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c axis, and their molecular planes titled about this long axis with respect to the lattice plane. Adjacent lattice planes along the b axis have molecules tilted in an opposite direction. From such a structure, it is not difficult to rationalize an ionic lattice with only a small variation of the basic pattern evidenced in the crystals of the neutral molecules. For example, from our measured density of K+AN--,1.41 f 0.05 g/cm3, and the assumption that formation of the salt involves an increase of the a axis to accommodate the K+ ions between the planes of adjacent AN+. ions, a simple calculation indicates that a would have to extend from 8.56 to 8.89 A while 0would simultaneously
change from 124.7 to 122.4". Many such arrangements are possible, and we describe this to illustrate that the changes need not be large to accommodate a fairly large cation. The energy states for the lithium, cesium, and potassium salts of tetracene and anthracene (Figures 5 and 6) show that the magnitude of the crystal lattice energies are similar in magnitude to the solvation enthalpies. These results are in agreement with the results from the anthracenesodium system, which was published in a preliminary communication of this work.2 Thus, the chemistry of the solid anion radical systems is expected to be very different from that in the gas phase.
Thermodynamics of Electron Transfer from the Cyclooctatetraene Anion Radical to a Series of Substituted Cyclooctatetraenes and [ 161Annulene Gerald
R. Stevenson' and Brad E. Forch
Nlinois State University, Depatjmnt of Chemistry, Normal, Il/inols 6 176 1 (Received June 17, 1980)
Electron spin resonance has been utilized to measure the free energy, enthalpy, and entropy changes for the electron transfer from the anion radical of cyclooctatetraene (COT) to several substituted cyclooctatetraenes (XCOT) and to [16]annulenein hexamethylphosphoramide (HMPA), where the anion radicals are free from ion association effects. There is a correlation between the enthalpy of the electron transfer (AH" for COT-. + XCOT e COT + XCOT) and the magnitude of the splitting of the degeneracy of the nonbonding molecular orbitals due to the presence of the substituent (A€): However, the fact that AH' for the electron transfer is much more sensitive to the presence of the substituent than is Ac leads us to conclude that At is greatly effected by solvation.
ESR spectra of the radical ions of benzene and substituted benzenes have provided a wealth of information concerning the molecular orbitals for the a system of benzene. The presence of an electron-releasingsubstituent in the benzene system splits the degeneracy of the lowest antibonding orbitals (LUMOs), resulting in the odd electron in the substituted benzene anion radical preferentially occupying the MO of lower energy. For the toluene system the splitting of the two near degenerate LUMOs due to the presence of the methyl group has been shown to be -1.2 kcal/mol.' Further, Lawler and Tabit2 have determined the relative solution electron affinities of benzene and several alkyl-substituted benzenes via ESR studies of the equilibrium given in eq 1. After the reduction of C&c 4- RC6Hc
G
C&3-' + RC6H5
(1)
known concentrations of benzene and the alkylbenzene by potassium-sodium alloy in dimethoxyethane, the ESR spectra were taken to obtain the equilibrium constants. Consistent with the fact that a methyl group raises the antibonding molecular orbital represented by the symmetric wave function relative to that represented by the antisymmetric wave function in benzene, the methyl group destabilizes the anion radical of toluene relative to that of benzene. For all of the alkyl-substituted benzene systems studied, the free energy of the reaction depicted in eq 1 is negative. In this study the entropy effects were (1) (a) de Boer, E.; Copla, J. P. J.Phys. Chem. 1967, 71,21. (b) Purins, D.; Karplus, M. J. Chem. Phys. 1969,50, 214. (2) Lawler, R G.; Tabit, C. T. J. Am. Chem. SOC.1969, 91, 5671. 0022-3654/81/2085-0378$01 .OO/O
found to be small, and the magnitude of A G O was considered to be the same as that for LW'. In the gas phase, however, Jordan et al.3 have found that the free energy and the enthalpy of reaction 1 are opposite in sign from those in solution. Thus,the gas-phase electron affinity of toluene and other alkyl-substituted benzenes are actually greater than that for benzene. In this sawe paper, Jordan et al.3 speculated upon the possibility t a t intrinsically an alkyl group stabilizes the symmetric state relative to the antisymmetric state. The nonbonding orbitals of cyclooctatetraene (COT) have two nodal planes similar to the benzene system; the presence of alkyl substituents has been found to split the degeneracy of the two orbitals as shown in Figure 1.4 The splitting of the nonbonding orbitals is -0.4 kcal/mol for an alkyl group and 0.78 kcal/mol for an alkoxy group, and a plot of this splitting ( A 4 vs. the n value for the substituent is linear and yields a positive p value. More recently, Hammons, Kresge, and Paquette5 have found that the anion radical of 1,5-dimethylcyclooctatetraeneshows a similar effect, and, if one uses twice the u value (Hammett substituent constant) for a methyl group, the A6 value for this anion radical lies on the previously published line. We now wish to report the thermodynamic parameters controlling the electron transfer between the anion radical (3) Jordan, K. D.; Michejda, J. A,; Burro, P. D. J. Am. Chem. SOC. 1976. - - . - ,98. - - .129.5. ---(4) Stevenson, G. R.; Concepcion, J. G.; Echogoyen, L. J. Am. Chem. SOC.1974, 96,5452. (5) Hammons, J. H.; Kresge, C. T.;Paquette, L. A. J . Am. Chem. SOC. 1976, 98, 8172.
