Department of Chemitry, Queen's University, Kingston...

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ELECTRON SPIN RESONANCE STUDY OF TRANSIENT RADICALS IN SOLUTION J.K.S. WAN and S.K. WONG Department of Chemitry, Queen's University, Kingston, Canada K7L 3N6 CONTENTS I. INTRODUCTION II. CHEMICAL INFORMATION FROM ANALYSES OF ESR SPECTRAL PARAMETERS 230 A. The Spin l-lamiltonian 230 B. g Factors 230 C. Isotropie I-Iypeffine Couplings 232 i. a Protons 234 2. fl Protons 237 3. Carbon-13 Hyperfine Couplings 237 D. Line Widths 238 1. Modulation of Isotropic g and Hyperfine Interations and the Study of Rates of Reversible Reactions. 239 2. Modulation of Anisotropic g and Hyperfine Interactions and the Determination of the Sign of Coupling Constants. 241 III. ESR KINETIC STUDIES OF TRANSIENT FREE RADICALS IN SOLUTION 242 A. Maximum Rate of Free Radical Reactions and Its Relation to Spin Inversion 242 B. Structure Reactivity Relationships 245 IV. CHEMICALLY INDUCED DYNAMIC ELECTRON POLARIZATION OF TRANSIENT RADICALS (CIDEP) 249 A. The Radical-Pair Theory 250 B. Mechanisms of "Initial Polarization" 252 V. ACKNOWLEDGEMENTS 256 VI. REFERENCES 257 Page 228 227

Transcript of Department of Chemitry, Queen's University, Kingston...

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ELECTRON SPIN RESONANCE STUDY OF

TRANSIENT RADICALS IN SOLUTION

J.K.S. WAN and S.K. WONG

Department of Chemitry, Queen's University, Kingston, Canada K7L 3N6

CONTENTS

I. INTRODUCTION II. CHEMICAL INFORMATION FROM ANALYSES OF

ESR SPECTRAL PARAMETERS 230 A. The Spin l-lamiltonian 230 B. g Factors 230 C. Isotropie I-Iypeffine Couplings 232

i. a Protons 234 2. fl Protons 237 3. Carbon-13 Hyperfine Couplings 237

D. Line Widths 238 1. Modulation of Isotropic g and Hyperfine Interations

and the Study of Rates of Reversible Reactions. 239 2. Modulation of Anisotropic g and Hyperfine

Interactions and the Determination of the Sign of Coupling Constants. 241

III. ESR KINETIC STUDIES OF TRANSIENT FREE RADICALS IN SOLUTION 242 A. Maximum Rate of Free Radical Reactions and Its

Relation to Spin Inversion 242 B. Structure Reactivity Relationships 245

IV. CHEMICALLY INDUCED DYNAMIC ELECTRON POLARIZATION OF TRANSIENT RADICALS (CIDEP) 249 A. The Radical-Pair Theory 250 B. Mechanisms of "Initial Polarization" 252

V. ACKNOWLEDGEMENTS 256 VI. REFERENCES 257

Page

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I. INTRODUCTION

Electron spin resonance (esr) spectoscopy concerns the observation of absorption or emission of electromagnetic radiation caused by the magnetic dipole transition between Zeeman energy levels of any system that possesses electronic magnetic moments. Since its discovery in 19451 esr has rapidly developed into a poweHul tool in physics, chemistry and biology. The information obtainable from esr spectra is contained in (a) the number and positions of the spectral lines, (b) the line widths, (c) the relative and total absorption intensities, (d) the absorptive or' emissive mode of transitions; this is termed "electron polarization" and (e) the time dependence of the above. Analysis of the number, positions and relative intensities of lines in conjunction with the development of theoretical principles leads to the determination of chemical structure of the species and assists in the identification of unkown or suspect samples. Examination of line widths may provide further structural as well as some dynamic information concerning the system. A comparison of total absorption intensity at thermal equilibrium with a standard can yield a measurement of the concentration. Analysis of the time dependence of concentrations can be correlated with kinetic data. The study of electron polarization can offer valuable information on the mechanism of free radical formation. The time decay of polarization to thermal equilibrium can provide information on spin-lattice relaxation.

The renewed and increasing interest in the field of free radical chemistry during the last decade can be partially attributed to the rapid development of electron spin resonance spectroscopy. Today esr has been developed to a point where much of the theoretical and experimental background material for chemists is readily available. A number of review articles with different emphases on various applications of esr to chemistry have appeared in the last five or six years 2"s. This short account will deal mainly with free radicals in solution with particular reference to their kinetic behaviour and

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reactivity. For completeness, as well as a base for the discussion of the main topics, the analysis of esr spectra and relationships-between radical structure and esr parameters, that is, g factors and hyperfme splitting, will be summarized and followed by a brief account of some of the relevant line-width effects. A brief account of the chemically induced dynamic electron polarization of transient radicals in solution will also be given. This exciting phenomenon is relatively new and it is expected that interest in this field will grow rapidly in future.

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II. CHEMICAL INFORMATION FROM ANALYSES OF ESR SPECTRAL PARAMETERS

A. The Spin ltamiltonian The number and positions of lines in an esr spectrum of a free radical

can be described by the spin Hamiltonian /x / k

~7 1 3 S . g . H + ~ t h S - A i - I i - g i13N'I i" (1) H)

where 13 is the Bohr magneton, 13N the nuclear magneton, h Planck's constant, gi the nuclear~ factor of the ith nucleus, and ~I is the external magnetic field vector; S and Ii are the effective spin operators for the unpaired electron and the ith nucleus. The first term in (1)which contains g, the spectroscopic splitting tensor of the radical, denotes the electron Zeeman interaction; the last term of the sum is the nuclear Zeeman interaction. The second term describes the interaction between the electron and nuclei by the hyperfme coupling tensors -~i-

For radicals in solution, the anisotropies of the Zeeman and hyperfme interactions are averaged to zero for sufficiently rapid tumbling. Since the nuclear Zeeman term produces no observable effect in the spectrum, (1) takes the simpler form

~K = g13S-I4 + ~. hai S . li (2) 1

were g and a i are one third of the trace of the respective tensors o f ( l ) . The following two subsections will discuss briefly how structural information and the identification of free radicals may be obtained from the measurement of g factors and the isotropic hyperfine coupling.

B. g Factors

For organic radicals in solution, the orbital angular momentum of the electron is almost completely quenched, so that g factors are dose to the free electron spin value ge = 2.00232. However, deviations from this value are observed, particularly when the unpaired electron is associated with atom's which have unshared pairs of electrons. The deviations are due to the fact that the unpaired electron can acquire some orbital momentum through spin-orbit interaction which mixes the ground state with excited states of non-zero orbital moment 6 .

