The effects of ion pairing on the EPR spectra of alkyl aromatic hydrocarbon radical anions

JOURNAL

OF MAGNETIC

RESONANCE

15,75-83

(1974)

The Effects of Ion Pairing on the EPR Spectra of Alkyl Aromatic Hydrocarbon Radical Anions* A. H. REDDOCH Division

of Chemistry,

National

Research

Council

of Canada,

Ottawa

KIA

OR6,

Canada

Received February 19, 1974 It is shown that the calculation of spin density changes in radical anions caused by a counterion can be usefully extended to radicals involving hyperconjugation. Such calculations are done for the acenaphthene and pyracene anions and show that the alternating linewidth effects in their EPR spectra are consistent with proposed double potential minima above the aromatic parts of these radicals. New experiments on acenaphthene are reported which support the calculations. The calculation is shown to account successfully for the effects of ion pair formation in 9,10-dihydroanthracene and in benzocyclobutane. Experiments with partially deuterated dihydroanthracene resolve some uncertainty about the assignment of the coupling constants. INTRODUCTION

The object of this paper is to examine and apply a very simple theoretical treatment of ion pairing effects on the spin densities of methylene protons in alkyl aromatic radical anions, particularly acenaphthene and pyracene. It will be shown that such a treatment, although it is rather approximate, is very useful in interpreting the structure and dynamics of these ion pairs. De Boer (1,2) showed that ion pair formation reduces the symmetry of the pyracene anion, splitting the eight aliphatic protons into two groups of four. This splitting, together with counterion motion, can cause an alternating linewidth in the EPR spectrum. It was later suggested (3), on the basis of a McClelland type (4) calculation of the cationic perturbation of the spin densities of the aromatic part of the radical, that the cation could not be located beyond the methylene groups as was originally proposed. Experiments then proved (5) that the average position of the cation is above the center of the molecular plane of the anion. De Boer also showed that the cation has a second motion which at quite low temperature causes another linewidth alternation. The cation is probably jumping between positions above the centers of the sixmembered

rings,

especially

in view of the double

potential

minima

at these positions

discussed by various authors (6-8). Attempts to prove this experimentally failed (5) and led to the present calculations which support this model. In the meantime Iwaizumi et al. reported (8) similar effects in acenaphthene.

They

proposed that the first splitting occurs when the cation is above the plane of the carbons and that

the second

alternation

The present calculations of it.

is caused

by jumping

between

the potential

support this model and predict additional

* Issued as NRCC No. 14002. Copyright 0 1974 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain

75

minima.

consequences

76

A. H. REDDOCH

The first calculation (3) mentioned above was a simple elaboration of McClelland’s treatment. In this the electrostatic perturbation term -e2/riM, where riM is the electroncation distance, is added to the usual Hiickel Hamiltonian. The basis set consists of the p-orbitals of the aromatic carbons and the matrix elements are (4) Hij = HiOj- Sije2/ri, Hf’, being the usual Hiickel matrix elements and ri the distance from the cation to carbon i. This basis set does not cover the aliphatic parts of the molecule. These might be treated by assuming a McConnell type relation, a = Qp, between the methylene proton coupling constants and the spin densities on the adjacent aromatic carbons. Unfortunately, this procedure cannot distinguish between the two protons on a given methylene group. This difficulty will be overcome here by using an enlarged basis set derived from hyperconjugation models (9).

