Tunnel effects on inter- and intramolecular hydrogen transfer reactions of transient dihydro- and hexahydrocarbazoles U. Kensy, M. Mosquera Gonziilez ’ and K.H. Grellmann
Max-Planck-Instttut ftir Blophyslkalrsche Chenue, Abterlung Spektroskopre, Postfach 2841, W-3400 Gettingen, Germany Received
23 July 1992
We examine inter- and intramolecular hydrogen-transfer processes in two related metastable dihydrocarbazoles in nonpolar solvents of different viscosity and compare them wrth similar transfer processes in transient hexahydrocarbazoles. N-ethyldiphenylamine (A’) and N-ethyl-2,6-dimethyldiphenylamine (A) photocyclize in their triplet states, yielding the triplet states of the zwitterionic dihydrocarbazoles ‘Z’* and 3Z*, respectively, which subsequently relax to their metastable smglet ground states ‘Z and ‘Z. In spite of their similarity, the two transients ‘Z’ and ‘Z stabilize by completely different pathways: the unsubstituted transient ‘Z’ is converted into N-ethylcarbazole (C) and an N-ethyltetrahydrocarbazole (THC) by a bimolecular disproportionation reaction. The methylsubstituted intermediate ‘Z is converted into a stable dlhydrocarbazole (D) by a sigmatropic, mtramolecular [ 1,8]-H-shaft and by an intermolecular, mutual hydrogen-exchange reaction within the encounter complex ‘(ZZ) which yields two molecules of D. The rates of the intra- and of the intermolecular transfer reactton of ‘Z are governed by tunnel effects. The rate of the intramolecular tunnel process does not depend on solvent frictton and becomes temperature independent at low temperatures. The rate of the intermolecular, reaction-controlled exchange reaction ’ (ZZ) -2 ‘D becomes also temperature independent if the solvent is fluid enough. In more viscous solvents the reaction becomes diffusion controlled and, therefore, strongly temperature dependent. The intermolecular disproportionation reaction 2 ‘Z’+C+THC IS also reaction controlled but no tunnel effects are observed.
1. Introduction In solution, the rearrangement of the zwitterionic hexahydrocarbazole 2 to the stable hexahydrocarbazole 3 constitutes a hydrogen-transfer process where tunnel effects determine the reaction rate entirely at low temperatures and to a large extent at higher temperatures. The transient 2 is photochemically formed in the triplet state from the enamine 1; the sigmatropic [ 1,4]-H-shift 2-+3 (rate constant kH) takes place in the singlet ground state [ 1,2]. An Arrhenius plot of kH between 80 and 300 K is not linear (cf. fig. 1); k” tends to become temperature independent at lower temperatures and large, strongly temperature dependent isotope effects are observed when the migrating hydrogen at carbon C, of 2 is replaced by deuterium (rate constant kD) [ 31. The isotope effects ’ Permanent address: Universtdad de Santiago de Compostela, Departamento de Quimica Fisica, Santiago de Compostela, Spain. ’ To whom correspondence should be addressed. 0301-0104/93/$06.00
0 1993 Elsevier Science Publishers
range from r(300
K) =8 to r(90
In la the methyl group of 1 at the cyclohexene ring is replaced by a hydrogen atom. Like from the enamine 1, the zwitterion 2a is formed on photoexcitation of la and rearranges subsequently to (the final photoproduct ) 3a (rate constant k: ). If the hydrogen atom at the carbon atom C, of 2a is replaced by deuterium, isotope effects are observed which have the same magnitude and which show the same temperature dependence as r(T). If, however, the hydrogen at Cb is replaced by deuterium the reaction
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(1. Kensy et al. /Chemical
Physics I70 (1993) 381-392
Fig. I. Comparison of tunnel rate constants. Upper part, solid lines: Keto-enol eqmhbration in the metastable triplet state of 2(2’-hydroxyphenyl )benzoxazole, HBO (hydrogen transfer) and DBO (deuterium transfer). Lower part, solid lines: Enamine 1, [ 1,4]-H-shift and [ 1,4]-D-shift 2-3, curves l(H) and 1 (D), respectively. Dashed lines: Enamine la, [ 1,4]-H-shift and [ 1,4]D-shift 2a-3a. curves la(H) and la(D), respectively. Dotted lines: N-ethyl-2.6-dtmethyldrphenylamine A, [ 1,8]-H-shift and [ 1,8]-D-shift ‘Z+‘D, curves An and Ao, respectively.