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If the orbital contribution arises from an excitation of the doubly occupied orbital to the singly occupied orbital, Zhg will be positive. If the contribution comes from an excitation of the odd electron into an empty orbital, Ag is negative. The increase in ~ from the methyl radical ('CHa, 2.00255) to the hydroxyl- (~H2OH, 2.00334) and the earbonyl-substituted (-CH2CHO, 2.0046) species is attributed to n-~Tr transitions on the oxygen atoms 7. For the carbonyl-substituted compound,/~g is larger than the hydroxyl-substituted one, because the carbonyl group contains two non-bonding electron pairs while the hydroxyl group has only one pair, the other being part of the conjugated lr system CH2-OH+~H2-OH. The g fa'ctors for the Si-, Ge-, Sn-, and Pb-substituted radical sequence, namely ~H2Si(CH3) 3, 2.0025; -CH2Ge(CH3)3, 2.0023; -CH2Sn(CH3)3, 2.0008; and -CH2Pb(CH3) 3, 1.9968, are lower than the g factors of the corresponding carbon-substituted radicals, for example CH2CH 3, 2.00260, and decrease with increasing spin-orbit coupling constant of the element s. This unusual behaviour is interpreted in terms of participation of d orbitals of the atom in the molecular orbital of the odd electron ~o and excitations from ~o to empty d orbitals a .

It is interesting and useful to note that normally the g factors for non-carbon-centred radicals increase from left to right and from top to bottom in the periodic table. Therefore the g factors of benzyl (PhCH2) , anilino (Phl~), and phenoxyl (PhO-) radicals are in the order 2.00259, 2.00309 and 2.0045 lo, and the series .CH 3, -Sill a 11, .GeH312 and -SnH312 have g factors 2.00255, 2.0032, 2.012 and 2.018 respectively.

These differences, though numerically small, correspond to signifi- cant shifts in the centre of the spectrum with respect to the magnetic fie~d. Thus, for a field of about 3,300 G a difference in the g-factor of 0.001 corresponds to a shift of "~ 1.65 G; shifts can readily be measured to within 0.05 G. Hence the measurement of g factors can provide valuable information about the structure of a known radical, and supply hints about the identification of an unknown. A slight dependence (a change in the fifth or at most fourth decimal) on temperature and solvents is often observed.

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C. Isotropie Hyperfme Couplings

Studies of hyperf'me couplings yield the most information about structure and identification of radicals. The proton and laC hyperfme couplings will be discussed as illustrations.

The isotropic hyperfme coupling a i in (2) arises through "Fermi contact" interaction and is proportional to the unpaired-electron spin density P(TL) at the ith nucleus,

8~r ai = 3 h ge {~giflNP ("/'i) (3)

From the multielectron wave function of the radical, P(qct) may be obtained as

,A

p ( T i ) = 2 < .~Szj~ij(Ti) > (4) J

where z is the direction of the external magnetic field, ~ij the Kronecker's delta and the average has to be taken over the spin and space coordinates of all electrons j. Equation (4) can be rewiitten to represent the difference between the probability density of finding an electron with ol spin at the nucleus and that of f'mding an electron with 13 spin at the same nucleus. If fl spin predominates, #(7i) is negative, and one speaks of negative spin densities. If the nuclear moment is positive such as with H and laC, the isotropic hyperfme coupling a i will be negative with a negative spin density.

Isotropic hyperfine couplings of protons arise through a net spin population in the hydrogen Is orbitals. If this spin population is 1, as for hydrogen atoms, the hyperfine coupling will be 507 G; therefore we may write

a n = 5 0 7 - p n (5)

Proton coupling constants seldom exceed 50 G, indicating that pH is lower than 0.1 for most free radicals. For small hyperfme couplings (this case is equivalent to the infinite field approximation) treatment of (2) by first-order perturbation theory gives the positions of the resonance lines at field strength

H = Ho - ~. a imii (6) 1

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where Ho =hog'lfl "1 , and the mli are the nuclear spin components along the field. For each nucleus with spin I the m! may take 2I+1 different values, namely, I, I-1 . . . . . -I+1, -I. Thus equation (6) gives a spectrum with Hi(2I i + 1) lines of equal intensities and which is symmetric with the centre H=H o. The g factor is obtained from the position of Ho. The hyperfme couplings ai are determined from the separations in line positions. Any individual line position is determined by a combination of the products aimli in (6). Since mli may be positive or negative, analysis of spectra by (6) does not give the signs of the a i.

In many cases several coupling constants are identical as a result of either geometrical equivalence (e.g. the methyl radical) or rapid geometrical isomerization (e.g. the ethyl radical where all the protons of the CH 3 group are made magnetically equivalent by rapid rotation of the group about the C-C axis). In such cases some of the lines appear at the same field stregth, and their intensities are additive. For a radical with n equivalent nuclei of spin I=½, as with H or 13C, only 2n+l lines are observed instead of N=2 n, with intensities given by the binomial expansion coefficients of (l+x) n. For example the five protons of the ethyl radical are divided into two equivalent groups, namely two a-protons and three ~-protons. One expects a triplet of quartets or a total of (2+ 1) (3+ 1 ) = 12 lines.

If the ratio a~/2Ho is larger than the line width, esr spectra of radicals with equivalent nuclei show additional free structure in the degenerate lines. Fessenden, who was the first to observe and analyze such second-order effects 13, concluded that these shifts do not provide the signs of the hyperffme couplings because of the a~ dependence. However he has recently shown 14 that higher order effects in line positions of radicals with several sets of equivalent nuclei may give information on the relative signs of the coupling constants. For instance a13c and a F are of same sign in "CF3 and aH(CH ) and aH(CH3) in (CH3)2CH have opposite signs 14. It should be noted that absolute signs can be obtaine.d from single crystal studies. For example the hyperfine couplihg constants of the CH group of the radical CH(COOH)2 were determined as a H =-21.2 G and a13 C = +33.1 G is ,16,

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Different mechanisms are required to induce spin density in the ls orbital of different types of protons:

1. ot Protons. Tables I and II give the hyperfine couplings and g factors for a number of carbon-centred radicals, many of which have t~ protons. It is useful to distinguish between rr-and o.-type radicals. In ~r 2 radicals the unpaired electron occupies essentially carbon 2pz(rt) orbitals, the axes of which are perpendicular to the axes of the carbon-substituent bonds. In o-type radicals the electron occupies sp 3 or sp 2 hybrid orbitals of carbon and the angles between the axes of these orbitals and the bond axes are 109 or 120 ° respectively. Phenyl and formyl radicals are good examples of o-type radicals whereas methyl is a typical lr radical.

