I. MODES OF ENERGY TRANSFER FROM EXCITED AND UNSTABLE IONIZED STATES INTRAMOLECULAR AND INTERMOLECULAR ENERGY CON- VERSION INVOLVING CHANGE OF MULTIPLlCITY BY GEORGE PORTER AND M. R. WRIGHT Dept. of Chemistry, The University, Sheffield 10 Received 16th January, 1959 Radiationless transitions between states of different multiplicity are considered with special reference to conversion between triplet and singlet energy levels. Rates of this conversion have been measured for naphthalene and anthracene and rate constants are given for the fist-order intramolecular process, the second-order process involving two triplet molecules and also of quenching by other species, particularly paramagnetic ions. It is established that the first-order rate is strongly viscosity dependent and this is attrib- uted to a structural difference between the two states. Conversion from the triplet state is induced by paramagnetic molecules and ions but the quenching rate constant shows no correlation with magnetic susceptibility. A general theory of " paramagnetic quenching " is proposed in which the function of the quenching molecule is one of overall spin conservation.All processes, including energy transfer, which involve a change in total electron spin momentum have a low probability compared with the corresponding processes in which spin momentum is conserved. Nevertheless it is now quite clear that conversion between electronic states of different multiplicity is often of primary importance in changes which involve excited molecules. The reason for these apparently conflicting statements lies in the high probability of radiation- less conversion between electronic states which may, in the absence of spin and other restrictions, have a rate constant exceeding 1011 sec-1.If a change of multip- licity is involved the rate may be reduced by a factor of 104 but is still high enough to compete effectively with other modes of deactivation of the excited state. Since the ground state of most molecules is a singlet, the multiplet of most interest is the triplet and, in particular, the triplet state of lowest energy. This has the following properties. (i) It is the lowest excited electronic state of the molecule. (ii) It has a lifetime, even in fluid solvents, which is typically of the order of 10-4 sec, i.e. several orders of magnitude greater than that of the excited singlet states.(iii) Its chemical behaviour is usually characteristic of a biradical. The triplet state is now frequently postulated as an intermediate in energy transfer processes and in chemical and biochemical change but only in a very few cases has its role been established. Most work on the triplet state has been concerned with the radiative process of phosphorescence in rigid media and only recently have data become available concerning its properties in the more common fluid solvents. By means of the flash photolysis technique it is possible to observe the triplet state directly by means of its absorption spectrum and to follow its concentration as a function of time after irradiation. In this way, fairly extensive data have now been 18a b c d e FIG.1 .-Oscillographic records of the decay of triplet naphthalene in (a) n-hexane, (6) water, (c) ethylene glycol, ( d ) paraffin r ] = 33 cp, ( e ) paraffin 3 = 167 cp. Time units : msec. [To face page 19.G . PORTER AND M. R. WRIGHT 19 accumulated on the triplet states of a variety of molecules. Here, two fundamental processes involving change of multiplicity will be discussed. The first is the intra- molecular process of radiationless conversion between triplet and singlet states and the second is the deactivation of the triplet state by other molecules, par- ticularly those which themselves have multiplicities higher than singlet. The experimental findings on each of these processes are somewhat unusual, and have not received a satisfactory explanation.RESULTS The data to be presented were obtained by a combination of flash photolysis and spectrophotometric recording. The apparatus has already been briefly described 1 and further experimental details will be given elsewhere. In this paper we are concerned mainly with first-order decay constants of the triplet state in various solvents and the constants of quenching by paramagnetic substances. r time, psec FIG. 2.-First-order plots of the decay of triplet naphthalene in water and in the presence of various ions. Concentration of Zn2+ and Ga3+ was 5 x 10-4 M and of all other ions 2.5 x 1 0 - 4 ~ . 