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Larry Kevan
to strong solvation of lithium cations in this s o l ~ e n t . ~ ~ (3) ~ ~G.~Levin, S. Claesson, and M. Szwarc, J. Am. Chem. SOC.,94,8672 (1972). We have found recently that this reaction proceeds much (4) B. Lundgren, G. Levin, S. Claesson, and M. Szwarc, J . Am. Chem. more rapidly in acetonitrile. On the basis of the proposed SOC.,97, 262 (1975). (5) G. Levin and M. Szwarc, J. Am. Chem. SOC.,98, 4211 (1976). model for solvent acidity and b a s i ~ i t y , DMF ~ ~ t ~ and ~ (6) G. Levin, S. Lundgren, M. Mohammad, and M. Szwarc, J. Am. Chem. acetonitrile are of approximately equal acidity so that Soc., 98, 1461 (1976). azobenzene free-radical anions are solvated to approxi(7) B. De Groof, G. Levin, and M. Szwarc, J. Am. Chem. SOC.,99,474 mately the same extent in both these solvents. On the (1977). (8) G. H. Aylward, J. L. Garnett, and J. H. Sharp, Rev. Poiarogr., Jpn., other hand, acetonitrile is a poorer Lewis base than DMF, 24, 322 (1967). so that lithium cations are more weakly solvated, and, (9) J. L. Sadler and A. J. Bard, J. Am. Chem. SOC.,90, 1979 (1968). therefore, (azobenzene)-- .Li+ ion pairs disproportionate (10) G. H. Cartledge, J . Am. Chem. Soc., 50, 2855 (1928). (1 1) H. Kryszczyhska, Ph.D. Dissertation, University of Warsaw, 1974. more readily in acetonitrile. (12) H.Kryszczydskaand M. K. Kalinowski, Roc.?. Chem., 48, 1791 (1974). It is premature to discuss here the details of the effects (13) G. K. Bot0 and F. G. Thomas, Austr. J. Chem., 28, 1251 (1973). of solvents on the kinetics of disproportionation of ion pairs (14) A. G. Evans, J. C. Evans, P. J. Emes, C. L. James, and P. J. Pomery, J . Chem. SOC.6,1484 (1971). because this subject is still under investigations. Let us (15) W. Kemula and 2 . Kublik, Anal. Chim. Acta, 18, 104 (1958). note only, that the polarographic method may be very (16) W. Kemula, Microchem. J., 11, 54 (1966). useful in this field. Although the results described in this (17) R. E. Visco, Presented at the Spring Meeting of the Electrochemical Society, Dallas, Tex., 1967. work are much less precise in comparison with the results (18) J. E. Rue and P. J. Sherrington, Trans. Faraday Soc., 57, 1795 (1961). reported in very elegant papers by Szwarc, polarography (19) M. E. Peover and J. D. Davies, J. Electroanal. Chem., 6, 46 (1963). seems to be attractive for investigation of compounds (20) T. Fulinaga and I. Sakamoto, J. Electroanal. Chem., 67, 201 (1976). (21) A. Lasia, J. Nectroanal. Chem., 42, 253 (1973). which decompose under photolytic conditions, and, (22) M. D. Ryan and D. H. Evans, J. Nectrochem. SOC.,121, 881 (1974). moreover, it may be easily applied in strongly polar sol(23) M. J. Hazeirigg, Jr., and A. J. Bard, J . Electrochem. SOC.,122, 211 vents. (1975).
-
Acknowledgment. This paper was sponsored by the Polish Academy of Sciences as a part of MR-1.9 problem. References a n d Notes (1) G. J. Hoytink, Adv. Electrochem., 7, 221 (1970). (2) M. Szwarc and J. Jagur-Grodzinski in "Ions and Ion Pairs in Organic Reactions", Vol. 11, M. Szwarc, Ed., Wiley-Interscience, New York, N.Y., 1974, pp 90-106.
