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The effects of orbital degeneracy and near degeneracy upon the g-values of organic free radicals
JOURNAL
OF MAGNETIC
RESONANCE
10,149-l
55 (1973)
The Effects of Orbital Degeneracy and Near Degeneracy upon the g-Values of Organic Free Radicals M.
T. JONES, T. C. KUECHLER, AND S. METZ
Department of Chemistry, University of Missouri-St. Louis, St. Louis, Missouri 63121 Presented at the Southeastern Magnetic Resonance Conference, Athens, Georgia, October, 1972 The temperature dependence of the g-values of the anion radicals in the series benzene, monodeuterobenzene, iso-propylbenzene, ethylbenzene, toluene, and p-xylene has been measured. All the g-values display negative temperature coefficients. At a fixed temperature the g-values decrease as one moves through the series. Our results suggest that there are two contributions to the observed g-value for the benzene anion, i.e., ion-pairing effects and thermal averaging over vibronic excited states. In the case of the alkyl-substituted benzene anions there may be an additional mechanism, i.e., that of thermal averaging over the two electronic states which in the case of the benzene anion radical are degenerate. INTRODUCTION
The first extremely accurate measurementof the orbitally degeneratebenzeneanion radical g-value was m a d e by Segalet al. (1) at a temperature of -101°C. They also reported that the benzene anion g-value is anomalous with respect to those they had observed for orbitally nondegenerateorganic radicals (I, 2). In a subsequent, brief report Kelm and M o b ius (3) noted that the benzene anion g-value is temperature dependent. At higher temperaturesthe g-value decreasesand moves toward the value expected for a nondegenerateradical system. The value for dg/dT (= -7.8 x IO-‘/“C) derived from the data reported by Kelm and M o b ius (3) is the largest of any reported for an organic free radical system(2). The purpose of the study reported herewas primarily to determine the source (or sources)of the temperature dependenceof the benzene anion g-value. Secondarily, it was hoped that some new insight into the source of the benzeneanion radical g-value anomaly m ight be obtained. The benzeneanion radical is known to be ion-paired under the experimental conditions for which the foregoing results were obtained (4,5). Moreover, it has beenreported that ion-pair formation between anion radical speciesand alkali metal ions leads to temperature dependentg-values(6-9). Thus, one very likely contribution to the benzene anion g-value temperature dependenceis the ion-pair formation. The problem then becomesone of finding a compound or a seriesof compounds whoseion-pairing characteristics do not change significantly through the series but whose nearnessto orbital degeneracy does. Such a series does exist, n a m e ly, the anion radicals of benzene, monodeuterobenzene,isopropylbenzene,ethylbenzene,toluene, and p-xylene. Both the benzeneandp-xylene anion radicals are known to be ion-paired, the former from a detailed lineshapeanalysis (4,5) and the latter becauseits line widths are sufficiently narrow to allow the resolution of the metal hyperfine splittings (10). The radicals Copyright All rights
0 1973 by Academic Press, Inc. of reproduction in any form reserved.
149
150
JONES,
KUECHLER,
AND
METZ
which lie between these two extremes display fairly broad and overlapping resonance lines. As a consequence the lineshape analysis of Jones et al. (4,5) cannot reasonably be applied nor does one expect to explicitly resolve metal hyperfine splittings of the magnitude observed for the benzene andp-xylene anion radicals. There is no reason to believe under similar conditions that all of the anion radicals in the above series are not ion-paired. TABLE
1
ENERGY SPL~NGS BETWEEN Two VIBRONIC STATES
LOWEST
Radical
E in cm-’
Monodeuterobenzene anion Isopropylbenzene anion Ethylbenzene anion Toluene anion p-Xylene anion
20” 178 251 4706 822
e Experimental (See Ref. II). Ir Experimental Value N 525-700 cm-’ (See Ref. 12).