0 No ion ; A [Cu(CN)z]- ; Ga3+ ; 0 Zn2+ ; x Ce3f; A Nd3+ ; Gd3+. The type of record obtained, as well as the two principal effects with which we are concerned, are illustrated by fig.1 and fig. 2. The former shows oscillographic records of the absorption by the triplet state of naphthalene in solvents of varying viscosity, as a function of time. Fig. 2 shows first-order decay plots derived from this type of trace which illustrate the effect of ionic solutes on the lifetime of triplet naphthalene in water. The first-order decay curves are not exactly linear and it is found that there is a small contribution from second-order (triplet-triplet) quenching which becomes quite consider- able at high triplet concentrations. The method of analysis of these curves which is used to derive first- and second-order decay constants has been described.1 As a result of the second-order contribution the first-order rate constants in earlier work were consistently higher than those reported here.In the flash photographic work of Porter and Windsor,2.3 rather high triplet concentrations were measured and owing to the lower accuracy of the method, separation of first- and second-order processes was not possible. Our rate constants are also slightly lower than those of Livingston and Tanner4 who used the present method but found no second-order contribution.20 C H A N G E OF MULTIPLICITY The occurrence of a second-order process immediately suggested a possible explanation of the viscosity dependence of triplet decay and it was therefore necessary to study the effect of viscosity on first- and second-order rates separately. The second-order rate was viscosity dependent as expected but the data in tables 1 and 2 show that the rate of first-order decay is also largely controlled by solvent viscosity.There are evidently some constitutional effects as well, which is not surprising since macroscopic viscosity is only approximately related to diffusion coefficients and to effects on a molecular scale. At the higher viscosities, when the encounter rate is truly diffusion controlled, the rate constant in related solvents, e.g. paraffins 1 and 2, is approximately inversely proportional to viscosity. The limiting values in rigid solvents refer to the radiationless process and are derived from phosphorescence lifetimes. TABLE 1 .-FIRST-ORDER (kl) AND SECOND-ORDER (k2) DECAY CONSTANTS OF TRIPLET NAPHTHALENE IN VARIOUS SOLVENTS AT 2 0 ° C .SECOND-ORDER CONSTANTS ARE BASED ON THE LIMITING VALUE E = 10,oOo AND C IS A CONSTANT WHICH IS LESS THAN UNITY solvent viscosity (cp) k1(sec- 1) ck2 (1. mole-1 sec-1) n-hexane 0.3 1.2 x 104 2.1 x 109 water 1-1 7.5 x 103 4.1 x 109 ethylene glycol 21.1 9.7 x 102 2-2 x 108 paraffin 1 33.0 1.5 x 103 3.9 x 108 paraffin 2 167 3.1 x 102 8.0 x 107 rigid glass very high < 1 < 106 TABLE 2.-FIRST-ORDER (kl) AND SECOND-ORDER (k2) DECAY CONSTANTS OF TRIPLET ANTHRACENE IN VARIOUS SOLVENTS AT 20°C k2 (1. mole-1 sec-1) solvent viscosity (cp) kl (sec-1) n-hexane 0.3 1.3 x 103 1.6 x 1010 tetrahydrofurane 0.5 2.3 x 103 1.0 x 1010 ethylene glycol 21.1 2.8 X 102 8.8 x 108 paraffin 1 33.0 5.6 X 102 1.2 x 109 rigid glass very high < 10 < 106 paraffin 2 167 1.6 X 102 2.5 x 10s The rate constants of quenching of triplet naphthalene by various ions, determined in the same way, are given in table 3.Of the ions investigated, diamagnetic ions have no effect (or at high concentrations possibly a small negative effect) whilst paramagnetic ions all quench the triplet state, though the efficiency varies over a wide range and is apparently quite unrelated to the magnetic susceptibility, provided the ion is paramagnetic. TABLE 3.-RATE CONSTANTS OF QUENCHING OF TRIPLET NAPHTHALENE BY IONS IN WATER AND ETHYLENE GLYCOL ko(1. mole-1 sec-1 x 10-7) ion K+ Zn2+ Ga3 + CU(CN)~- cu2+ Ni2 + co2+ Cr3 + Fe2+ Fe3 + Mn2+ Nd3 + Gd3 + in water 0.00 & 001 0 0 f 0.2 0 0 f 0.1 0 0 f 0.1 7-5 f 0.7 2.3 rt 0.4 5.0 &- 0 6 6.9 f 0.6 2.9 i 0.4 2.8 rt 0.4 - - - in ethylene glycol 0 f 0.1 0 f 0.2 0 rt 0.2 7.3 0.7 2.4 i 0.3 4-4 rt 0.4 3.8 f 0.3 1.6 f 0.2 0.04 k 0.005 0.007 f 0.002 - - - no.of unpaired electrons 0 0 0 0 1 2 3 3 4 5 5 3 7 paramagnetic susceptibility (Bohr magnetons) diamagnetic diamagnetic diamagnetic diamagnetic 1-93 3-21 5.01 3-82 5-30 5.85 5.8 1 3.60 8.01G . PORTER A N D M . R . WRIGHT 21 Preliminary data indicate that the same is true of anthracene triplet quenching, but that the quenching rate constants of a particular ion depend both on the triplet molecule and on the solvent. The only other paramagnetic molecules, for which quenching constants are available, are given in table 4. The rate constants of quenching by 0 2 and NO are taken from the results of Porter and Windsor.3 The effects are certainly general to other molecules, as well as anthracene, but rate constants have not yet been accurately determined.TABLE 4.