The ffproton hyperfine coupling constant of methyl is-23.04 G. The unpaired electron occupies the carbon 2pz orbital in this planar radical and the protons are in the nodal plane of this orbital. No direct coupling is possible, so that the observation of hyped'me couplings of t~ protons of rr radicals was a surprise in the early development of esr. The non zero value of a is now believed to be induced by an indirect coupling, called "spin polarization" of the C-H bond orbitals .7. This results in a net spin density in the hydrogen ls orbital of spin orientation opposite to that of the electron spin in the carbon 2pz orbital and, simultaneously, generates a net spin density in the carbon sp 2 hydrid of the same sign as that of the electron in the carbon 2pz orbital. Because of the inversion of sign of the net spin density, the hypert'me coupling constant of such protons is negative.

To a very good approximation, the spin density of the hydrogen ls orbital is proportional to only the spin density of the adjoining carbon 2pz orbital. Therefore for a protons in planar radicals with conjugated rr systems, the McConnell relationship n may be applied,

aHC ~ = 507 "PH = Q ' P l r (7)

where P;r is the spin density in the carbon 2pz orbital and Q is a proportionality constant. From the methyl ct coupling (2,, = 1) the value Q =-23 G follows. However, on the basis of a comparison of the

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Table I. lsotropic Hyperfine Coupling Constants and g Factors of some 7r-Type Carbon-Centred Radicals a

a(Ho~) a(13Cot) Other Radical (G) (G) Splitting ((3) g Ref.

• CH 3 (-)23.04 (+)38.34 2.00255 29 -CD 3 - (+)35.98 Di(-3.58) - 21 -CH2CH 3 (-)22.38 (+)39.07 CH 3:(+)26.87 2.00260 21,29 • CH(CH3) 2 (-)22.11 (+)41.3 CH 3 :(+)24.68 2.0026 4,29 • C(CH3) 3 - (+)45.2 CH 3 :(+)22.72 2.0026 4,29 • CH2OH (-)17.68 (+)45.89 HO:1.63 2.00334 100 • CH2F (-)21.1 (+)54.8 F:(+)64.3 2.0045 22 • CHF 2 (+)22.2 (+)148.8 F:(+)84.2 2.0041 22 -CF 3 - (+)271.6 F:(+)142.4 2.0031 22 • CH(COOH)2 -21.2 +33.1 - 2.00282 15,16

'CH 2 - CH = CH 2 (-)14.83 - (+)4.06 2.00254 21 (-)13.93

C6HsCH 2 (-)16.3 - Hortho:(-)5.15 2.0025 9,19 Hmeta:(+)1.77 Hpara :(-)16.18

aSigns given in parentheses have not been determined experimentally~

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Table iI. Isotropic Hyperfine Coupling Constants and g Factors of some o-Type Carbon-Centred Radicals a

Radical a(G) g Ref.

H \ I-I~: (+) 13.39 2.00220 21.29 H / C = C ~ , , H H~(c/s):(+)37.0

H~ ( trans) :( + )65 .0 13Co~:(+)107.57 13Cfl:(-)8.55

Ho:(+)17.4 2.00234 101,102 • Hm:(+)5.9

Hp:(+)1.9

H - C % Hd(+)136.5 2.0009 103 0 13 C : (+) 134.5

C=O

Hm:(+) 1.16 2.0008 (2.0014)

4,104

aSigns given in parentheses have not been determined experimentally.

experimental splitting with results of INDO calculations on a large variety of radicals, a value of Q = -22 G has been suggested to be more suitable. Application of the McCormell relationship can provide a means of determining the distribution of the unpaired electron over the 7r system such as in allyl la, benzyl radicals 19 and aromatic radical ions ~° from the observed proton hyperfine eomplings.

There.proton coupling constants of most substituted methyl radicals are significantly lower in absolute magnitude, that is, more positive, than those of the parent compound. While part of this is certainly due

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to delocalization of the unpaired electron onto the substituents, i.e. p~r< 1, for several of the radicals it may also result from deviations in planarity so that direct contact interactions can occur; these give positive contributions to the couplings.

2. t3 Protons. The 3-proton coupling constant of the ethyl radical is larger than that of its a protons. The mechanism giving rise to this hyperfme interaction results from a hyperconjugative delocalization of the unpaired electron into the Is hydrogen orbitals. Such a mechanism can only operate when the 3-hydrogens are not located in the nodal plane of the a.carbon 2pz orbital. The value of aHfl depends on the angle O between the 2pz axis and the plane containing Coe C/3 and H3. For radicals in rigid media, analysis of the /5 couplings leads to the angular dependence

all/3 = Bo + B l " c o s 2® (8)

where the constants B o and B 1 are found to be in the ranges 0 - 5 G and 40--45 G respectively 4.

Often in solution the fl protons are those of a methyl group that can rotate rapidly about the C3--Cc~ bond. Thus, in the case of the ethyl radical, the three hydrogens will appear to be equivalent and each will have a coupling constant equal to Bo+B 1 < c o s 2 0 > = B o + B 2 . ~ c o s 2 0 > is the average over the free rotation. If the rotation of the C~--CI3 bond is hindered and the different conformations have different energies, the observed aHfl wilt exhibit a marked temperature dependence. Analysis of this dependence may yield the energy of the barrier to rotation between the various conformations.

3. Carbon-13 Hyperfine Couplings. It is important to study the c~-carbon-13 splittings to distinguish between 7r type and o type radicals. Because of the large contribution of the 2s orbital to the singly occupied orbital, a-radicals have much larger laC ¢xcoupling constants than 7r radicals (cf. Tables I and II). The fluorinated radicals -CH2F, • CHF 2 and CF 3 have carbon hyperfine couplings which are considerab- ly larger than that of methyl, a typical 7r planar radical. This indicates non-planarity of the radicals since deviations from planarity are expected to increase the 2s character of the odd electron orbital, and

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this leads to an increase in a c. For the dependence of ac on the angle O between the CH bonds and the plane of three substituent atoms, the formula

ac (O ) = a c ( 0 ) + l 1 9 0 ( 2 t a n 2 0 ) (9)

has been derived 21 'm and applied to estimate radical geometries. The term 2 tan20 in (9) corresponds to 2s character of the orbital and ac(0 ) is the value for a planar radical.