METHOD

A common approach (9) to hyperconjugation

of a methylene group is to use the

p orbital of the aliphatic carbon and a group orbital of 7csymmetry constructed from

the hydrogen 1s orbitals, i.e., (Is, - ls,)/2/2. These interact with the rr system. An unsymmetric cation perturbation would mix the symmetric G group orbital (Is, + lsJ/z/z with the 71systems. It is then necessary to include the carbon 0 orbital, as well, to allow for the effect of the methylene C-H bonding. Here it was decided to use the hydrogen 1s orbitals directly in the basis set instead of the group orbitals to study the splitting caused by the cation. It is still necessary to include the carbon 0 orbital in this case. Since the C-C-C angle centered on the methylene carbon in acenaphthene and pyracene is about 105” for idealized bond lengths and angles (aromatic carbon-carbon bonds 1.40 A, others 1.54 A, aromatic C-C-C angles 120”) or almost the tetrahedral angle, the two bonds forming this angle may be conveniently represented as sp3 hybrids. These are not used in the calculation, but the remaining carbon orbitals, which are, can then be described as ap orbital of 71symmetry and an sp hybrid of 0 symmetry. The matrix elements used for orbtials centered on the methylene atoms are clco= mCn= -O.lp, aH = -0.5/?, &, = 0.85/?, PHn = *I .7p (above and below the molecular plane), and pnn = /?nring= O.Sp. Within the aromatic part of the radical, c(c= 0 and &, = 8. These values are consistent with those commonly used in standard hyperconjugation treatments (8, 9). Better agreement with experiment could probably have been obtained by adjusting these parameters. This was not done because the physical significance of the parameters would decrease as they compensated for the various approximations of the calculation. However, certain parameters advocated by other authors are considered below. Each of the matrix elements was varied by a small amount to determine the sensitivity of the results to these inputs. In addition, certain elements were given large variations representing conceivable ranges for some of the more arbitrary parameters. As indicated below, most of the significant qualitative results are fairly insensitive to such changes.

ION PAIRS OF HYDROCARBON ANIONS

77

After the matrix was diagonalized, the coupling constants were obtained from the spin densities through the equations uHarom= 28 pc and aHaliph = 508 pH. The first Q value should be -28, but the sign is ignored here since it has no effect on the present results. An expression analogous to that of Levy (10) for aHaliph was derived for the present basis set to allow for the Fermi contact interaction of the methylene proton with spin density on both the carbon x and B orbitals and on the adjacent hydrogen. These terms contributed not more than 2 % of the coupling given by 508 pH and consequently will be ignored in this treatment. Other interactions such as TI-rt spin polarization and charge density effects, which in benzene and naphthalene have a small influence, will also be ignored since they are not likely to change the general effects of the cationic perturbation in the substituted benzenes and naphthalenes considered here. RESULTS

Acenaphthene

The matrix elements listed above gave a poor approximation to the observed coupling constants of the free anion, i.e., a&!,, = 4.8, ay = 1.90, and a:’ = 1.84 gauss instead of the observed values of 7.5, 1.07, and 2.36, respectively (8, 9). Inclusion of an inductive term (9) H, 1 = H,, = -O.l3p, which Moss et al. (II) found would best describe the ring protons of substituted naphthalenes, gave CZ~= 1.52 and uy = 2.07. When this term was changed to -0.31/?, the value they advocated to fit the methylene protons, very good values of a: = 1.03 and a; = 2.45 resulted. However, neither inductive term raised a&!,, beyond 5.24. On the other hand, Iwaizumi et al. (8) found good agreement

6

FIG.

I. Structures and numbering of anions with position adopted for cation.

by using interaction terms between the methylene protons in their group orbitals and the next-nearest carbons. Here these terms become Hlscf = +0.2 p for hydrogens above and below the plane respectively. These yield a satisfactory result, a& = 6.95, a; = 1.28, c$= 2.19, and uy = 4.62. The coupling constants of the ring protons have been improved by the interaction between the protons and the ring carbons, e.g., H,, 1, while those of the methylene protons improved as a result of the interaction with the other methylene carbon, e.g., H,, 12.The procedures of both Moss and Iwaizumi lead to improved descriptions of acenaphthene, but their physical significance is not clear, for the difference in the coupling constants a: and ay is much larger in this radical

78

A.