-RATE CONSTANTS OF QUENCHING OF TRIPLET ANTHRACENE BY PARAMAGNETIC MOLECULES IN HEXANE SOLUTION quenching molecule no. of unpaired electrons k (1. rno1e-l sec-l) Q 0 2 2 4 x 109 NO 1 4 x 109 triplet anthracene 2 1.6 x 1010 DISCUSSION INTRAMOLECULAR RADIATIONLESS CONVERSION BETWEEN TRIPLET AND SINGLET STATES It is not always appreciated that the appearance of phosphorescence in a wide variety of molecules and its absence in fluid solvents is largely unexplained. In molecules such as the aromatic hydrocarbons, radiationless crossing from the upper singlet state S1 to the triplet TI occurs with a rate constant which is typically of the order of 108 sec-1 in rigid media, whilst the apparently similar conversion from TI to the ground state SO is not observed in rigid media and must have a rate less than 10-1 sec-1 in benzene and other molecules with similar radiative triplet lifetimes.If the rates of the two radiationless conversions were of com- parable magnitude, no phosphorescence would be observed, and this is the reason for the absence of phosphorescence in ordinary solutions and gases. Studies of the kinetics of triplet state decay in different solvents have shown that a number of bimolecular processes may occur, e.g. quenching by oxygen or a second triplet, but that, in the absence of such quenchers, the triplet state has a natural lifetime which is generally much less than the radiative life and which must be attributed to the process of radiationless conversion to the ground state.2 The second-order decay would of course be diffusion controlled in view of its high rate and a viscosity dependence is to be expected and is, in fact, found.The results in table 1 and 2 establish that the first-order decay, which is the predominant process at low intensities, is also a function of solvent viscosity. I t is clearly unprofitable to consider the triplet decay as a process which is rate-determined by energy transfer to the solvent, particularly since the rate attains its maximum value in the gas phase.5 It has also been established that the first- order process being considered occurs without the intervention of any molecules other than those of the solvent.We must therefore conclude that the rate con- stants measured are those of the intramolecular radiationless conversion process from the triplet state T1 to the ground state So. Energy transfer to solvent occurs after crossing and is not rate-determining. The outstanding problem is why the radiationless crossing TI-& should be viscosity dependent to such an extent that it is totally inhibited in rigid media. The radiationless transition probability between two states i and j is propor- tional to the square of the matrix element Wg of the perturbation function W which in turn is given by where # j and $j are the eigenfunctions of the two states i and j . The eigenfunctions can be separated into a product of electronic-rotational and vibrational functions which are independent to a first approximation and the electronic function can22 CHANGE OF MULTIPLICITY again be separated into a product of spin and co-ordinate functions.The spin functions of two electronic states of different multiplicity are orthogonal so that, in so far as the separation of the functions is a good approximation, the transition probability is zero, but it becomes finite in the presence of spin-orbit interaction. The electronic eigenfunctions will be modified only slightly by the solvent and the dependence of transition probability on viscosity cannot be explained in any general way by a difference in the electronic terms of the matrix element. The position with regard to rotation is less clear. The selection rule for perturbations in isolated diatomic molecules is that both states must have the same total angular momentum, i.e.AJ= 0. In solution, free rotation is inhibited but the con- servation of angular momentum is still at least as probable as in the isolated molecule. Further theoretical work on this point would be helpful but explana- lions of the viscosity effect in terms of inhibited rotation are made very unlikely by the experimental fact that predissociations and internal conversions are ob- served, even in rigid media, with high probability, e.g. crossings from state S1 to TI. A general selection rule based on