For planar 7r systems the isotopic coupling constants of carbon-13 are related to the 7r spin density via the Karplus-Fraenkel z3 equation

c C a c = (S c + ZQCcx)PTr + Z Q x c p x (10)

where pCis the spin density of the 2pz orbital of the considered carbon, and pX are the spin densities of the corresponding orbitals of the three neighbouring atoms X of this carbon. The coupling arises through spin polarization mechanisms, as suggested for a protons. The term S C represents a spin polarization of the carbon ls shell. The parameters S C and Qc have been determined empirically. S c = -12.7G, QcCH = + 19.5G, QCc0 = 14.5G and Qc'c = 13.9G (trigonal hybridization of C') and

QcC,c = +30.0G (tetrahedral hybridization of C') are commonly accepted.

The analysis 24, zs of the 13C hyperfine coupling constant for the t-butyl radical and its temperature dependence has been carried out to settle the controversy over whether the t-butyl radical is planar or pyramidal. The recent detailed analysis of Wood and coworkers 2s showed that the radical is essentially non-planar.

D. Line Widths

The analysis of line widths can provide valuable information about the radicals as well as their environment. Interested readers should consult the excellent reviews by Fraenkel ~ and by Atkins ~7. Outlined here are two commonly observed line width phenomena in solutions,

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namely the effects caused by modulation of the isotropic g and hyper- fine interactions and of the anisotropic g and hyperfine interactions.

1. Modulation of Isotropic g and Hyperfine Interations and the Study of Rates of Reversible Reactions. As was seen, the position of any one line in a complex esr spectrum of a free radical is determined by the g factor, the coupling constants a i of the interacting nuclei, and a set of quantum numbers mli of the nuclei. If these quantities fluctuate in a random but reversible manner, the line will shift its field position and the line width will change. Several different processes may cause this effect.

The spectrum of the durosemiquinone radical-cation exhibits a marked alternating line width effect which is temperature dependent; it is ascribed to cis-trans isomerism and the methyl group proton couplings depend on the orientation of the hydroxyl groups 2s.

O / H O/H

M e . M e ~ " M e . M e

Me" " ~ "Me M e " ~ "Me

0 H H/0

(ll)

The reversible structural rearrangement of the vinyl radical interchanges the coupling constants of the cis and trans protons 29.

H a ~ c = C./Hc ~ Ha~"C = C"

Hb / H b , H c

(12)

Inversion of the cyclohexyl radical is another familiar example where exchange of the coupling constants of 13 protons takes place 29. There are also atom-exchange reactions3°, 31 and electron-exchange

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reactions32,33 where the g fractor, coupling constants and the mli may vary.

To illustrate these effects consider the interconversion between R- and R.' two isomeric radicals with different coupling constants but the same g factor such that R-and R-' have different esr spectra and each line in one spectrum corresponds to one and only one line in the other but belonging to the same set of mli. In frequency units, the difference in the positions of a corresponding pair of lines j is

8vj = gflh 5 H i - g/3h Z(i -ai - a i ) m n ' (13)

If there were no exchange one would observe the two spectra of R" and R-' superimposed. If the rate of interconversion v C is slow compared to Avj, the corresponding lines of R- and R.' are still observed separately, but the lines of a pairj are broadened by an amount

Av ~ v c (14)

When v c is comparable to ~ v i, the pairs of lines collapse to broad lines centred at the average field position. For very high exchange rates, v C >> 5 vj lines are seen at the average field position with widths

txv ( vJ)2 (15)

v C

Since the broadening of the lines depends on ~ ~j, different lines in esr spectra may show different widths. For g=g', the broadening will be symmetric with respect to the centre of the spectrum because there are two pairs with equal[~ vi •

The analysis of the spectrum of vinyl radicals and its temperature dependence is used to illustrate this point. Trapped in solid matrices at very low temperatures, the vinyl radical in (12) shows the expected eight-line spectrum with line positions at about ~ 8 , +44, +24 and - 1 0 G from the centre 34-36. With the coupling constants

a a = a~ = a b = 68 G (tram proton), a{~ = a~ = 34 G (cis proton),and a c = 14 G (a proton), these positions are interpreted as belonging to

,~aimli = +~(aa + ab + ac) or +~ (a a + ab + ac), +Y~(-aaa + ab - ac),

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or -+Y~(aa+a~-ac); +Y~(aa-ab+a c) or + ½ ( - a a + a g + a c ) , a n d -+(aa -ab -ac) or _+~(-a a -ag -ac)respectively. In solution at -180°C and on silica gel between -120 and -70°C, the radical has a four line spectrum with positions at -+58 and +44 G 29'~. For higher temperatures a six-line spectrum at -+58,-+44, -+7 G is found 36. These changes are ascribed to the inversion of the/3 protons in reaction (12) with the associated oscillation between the two coupling constants. The lines at -+58 and -+44 G are not affected and remain narrow because

a a + a b + a c = a a + a g + a c and a a + a b - a c = a a + a g - a c. The other lines are correlated as -24G -~+ 10 G and -10 G ~+24 G and show broadening. Only the outer four lines were observed at intermediate temperatures as the inner four lines were broadened to an extent which prevents their observation. When the rate of the inversion increases as the temperature rises, the inner lines emerge at the average position -+7 G resulting in a six-line spectrum as expected. The inversion frequency may be estimated at the intermediate temperatures to be about v C ~ ~ m 95 MHz.

2 Modulation of Anisotropic g and Hyperfine Interactions and the Determination of the Sign of Coupling Constants. Variations in the line widths among the different hyperfine lines in the esr spectra from free radicals in solution may be caused by the incomplete "average-to-zero" of anisotropic g and hyperfine interactions. For a radical with one interacting nucleus of spin I, the line width variations for different m 1 may be expressed by 26 ,27

A H ( r n I ) = A + B m I + C m ] (16)

The constants A, B and C are related to anisotropic g and hyperfme interactions. The first term of equation (16) causes the same broadening of all lines, while the second causes asymmetric broadening; this is, the outer lines are broader on one side of .the spectrum than on the other. The last term produces symmetric broadening, to make the outer lines broader than the inner o~aes.

Analyses of the observed line broadening with equation (16) may yield the sign of the isotropic hyperfine coupling constant a of the interacting nucleus. An example is the work of deBoer and Mackor a7

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where the 13C coupling constants for the tx and fl positions in naphthalene anion radical were shown from line-width differences to be positive and negative respectively, corresponding to positive spin density at both of these positions.