H. REDDOCH

than it is in the anions of 1,8-dimethylnaphthalene or phenalane (I?, 13) which might be expected to have similar matrix elements. If the counterion is placed 3.5 A above the center of the right-hand six-member ring, the derived coupling constants, using Iwaizumi’s terms, are given in Table 1. From these results several conclusions may be drawn. (1) Protons 13 and 14, on the same side as the cation, have a larger average coupling constant, 7.80 gauss in the fast TABLE

1

CALCULATEDCOUPLINGCONSTANTS a:’ INGAIJSSOFPROTONS i IN PERTURBEDANJONS

a!’

2 3 4 13 14

i

Acenaphthene 1.17 7 6 2.83 6.08 5 9.65 5.95

15 16

a!’

1.22 1.79 2.83 7.96 5.35

Pyracene 2 13 14

1.75 8.90 5.16

1

8.79 2.09 3.43

7 15 16

1.29 7.07 4.53

9,10-Dihydroanthracene 2 15

8 7 17

0.00 0.00 2.47

exchange limit, and a greater linewidth, proportional to (C &x)~T = (aI3 - u1J27 = 13.72, than protons 15 and 16 on the opposite side with corresponding values of 6.66 gauss and 6.82. (2) Protons 4 and 5 generate comparable broadening, 10.62. (3) The remaining protons cause much less broadening ~1.1~. These three qualitative results may be accepted with some confidence for they were obtained with all sets of matrix elements which were examined. However, omission of the carbon Q orbitals resulted in quite unrealistic numbers. Conclusion 1 is supported by the results of Iwaizumi et al. (8) to the extent that the methylene protons with the larger coupling cause the greater broadening. It does not seem feasible to determine experimentally whether these are the ones closer to the cation. The calculated difference between the upper and lower coupling constants, 1.15 gauss, is greater than the experimental value of 0.55 found for K+. Some sets of parameters reduced the former number to about 0.7 gauss. Some of the discrepancy is probably caused by the interionic distance used. Conclusion 3 is also supported to the extent that no broadening has been associated with these protons either in the experiments of Iwaizumi or in those of this laboratory.

ION

PAIRS

OF HYDROCARBON

79

ANIONS

Since conclusion 2 could not be tested from the spectra published by Iwaizumi, new spectra were obtained here for this purpose. These were recorded with potassium in diethyl ether at -95°C. The coupling constants are 8.02,7.46,4.15,2.46, and 1.11 gauss for the protons and 0.10 gauss for the potassium. A number of lines are shown in the I gauss

FIG. 2. Selected lines from low-field half of EPR spectrum of acenaphthene anion with K+ in diethyl ether at -95°C. Numbers correspond to those in Table 2.

figure and are described in Table 2. The spin quantum numbers mi for each pair of protons are listed in order of decreasing average coupling constant. The contribution to the linewidth 6(T;l) is proportional to (1 hi)‘, where i labels the proton pairs in the same order as above and 6, = ai - afi is the change in coupling constant when the cation TABLE PARAMETERS

OF ACENAPHTHENE

2

LINES IN FAST EXCHANGE

Components Line

mi

N

11100

4 4 4 8 4 8 8 8 8 8 8 8

11010 11001 11000 10110 10100 10000 8

01000

9

00100

LIMIT

Overlapping NT;‘)

mi

lines N

moves from one potential minimum to the other. This change is simply the difference in the calculated constants for the two protons which would be equivalent in the free anion. The degeneracy N of the line is a measure of its relative intensity in the absence