rates are not affected. This observation allows the conclusion, that in la only the hydrogen (or deuterium) at C, migrates by a [ 1,4]-H-shift and that 3a is not formed in detectable yield by an initial [ 1,2 ]-shift of the hydrogen at C,,, followed by a second [ 1,2]shift of the hydrogen at C, to the carbon atom C,,, otherwise an isotope effect would have been observed, especially at low temperatures [ 4 1. Besides this interesting mechanistic observation, the comparison of the reactivity of 2 with 2a revealed (cf. fig. 1) that the [ 1,4 J-shift 2a-+3a is at all temperatures about 30 times slower than the corresponding shift 2+3. Hence, replacement of the (nonreactive) hydrogen at Cb by a methyl group obviously affects the tunnel rates. Presumably, steric effects are responsible for this difference in rates, because a methyl-, ethyl- or isopropyl-group placed in meta position to Cb of 2 has no effect on the kinetics of the hydrogen transfer [ 5 1.
In analogy to la, the fully aromatic, 2,6-methylsubstituted diphenylamine A is converted into the zwitterionic dihydrocarbazole Z by photocyclization in the triplet state [ 61. The transient Z rearranges in its singlet ground state, ‘Z, to the stable dihydrocarbazole D by a [ 1,8 ]-H-shift, as a product analysis has shown [ 71. A [ 1,4]-shift, analogous to 2a+3a, does not take place with measurable yield. Again, the rate of the reaction ‘Z-t’D is determined by tunnel effects [ 3 1. In contrast to the transient hexahydrocarbazoles 2 and 2a, the zwitterionic dihydrocarbazole ‘Z decays in addition to the rearrangement ‘Z+‘D by the thermally activated back reaction ‘Z-+‘A, and by a second-order reaction,
the latter yielding the same photoproduct D as the first-order rearrangement ‘Z-+ ‘D. The unsubstituted N-ethyl-diphenylamine A undergoes the same photocyclization reaction as A, yielding the zwitterionic intermediate ‘Z’. The decay of ‘Z’, however, differs from the decay of ‘Z, except at higher temperatures where both ‘Z and ‘Z’ mainly revert by ring opening to ‘A and ‘A’, respectively. At lower temperatures ‘Z’ does not, in contrast to ‘Z, form a stable dihydrocarbazole. Instead, the bimolecular disproportionation reaction (2) takes place, yielding N-ethyl-carbazole (C) and a tetrahydrocarbazole ( THC ) [ 6 1, 2
Initially, the latter has presumably the structure shown here, but it isomerizes further to more stable tetrahydrocarbazoles. (It is known from the literature that tetrahydrocarbazoles are very labile compounds [ 81.)
U. Kensy et al. /Chemical Physrcs 170 (I 993) 381-392
the mixture methylcyclopentane/cyclopentane/isobutane (2 : 1: 1 by volume: MCB) [ 9 ] is described in detail in ref. [ lo]. The N-ethyl-diphenylamine derivatives An, A,,, A;, and A;, were prepared from the appropriate Nacetylanilines and bromobenzene according to Goldberg [ 111. The acetylderivatives were reduced with lithium-aluminium hydride, yielding the corresponding N-ethyl-diphenylamines. The compounds were purified chromatographically on silica columns with cyclohexane/diethylether ( 1: 1 by volume) as eluant. All sample solutions were carefully dried over a liquid Na/K alloy and degassed on a greaseless vacuum line as described recently [ 12 1.
Thus, the three amines 1, A and A’ undergo the same adiabatic photocyclization reaction in the triplet manifold, yielding quite similar zwitterionic intermediates. Yet, their subsequent rearrangement reactions differ substantially. Since some of the rearrangement rates are determined by temperature dependent hydrogen tunnel effects, a detailed study of such effects appeared to be of interest because we believe that for a quantum mechanical description of such effects and, especially, their temperature dependence, more experimental data are still needed. The second-order hydrogen transfer reactions ( 1) and (2) are of particular interest because they offer the possibility to investigate under which conditions tunnel effects become important in bimolecular reactions, To our knowledge, only tunnel effects on pseudomonomolecular reactions have been reported in the literature so far.
