10TH SPIERS MEMORIAL LECTURE TRANSFER MECHANISMS OF ELECTRONIC EXCITATION BY TH. FORSTER Laboratory of Physical Chemistry, Technische Hochschule, Stuttgart Received 14th April, 1959 Let me say at the beginning that I feel extremely honoured by the invitation to deliver the 10th Spiers Memorial Lecture. Though I never had the pleasure of meeting Mr. Spiers, whose death occurred before I began my own studies, I am well aware of his contributions to the development of your Society. There is no doubt that he has determined essentially the character of these Discussions by which the Faraday Society has become famous throughout the world. When I was informed that your Society planned to devote this Discussion to the subject of Energy Transfer, I felt fascinated. Twelve years ago, when I began to occupy myself with this subject, it was a very neglected one.In the meantime, many people have become interested in it, and its applications range from radiation physics to biology. While the Discussion isconcerned with energy transfer of any possible mechan- ism, I should like to restrict this Introductory Lecture to a more specific mechanism of energy transfer. This is the transfer of electronic excitation energy between otherwise well-separated atomic or molecular electronic systems. The most simple case is that of two distinct atoms in the empty space where electronic excitation of one atom may result in excitation of the other one. Similar cases are of atoms or molecules in solution or in crystalline environment, provided this environment does not allow electronic transfer from one to the other.Furthermore, we should exclude the trivial case of an excitation transfer that consists in the emission of one quantum of light by the first atom or molecule followed by re-absorption by the second one. This mechanism can be under- stood easily by the familiar laws of optics and, is, therefore, of not much interest, even if it may contribute to transfer in special cases. It is only the non-radiative transfer of excitation occurring during the short lifetimes of excited electronic systems which we shall consider here. Although this mechanism is a very specific one, it seems to be of general occur- rence. It is responsible for the phenomenon of sensitized fluorescence -of atoms and molecules which has been observed in the vapour phase as well as in solution and in the crystalline state.It leads to the so-called concentration depolarizution of fluorescence and sometimes contributes to concentration quenching. Moreover, it plays an essential part in the properties of organic scintillators and of certain types of inorganic crystalline phosphors. Finally, it contributes to reactions observed in radiation chemistry and in the photochemistry of biological systems, and it is considered today even in connection with other biological processes. The first observation of energy transfer was made by Cario and Franck (1922) in their classical experiments on sensitized fluorescence of atoms in the vapour phase. A mixture of mercury and thallium vapour, when irradiated with the light of the mercury resonance line, shows the emission spectra of both atoms.Since thallium atoms do not absorb the exciting light, they can get excited only indirectly by an excitation transfer from mercury atoms. A transfer by re- absorption is impossible here. Therefore, this transfer must be a non-radiative one with a mercury atom as the donor or sensitizer and the thallium atom as the 78 TENTH SPIERS MEMORIAL LECTURE acceptor. Unfortunately, in this case it cannot be decided whether the transfer occurs between distant atoms or during a normal collision or even in a labile molecule formed as an intermediate. This decision, however, was possible in similar cases, as in the mercury-sensitized fluorescence of sodium and in the mutual sensitization of the fluorescence of different mercury isotopes.In these cases, the transfer occurs over distances very much larger than those in normal collisional separations. A more complete discussion of these and similar cases has recently been given by Livingston.2 Similar observations of sensitized fluorescence have been made with molecular vapours. The experiments of Terenin and Karyakin 3 with naphthalene as sensitizer and acridine as acceptor may be mentioned as an example. Another case will be reported later by Dr. Stevens.4 More numerous are the investigations on sensitized fluorescence in solution, some examples of which are presented in table 1. Only such cases are considered here, where both sensitizer and acceptor are at low concentrations in an inert solvent. Without exception, the transfer takes place from a sensitizer absorbing at lower wavelengths to an acceptor absorbing at higher ones, because a transfer in the opposite direction would be impossible for energetic reasons.As we shall see later, a moderate red shift is favourable to this kind of transfer. TABLE 1 .