, 158 (1936); (b) R. Peierls, Ann. Physilc, 13, 905 (1922); (c) J. Franck and E, Teller, J. Chern. Phys., 6, 861 (1938).
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tion is probable only when there is a strong coupling between the molecules which make up the crystal. A marked change in the absorption and emission spectra results. The life time of the excited state is decreased. Experimental studies of the transfer of excitation have been made with gases, liquid solutions and solids, between like as well as unlike atoms and molecules. Between like molecules, it leads to depolarization and self-quenching of fluorescence; between unlike molecules, to sensitized fluorescence and the concurrent quenching of the fluorescence of the primary absorber. Certain relatively simple photosensitized reactions are almost surely the result of such energy transfer, and more complex photochemical and spectroscopic phenomena can be explained simply in terms of this process. Transfer of Excitation between Atoms.8-Over thirty years ago, the existence of sensitized fluorescence was demonstrated clearly and unequivocally by Cario and Franck.9 They illuminated a mixture of Hg and T1 vapors with light (A 2537 A.) from a Hg-resonance lamp. This vapor emitted, in addition to the Hg-resonance line, a number of T1 arc lines. I n the absence of Hg, the T1 vapor neither absorbed nor emitted radiation. While the detailed analysis of this case is somewhat complicated, an analogous study of the Hg-Na appears to be straightforward.10 When a mixture of Hg and Na vapors is illuminated with Hg-resonance radiation (A 2537 A.1, the distribution of the emitis the state to ted Na lines indicates that 92S~/, which the Na atoms are primarily excited. Since (92S1/,)Na and (63P1)Hg have nearly the same energy of excitation, very little electronic energy is converted into kinetic energy of translation by the process
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ponent is absorbed only by the odd isotopes, this one wave length is re-emitted as resonance radiation. The addition of He (or N2), a t a pressure less than 1 mm., results in the emission of all of the components which can arise from the odd isotopes. This effect is similar to the conversion of 63P1 to 63P0Hg by collisions with N2; but since the energy difference between the hyperfine levels is so small, it can be taken up as kinetic energy of translation. If the Hg vapor pressure is increased to 0.1 mm., the components of X 2537 A. due to the even as well as to the odd isotopes appear in the resonance spectrum. This is a case of sensitized fluorescence where the excitation energies of the acceptor and the donor are almost identical and, as a r e ~ u l t , ~ the exchange of excitation is very efficient at distances as great as 50 A. The depolarization of fluorescence, excited by linearly or circularly polarized light, can result from resonance exchange of excitation between atoms in different magnetic quantum states.8 In weak magnetic fields, the energy resonance between such states is practically perfect, and depolarization is noticeable even a t very low pressures (2 X mm. for Na resonance radiation).13 Transfer of Electronic Energy from an Atom to a Diatomic Molecule.-Energy of electronic excitation can be transferred, by a collision of the second kind, from an atom to a diatomic molecule. In the Hg-sensitized dissociation of H214unstable HgH molecules are formed, and it is not clear15which of the following processes is dominant. (6’Pi)Hg
++ Hz +(6’So)Hg + 2H HgH + H
The Xe-sensitized dissociation of Hz appears to be simpler.le The excitation energy corresponding to the first resonance line (A 1470 8.)of Xe is ap(G3P1)Hg + (32S1/~)Na +(6lSo)Hg + (92SI/2)Na proximately 8.5 e.v. Since this is about 4.0 e.v. Molecular nitrogen quenches the fluorescence of Hg greater than the thermochemical energy of disvapor, converting (63P1) Hg to the metastable sociation of Hz, it might appear that this process, (63P0)Hg and accepting the difference in energy in involving the conversion of so much electronic to its vibrational degree of freedom. Since the ex- kinetic energy, would be most improbable. How8 to 10 e.v. citation energy of ( 6 3 P ~Hg ) is within 0.03 e.v. of ever, there is a repulsive state (322,+) that of (72S~/,)Na, the following exchange should above the ground state (‘2,+)of the Hz molecule, The transition occur efficiently. (G3Po)Hg (32S1/2)Na+(6’So)Hg (72Sl/2)Na X,* (‘&+)HZ +Xe (*2Z,f)Hz The fact that the addition of N2 to a mixture of Hg violates neither the Franck-Condon principle nor and Na vapors quenches the Na line corresponding the spin conservation rule and should occur with to the transitions 9s + 3P and simultaneously a good probability. Within the time of a single greatly intensifies the line due to 7 s + 3P, strongly vibration, the (32u+) Hz will break up into two supports the general and detailed explanation of ground-state hydrogen atoms with very high these results. Similar results were obtained with kinetic energy. Hg and Inll and, less ccnvincingly, with other sysSensitized Fluorescence in Molecular Crystals.Probably the most impressive examples of sensiA striking special case of sensitized fluorescenceI2 sitized fluorescence are those which can be observed is the sensitization of the even by the odd isotopes with molecular lattic crystals, such as anthracene of Hg. If Hg vapor a t a low pressure (
