J. Phys. Chem. 1984, 88, 5914-5919
5914
Disproportionation-Recombination Rate Ratios for Hydroaromatic Radicals Michael J. Manka Chemistry Department, The Catholic University of America, Washington, D.C. 20016
and Stephen E. Stein* Chemical Kinetics Division, National Bureau of Standards, Washington, D.C. 20234 (Received: June 25, 1984)
+
Relative rates for radical disproportionation (R. R'. k RH + R'd) and recombination (R- + R'. 9 RR') have been determined in the liquid phase at 150 OC for a series of reactions involving resonance-stabilized hydroaromatic radicals. Self-reactions were studied for the 1-tetralyl, 1-indanyl,9,10-dihydro-9-phenanthryl, and 9,10-dihydro-9-anthrylradicals. Four cross-radical reactions involving benzyl, diphenylmethyl, and 1-tetralyl radical as H-atom acceptors were also examined. Rate constant ratios (kd/k,)span the range of 1.34 for the self-reaction of 9,1O-dihydro-9-phenanthrylradicals to 0.05 for the self-reaction of 9,10-dihydro-9-anthryl radicals. When disproportionation reaction exothermicity is sufficiently small, -AHd 5 50 kcal mol-' (210 kJ mol-'), disproportionation rate constants decrease with decreasing exothermicity. A fit of liquid-phase data yields ln (kd/k,) per H atom = -10.1 - o.163AHd (kcal mol-').
Introduction During the course of our studies of the pyrolysis of aromatic molecules, it became evident that rates of disproportionation of resonance-stabilized hydroaromatic radicals could determine reaction mechanisms. For instance, in the liquid-phase pyrolysis of 1,2-diphenylethane, due to the relative slowness of disproportionation, trans- 1,2-diphenylethene was formed by an indirect pathway involving recombination of resonance-stabilized radicals rather than directly by disproportionation of 1,2-diphenylethyl radicals.' In another case it was shown that the reverse of a radical disproportionatidn reaction can provide a steady source of free radicals in aromatic pyrolysis reactiom2 Estimating such rates requires a knowledge of radical disproportionation rates. Since radical disproportionation rates cannot yet be reliably estimated and relatively few have been determined for reactions between resonance-stabilized radical^,^^^ particularly when hydroaromatic radicals are involved, we have measured rates of disproportionation relative to recombination for a series of hydroaromatic radicals. In addition to their involvement in aromatic chemistry, these reactions form a unique series in which reaction enthalpy varies over a wide range while reaction entropy remains relatively constant. Experimental Section Reactions were done in sealed, evacuated Pyrex glass tubes at 150 O C for periods of time ranging from 1 to 30 min. Reaction mixtures contained one or two resonance-stabilized free-radical precursors, a radical initiator, di-tert-butyl peroxide (DTBP), and occasionally a diluent, benzene. Where two different radicals were to be generated, relative amounts of free-radical precursors were adjusted to generate one radical in at least an eightfold excess. The radical initiator was added in amounts ranging from 5 to 33 wt%. Pyrex glass tubes, 3.5 mm id., were prepared by first rinsing with a solution of HF, then with distilled water, and finally with methanol. No evidence was found to indicate that heterogeneous reactions with the glass walls occurred. The tubes were dried by passing nitrogen through them and cut to 15 cm lengths. Each tube was sealed at one end and thoroughly dried in a flame. The reaction mixture was delivered to the bottom of the tube with a (1) Miller, R. E.; Stein, S . E. J . Phys. Chem. 1981, 85, 580.
(2) Stein, S. E. In "New Approaches in Coal Chemistry"; America1 Chemical Society: Washington, DC, 1981; ACS Symp. Ser. No. 169, p 97. (3) Gibian, M. J.; Corley, R . C. Chem. Reu. 1973, 73, 441. (4) Kerr, J. A.; Moss, S. J. "Bimolecular and Termolecular Gas Reactions"; CRC Press: Boca Raton, FL, 1981; Vol. 11.