-SENSITIZED FLUORESCENCE IN SOLUTIONS sensitizer acceptor remarks ref. phenosafranine tetrabromresorufin qualitatively 5 trypaflavine rhodamine-B only sensitizer 6, 7 benzo flavine rhodamine-B sensitizer life-time 8 chlorophyll-b chlorophyll-a both components 9 1 -chloroanthracene perylene quantitatively 10, 11, 12 quenching quantitatively and many other systems measured The first observations of sensitized fluorescence in solution, though of a more qualitative nature, were made very early by J.Perrin and Choucroun.5 In our own first experiments with trypaflavine and rhodamine,69 7 only the quenching in sensitizer fluorescence resulting from excitation transfer could be followed quanti- tatively. Nevertheless, transfer over a separation of 70 8, was established and the non-trivial kind of this transfer recognized by quenching experiments which indicated a decrease in lifetime of the excited sensitizer. Similar results were obtained by Galanin and Levshin 8 for a large number of similar systems, where the decrease in sensitizer lifetime was measured directly. The first measurements where the intensities of both fluorescence components could be followed quanti- tatively were those of Watson and Livingston 9 with both chlorophylls.Of special importance are the experiments of Bowen, Brocklehurst and Livingston 10-12 with 1 -chloroanthracene and perylene where any possible trivial mechanism was excluded with special care. Some of their results are reported in fig. 1. With a constant ratio of both components, sensitizer and acceptor absorb constant fractions of the exciting light. The increase in perylene fluorescence with increasing concentration must, therefore, result from energy transfer by chloroanthracene. At the same concentrations, a decrease in chloroanthracene fluorescence due to this transfer is observed. Furthermore, the total quantum yield of fluorescence increases with concentration. This results from the fact that chloroanthracene by itself has low fluorescence efficiency due to internal quenching.This internal quenching is diminished when the lifetime of the excited chloroanthracene molecule is decreased by excitation transfer to perylene. A trivial re-absorption process would not shorten the lifetime of the sensitizer and, therefore, not increase the total fluorescence yield.T. FORSTER 9 Further experiments have shown that in this case the transfer occurs not over collisional distances but over the mean intermolecular distances of sensitizer and acceptor, corresponding to a concentration of 10-3 to 10-2M. This is demon- strated by the fact that sensitization occurs with similar half-value concentrations in solution of very different viscosities and even in organic glasses at low tem- perature. The possibility of the formation of a complex between sensitizer and acceptor molecules was excluded by the additivity of the absorption spectra and the different dependence on concentration to be expected in this case.It must be concluded, therefore, that excitation transfer of a non-trivial nature occurs over the mean distances between statistically distributed molecules which are about 40A in this case. X 3 o--------”----o I 12 14x I FIG. 1 .-Fluorescence of mixed solutions in benzene of 1 -chloroanthracene and perylene in 5 : 1 molar ratio (taken from Bowen and Brocklehurst 10). Table 2 summarizes some qualitative features of this kind of long-range transfer and of some more or less trivial mechanisms. The non-trivial transfer differs from re-absorption transfer by its independence of the volume of the solution, by the decrease in sensitizer fluorescence lifetime, and by the invariability of the TABLE 2.