III. ESR KINETIC STUDIES OF TRANSIENT FREE RADICALS IN SOLUTION

Esr provides a unique method of studying kinetics of free radical reactions because it gives absolute radical concentrations as well as the identity of the reacting species. The most common and convenient kinetic esr method u s e s pulse techniques. That is, the radicals are generated by a pulsed high energy electron beam or a pulse of light from a rotating sector or switched laser, and the concentrations of the radicals are then monitored. Because of the transitory nature of most of the intermediate radicals, the concentrations are usually tow, and computer assisted enhancement of the signals or other techniques are normally required for such studies. Rate constants for free radical reactions and useful experimental techniques have been recently reviewed by Ingold 3a. Also described are methods other than esr.

In this section two important aspects of free radical reactions will be discussed, namely, the maximum rate of a free radical reaction and its relation to spin inversion, and structure-reactivity relationships.

A. Maximum Rate of Free Radical Reactions and Its Relation to Spin Inversion

Only radical-radical reactions occurring in solution will be considered here. When two radicals react with one another at every encounter, chemical change can take place only as fast as the reactants can diffuse together. Such a process is called a "diffusion-controlled" reaction. Second~rder rate constants for such a reaction can, in principle, be calculated from the law of diffusion ag. The maximum rate constant for a diffusion controlled reaction is given by

kdiff = ( 4 7 r N / 1 0 0 0 ) ( t y A + O B ) ( D A + DB) (17)

where DA and DB are the diffusion coefficients for the radicals A and B in the liquid medium, and o A and a B are reaction cross sections defined

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in terms of the distance across which reaction can take place between A and B. In the absence of diffusion coefficient data, it is common to use the Stokes-Einstein equation

D = k T / 6 r r r / r (18)

where 77 is the viscosity of the solution and r, the diffusion radius, is identified with the radius for reaction. Therefore (17) is simplified to yield

kdiff = 8 R T / ( 3 x 103r / )M -1 sec -t (19)

For reactions between like radicals a factor of half should be introduced. For commonly used solvents such as benzene, cyclohexane and water, equation (19) gives a value for kdiff of approximately 8 x 109 M "1 sec-:.

If the product of a radical-radical reaction is in the singlet state, and if this demands a singlet precursor of the radical-radical pair then the maximum reaction rate has to be modified because statistically, only one quarter of the encounters result in a singlet state. The picture is further complicated by the possibility of spin. inversion between the singlet and triplet pairs. The question of spin inversion is closely related to the so-called "spin correlation" effect 4° which states that the subsequent behaviour of radicals depends upon their multiplicity. A number of photochemical investigations of these effects have been carried out by comparing results of sensitized reactions versus direct photolysis. The assumption underlying this type of experiment is that a triplet sensitizer gives triplet radical pairs. Direct photolysis is presumed to proceed by singlets. For example, the triplet-sensitized decomposi- tion of N-(1-cyanocyclohexyl)-pentamethylene-ketenimine gives only 8% succinonitrile in carbon tetrachloride; direct photolysis under identical conditions gives 24%. Thus the triplet pairs have only about one-third of the probability of combining shown singlet pairs al . This indicates that the spin inversion is relatively slow compared to diffusion and that the singlet state has higher probability of combination. On the other hand the yields of combination products are almost identical from either the direct or sensitized decomposition of azobiscyclohexyl-

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nitrile 41 or azocumene 4z. This was attributed to rapid spin inversion. However it has recently been shown that azo compounds also interact very efficiently with sensitizers in the singlet state and go through radical pairs of the same spin multiplicity as those in the direct photolysis 4°.

The reversal in the sign of the chermcally induced dynamic nuclear polarization* (CIDNP) observed in the dimerization products of the direct photolysis of benzyl-9-azofluorene (singlet) as compared to 9-diazofluorene (triplet) in toluene has been explained 4a in terms of the requirement of triplet-singlet inversion as a step prior to combination. Similar reversals in sign of the polarization have been reported recently in the direct (or thermal decomposition) versus sensitized photolysis of benzoyl peroxide 44'4s. These experiments show that spin inversion is possible, but is not rapid compared to diffusion so that the initial multiplicity is largely retained.

Because of its direct measurement of absolute rate constants of free radical reactions, the kinetic esr method may provide a means to measure the probability of spin inversion in diffusion-controlled radical recombination reactions. The most simple approach is to compare the experimental rate constant and the theoretical diffusion rate constant assuming the precursors of the products are necessarily singlet pairs. But this presents great difficulty in obtaining a precise value for comparison, as equation (19) is oversimplified. There has been some renewed interest in the theory of diffusion-controlled chemical reactions in recent years 46'47. As well, the experimental measurement of rate constants by esr is not really accurate enough due to uncertainties involved in determining absolute concentrations. The best values of the rate constants determined by esr are at present probably

with£n + 50%. An error of ~10% is necessary for investigating the problem of spin inversion.

Even if there were no complication by spin inversion on radical-radical reactions the measurement of rate constants of diffusion- controlled reactions would not be of great value for the study of structure-reactivity relationships. One expects that spin inversion depends on the structure of the radicals since a variety of singlet and triplet state mixtures has been invoked in explaining CIDNP effects.

* For a comprehensive review of CIDNP phenomena, see references quoted in (80)

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B. Structure Reactivity Relationships Free radicals are reactive because of their unpaired electrons and it

has been shown that the site bearing the unpaired electron is the reac- tion centre. It is, therefore, natural to investigate the relationship bet- ween reactivity and the density distribution of the unpaired electron. This is particularly interesting to esr spectroscopists because the distri- bution of the unpaired electron density in the radical can be determined by the hyperfine coupling and g value (as described in Section II).

In general the bimolecular self-reactions of radicals are diffusion- controlled if dimerization is through the atom which bears most of the unpaired electron and yields stable products. Typical examples are methyl 48, ethyl 49, cyclopentyl s°, cyclohexyl s° dimethylamino and diethylamino sl radicals. This is also true for some delocalized radicals such as allyl s2, cumyl s3 and phenoxy154 radicals, although the reaction centres may only bear a small fraction of the unpaired electron density.

Equation (19) predicts that the diffusion-controlled rate constant for a bimolecular reaction is independent of the size of the reactants in the same solvent. However, reactions believed to be diffusion- controlled ss have different rate constants, decreasing as the size of the radical increases. This has been shown for the self-reactions of some group IV radicals ~ and the self-disproportionation of some semi- quinone radicalsS6, s7. It is noteworthy that the recombination of t-butyl radicals in solution is diffusion-controlled as studied by esr 48's3 whereas the gas phase recombination rate is higher by a factor of l0 s sa

Hammond and Weiner have studied para-substituent effects in- cumyl s3 and benzophenoneketyl radicals s9 in order to shed some light on the structure- reactivity relationship. Although the observed effects are fairly significant, the origin is still not clear. On possibility is that the rates, being close to the diffusion rate, may be complicated by such factors as spin conservation and radical size, as discussed above.