80

A. H. REDDOCH

of cationic broadening. Overlapping lines, if any, are similarly described. Most other lines of the spectrum are too seriously overlapped or too weak to permit measurement except by fitting the entire spectrum. The lines which have been selected may still have some slight overlap with other lines on the outer components of the quartets but the central pair of lines should be usable. Lines 7, 8, and 9 are each overlapped to the same extent by a weak line. There may be some dipolar broadening in the spectrum at -95°C for it is quite evident at -105°C. However, since the methylene protons should contribute very little to that, it can be shown that the inequalities deduced below will not be changed by this effect. Comparison of lines 2, 3, and 4 with line 1 shows clearly that 6, # 0, while lines 5 and 6 show that 6, # 0. The pairs of lines, 25; 3,5; and 4,6 show that S: > S: although the difference is not great. If 6, were negligible, then lines 7 and 8 would show that S: > 6%.However, the situation is more complex because the nonzero value of (5, gives rise to two components of different width for each of the three lines. Since the central members of the quartet of line 8 are slightly weaker than those of line 4, each of the two components of the former, listed in Table 2, must be broadened more than line 4. Hence, it may be deduced that I6,I > 2 I&I. Similarly from lines 6 and 9, /6, / > 2 /(5,I. The intensities are such that these two inequalities are not very strong. Finally, line 7 is not broadened as much as 8 or 9 since, as shown above, IS,/ and IS,/ are of similar magnitude and less than 16, I. Since the coupling constants of the ring protons should be negative while those of the methylene protons should be positive, 6, should have the opposite sign to 6, and 6,. However, that cannot be observed in the fast exchange limit, which seems to be the only region experimentally accessible with this system. In summary, the conclusions from the spectrum are

Thus, as Iwaizumi reported, the methylene protons with the greatest coupling have the greatest broadening effect. The present calculations indicate that these are the methylene protons nearest the cation. As predicted at the same time, protons 4 and 5 do contribute to line broadening as shown by the parameter 6,. Unfortunately, the calculated broadening of the methylene protons is more sensitive to the matrix elements than is the broadening of protons 4 and 5. Hence it is not possible to predict with confidence whether the latter is greater or less than that of the methylene protons remote from the cation. Experimentally, the effects seem to be comparable. The linewidth in the absence of cation broadening is about 50 mG peak-to-peak, while the calculated difference in coupling constants for protons 13 and 14 is 3.7 gauss. While this latter number is rather crude, it is possible to make an order-ofmagnitude estimate of z = (2h/rc2g/?)6w/(6a)2, the lifetime of the cation in one potential minimum, since the broadening 60 due to cation motion is about 40 y0 of the natural width. The result for the potassium ion in DEE at -95°C is about IO-” set before it jumps to the other minimum on the same side of the anion. On the other hand, from lines 4 and 7 it is possible to show that in the slow exchange limit, applicable to a jump from one side of the molecular plane to the other at this temperature, the lifetime is not less than 10m4sec. As a result of these very different time scales for the two motions, the radical can be treated in terms of two two-jump models instead of one four-jump model.