-cHARACTERISTIC PROPERTIES OF TRANSFER MECHANISMS non-trivial transfer reabsorption complexing encounter dependence on none increase none none volume dependence on none none none decrease viscosity sensitizer decreased unchanged unchanged decreased lifetime sensitizer fluor- unchanged changed unchanged unchanged escence spectrum absorption unchanged unchanged changed unchanged spectra sensitizer fluorescence spectrum.It differs from short-distance collisional transfer by its independence of solvent viscosity and from transfer within a molecular complex by the constancy of absorption spectra and the decrease in sensitizer fluorescence lifetime.In most cases, some of these different properties allow a decision between trivial and non-trivial transfer mechanisms. Further dis- criminations may be made by quantitative studies of these properties.10 TENTH SPIERS MEMORIAL LECTURE Let us now consider the mechanism of this long-range excitation transfer in more detail. It may be astonishing that such a transfer is possible at all during the short lifetimes of excited molecules which usually are of the order of 10-8 sec. One should consider, however, that this is actually a long time for electronic systems, where orbital motions occur during 10-15 sec. Therefore, the comparatively weak interaction between distant atoms or molecules may be sufficient for ex- citation transfer, provided some kind of resonance condition is fulfilled.This was recognized already by J. Perrin 13~14 who formulated a first theory of excitation transfer between molecules in solution based on the principles of classical physics. This theory, as well as its later quantum-mechanical refinement by F. Perrin 15 predicted transfer distances of more than 100 8, but was insufficient quantitatively. The simpler case of energy transfer between atoms has been treated by Kallmann and London 16 who arrived at similar transfer distances. FIG. 2.-Simplified energy level diagram of sensitizer (S) and - . . ... - - - - acceptor (A). radiative transitions non-radiative transitions transfer transitions. I coupled transitions We shall here consider the molecular case only, where the superposition of electronic and nuclear vibrational levels is essential.Fig. 2 represents the sim- plified energy level diagram of both molecules. During the absorption process, the sensitizer is excited to one higher vibrational level of its first electronic ex- citation state. From there it is converted to lower vibrational levels of the same electronic state by obtaining thermal equilibrium with the surrounding medium. In solution or in other condensed systems, this thermal relaxation takes place during 10-13-10-12 sec. It may be assumed for simplicity that the temperature is low enough for the excited molecule to remain in its lowest vibrational level for the rest of its lifetime of about 10-8sec duration. After this time-interval it returns to the ground state by spontaneous radiative or non-radiative processes.Let us now suppose that the energy difference for one of these possible de- activating processes in the sensitizer molecule corresponds exactly to that for a possible absorption transition in a nearby acceptor molecule. Then, with sufficient energetic coupling between these molecules, both processes may occur simul- taneously, resulting in a transfer of excitation from sensitizer to acceptor. With the broad spectra of polyatomic molecules in solution, there is always sufficient coincidence between sensitizer and acceptor transitions, if the absorption spectrum of the acceptor overlaps the fluorescence spectrum of the sensitizer. Therefore, a moderate red shift of the acceptor spectra towards those of the sensitizer is favourable to this kind of transfer.With regard to this condition, this kind of energy transfer is often called " resonance transfer " or " transfer by inductive resonance ". This peculiar kind of resonance condition results from thermal relaxation together with the Franck-Condon principle which act here essentially in the same manner as in producing the common Stokes shift.T. F ~ R S T E R 11 It may be somewhat confusing that this condition is similar to that for re- absorption of the sensitizer fluorescence by the acceptor. Nevertheless, the mechanism of the non-trivial process is an entirely different one, leading to transfer before the emission of sensitizer fluorescence takes place. Also it needs some amount