(24) J. Chcdkowski, A. Chrzanowski, and M. K. Kalinowski, J. Electrmnai. Chem., 74, 236 (1976). (25) B. Kastening in "Progress in Polarography", Vol. 111, P. Zuman, L. Meites, and I. M. Kolthoff, Ed., Wiley-Interscience, New York, N.Y., 1972, p 195. (26) B. Kastening, J. Electroanal. Chem., 24, 417 (1970). (27) V. Gutmann and E. Wychera, Inorg. Nuci. Chem. Lett., 2, 257 (1966). (28) V. Gutmann, Top. Current Chem., 27, 59 (1972). (29) T. M. Krygowski and W. R. Fawcett, J. Am. Chem. Soc., 97, 2143 (1975). (30) W. R. Fawcett and T. M. Krygowski, Can. J. Chem., 54,3283 (1976).
Localization and Solvation of Electrons in Condensed Media. The Simplest Radical Ion? Larry Kevan Department of Chemistry, Wayne State University, Detroit, Michigan 48202 (Received September 2, 1977)
General criteria for electron localization are discussed with particular application to predictions of localization in alkanes based on a new model of electron-solvent interactions for nonpolar media. The kinetics and electronic structural changes occurring after electron localization that lead to solvation are shown to be consistent with simple molecular dipole orientation about localized electrons. The final equilibrium structure of the electron solvation shell in several different molecular media is determined by electron magnetic resonance studies.
When an electron is suddenly injected into a liquid or solid that is relatively inert to chemical reaction with electrons one is immediately confronted with two questions. The first question is whether the electron is localized or delocalized. If the electron is localized one then asks whether or not it becomes solvated and if so what the geometrical structure of the solvation shell is. Electron Localization We define electron localization as follows. An electron in free space can be described by a plane wavefunction $ = elkr where k is the wave vector. The probability density of this wavefunction is constant in space so the electron is delocalized. The same type of wavefunction can be used for delocalized electrons in condensed media. In contrast, an electron in a potential well or an atom is localized in 0022-385417812082-1144$01.OO/O
the region of the potential well or the atom. We can write a simple wavefunction for such a localized electron in the form )I = e-Xrwhere X is a real constant. For this wavefunction the probability density falls off with increasing r so the electron is localized in space. It will be easier to talk about criteria for electron localization in terms of energy levels. A general localization criteria can be written as
Et vo (1) where Et is total ground state energy of the localized electron relative to vacuum in the medium and Vo is the energy level for the conduction electron state or the bottom of the conduction band. If Et C Vo the stable equilibrium state of the electron must be a delocalized state. However, if Et I V,, the stable equilibrium state of the electron is 0 1978 American Chemical Society
Solvation of Electrons in Condensed Media
delocalized or quasi free and the energy of the electron will be Voor above depending on its kinetic energy. To be able to predict electron localization in different media we want to calculate E, and V,,. A simplified method for calculating Vohas been given1 and has been applied to condensed rare gases. In this simplified model Vois a function of the molecular polarizability, the density, and the hard core electron scattering radius of the atoms due solely to the atomic Hartree-Foch potential. Unfortunately it is difficult to calculate this hard core radius for an atomic system much less for a molecular one. Therefore, one must obtain Vofrom experimental measurement. The most direct and reliable method developed today appears to be the measurement of work function changes of metal electrodes in vacuo compared to a nonpolar liquid.2 With this method a number of values of Vo for different alkanes have been obtained and the comparison between different laboratories is reasonably good. However, this method has not been successful in polar liquids because the background currents are too high or in glassy matrices because the photocurrents are too low. A more general but indirect method is that of solute photoionization. This has been used successfully both in liquids3 and in s01ids.