The separation in energy between the two originally degenerate states (i.e., the two states which in the case of benzene are degenerate) has been measured experimentally for the monodeuterobenzene and toluene anions (II, 12) from the temperature dependence of their hyperfine splittings. Also, Hobey (13) has calculated the expected separation for the series. The results of his calculations which include vibronic interactions are shown in Table 1. Experimentally, all of the alkyl-substituted anions in Table 1 show temperature-dependent proton hyperfine splittings except for p-xylene. In the case of the latter, the energy separation between the two states is too large for the upper state to be significantly populated over the temperature range of the study. EXPERIMENTAL
The g-values were measured on a Varian E-12 ESR spectrometer using the dual cavity technique (24). The same reference sample was used for all of the measurements reported here. The reference sample was a dilute solution (~10~~ M) of lithium tetracyanoethylene in tetrahydrofuran. The g-value of the reference sample was carefully measured with respect to the anthracene and pyrene anion radicals1 and found to be ,equal to 2.002780 (~0.000002). This value is not corrected for second order shifts. The g-value of the reference sample was found to be independent of temperature in the range -10-+3O”C. ’ 1 Recently, Allendoerfer (15) pointed out that Segal et al. (I) errored in the value of the mineral oil proton NMR frequency which they used in their measurements. This error amounts to 7.2 ppm and leads to the result that all the g-values reported by Segal et al. (and all others who have standardized their measurements against values reported by Segal et al.) are too large by 1.4 x lows. All g-values ireported herein have been so corrected where necessary.
151
g-VALUES OF ORGANIC FREE RADICALS
All of the samples were prepared in a 2:l m ixture of tetrahydrofuran and 1,2dimethoxyethane. The reducing agent was a eutectic m ixture of sodium and potassium metals. The concentration of the radical anion parent compound was 0.1 M . Previous experimental studies have indicated that under these conditions the predominant cation is potassium (5). RESULTS
Figure 1 shows a plot of the observed g-values against temperature for the series of anion radicals studied. The observed g-values and their temperature dependence for the benzene and monodeuterobenzene anions are within experimental error of each
1
-120
-100 -80 TEMPERATURE “C
/
-60
FIG. 1. A plot of the observed g-values vs temperature for the anion radicals included in the study. The circled dots represent the benzene anion radical g-values. The stars represent the monodeuterobenzene anion radical g-values. The remaining points are sufficiently separated so that they do not require separate symbols.
other. This observation confirms that reported by Lawler and Fraenkel (II) who although they did not measure the g-values, reported that the g-values of the benzene and monodeuterobenzeneanions were equal to within&l part in 106.The benzeneanion g-value observed by Segal et al. (I) falls within experimental error of those shown in Fig. 1. However, each of the values reported by Kelm and Mobius (3) is lower than those shown in Fig. 1 and, except for the value observed at -84°C clearly falls out of the range of experimental error. Table 2 summarizes the data in a somewhat different way. The data in Table 2 are the result of fitting the experimental g-values for each radical to the equation g(T)=A+B*T;
PI
T is in “C. The uncertainties given for A are the root-mean-square deviations between the g-values calculated from the Eq. [l] and the experimental value at the sametemperature. Table 2 lists data for the benzene and monodeuterobenzene anion radicals as well
152
JONES, KUECHLER, AND METZ
as for the combined set. The variation in (dg/dT) for the benzene and monodeuterobenzene anion radical may be due to variation in the exact ratio of tetrahydrofuran to 1,Zdimethoxyethane in the mixed solvent system. Two prominent features stand out in the data shown in Fig. 1 and Table 2. First, at a fixed temperature the g-value decreases in the series benzene to p-xylene, i.e., as the energy separation between the originally degenerate level increases. Second, as the energy separation increases, the temperature dependence of the g-value decreases and appears to reach a limiting value in the case of thep-xylene anion radical. An exception to the later observation appears to exist in the case of the isopropylbenzene and ethylbenzene anion radicals. However, this inversion may be the result of variation in the composition of the mixed solvent system. TABLE SUMMARY OF
Radical Benzene anion Monodeuterobenzene anion Combined benzene anion data Isopropylbenzene anion Ethylbenzene anion Toluene anion p-Xylene anion Tropyl
g-VALUE
2
TEMPERATURE
Counter-ion K+ K+ K+ K+ K+ K+ K+
(Na-K) (Na-K) (Na-K) (Na-K) (Na-K) (Na-K) (Na-K) c
DEPENDENCE~
Ab
2.002771 2.002776 2.002773 2.002784 2.002746 2.002736 2.002711 2.002674
B x 107b
(k3) (G) (*4) (*2) (53) (&2) (%2) (&3)
-7.00 -6.60 -6.92 -4.55 -4.70 -3.23 -2.70 -1.57
Temp. range of input data (“C) -43 -59 -43 -60 -59 -60 -54.5 +111
to -122 to -109 to -122 to -117 to -126 to -122 to -118 to +180
n Corrected for second order shifts. b g(T) = A + B-T, where T is in “C and the uncertainty in A represents the rrns deviation in the last place between the calculated and experimental values of g. c Solvent was neat ditropyl. See Ref. 20 for the method of preparation of the tropyl radical. DISCUSSION
The values given for (dg/dT) in Table 2 can be corrected for the effect of ion-pair formation if one makes the following assumptions. One, the only contribution to the temperature dependence of the p-xylene anion g-value is due to ion-pairing effects. Two, the ion-pair contribution to the g-value temperature dependence is essentially constant throughout the series. The first assumption is based on the fact that the p-xylene anion is known to be ion-paired under the conditions for which its g-value was measured and that there is no measurable amount of thermal averaging over the originally degenerate states. The second assumption is more difficult to justify. However, it will appear more reasonable when we compare the benzene anion value for (dg/dT) which has been corrected for ion-pairing with the value obtained from the tropyl radical. Table 3 lists the values for (dg/dT) which have been corrected for ion-pairing effects. The value obtained for the benzene anion of -4.2 x IO-‘/C is to be compared with the value of -1.57 x 10-‘/C obtained for the tropyl radical. Obviously, in the latter case there can be no ion-pairing contributions to the g-value or its temperature *dependence.