of mutual coupling between the electronic systems of both molecules and can, therefore, take place only over limited distances.This coupling is strongest if the corresponding optical transitions in both molecules are allowed for electric dipole radiation. Then these transitions are coupled not only to the radiation field but also to each other. Naturally, the interaction energy is of a dipole-dipole nature, depending on an inverse propor- tionality to the third power of the molecular distance. The probability of energy transfer is then proportional to the square of this interaction energy and decreases, therefore, with the sixth power of the distance.17 A quantitative treatment leads to the following expression for the rate constant of the transfer process : Here v is the wave number, E(V) the molar decadic extinction coefficient, f ( v ) the spectral distribution of fluorescence (measured in quanta and normalized to unity on a wave number scale), N Avogadro's number and T; the intrinsic or radiative lifetime of the excited sensitizer.n is the refractive index of the solvent, R the mutual distance between both molecules and K an orientation factor. More specifically, this is where $SA is the angle between the transition moment vectors of both molecules while 4s and #JA are the angles between these respective vectors and the direction S --f A. K = cos 4SA 3 cos 4s . cos#A The average value for a random directional distribution is 19 ~2 = 4. Eqn. (1) may be rewritten more conveniently as Here 7s is the actual mean lifetime of the excited sensitizer. It is connected to and to the quantum yield v i of the sensitizer fluorescence (without transfer) by 0 0 r s = T~ .rs . (3) Obviously Ro is the critical transfer distance for which excitation transfer and spontaneous deactivation of the sensitizer are of equal probability. From eqn. (1) to (3) one gets This is valid for any thermal equilibrium distribution over the vibrational levels of both molecules, provided the spectra are taken at the corresponding tem- perature. The transfer probability is independent of the exciting wavelength even if higher electronic states of the sensitizer are involved. As is to be expected, Ro increases with the quantum yield of the sensitizer and with the overlap of the spectra. In typical cases, Ro-values from 50 to 100 A have been calculated. These formulae become invalid when energy transfer occurs before thermal equilibrium is established.This would be expected for gases under low pressure where thermal relaxation is slow, but also in liquid or solid medium when, due to strong interaction, the transfer is very rapid. In these cases, the transfer may take place from the vibrational level obtained by excitation directly and depend, therefore, on the exciting wavelength. This stands in some analogy to the phenomenon of resonance fluorescence of molecular vapours where the emission spectra show such a dependence.12 TENTH SPIERS MEMORIAL LECTURE Under extremely strong interaction, the transfer may even be faster than molecular vibrations. In this case the absorption spectra are no longer additive and it would be diacult to consider the excitation even temporarily localized at one molecule or the other.This is realized in some cases of molecular aggregation, preferably of alike molecules,20-22 and will not be considered further. Let us return again to energy transfer under conditions of thermal equilibrium in the vibrational levels. Even in this case, eqn. (1) to (4) are not generally valid because they refer to dipole-dipole interaction only. Therefore, eqn. (1) is rather the first term of an expansion in powers of R-1. Other terms must be considered when the transfer occurs over small distances of when dipole-dipole interaction is weak because of forbidden optical transitions in sensitizer or acceptor. Such forbiddeness may result from molecular symmetry or from spin inter- combination (e.g.for transitions between singlet ground states and triplet excited states). In both cases, it must be considered first that transitions of this kind are never strictly forbidden. Symmetry-forbidden transitions become partially allowed in combination with certain molecular vibrations, intercombination transitions by mixing of states with different multiplicities, especially in the presence of atoms with higher nuclear