Faraday Discuss. Chem. SOC., 1987, 84, 25-37 Dynamics of Endoergic Aromatic Substitution Reactions Gary N. Robinson, Robert E. Continetti and Yuan T. Lee Materials and Chemical Science Division, Lawrence Berkeley Laboratory, and Department of Chemistry, University of California, Berkeley, CA 94720, U.S.A. The endoergic substitution reactions Br+ 0-, m-, p-CH3C6H4Cl + 0-, rn-, p-CH,C6H4Br+ C1 (AH: == 15 kcal mol-') have been studied using the crossed beams method in the collision energy range 20-30 kcalmol-I. o-Chlorotoluene was found to be more reactive than p-chlorotoluene at the highest energy but the reverse was true below 25 kcal mol-'. No reaction was observed for the meta isomer. An explana- tion for the lower reactivity of rn-chlorotoluene is offered in terms of possible features of the potential-energy surface.In all of the reactions observed, the products are largely forward scattered, indicating that the majority of collision complexes survive for less than one rotational period. This is understandable in light of the ca. 2 kcal mol-' endoergicity to Br addition that results from the loss in resonance stabilization energy. Very little of the energy available to the products of these reactions is channeled into transla- tion. The experimental product translational energy distributions and excita- tion functions suggest that, in those complexes that decompose through CI elimination, only a few vibrational degrees of freedom in the vicinity of the collision are involved in energy redistribution. Although homolytic, or free-radical, aromatic substitution reactions have been the subject of many kinetic studies,'-3 their detailed dynamics in both the liquid and gas phases are only partially understood.In the gas phase they proceed by addition of an atom or radical to an aromatic ring to form an activated cyclohexadienyl radical which subsequently decomposes through emission of another atom/radical. Questions relating to the dynamics of atomic addition to the ring, the features of the potential energy surface along the reaction coordinate, the extent of intramolecular vibrational energy redistribution prior to unimolecular decomposition and the relative importance of all of these factors in determining 'the energy dependence of the reactive cross-section can all be addressed by the method of crossed-beams scattering.Endoergic substitution reactions are particularly intriguing, since cleavage of the stronger bond is not the statistically favoured mode of decay of the chemically activated radical. Thus, observing the endoergic channel may offer some insight into factors other than the amount of phase space available to the activated radical and products that determine the course of the reaction. In the case of aromatic substitution reactions, one may, in addition, observe the effects of substituents on the reactivity of different sites on the aromatic ring. Since these effects are related to the energetics of adduct formation, they should be most pronounced in those reactions where the reagent atom/radical bonds weakly to the ring. In this respect Br is an ideal reagent.We have carried out a crossed-molecular-beam study of the endoergic substitution reactions (fig. 1 ) Br+ 0-, m-, p-CH3C6H4Cl + C1-k 0-, m-, p-CH3C6H5Br in the collision energy range of 20-30 kcal mol-'. The results of these experiments shed new light on the role of substituents in controlling the orientation of aromatic substitution and on the dynamics of these reactions in general. (A&* 15 kcal mol-') 2526 Endoergic Substitution Reactions 3 5 1 C7H7Br + CI -51 -10 I Fig. 1. Generalized reaction coordinate diagram. Shaded region indicates approximate collision energy range. Experimental The crossed-beam apparatus used in these experiments has been described previously.435 Two seeded, differentially pumped reagent beams cross at 90" in a vacuum chamber held at ca.lO-'Torr.t The products are detected with a triply differentially pumped mass spectrometric detector that rotates in the plane of the two beams. The bromine atom beam was generated by passing a mixture of Br, in rare gas through a resistively heated high density graphite oven designed in this laboratory by Valentini et aL6 The Br,-rare gas mixture is created by bubbling ca. 700 Torr of He, Ne or Ar through liquid bromine (reagent-grade, Fischer and Mallinkcrodt) at 0 "C [ p ( Br,) a 60 Torr]. The oven had a nozzle diameter of 0.14mm and was run at ca. 1380 "C. A conical graphite skimmer having an orifice diameter of 0.10 cm was positioned 0.76 cm from the nozzle. 