0022-3654 I84 12088-59 14%01.50,I O I
,
disposable pipet. To minimize the possibility of pyrolyzing some of the sample during sealing, special care was taken to avoid depositing material on the tube wall. Typical sample sizes were 0.4-0.6 mL. Prior to sealing, the liquid sample was cooled in liquid torr). At reaction temperatures nitrogen and evacuated (1 X the vapor volume was always less than one-fifth the volume of the liquid. Sample tubes were heated in a fluidized bath of aluminum oxide particles at 150 OC. The temperature was monitored with a chromel/alumel thermocouple and & Doric Model 4 12A22digital readout device with a precision of fO.l "C. The thermocouple was placed in the bath next to the center of the sample tube. The temperature drift within the zone in which the sample tube was heated was typically no more than f0.2 OC and uniformity was better than f l "C. The time required for the sample to reach the reaction temperature was obtained from a plot of decomposition of the radical initiator vs. time for short immersion periods. The induction period was found to be 20 s. Reactions were assumed to occur entirely within the liquid phase since vaporpressure estimates of DTBP indicate that less than 1% of it was in the gas phase. Reaction products were analyzed with temperature-programmed gas chromatography (GC). High-pressure liquid chromatography (HPLC) was also used to analyze the products of the self-reaction of 9,10-dihydro-9-anthryl radicals. The gas chromatograph used was a Hewlett-Packard Model S880A equipped with flame ionization detectors (FID). Peak areas were determined by this instrument by electronic integration. Care was taken to ensure that the best integration method was used for each peak. For reactions where the disproportionation product of interest was 1,2-dihydronaphthalene or indene, a 4-mm i.d., 1.83-m long glass column packed with 10% FFAP on 80/100 mesh Chromosorb WAW was used to separate products. For the other G C analyses a column of the same dimensions packed with 10% OV-101 was used. An automatic sampler, Hewlett-Packard Model 767 1A, was used to make sample injections which were typically 1 wL. All reported results are averages of at least two separate G C analyses. Typically, relative peak areas varied by less than 5% from one analysis to another. The liquid chromatograph used was a Varian Model 5000 with UV absorbance and fluorescence detectors. A 25-cm C-18 reverse phase column with 10-pm particles was used. The mobile phase, composed of water and acetonitrile, was programmed from 50 to 100% acetonitrile to form the solvent gradient at a flow rate of 1 mL min-'. Prior to analysis an amount of the reacted sample mixture (-0.2 g) was diluted with methanol or tetrahydrofuran to 25 mL. A 1O-fiL injection volume was manually filled with 0 1984 American Chemical Society
Disproportionation/Recombinationof Hydroaromatics
The Journal of Physical Chemistry, Vol. 88. No. 24, 1984 5915
TABLE I: Self-Disurouortionation-RecombinationReaction Results at 150 OC
reaction
[+OO+],/ [RHloQ
reaction time, a
kdIkrb
t+oo+c
ERH~
mass balancee
0.39
60 120 240 480 7 20 960 1920
0.088 0.080 0.087 0.083 0.084 0.083 0.086 av 0.084 t 0.003
0.011 0.021 0.042 0.083 0.122 0.159 0.292
0.007 0.013 0.028 0.064 0.095 0.108 0.157
0.92 0.88 0.95 0.99 0.99 0.99 0.77
0.27
60 160 240 480
0.123 0.121 0.124 0.122 av 0.122 e 0.002
0.015 0.038 0.055 0.103
0.005 0.012 0.018 0.033
0.95 0.99 0.99 0.96
60 120 240 120 240 480 7 20
0.050f 0.053f 0.072f 0.060 0.056 0.058 0.049 av 0.054 t 0.004
0.016 0.033 0.070 0.029 0.064 0.111 0.165
0.025 0.046 0.097 0.012 0.022 0.040 0.058
0.93 0.95 0.80 1.oo 0.86 0.89 0.87