charges. Such transitions occur, therefore, in absorption as well as in emission. Naturally, the extinction is low and the emission delayed, being a typical phosphorescence in the case of intercombination transitions. Eqn. (1) to (4) should represent, at least approximately, even then the inverse sixth power term of our expansion.If the optical transition is forbidden in the sensitizer but allowed in the acceptor, eqn. (4) still predicts large transfer distances in as far as the fluorescence (or phos- phorescence) yield 7s is high. This results from the fact that the slower transfer rate calculated from eqn. (1) is compensated by a longer lifetime of the excited sensitizer, in as far as deactivation does not occur mainly by non-radiative pro- cesses. According to these considerations, long-range excitation transfer should be possible under suitable conditions even from the triplet state of a sensitizer to the singlet state of an acceptor. On the other hand, a forbidden transition on the acceptor side results in low EA(V) so that eqn. (4) predicts only short transfer distance. Actually, this may be somewhat larger due to higher-order terms.For a symmetry-forbidden transition where dipole-dipole interaction is small, the transfer might be determined by dipole-quadrupole interaction and show an inverse 8th power dependence. As Dexter 23 has demonstrated, the transfer occurs over distances larger than those of molecular contact even in that case. Finally, at small distances, exchange terms in the interaction operator must be considered.23 These are essential if the transition is intercombination forbidden in the acceptor so that neither dipole-dipole nor higher multipole interaction leads to strong coupling. Electron-exchange interaction allows transfer only under conservation of the total multiplicity of the system, e.g. between tr;plet states of both sensitizer and acceptor.It needs some overlap of the electronic clouds of both molecules and occurs, therefore, at shorter distances only. Since resonance transfer does not need strong interaction, the transfer distances should be some- what larger than contact separations. So even then transfer may occur between molecules otherwise considered as independent of each other. The occurrence of energy transfer between triplet states has been demonstrated by Terenin and Ermolaev 24-27 with solid solutions of benzophenone or benz- aldehyde as sensitizers and substituted naphthalenes as acceptors. The transfer distances are about 14A which is much larger than calculated from eqn. (4) for dipole-dipole interaction in these cases. As already stated by the authors, an exchange mechanism as described before should be considered here.It is quite natural that excitation transfer may not only occur between different molecules but also between separate electronic systems of the same molecule. Weissman,28 Sevchenko and co-workers,29~ 30 and also Crosby and Kasha 31 haveT . FORSTER 13 observed that in aromatic rare-earth chelate complexes, the rare-earth luminescence is sensitized by absorption in the aromatic component. Weber 32 and Teale 33 have reported similar observations with molecules containing two independent aromatic systems. Phosphorescence experiments demonstrating intramolecular excitation transfer between triplet levels have been performed by Ermolaev and Terenin.27 Returning to excitation transfer between different molecules we must adapt our treatment of the elementary process between two molecules to the conditions in solution where molecules are distributed at random. Let us suppose that energy transfer occurs only from sensitizer to acceptor molecules and that the inverse sixth power dependence of pure dipole-dipole interaction holds.We shall assume further that Brownian translational movement of all molecules is slow enough so that each individual transfer process may be considered at constant distance. On the other hand, Brownian molecular rotation will be considered to be much faster than transfer, so that the average value of the orientation factor ~2 = 5 may be used. These conditions are realized approximately in solutions of moderate viscosity.In this case a straightforward calculation 78 349 35 leads to the following expression for the quantum yield TA of the acceptor fluorescence : with I - !&>) , vrr c 2 co x = - - (+(x) : error function). 