2. Experimental 2.1. Compounds and solvents The solvents 3-methylpentane (3MP), cyclopentane, isopentane ( = 2-methylbutane) and methylcyclopentane (all Fluka, purum) were purified chromatographically on a silica-aluminum oxide column immediately before use. Isobutane (Linde, 99.95%), diethylether and tert-butylmethylether (Merck, UVASOL) were used as received. The preparation of
2.2. Transient kinetics Solutions of A and A’ ( - lop4 M) were either excited with an exciplex laser [ lo] or, for long-term experiments, with a high-pressure 450 W xenon lamp as described in ref. [ 4 1. To improve the kinetic analysis the transmission/time data pairs were digitalized and stored on a disc for further handling [ 91.
3. Results 3.1. N-ethyl-2,6-dimethyldiphenylamine
3.1.1. The formation of the transient Z The photocyclization
reaction A-Z (rate constant in the triplet manifold, followed by triplet-singlet intersystem crossing (rate constant k,,,) from the triplet state 3Z* to the singlet ground state of the transient dihydrocarbazole, ‘Z, which rearranges to the final product D [ 6 ] :
k,) takes place adiabatically
The intersystem crossing from the first excited singlet state of the amine, ‘A*, to the amine triplet state, 3A*, takes place within a few nanoseconds, i.e., instantaneously compared to the cyclization (k,) and the intersystem crossing reaction (k,,,). On the time scales of k, and k,,,, on the other hand, the rearrangement ‘Z+ ‘D is very slow. Thus, the kinetics of the formation of ‘Z can be analysed on the basis of a simplified scheme, consisting of two consecutive steps:
U. Kensy et al. /Chemrcal Physm I70 (1993) 381-392
In fig. 2 two typical transient absorption decay traces are depicted which one observes after flash excitation of a 1 x 10e4 M solution of A in 3MP with the KrF line (248 nm) of an exciplex laser. At the monitoring wavelength A,=430 nm (fig. 2a) the two short-lived transients 3A* and 3Z* absorb as well as the long-lived intermediate ‘Z ; at A,=630 nm only 3A* and ‘Z absorb. Decay traces like those shown in fig. 2 were recorded at different temperatures and kinetically analysed on the basis of eq. (4), as described recently [ 13 1. In addition to the fit of eq. (4) to the data, the calculated contribution of 3A*, ‘Z* and ‘Z (fig. 2a) or of 3A* and ‘Z (fig. 2b) to the total absorbance is also shown. In fig. 3 Arrhenius plots of the obtained rate constants k,(T) and k,,,(T) are depicted. Within experimental error, the triplet-singlet intersystem crossing reaction 3Z*-+1Z is temperature independent, with k,,,= (2.8 f 0.1) x lo6 s-i. The adiabatic cyclization
time I ps -
Fig. 2. Transient absorptions observed after excitation of a 1 x 1O-4 M solution of An in 3MP at 150 K with the 248 nm KrF line of an exciplex laser. In addition to the observed (wavy) decay traces the fit of eq. (4) to these traces and the calculated individual contribution of the transients are shown. Panel a: monitoring wavelength I.,,,=430 nm. Fit parameters: &(‘A*) =0.114, &,(‘2*)=0.485, E,(‘Z)=O.O30, !+=9.16x 10’ s-‘, L= 3.28x 106s-I. (For the detinitton ofthe &values see ref. [ 131.) Panel b: monitonng wavelength I.,=630 nm. Fit parameters: E,,(‘A*)=0.255, ErJ3Z*)=0, E,,(‘Z)=l.OO, k,=6.93x105 s-‘, k,,=3.26x 106s-‘.
Fig. 3. Arrhenms plot of the rate constants k,, (0, W and V ) and k, (0, 0 and A ) obtained from traces like those shown in fig. 2. Open symbols: solutions of An, tilled symbols: solutions of An. Solvents: ( A and V ) diethylether/tert-butylmethylether; (0, 0, n and 0 ) 3MP.