To obtain meaningful structure-reactivity relationships about radical reactions non-diffusion-controlled reactions should be studied; their rate constants should be at least two orders of magnitude lower than those calculated from equation (19). For very reactive radicals, radical- molecule reactions should be studied because their self-reactions or

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other radical-radical reaction rates are likely to be close to the diffusion-controlled rates. There is little esr work of this kind in the literature. The only but well-known example is the measurement of the reaction rates of hydrogen atoms 6°,61 . An interesting qualitative study by esr on the selectivity of radical reactions has shown that phenyl radicals add mainly to the terminal end of the double bond in propene, while hydroxyl radicals add onto both sites and t-butyl radicals abstract the allylic hydrogen 62.

There have been more efforts expended in esr studies of self-reactions using less reactive radicals such as hindered phenoxyl radicalsS1,54,63, tertiary and many secondary peroxyl radicals 64'6s and certain nitroxides 66"6s, iminoxy radicals 69 and amino radicals sl . The results of these studies confirm earlier predictions 7° of the stability of radicals, in terms of extensive delocalization of the unpaired electron and steric hindrance. But a quantitative relationship between the self-reaction rate and the electron density distribution in the radical has not been developed because reactions other than head-to-head recombination may complicate the total kinetics and lead to spurious values of the recombination rate constant. This is particularly true in esr kinetic studies because only the total decay of radicals in monitored. Disproportionation is a well-known complication, and therefore the availability of hydrogen atoms 13 to the radical site will affect the stability of the radical significantly 71 .

New recombination mechanisms have been discovered from studies involving stable radicals and some structural effects have been elucidated. The approach will be outlined using hindered phenoxyl radicals as an example. The unsubstituted phenoxyl radical has a 2k t value of 1.2x10 9 M "l see "1 and the 2,6-di.t-butyl-substitured phenyl radicals have 2k t values ranging from 10 8 M -l see -l to zero (see Table III). The self-reaction of the unhindered phenoxyl radical may proceed via five major routes.

The reactive centres of all of these reactions have large unpaired electron densities. In the case of the 2,6-di-t-butyl phenoxide radical however, the rates of reactions (20) and (22) and, to a lesser extent, reactions (21) and (23) would be expected to be slower than the

* k t represents the rate constant of the termination reaction.

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TABLE III.

Table III. Rate Constants of Self-Reaction of Unsubstituted and 2,6-di- t-Butyl-Substituted Phenoxyl Radicals in Benzene

Phenoxyl 2kt 25 o Substituents (M "1 sec "1) Ref.

H 1.2 x 109 54 2,6-(t-C4Hg)2 6 x 107 54 2,6-(t'C4H9)2 -4-i-(C3H7) 2 2.2 105 2,4,6-t-(C4HQ) 3 stable 70

O"

O'

O'

O"

O'

0 o 0

O'

© O'

O"

O"

0 0

0

(20)

(21)

(22)

(23)

(24)

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corresponding reactions of the unsubstituted phenoxy radical as a result of steric hindrance.

The fully substituted 2,4,6-tri-t-butyl phenoxyl radical is very stable at room temperature, because none of the above five recombination paths would be available. However, if the para substituent is an iso-propyl group rather than a t-butyl group, a new but much slower reaction becomes possible, as shown in (25).

o e

O ---H---O p

O O}t (25)

There is another interesting area where little work has been done: comparative reactivity studies of o and rr radicals, o Radicals, e.g. pheny1 and formyl, are generally thought to be more reactive s'72 possibly due to the unpaired electron being highly localized. However, iminoxyl radicals, a class of o radicals, are quite stable 69,73'~, in fact more so than many rr radicals.

The disadvantages of the kinetic esr method should also be mentioned. Because of the relatively low sensitivity, (10"7M is the minimum concentration detected by the present instrumentation) many highly reactive radicals have not yet been observed as reaction intermediates in solution, as for example the phenyl and formyl radicals. The esr spectrum of the hydroxyl radical has not been observed in solution for another reason, due to the orbitaliy degenerate ground state. Fluctuations in the liquid phase would greatly modify the g factor and hence would provide an efficient mechanism for spin relaxation leading to broadening of the spectral lines beyong

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detection 7s . The same considerations appear to be valid for alkoxy, hydrosulfur and thiyl radicals 76. However, Ayscough and Scaly "rr have been able to obtain rate constants for hydrogen abstraction by excited triplet molecules from esr studies, although the esr spectra of the excited triplet state molecules were not observed in solution.

IV. CHEMICALLY INDUCED DYNAMIC ELECTRON POLARIZATION OF TRANSIENT RADICALS (CIDEP)

Under normal conditions, when an esr spectrum is recorded, it is usually assumed that the electron spin system attains thermal equilibrium. This is particularly true for systems of "stable" radicals having short electron spin-lattice relaxation times and when low microwave power is used. Electron polarization is here defined as any deviation from the thermally equilibrated spin populations. Thus, for a doublet system, the ration of the population of the lower state (N~ to that of the upper state (N~) is not equal to the Boltzmann factor, i.e.

N~ / Net 4: exp ( g/3e Bo / kT )

where g is the electron g-factor, fie is the electron Bohr magneton, Bo is the applied magnetic field, k is the Boltzmann constant and T is the absolute temperature. Generally, it is convenient to express the polarization in terms of the population difference, n = N/3 - Net, since the observed esr intensity at low microwave power is proportional to n. At room temperature and using an X-band spectrometer, no](Nct+Nl~)~0.075%, where n o is the population difference at thermal equilibrium. A polarization factor f may now be defined as

f= n/n o. If Not>N/3, f is negative and esr emission will be observed. When f is positive and greater than unity, enhanced absorption will be expected. For a positive value of f less than unity, polarization is still defined, but the esr is a "diminished" absorption mode..Finally, when f is equal to sero, no esr signal will be observed, even if the concentration of the radicals is relatively high.

Chemically induced dynamic electron polarization (CIDEP) refers to electron polarization resulting from chemical reactions, in contrast to polarization induced by physical means such as microwave power

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saturation. During the decay of the polarization via spin-lattice relaxation, the transient radicals may also decay chemically. However, since spin relaxation in liquid systems normally occurs very fast (in the order of 10 -4 to 10 .6 sec.) it is reasonable to assume that the rate of chemical decay is negligible compared with that of spin relaxation and that the initial polarization may be observed with a time-resolved esr spectrometer.