90% of the BrZ dissociated into Br atoms, as determined from a direct measurement of Br/Br2 in the beam.The secondary molecular beam was formed by bubbling 450Torr of He through chlorotoluene heated to 60°C in a bath and expanding the mixture through a 0.21 mm diameter aperture nozzle. A stainless-steel skimmer with an orifice diameter of 0.66 mm was positioned 0.89cm from the nozzle. The source and feed line were heated with coaxial heating wire to a temperature of 200 "C. o- and p-Chlorotoluene (o-, p-CT) were purchased from MCB and m-CT from Aldrich. All of the compounds were used without further purification, except for the p-CT, which was distilled on a spinning band column. In order to reduce the background at the product mass, a liquid-nitrogen-cooled copper cold finger was placed against the differential wall inside the scattering chamber so that the detector would always face a cold surface during the angular scans.Product angular distributions were measured by modulating the CT beam with a 150 Hz tuning fork chopper and collecting data with the beam on and off using a dual channel scaler. Data were collected for ca. 6 min per angle. t 1 Torr = 101 325/760.Pa.G. N. Robinson, R. E. Continetti and Y. T. Lee 27 h v) U .- E - 5 - - - - - 0 ' 1 - I I I I I I 1 7 I I ' 10 20 30 40 50 60 70 20 30 40 50 60 70 I laboratory angle, @ / O laboratory angle, @/' 3 Fig. 2. 0- and p-BT laboratory angular distributions ( m / e = 170) normalized to constant reactant flux. Br beam is at 0". Solid lines are fits to data. Arrows indicate positions of centre-of-mass angles with collision energy decreasing from left to right.( a ) o-BT: E, = 31 .O; E, = 25.3; A E, = 20.9 kcal mol-'. (b) p-BT: 0 E, = 31.5; E, = 25.3; A E, = 21.4 kcal mol-'. In order to compute relative cross-sections for a given reaction at different collision energies, we scaled the product number density by the reactant flux, which is proportional to nBrncTurel, where ni = number density of beam i and ureI = relative velocity. Since the wide-angle Br elastic scattering cross-section does not change drastically as a function of energy, measuring Br on CT elastic scattering allows us to measure changes in this quantity. During each scan, the rn/e = 79 signal was monitored at three different LAB angles. The angles were all beyond the cutoff angle for elastic scattering of Br on He so the Br+ signal observed was from Br scattering on CT.The contribution of undissoci- ated Br2 to the rn/e = 79 signal was very small and was neglected. Relative values for nBrnCTurel derived from the Br elastic number density at angle of 16" are given in table 1. The velocities of the reactant beams were measured using the time-of-flight (TOF) technique. A 256-channel scaler interfaced with an LSI-11 computer accumulated the data. No TOF measurement was made for the rn-CT beam, but its velocity should be identical to that of o-CT since both have the same vapour pressure (22 Torr; p-CT = 21 Torr) at 60 "C. The peak beam velocities (in units of lo5 cm s-'), and speed ratios, S, are: Br/He: 1.85, S = 6.1; Br/Ne: 1.55, S = 6.9; Br/Ar: 1.29, S = 8.4; o-CT/He: 1.33, S = 11.3; p-CT/He: 1.35, S = 11.8.Product TOF were measured using the cross-correla- tion method.' Counting times were ca. 1 h per angle. Results and Analysis The 0- and p-bromotoluene (BT) substitution products were detected at m / e = 170 ( 79Br), however, the quadrupole mass spectrometer resolution was set sufficiently low to allow some of the *lBr product to be detected as well. The product angular distributions are shown in fig. 2. Elastic scattering of impurity in the p-CT beam contributed to background at rn/e = 170 near