g-VALUES
153
OF ORGANIC FREE RADICALS
Moss and Perry (16) have extended Stone’s theory (27-19) of g-values to orbitally degenerate free radicals. They show that a temperature dependent g-value could arise from orbital angular momentum contributions to the g-value which vary with temperature because of differences in the populations of thermally accessible vibronic states. In view of Moss and Perry’s calculations the values for (dg/dT) for the benzene anion and tropyl radicals do not appear to be unreasonable. It is not obvious that the same mechanism applies in the case of the nearly degeneratesystems, i.e., isopropylbenzene, ethylbenzene, and toluene anion radicals. However, it may apply becausesuch systems do undergo vibronic interactions (23). TABLE g-VALUE
3
TEMPERATURE DEPENDENCIES ION PAIRING EFFECTS
CORRECTED
FOR
Radical
Corrected (dg/dT) x 10’
Benzene Isopropylbenzene anion Ethylbenzene anion Toluene anion
-4.2 -1.9 -2.0 -0.5
Let us now consider the relative g-values as we move through the series.Vincow et al., (20) reported for the tri-1,3,5-t-butyltropyl radical that (dg/dT) = -2.75 x 10-‘/C and g = 2.00267 over the temperature range 150-I 80°C. They proposed that the g-value temperature dependencecould be explained by thermal averaging over the two nearly degenerate states, G and E. The average g is given by g(T) = gG + gE exp (-A-WY If exp (-AE/kT)
’
PI
gG and gE represent the g-values in the ground and excited states,respectively. For such a mechanism, if gG > gE, then (dg/dT) is negative and vice versa. As AE decreases,g(T) approaches the value of (g” + gE)/2. The two states G and Erepresent the antisymmetric and symmetric states, respectively, obtained from a simple Hiickel MO calculation. Application of this idea to the g-value (and its temperature dependence) of the tri-tbutyltropyl studied by Vincow et al. (20) gives gG > gE. If we assumethat the symmetric and antisymmetric states of the tropyl radical have approximately the same g’s as they do in the tri-t-butyltropyl then we would predict a smaller g-value for the tropyl radical. This is in agreement with both the g-value that Vincow et al. have reported and that we report in Table 2. Unfortunately, the application of the prior model to the anion radicals of benzene and substituted benzene does not yield a set of self consistent observations. The relative order of the g-values at a fixed temperature suggeststhat any contribution to (dg/dT) from this source must be positive whereas the experimental values are negative. We have calculated the possible contributions to (dg/dT) for the alkyl-substituted benzene anion radicals from this source using the following input parameters : AE was taken to be the value given in Table 1, gG was taken as the value associated with the p-xylene
154
JONES, KUECHLER, AND MET2
anion radical, and gE was taken as equal to the benzene anion g-value plus the difference between the benzene anion g-value and that of thep-xylene anion. The results of these calculations are shown in Table 4 for two different temperatures. At this point, it is obvious that a mechanism such as that proposed by Vincow et al. could be operable. Ifit were, it would mean that the “corrected” values for (dg/dT) would be more negative than those in Table 3, but even so, certainly within the realm of being reasonable. Finally, let us consider the various g-values which have been measured, relative to the value predicted by Stone’s theory (I, 27-20). According to Stone’s theory, g = 2.002626(~0.000004)-(16.6 i l.O)J x 10-5, 131 where 1 is the factor associated with the energy of the Htickel MO in which the unpaired electron is found, in units of /I (i.e., E = a + nj?). The dashed line in Fig. 1 traces the g-value predicted for the benzene anion radical by Eq. 3. This is the same value predicted for all other members of the alkyl substituted benzene anion series. The troublesome TABLE