step 3A*-+3Z* is temperature dependent: kr( s-l ) =(6~1)x10’0exp(-~~/RT); AE,=15.1?0.3 kJ/mol. Because of this temperature dependence, the two rate constants k,,, and k, become equal at about 179 K. Above that temperature k,> k,,, and the triplet-singlet intersystem crossing 3Z*+ ‘Z is rate determining for the formation of ‘Z. Below 179 K the relation k,< k,,, holds, and, as a consequence, the accumulating 3Z* concentration becomes increasingly smaller at lower temperatures and the rate constant k,,, cannot be determined accurately below % 150 K. Both rate constants are insensitive to isotopic substitution, i.e., An and A,, are indistinguishable kinetically as far as the formation of the dihydrocarbazole Z is concerned. Furthermore, the rate constants k,(T) and k,,(T) have the same values in 3MP, in the mixture diethylether/tert-butylmethylether 3 : 7 by vol. (cf. fig. 3 ) and in ethanol (not shown in fig. 3), i.e. the reaction rates do not depend on solvent polarity. Due to the activation energy of the photochemical step 3A*-+3Z* (A&= 15.1 kJ/mol) the quantum yield of ‘Z formation decreases strongly below x 100 K because the radiationless deactivation of the amine triplet state, 3A*-+ ‘A, has a much lower activation
U. Kensy et al. /Chemtcal
energy and starts to compete effectively with product formation. In the glassy state of the three solvents one observes 3A* phosphorescence emission and the quantum yield of ‘Z formation drops to virtually zero. 3.1.2. The decay of the transient ‘Z The decay of the transient ‘Z occurs on much longer time scales than its formation. It has been monitored at its absorption maximum A,,,=634 nm. The halflife of ‘Z depends strongly on the temperature and ranges from milliseconds around room temperature to several minutes ( iZH) or several days (‘Zp) below 100 K. Between 293 and 240 K the decay rate constants ky and ky of the isotopomers ‘ZH and ‘Zr, are equal at a given temperature and the decay is monoexponential. In fig. 4a a typical decay trace is shown for this temperature region. The Arrhenius plot of the corresponding rate constants is linear (cf. fig. 5 ). From the high-temperature values (straight line infig. 5) resultsk,(s-‘)=(5+1)xlO’*exp(-AE,/ RT); AE, = 57? 4 kJ/mol. Below z 220 K the half-lifes of ‘Zn increase much more strongly than those of ‘Zu and the decay of both transients is no longer monoexponential. A typical ‘ZH decay trace is shown in fig. 4b. Obviously, a firstorder decay cannot be fitted to such traces. Therefore, to describe the low-temperature, nonexponential decay pattern we assume (at the moment only formally) the mixed first- and second-order decay law -d[‘Z]/dt=k,[‘Z]+k,[‘Z]*.
With E= E[ ‘Z]d, integration
&k, ew( -b t) E=k,+E,k;[l-exp(-k,t)]’
time/sFig. 4. Transient absorptions observed after excitation of a 1 x 10m4 M solutton of Au m CI, monitored at A=630 nm. Panel a: excitatton with an exctplex laser, T= 278 K. To the decay trace a monoexponenttal decay is fitted with the parameters Ee~4.21 x lo-* and k, =402.9 s-‘. The lower part of panel a shows the residues of this fit. Panel b: excitation with filtered hght from a high-pressure xenon lamp (Schott filter UG 11) at T= 106 K (see text). Ftrst-order fit with &,=0.203 and k,=4.91 X 10e3 s-l. The corresponding residues (lower part ofpanel b) have the larger values of the two traces. Mixed first- and second-order fit withE,=0.215, k,=4.66x10-3s-‘andk~=1.08~102s-‘.