3000 co = ~ 4rrNRJ ' Here vZaX is the maximum quantum yield of the acceptor fluorescence obtained either by direct excitation or by complete transfer. The acceptor concentration is expressed by the dimensionless quantity x. The reference concentration co which may be called a critical transfer concentration corresponds to an average of one acceptor molecule in a sphere of the radius Ro. The expression (5) is represented in fig. 3. Another expression which considers transfer to the nearest acceptor molecule only has been used by Dexter.23 In solutions of higher viscosity as well as in cases of a very rapid transfer, the assumption of rapid Brownian rotation is not valid. In these cases the transfer must be calculated for all individual orientations and averaged afterwards.An approximate calculation based on a largely simplified model 36 leads to somewhat different function, represented also in fig. 3. For the inverse 8th power law of dipole-quadrupole coupling, Dexter 23 has calculated the dependence on con- centration, assuming transfer to the nearest molecule only. Experimental data have often been represented by simpler formulae. With the assumption of a sharp transfer distance with instantaneous transfer for shorter and no transfer for longer distances, the simple exponential formula results. By a formal kinetic treatment of excitation transfer concurring with the spontaneous deactivation of the sensitizer one arrives at an equation of the Stern- Volmer type : These different functions are compared to each other in fig.4 with the parameters a and /? so adjusted as to give a half-value concentration equal to that of eqn. (5). These values are a = 1.42 and /3 = 2.05. Identical slopes at lower concentrations would be obtained with a = = 1.57 while the " theoretical " value of a would be 1.00. It should be mentioned here that, notwithstanding the inverse sixth14 TENTH SPIERS MEMORIAL LECTURE I 10 CICO FIG. 3.-Relative intensity of sensitizer fluorescence against acceptor concentration for dipole-dipole coupling. left curve : right curve : molecules with fixed orientations.fast rotating molecules ; 1 : 2 : 3 : X 0.1 I 10 100 cico FIG. 4.-Relative intensity of sensitizer fluorescence against acceptor concentration. 1. calculated for dipole-dipole coupling and fast rotating molecules, 2. approximated by exponential formula eqn. (7), 3. approximated by Stern-Volmer formula, eqn. (8).T. F ~ R S T E R 15 power dependence on distance, eqn. (6) as well as the other formula predict a linear increase of sensitization at low concentrations. An expression for the decrease in sensitizer lifetime with increasing acceptor concentration has been derived by Galanin 34 for dipole-dipole coupling. In correspondence with experimental data,6* 8 it predicts that the decrease in lifetime is markedly slower than that of the intensity of sensitizer fluorescence.As was stated before, the conditions for excitation transfer are optimal if the electronic level of the acceptor is somewhat lower than that of the sensitizer. Therefore, the conditions are not optimal for transfer between alike molecules. They are most unfavourable at very low temperatures where only the 0,O transition is common to absorption and fluorescence. But they are more favourable at higher temperatures where some vibrational levels are thermally excited and, correspond- ingly, absorption and fluorescence spectra of the same molecule overlap to some extent. Fig. 5 tries to illustrate these different conditions at low and higher temperatures. Apart from less optimal overlap, the conditions for excitation transfer are the same for alike molecules, and eqn.(1)-(4) may be applied for dipole-dipole coupling. I 1 I I I D I T=O I I I I l l I I I l l I I I I I T>O I I I I I I I I l l I I I l l I I I l l I I t l l I I I 1 I I I J FIG. 5.