4
VALUESFOR (dg/dT) CALCULATEDFROMAVERAGINGOVERELECTRONICSTATES Radical
(dg/dT) x 107(-12O’C)
(dg/dT) x 107(-6O’C)
Monodeutrobenzene anion Isopropylbenzene anion Ethylbenzene Toluene anion p-Xylene anion
+0.69 +3.3 +2.8 +0.19 +0.053
+0.28 +1.8 +1.8 +1.02 +0.18
feature here is that some of the g-values fall as far below the value calculated for “nondegenerate” benzene as the benzene lies above it. We have no satisfactory explanations of this behavior at this time. CONCLUSIONS
We have shown for the benzene anion radical that there may be two contributions to the observed g-value, i.e., ion-pairing effects and thermal averaging over vibronic excited states. For the alkyl-substituted benzene anions there may be an additional mechanism, namely that of thermal averaging over the two electronic states which in the case of the benzene anion are degenerate. We have also noted that some members of the alkyl-substituted benzene anion series display g-values as far below the “Stone g-value” as the benzene anion radical g-value lies above it. Studies are in progress in which pure solvents are being used rather than the mixed solvent system. By this means we hope to obtain a better understanding of the ion-pair contributions to the g-values of the members of the series in Table 1. Also, we are attempting to measure the equilibrium constant for the following reaction C6Hs-* + RC6H5 Z? C,H, + RC6HS-. so that we can make appropriate modification to the value of il in Eq. 3.
141
g-VALUES
OF ORGANIC FREE RADICALS
155
ACKNOWLEDGMENT The support of this research by the National Science Foundation through Grant GP-28436 and the University of Missouri-St. Louis is acknowledged. REFERENCES 1. B. G. SEGAL, M. KAPLAN, AND G. K. FRAENKEL, J. Chem. P&s. 43,419l (1965). 2. M. T. JONES, “Advances in Magnetic Resonance” (J. S. Waugh, Ed.), Vol. VII, Academic Press Inc., New York, 1973. 3. J. KELM AND K. MOBIUS, Angew. Chem. Intern. Edit. 9,73 (1970). 4. M. T. JONES, M. KOMARYNSKY, AND R. D. RATAICZAK, J. Phys. Chem. 75,2769 (1971). 5. M. T. JONES AND M. KOMARYNSKY, J. Chem. Phys. 56,4404 (1972). 6. C. L. DODSON AND A. H. REDDOCH, J. Chem. Phys. 48,3226 (1968). 7. W. G. WILLIAMS, R. J. PRITCHETT, AND G. K. FRAENKEL, J. Chem. Phys. 52,5584 (1970). 8. J. L. SOMMERDIJK AND E. DE BOER, “Ions and Ion Pairs in Organic Reactions,” Vol. 1, Chapter 8, John Wiley & Sons, New York, 1972. 9. T. TAKESHITA AND N. HIROTA, J. Amer. Chem. Sot. 93,642l (1971). 10. E. DE BOER AND C. MACLEAN, J. Chem. Phys. 44,1334 (1966). II. R. G. LAWLER AND G. K. FRAENKEL, J. Chem. Phys. 49,1126 (1968). 12. T. R. TUTTLE, J. Amer. Chem. Sot. 84,1492 (1962). 13. W. HOBEY, J. Chem. Phys. 43,2187 (1965). 14. J. E. WERTZ AND J. R. BOLTON, “Electron Spin Resonance: Elementary Theory and Practical Applications”, p. 464, McGraw-Hill, New York, 1972. 15. R. D. ALLENDOERFER, J. Chem. Phys. 55,3615 (1971). 16. R. E. Moss AND A. J. PERRY, Mol. Phys. 22,789 (1971). 17. A. J. STONE, Prac. Roy. Sot. London A271,424 (1963). 18. A. J. STONE, Mol. Phys. 6, 509 (1963). 19. A. J. STONE, Mol. Phys. 7,311 (1963/64). 20. G. VINCOW, M. L. MORRELL, F. R. HUNTER, AND H. J. DAUBEN, JR., J. Chem. Phys. 48,2876 (1968).
