Pulse Radiolysis in an Applied
Magnetic Field
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Pulse Radiolysis in an Applied Magnetic Field. The Time Dependence of the Magnetic Field Enhancement of the Fluorescence from Solutions of Fluorene in Squalane F. P. Sargent," B. Brocklehurst, R. S. Dixon, E. M. Gardy, V. J. Lopata, and Ajlt Slngh Research Chemistry Branch, Atomic Energy of Canada Limited, Whiteshell Nuclear Research Establlshment, Plna wa, Manitoba, Canada ROE 1LO (Received October 12, 1976) Publication costs assisted by Atomic Energy of Canada Limited
The effect of a magnetic field on the light emission from squalane solutions of fluorene, pulse irradiated at the center of a large electromagnet, is described. The fluarescenceintensity following pulse radiolysis was found to be 40-50% higher in an applied field of 0.3 T (3000 G) and the triplet yield showed a small decrease. The enhancement of the singlet emission is attributed to an increase in the fraction of geminate solute ion recombinations leading t~ excited singlet fluorene. The magnetic field effect was time dependent,being undetectable during the pulse and reaching a maximum value after about 100 ns. These observations are compared with the theory of Brocklehurst which describes the singlet to triplet conversion of geminate solute ion pairs quantitatively in terms of the electron-nuclear hyperfine interactions in the radical ions. After correction for the large in-pulse fluorescence and its decay, satisfactory agreement between experiment and theory WF obtained. The results emphasize the importance of ion recombination in the generation of excited states in radiolysis and confirm the role of the electron-nuclear spin interaction in determining the ratio of ginglet and triplet yields.
Introduction Radiolysis of solutions of aromatic hydrocarbons in alkanes produces both singlet and triplet excited states of the solute.'-4 There are several possible mechanisms for the formation of these excited states but in the time range to lo4 s after the initial irradiation event, and at high concentrations of the solute, M, ion recombination of the solute ions M+ and M- is the major process. In these solutions, the ion recombination is almost entirely gemina;te5and the cecombination time for each solute pair of ions, M+-M-, depends on its separation. Since the electron spins of the ion pair were initially correlated (or paired) in the solvent molecule prior to ionbation and since 4 the processes from the solvent ionization through to the charge scavenging are considered to be Coulqmbic, these will not effect the spin. Thus the initial spin state of M+-M- pairs prior to ion recombination will be singlet. However, since triplet states are known to be formed in the solutions, there must be soinng process which leads to the loss of correlation af the spins in some M+-M- pairs prior to recombination. What is the process and what 'is its rate? This was first discussed by Brocklehurst' in terms of spin relaxation where conversion of a singlet state of the ion pair, M+-M-, to a triplet state would occur at rates comparable to the conventional spin-spin relaxation time for the solute ions. The spin relaxation times for aromatic ions have not been studied in detail but the line widths of their electron spin resonance spectra suggest they aTe of the order of microseconds.' Brocklehurst concluded that if the ion recombination time could be slowed down by the use of a viscous solvent, the triplet yield would increase and become magnetic field dependent. The field lowers the ra;te of loss of spin correlation in the geminate ion pair prior to recombhatian and therefore sustains a higher singlet yield. In a preliminary r e ~ o r twe , ~ showed that the sjriglet yield of fluorene in the viscous solvent squalane was indped enhanced when irradigted in a magnetic field. However, this field effect, which was small during the pulse, developed on ti panosecond time scaie rather tlian in the microseconds required' for conventional spip rglaxation. A'new interpretation8,' involving the electron-
nuclear hyperfine interactions in the two parts of the geminate ion pair, M+-M-, was developed. This rnechanism gives a much faster loss of correlation. Further experiments were carried out to determine more precisely the actual time scale of the development of the magnetic field effect. It will be shown that the new mechanism is consistent with these results. Experimental Section The object of these experiments was to determine the time dependence of the effect of an applied magnetic field on the yield of excited states formed from ion recombination. This was achieved by performing pulse radiolysis of solutions at the center of a large magnet. The experihental setup is shown schematically in Figure 1. The electron beam flight tube from a nominally 4-MeV electron accelerator was extended axially into a Varian fr-3400 ESR electromagnet. The hole through the yoke and pole pieces was 25 mm diameter and that through the pole cap 9 mm. The electron beam flight tube was terminated by a thin (0.03 mm) brass windaw and the magnet pole caps were fitted with a shim assembly to compensate for tbe field inhomogeneity caused by the holes. The pylse radiolysis cell was placed at the center of the magnet 1mm from the beam window. Salutions of fluorene in squalane were deaerated by vigorous bubbling with 99.999% argon and then passed ipto the radiolysis cell by mews of an all-glass flow system. Transient light emission during and following pulse radiolysis with 5,15, or 50 ns pulses of &MeV electrons was detected spectrophotometrically using a 1P28 photowultiplier tube and a Hewlett-Packard 183A oscilloscope with a camera using Polaroid film. Preliminary egperiv e n t s were performed with a remotely controlled monochromator and the photomultiplier tube in the target rwm. However, the long length of cable to the oscilloscope made the response of the system too slow and also the electron beam pulse caused a dark transient. The response time was improved and the dark transient eliminated by taking the light out of the target room by means of front-surfaced mirrors (Figure 1). The overall response The Journal of Physical Chemistry, Vol. 81, No. 9 , 1977
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Sargent et al.