120 240 480 960
1.48 1.40 1.28 1.26 av 1.34 e 0.10
0.019 0.046 0.099 0.145
0.004 0.007 0.017 0.030
1.oo 0.84 0.89 0.83
0.23
Initial concentration ratio of di-tert-butyl peroxide and radical precursor, RH. Disproportionation-recombination rate ratio. kc/kr = [ R d ] / [ R R ] . Extent of the decomposition reaction of di-fert-butyl peroxide calculated from amount of t-BuOH produced and remaining = 2[+OH]/(2[+OH] + [+OO+]). Extent of reaction of RH calculated from amounts of disproportionation di-tert-butyl peroxide. t+,,,+ and recombination products and remaining RH. ~ R = H ([Rd] + 2[RR])/([Rd] + 2[RR] + [RH]). e Molar ratio of twice the amounts of disproportionation and recombination products and f-BuOH, in some cases deviations from unity reflect overall errors in response factors rather than loss of products. Mass balance = 2([Rd] + [RR])/[+OH]. Results averaged from GC and HPLC analyses. TABLE 11: Cross Disurouortionation-RecombinationReaction Results at 150 "C
reaction
[RH],/ [+0O+lg/ [R'HIoa [RH],
reaction time, s
kd/krc
mass balancef [R.]/[R'.]g
t+oo+
ER'H~
0.020 0.031 0.054 0.111 0.151
0.019 0.030 0.056 0.108 0.150
0.90 0.93 1.oo 0.98 1.01
8.08 8.34 8.60 9.34 9.80
0.022 0.032 0.061 0.119 0.173 0.228
0.017 0.024 0.073 0.124 0.155 0.188
1.04 0.94 0.90 0.91 1.oo 0.91
11.20 13.80 8.66 8.80 9.46 8.14
0.070
60 120 240 480 7 20
0.0416 0.0415 0.0413 0.0415 0.0348 av 0.0415
0.128
60 120 240 480 7 20 960
0.0274 0.0283 0.0280 0.0279 0.0265 0.0218 av 0.0276
0.184
300 600 900 1200 1800
0.611 0.637 0.640 0.664 0.696 av 0.650 e 0.032
0.057 0.107 0.157 0.210 0.309
0.016 0.030 0.040 0.058 0.081
1.05 1.oo 0.95 0.92 0.88
18.1 18.1 18.2 18.4 18.8
0.138
120 240 4 80 720 960 1200
0.207 0.230 0.223 0.221 0.244 0.245 av 0.228
0.022 0.038 0.078 0.129 0.163 0.200
0.044 0.079 0.156 0.234 0.293 0.344
1.02 1.02 0.98 0.98 0.92 0.89
65.7 66.4 72.4 78.4 80.4 83.5
?
t
e
0.0010
0.0007
0.014
Initial molar ratio of radical precursors RH and R'H listed first and second, respectively, in reaction column. Initial molar ratio of ditert-butyl peroxide and radical precursor RH. e Disproportionation-recombination ratio. kd/kr = [R'd]/ [RR' 1. Extent of decomposition reaction of di-tert-butyl peroxide calculated from the amount of t-BuOH formed and remaining di-tert-butyl peroxide. (+oo+ = 2[ +OH]/ (2[ +OH] + [ + O O + ] ) . e Extent of reaction of radical precursor R'H calculated from the amounts of disproportionation and cross-recombination products and remaining R'H. [R"= ([R'd] + [R'R] + 2[R'R'])/([R'd] + [R'R] + 2[R'R'] + [R'H]). f Molar ratio of twice the disproportionation and all recombination products and t-BuOH; in some cases deviations from unity reflect overall errors in response factors rather than loss of products. Mass balance= 2([R'd] + [RR] + [R'R] + [R'R'])/[+OH]. Ratio of radicals, R. and R'., produced during reaction. Calculated from the ratio (2[RR] + [RR'])/([R'd] + [RR'] + 2[R'R']). a
5916 The Journal of Physical Chemistry, Vol. 88, No. 24, 1984
Manka and Stein TABLE 111: Summary of Disproportionation-Recombination Rate Ratios per Abstractable H Atom and Disproportionation Reaction Enthalpies reaction
(kalk,L
0.0211
40
30
kcalimol 42.1
0.0305
41.3
0.0210
44.9
0.0233b
37.5
0.0046c
35.7
0.0238d
41.9
0.0375e,f
47.6
0.008f7g
28.4
50
-AHd kcal mol"
,
Figure 1. Plot of In (kd/kr)Hvs. disproportionation reaction enthalpy. Number in plot refers to reaction number in Table 111. Results from reactions 1-1 1 were used to obtain least-squares regression line. Circles