OF MAGNETIC
RESONANCE
10,149-l
55 (1973)
The Effects of Orbital Degeneracy and Near Degeneracy upon the g-Values of Organic Free Radicals M.
T. JONES, T. C. KUECHLER, AND S. METZ
Department of Chemistry, University of Missouri-St. Louis, St. Louis, Missouri 63121 Presented at the Southeastern Magnetic Resonance Conference, Athens, Georgia, October, 1972 The temperature dependence of the g-values of the anion radicals in the series benzene, monodeuterobenzene, iso-propylbenzene, ethylbenzene, toluene, and p-xylene has been measured. All the g-values display negative temperature coefficients. At a fixed temperature the g-values decrease as one moves through the series. Our results suggest that there are two contributions to the observed g-value for the benzene anion, i.e., ion-pairing effects and thermal averaging over vibronic excited states. In the case of the alkyl-substituted benzene anions there may be an additional mechanism, i.e., that of thermal averaging over the two electronic states which in the case of the benzene anion radical are degenerate. INTRODUCTION
The first extremely accurate measurementof the orbitally degeneratebenzeneanion radical g-value was m a d e by Segalet al. (1) at a temperature of -101°C. They also reported that the benzene anion g-value is anomalous with respect to those they had observed for orbitally nondegenerateorganic radicals (I, 2). In a subsequent, brief report Kelm and M o b ius (3) noted that the benzene anion g-value is temperature dependent. At higher temperaturesthe g-value decreasesand moves toward the value expected for a nondegenerateradical system. The value for dg/dT (= -7.8 x IO-‘/“C) derived from the data reported by Kelm and M o b ius (3) is the largest of any reported for an organic free radical system(2). The purpose of the study reported herewas primarily to determine the source (or sources)of the temperature dependenceof the benzene anion g-value. Secondarily, it was hoped that some new insight into the source of the benzeneanion radical g-value anomaly m ight be obtained. The benzeneanion radical is known to be ion-paired under the experimental conditions for which the foregoing results were obtained (4,5). Moreover, it has beenreported that ion-pair formation between anion radical speciesand alkali metal ions leads to temperature dependentg-values(6-9). Thus, one very likely contribution to the benzene anion g-value temperature dependenceis the ion-pair formation. The problem then becomesone of finding a compound or a seriesof compounds whoseion-pairing characteristics do not change significantly through the series but whose nearnessto orbital degeneracy does. Such a series does exist, n a m e ly, the anion radicals of benzene, monodeuterobenzene,isopropylbenzene,ethylbenzene,toluene, and p-xylene. Both the benzeneandp-xylene anion radicals are known to be ion-paired, the former from a detailed lineshapeanalysis (4,5) and the latter becauseits line widths are sufficiently narrow to allow the resolution of the metal hyperfine splittings (10). The radicals Copyright All rights
0 1973 by Academic Press, Inc. of reproduction in any form reserved.
149
150
JONES,
KUECHLER,
AND
METZ
which lie between these two extremes display fairly broad and overlapping resonance lines. As a consequence the lineshape analysis of Jones et al. (4,5) cannot reasonably be applied nor does one expect to explicitly resolve metal hyperfine splittings of the magnitude observed for the benzene andp-xylene anion radicals. There is no reason to believe under similar conditions that all of the anion radicals in the above series are not ion-paired. TABLE
1
ENERGY SPL~NGS BETWEEN Two VIBRONIC STATES
LOWEST
Radical
E in cm-’
Monodeuterobenzene anion Isopropylbenzene anion Ethylbenzene anion Toluene anion p-Xylene anion
20” 178 251 4706 822
e Experimental (See Ref. II). Ir Experimental Value N 525-700 cm-’ (See Ref. 12).