ELECTROMAGNET
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Flgure 1. (a) The experimental setup for performing pulse radiolysis at the center of an electromagnet. (b) Extension of the Van de Graaff accelerator flight tube into the magnet: (1) cubic 1 mL quartz cell; (2) field compensation device; (3) magnet pole cap. Fluorescence was collected by means of a lens placed between the cell and the mirrors.
time, including the pulse shape, was determined to be 2-3 ns by analyzing the Cerenkov emission from pulse irradiated squalane. To compensate for the decrease in sensitivity due to light losses, the monochromator was replaced with a Corning 7-59 (5850) band pass filter, once the identity of the fluorescence was established from its spectrum. Absorption measurements were done using the monochromator and a 450-W xenon lamp operated either in a pulsed mode for short-lived transients or continuously with optical feed-back stabilization for longer-lived species. Since the magnetic field can change the focusing of the electron beam and thereby change the dose delivered to the cell, dosimetry was performed at the center of the magnet with the field on and off. A set of electron beam transport parameters, such as quadrupole focusing, electrostatic and magnetic steering, was found for which the field had least effect on the dose delivered to the aqueous potassium thiocyanate. With these optimum settings, applied fields of 0.1 T (1000 G ) or less had no effect and at 0.3 T (3000 G ) the dose only varied by about 5%. This conclusion was supported by other tests, involving the use of a phosphorescent dye painted on the accelerator window and a remotely operated TV camera in the target room. Typical doses were of the order of 1 krad. After our preliminary communication,' it was found that the electromagnet has a residual field of 2-3 mT (20-30 G) which can have a small effect on the fluorescence yield from pulse-irradiated solutions. In the experiments reported here, the residual field was cancelled by passing a small reverse current through the electromagnet's coils. The minimum field was determined by means of a small The Journal of Physical Chemistry, Vol. 81, No. 9 , 1977
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Figure 2. Fluorescence spectrum observed from pulse-irradiated solutions of fluorene (0.001 mol/dm3) in squalane taken at end of 15-ns pulse (uncorrected for spectral response of the detection system).
Figure 3. (a) Time profile of fluorene (0.01 mol/dm3)fluorescence during and after pulse radiolysis of a squalane solution: (1) no field; (2) magnetic field on (0.3 T). (b) As in (a) but on expanded scales.
Hall-effect type gaussmeter with the probe taped to the magnet pole face. Minimum field was defined as the point at which the output from the gaussmeter changed sign as the reverse current was increased. However, since the direction of the field in the magnet gap was not coincident with the earth's magnetic field vector, the sample experienced fields of the order of 0.05 mT (0.5 G). The solvent squalane was purified by passing through activated silica gel columns until it gave a constant UV cutoff. Fluorene was zone refined prior to use.