that beam. This was most problematic at a collision28 1.0 - Endoergic Substitution Reactions I I I 1 I I h - . h v) U ._ E 1.0 0.5 0.0 0.5 0.0 1.0 0.5 0.0 200 300 400 500 flight time/ps I I I I 100 200 360 400 500 flight time/ p s Fig.3. Time-of-flight spectra of p-BT, E, = 31.5 kcal mol-' ( m / e = 170), at five different angles. Solid lines are fits to data. energy, E,, of 21.4 kcal mol-', where the product signal level was lowest. At this energy the elastic scattering background was measured by substituting a properly diluted beam of Kr in Ar for the Br in Ar beam. It was then scaled to the product angular distribution at 74" and subtracted from it. At the peak of the E, = 31.0 kcal mol-' o-BT angular distribution, the product count rate was 20 Hz. The angular distributions reveal that, at all energies, the 0- and p - products are mostly forward scattered with respect to the centre-of-mass angle for the collision. Remarkably, no BT product was detected for the reaction Br+ rn-CT at a collision energy as high as 29.3 kcal mol-'.TOF spectra of p-BT, E, = 31.5, 21.4 kcal moll', and o-BT, E, = 25.3, 20.9 kcal mol-I, are presented in fig. 3 and 4. At each collision energy the TOF spectra at different angles have peak flight times close to that of the velocity of the centre-of-mass (fig. 7, see later), indicating that little energy is channeled into translation. The product angular distributions and TOF spectra were fitted using a forward convolution program' that starts with a separable form for the centre-of-mass (CM) reference frame product flux distribution, ICM( 8, E ' ) = T( 8 ) P ( E'), and generates labora-G. N. Robinson, R. E. Continetti and Y. T. Lee 29 10 0.5 0.0 1.0 h v) c1 .e c -e 0.5 h \.) v 2 0.0 1.0 0.5 0.0 160 260 360 460 260 360 460 5 flight time/ps flight time/ps 0 Fig.4. ( a ) TOF spectra of o-BT, E,= 25.3 kcal mol-'; (b) TOF spectra of p-BT, E, = 21.4 kcal mol-'; ( c ) TOF spectrum of o-BT, E, = 20.9 kcal mol-'. Solid lines are fits to data. tory (LAB) frame angular distributions and TOF spectra suitably averaged over the spread in relative velocities. T ( 8 ) , the CM frame angular distributions, is taken to be a sum of three Legendre polynomials whose coefficients are varied to optimize the fit. A RRK functional form is used for P ( E ' ) , the CM frame product translational energy distribution : where B is related to any barrier in the exit channel and E,,, is the total energy available to the products (E,-AH;). AH: was taken to be 15 kcal mol-' (see Discussion). The parameters p , q and B were optimized to give the best fit to the data.For a given experiment, the spread in beam velocities and intersection angles gives rise to a spread in relative velocities and hence in collision energies. A EJ E,( FWHM) = 30% for the reactions with Br seeded in He and =25% for the reactions with Br seeded in Ne and Ar. Each beam velocity and intersection angle permutation corresponds to a different kinematic configuration (Newton diagram) over which the calculated angular distribution and TOF fits must be averaged. The collision energies corresponding to P ( E ' ) = ( E ' - B ) P ( E,,, - E')'30 Endoergic Substitution Reactions the most probable kinematic configurations are listed in table 1. Since, for an endoergic reaction, the maximum translational energy of the products will depend strongly on E,, a P ( E ' ) with a unique value of E,,, was used for each kinematic configuration in the analysis.Also, since the cross-section is found to depend on collision energy, each kinematic configuration was weighted according to E,. Because of the large spread in E,, it was necessary to extrapolate the excitation function used in the weighting routine beyond the most probable experimental collision energies. This was done by taking the cross-section at E, = 15 kcal mol-' to be 0.0 and extrapolating linearly beyond the highest energy. The high-energy extrapolation has a marked affect on the fits to the E,= 31 kcal mol-'data, since it is used to determine the most probable collision energy and centre-of-mass angle.Linear extrapolation, however, appears