represent data obtained from this work (see text). the diluted sample by using a syringe. Peak areas were determined by a Hewlett-Packard Model 3390A reporting integrator. When possible, product identification was made by coinjection with the known compound. Since none of the recombination products were available commercially, they were analyzed by mass spectrometry using a Hewlett-Packard Model 5970A mass-selective detector. In each case the mass spectra of the recombination products gave primary peaks corresponding to the expected recombining radicals. A previous synthesis of 1,l'-ditetralin5 gave two well-resolved peaks, meso and dl isomers, that agreed with expected 1-tetralyl radical recombination products in the present study. In no case were major product peaks observed that could not be attributed to either disproportionation or recombination products, and in all cases all expected peaks were observed. In addition, when both meso and dl isomeric recombination products were expected, a pair of closely spaced chromatographic peaks of equal area was observed. Calibration of the FID and UV absorbance detectors was performed with appropriate mixtures of pure compounds for all reactants and products except the recombination products. It was necessary to calibrate the HPLC fluorescence detector only for anthracene. Detector sensitivities used for the recombination products are discussed later. Commercially available compounds of high-purity were obtained from several sources. Tetralin, 1,2-dihydronaphthalene, 1,4-dihydronaphthalene, indan, and indene were obtained from Wiley Organics. Tetralin and indan were further purified by washing with concentrated sulfuric acid using the procedure of King and Stock.6 This tetralin was then distilled by spinning band distillation at reduced pressure (1-3 torr). The purity of tetralin and indan was determined with the FFAP column and found to be 99.8 and 99.6%, respectively. 1,2-Dihydronaphthalene, 1,4dihydronaphthalene, and indene were used to confirm product identities and were not purified further. DTBP, 9,lO-dihydroanthracene, and 9,lO-dihydrophenanthrenewere obtained from ICN Pharmaceuticals. Diphenylmethane, anthracene, and phenanthrene were obtained from Aldrich Chemical. DTBP was used as received. Diphenylmethane was purified by repeated freezing and decanting of the liquid phase. 9,lO-Dihydroanthracene, 9,lO-dihydrophenanthrene,anthracene, and phenanthrene were recrystallized from either methanol or ethanol. The purity of each reactant was found to be greater than 99.6% as determined by gas chromatography using either the FFAP or OV-101 column. Fisher ACS grade toluene and benzene were used without further purification. ( 5 ) Franz, J. A,; Skiens, W. E. Fuel 1978, 57, 502. (6) King,H.-H.; Stock, L. Fuel 1982, 61, 257.
"A (@-,@- )
,
".A(O*,O I3.A(
=!, ) 7
Disproportionation reaction enthalpies (md)were calculated from the data given in Table IV and the following eq:2 - a H d = DH(R-H) + DH(R'-H) + mH2(Rd) - 2AHf(H.) where DH(R-H) and DH(R'-H) are bond strengths, (Rd) is the heat of hydrogenation of the double bond formed by'disproportionation, and nHf(H.1 is the heat of formation of atomic hydrogen (AHf(H*)= 52.1 kcal/mol). Reference 14. Reference 12. Reference 14. e Reference 17. Obtained from gas-phase studies. Reference 16. ResuIts Relative self-disproportionation-recombination rate constant ratios, k d / k , ,were determined in chemical systems containing a thermal radical initiator, DTBP, a radical precursor, RH,and in some cases a diluent, benzene. Results are interpreted in terms of the following mechanism: ki
t-BuOO-t-Bu -* 2t-BuO. t-Bu-0.
k
A
1+
CH,.
(1) (2)
-. . . . .. . visproportionation/ Kecombination or nyaroaromatics 2-
*
..TI
+ RH k3 CH3. + R H
t-BuO.
+
t-BuOH
4
4
2R.
kr +
CH4
+ R.
