J. Phys. Chem. 1987, 91, 5840-5842
5840
the polarization with a polarization of a material in which the methoxy group has been replaced by a methyl group. From these unpublished result, it appears that the methyl-substituted material has a larger polarization. However, an accurate comparison is not possible because of the complex nature of the species that may be involved. Yet it is interesting to note that the crossover in the sign of the polarization occurs when the chiral center is at the second atom in the terminal chain. This may be related to gauche conformations allowing a bending in the terminal chain causing an interaction between the carbonyl group and the chiral center in a form of hexagonal "transition state". This interaction is less likely to occur when the chiral center is not at the second position. In fact in all of the other pure materials that we have examined
that exhibit this crossover phenomenon, the chiral center is at the second position in the terminal aliphatic chain. In conclusion it is shown that the temperature at which the polarization changes sign is dependent on the concentration of the chiral material in the nonchiral host. Although this phenomenon has hitherto been unobserved in the limited number of mixed systems that have been studied in detail, it is expected that this behavior should proliferate in other mixed systems. In view of this it should be emphasized that the magnitude of the polarization of the doped material, determined from mixture studies, should be viewed with caution, because the presence of the behavior described in this letter can lead to false extrapolated values of the spontaneous polarization of the chiral dopant.
Deuterlum Isotope Effect on the Branching Ratlo in O(3P)
+ Ethylene Reaction
Seiicbiro Koda, * Department of Reaction Chemistry, Faculty of Engineering, The University of Tokyo, Hongo, Bunkyo- ku, Tokyo 11 3, Japan
Yasuki Endo, Eizi Hirota, Institute for Molecular Science, Okazaki 444, Japan
and Soji Tsuchiya Department of Pure and Applied Sciences, College of Arts and Sciences, The University of Tokyo, Komaba, Meguro- ku, Tokyo 153, Japan (Received: July 10, 1987: In Final Form: August 21, 1987) The branching ratio of the two channels of 0(3P)+ ethylene reaction, one yielding vinoxy + atomic hydrogen (a) and the other methyl formyl (b), was determined for C2H4and C1D4by means of a microwave kinetic spectroscopicmethod. The ratio of (b)/(a) was found to be 6 f 1.5 in the C2D4reaction compared with 1.2 f 0.2 in the C2H4 reaction. This fact could be interpreted by a reaction mechanism in which the unimolecular dissociation on the triplet surface (channel a) competes with the intersystem crossing to a singlet surface followed by 1,2-hydrogen migration and C-C cleavage (channel b).
+
Introduction Kinetic study of the reaction of ethylene with the ground-state oxygen atom (O(3P)) is of fundamental importance, since it is one of the basic oxidative or combustion reactions. The reaction proceeds via two main channels: one yielding vinoxy + hydrogen (a) and the other, methyl formyl (b). The branching ratio is, however, not yet conclusively determined, and the branching mechanism still remains unclear. Our previous study' showed that the branching ratio is 1.2 at a pressure of 30 mTorr, indicating that it is almost independent of pressure over the very wide range from 30 mTorr to 1 atm. This conclusion apparently contradicts the finding of Buss et a1.2 that the exclusive channel was (a) under molecular beam conditions at a collision energy of 5-10 kcal mol-'. In order to solve this discrepancy, we have determined the branching ratio in the C2D4 reaction for the first time. The result is discussed on the basis of a mechanism in which hydrogen atom elimination from an intermediate triplet biradical is competing with intersystem crossing to a singlet biradical which yields methyl formyl via an intramolecular 1,2-hydrogen migration.
+
+
Experimental Section The experimental apparatus and the procedure of data treatment were already described in detail in the previous publication.' Briefly, the reaction was initiated by a pulsed mercuryphotosensitized production of O('P) in a mixture of ethylene and nitrous oxide containing mercury vapor. The duration of individual (1) Endo, Y.; Tsuchiya, S.; Yamada, C.; Hirota, E.; Koda, S. J . Chem. Phys. 1986,85,4446. (2) Buss, R. J.; Baseman, R. J.; He, G.; Lee, Y. T. J . Photochem. 1981, 17, 389.