Results When solutions of fluorene in squalane were pulse irradiated, the fluorescence spectrum during and after the pulse were the same (Figure 2) and very similar to that observed photochemically in cyclohexane." Similar spectra were observed for pulse irradiated 0,001 and 0.01 mol/dm3 solutions. Therefore, we have assigned the emission observed in our system to the radiative decay of fluorene excited singlet states. The time profile of this fluorescence is shown in Figure 3. If the fluorescence intensity following the pulse is plotted on a logarithmic scale (Figure 4), it is clearly not an exponential decay and, as the insert in Figure 4 shows, it is slower than the decay lifetime (7)of 10 ns reported for the photochemical system.1° This is because singlets continue to be produced from solute ion recombination after the pulse at a rate that is slow compared to T-'. Also shown in Figure 3 is the effect of applying a magnetic field of 0.3 T (3000 G ) on the fluorescence. The in-pulse emission is not changed appreciably but the intensity of the "tail" is increased. This
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Pulse Radiolysis in an Applied Magnetic Field 60 [
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Figure 6. The time dependence of the magnetic field enhancement of the fluorescence intenslty from pulse-irradiated solutions of fluorene (0.01 mol/dm3) in squalane: A, 15-ns pulse; H, 50-ns pulse.
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Figure 4. Decay of the fluorescence from pulse-irradiated solution of fluorene (0.01 mol/dm3) in squalane using a band pass filter. The insert permits comparison of the observed fluorescence decay with that which would be observed from fluorene singlets decaying with their natural fluorescence lifetime of 10 ns.
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Figure 5. The effect of magnetic field on the percentage increase in fluorescence intensity at 200 ns after the pulse for 0.01 moi/dm3 solution of fluorene in squalane using a band pass filter.
increase is a function of the magnitude of the magnetic field. It rises rapidly in the 0-0.05 T (500 G) range and then appears to approach a plateau in the 0.1-0.2 T (1000-2000 G) range (Figure 5). If the increase in fluorescence intensity following pulse radiolysis, induced by the magnetic field, is due to an increase in the fraction of ion recombinations giving singlets, there should be a corresponding decrease in the triplet yield. This will be more difficult to detect since the triplet lifetime is long, 750 ps, compared to the time of observation after the pulse, 100 ns. The triplet absorption represents the sum of all triplets formed from all previous ion recombinations, from singlets via intersystem crossing, and from any other processes. Thus, the triplet absorption does not represent solely those events occurring at the time of observation. Another problem is that the absorption 375 nm) overlaps the anion by the fluorene triplet (A,, absorption (Ama 390 nm). Absorption spectra of irradiated solutions of fluorene 100 ns after the pulse showed no definite peak at 375 nm, but the magnetic field effects were quite different at 375 and 390 nm. The absorption at 390 nm showed a small increase with increasing field whereas
that at 375 nm gave a small decrease. The small increase of the absorption at 390 nm was probably due to a focusing effect of the magnetic field on the electron beam leading to an increase in the dose rate in this particular experiment. Thus the small decrease at 370 nm, although not conclusive, is evidence for a small decrease in the triplet yield. The magnetic field enhancement of the fluorescence from pulse-irradiated solutions of fluorene is shown as a function of time after the pulse in Figure 6. More than one pulse width was used and time zero was taken as the end of the pulse. The magnetic field effect is very small or zero during the pulse but rapidly reaches an apparent plateau after about 100 ns. There is some suggestion that the enhancement decreases at longer times but the experimental uncertainty is high since the fluorescence intensity is low at long times. Results similar to the above were found for cyclohexane solutions but the maximum field enhancement was less. In benzene solutions, there was no detectable magnetic field enhancement of the fluorescence intensity.
Discussion of Results In pulse-irradiated solutions of aromatic hydrocarbons in alkanes, most of the ion recombination is geminate5and is an important source of solute excited This is shown schematically in reactions 1-6 where S is a solvent S
+ S+ t e -
(11
S'
+ M - M'
(2)
t S
e-+ M+M-
(3)
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(4)
M* S' t M- M* t S M' + M-+ M* t M e-
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-f
(5) (6)
molecule, M the solute, and M* may be either a singlet or triplet excited state. At high concentrations of M, reaction 6 is the major ion recombination reaction occurring following pulse radiolysis. Reaction 1,the charge separation and thermalization, is very rapid. Although the rates of the charge-scavenging reactions 2 and 3 have not been measured for fluorene in squalane, they are known to be very rapid for other aromatic solutes in alkanes''-l8 and even in the more viscous liquid squalane, they should be complete in 1ns for concentrated solution^.^^^ The lack of any growth in the absorption or emission following the pulse supports this contention. Since the rate of formation of the geminate solute cation-anion pairs is rapid, the initial spin state is assumed to be preserved. All the The Journal of Physical Chemistry, Vol. 81, No. 9 , 1977
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Sargent et al.