+ Re
The Journal of Physical Chemistry, Vol. 88, No. 24, 1984 5917 (3) (4)
RR
extents of reaction and under conditions where derived kd/ k, values were independent of the extent of reaction. Of all the reactions reported in this work, self-reactions of 9,1O-dihydro-9-anthryl radicals were the most difficult to study. The recombination product of this radical underwent noticeable decomposition upon standing for periods exceeding 6 h to form anthracene as a major product. Therefore product analysis was performed immediately after reaction using both liquid and gas chromatography. The gas chromatogram indicated that the recombination product qecomposed in the column during temperature programming. Reactions involving two different radicals (R. and R’.) were studied in reaction systems similar to those discussed above, except that two radical precursors, R H and R’H, were used. Relative precursor concentrations were adjusted so that the rate of formation of one of the radicals (R-) was at least eight times greater than the other (R’.). In all cases, the concentrations of the recombination products were in the following order: [RR] > [RR’] >> [R’R’]. Values for k d / k ,were obtained from ratios of the concentrations of Rid and RR’. Results are given in Table I1 for reactions of four different radical pairs. The radical listed first is the hydrogen acceptor in the disproportionation reaction. In addition to k d / k ,values, these studies provide relative rate constants of hydrogen abstraction, kab, by initial radicals, primarily t-BuO. radicals, from the two radical precursors (Table 11). These values are obtained from the concentration of the recombination products and the radical precursors as follows:
Rd and R R are disproportionation and recombination products, respectively. Values for k d / k ,were derived from ratios of concentrations of & and RR. Concentrations of acetone were always found to be less than onefifth as large as that of tert-butyl alcohol, hence reaction 4 provided a relatively minor fraction of R.. Considering the high concentrations and reactivity of R H in the present experiments, this is consistent with results of other workers.’ A preliminary study using tetralin as the radical precursor was carried out over a wide range of conditions to check the above mechanism. The only detectable primary products were 1,l’ditetralin and 1,2-dihydronaphthalene. No 1,4-dihydronaphthalene was observed even though it would have been clearly resolved by the FFAP column. Naphthalene was also not observed as a product although a very small amount of it was present as an impurity in tetralin (-0.2%). Rate constants for dissociation of DTBP ( k l ) ,determined from amounts of t-BuOH relative to the unreacted DTBP, agreed reasonably well with literature A key result of these studies is that relative disproportionationrecombination rate ratios varied little over a wide range of temperature (1 25-225 “C), radical initiator concentration (3-30 wt %), and extent of reaction (0.4-15% decomposition of tetralin). The disproportionation-recombination rate ratio increased by only 15% for the above 100-deg temperature range. Also significant is the finding that two independent measures of mass balance also showed little systematic variation with extent of reaction except perhaps at the higher temperature. These results indicate that secondary reactions (reactions of products) are not important. Apparently, addition of 1-tetralyl radicals to 1,2-dihydronaphthalene is slow, as is hydrogen abstraction from 1,l’-ditetralin and 1,2-dihydronaphthalene. To further confirm the absence of significant secondary reactions several reactions were run in which small concentrations (- 1%) of 1,2-dihydronaphthalene were added to reaction mixtures of 16% DTBP in tetralin. Results at 150 O C indicated that the half-life of 1,2-dihydronaphthalene in this system was of the order of 50 min, appreciably longer than reaction times used for k d / k , determinations. From these studies we found that if we used our measured FID response factor of t-BuOH relative to tetralin and estimated the response factor for 1,l’-ditetralin as being twice that of tetralin on a molar basis, on the average the yield of products was 15% lower than expected. This problem was assumed to be due to an error in our estimated response factor for 1,l’-ditetralin. This same discrepancy was also observed in other reactions reported in this work. Accordingly, the estimated FID response factors for all recombination products determined by G C were reduced by 15% since no other reasonable explanation, such as additional products, could account for this discrepancy. This problem did not arise when the UV absorbance detector was used and the response factor for the recombination product of 9,lO-dihydro9-anthryl radicals was assumed to be twice that of 9,lO-dihydroanthracene. In Table I are given k d / k ,ratios for the self-reactions of the following radicals: 1-tetralyl, 1-indanyl, 9,10-dihydro-9phenanthryl, and 9,10-dihydro-9-anthryl. These studies were done a t 150 O C where the half-life of DTBP is 64 min. DTBP is a widely used radical initiator whose decomposition has been studied in a wide range of chemical system^.^*^ Potential problems with secondary reactions were avoided by carrying out reactions at low
0.06,’* respectively.
(7) Denisov, E. T. “Liquid-PhaseReaction Rate Constants”;Plenum Press: New York, 1974. (8) Kochi, J. K. Ed. “Free Radicals”; Wiley: New York, 1973; Vol. I. (9) Batt, L.; Benson, S . W. J . Chem. Phys. 1962, 36, 895.
(10) Benson, S . W. “Thermochemical Kinetics”, 2nd ed.; Wiley: New York, 1976. (11) Benson, S. W. Can. J . Chem. 1983, 61, 881. (12) Nelson, S. F.; Bartlett, P. D. J . A m . Chem. SOC.1966, 88, 137.
Small corrections for disproportionation were made where appropriate. These values are in accord with related values obtained by other worker^.^ These results also indicate that H abstraction by stabilized radicals is slow relative to recombination in our experiments. If H abstraction by hydroaromatic radicals were rapid, the following equilibrium would be approached: R*
+ R’H G R H + R’.