TABLE I: Transition and Absorption Coefficients of Vinoxy and Formyl width/ species v/MHz transition cc/D a/N MHza 1.60 CH2CHO 342311.5 170,17-160,1~2.843 1.83 X lo-'' CD$DOb 350654.9 200,20-190,~~ 2.25 2.843 1.26 X 10'' CHO 346708.5 40.4-30.3, FIC 1.363 6.76 X lo-'* 1.35 CDOb 1.35 359154.1 51,4-4,,4, Fl 1.363 5.14 X
Full width at half-maximum. bAnalysis of microwave transitions will be published shortly. c F = 5-4. TABLE 11: Observed and Estimated Branchine Ratios obsd calcdb 1.2 f 0.2a (1.2)d C2H4 6 f 1.5" 4.4 C2D4 ~~
C2H4e
0'
0.35
(b)/(a) calcdC (1.2)d
4.4 0.16
"The main source of the uncertainties is the estimation of the absorption coefficients.' bCalculation on the surface of Dupuis et al.438 'Calculation on the surface of Melius et aL6 dArbitrarily taken as 1.2 as the reference value. e A reaction with an additional available energy of 5.9 kcal mol-{. fThe molecular beam result by Buss et a1.* light pulses was 4 ms. Time evolution of the two channels was monitored by the microwave absorption of vinoxy and formyl, respectively. The transitions and effective absorption coefficients which are estimated by use of relevant permanent dipole moments are tabulated in Table I. The sample of C2D,was purchased from Canada Merck Ltd. (stated purity, 99.4 atom %) and used without further purification. The other sample gases are described in the previous publication.'
0022-3654/87/2091-5840$01.50/0 0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 23, 1987 5841
Letters
vinoxy * H(orD)
I
I
react ion coordinate
Figure 3. Schematic potential surface for the O('P) time I ms
Figure 1. Examples of the time evolutions of vinoxy and formyl. The radicals are generated from a mixture of NzO (20 mTorr) and ethylene (10 mTorr). The oxygen atom production rate was not determined quantitatively in the present experiments, but around 3 X lOI4 atoms cm-3 s-' according to previous comparable experiments.'
D 0
I
I
I
1 2 ~ i n o x y l / e t h y l e n e l/ lo-'
3
Figure 2. Abundance ratio plotted against [vinoxy]/ [ethylene]: ( 0 ) O('P) CzD4; (0) O(3P)+ C2H4. (The dashed line is transferred from Figure 6 of the previous pub1ication.l)
+
Results and Discussion Figure 1 shows the time evolutions of vinoxy and formyl radicals in the reactions of C2H4 and C2D4. The light pulse of 4-ms duration starts at time = 0. In order to determine the branching ratio, the ratio of the concentrations of formyl to vinoxy is plotted against the relative concentration of vinoxy in Figure 2. The plot is extrapolated to zero concentration for vinoxy to exclude contributions of secondary reactions. The branching ratio, (b)/(a), is determined as the intercept value of the above linear relationship. The validity of the above procedure was discussed in detail in the previous publication.' The determined ratios are tabulated in Table 11. The ratio for the C2D4 reaction is 6 f 1.5, which is quite different from that for the reaction of C2H4, 1.2 f 0.2. Thus, the relative contribution of channel b is greatly enhanced by the deuterium substitution. On the other hand, the sum of the reaction rates for the two channels is not different between the C2H4 and C2D4 reactions within the experimental uncertainty (f20%), which implies that the rate constant itself is not affected by the deuterium substitution. This latter finding is in accord with the experimental result by Nicovich and Ravishankara3 that the overall rate constant for the ethylene consumption in the C2H4reaction is almost the same as the one for C2D4over a wide temperature range. According to recent experimental studies," the primary process is addition of the oxygen atom to the C = C double bond to form (3) Nicovich, J. M.; Ravishankara, A. R. Symp. (In?.)Combust. [Proc.], 19th 1982, 23. (4) Hunziker, H. E.; Kneppe, H.; Wendt, H. R. J . Phorochem. 1981,17, 377. The potential surface by M. Dupuis is cited. (5) Smalley, J. F.; Nesbitt, F. L.; Klemm, R. B. J . Phys. Chem. 1986, 90,
+ ethylene reaction.