collision processes involved in reactions 2-6 leading to the geminate ion pair, M+---M-,are Coulombic in nature and therefore do fiat change the spin. Furthermore, since the electrons involved were originally paired in a solvent molecule, this spin state will be singlet for the isolated solute ion pairs. However, if a spur contains two or more ion pairs formed close together, cross recombination is possible;lg also a secondary electron may reverse its spih by exciting a solvent molecule to a triplet state." In both cases triplet ion pairs are formed but they can convert to singlet by the reverse of the process described below. If I I I either of these processes is important, the magnetic field 0 100 200 3CO effect would be reduced in magnitude. Time ,IS Jsoiated geminate recombination can lead only to singlet ex+d states unless some process changes the relative spin Figure 7. The time dependence of the magnetic field enhanced orientation. Previously, it was thought that electron fluorescence intensity froin pulse-irradiated fluorene (0.01 mol/dm3) in squalane, when corrected for the in-pulse field independent conspin-spin would be such a process6and that tributions: A, 15-11s pulse; ,. 50-11s pulse. under certain circumstances the yield of singlets would be enhanced in a magnetic field. However, typical relaxation prevented by the Zeeman splittifig. Therefore anly the times for anions and cations of aromatic hydrocarbons can interconversion between two states, S = 0, @, = 0 and S be deduced from the lihe widths of their ESR spectra, and = 1, p,= 0, need be considered and the limiting value far are in the microsecond range. Clearly, this is much too the probability of singlet formation from geminilte ion slow to account for the effects reported here. For example, recombination will be one-half (1/2). In the dbsence of the field effect in Figure 6 develops on a nanosecond time a maknetic field, all four states, S = 1, m, = 0, f l and S scale. In a further development of the t h e ~ r y ,Brock~,~ = 0,rn, = 0, are degenerate, allowing electron spin flips lehurst suggested a different process involving the between the S = 0, m,= 0 ana the S, = 1; ma= hl states. teractiop of the unpaired electron of the solute ion with This leads tb,a much faster cohversibn of singlet ihtn triplet the nuclear magnetic moments of the protons present. ion pairs. The limiting probability for siriglkt formation This is the'ihteraction which gives ESR spectra their from ion recombiriation in zero field is one %quarter(1/4). chdracteristic hyperfine structure20-22and has been used In quantum mechanical terms, the state of the M+---Mto explain the population inversion effects known as CIDNP and CIDEP in NMR and ESR, re~pectively.~~ geminate ion pair is nonstationary but it is a time dependent combination of the usual stationary states of the Both the earlier6 and the more theories predict unpaired electrons. an enhancement of the solute excited singlet yield in the The time dependence of the magnetic field enhancement presence of arl applied field. Therefore the magnetic field of the yield of singlet excited states has been computed effects described here, Figures 3, 5 and 6, support either for typical aromatic solute moleculess~9to be kqro at zero theory but the observed time dependence is inconsistent time ahd to reach a maximum in about 25 ns and then to with the spih-spin relaxation mechanism. The qualitative decrease slowly over a period of microseconds because of features of the revised theory will now be described. The spin relaxation. Although Figure 6 shows this gmeral form, detailed mathematical basis has been reported the field effect seems to take about 100 ns to reach its Consider first a geminate ion pair formed by reactions maximum rather than the 25 ns predictdd by the theory. (1-3 and 6) which has sufficient energy to produce, both However, there is a large in-pulse emission which is field solute excited singlet and triplet states from recombination. independent (Figure 3). If we assume all the in-pulse The ions are held together by Coulombic forces but may intensity is due to fluorene singlet fluorescence (Cerenkov be separated by distances of up to -30 nm.5 During most emission riegligible) and that it decays with the reported" of the time they are separated, the unpaired elections of decay: time of i 0 ns, then a correction may be applied to the two parts are not coupled together. The nuclear the after pulse intensities to corripute the fluorescence magnetic moments of the protons on the separate parts arising solely from the ion recofhbination aftes: the pulse. of the ion pair will not necessarily be in the same spin state. This correction leads to a more rapid development of the Therefore, the unpaired electron of M+ experiences a field effect which reaches a value of &40% in 25-40 ns different local magnetic field compared to the unpaired (Figure 7). It should be pointed Gut that time zeto has electron of M- due to the electron-nuclear hyperfine inbeen taken as the end of the 15- and 