Experimental CIDEP results reported to date are still relatively rare compared to CIDNP studies. No doubt part of the reason is the higher degree of difficulty in performing CIDEP experiments. In CIDNP studies, one is dealing with spectra of stable reaction products and the nuclear spin-lattice relaxation times are usually much longer than those of electron spin relaxation.

Despite the scarcity of experimental results, Kaptein and Ooster- hoff 78 formulated a theoretical basis for CIDEP in 1969. This treatment is now recognized as the foundation of the so-called "radical-pair theory" which initially appeared to account for CIDEP results. The theory has not been tested experimentally to any vigorous degree, partly because CIDEP experiments are more difficult to perform. The early development of CIDEP has been reviewed by Atkins and McLauchlan 79 while a more recent account of this exciting phenomenon was given by Wan, Wong and Hutchinson 8°. Only the salient features of the two main approaches in dealing with CIDEP results will be outlined here.

A. The Radical-Pair Theory The radical-pair model assumes that a radical-pair formed in an initial

stage of a chemical reaction, (e.g. molecular dissociation into two fragments, hydrogen abstraction by an excited molecule or two radicals generated independently upon collision) may not immediately react but instead may separate into a region where the singlet-triplet splitting (2J=E s -ET) of the radical-pair is comparable to their magnetic energy. In this region, mixing of the singlet (S) and triplet states (T-l, To T+l) of the radical-pair by magnetic interactions (~M) may lead to a growth of electron spin density on one radical, and a corresponding decrease of electron spin density on the other radical.

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Only the mixing of S and T O is considered here, since the S and T+I mixing is believed to be unlikely, particularly in the presence of a strong external magnetic field which increases the energy gap between the S and T+ states rs Sl

The initially formulatedd radical-pair theory has been developed to explain the esr spectra of mixed emission and absorption patterns. Let us consider the simplest example of a pair consisting of an H atom (radical 1) and a radical 2, both having identical g-factors. If the radical-pair is formed by dissociation of the molecule HX in an excited state, J will be either greater or less than zero depending on whether the excited state is a singlet or a triplet state, respectively. In the case of H atoms the low-field hyperfme line will be in an emission mode and the high-field line will be absorptive. The theory is thus in agreement with the experimental observation of the mixed patterns on the H atom sz. For radicals with more than two hyperfine lines, the theory predicts a mixed pattern esr spectrum, provided that the matrix element ~fM is primarily determined by the hyperfine interactions rather than by the electron Zeeman interactions. The radical-pair theory also accounts for the relative intensities of the esr lines observed in some experiments sa .

It should be noted that this theory also explains totally emissive esr spectra, provided the electronic g-factors of the two radicals in the pair are significantly different to cause heavier contributions of the electronic Zeeman interactions to the matrix element of ~fM If, in such a case, gl ) g 2 , the esr spectrum of radical 1 will be totally emissive while the spectrum of radical 2 will be correspondingly absorptive.

One of the weaknesses of the initial radical-pair theory is that in order to achieve the observed polarization, the radicals must remain at a separation corresponding to J "" .~fM for a time interval of 10 "1° seconds or longer 7s. J decreases very rapidly with increasing radical separation. Because the correlation times of the Brownian motions in liquid are about 10 "12 seconds and the time involved in the breaking of a chemical bond is very short, it is thought that the required interval of 10 "l° second or longer is quite improbable. Recent developments of the theory have been aimed mainly at solving this difficulty.

In an experimental and theoretical study, Verma and Fessenden s3 reinvestigated the CIDEP of H atoms in a pulse radiolysis system with a

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microsecond time-resolved spectrometer. They developed a kinetic model based on the Fischer and Lehnig formulation of the radical-pair theory 8a which considers that radical combinations can be partly adiabatic for radical separations in the region where J is comparable to the hyperf'me splitting. Their kinetic model fits satisfactorily the details of the observed time dependence curves, including the initial growth and the oscillatory behaviour. They also argued that the initial polarization produced at the radical formation stage is inadequate to account for all of the experimental results.

Before we turn to a discussion of "initial polarization", it is worth noting that the ringlet and triplet states of the radical-pair have not been consistently and precisely defined in the radical-pair theory. This causes some uncertainty and confusion about the signs of the singlet-triplet splitting J, i.e. whether the ringlet state lies below or above the triplet state. Since the sign of J often determines the nature of the polarization (emission or absorption), this uncertainty must be removed in future development of the theory.

B. Mechanisms of "Initial Polarization". So far the radical-pair model considers only how electron polariza-

tion is produced after a pair of radicals is formed. It assumes no initial polarization of the radicals during their chemical formation stage. Recently Wan and co-workers have made attempts as'as to probe the mechanism of initial electron polarization, without recourse to the familiar radical-pair model. If we assume that the formation of hydrogen atoms in the radiolysis of an acid proceeds in two stages a9:

H + + eaq ~- (H +, e - ) -+ H (2S~)

with the second step being rate-determining, and that the species (H +, e-) represents a complex, probably in some higher excited state, it could be argued a6 that the second step is equivalent to a cascade process, presumably following the selection rule AF = 0 or +1. It must be pointed out that the use of such an optical selection rule is arbitrary, similarily to the random choice of the sign for J in the radical-pair theory. It is hoped, however, that furthe.r studies may justify the use of the optical selection rule.

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By accepting these basic assumptions, it can be readily seen that the F=I triplet sublevels of the ground state 2Sy~ have more precursors than those of the F=O singlet sublevel. Such a preference for the F=I hyperfme level of the ground state could account for a population difference between the F=I and the F=O sublevels. The probability Pr of formation of the field dependent state lur> is obtained by an adiabatic mixing between the F=I and F=O states by the external magnetic field. The results predict the low-field line to be emissive and the high-field line to be absorptive, as obselved experimentally 9°'92. The model also predicts that the absolute initial magnitude of the polarization of the low-field line is greater than that of the high field line. On the other hand, the radical-pair theory predicts equal intensity for the two lines. This cascade model has also been applied to the case of D atoms s6 and the results are again in qualitative agreement with experiment~. Further calculations have been extended to simple organic radicals containing two and three equivalent protons s8.

At this point, it should be recalled that Verma and Fessenden 83 argued that such an initial polarization produced upon H atom formation is inadequate to to account for all the experimental results. The strongest evidence in favour of a radical-pair mechanism is that the polarization persists for times longer than the spin-lattice relaxation time 93. (Fessenden93 has also applied his interpretation to the CH(C02-)2, CH2CO ~ , and hydroxycyclohexadienyl radicals formed by reactions of OH radicals.)