a biradical, .CH2CH20.. This addition process is expected not to be strongly affected by the deuterium substitution. Therefore, the observation of almost no isotope effect for the total rate constant indicates that the addition process is the rate-determining step for the overall reaction, in accordance with the predictions of recent quantum chemical ~ a l c u l a t i o n s . The ~ ~ ~branching ratio should be determined in subsequent reaction processes. The following three molecular beam experiments are informative regarding the fate of the primarily produced biradical. Buss et al.2 found that the exclusive channel under single-collision conditions was (a) when the collision energy was 5.9 or 9.7 kcal mol-'. Kleinermanns and Luntzg found a cold vibrational distribution in optical modes of the vinoxy radical by use of a laser-induced fluorescence technique and suggested that no long-lived biradical is the precursor in the formation of the vinoxy radical. According to Clemo et al.,1° the angular distribution of the product vinoxy is almost isotropic but slightly favors the forward hemisphere when the collision energy is 6 kcal mol-'. Thus, the reaction intermediate, .CH2CH20., must possess a lifetime comparable to its rotational period. Clemo et al. also found that substantial energies are partitioned into translation, which, together with the abovementioned finding of Kleinermanns and Luntz, suggests that a small potential barrier exists in the exit channel. The relevant potential energy surface is illustrated in Figure 3 according to the quantum chemical calculations,',* which is also in accord with the above-mentioned experimental findings. There are four triplet surfaces close to each other in energy, and some of them correlate with the ground-state vinoxy hydrogen atom with a low potential barrier (TS2). The production of methyl formyl is considered to be possible only on a singlet biradical surface, which is not shown in Figure 3, and on which the prerequisite 1,2-hydrogen migration could proceed readily. The question is, therefore, whether a rapid intersystem crossing from the triplet surfaces to such a singlet surface is possible or not. An idea of Hunziker et aL4 is that the intersystem crossing is only possible as a collision-induced process. However, this mechanism cannot explain the pressure independence of the branching ratio over a wide range. Thus, we propose a rapid collision-free intersystem crossing to interpret the relevant experimental information. It is assumed that the branching ratio is determined by the unimolecular dissociation rate of the triplet intermediate yielding vinoxy + hydrogen atom compared with the rate of the intersystem crossing to the singlet surface. Though Kleinermanns and Luntzg found a colder vibrational distribution compared with their statistical calculation in optical modes of the vinoxy radical, the difference between the observed and statistical distributions may be partly ascribed to the existence of the exit barrier which was not taken into account in their statistical calculation. Moreover, even if a nonstatistical parti-
+
+
491. ( 6 ) Mahmud, K.; Marshall, P.; Fontijn, A. J . Phys. Chem. 1987, 91, 1568.
(7) Yamaguchi, K.; Yabushita, S.; Fueno, T.; Kato, S.; Morokuma, K. Chem. Phys. Lett. 1980, 70, 27. (8) Dupuis, M.; Wendoloski, J. J.; Takada, T.; Lester, Jr., W. A. J . Chem. Phys. 1982, 76, 481. (9) Kleinermanns, K.; Luntz, A. C . J . Phys. Chem. 1981, 85, 1966. (10) Clemo, A. R.; Duncan, G. L.; Grice, R. J . Chem. Soc., Faraday
The potential surface by C. F. Melius is cited.
Trans. 2 1982, 78, 1231.