to be the most unbiased approach to this problem. Although the data offer some latitude with regard to the exact form of the CM angular and energy distributions, they do place certain constraints on the fits. The best fits were obtained with T ( 8 ) distributions that peak at 0 and 180" with maxima at 0" (fig. 5). There is a range of acceptable values for the P ( E ' ) parameters [as there is for the coefficients of the Legendre polynomials that constitute T ( 8 ) ] , yet the average energy, ( E ' ) (table l), does not vary much within this range. Since the fits were relatively insensitive to the q parameter, which governs the curvature of the tail of the P ( E ' ) , this parameter was fixed for all the fits and the other parameters optimized. The resulting P ( E ' ) distributions (fig.6) peak between 0.0 and 1.2 kcal mol-', with the o-BT P ( E ' ) distributions peaking at lower energies and having slightly lower values of ( E ' ) than those for p-BT. The following changes in the P ( E ' ) for p-BT, E, = 25.3 kcal mol-', while not significantly affecting the fit, produced the indicated changes in ( E ' ) : *25% in q, stlo% in ( E ) ; k0.4 kcal mol-' in peak position, *2'/0 in ( E ' ) ; *2 kcal mol-' in endoergicity, ca. *15% in ( E ' ) . A CM frame product flux contour diagram for Br+ p-CT+p-BT+Cl, E, = 31.5 kcal mol-', is given in fig. 7. The overall quality of the fits justifies our use of a separable form for the CM flux distribution. The asymmetric CM angular distributions that we obtain indicate that the majority of 1-bromo- 1 -chloro-2-( -4-)-methylcyclohexa-2,4-dienyl (BCMC) complexes decompose in a time less than one rotational period.8b The p-BTCM angular distributions show more forward-backward symmetry at lower collision energies, suggesting that the lifetime of the BC4MC complex increases relative to its rotational period as E, decreases.We Table 1. Relevant experimental quantities reaction E," ( E ' ) S , (arb. units) nBrnCT~rel Br/ He + p-CT 31.5 5.0 0.7 1 0.98 Br/ Ne + p-CT 25.3 3.1 0.48 0.59 Br/Ar + p-CT 21.4 2.1 0.3 1 0.53 Br/ Ne + o-CT 25.3 2.9 0.45 0.54 Br/Ar+ o-CT 20.9 1.9 0.18 0.44 Br/ He + rn-CT CQ. 29.3 - 0.00 b Br/ He + o-CT 31.0 4.6 1 .oo 1 .oo All energies are in kcal mol-'; collision energies reflect cross-section weighting.' The rn-CT reaction was studied several weeks after the 0- and p-CT experiments were completed. The Br/ He + o-CT angular distribution was remeasured at this time, however. The o-BT and Br elastic signal levels indicated that the Br beam intensity was ca. 50% lower than during the earlier experiments; the o-BT signal-to- noise ratio had dropped by 20%. However, given the presence of elastic scattering background in the rn-CT experiment (ca. 2 Hz at 46"), it is doubtful that would have been able to see signal even if the Br beam were twice as intense.G. N. Robinson, R. E. Continetti and Y. T. Lee 31 CM angle, 8 / O CM angle, 8/" Fig. 5. CM frame product angular distributions for ( a ) o-BT and ( b ) p-BT. (-) o-BT: E, = 31.0; p-BT: E, = 31.5 kcal mol-'; (- - -) 0- andp-BT: E, = 25.3 kcal mol-'; (- .-) o-BT: E, = 20.9; p-BT: E, = 21.4 kcal mol-'. h Y 4 v Fig. 6. CM frame product translational energy distributions for ( a ) o-BT and ( b ) p-BT. (-) o-BT: E, = 31.0; p-BT: E,= 31.5 kcal mol-'; (- - -) o- and p-BT: E, = 25.3 kcal mol-'. (- . -) o-BT: E, = 20.9; p-BT: E, = 21.4 kcal mol-'. ( - .) Four-mode RRKM translational energy distribution.32 Endoergic Substitution Reactions Fig. 7. CM frame product flux contour diagram for p-BT, E, = 31.5 kcal mol -'. Scale given is for contour diagram. Scale of Newton diagram is half that of contours. Centre-of-mass velocity vector is represented by arrow between beam vectors. can estimate the rotational period of the BC4MC complex by assuming, for the sake of simplicity, that the Br atom collides perpendicular to the ring with an impact parameter of 0.9 A (the distance from the centre of mass of p-CT to the chlorinated carbon) and that the rotational angular momentum of the reagent is negligible.For the collision of Br with p-CT, E, = 31.5 kcal mol-', the magnitude of