It is conceivable that in a chemical system, polarization can be induced simultaneously by a combination of mechanisms, including both the radical-pair and the initial polarization models. It may be just a coincidence that the cascade model happens to predict the right magnitude of polarization in simple cases such as H and D atoms. Nevertheless, further and specific experimental tests of these models are very much desirable. In the authors' laboratory, an approach using an S-band spectrometer with a much lower magnetic field is being considered to test the models.

CIDEP in photochemical systems will now be discussed. In 1970 Livingston and Zeldes 94 discovered a totally emissive esr spectrum in the photolysis of a tartaric acid solution. Atkins and co-workers 9s also observed a totally emissive esr spectrum in the laser-flash photolysis of

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some carbonyl compounds such as benzophenone in liquid paraffin. These authors 96 suggested that the polarization in a totally emissive mode could be attributed to S o +~T% intersystem crossings by some magnetic interactions such as hyperfme and spin- rotation interactions. Their mechanism predicts that the radicals in the pair (the ketyl and the solvent radicals) will have the same sign of polarization. In other words the counter solvent radicals are predicted to be emissive. This is in contrast to the original radical-pair theory which considered only the S -+To mixing, which leads to the prediction that the ketyl radical and the counter solvent radical have the opposite sign of polarization. While the benzophenone ketyl radicals have been observed in a totally ernissive mode 9s, the counter solvent radicals have eluded observa- tion and their sign of polarization thus is not determinable. Recently Wong and Wan ~ investigated the photochemical reaction of triplet benzophenone with 2,6-di-t-butylphenol in acetic acid solvent. They found that the phenoxy counter radical indeed showed a totally emissive character. They further established that the magnitude of polarization is dependent upon the concentration of the phenol, a fact which cannot be accounted for by the simple radical-pair theory. Nevertheless, these, experiments 9s,~ clearly established that the photochemical reaction of triplet benzophenone leads to a ketyl radical and a counter radical, both being in the emissive mode.

Wong and Wan 8s have also reported a totally emissive esr spectrum of 1,4-naphthosemiquinone radicals produced in the pulsed photolysis of the parent quinone in 2-propanol. Subsequently, they established that when 2,6-di-t-butylphenol was used as the reactant, both the semiquinone radical and the counter phenoxy radical are totally emissive sT. They approached the polarization problem by considering a "photochemical" mechanism leading to "initial polarization". It was proposed that the electron polarization is due to the optically spin polarized triplets of the parent quinones which subsequently abstract hydrogen with retention of polarization in the resultant semiquinone and phenoxy radicals. Obviously the rate of the hydrogen abstraction reaction must be comparable to, or greater than, the spin-lattice relaxation rate of the triplet quinone (i.e. depolarization).

A forr0al theoretical development of the "photochemical" theory to account for the polarization in quinone photochemical systems was

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given by Wong, Hutchinson and Wan aa. The treatment was extended by Atkins and Evans ~ to include an anisotropically rotating triplet model.

Needless to say, there are many inadequacies in the photochemical theory. It is our hope that the proposed theory will stimulate further refinement and development of an ultimate theory for the CIDEP phenomenon. Indeed, Atkins, McLauchlan and co-workers 99, who contn~outed much to the development of the current radical-pair theory, have recently obtained some experimental evidence against the simple radical-pair model. They studied the photolysis of duroquinone in the presence of various amines and observed a totally ernissive behaviour of the durosemiquinone radical anions. The counter amine radical cations were not detected. They found that the magnitude of the polarization depends on the nature of the amine, its concentration, and the solvent. The current radical-pair theory is not able to account for these observations. In addition, they presented some experimental observations which cannot be satisfactorily explained by the photo- chemical theory.

Future developments of CIDEP theories will require more quantita- tive experimental data in a variety of chemical systems. When a better understanding of CIDEP is acquired, the data can be applied to obtain spin-lattice relaxation times of radicals or triplet molecules in solution, further information on the complex intersystem crossing phenomena in organic photochemical systems, and to deduce reaction mechanisms. For example, Wong and Wan 97 have suggested the potential application of photo-CIDEP to the study of intersystem crossing in benzophenone.

The importance of organic triplet states in photochemistry has been well recognized in the past decade. The fact that repopulation of the

lowest excited singlets can result from the thermal equilibrium existing in the triplet states has led to the question of whether or not the photochemical reactivity in some organic systems originates directly from the triplet state. With the development of a better photochemical CIDEP theory, such problems can be at least partially answered by a direct observation of esr emission of the resulting radical. CIDEP experiments can also be extended to investigate energy-transfer mechanisms in triplet photosensitization reactions.

The radical-pair theory can provide direct insight into the nature of the radical-radical reactions and their dependence on nuclear spin

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states. Information about rate constants, the multiplicity of the precursor radical pair, and the exchange interaction J can also be obtained. The theory dealing with initial polarization can provide some details of the mechanism of radical formation and the nature of the precursors.

V. ACKNOWLEDGEMENTS

We thank Drs. P.W. Atkins and K.A. McLauchlan for providing us with preprints of their recent work. This work is supported by the National Research Council of Canada and by the School of Graduate Studies and Research at Queen's University.

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VI REFERENCES 1. E.Zavoisl~i,J.Phy~ U.S.S.R.,9, 211,245 (1945).

,2. R.O.C. Norman and B.C. Gilbert in "Advances in Phys. Org. Chemistry", ed. by V. Gold, Academic Press, London, 1967.

3. R.W. Fessenden and R.H. Schuler in "Advances in Radiation Chemistry", ed. by M. Burton and $.L. Magee, 2, 1 (1970).

4. H. Fisher in"Free Radicals", ed. by J.K. Kochi, 2,435 (1973). 5. J.K.S. Wan, in "Advances in Photochemistry", 9, in press (1974). 6. H.M. McConnel and R.E. Robertson, ZPhys. Chera. 61, 1018 (1957). 7. R.O.C. Norman and R.J. Pritchett, Chem. Ind., 2040 (1965). 8. J.H. Mackey and D.E. Wood, Mol.Phys., 18, 783 (1970). 9. R.V. Lloyd and D.E. Wood, Mol. Phys., 20, 735 (1971).

10. Apparently the g value of the unsubstituted phenoxyl radical has not been reported in the literature, but those of subsituted phenoxyl radicals in the range 2.0045 +_ 0.0003; see for example, P.B. Ayscough and K.E. Russell, Can. J. Chem., 43,3039 (1965);45, 3019 (1967).

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Chem~oc., 82,766 (1960). 16. i'.Cote and C. Heller./. Chem. Phys., 34, 1085 (1961). 17. R. Bersohn, J. Chem. Phys., 24, 1066 (1956): S.I. Weissman, J.

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