5842 The Journal of Physical Chemistry, Vol. 91, No. 23, 1987
tioning is realized, it does not necessarily invalidate the usage of statistical method for calculating the dissociation rate of the reaction intermediate which possesses a lifetime comparable to its rotational period. Thus, we assume that the unimolecular rate constant can be calculated by the RRK formula for simplicity
k = ~ ( -l EO/E)'-' where E is the available energy and Eo the threshold energy. The available energy E may be obtained as the sum of the potential energy difference and the zero-point energy difference between the inlet transition state (TS1) and the biradical state. The potential energy difference is 15 kcal mol-' according to the calculation by Dupuis et a1.4g8 or 24 kcal mol-' according to Melius et aL6 In the following discussion, values corresponding to the latter literature will be shown in parentheses. The zero-point energy difference is assumed to be the Same for the CzH4and C2D4 reaction, because the reverse reaction to ethylene O(3P)should have no primary isotope effect. The value is assumed to be zero for simplicity. On the other hand, the threshold energy Eo is the sum of the height of the potential barrier for TS2 measured from the biradical state and the zero-point energy difference between TS2 and the biradical state. The potential barrier height is around 6 kcal mol-' (1 5 kcal mol-'). Because the C-H (or C-D) bond is broken during the passage through the transition state TS2, the zero-point energy difference is different for the C2H4and C2D4 reactions. The difference for the two reactions is assumed to be the half of the difference between the ordinary C-H and C-D bond stretching frequencies, which is about 1.5 kcal mol-'. Thus, the energy Eo for the C2H4and C2D4reactions is taken as 6.0 (15.0) and 7.5 kcal mol-' (16.5 kcal mol-'), respectively. The number of effective oscillators, s, is taken to be half the number of internal degrees of freedom, that is 8, according to the previous discussion." The values of s and the frequency factor Y are assumed to be independent of the deuterium substitution for simplicity. By use of eq 1, the ratio of the rate constants for the hydrogen atom elimination channel is calculated to be k(H, thermal):k(D, thermal):k(H, thermal + 5.9 kcal mol-' collision energy) = 1:0.28:3.4 (1:0.28:7.3). Here the collision energy in the molecular beam experiment is simply added to the thermal energy to define the total available energy. In order to estimate the corresponding branching ratios, the individual intersystem crossing rates, or at least the relative changes in the intersystem crossing rates caused by the change in the available energy and by the deuterium substitution, are required. They are, however, not available now, particularly because neither the energy of the crossing point nor the dominant vibrational modes which influence the crossing are known. Thus, we simply assume
+
(1 1) Robinson, R. J.; Holbrook, K. A. Unimolecular Reactions; Wiley:
New York, 1972; Chapter 3.
Letters as one possible mechanism that the intersystem crossing rate is independent of the deuterium substitution as well as of the available energy. Then the branching ratio for the C2D, reaction is calculated to be 1.2/0.28 = 4.4 (4.4). A comparison between observed and predicted results is shown in Table 11. The branching ratio for the reaction at the collision energy of 5.9 kcal mol-' is estimated to be 1.2/3.4 = 0.35 (0.16). Thus, it is predicted that the exclusive channel under molecular beam condihons is (a), in agreement with the observation by Buss et ale2The experimental finding of Smalley et al.5 that the contribution of channel a slightly increases with the increase in reaction temperature is also consistent with the above prediction. It is important to note that the present prediction for the very large deuterium isotope effect in the branching ratio is not altered even when the potential energy is changed to a certain extent. The requirement is that the exit potential barrier (TS2) is slightly lower than that of the inlet potential barrier (TS1). Assumptions that s and Y are independent of the deuterium substitution are also not indispensable to the above conclusion. In fact, s may become slightly larger and v slightly smaller by the deuterium substitution. Such changes, however, result in a decrease of the dissociation rate on the triplet surface, which is more favorable in explaining the observed larger branching ratio for the C2D4 reaction. The tunneling effect in the dissociation process, if it contributes, also favors the larger branching ratio for the C2D4 reaction. However, in order to predict the very small branching ratio when the available energy is large, the higher potential barrier for TS2 is more favorable. In this sence, the Melius surface is in better agreement with the molecular beam experiments.2 The relatively short lifetime of the intermediate shown by Clemo et al.IOrequires a very large intersystem crossing rate, such as 1O'O to 10'' s-'. In ordinary simple carbonyl compounds such as acetaldehyde, the intersystem crossing rate from the first excited singlet state is on the order of lo9 s-'.I2 Considering the relatively small energy difference among the relevant potential surfaces and also the orthogonality of the p-type biradical orbitals, an intersystem crossing rate more than 10 times larger than that of ordinary carbonyl compounds may be possible. In conclusion, the enhancement of the branching ratio of (b)/(a) by the deuterium substitution could be interpreted by assuming a unimolecular dissociation on the triplet biradical surface and a competitive triplet-singlet crossing. At the same time, the finding that the exclusive channel was (a) under molecular beam conditions could be made compatible with the pressure-independent branching ratio. R e t r y NO. 0, 17778-80-2; D2, 7782-39-0; .CH2CH,O., 67353-85-9; CHz=CHO*, 691 2-06-7; CDZ=CDO*, 83364-09-4; C H O , 2597-44-6; C D O , 24286-05-3; ethylene, 74-85-1; nitrous oxide, 10024-97-2.
(12) Lee,E. K. C.; Lewis, R. S. In Advances in Photochemistry; Pitts, Jr., J. N., Hammond, G. S., Gollnick, K., Eds.;Wiley: New York, 1980; Vol. 12, Chapter 1.