(8)
However, relative concentrations of radicals as deduced from their termination products were far from estimated equilibrium values. For example, the equilibrium ratio
is estimated’O as 7 X lo”, while the observed value is 0.13 (Table 11). Discussion At the present time, predictive ability for k d / k , ratios is unsatisfactory. While various qualitative models are in accord with trends observed in kd/k, for homologous series of reaction^,^,^^ these models are not broadly applicable. Of particular concern in the present work is the fact that no current model can account for large differences in kd/k, observed between self-reactions of stabilized vs. nonstabilized radicals. For instance, k d / k , for self-reactions of tert-butyl and cumyl (I) radicals are 2.64 and
d I
5918
The Journal of Physical Chemistry, Vol. 88, No. 24, 1984
TABLE IV: Thermodynamic Data Used for Calculating Disproportionation Reaction Enthalpies
C-H bond bond
strength, kcal/mol
reaction
oa
83d
85a
heat of hydrogenation kcal/mol
&
t
n,
+ @J"
t
n,
+
,&
83a
-26*7e
-23.gg t
5.ge
86a
C=C=C t
n,
4
-40.0e
a Reference 13. Reference 19. Assumed equal to benzylic C-H bond strength in ethylbenzene." Calculated relative to benzylic C-H bond strength by using structure-resonance theory.2 e Reference 20. Reference 21. 8 Heat of hydrogenation of trans-l,2-diphenylethenewas calculated from data of ref 20.
A significant difference between such reactions is that termination reactions of stabilized radicals are generally accompanied by a loss of resonance stabilization energy. Thus, self-disproportionation of tert-butyl radicals is roughly 20 kcal mol-' (84 kJ mol-') more exothermic than self-disproportionation of cumyl radicals. This factor along with the observation that kd/k, for the radical self-reactions studied in this work seemed to vary with reaction exothermicity prompted us to examine this relationship more closely. In Table I11 disproportionation enthalpies, AH,, are listed along with disproportionation-recombination ratios per transferrable H atom (kd/kr)Hfor reactions studied here and for related reactions reported by other workers.'e16 These values are plotted in Figure 1. Enthalpies of recombination are not considered since available data clearly show that k, does not depend on the magnitude of this quantity.8 The overall correlation between In (kd/k,) and AHd for all liquid-phase data (the first eleven reactions) is only fair with a correlation coefficient of 0.78. A linear regression fit of these data gave the equation hl (kd/kr)H = -10.1 - 0.163AHd (kcal mol-') = -10.1 - 0.68AHd (kJ mol-')
The average deviation of 1n (kd/k,)H from this line is h0.68.
Manka and Stein Uncertainties in estimated A f f d values, however, may account for some of the scatter. If, for example, the C9-H bond strength in 9,lO-dihydroanthracene were 4 kcal mol-' greater than reported,I3 then the correlation coefficient increases to 0.91 and the average deviation is reduced to f0.42. The two disproportionation reactions involving arylmethyl radicals have smaller (kd/kr)H values than do reactions of pairs of hydroaromatic radicals with similar reaction exothermicities. This is opposite the trend that would be expected if reaction entropy were the significant rate-determining factor since disproportionation reactions of arylmethyl radicals are expected to have higher entropies than comparable reactions of hydroaromatic radicals (bending modes in the former radicals are converted to internal rotationsI0). Literature (kd/kJH values for self-reactionsof l-phenylethyl,'4J5 ally1,I6 and 1,2-diphenylethylI4 radicals fall close to the line based on the present data while the liquid-phase value for cumyl12 radicals lies appreciably below this line. Gas-phase disproportionation of 1,3-cyclohexadien-5-y1 radicals is more exothermic than most of the reactions studied ( A f f d = -48 f 10 kcal mol-'), which is consistent with its relatively high value for (kd/kr)H. In cases where disproportionation results in the destruction of aromaticity to form a quinoid structure, reaction exothermicity is far smaller than for reactions reported here and this reaction is predicted to be very slow. This is in fact the case for disproportionation of alkyl-substituted triphenylmethyl radicals near room temperature,'* where AHd/kcal mol-' is estimated to be --lo f 10 and kd/M-' s-' appears to be in the range lo-' to Radical-radical reactions involving two nonresonance stabilized radicals are more exothermic than those investigated here and their relative reaction rates cannot be rationalized by the present approach. In fact, for self-reactions of ethyl, isopropyl, and tert-butyl radicals, (kd/kr)H may actually decrease slightly as reaction exothermicity