conservation of total angular momentum would apply to all such transitions and it is probable that rotation can be neglected in discussing the transition probability as it can in discussing the Franck-Condon principle for radiative transitions.6 The part of the matrix element depending on the vibrational eigenfunction is W; = J flWV$'dr where Wv is the part of the interaction energy depending on nuclear co-ordinates and $7 and $7 are the vibrational eigenfunctions.The transition probability therefore depends on the overlap of vibrational eigenfunctions and the Franck- Condon principle is valid just as in the more familiar case of radiative transitions in diatomic molecules. A high transition probability will be found only when, classically, the system can pass from one state to the other without a large alter- ation of position or momentum. In a polyatomic molecule and in a viscous medium this restriction may be very important if the equilibrium configuration of the molecule in the two states is different.Recent work on simple molecules has shown that such is often the case.7 The structures of molecules in their triplet states, and particularly aromatic ones in which we are most interested, are not known and evidence obtained from the weak absorption spectra or diffuse emission spectra in rigid media is at present uncertain. We believe, however, that the low radiationless transition probability from the triplet to the ground state and its viscosity dependence in a wide variety of molecules must be interpreted as showing that the triplet state has an equilibrium nuclear configuration which is considerably different from that of the ground state and that the configurational change which is necessary to attain a position with low reverse-crossing probability is inhibited by clamping of the distorted structure by the viscous or rigid solvent.There are theoretical reasons for believing that the structure of the triplet state even of a molecule as simple as benzene, may differ significantly from that of the ground state. Because of the Pauli principle the probability distributions of two electrons in different orbitals with respect to each other are different in singlet and triplet states. For two electrons in a circle, Dickens and Linnett 8 have shown that $s#s* = (3.r>2(1 + cos [(m - 4 ( 4 2 - 41)11, #T#T* = (inP(1 - cos [(m - nX+2 - 41>I>, where 4s and $T are the wave functions of the singlet and triplet systems, m and n axe the quantum numbers of the two orbitals, and $2 - $1 is the angular separation of the electrons.The products $$* are proportional to the probability that the electrons have the angular separation $2 - $1. It is seen that, for the singletG . PORTER AND M. R . WRIGHT 23 state, the probability is a maximum when the electrons are coincident whilst in the triplet state the electrons have zero probability of being in the same place. Electron repulsion will change the situation quantitatively but the difference remains as is shown by the large splitting of singlet and triplet levels in aromatic molecules. In benzene the instantaneous electron distributions in the three states of interest may be schematically represented as follows : singlet So singlet S1 triplet TI The most stable nuclear configuration of a single Dewar form of TI would probably be folded about the vertical axis, a structure suggested on quite different grounds by Lewis and Kasha.9 Experimental evidence, which may indicate a different equilibrium configur- ation in the triplet and singlet ground states comes from the results of Craig, Hollas and King,lo following work of Evans.11 It is found that the radiative life- time of the triplet state of benzene calculated from the integrated absorption coefficients is greater than 700 sec, earlier work being incorrect owing to the presence of oxygen. On the other hand, the measured lifetime from phosphor- escence decay is 7 sec.These findings would be in accordance with our con- clusion that transition from the triplet state occurs to a ground state molecule with a configuration very different from the equilibrium one.If the structural difference between triplet and ground singlet states of benzene is accepted there is little difficulty in extending the arguments to most other aromatic molecules. It is interesting to note that structural isomeric differences between these states were originally proposed as an explanation of the phos- phorescent state 12 but were later discarded in favour of the triplet state theory. In our view both spin and structural restrictions