of eq. (5) gives
where t is the extinction coefficient of ‘Z at the monitoring wavelength, d the optical path length, E0 the absorbance at t = 0 and k; = k,led. Eq. (6) was fitted to the decay trace in fig. 4b with the parameters E,=O.215, k,=4.66x lop3 s-’ and k;= 1.08x lo-* s-l. The residues of this fit show (cf. fig. 4b) that the kinetic description of the results with eq. (6) is satisfying. The tit is much worse if a purely firstorder decay is assumed. To estimate the contribution of the second-order reaction to the total decay we define as “second-order yield” the ratio @,=k;E/(k;E+k,)
Physics 170 (I 993) 381-392
From the trace in fig. 4b one obtains @ i = 0.33 at t = 0 (&=0.215) and, still, @*=0.20 when E(t)=$E,. Thus, a substantial part of ‘Z decays by a second-order process. We measured the decay of ‘ZH in the low-temperature region down to 68 K and the decay of ‘Zp down to 83 K in the three nonpolar solvents 3-methylpentane (3MP), cyclopentane/isopentane, 1: 4 by volume (CI ), and methylcyclopentane/cyclopentane/ isobutane2:2:1,byvolumeat -18°C (MCB).The rate constants k, ( T) and k;( T) obtained from fits of eq. (6) to E(t) traces like that in fig. 4b are shown as Arrhenius plot in figs. 5 and 6, respectively. In contrast to the high-temperature region, the Arrhenius
lJ. Kensy et al. /Chemical Physics 170 (I 993) 381-392
3.2. N-ethyl-diphenylamine (A’) 3.2.1. Nonoxidativephotocyclizatlon The kinetics of the photocyclization reaction 3A‘*+3Z’*+‘Z’ and of the thermally activated backreaction ‘Z’+‘A’ has been studied with the light isomer An some years ago [ 6 1. At that time the disproportionation reaction (2) was studied mainly by steady-state experiments and product analysis. Only a few low-temperature kinetic experiments were carried out. They were difficult to analyse because of the long transient lifetimes which required a detection system with good long-term stability. In view of the hydrogen and deuterium transfer reactions summarized above it was, of course, of interest to investigate whether the rates of reaction (2) are sensitive to isotopic substitution. Therefore, we compared the photophysical properties of A;, and A’, with an improved detection system [ 4,9]. Between 320 and =200 K the decay of the transient ‘Z’ is of mixed first and second order and it has been analysed by fitting eq. (6) to ‘Z-decay traces monitored at 630 nm. The first-order contribution (rate constant k’, ) is in this temperature range entirely due to the ring opening of the zwitterion, back to the starting material. ‘Z’-+ ‘A’. It is therefore not surprising that this reaction does not show an isotope effect. From the Arrhenius plot of k’, in fig. 7 results k;(s-‘)=(5?2)x10’2exp(-AE;/RT); A,!?;= 60 & 4 kJ/mol. For comparison with the methyl-substituted amine A, the k’, data are also shown in fig. 5. The activation energy A.& is slightly higher than the corresponding value AE’=57*4 kJ/mol of A, whereas the frequency factors are about equal. As a result of this small difference in activation energies the back-reaction ‘Z’L’A’ is much slower than the back-reaction ‘Z+ ‘A already at relatively high temperatures (cf. fig. 5 ). Therefore. the Arrhenius-type first-order contribution to the decay of ‘Z’ becomes immeasurably small at temperatures below T~200 K. As a consequence, the second-order disproportionation reaction (2) dominates the decay of ‘Z’below 200 K. (In contrast to the methyl-substituted amine, the unsubstituted zwitterion ‘Z’ does not rearrange with measurable yield by a [ 1,8]-shift, whose rate is governed by tunnel effects.) Accordingly, ‘Z’ decay traces monitored below 200 K were analysed assuming a purely second-order decay:
-2 -3 1
Fig. 7. Summary of rate constants obtained wth 10e4 M solutions of the unsubstltuted diphenylamines Ah (open symbols) and AD (tilled symbols). k,,: air-equilibrated solutions m 3MP (m, 0). k’,: degassed solutions m 3MP (V, A). k&‘:degassed solutions m 3MP (0, 0 ). The li,(diff )MP curve is taken from fig. 6.
with E’=E’[ ‘Z’]d and k; = k&t’d, where 6’ is the extinction coefficient of ‘Z’ at the monitoring wavelength. The rate constants k; are also shown as Arrhenius plot in fig. 7. In contrast to the second-order decay of the methyl-substituted zwitterion ‘Z, the second-order decay rate constants of ‘Z’ are not sensitive to isotopic substitution, i.e. the amines An and A;, give within experimental error the same kinetic results. Included in fig. 7 are (from fig. 6) the rate constants k, (diff ) 3MPexpected for a diffusion-controlled reaction in 3MP. Similar to ‘Z, the secondorder decay of ‘Z’ is obviously not diffusion controlled. 3.2.2. Oxydativephotocyclizatlon In the presence of oxygen the zwitterion ‘Z’ is oxidized yielding N-ethylcarbazole, C, and H202 [ 15,161. In an air-equilibrated solution of A’ in 3MP this reaction has been studied with Au and AD between 290 and 235 K. The temperature range is rather narrow for kinetic reasons [ 15,16 ] : below 235 K the
U. Kensy et al. / Chemcal Physrcs I70 (I 993) 381-392
yield of ‘Z’ formation becomes very small due to increasingly efficient amine triplet state quenching by oxygen whose activation energy is much lower than that of the competing adiabatic photocyclization ‘AI*+‘Z’*, which yields 3Z’*, the precursor of ‘Z. The resulting first-order rate constants koX of the pseudo-monomolecular reaction ‘Z’+02-*C+Hz02
are shown in fig. 7, too. In the temperature range investigated, oxidation is faster than ring opening (k,, >> k’,) and in typical experiments with absorbancies EL >0.2 the relation k,, z+ k;E’( t) also holds. In contrast to the oxydation of 4a,4b-dihydrophenanthrene to phenanthrene [ 171, there is obviously no isotope effect on the kinetics of reaction (10).