-Simplified energy level diagram for transfer between alike molecules (notations as in fig. 2). Naturally, excitation transfer between alike molecules can occur in repeated steps. So the excitation may migrate from the absorbing molecule over a con- siderable number of other ones before deactivation occurs by fluorescence or some other process. Though this kind of transfer cannot be recognized from fluor- escence spectra, it may be observed by the decrease of fluorescence polarization with increasing concentration. This so-called " concentration depolarization " which was discovered by Gaviola and Pringsheim 37 (1924) results from an ex- citation transfer to molecules with different orientations from the absorbing one.With typical dyes, it has been observed at concentrations of about 10-3 M where the mean distances are 70 A. The possibility of excitation migration complicates all experiments on sensitized fluorescence under higher sensitizer concentrations. Extreme cases are those, where the sensitizer itself is used as the solvent in which the acceptor is present at minor concentration. One of the best known systems is that of crystalline an- thracene containing traces of naphthacene as an impurity. In such crystals the green fluorescence of naphthacene is observed 389 39 even at molar ratios lower than 10-5, where the distance from an average anthracene molecule to the nearest naphthacene molecule is about lOOA.This seems somewhat large for a single- step transfer of excitation. The other possibility is that of migration transfer where the excitation travels from one anthracene molecule to another in some kind of Brownian movement until it reaches the neighbourhood of one of the few naphthacene molecules present.16 TENTH SPIERS MEMORIAL LECTURE A recent observation by Lyons and White 40 is in favour of this second mechan- ism. These authors found that with a molar ratio of 10-5 no fluorescence sen- sitization occurs at 4°K. Such a suppression of excitation transfer would be expected for migration transfer between alike molecules which, as was stated before, should essentially depend on thermal vibrations (cp.fig. 5). A similar case has been reported by Kanda and Sponer 41 for benzaldehyde in solid toluene where sensitization of phoshorescence is suppressed at low temperature. Other arguments favouring migration-transfer in such crystalline systems have been given by Schmillen 42 from life-time measurements. On the other hand, Bar and Weinreb 45 have shown that a liquid solution of anthracene in toluene (ca. 2 x 10-3 M) still shows fluorescence sensitization when most of the toluene is replaced by an inert solvent. This is in favour of a single- step transfer. It seems natural that in such systems the prevalence of one or the other mechanism would largely depend on the acceptor concentration and on the properties of both molecules.Similar considerations may apply to the observa- tions of sensitized fluorescence in natural pigments by Duysens 44 and 0thers.45-47 We have confined our interest here mainly to the phenomena of sensitized fluorescence and phosphorescence where excitation is created by absorption of a quantum of light and finally results in emission of another quantum. But our considerations are also valid for other mechanisms of primary excitation or of final deactivation. Another possibility of excitation is that by high-energy radi- ation with x-, fl-, or y-rays. In these cases, excitation occurs either directly or indirectly via primary ionizations. The excitation, after having been converted to the lowest excited state in the usual way, will undergo similar transfer processes under suitable conditions.The usefulness of organic scintillators depends essen- tially on this possibility as investigations of Kallman and Furst,'@ Swank and Buck,499 50 Hartwick,Sl Knau 52 and others have demonstrated. Prof. Kallman 48 and Dr. Birks 53 will discuss this problem in more detail. Excitation produced by light or by high-energy radiation often results in chemical processes instead of luminescence. This leads to photochemical or radiochemical reactions. In these cases, too, production and final disappearance of excitation may be separated by one or more steps of excitation transfer. In the usual photochemistry of gases and solutions, the conditions for this are not favourable because the absorbing substances are commonly used in low con- centrations.However, other conditions prevail in radiochemical reactions for which only absorbing solvents exist. As Prof. Burton 54 and Prof. Dole 55 will later deal with this topic, I shall not further discuss it here. In biological systems the conditions for excitation transfer are very favourable because nature often prefers high local concentrations of absorbing matter. Prof. Rabinowitch 56 and Prof. Lumry 57 will tell us