ION

PAIRS

OF HYDROCARBON

ANIONS

81

Pyracene Similar considerations apply to pyracene as to acenaphthene. Calculated coupling constants of a& = 6.30 and a’;’ = 1.54 gauss were obtained for the free ion from the matrix elements’of Iwaizumi et al. The experimental values (2) are 6.58 and 1.58. With the cation 3.5 A above the right-hand six-member ring, the results given in Table 1, analogous to those for acenaphthene, were obtained. Again, the methylene protons on the same side as the cation have the larger average coupling, 7.03 gauss vs 5.80, and the greater broadening, 13.97 vs 6.5~, while the ring protons have little broadening (0.22). Experimentally, no broadening has been found for the ring protons, while the difference in the upper and lower proton coupling constants, 0.56 gauss, is about half the predicted value, 1.23, although it depends on the cation. De Boer (2) reported that the methylene protons with the greater coupling broadened while the others did not. This would be compatible with the predicted result only if the broadening were not too great. An examination of de Boer’s Figs. 4 and 7 in Ref. 2 suggests that in fact some broadening also occurs with the other methylene protons, as predicted. Attempts to obtain better spectra to confirm this were unsuccessful. The agreement between the observed and calculated effects strongly supports the view that the cation jumps from one six-member ring to the other on the same side of the radical and less frequently jumps to the other side of the plane defined by the carbon nuclei. Calculations were made for other conceivable cation positions, but as in the simpler calculations (3) these did not agree with the experiments. Thus such positions are unlikely to be frequently occupied. Dihydroanthracene Ion pairs of this radical anion were studied by Iwaizumi and Bolton (14). As in their paper, the calculation was simplified by making the approximation that the molecule is planar, aside from the methylene protons, since the spectra show that the average conformation is planar. The same matrix elements were used, where applicable, as in acenaphthene. However, the interaction between the methylene protons and the next nearest carbons, used by Iwaizumi (8) in acenaphthene, had little effect on the spin densities of the free anion and was not used. The difficulties encountered by Levy (10) with the order of the molecular orbital energy levels in substituted benzenes also arose here. They disappeared, however, when the inductive term Hi,,, etc. = -0.308 was used. Hence this term was retained even though it resulted in overly large methylene coupling constants. The calculated free anion constants are a: = 4.34, a! = 1.05, aGi, = 6.03 gauss. The experimental values are 3.85, 0.92, and 4.23 gauss. With the cation 3.5 A above the right-hand six-member ring, the values in Table 1 were obtained. As with acenaphthene and pyracene, the methylene proton nearer the cation has the larger coupling constant. The localization of charge on the ring near the cation, derived by Iwaizumi (14) is also obtained here. The calculated magnitudes of the fluctuations in the coupling constants associated with jumps of the cation among the four equivalent positions are Aa, = 8.8, Aa, = 2.1, and da,,, =0.95 gauss. Iwaizumi obtained 2.6, 0.65, and 0.36 gauss for these parameters from a spectrum simulation based on a fourjump model, assuming l/k, = l/k, = r = 5.5 x lo-’ sec. Here k, is the jump rate on one side of the plane and k2 is the rate from one side to the other. The calculated fluctuations are proportional to those used in the simulation, suggesting that these

x2

A. H. REDDOCH

theoretical values could fit the spectrum fairly well if the time constant were reduced by an order of magnitude. This would imply that the assumption of Iwaizumi that k , -=k2, required to utilize the four-jump simulation, may be approximately correct. The accuracy of the present calculations is not great, however, and this implication is tentative. In a recent paper (15) Pyykkii and Eloranta have proposed on the basis of an INDO calculation that the assignment of the 3.846- and 0.920-gauss coupling constants by Iwaizumi and Bolton should be reversed. To resolve this question, the EPR spectrum of the 1,4,5,8-tetradeutero-9,10-dihydroanthracene anion was obtained at -100°C in 2-methyltetrahydrofuran with potassium. It was necessary to prepare and maintain the sample at about this temperature to avoid decomposition. The spectra showed clearly that the 3.846-gauss coupling constant was replaced by a coupling constant of 0.60 gauss from four deuterons while the other couplings were not much changed at 4.32 and 0.99 gauss. Thus the original assignment of Iwaizumi and Bolton, which was adopted here, is correct. It may be that Pyykko and Eloranta have had difficulty with the near degeneracy of the lowest antibonding orbitals, mentioned above. Benzocyclobutane This radical anion has been studied by Rieke and coworkers (16, 17). The four member ring, having both aliphatic and aromatic bonds, would suggest that the C-C-C angle at the methylene may be less than 90”. If the two bonds forming this angle were taken as carbonp orbitals to give an angle of 90”, then the bonds to the two hydrogens would be a pair of collinear sp hybrids. The situation seems to demand bent bonds and hence additional variables, and makes the location of the protons uncertain. The problem would not be easily overcome in a Htickel calculation. As a very rough approximation, the basis set and proton position of the CH, in acenaphthene will be used. The use of the proton interaction with next nearest carbons leads to a very low methylene proton coupling of 1.8 gauss. The inductive term H,, = HZ2 = -0.308 gives tolerable coupling constants a: = 8.78, a! = 2.11, and a&, = 3.83 gauss, compared with experimental values (15) 7.5, 1.4, and 5.5, as well as ensuring the proper order of energy levels. With the cation 3.5 A above the benzene ring, the ring protons are essentially unchanged at 8.78 and 2.09 gauss while the nearer methylene proton coupling becomes 3.7 gauss and the other 2.7. This difference is again about twice the experimental value (16) of 0.5 gauss, and again the proton nearer the cation has the larger coupling. CONCLUSIONS