4. Discussion 4. I. N-ethyl-2,6-dimethylphenylamme
The formal fit of eq. (6) to the decay traces of the zwitterion ‘Z (cf. fig. 4b) needs, of course, justification. To traces like that shown in fig. 4b a multiexponential decay law could certainly also be fitted without difficulty. The assumption of a mixed firstand second-order decay law is based on the photoproduct analysis [ 7 1. For this analysis _ 1O-’ M solutions of the methylsubstituted amines AH and A’, were irradiated with a mercury resonance lamp (254 nm) at 173 K. As main result we observed that only one final product, 9-ethyl- 1,4a-dimethyl-4,4a-dihydrocarbazole, D, was produced under such conditions, provided, only a small fraction of the starting material was converted. Otherwise, the product itself is photolysed under ring opening, yielding butadienylindoles [ 7 1. The Woodward-Hoffman rules predict that the photocyclization 3A*+3Z* takes place conrotatorily, i.e., L and R at the bridge of the five-membered ring of ‘Z will be in trans position. Furthermore, one expects that the [ 1,8 ]-H-shift ‘Z+ ‘D is suprafacial. In agreement with these predictions the NMR spectra of D and the product analysis of subsequent photoreactions of D show that the methyl group at the bridge of ‘D and the shifted hydrogen are in trans po-
sition [ 71. Thus, the decay of ‘Z is a well defined, stereospecitic reaction. At 173 K this decay is determined by tunnel effects as the deviation from Arrhenius-type behaviour and the large isotope effects (figs. 5 and 6) show. The concentration of the transient ‘Z was in the steadystate experiments for product analysis such that the decay of ‘Z was certainly nonexponential, according to the results of the kinetic experiments. Since only one, stereospecifically formed photoproduct is observed, we make the basic assumption that the possibility of a multiexponential decay law can be discarded and that the assumption of a mixed first- and second-order decay is justified. This then implies that the first-order as well as the second-order process yield the same photoproduct, namely D. Except for the ring-opening reaction ‘Z-t ‘A above = 200 K, the first-order contribution to the decay of ‘Z is due to the sigmatropic [ 1,8]-H-shift ‘Z-+‘D. Below = 150 K its rate is entirely determined by tunnel effects. as the Arrhenius plot in fig. 5 shows. Unfortunately, only with the light amine An precise data of the rate constants could be determined, because the reaction ‘Zb+ ‘Db becomes, compared to the second-order reaction, very slow. Due to this difficulty the rate constants kf’ below = 150 K reported in an earlier publication [ 31 are too large. The few newer, more accurate kf’ data (cf. fig. 5 ) we could obtain, show however, that the Arrhenius plots of the [ 1,8]-shift of ‘Z (curves An and Ar, in fig. 1) are quite similar to the Arrhenius plots of the [ 1,4]-shift of the transient 2 generated from the enamine 1 (curves 1 (H) and 1 (D) ), as the comparison of the data in fig. 1 shows. It is interesting to note that the accurately known rates of the ‘Z, + ‘Dn shift are absolutely insensitive to solvent friction. Lately, we made the same observation on a completely different system [ 10,12,18 ] : the hydrogen tunnel processes which occur during the keto-enol tautomerization of 2-( 2’-hydroxyphenyl)benzoxazole (HBO) in the excited triplet state are also insensitive to solvent friction. This tautomerization takes place on an entirely different time scale, namely in the microsecond range for the hydrogen (HBO) and in the millisecond range for the deuterium transfer reaction (DBO). For comparison, we include these data in fig. 1. If one compares, for instance, the curves HBO and An, the dynamic range
V. Kensy et al. / Chemcal Physm I70 (1993) 381-392
comprises 9 orders of magnitude. Yet, the plots are astonishingly similar as far as the isotope effects and the smooth increase of the tunnel rates with increasing temperature are concerned. Obviously, low-frequency, but solvent-friction insensitive modes in the range of 100 cm-’ must be responsible for the thermally activated tunnel rates [ lo] in both systems. Under the conditions of the steady state as well as the kinetic experiments there is a substantial fraction of transient molecules which decay by the second-order process. Since, in our opinion, the basic assumption is well justified that this process also contributes to the formation of ‘D, we propose that in the encounter complex ’ (ZZ) a mutual exchange of hydrogen (or deuterium ) atoms takes place:
that above z 100 K the second-order ‘Z decay rate constants k; are far from being diffusion controlled. We therefore assume (cf. scheme 1) that two ‘Z molecules approach each other with the diffusion rate constant lid, forming an encounter complex ’ (ZZ) which either separates again (k-d) or reacts further by mutual hydrogen exchange (k,,), yielding ‘D: ‘Z+‘Z&‘(ZZ)A2’D. k-d With this mechanism becomes k, =k,,k,l(k-d
the rate constant
k2 in eq. (5)
i.e. the rates are reaction controlled. When the solvent viscosity increases at lower temperatures, the opposite relation, k_d << k,,, may hold and the reaction may become diffusion controlled: k2zkd.