how far this possibility seems actually to be used in photosynthesis. As Prof. Szent-Gyorgyi 58 has emphasized, nature may use this possibility even in ordinary biochemical reactions. In order to arrive at a better understanding of excitation transfer and of its role in molecular energy exchange, further knowledge of the many competing processes like internal conversion and deactivation is necessary.These problems will be discussed by Dr. Bowen,59 Prof. Porter60 and Prof. Livingston61 and Dr. Weller 62 in their respective contributions. Furthermore, we should not forget that excitation transfer is by no means the only possible mechanism of energy transfer. Electron transfer as well as proton transfer must also be taken into consideration, and it is very fortunate that Prof. Terenin's 63 paper is devoted to these aspects of our general subject. 1 Cario and Franck, Z. Physik, 1923, 17, 202. 2 Livingston, J. Physic Chern., 1957, 61, 860. 3 Terenin and Karyakin, Isvest. Akad. Nauk. S.S.S.R., ser. Fiz., 1951, 15, 550. 4 Stevens. this Discussion.T. FORSTER 17 5 Perrin J. and Choucroun, C.R. hebd.Se'ances Acad. Sci., 1929, 189, 1213. 6 Forster, 2. Elektrochem., 1949, 53, 93. 7 Forster, 2. Naturforsch., 1949, 4 4 321. 8 Galanin and Levshin, J. exp. th. Fiz., 1951, 21, 121. 9 Watson and Livingston, J . Chem. Physics, 1950, 18, 802. 10 Bowen and Brocklehurst, Trans. Faruduy SOC., 1953, 49, 1131. 11 Bowen and Livingston, J. Amer. Chem. SOC., 1954,76, 6300. 12 Bowen and Brocklehurst, Trans. Favaduy SOC., 1955, 51, 774. 13 Perrin, J., 2me conseil de Chimie SoZvuy (Gauthier and Villar, Paris, 1925), p. 322. 14 Perrin, J., C.R. hebd. Skances Acad. Sci., 1927, 184, 1097. 15 Perrin, F., Ann. Chim. Physique, 1932, 17, 283. 16 Kallmann and London, 2. physik Chem. B, 1928,2, 207. 17 Forster, Naturwiss., 1946, 33, 166. 18 Forster, Ann. Physik, 1948, 2, 55. 19 Forster, Fluoreszenz orgunischer Verbindungen (Vandenhoeck and Ruprecht, 20 ref.(19), p. 254. 21 Lavorel, J. Physic. Chem., 1957, 16, 1600. 22 Forster and Kasper, Z. physik Chem., 1954, 1, 275. 23 Dexter, J. Chem. Physics, 1953, 21, 836. 24 Terenin and Ermolaev, Dokludy Akad. Nuuk, 1952, 85, 547. 25 Ermolaev, Doklady Akad. Nauk, 1955, 120, 925. 26 Terenin and Ermolaev, Trans. Faruday SOC., 1956, 52, 1042. 27 Ermolaev and Terenin, 8me rkunion annuelle de la Socie'te' de Chimie Physique (Paris, 28 Weissman, J. Chem. Physics, 1942, 10, 214. 29 Sevchenko and Morachevskii, Isvest. Akad. Nuuk S.S.S.R. ser. Fiz., 1921, 15, 628. 30 Sevchenko and Trofimov, J. exp. th. Fiz., 1951, 21, 220. 31 Crosby and Kasha, Spectrochim. Acta, 1958, 10, 377. 32 Weber, Nature, 1957, 180, 1409. 33 Weber and Teale, Trans. Faruduy SOC., 1958, 54, 640. 34 Galanin, J. exp. th. Fiz., 1955, 28, 485. 35 Antonoe-Romanoescu and Galanin, Akad. Nuuk S.S.S.R., 1957, 3, 389. 36 In this model the spherically symmetrical distributions of sensitizer and acceptor molecules have been approximated by tetrahedral distributions of different mutual orientations. Gottingen, 1951), p. 85. 1958). 37 Gaviola and Pringsheim, 2. Physik, 1924, 24, 24. 38 Bowen, J. Chem. Physics, 1945, 13, 306. 39 Bowen, Mikiewicz and Smith, Proc. Physic. SOC. A, 1949, 62, 26. 40 Lyons and White, J. Chem. Physics, 1958, 29, 223. 41 Kanda and Sponer, J. Chem. Physics, 1958, 28, 798. 42 Schmillen in Halbleiter und Phosphore, Berichte des internationulen Colloquiums in 43 Bar and Weinreb, J. Chem. Physics, 1958, 29, 1412. 44 Duysens, Nature, 1951, 168, 548. 45 French and Young, J. Gen. Physiol., 1952, 35, 387. 46 Bannister, Arch. Biochem. Biophys., 1954, 49, 222. 47 Brody, J. Chim. Physique, 1958, 55, 942. 48 Brown, Furst and Kallman, this Discussion, and further references quoted there. 49 Buck and Swank, Physic. Rev., 1952, 87, 191. 50 Swank and Buck, Physic. Rev., 1953, 91, 927. 51 Hartwick, J. Chem. Physics, 1957, 26, 323, 1463. 52 Knau, Z. Naturforsch., 1957, 12a, 881. 53 Birks, this Discussion. 55 Dole and Williams, this Discussion. 56 Rabinowitch and Brody, this Discussion. 57 Lumry, Mayne and Spikes, this Discussion. 5 8 Szent-Gyorgyi, J. Chim. Physique, 1958,55, 916. 59 Bowen, this Discussion. 60 Porter and Wright, this Discussion. 62 Weller, this Discussion. Gurn?isch, 1956 (Vieweg and Sohn Braunschweig, 1958), p. 445. 54 Burton, this Discussion. 61 Livingston, this Discussion. 63 Terenin, this Discussion.