The separation in energy between the two originally degenerate states (i.e., the two states which in the case of benzene are degenerate) has been measured experimentally for the monodeuterobenzene and toluene anions (II, 12) from the temperature dependence of their hyperfine splittings. Also, Hobey (13) has calculated the expected separation for the series. The results of his calculations which include vibronic interactions are shown in Table 1. Experimentally, all of the alkyl-substituted anions in Table 1 show temperature-dependent proton hyperfine splittings except for p-xylene. In the case of the latter, the energy separation between the two states is too large for the upper state to be significantly populated over the temperature range of the study. EXPERIMENTAL
The g-values were measured on a Varian E-12 ESR spectrometer using the dual cavity technique (24). The same reference sample was used for all of the measurements reported here. The reference sample was a dilute solution (~10~~ M) of lithium tetracyanoethylene in tetrahydrofuran. The g-value of the reference sample was carefully measured with respect to the anthracene and pyrene anion radicals1 and found to be ,equal to 2.002780 (~0.000002). This value is not corrected for second order shifts. The g-value of the reference sample was found to be independent of temperature in the range -10-+3O”C. ’ 1 Recently, Allendoerfer (15) pointed out that Segal et al. (I) errored in the value of the mineral oil proton NMR frequency which they used in their measurements. This error amounts to 7.2 ppm and leads to the result that all the g-values reported by Segal et al. (and all others who have standardized their measurements against values reported by Segal et al.) are too large by 1.4 x lows. All g-values ireported herein have been so corrected where necessary.
151
g-VALUES OF ORGANIC FREE RADICALS
All of the samples were prepared in a 2:l m ixture of tetrahydrofuran and 1,2dimethoxyethane. The reducing agent was a eutectic m ixture of sodium and potassium metals. The concentration of the radical anion parent compound was 0.1 M . Previous experimental studies have indicated that under these conditions the predominant cation is potassium (5). RESULTS
Figure 1 shows a plot of the observed g-values against temperature for the series of anion radicals studied. The observed g-values and their temperature dependence for the benzene and monodeuterobenzene anions are within experimental error of each
1
-120
-100 -80 TEMPERATURE “C
/
-60
FIG. 1. A plot of the observed g-values vs temperature for the anion radicals included in the study. The circled dots represent the benzene anion radical g-values. The stars represent the monodeuterobenzene anion radical g-values. The remaining points are sufficiently separated so that they do not require separate symbols.
other. This observation confirms that reported by Lawler and Fraenkel (II) who although they did not measure the g-values, reported that the g-values of the benzene and monodeuterobenzeneanions were equal to within&l part in 106.The benzeneanion g-value observed by Segal et al. (I) falls within experimental error of those shown in Fig. 1. However, each of the values reported by Kelm and Mobius (3) is lower than those shown in Fig. 1 and, except for the value observed at -84°C clearly falls out of the range of experimental error. Table 2 summarizes the data in a somewhat different way. The data in Table 2 are the result of fitting the experimental g-values for each radical to the equation g(T)=A+B*T;
PI
T is in “C. The uncertainties given for A are the root-mean-square deviations between the g-values calculated from the Eq. [l] and the experimental value at the sametemperature. Table 2 lists data for the benzene and monodeuterobenzene anion radicals as well
152
JONES, KUECHLER, AND METZ
as for the combined set. The variation in (dg/dT) for the benzene and monodeuterobenzene anion radical may be due to variation in the exact ratio of tetrahydrofuran to 1,Zdimethoxyethane in the mixed solvent system. Two prominent features stand out in the data shown in Fig. 1 and Table 2. First, at a fixed temperature the g-value decreases in the series benzene to p-xylene, i.e., as the energy separation between the originally degenerate level increases. Second, as the energy separation increases, the temperature dependence of the g-value decreases and appears to reach a limiting value in the case of thep-xylene anion radical. An exception to the later observation appears to exist in the case of the isopropylbenzene and ethylbenzene anion radicals. However, this inversion may be the result of variation in the composition of the mixed solvent system. TABLE SUMMARY OF
Radical Benzene anion Monodeuterobenzene anion Combined benzene anion data Isopropylbenzene anion Ethylbenzene anion Toluene anion p-Xylene anion Tropyl
g-VALUE
2
TEMPERATURE
Counter-ion K+ K+ K+ K+ K+ K+ K+
(Na-K) (Na-K) (Na-K) (Na-K) (Na-K) (Na-K) (Na-K) c
DEPENDENCE~
Ab
2.002771 2.002776 2.002773 2.002784 2.002746 2.002736 2.002711 2.002674
B x 107b
(k3) (G) (*4) (*2) (53) (&2) (%2) (&3)
-7.00 -6.60 -6.92 -4.55 -4.70 -3.23 -2.70 -1.57
Temp. range of input data (“C) -43 -59 -43 -60 -59 -60 -54.5 +111
to -122 to -109 to -122 to -117 to -126 to -122 to -118 to +180
n Corrected for second order shifts. b g(T) = A + B-T, where T is in “C and the uncertainty in A represents the rrns deviation in the last place between the calculated and experimental values of g. c Solvent was neat ditropyl. See Ref. 20 for the method of preparation of the tropyl radical. DISCUSSION
The values given for (dg/dT) in Table 2 can be corrected for the effect of ion-pair formation if one makes the following assumptions. One, the only contribution to the temperature dependence of the p-xylene anion g-value is due to ion-pairing effects. Two, the ion-pair contribution to the g-value temperature dependence is essentially constant throughout the series. The first assumption is based on the fact that the p-xylene anion is known to be ion-paired under the conditions for which its g-value was measured and that there is no measurable amount of thermal averaging over the originally degenerate states. The second assumption is more difficult to justify. However, it will appear more reasonable when we compare the benzene anion value for (dg/dT) which has been corrected for ion-pairing with the value obtained from the tropyl radical. Table 3 lists the values for (dg/dT) which have been corrected for ion-pairing effects. The value obtained for the benzene anion of -4.2 x IO-‘/C is to be compared with the value of -1.57 x 10-‘/C obtained for the tropyl radical. Obviously, in the latter case there can be no ion-pairing contributions to the g-value or its temperature *dependence.