The isotope effects on the second-order rates corroborate this assumption because they show that hydrogen atoms have to be involved in the transient decay. Unfortunately, for technical reasons, we could not monitor the second-order decay of the deuterated transient ‘Zr, below z 100 K, because at lower temperatures the transient lifetime is very long (several days) and the stability of the solvent becomes a severe problem. (In 3MP, where one experiment was carried out at 83 K (cf. fig. S), the solvent viscosity was very high and the second-order process completely suppressed. ) In contrast to the first-order reaction, the rates of the second-order contribution to the transient decay strongly depend on the viscosity, I], of the solvent. The temperature dependence of the viscosities of 3MP, qMP, and of CI, qcI, have been determined accurately down to 100 K by Nickel and co-workers [ 141. Transferred into the modified diffusion rate constants k,(diff ) they are included in fig. 6. It is clear
If the dissociation of the encounter complex is faster than the hydrogen exchange (k_,, s k,,), k2 becomes kz = k,,k,lk-d
Luckily, the temperature dependences of qMp and of qc’ are such that both reaction regimes, ( 12a) and (12b), can be observed. In 3MP, a moderate extrapolation of the experimental viscosity data ( k2 (diff ) values in fig. 6) to temperatures below 98 K fits quite well to the last three k; values in fig. 6 (triangles) around 90 K. We conclude that in the solvent 3MP the hydrogen-exchange reaction becomes diffusion controlled below ~93 K. In the much less viscous solvent CI (at 100 K, qMp= 2 100 qcI) the rate constants k; (CI ) become temperature independent between 100 and 80 K and drop precipitously only below 76 K. Considering the results in 3MP, we conclude, that in the solvent CI the onset of the diffusion controlled regime occurs below 80 K. The viscosity data of CI, although only known down to 100 K, support this conclusion and the, somewhat daring, extrapolation of the kz(diff )c’ values in fig. 6 from 100 to 75 K appears to be acceptable. It is corroborated by the k; data obtained in the solvent mixture MCB, for which viscosity data are not available but which is at all temperatures more fluid than CI. Obviously, the onset of diffusion control is in this
U Kensy et al. /Chemrcal Physm 170 (1993) 381-392
solvent at lower temperatures than in CL A most obvious experiment would be to shift the onset of diffusion control to higher temperatures by using a solvent with higher viscosity. One would expect that in such a solvent the isotope effect on k$ should vanish because it is very unlikely that the diffusion process is sensitive to isotopic substitution. Our experiments in this direction met so far with failure because we could not find a high-viscosity solvent which is at low temperatures stable over the required long time periods. Methylcyclohexane with a few percent isopentane added, for instance, is known to form a good glass, but after a few hours it starts to become opaque and eventually crystallizes, making reliable experiments impossible. The most important aspect of the Arrhenius plots in fig. 6 is the observation that in CI and in MCB the exchange rates become temperature independent between 100 and 75 K. Because of this temperature independence we propose that at least in this region the hydrogen exchange reaction rates (eq. ( 11) ) are determined by tunnel effects. (Presumably, the increase of the rate constants k? above = 110 K is also caused by, thermally activated, tunneling. This would imply that the pre-equilibrium kd/k_-d (cf. eq. 12a) is temperature independent and that low-frequency modes in the encounter complex ’ (ZZ) are thermally activated.) The exchange reaction in scheme 1 is the first example for tunnel effects on an inlennolecular