50-11s pulses, teractions. Since the electron spins of the separate parts Therefore, half of the ions have been in existence for 7.5 are no lOnger coupled to one another, they precess about and 25 ns, respectively, and the effective zero time is the tot$ field and at different rates. It is this difference somewhere in mid-pulse. Although this is ill-defined, it in the rate of precession which converts an ion pair, does mean that the developmerit of. the field effect will M+---M-, initially in a S = 0, m, = 0 singlet state to a S occur at shorter times than shown in Figure 7 and will = 1, m,= 0 triplet electron spin state. If ion recombinatioh therefore be in better agreement with theory. now occurred a solute excited triplet state would be Some of the prsblems discussed abqve could be avoided produced. The probability of geminate solute ion reby the use of a solute with a shorter fluorescence lifetime combination giving a singlet state is time dependent and, such as p-terphenyl (T = 1-2 ns). Results with this solute in principle, should cycle between 1 and 0. However, it are consistent with a faster onset of the field effect but limited solubility and correspondingly low fluorescence has been s h o ~ &that ~ as the number of magnetic nuclei intensities did not allow precise m e a s ~ r e m e n t . ~ ~ increases, the probability of recurrence of the singlet state We have attributed the magnetic field enhancement of decreases and the cyclic process approaches a steady decay the fluorescence from pulse-irradiated solutions to an in complex molecules such as aromatic hydrocarbons. In increase in the fraction of ion recombinations leading to the presence of a strong magnetic field, conversion of the excited singlets. In principle, other causes are possible, S = 0, m, = 0 state into the S = 1, m, = fl states is
b-
The Journal of Physical Chemistry, Vol. 81, No. 9 , 1977
Pulse Radiolysis in an Applied Magnetic Field
for example, a field dependence of any of the following: the yield from the triplet-triplet annihilation, the fluorescence efficiency, the fluorescence lifetime or the fluorescence decay time. However, these may be rejected for the following reasons: only the first of these is known to be changed by magnetic field^;'^,'^ the effect is small and shows a field dependence quite different to that reported here. Furthermore, the effects of triplet-triplet annihilation can be shown to be negligible because the decay of related triplets in the viscous solvent, liquid paraffin, decay by a predominantly first-order process which has little or no second-order contribution.’’ In benzene solutions, the fluorene fluorescence is not affected by an applied magnetic field either in ulse or continuous radiolysis with a small y source.‘ Therefore the fluorescence lifetime, the fluorescence decay time, and the fluorescence efficiency are not changed by a magnetic field and, assuming the same to hold in squalane, the fluorescence observed in our system after the pulse is justifiably attributed solely to ion recombination. The results presented here are in good agreement with the theory of B r o c k l e h u r ~ t .Other ~ ~ ~ predictions of this theory such as the effects of solvent, deuteration, and introduction of methyl groups have also been substantiated by the observation of magnetic field effects on the fluorescence from solutions during continuous radiolysis ’ ~ theory ~ ~ also accounts, at least in with a y s o ~ r c e . ~The part, for the deviation of the observed tripletsinglet ratios (T/S), which are in the range of 1-2,30,31from the statistically expected value of 3. Any value in the range of 0-3 is permitted depending on the rate of ion recombination. In discussing excited state yields, Magee and Huanglg considered the formation of triplet ion pairs by cross recombination in multiple ion pairs in spurs and by spin reversal of a secondary electron when it excites a solvent molecule to a triplet state. If these processes are significant, the presence of triplet ion pairs will reduce the extent of the magnetic field effect. This may be one reason why the observed enhancement is less than the limiting value of two, but several other factors are i n v o l ~ e d . ~ If’ ~ triplet ion pairs are present, then some triplet excited states should be formed at very short times. However, Beck and Thomas” were unable to observe triplet states at times between 0 and 0.77 ns. Further work is required to solve this problem. In summary, the magnetic field enhancement of the fluorescence yield in pulse radiolysis of solutions of aromatic hydrocarbons in the alkane, squalane, has demonstrated the importance of geminate ion recombination
819
in the formation of excited states in radiation chemistry. Acknowledgment. B. Brocklehurst of the Department of Chemistry, The University of Sheffield, England, is grateful to Atomic Energy of Canada Limited for a summer appointment (1973) as a Visiting Scientist. We are indebted to M. Tomlinson for initiating the project and for his continued support and interest.