are necessary to the appearance of phosphorescence of long duration. INTERMOLECULAR PROCESSES OF TRIPLET STATE DEACTIVATION All energy transfer processes from excited states must involve other molecules but we have seen that, when only an inert solvent is present, energy transfer is not itself the rate-determining process.In the presence of certain molecules, however, the rate of deactivation of the triplet state is greatly enhanced. There are undoubtedly several mechanisms of quenching by which this may occur, some of which involve electron transfer, hydrogen atom transfer or other chemical reactions. Since most chemical reactions result in the formation of an addition compound or of two doublet radicals so that spin conservation is always possible, we shall not be concerned with such processes here. A quenching molecule may induce a change of multiplicity in a second molecule without chemical change in at least three ways : (i) It may induce perturbations, and particularly increase spin-orbit coupling, so that the spin selection rule is partially broken down.(ii) A transfer of electronic energy may take place, spin momentum being conserved by excitation of the quencher to a state of different multiplicity. (iii) Conservation of total spin momentum may be made possible during the encounter without, necessarily, any multiplicity change of, or energy transfer to, the quenching molecule.24 CHANGE OF MULTIPLICITY We shall be concerned mainly with the third of these processes which gives a new interpretation of so-called " paramagnetic quenching ". Since the quench- ing molecule is unchanged it will be appropriate to describe the process as " cata- lyzed spin conservation ". Perturbations resulting in a breakdown of the spin selection rule may be brought about, in principle, by heavy atoms or by a magnetic field including the magnetic field of a neighbouring molecule.No effect which can be attributed to heavy atom catalysis of radiationless conversion between triplet and singlet states has been found. Table 3 shows that diamagnetic ions such as Zn2+ and Ga3+ have no measurable quenching effect on the triplet state of naphthalene in water. Livingston and Tanner4 found no marked effect of carbon disulphide or of substituted benzenes, e.g. bromobenzene, on the triplet state lifetime of anthracene. Furthermore approximate measurements of triplet yields in solution indicate that heavy atoms in the solvent have no measurable effect on the Sl-Tl crossing either. On the other hand, paramagnetic molecules have a considerable effect on triplet state lifetimes and this has been attributed by some workers to magnetic perturbations, and breakdown of the spin selection rule.The data given in table 3 makes this interpretation very unlikely. Not only is there a wide variation in efficiency but in a related group, such as the ions of the first transition series, there is no correlation whatever with magnetic susceptibility except that all para- magnetic ions quench to some extent and diamagnetic ions have no effect. Quenching by magnetic perturbation would be expected to be a general and rather unspecific effect of all paramagnetic molecules which was closely related to mag- netic susceptibility as it is in the process of nuclear spin change in the para-ortho hydrogen conversion induced by these same ions.ENERGY TRANSFER WITH SPIN CONSERVATION In a collisional process it is only necessary that the total spin momentum of the whole system be conserved rather than that of each separate partner. One process by which this may be achieved is by " spin transfer " from the excited molecule A to the quencher Q. This is automatically accompanied by energy transfer since a change of electronic state of both partners is involved. If the quenching molecule Q is a singlet this is the only process (apart from chemical reaction) by which a change in multiplicity of A can be induced whilst conserving spin momentum. In the case of a triplet state of A the process becomes A* (triplet) + Q (singlet) -+ A (singlet) + Q* (triplet).It is therefore a necessary condition for this type of quenching that the quencher Q shall have a triplet level lower than that of A. Such cases have been found by Terenin and Ermolaev 13 for transfer from the triplet state of benzophenone and a number of similar molecules to naphthalene and its derivatives. The rate con- stants are very low in rigid solvents and are not yet known in ordinary solutions. CATALYZED SPIN CONSERVATION All paramagnetic molecules which we have investigated quench the triplet