hydrogen transfer process which is purely bimolecular. In a few other systems (for a recent review see ref. [ 191) intermolecular hydrogen transfer reactions of the type CHS + RH-tCH4 + R have been studied, where RH usually is the solvent, making the reaction pseudo-monomolecular. In the viscosity-“wmdow” of the solvents CI and MCB between 100 and 75 K (cf. fig. 6) where the exchange rates are reaction controlled (eq. ( 12a) ) and temperature independent, the exchange rate constant k,, is obviously determined by tunnel effects. It would be quite interesting to know its absolute value, but it can only be roughly estimated because the preequilibrium constant Kd= kd/k_* (cf. eq. ( 12a) ) is not known. To estimate Kd, we assume for the rate constants k,, and k_,: k,=4rcN~x2Dza and
Hence, Kd =kd/k_d
NL = N i x lo3 is the Loschmidt number, a (in cm) the center-to-center distance in the encounter complex ’ (ZZ) and Dz is the diffusion coefficient of ‘Z. To calculate the encounter distance a with eq. ( 13) one needs to know kd and Dz. We evaluate kd and Dz from data in fig. 6 and pick the temperature T= 9 1 K. At this temperature, the solvent 3MP is still fluid and well behaved [ 201 (its glass-transition point lies at = 88 K) but viscous enough to make the exchange reaction diffusion controlled. In the solvent CI, on the other hand, the exchange is reaction controlled (eq. ( 12a) ) and, in addition, temperature independent. To estimate the diffusion coefficient of ‘Z at 9 1 K in 3MP, Dp’ (9 1 K), we assume that the experimentally determined [ 21 ] diffusion coefficient of anthracene, DA, in hexane, Hx, is equal to Dz in 3MP at equal solvent viscosities, qHx and ~,,r, respectively and that the relative temperature and viscosity dependences of the diffusion coefficients can be expressed by
VMP(TZ)T, QP.(T, 1 Tz
At T, = 273 K, the diffusion coefficient of anthracene in hexane is D,(273 K) =2.2x lop5 cm2 s-’ [ 211 and the viscosity of hexane is ~~~(273 K) = 0.38 10 cP. At T2 = 9 1 K, the viscosity of 3MP is qMP (9 1 K) = 1.Ox 1OSCP (taken from the extrapolated k, (diff ) 3MPcurve in fig. 6). With eq. (16) results for the diffusion coefficient of ‘Z in 3MP at 9 1 K the value Dz(91 K)=2.8~ lo-l4 cm2 s-l. With k2(91 K)= 1.0~ lo-’ s-’ in 3MP (cf. fig. 6), cd =2x lo4 M-’ and eq. (12b) we obtain for kd=20 M--’ s-’ and, with eq. (13) for the encounter distance a=0.47 nm. Although azO.5 nm is a reasonable value for an encounter distance, we realize that the extrapolation of the D,(273 K) value to 91 K for obtaining the Dz( 9 1 K) value may contain a large error because it implies that eq. ( 16) is valid for an increase of the solvent viscosity by almost 9 orders of magnitude. If one takes as estimate a=0.5 AI0.25 nm, the limits for
U. Kensy et al /Chemrcal Physics 170 (1993) 381-392
the pre-equilibrium constant Kd (cf. eq. ( 15) ) are 0.04 < k,/M-’ < 1.1. In the more fluid solvent CI the reaction-controlled rate constant k$ (CI) has between 100 and 80 K the constant, i.e. temperature independent,valuek;(CI)=1.6x10-2s-’ (cf.lig. 6) and it is safe to assume that in CI the encounter distance is the same as in 3MP. Then, with cd =2x104M-‘andeq. (12a)weget&k,.=3.2xlO’ M-’ s-’ and, with the above estimation of Kd, the tunnel rate constant k,, ( 80- 100 K) has a value within thelimits3x102s-‘
Which process is rate determining question.
Acknowledgement This investigation was supported by the Deutsche Forschungsgemeinschaft (SFB 93, “Photochemie mit Lasern”, Teilprojekt D2). MMG thanks the Consejo Superior de Investigaciones Cientificas, the MaxPlanck-Gesellschaft and the Deutsche Forschungsgememschaft for scholarships. We thank Professor A. Weller and Professor J. Troe for helpful discussions and Mrs. A. Heinrich for technical assistance.
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