increases. Data for cross reactions between stabilized and nonstabilized radicals are too few in number and do not span a wide enough range of reaction enthalpies to make meaningful comparisons with AHd values. On the basis of the above discussion, there does not appear to be any general relationship between (kd//& and reaction enthalpy when the reaction is sufficiently exothermic (-AHd 5 50 kcal mol-'). In this regime (kd/kr)Hfor different hydrocarbon radicals generally fall in a rather narrow range between 0.04 and 0.23 and are apparently controlled by entropic fact0rs.l' As reaction exothermicity declines below -50 kcal mol-', (kd/kr)Hvalues decline. In this regime disproportionation rates become increasingly sensitive to reaction enthalpy while recombination rates remain insensitive. The substantial degree of scatter around the line in Figure 1 suggests that nonenthalpic factors are as important for these reactions as they are for more exothermic reactions. In view of apparent activation energies of several kcal mol-' for diffusion-controlled recombination rates and the small activation energies that might be expected for disproportionation reactions of resonance-stabilized radicals, we cannot extract conclusive quantitative evidence concerning these reactions from the weak temperature dependences reported in the literature and (13) McMillen, D. F.;Golden, D. M. Annu. Reu. Phys. Chem. 1982,33, 493. (14)Gibian, M.J.; Corky, R. C. J . Am. Chem. SOC.1972,94, 4178. (15)Greene, F. D.; Berwick, M. A.; Stowell, J. C. J . Am. Chem. SOC. 1970,92, 867. (16)James, D. G. L.; Kambanis, S. M. Trans. Faraday SOC.1969,65, 1305. (17) James, D. G. L.; Stuart, R. D. Trans. Faraday SOC.1968,64,2752. (18)(a) Marvel, C. S.; Rieger, W. H.; Mueller, M. B. J . Am. Chem. SOC. 1939,61,2769.(b) Marvel, C. S. et al. J . Am. Chem. SOC.1939,61,2771. (19)Robaugh, D. Ph.D. Dissertation, West Virginia University, Morgantown, WV, 1982. (20)Cox, J. D.; Pilcher, G. "Thermochemistry of Organic and Organometallic Compounds"; Academic Press: New York, 1970. (21)Lee-Bechtold, S.H.et al. J . Chem. Thermodyn. 1979,11, 469. (22)Certain commercial materials and equipment are identified in this paper in order to specify adequately the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply the material or equipment identified is necessarily the best available for the purpose.
J. Phys. Chem. 1984, 88, 5919-5923 in this paper for kd/kr ratio^.^ However, arguments in the previous paragraph and the limited experimental evidencelEsuggest that a hypothetical thermoneutral radical disproportionation reaction has an appreciable activation energy, perhaps similar to that for thermoneutral H-atom abstraction by a radical from a molecule (typically 10-15 kcal mol-14). In addition, (kd/kJH values are predicted to increase with temperature for very highly stabilized radicals. The opposite, albeit weak, behavior is often observed
5919
for reactions of nonstabilized radical^.^ Further experiments are needed to test these ideas.
Acknowledgment. The authors thank the Gas Research InStitUte for support of this work. Registry No. 1-Tetralyl, 69339-77-1; I-indanyl, 55003-52-6; 9.10dihydro-9-anthryl, 58194-37-9;9,10-dihydro-9-phenanthryl,77465-05-5; benzyl, 21 54-56-5;diphenylmethyl, 4471-17-4.
Two-Dimensional Potential Surfaces for Bridged Mlxed-Valence Dimers Mary Jo Ondrecheb* Jaeju KO,and Leslie J. Root Department of Chemistry, Northeastern University, Boston, Massachusetts 021 15 (Received: July 18, 1984)
A three-site model for bridged mixed-valence dimers is presented. Within the framework of this model, adiabatic potential energy surfaces depend upon two nuclear coordinates, the vibrational sum end difference coordinates. Potentials developed previously for complexes of this type depend upon the difference coordinate only. The coupling to the sum coordinate emerges naturally from the present three-site model. We show that indeed the dependence of the potentials upon the vibrational sum coordinate is necessary for proper descriptions of these complexes, as was originally pointed out b j N. S. Hush. From the present work, one cansalculate the contribution of this effect to the absorption profile of the intervalence transfer (IT) band. Expressions which are exact within the Born-Oppenheimer scheme are given for the potential energy surfaces. For delocalized complexes, which have strong electron exchange interaction, we derive simpler, approximate expressions for the potential energy surfaces using second-order perturbation theory. For complexes with significant exchange interaction between the termini and the bridge, the contributions of both of the nuclear coordinates to the line shape of the IT band become clear.