0 1981 American Chemical Society
The Journal of Physical Chemistty, Vol. 85, No. 4, 1981 379
Electron Transfer from the COT Anion Radical
COT-'
"n-
"n+ -
--.--
lines
-
Figure 1. The two nonbondingdegenerate molecular orbitals of planar COT being split because of the presence of an "electron-releasing" group at the position marked by a double arrow.
of COT and a series of substituted COTStogether with the fact that there appears to be a weak correlation between the magnitude of the splitting of the two nonbonding molecular orbitals and the relative solution electron affmity of the substituted COTS. The work described here was carried out in hexamethylphosphoramide (HMPA), where neither the dianions nor the anion radicals form ion pairs with the Na+ cation. Ion association would affect both the enthalpies of electron transfer and the measured values for A€. Experimental Section X-band ESR spectra were recorded by using a Varian E-4 ESR spectrometer. The temperature was controlled by using a Varian V-4557 variable-temperature controller calibrated with a Whal digital thermometer. The sample preparation was exactly as previously described.6 Ethylcyclooctatetraene (ETCOT), a yellow liquid, was prepared by the method of Cope and van Orden.' tertButoxycyclooctatetraene (TBCOT) and naphthocyclooctatetraene (NCOT) were synthesized by the method of
ETCOT
BCOT
TBCOT
PCOT
NCOT
Krebs.s The TBCOT, an orange liquid, was purified by vacuum distillation, and the NCOT, a yellow crystalline solid, was recrystallized from methanol. Phenyl-d5cyclooctatetraene (PCOT) was synthesized by the method of Cope and Kinderg using pentadeuteriobromobenzene in place of bromobenzene. The product was fractionally distilled and gave an lH NMR spectrum that is identical with that for phenylcyclooctatetraene, except that no proton resonance was observed for the phenyl ring. Biscyclooctatetraene (BCOT) was prepared as described by Cope and Marshalllo and was recrystallized from ether. [16]Annulene was prepared from the photolysis of the 2 + 2 COT dimer as described by Schroder et al.ll Well-resolved ESR spectra of all of the anion radical species utilized in this study were obtained, because the rate of electron transfer between the anion radical and the neutral molecule is very slow on the ESR time scale. For (6) Stevenson, G. R.; Concepcion, J. G . J. Phys. Chem. 1972, 76,2176. (7) Cope, A. C.; van Orden, H. 0. J . Am. Chem. SOC.1952, 74, 175. (8)Krebs, A. Angew. Chem. 1965, 77, 966. (9) Cope, A. C.; Kinder, M. R. J. Am. Chem. SOC. 1951, 73, 3424. (10) Cope, A. C.; Marshall, D. J. J. Am. Chem. SOC.1953, 75, 3208. (11) Scroder, G.;Kirsch, G; Oth, J. F. M. Chem. Ber. 1974,107,460.
j t h line for TBCOT-.
Flgure 2. ESR spectrum of the anion radicals formed by the sodium reduction of a mixture of TBCOT and COT in HMPA at 25 'C. The concentration of COT-. is larger than that for TBCOT-e. The seventh ESR line for TBCOT-. was chosen to determine its relative concentration. The ESR spectrum of the isolated TBCOT anion radical in HMPA appears in ref 13.
this reason, relatively narrow line widths were obtained even in the presence of high concentrations of neutral species. The square of the line width multiplied by the line height was used as a measure of the relative line intensities. This does require that both lines used in the comparison have the same line shape. The line shapes were shown to be the same (as close as we could tell) by generating a computer simulation of one line and then rescaling it on a computer vidio screen (VT-105 by Digital) to superimpose upon the other line. This method is not entirely satisfactory, since the wings of the lines are not completely free of obstruction. Thus, some error in our measurements may result from these line-shape problems. Results The reduction of a 1:l mole mixture of TBCOT and COT with a very deficient amount of sodium metal under high vacuum yields a solution that exhibits only the nine-line pattern for the COT anion radical upon ESR analysis. However, if a mixture of TBCOT and COT is used where [TBCOT]/[COT] is between 10 and 20, this same experiment yields a solution in which both the COT and the TBCOT anion radicals can be observed simultaneously in the ESR spectrum (Figure 2). The relative intensities of the two spectra are controlled by the thermodynamic equilibrium constant for reaction 2. This is TBCOT
+ COT-. F! TBCOT-* + COT
(2) the case, since it has been demonstrated that substituted COT anion radical solutions in HMPA are free from ion pairing with Na+.12 Further, less than 0.02 mol of sodium per mole of either of the two neutral hydrocarbons was used to carry out the reduction. This means that the dianion concentrations must be much lower than the neutral hydrocarbon concentrations. (12)Stevenson, G. R.; Ocasio, I. J. Am. Chem. SOC. 1976, 98, 890.
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The Journal of Physical Chemistry, Vol. 85, No. 4, 1981
Stevenson and Forch
TABLE I : ESR Data and Thermodynamic Parametes Controlling the Electron Transfer from COT-. (eq 4 ) compd COT TBCOT ETCOT PCOT BCOT NCOT [16Jannulene a
Keq(25 " C ) 1.0 0.028 i 0.003 0.0025* 0.0003 0.79 r 0.07 0.12 f 0.03 0.66 i 0.02 > 200
AH'
A s
0.0
0.0
Line intensity for the chosen line over the sum of the line intensities.
i
1 G
- 2.1
1.5 i 0.2 0.54 i 0.03 - 2.4 * 0.2 7.8 f 0.4 3.8 * 0.4