These results show that where a set of matrix elements is selected which gives a good account of the spin densities of a radical anion by means of a Hiickel calculation which explicitly includes hyperconjugation, it is possible to calculate the effects of the cation perturbation following the method of McClelland. The results will be useful in the qualitative interpretation of experimental results. It may be desirable to check the sensitivity of the calculations to variations in parameter values. The use of an inductive term of 0.38 seems to improve the calculated coupling constants in each case. The interaction term between the CH, proton and the next-nearest carbon helps in the case of pyracene and acenaphthene but not in that of the other two radicals.

ION PAIRS OF HYDROCARBON ANIONS

83

In the four radicals considered, the methylene proton on the same side as the cation has the larger splitting, and in the case of acenaphthene and pyracene causes the greater broadening. This result is not obtained if the carbon CJorbital is neglected. For acenaphthene and pyracene, these calculations, together with the experimental results, support a model in which the cation, once localized on one side of the molecular plane, jumps from above one six-member ring to above the other. This, in turn, supports the existence of double potential minima in these radicals. ACKNOWLEDGMENTS I am indebted to Mr. D. Northcott for obtaining the EPR spectra of the acenaphthene and dihydroanthracene anions, and to Dr. R. N. Renaud for his kindness in preparing the deuterodihydroanthracene. REFERENCES 1. E. DE BOER AND E. L. MACKOR, J. Amer. Chem. Sot. 86, 1513 (I 964). 2. E. DE BOER, Rec. Trav. Chim. Pays-Bas 84,609 (1965). 3. A. H. REDDOCH, in “La Structure Hyperfine Magnetique des Atomes

4. 5. 6. 7. 8. 9.

IO. II.

12. 13. 14. 15. 16. 17.

et des Molecules” (R. Lefebvre and C. Moser, Eds.), Editions du Centre National de la Recherche Scientifique, Paris, 1967. B. J. MCCLELLAND, Trans. Faraday Sot. 57, 1458 (1961). A. H. REDDOCH, Gem. Phys. Letters 10, 108 (1971), and Erratum Chem. Phys. Letters 12, 436 (1971). S. AONO AND K. OOHASHI, Prog. Theor. Phys. 32, 1 (1964). I. B. GOLDBERG AND J. R. BOLTON, J. Phys. Chem. 74,1965 (1970). M. IWAIZUMI, M. SUZUKI, T. ISOBE, AND H. AZUMI, Bull. Chem. Sot. Japan 40,2754 (1967). J. P. COLPA AND E. DE BOER, Mol. Phys. 7,333 (1964). D. H. LEVY, Mol. Phys. 10,233 (1966). R. E. Moss, N. A. ASHFORD, R. G. LAWLER, AND G. K. FRAENKEL, J. Chem. Phys. 51,1765 (1969). D. H. PASKOVICH AND A. H. REDDOCH, Can. J. Chem. 50,1523 (1972). R. F. C. CLARIDGE, B. M. PEAKE, AND R. M. GOLDING, J. Msg. Resonance 6,29 (1972). M. IWAIZUMI AND J. R. BOLTON, J. Msg. Resonance 2,278 (1970). P. PYYKKG AND J. ELORANTA, Chem. Phys. Letters 17, 101 (1972). R. D. RIEKE, S. E. BALES, P. M. HUDNALL, AND C. F. MEARES, J. Amer. Chem. Sot. 93,697 (1971). R. D. RIEKE AND S. E. BALES, Chem. Phys. Letters 12,631 (1972).