References and Notes (1) (2) (3) (4) (5) (6) (7)
(8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29)
(30) (31) (32)
B. Brocklehurst, Radiat. Res. Rev., 2, 149 (1970). J. K. Thomas, Annu. Rev. Phys. Chem., 21, 17 (1970). A. Singh, Radiat. Res. Rev., 4, 1 (1972). A. Slngh, Ed., Inf. J . Radiaf. Phys. Chem., 8 (1976), “Formation and Role of Excited States In Radiolysis”, a special issue. A. Smmel, Adv. Radiat. Chem., 4, 1 (1974). B. Brocklehurst, Nature (London), 221, 921 (1969). B. Brocklehurst, R. S.Dixon, E. M. Gardy, V. J. Lopata, M. J. Quinn, A. Singh, and F. P. Sargent, Chem. Phys. Lett., 28, 361 (1974). B. Brocklehurst, Chem. phys. Left., 28,357 (1974); 29,635 (1974). B. Brocklehurst, J. Chem. Soc., Faraday Trans. 2 , 72, 1869 (1976). I. B. Berlman, “Handbook of Fluorescence Spectra of Aromatic Molecules”, 2nd ed, Academic Press, New York, N.Y., 1971. J. H. Baxendale and E. J. Rasburn, J. Chem. SOC., Faraday Trans. 1 , 70, 705 (1974). J. H. Baxendale, B. P. H. M. Geellen, and P. H. G. Sharpe, Inf. J. Radiat. Phys. Chem., 8, 371 (1976). G. Beck and J. K. Thomas, J. Chem. Phys., 57, 3649 (1972). G. Beck and J. K. Thomas, J. Chem. Phys., 60, 1705 (1974). G. Beck and J. K. Thomas, J. Phys. Chem., 76, 3856 (1972). A. Hummel and L. H. LuthJens, J. Chem. Phys., 59, 654 (1973). E. Zador, J. M. Warman, and A. Hummel, Chem. Phys. Left., 23, 363 119731. M. P:De&as, J. M. Warman, P. P. Infelta, and A. Hummel, Chem. Phys. Left., 31, 382 (1975). J. L. Magee and J-T. J. Huang, J. Phys. Chem., 76, 3801 (1972). A. Carrington and A. D. MELachlan, “Introduction to Magnetic Resonance”, Harper and Row, New York, N.Y., 1967. P. B. Ayscough, “Electron Spin Resonance in Chemistry”, Methuen, London, 1967. N. M. Atherton, “Electron Spin Resonance, Theory and Appllcations”, Ellis Horwood Ltd., Chichester, 1973. A. R. Lepley and G. L. Closs, Ed., “Chemically Induced Magnetic Polarization”, Wiley, New York, N.Y., 1973. F. P. Sargent, R. S.Dixon, V. J. Lopata. and E. M. Gardy, unpublished results. L. R. Faulkner, H. Tachikawa, and A. J. Bard, J. Am. Chem. Soc., 94, 691 (1972). H. Tachikawa and A. J. Bard, Chem. Phys. Lett., 26, 10 (1974). R. S. Dixon, E. M. Gardy, V. J. Lopata, and F. P. Sargent, Chem. Phys. Left., 30, 463 (1975). J. Fuller, N. Peteleski, D. Ruppel, and M. Tomlinson, J. Phys. Chem., 74, 3066 (1970). R. S. Dixon, F. P. Sargent, V. J. Lopata, E. M. Gardy, and B. Brocklehurst, Can. J . Chem., accepted for publication; presented at the InternationalConferenceon Electrons in Fluids, Banff, Canada, Sept. 1976. J. H. Baxendale and P. Wardman, Trans. Faraday Soc., 87, 2997 (1971). F. S. Dainton, M. B. Ledger, R. May, and G. A. Salmon, J. Phys. Chem., 77, 45 (1973). J. W. Hunt and J. K. Thomas, J. Chem. Phys., 46, 2954 (1967).
The Journal of Physical Chemistry, Vol. 81, No. 9 , 1977