the orbital angular momentum, L, will be 160 A. The moment of inertia about the rotation axis of the complex is ca. 880 amu A', assuming that the halogenated carbon is sp3 hybridized, that the C-Br and C-C1 bond lengths are 2.0 and 1.7 A, respectively, and that the ring is undistorted. The rotational period, given by T , , ~ = 27rI/L, will therefore be ca. 5 ps in the present example. At E, = 21.4 kcal mol-', T , , ~ = 7 ps. If we calculate the approximate product orbital angular momentum, L', for the p-CT reaction, E, = 3 1.5 kcal mol-', using a relative velocity corresponding to ( E')p- HT = 5.0 kcal mol-' and an impact parameter of 0.1 A (the distance between the chlorinated carbon and the centre-of-mass of the complex, with the C-Cl bond perpendicular to the ring and the C-Br bond in the plane of the ring), we obtain IL'I == 6 h, far lower than the initial 160 h.It would take an average exit impact parameter of 2.7 A for the total angular momentum of the complex to be carried away as product orbital angular momentum. However, even if most of the angular momentum of the collision were carried away in rotation of the BT product, the rotational energy of the product would be small (only ca. 1 kcal mol-' for p-BT in the present example) because of its large moment of inertia ( I = 770 amu A2 for p-BT).The lack of a strong correlation between L and L' is the reason why the CM angular distributions do not peak more strongly in the forward and backward directions.8" The larger amount of sideways scattering for o-BT at 3 1 .O kcal mol-' could indicate an even weaker L to L' correlation in the Br + o-CT reaction at high collision energies. This may be due to the more complicated rotational motion of the asymmetric BC2MC complex. A fraction of the translational energy of BT must come from rotation of the complex at its exit transition state (TS). In the absence of extensive vibration-rotation couplingG. N. Robinson, R. E. Continetti and Y. T. Lee 4 / / / / / / / I I I I 16 20 25 30 .EJkcal mol-' 33 Fig. 8. Plot of relative cross-section us. collision energy. 0 p-BT; o-BT; 0 rn-BT. (-) Three-mode RRKM branching ratio curve. Normalized to equal (0.99)S,,,-BT at 31.5 kcal mol-'. (- - -) Six-mode RRKM branching ratio curve. Normalized to equal (O.97)Sr,,-,, at 3 1 .O kcal mol-.'. in the complex, the rotational energy at this TS will be ca. 1.2 kcal mol-' for BC4MC ( E , = 31.5 kcal mol-', C-CI bond perpendicular to the ring with a bond length of 2.6 A9). If this energy went entirely into relative motion of the products, p-BT would acquire only 0.2 kcal mol-' in translation. The rotational motion of BC2MC will, as noted above, be more complex. However, the fact that the o-BT P ( E ' ) distributions peak at slightly lower energies than those for p-BT could indicate that the ortho complex has a lower rotational energy at its exit TS than the para complex.Lastly, relative cross-sections, S,, were calculated at the most probable collision energies by integrating the CM frame product flux: S , = 2 ~ 1 ~ ~ 1; P ( E ' ) T( 6) sin 8 dE' do. The computed S , values were used to weight the collision energies used in the analysis. This procedure was repeated until the input and output values of S , agreed. Final values of S, as a function of E, are given in table 1 and are plotted in fig 8. A range of collision energies contributes to each value of S,, although we assign each to a single, most probable collision energy. This spread in E, is the dominant source of uncertainty in the derivation of S,. Another source, however, is the uncertainty in the form of the P ( E ' ) .By fixing the q parameter in the fits, we believe that we have eliminated this source of uncertainty in the relative cross-sections.34 E ndoergic Substitution React ions Discussion The endoergicities of the different isomeric reactions under study should not differ markedly from one another. The heats of formation of 0-, rn- and p-CT [AH&8(g)] are 3.8, 4.1 and 5.3 kcal mol-', respectively.'09'' We were able to find heat of formation data for the para isomer of bromotoluene (BT) only [AHLg8(g) = 13.0 kcal