~The solute photoionization method for Vo depends upon an estimate or calculation of the electronic polarization energy but in solution this can be calibrated against direct work function measurements to make this solute photoionization method reasonably accurate. Thus we have one energy quantity Vo in our basic criterion for electron localization. If the electron is localized its total ground state energy Et can be obtained experimentally in principal by measuring the photoionization threshold of the trapped electron. In fact this is only possible for electrons in solids where the excess electron has always been found to be l~calized.~ In liquids we must resort to theory to predict this energy quantity. The molecular media of most uncertainty with regard to electron localization are the alkanes. An approximate experimental criterion for electron localization is given by the magnitude of the electron mobility in the medium. If the electron is quasi free it should have a high mobility but if the electron is localized it should have a low mobility. The definitions of “high” and “low” are somewhat unclear but a rough guide is pe 2 10 cm2 V-l s-l (delocalized state stable) and pe I 1 cm2 V-l s-l (1ocalized state stable). Electron mobilities in alkanes span a range of 0.01-100 cm2 V-l s-l at room temperature.6 Thus, our major consideration here will be to indicate how to calculate E, for electrons in alkanes. S t r u c t u r e d Semicontinuum Model A fairly successful model for treating energy levels of electrons in condensed polar media has been the semicontinuum model in which the interaction with the first solvation shell molecule is considered in terms of electron-point dipole and electron-point polarizability interactions while the interaction of the electron with the rest of the molecules is incorporated in a polarization potential.'^^ The semicontinuum model as first formulated does not take into account the molecular structure of the solvent molecule. A more refined model involving an ab initio treatment of the first solvation shell interactions which does include the molecular structure of these molecules plus a polarization potential for the continuum molecules has recently been formulated and applied to electrons in water and a m m ~ n i a .However, ~ it is difficult to extend this refined model to more complex molecular systems such as alkanes.
The Journal of Physical Chemistry, Vol. 82, No. 10, 1978
T
I I
1145
,c
I I Figure 1. Geomtery of an electron interacting with ethane for the structured semicontinuum model. The symbols are defined in the text.
Therefore, we have recently formulated a model of intermediate complexity which is based on the semicontinuum model but does take into account the molecular structure of the first solvation shell molecules in a rather simple way.1° We will utilize the semicontinuum potential model in which the total energy can be written as Et = Ek Ees Eel t Ems Em1
+
+
+
+
(2) + 4 + EHH where Ekis the kinetic energy, E,S and E,’ are the shortand long-range contributions to the electronic energy, Ems and E,,’ are the short- and long-range contributions to the medium rearrangement energy, E , is the short-range inEg
teraction energy of the excess electron with the medium electrons, E, is the void or surface tension energy, and Em is the hydrogen-hydrogen nonbonded repulsive interaction energy. All of these energy terms have been discussed bef~re.~JO Here we are mainly interested in the critical term that involves molecular structure. This term is the short-range electronic energy which is generally written as a sum of an electron-dipole interaction and an electron-polarizability interaction. For nonpolar systems like alkanes the dipole moment is equal to zero so we only have the electron-polarizability term. For a point molecule we have