state to some extent and we have given reasons why this is not to be attributed to the magnetic field alone. In many of the cases given in table 3, chemical re- action, particularly electron transfer, might reasonably be expected but it is highly improbable that this is the genera! explanation of the quenching action of para- magnetic molecules.There is no correlation with the oxidation-reduction poten- tials of the quenchers and, since both oxidizing and reducing ions are effective, it would be necessary to postulate formation of both the negative and positive radical ions of the hydrocarbons. Most of the paramagnetic molecules studied have low-lying energy levels and quenching might therefore be interpreted simply as an electronic-energy transferG . PORTER AND M . R. WRIGHT 25 process. This may indeed contribute to the quenching mechanism when the energy levels are favourably situated. But there are many difficulties in accepting this as the general mechanism of " paramagnetic quenching ". It is improbable that nitric oxide has a quartet level lower than the triplet level of anthracene and no correlation with the excited levels of the paramagnetic molecules and their quenching efficiency can be found.An alternative explanation of the quenching effect of paramagnetic molecules on the triplet state will now be given. The collisional process A (triplet) + Q (singlet) -+ A (singlet) + Q (singlet) is forbidden by spin conservation rules.14 On the other hand the process is allowed if the multiplicity of Q is higher than singlet. More generally, in the process A* (S = X) + Q(S = y ) -+ A(S = x - 1) + Q(S = y ) , where S is the spin quantum number and x and y are integral or half integral numbers with x > 1, the change is allowed by spin conservation rules for the overall system provided y > 0.We immediately obtain a common property of paramagnetic molecules which distinguishes them from singlet molecules. The otherwise forbidden spin change of A becomes allowed in the presence of a paramagnetic Q without necessarily involving energy transfer or other change in Q. Molecules of solvent must of course be present to remove the excess energy of A after the transition, just as occurs in the intramolecular conversion. This quenching mechanism is quite distinct from magnetic perturbation effects and indeed its rate will be shown to be independent of magnetic susceptibility provided the quencher is not a singlet. It is useful to consider the process in two steps : (i) the formation of the collision complex AQ, and (ii) the dissociation of AQ to A and Q.The quenching rate constant will depend on the following factors : (i) spin-spin coupling between A and Q in the complex AQ, (ii) the lifetime of AQ, (iii) a spin statistical factor. Consider first the spin statistical factor. If x < y , the possible spin quantum numbers of the complex AQ are y + x , y + x - - 1 , . . . y - x , and the total statistical weight g is given by Of these possible states the only ones which can give the required products with spin x - 1 and y are y + x - I , . . . y - x + l , the statistical weight of these states being g q = 2 ( y + x - l ) + 1 + . . . 2 ( y - x + 1 ) + 1 . The probability that AQ will have a spin momentum which correlates with the required products is g,/g, the general expressions for which are and26 CHANGE OF MULTIPLICITY Values of gq/g for values of x and y of interest are given in table 5.X TABLE 5.-sTATISTICAL FACTORS FOR THE PROCESS Y If we confine ourselves to the process given, where the multiplicity of Q is unchanged and that of A must decrease, the only possibilities for the dissociation of AQ are to the products or to the original reactants unless x > 2. Two possi- bilities may now be distinguished. CASE 1 The complex AQ is stable with respect to dissociation to the original reactants. In this case the probability of dissociation to products with altered spin is unity and the statistical probability of the overall process is given directly by gq/g. CASE 2 The energy of AQ with respect to original reactants is small compared with kT.In this case the probability of formation of products with changed spin will be given by probability that AQ will dissociate to A(S = x - 1) = statistical weight of A(S = x - 1) sum of statistical weights of all allowed states of A - -5 gt and values of gp/gt are given in table 5. The overall probability of conversion of A in this case is given by the product gqgp/ggt in the final column. In the last two rows, referring to quintet quenching, the factor gp/gt = 3 