m ~ l " ] , ' ' ~ ' ~ but Szwarc's indicates that the C-Br bond dissociation energies in 0-, rn- and p-BT differ by only 0.6 kcal mol-'. Using the known values for AH&98 of Br, Cl,30 p-CT and p-BT, we calculate AH&8 = 10.1 kcal -mol-' for the reaction Br+p-CT-p-BT+ C1.This value strikes one a? being too low, considering that = 15 kcal mol-' for the reaction Br+ C6H5Cl -+ C6H5Br+ CLi4 In the absence of firm values for the heats of formation of the CT and BT isomers, we have used an endoergicity of 15 kcal mol-' for the present reactions. The energetics of Br addition to CT are, as far as we can tell, unknown. Ref. (15) gives AH = -8.8 kcal mol-' for Br+C2H4 + C2H4Br. The exothermicity of Br addition to benzene will be decreased by the loss in resonance stabilization energy ( E J that results from the disruption of the .rr-electron framework of the ring. In the case of H atom addition to benzene the loss in E,, will be CQ.1 1 kcal mol- ' . I 6 We conclude, therefore, that the BCMC radical will be unbound by ca. 2 kcal mol-' relative to reactants! Benson et a1." arrive at a similar value for the endothermicity of Br addition to benzotrifluoride. As a result, we do not expect there to be a potential minimum along the reaction coordinate corresponding to the BCMC complex. Based on the energetics for Br addition to CT, it is not surprising then that substitution occurs in less than one rotational period. We have calculated RRKM lifetimes, T R K K M , for the BCMC complex,20 using modified normal mode frequencies for toluene, and frequencies corresponding to C-Cl and C-Br stretching and Br-C-CI, C-C-Br and C-C-Cl bending modes.*l Including all 42 frequencies, TRRKM at E, = 30 kcal mol-' ( E * = 28 kcal mol-') is 0.02 ps, much lower than the estimated rota- tional period.TRRKM changes little as the collision energy is lowered, indicating that a quantitative comparison of the angular distribution data with the lifetime and rotational period calculations is not possible. It is interesting to note, however, that product angular distributions measured for the reactions Br + CH2CC12 - C1+ CH2CBrCl" are more symmetric about the centre-of-mass angle. In this reaction, adduct formation is indeed exoergic. Remarkably, very little of the energy available to the products ends up in translation. Apparently the vibrational modes of the aromatic ring act as a strong energy sink, with C1 elimination occurring only when sufficient energy has accumulated in the C-C1 bond.Yet, although intramolecular vibrational energy redistribution appears to be extensive prior to C-Cl bond rupture (there is certainly much in the current literature that indicates that, at these energies, it should be19) it does not seem likely that C1 elimination from BCMC is a statistical process involving energy sharing among a large number of vibrational degrees of freedom. We have calculated RRKM-AM P ( E ' ) distributions22 for BT, E, = 3 1 kcal mol- ', using different numbers of modes and a variety of values for the maximum centrifugal barrier, B,. Since the activation energies for C1 addition reactions are known to be very near zero,23 we have no reason to expect that there will be a barrier above the threshold for C1 elimination. Although a definitive comparison between the experimental and RRKM P( E ' ) distributions is not possible given the uncertainties in the fits, we obtain reasonable agreement between the experi- mental o-BT P ( E ' ) , E, = 3 1 .O kcal mol-', and a four-mode ( Y = 800-700 cm-') RRKM P( E ' ) with B,, = 0.028 (fig.6). [Using six modes ( Y = 900-700 cm-') gave a P ( E ' ) that fell too steeply.] Thus the data seem to indicate that only a limited number of degrees of freedom in the vicinity of the collision participate in energy sharing prior to C1 elimination.G. N. Robinson, R. E. Continetti and Y T. Lee 35 Such a mechanism is not unexpected. Endoergic substitution at collision energies not far from threshold must occur in a quasi-direct fashion or not occur at all since, as more vibrational modes participate in energy redistribution, the probability of C1 elimination, qcl, drops