Ees = -Nae2CI2(rd)/2rd4 (3) where N equals the number of equivalent molecules in the first solvation shell, a is the molecular polarizability, rd is the distance from the electron to the point dipole, and Ci is the charge density enclosed within distance rd. Now for a structured molecule we distribute the total polarizability over the molecule. Specifically we do this by uniformly distributing the polarizability over all n carbon-carbon bonds. Thus a / n is assigned to each C-C bond. Furthermore we must pick a particular molecular orientation with respect to the electron position for any explicit calculation. Let us consider an electron in ethane and the explicit geometry shown in Figure 1. The differential interaction energy along a C-C bond is (rd)
dEes =
-ae2C2(r) dr 2nl cos Or4
(4)
where the polarizability at any point along the C-C bond is alnl cos 0. We then integrate from rmhto rmmto obtain the effective interaction energy along a finite length C-C bond. This gives
(5)
1146
Larry Kevan
The Journal of Physical Chemistry, Vol. 82, No. 10, 1978
TABLE I: Electron Localization Predictions in Alkanes Medium Ethane Propane n-Pentane Neopentane
Temp, K V,,eV Et,eV 182 179 296 296
0.02 0.11 0.04 - 0.43
-0.25 -0.18 -0.16 -0.40
Vo-Et(N=6),eV t0.27 Localized t0.29 state tO.20 stable -0.03 Delocalized state stable
}
I
ZP
Et,eV 0.01
where P = (rmin+ rmax)/2.For example, for ethane with its C-C bond oriented toward the electron so that 6 = 0" we have
Note that for 1 = 0 this reduces to the point molecule model. For more complex molecules we have E," = NX,,,E,"G) where j is the j t h C-C bond per molecule. In this simple way the structure of complex molecules such as alkanes can be incorporated into the semicontinuum model. T o actually calculate the total energy we use a ground state hydrogenic wavefunction with one variable parameter and apply the variational procedure to calculate the minimum energy as a function of rd, A plot of the minimum energy vs. rd gives a configuration coordinate plot which shows a minimum at a particular value of r d for the alkanes such as ethane, propane etc. that we have studied. This minimum energy determines E , (1s). Calculations have also been made with a variety of different geometries for the more complex molecules such as propane and pentane and we find that the changes in the total ground state energy are relatively small for the various configurations tried. Results on predictions of electron localization in various alkanes are shown in Table I for six molecules in the first solvation shell which has been shown experimentally to be a reasonable number, at least for 3-rneth~1pentane.l~ Using the calculated values of E, the localization criterion predicts that the electron will be localized in ethane, propane, and n-pentane and will be delocalized in neopentane. This correlates well with the experimental criterion of electron Iocalization based upon the electron mobility in these alkanes. The electron mobility is less than 0.14 cm2 V-l s-l for ethane, propane, and n-pentane for neopentane. These prewhile it is 50-70 cm2 V-I dictions may be somewhat fortuitous but the important point is that differences in total ground state energy due to molecular structure are predicted by this relatively simple structured semicontinuum model. Electron Solvation. Kinetics If the stable state of an electron in a condensed medium is the localized state one can then ask how long it takes the electron to reach an equilibrium configuration with the solvent molecules. In liquids and perhaps also in glasses the electrons appear to be initially localized in transient potential wells in which the electron is not surrounded by an equilibrium configuration of solvent molecules. We may call this nonequilibrium configuration a presolvated electron. The presolvated electron is localized and has an absorption spectrum which can be observed by pulse radiolysis or laser photolysis methods.6J2 Typically the absorption spectrum as a presolvated electron is in the infrared in the range of 1400-2000 nm depending on the polarity of the liquid. Since this is a nonequilibrium species the presolvated electron is unstable and changes in time to reach an equilibrium configuration.
L
0
40
80
0 , deg Figure 2. Variation of the energy levels of the trapped electron in ethanol glass at 77 K with the angle of dipole orientation 15' for V , = 0.5 eV and N = 4 at radii corresponding to the configurational minimum energy of the ground state.