does not include the small probability of singlet formation. The interesting conclusion emerges from the figures of table 5 that, on purely statistical grounds, all paramagnetic molecules have an equal probability of in- ducing the transition between a triplet and a singlet state. Differences between quenching rate constants will therefore arise as a result of the other two factors mentioned above and, since these are not related in any direct way to the magnetic susceptibility, the experimental finding that molecules with unpaired electrons are quenchers but that their efficiency is not related to the multiplicity, becomes comprehensible.The large difference in quenching rates between different molecules is now to be considered in terms of spin-spin interaction and the lifetime of the collision complex. These two factors are closely related since both depend on the overlap of the orbitals of the unpaired electrons in A and Q. If there is no interaction between the spin moments, each molecule must individually conserve spin mo- mentum and no change will occur.If interaction is small quenching will occur with a probability less than that calculated on purely statistical grounds.G. PORTER AND M. R. WRIGHT 27 The rates in tables 3 and 4 fall broadly into three groups : GROUP 1 GROUP 2 GROUP 3 On passing from group 1 to group 3 the orbitals of the unpaired electrons be- come increasingly deep-seated as we go from p to d to f electrons. The d electrons of the transition metal ions overlap readily with orbitals of other molecules but they form complexes in aqueous solution which shields the unpaired electrons and reduces overlap with electrons of the triplet. The f electrons of the rare earths are known from many different lines of evidence. e.g. magnetic suscepti- bility theory15 to have relatively little interaction with the solvent or other environment.The three examples of group 1 on the other hand are typical radicals or bi- radicals and the collision complex formed with a triplet state probably has a stability of at least several kcal. Spin-spin interaction will therefore be strong and the complex may have a considerable life. In view of the strong interaction, case 1 is almost certainly applicable here and the statistical factor is therefore g,/g. The product of the reciprocal of this factor and the quenching rate constant is in close agreement with the calculated diffusion-controlled encounter rate. It is to be expected that the radiationless transition probability is increased in the presence of an efficient paramagnetic quencher only by an amount correspond- ing to the difference between a spin forbidden and a spin allowed transition, i.e. by a factor of about 104. Now the lifetime of triplet anthracene in n-hexane in the absence of quenchers is 10-3 sec so that its lifetime when the spin restriction is removed should be about 10-7 sec. The average lifetime of the collision com- plex between triplet anthracene and oxygen, nitric oxide or a second triplet should therefore also be about lO-7sec which is much longer than the duration of an encounter not involving chemical interaction and is in accordance with kinetic studies of anthracene photosensitized oxidation.16 k m 1010 1. mole-1 sec-1 k w 5 x 107 1. mole-1 sec-1 k m 2 x 105 1. mole-1 sec-1 0 2 , NO, aromatic triplet metal ions of first transition series ions of lanthanide rare earths. We are grateful to the Royal Society for the loan of a monochromator and to the Geophysics research directorate, Air Force Cambridge research centre of A.R.D.C., USAF through its European Office for support of part of this work. 1 Porter and Wright, M. R., J. Chim. Physique, 1958, 55, 705. 2 Porter and Windsor, Faraday SOC. Discussions, 1954, 17, 178. 3 Porter and Windsor, Proc. Roy. SOC. A , 1958, 245, 238. 4 Livingston and Tanner, Trans. Faraday SOC., 1958, 54, 765. 5 Porter and Wright, F. J., Trans. Faraday SOC., 1955, 51, 1205. 6 Herzberg, Spectra of diatoinic molecules (Van Nostrand, 1950). 7 Ramsay, Ann. N. Y. Acad. Sci., 1957, 67, 485. 8 Dickens and Linnett, Quart. Rev., 1957, 11, 291. 9 Lewis and Kasha, J . Amer. Chem. SOC., 1944, 66, 2100. 10 Craig, Hollas and King, J. Chem. Physics, 1958, 29, 976. 11 Evans, J . Chem. SOC., 1957, 1351, 3885. 12 Lewis, Lipkin and Magel, J. Amer. Chenz. SOC., 1941, 63, 3005. 13 Terenin and Ermolaev, Trans. Faraday SOC., 1956, 52, 1042. 14 Wigner, Gottinger Nachrichten, 1927, 375. 15 van Vleck, Theory of Electric and Magnetic Susceptibilities (Oxford, 1932). 16 Livingston, J. Chim. Physique, 1958, 55, 887.