Introduction Bridged mixed-valence dimers, especially those of ruthenium, have captured considerable attention r e ~ e n t 1 y . l ~ One ~ such species, the Creutz-Taube ion,1b-2,4*5 a pyrazine-bridged mixedvalence complex of ruthenium, has been the focus of intense controversy regarding the nature of its ground state. The critical unresolved issue has been the extent of electron delocalization. It is not yet clear whether the ion has an asymmetric ground state, with the unpaired 4d electron best described as trapped on one Ru site, or whether the ion has a symmetric ground state, with the unpaired electron best described as delocalized over both Ru sites.s Mixed-valence compounds generally possess spectra and properties which are not simply the sum of those of the constituent ions in their respective distinct oxidation levels. Probably the best known example of this is Prussian blue, Fe4[Fe(CN)6]3.14H20, the color of which is characteristic of neither the iron(I1) nor the iron(II1) ions it contains. Robin and Day have designated three classes of mixed-valence compounds.6 In class I, two metal ions are very weakly coupled. One expects a very high thermal barrier to electron transfer and the optical absorption band corresponding to intervalence transfer (IT), e.g. M~I...MIII
-,MW..MII
(1)
(1) (a) S . J. Lippard, Prog. Inorg. Chem., 30 (1983); (b) C. Creutz, ibid., pp 1-73; (e) A. Haim, ibid., pp 273-357; (d) T. J. Meyer, ibid., pp 389-440; ( e ) N. Sutin, ibid., pp 441-498. (2) (a) D.B. Brown, Ed., “Mixed Valence Compounds”, D.Reidel, Dordrecht, Holland, 1980; (b) P. N. Schatz, ibid., pp 115-150; (e) N. S. Hush, ibid., pp 151-188. (3) M. Tanner and A. Ludi, Inorg. Chem., 20, 2348-2350 (1981). (4) C. Creutz and H. Taube, J. Am. Chem. SOC.,91, 3988 (1969); 95, 1086-1094 (1973). ( 5 ) U. Fiirholz, H.-B. Biirgi, F. E. Wagner, A. Stebler, J. H. Ammeter, E. Krausz, R. J. H. Clark, M. J. Stead, and A. Ludi, J. Am. Chem. SOC.,106, 121-123 (1984), and references cited therein. (6) M. B. Robin and P. Day, Adv. Inorg. Radiochem., 10,247-422 (1967).
is extremely weak. Class I11 on the other hand is completely delocalized. The two metal sites are strongly coupled and occupy equivalent ligand environments. A strong transition characteristic of none of the oxidation levels of the corresponding mononuclear complexes is observed. There is no barrier for intramolecular electron transfer, and one cannot define a site-to-site electron transfer rate. The strong transition observed in class I11 compounds is not a true IT transition but really a bonding-to-antibonding transition. (However, it is often still called IT.) Class I1 is intermediate: There is a finite barrier to thermal electron transfer, electron transfer occurs at a faster rate than for class I, and the intensity of intervalence absorption lies between those for class I and class IIL6 The work of N. S . Hush7 has been especially valuable in the establishment of direct connections between the measurable physical properties of these systems and the classical theory of electron t r a n ~ f e r . ~ For , ~ instance, for localized, homonuclear dimers undergoing one-electron transfer at 300 K, the width of the IT band at half-maximum is given by
where smax is the frequency in cm-’ at the absorption maximum. If the nuclear motion is harmonic, the energy of the IT band is related to AE* of classical electron transfer theory8s9by the simple relation AE,, = 4AE*
(3)
where AE* is the energy required for the nuclei to reach the activated complex c~nfiguration.~ For the systems of interest in the present work (having harmonic nuclear motion and no shifts (7) N. S . Hush, Prog. Inorg. Chem., 8, 391-444 (1967). (8) R. A. Marcus, Annu. Rev. Phys. Chem., 15, 155 (1964), and earlier
papers.
(9) N. S . Hush, Trans. Faraday SOC.,57, 557 (1961).
0022-3654/84/2088-5919$01.50/00 1984 American Chemical Society