This is the process of electron solvation and it is characterized by a blue shift of the absorption spectrum. The blue shifts are smallest in nonpolar media such as alkanes and most dramatic in polar media such as alcohols. In alcohols the presolvated electron may be observed to decay in the infrared and the solvated electron grows in the visible. Both appear to be first-order processes and correlate if the decay is measured far enough into the infrared. There is no stationary point in the spectrum so spectra corresponding to intermediate configurations must exist. Our interest at this stage is the kinetics of this solvation process which can be characterized by a solvation time T , , ~ defined as k0bsd-lwhere the rate constant refers to the decay in the infrared or the growth in the visible. It is found empirically that 7,,1 correlates with the dielectric relaxation time in alcohols corresponding to single molecule rotation.12 The temperature dependence of 7801 also correlates with this dielectric relaxation time. Thus electron solvation appears to ignore hydrogen bonding although it is not clear why this appears to be the case. Based on the idea that simple alcohol monomer rotation accounts for electron solvation in liquid alcohols we will use the semicontinuum potential to try to predict how much of an optical shift this model implies. Recall that in the semicontinuum potential we consider the specific charge-dipole interactions of the electron with the first solvation shell molecule. In polar systems, such as alcohols, we can represent the first solvation shell molecule by point dipoles. Then the short-range electronic and medium rearrangement energies depend on the orientation of these dipoles toward the electron. Both of these energy quantities depend upon I.L cos 6 where 0 is the angle between the point dipole orientation and the line connecting the electron with the point dipole. The total energy for the ground and first excited states of the partially solvated electron can be calculated using 1s and 2p hydrogenic wavefunctions as a function of Typical results are shown in Figure 2. In the framework of this model the optical absorption energy equals E2,, - E l , where E2 is calculated within the Franck-Condon approximation. $he calculated optical transition energy for 6 = 80" is 1460 nm which compares with the experimental value of 1450 nm
The Journal of Physical Chemistry, Vol. 82, No. 10, 1978
Solvation of Electrons in Condensed Media
1147
seen a t the earliest times observed in a pulse radiolysis experiment. When the angle 0 decreases to zero the optical transition energy is calculated to be 660 nm which compares with an experimental value of 550 nm for a solvated electron. So this theoretical model appears to account for most of the observed spectral shift. Other points of interest which come out of this type of calculation13are as follows. First, the point dipole distance from the electron only changes slightly with 0 from approximately 2.43 A at 6 = 80" to 2.54 A at 0 = 0". Second, the charge density enclosed within the total first solvation shell radius only changes slightly with 0. For example, it varies from 87% a t 0 = 80" to 94% a t 0 = 0 ' for the conditions shown in Figure 2. Third, the charge density distribution in the excited state within the first solvation shell radius increases greatly with 0. It changes from 14% a t 0 = 80" to 32% at 0 = Oo for the conditions shown on Figure 2. Finally, no large change in the oscillator strength is observed as the dipoles orient. Now let us consider the time scale of electron solvation. If we assume that electron solvation occurs by simple alcohol monomer rotation and we represent the monomers by point dipoles we can use the Debye model of dipole relaxation. We can use semicontinuum model parameters to obtain the force acting on the point dipole and then the Debye relaxation equation takes the following form:14
would lengthen the calculated
dB 8n77a3 - = -ptCbe sin 8 /(rdo))2
r ( A )= (40n1'2/AHp,)''3 (9) In eq 9 AHppis the derivative peak-to-peak line width
dt
(7)
In eq 7 7 is the viscosity, a is the effective spherical radius of the molecule, and rdois the equilibrium point dipole distance to the electron. The time of dipole rotation to an equilibrium value can finally be written as
rr =
8n77a3(rd0))" Peck3 ln [tan tan (eth/2) (e,:,)]
(8)
where Bo is the initial unoriented point dipole orientation chosen (typically 80") and Bth is the thermal equilibrium dipole orientation depending on the temperature and the local electric field via the Langevin relation. In eq 8 values for On, rdo,and C, are obtained from semicontinuum model calculations. The calculated results of 7, agree well with experimental values of 7,,1 if the macroscopic viscosity is used in the theoretical model. There are no adjustable parameters then but the order of magnitude of the experimental solvation times is predicted within a factor of 3-5. Furthermore the trend with alcohol size from methanol to ethanol to propanol is reproduced by the calculations. In general, 7, C T,,~. At sufficiently low temperatures the use of the macroscopic viscosity becomes invalid so 7, cannot be predicted for electrons in glassy matrices. In this case one should really use some sort of a microscopic viscosity close to the electron about which there is no experimental information. In the above simple model we have only included rotation of the first solvation molecules. If we include dielectric relaxation of the medium beyond the first solvation shell by considering the change in electronic charge distribution during dipolar rotation we find that it does effect 7, but it only increases it by about 25 % .I5 Thus neglect of the complications of medium polarization seems to be good approximation. We should caution that the Debye model for dielectric relaxation was developed for weak electric fields whereas we probably have relatively strong fields at the electron point dipole distances of 2-3 A which apply. This would lead to some dielectric saturation and
7,
values.