g-VALUES
153
OF ORGANIC FREE RADICALS
Moss and Perry (16) have extended Stone’s theory (27-19) of g-values to orbitally degenerate free radicals. They show that a temperature dependent g-value could arise from orbital angular momentum contributions to the g-value which vary with temperature because of differences in the populations of thermally accessible vibronic states. In view of Moss and Perry’s calculations the values for (dg/dT) for the benzene anion and tropyl radicals do not appear to be unreasonable. It is not obvious that the same mechanism applies in the case of the nearly degeneratesystems, i.e., isopropylbenzene, ethylbenzene, and toluene anion radicals. However, it may apply becausesuch systems do undergo vibronic interactions (23). TABLE g-VALUE
3
TEMPERATURE DEPENDENCIES ION PAIRING EFFECTS
CORRECTED
FOR
Radical
Corrected (dg/dT) x 10’
Benzene Isopropylbenzene anion Ethylbenzene anion Toluene anion
-4.2 -1.9 -2.0 -0.5
Let us now consider the relative g-values as we move through the series.Vincow et al., (20) reported for the tri-1,3,5-t-butyltropyl radical that (dg/dT) = -2.75 x 10-‘/C and g = 2.00267 over the temperature range 150-I 80°C. They proposed that the g-value temperature dependencecould be explained by thermal averaging over the two nearly degenerate states, G and E. The average g is given by g(T) = gG + gE exp (-A-WY If exp (-AE/kT)
’
PI
gG and gE represent the g-values in the ground and excited states,respectively. For such a mechanism, if gG > gE, then (dg/dT) is negative and vice versa. As AE decreases,g(T) approaches the value of (g” + gE)/2. The two states G and Erepresent the antisymmetric and symmetric states, respectively, obtained from a simple Hiickel MO calculation. Application of this idea to the g-value (and its temperature dependence) of the tri-tbutyltropyl studied by Vincow et al. (20) gives gG > gE. If we assumethat the symmetric and antisymmetric states of the tropyl radical have approximately the same g’s as they do in the tri-t-butyltropyl then we would predict a smaller g-value for the tropyl radical. This is in agreement with both the g-value that Vincow et al. have reported and that we report in Table 2. Unfortunately, the application of the prior model to the anion radicals of benzene and substituted benzene does not yield a set of self consistent observations. The relative order of the g-values at a fixed temperature suggeststhat any contribution to (dg/dT) from this source must be positive whereas the experimental values are negative. We have calculated the possible contributions to (dg/dT) for the alkyl-substituted benzene anion radicals from this source using the following input parameters : AE was taken to be the value given in Table 1, gG was taken as the value associated with the p-xylene
154
JONES, KUECHLER, AND MET2
anion radical, and gE was taken as equal to the benzene anion g-value plus the difference between the benzene anion g-value and that of thep-xylene anion. The results of these calculations are shown in Table 4 for two different temperatures. At this point, it is obvious that a mechanism such as that proposed by Vincow et al. could be operable. Ifit were, it would mean that the “corrected” values for (dg/dT) would be more negative than those in Table 3, but even so, certainly within the realm of being reasonable. Finally, let us consider the various g-values which have been measured, relative to the value predicted by Stone’s theory (I, 27-20). According to Stone’s theory, g = 2.002626(~0.000004)-(16.6 i l.O)J x 10-5, 131 where 1 is the factor associated with the energy of the Htickel MO in which the unpaired electron is found, in units of /I (i.e., E = a + nj?). The dashed line in Fig. 1 traces the g-value predicted for the benzene anion radical by Eq. 3. This is the same value predicted for all other members of the alkyl substituted benzene anion series. The troublesome TABLE