relative to qBr. This is due to the fact that qx is proportional to the density of states at the TS for X elimination.The smaller the number of active vibrational modes, the smaller the difference between the state densities for the exoergic and endoergic channels and the more C1 elimination will compete with Br elimination. For example, taking qx to be the microcanonical RRKM rate constant for X elimination, at E, = 30 kcal mol-' qBr/ qcl = 270 with 12 active modes ( Y = 800-300 cm-I), whereas with six active modes qBr/ qcl = 15. We attempted to detemine the relative importance of the Br elimination channel in both the p-CT reaction, E, = 21.4 kcal mol-I, and the o-CT reaction, E, = 31 .O kcal mol-', by measuring the TOF of CT from the channel BCMC --* Br + CT near the centre-of-mass angle.In both cases the TOF of non-reactively scattered CT obtained by substituting Kr for Br was very similar to that obtained with Br. This indicates that the Br addition cross-section is substantially smaller that the elastic/inelastic scattering cross-section. Yet, if qBr were indeed two orders of magnitude larger than qcl (as one would predict from a 12-mode RRKM calculation), we would have been able to see a substantial peak in the o-CT TOF spectrum corresponding to slow o-CT travelling at the velocity of the centre-of-mass, since the fast and slow components of the elastic scattering TOF spectrum were well resolved at E, = 31.0 kcal mol-'.Thus, our inability to observe slow o-CT provides additional (although indirect) evidence that only a few modes are active during the reaction. Further support for the reduced mode mechanism comes from an examination of the excitation functions. The measured relative cross-sections can be expressed as the product of the cross-section for forming the BCMC adduct and the relative probability of decomposition of the adduct through c1 elimination, s, = cradd[ qcl/(qcl + TBr)]. If cr,dd were constant over the energy range studied, and intramolecular energy randomi- zation were complete prior to atomic elimination, the quantity in brackets would be equivalent to the RRKM branching ratio, S R R K M . We have calculated S R R K M for the present system, using 35 ( v = 1600-200 cm-I), 12, 6 and 3 ( v = 800-700 cm-') modes. The 35- and 12-mode curves both rise steeply with energy and are essentially identical in slope.The 3- and 6-mode curves, scaled to Sr,p-BT and Sr,o-BT respectively, are plotted in fig. 8 alongside the experimental results. There is good qualitative agreement between the Slopes Of s ~ ~ ~ ~ ( 6 - m O d e ) and S r , o - ~ ~ , and between the Slopes Of s ~ ~ ~ ~ ( 3 - m O d e ) and Sr,p-BT* It is certainly plausible that the BC2MC collision complex has a larger number of active vibrational modes than BC4MC. We have already noted that the o-BT P ( E ' ) distributions have slightly lower values of ( E ' ) than those for p-BT. The reduced symmetry of the BC2MC complex may allow for enhanced vibrational energy redistribu- tion through state mixing.Coupling of the internal rotation of the methyl group to the ring vibrations is believed to be responsible for accelerated IVR in S, p - f l u o r ~ t o l u e n e . ' ~ ' ~ ~ ~ Although the barrier to methyl torsion is likely to be higher in o-CT than in p-CT,' the methyl group is closer to the collision site in the ortho isomer. The normalization factor used to scale S ~ ~ ~ ~ ( 6 - m o d e ) to Sr,o.BT is a factor of five higher than that used to scale s ~ ~ ~ ~ ( 3 - m O d e ) to Sr,p-BT, indicating, in the present context, that 0 , d d for Br+ o-CT is five times higher than for Br+p-CT. A higher addition cross-section for o-CT can be rationalized along the above lines. The greater number of active modes in BC2MC might serve to dissipate the energy of the collision better, allowing Br to add more readily to o-CT than to p-CT.There still remains the possibility that (T& changes with energy. If this were true, one could not attribute the energy dependence of S, solely to the statistical branching ratio. Using a semi-empirical potential-energy surface (PES) to calculate