Electron Solvation. Geometrical Changes For a more complete picture of electron solvation one would like to know the geometrical changes that occur in the first solvation shell during solvation and more specifically the average structures of the presolvated and solvated states. Thus far we do not have detailed structural information on presolvated electrons but it is possible to measure the average electron-proton distance changes that occur during solvation. Such information can be obtained by electron spin resonance methods applied to stabilized presolvated and solvated electrons. It is possible to stabilize presolvated electrons, in other words trap them, by irradiating glassy matrices at a low enough temperature, typically 4 K.16-18 We have found that a quantitative analysis of the second moments of the ESR line shapes can be used to obtain average electron-proton distances in the presolvated and solvated states for electrons in those matrices not having a significant isotropic hyperfine interaction with the e1e~trons.l~ This excludes alcohols but includes ethers and alkanes. If the line shape is Gaussian and symmetric and we can ignore any isotropic hyperfine interaction with the surrounding protons we obtain the following simple formula:
which is different for presolvated and solvated electrons in the same matrix and n is the number of equivalently interacting protons. From electron spin-echo data it has been found that for alkanes and ethers n is approximately 20.11 From the line width data we then find that the average electron-proton distance changes during electron solvation are 0.2-0.3 A. It is found that the distance increases with solvation so the protons get farther away from the electron during solvation. This is consistent with a H--C+ dipole assignment. This is also consistent with approximately a +0.1 A change for rdo during dipole orientation as calculated from the semicontinuum potential. It is also possible to obtain independent information on the electron-proton distance changes during solvation by an analysis of the electron nuclear double resonance (ENDOR) line shape.20 This independent analysis shows that the average electron to CH proton distance changes during solvation are +0.2-0.3 A in good agreement with the results based on the ESR line shape. Finally let us consider the geometrical structure of the final equilibrium solvated electron state. This information comes from electron magnetic resonance studies of stabilized solvated electrons in glassy matrices ranging from aqueous glasses through organic glasses. The most detailed geometrical information has been obtained by a pulsed electron spin resonance method called electron spin-echo spectroscopy.21i22Electron spin-echoes are a consequence of classically precessing dipoles. Two microwave pulses separated by a time 7 are appiied to a spin system located in an external magnetic field and an echo is observed at time 27 from the first pulse. The amplitude of the echo decays with 7 because of the various relaxation processes taking place in the system. In certain cases it is observed that the echo envelope exhibits an intensity modulation, predominantly due to the dipolar coupling between the unpaired electron and the nuclear magnetic moments of the surrounding nuclei. The period of the modulation is related to the nuclear Larmor frequency. When the decay is divided out one obtains the normalized modulation. It
1148
The Journal of Physical Chemistry, Vol. 82, No. 10, 1978
is this normalized modulation which is analyzed to obtain structural information about the nuclei surrounding the unpaired spin. Even in disordered systems it is possible to obtain rather detailed average structural information. By suitable simulations of the experimental modulation one can determine the distance of the electron to the surrounding magnetic nuclei, the isotropic coupling constant of the magnetic nuclei, and the number of equivalent interacting nuclei. By means of such an analysis of electron spin-echo modulation patterns and specifically deuterated molecules, the geometry of methyltetrahydrofuran (MTHF) molecules surrounding solvated electrons has been worked out in some It is found that probably four MTHF molecules are in the first solvation shell with their closest protons about 3.1 A from the electron. In the case of alkanes no studies involving specifically deuterated molecules have been carried out so less specific information is available.ll However, it appears that the nearest protons are about 3.1 A away from the electron and that there are about 20 equivalently interacting nearest protons. This may be interpreted as approximately six molecules surrounding the electron in the solvated state with perhaps a CH3 group of each alkane oriented toward the electron. The most detailed information on the specific geometry of a solvated electron has been obtain for electrons in aqueous mat rice^^^-^^ where the electron spin-echo modulation analysis and second moment analyses of the ESR line shape have been combined. The results show that the electron is surrounded by six approximately equivalent water molecules presumably arranged octahedrally with one OH bond of each molecule oriented toward the electron. The nearest electron proton distance is 2.1 A and the next nearest electron proton distance is 3.6 A. In summary, it appears that the electron localization and solvation in condensed media can be studied to provide rather detailed information. The theoretical and experimental studies complement one another to give an overall self-consistent picture of the gross details of electron localization and solvation. However, it should also be clear
Larry Kevan
that many details remain to be delineated. The solvated electron may only nominally be the "simplest radical ion" due to its complex interactions with its surrounding molecular environment, but it is also the radical ion for which perhaps the most is known about the details of the ion-solvent interactions.