4
VALUESFOR (dg/dT) CALCULATEDFROMAVERAGINGOVERELECTRONICSTATES Radical
(dg/dT) x 107(-12O’C)
(dg/dT) x 107(-6O’C)
Monodeutrobenzene anion Isopropylbenzene anion Ethylbenzene Toluene anion p-Xylene anion
+0.69 +3.3 +2.8 +0.19 +0.053
+0.28 +1.8 +1.8 +1.02 +0.18
feature here is that some of the g-values fall as far below the value calculated for “nondegenerate” benzene as the benzene lies above it. We have no satisfactory explanations of this behavior at this time. CONCLUSIONS
We have shown for the benzene anion radical that there may be two contributions to the observed g-value, i.e., ion-pairing effects and thermal averaging over vibronic excited states. For the alkyl-substituted benzene anions there may be an additional mechanism, namely that of thermal averaging over the two electronic states which in the case of the benzene anion are degenerate. We have also noted that some members of the alkyl-substituted benzene anion series display g-values as far below the “Stone g-value” as the benzene anion radical g-value lies above it. Studies are in progress in which pure solvents are being used rather than the mixed solvent system. By this means we hope to obtain a better understanding of the ion-pair contributions to the g-values of the members of the series in Table 1. Also, we are attempting to measure the equilibrium constant for the following reaction C6Hs-* + RC6H5 Z? C,H, + RC6HS-. so that we can make appropriate modification to the value of il in Eq. 3.
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g-VALUES
OF ORGANIC FREE RADICALS
155
ACKNOWLEDGMENT The support of this research by the National Science Foundation through Grant GP-28436 and the University of Missouri-St. Louis is acknowledged. REFERENCES 1. B. G. SEGAL, M. KAPLAN, AND G. K. FRAENKEL, J. Chem. P&s. 43,419l (1965). 2. M. T. JONES, “Advances in Magnetic Resonance” (J. S. Waugh, Ed.), Vol. VII, Academic Press Inc., New York, 1973. 3. J. KELM AND K. MOBIUS, Angew. Chem. Intern. Edit. 9,73 (1970). 4. M. T. JONES, M. KOMARYNSKY, AND R. D. RATAICZAK, J. Phys. Chem. 75,2769 (1971). 5. M. T. JONES AND M. KOMARYNSKY, J. Chem. Phys. 56,4404 (1972). 6. C. L. DODSON AND A. H. REDDOCH, J. Chem. Phys. 48,3226 (1968). 7. W. G. WILLIAMS, R. J. PRITCHETT, AND G. K. FRAENKEL, J. Chem. Phys. 52,5584 (1970). 8. J. L. SOMMERDIJK AND E. DE BOER, “Ions and Ion Pairs in Organic Reactions,” Vol. 1, Chapter 8, John Wiley & Sons, New York, 1972. 9. T. TAKESHITA AND N. HIROTA, J. Amer. Chem. Sot. 93,642l (1971). 10. E. DE BOER AND C. MACLEAN, J. Chem. Phys. 44,1334 (1966). II. R. G. LAWLER AND G. K. FRAENKEL, J. Chem. Phys. 49,1126 (1968). 12. T. R. TUTTLE, J. Amer. Chem. Sot. 84,1492 (1962). 13. W. HOBEY, J. Chem. Phys. 43,2187 (1965). 14. J. E. WERTZ AND J. R. BOLTON, “Electron Spin Resonance: Elementary Theory and Practical Applications”, p. 464, McGraw-Hill, New York, 1972. 15. R. D. ALLENDOERFER, J. Chem. Phys. 55,3615 (1971). 16. R. E. Moss AND A. J. PERRY, Mol. Phys. 22,789 (1971). 17. A. J. STONE, Prac. Roy. Sot. London A271,424 (1963). 18. A. J. STONE, Mol. Phys. 6, 509 (1963). 19. A. J. STONE, Mol. Phys. 7,311 (1963/64). 20. G. VINCOW, M. L. MORRELL, F. R. HUNTER, AND H. J. DAUBEN, JR., J. Chem. Phys. 48,2876 (1968).