classical36 Endoergic Substitution Reactions trajectories, Hase et a1.26 found that the cross-section for H atom addition to C,H, varies with collision energy and that this variation is dependent on the shape of the entrance valley of the PES. Perhaps, then, the lower cross-section that we observe for o-CT substitution below E, = 25 kcal mol-' reflects a narrowing of the acceptance angle of the PES as a result of the presence of the methyl group? If this were the case, the methyl group would also raise the effective threshold for C1 elimination.One might imagine, therefore, that the o-BT excitation function could be modelled using a higher endoergic threshold and a smaller number of modes. We investigated this by calculating SRR,, using three modes and Eo = 17-20 kcal mol-'. Although the closest agreement with Sr,o-BT was obtained with Eo = 18 kcal mol-', the calculated branching ratio fell much more rapidly to zero than the experimental excitation function. If a reduced cross-section for Br addition at lower energies were included, the calculated excitation function would disagree even more sharply with the experimental result. Based on our experimental signal levels, the substitution cross-section for rn-CT must be at least a factor of 10 lower than for o-CT at E, = 31.0 kcal mol-'.It is well known that the methyl group is an ortho-para directing substituent in electrophilic (ionic and atomic) substitution reactions. This phenomenon is usually explained in terms of the electron donating capability of the methyl group, which stabilizes the o- and p- adducts by either increasing the 0- and p- frontier electron populations in the reactant molecule or lowering the total .;rr-electron energy of the 0- and p-adducts relative to the r n - a d d ~ c t . ~ ~ Considering the large excess of translational energy at E, = 31.0 kcal mol-', however, it is difficult to understand how the decreased stability of the BC3MC complex could cause the rn-CT cross-section to be so low.A possible explanation is that the reactivities of the isomers of CT are governed by the shape of the Br-CT PES rather than by fixed barriers. The increased electron populations ortho and para to the methyl group in CT could enhance the long-range attraction between Br and these sites, but again, this effect is unlikely to be strong at high collision energies. The shape of the potential in the exit valley might be the key.'* By microscopic reversibility, the reverse reactions, C1+ 0-, p-BT -+ Br + o,p-CT, must also be accelerated. A longer range attraction between C1 and 0- and p-BT will manifest itself in a more gradually sloping potential in the reverse endoergic direction. Alterna- tively, the lower 7r-electron energies of the BC(2,4)MC complexes could cause the o- and p- surfaces to rise more gradually.In either case, translational energy will be better able to promote the endoergic reaction. Classical trajectory studies on several different potential-energy surfaces lend support to these ideas. Polanyi et al.2xb have observed that translational energy is favoured over vibrational energy in endoergic reactions with a gradual ascent to the barrier crest. Likewise Chapman" has found that the curvatures of the Be+ HF- BeF+ H and NO+ O3 + N0,+02 surfaces have marked effects on the excitation functions and product energy distributions of these reactions. In conclusion, both limited intramolecular vibrational energy redistribution and the slope of the potential-energy surface along the reaction coordinate are likely to be responsible for the interesting dynamics that we observe for these substitution reactions.We thank Ms Anne Williamson for her assistance during these experiments and Prof. Sidney Benson, Prof. Andrew Streitweiser, Dr David Golden and Dr Gil Nathanson for helpful discussions. This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the U.S. Department of Energy under contract no. DE-AC03-76SF00098. References 1 G. H. Williams, Hornolytic Aromatic substitution (Pergamon, New York, 1960). 2 M. J. Perkins, in Free Radicals, ed. J . 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