Acknowledgment. This research was supported by U.S. ERDA under Contract E(11-1)-2086.
References and Notes 8. E. Springett, J. Jortner, and M. H. Cohen, J . Chem. Phys., 48, 2720 (1968). R. A. Holroyd and M. Allen, J . Chem. Phys., 54, 5014 (1971). R. A. Holroyd and Russell, J . Phys. Cbem., 78, 2128 (1974). A. Bernas, M. Gauthier, and D. Grand, J . Phys. Chem., 76, 2236 (1972). L. Kevan, Adv. Radiat. Chem., 4, 181 (1974). W. F. Schmidt in "Electron-Solvent and Anion-Solvent Interactions", L. Kevan and B. Webster, Ed., Elsevier, Amsterdam, 1976, Chapter 7.
K. Fueki, D. F. Feng, and L. Kevan, J . Am. Chem. SOC.,95, 1398 (1973). N. Kestner in "Electron-Solvent and Anion-Solvent Interactions", L. Kevan and B. Webster, Ed., Elsevier, Amsterdam, 1976, Chapter 1. M. Newton, J. Pbys. Cbem., 79, 2795 (1975). T. Klmura, K. Fueki, P. A. Narayana, and L. Kevan, Can. J. Chem., 55, 1940 (1977). P. A. Narayana and L. Kevan, J . Chem. Phys., 65, 3379 (1976). W. J. Chase and J. W. Hunt, J. Phys. Chem., 79, 2835 (1975). K. Fueki, D. F. Feng, and L. Kevan, J. Chem. Phys., 56, 5351 (1972). K. Fueki, D. F. Feng, and L. Kevan, J. Phys. Chem., 78, 393 (1974). K. Fueki, D. F. Feng, and L. Kevan, J. Phys. Chem., 80, 1381 (1976). D. R. Smith and J. J. Pieroni, Can. J . Chem., 45, 2723 (1967). H. Yoshida and T. Higashimura, Can. J. Chem., 48, 504 (1970). H. Hase, M. Noda, and T. Higashimura, J . Chem. Phys., 54, 2975 (1971). D. P. Lin and L. Kevan, Chem. Phys. Lett., 40, 517 (1976). H. Hase, F. Q. H. Ngo, and L. Kevan, J. Chem. Phys., 82, 958 (1975). W. B. Mims in "Electron Paramagnetic Resonance", S.Geschwind, Ed., Plenum Press, New York, N.Y., 1972, Chapter 4. K. M. Salikhov, A. G. Semanov, and Yu. D. Tsvetkov, "Electron Spin Echoes and Their Application", Nauka, Novosibirsk, 1976 (in Russian). L. Kevan, M. K. Bowman, P. A. Narayana, R. K. Boeckman, V. F. Yudanov, and Yu. D. Tsvetkov, J . Chem. Phys., 63, 409 (1975). B. L. Bales, M. K. Bowman, L. Kevan, and R. N. Schwartz, J. Chem. Phys., 63, 3008 (1975). P. A. Narayana, M. K. Bowman, L. Kevan, V. F. Yudanov, and Yu. D. Tsvetkov, J . Chem. Phys., 63, 3365 (1975). S.Schick, P. A. Narayana, and L. Kevan, J . Chem. Phys., 64,3153 (1976).
