J. Phys. Chem. 1983,87,5234-5236
5234
Tunneling in Thermal Unimolecular Reactions: Formaldehyde-d, Wendel Forst Deparment of Chemistry and Centre de Recherches sur /es Atomes et les Mo/6cu/es,Lava/ Un/vers/v, Quebec, Canada G1K 7P4 (Received: June 2, 1983)
The previously developed model fof the decomposition of formaldehyde into molecular and radical channels is used to calculate, for the isotope D2C0, specific-energy rate constants k ( E ) and the coupled-channelthermal unimolecular rate constants kuniand associated activation energy E,. It is found that the k ( E ) show a fairly large isotope effect that declines as the energy increases. However the thermal kmi and E,, calculated at 2000 K, show a small isotope effect because of the contribution mostly from high-energy k(E) where the isotope effect, already not large, is further reduced as a result of channel coupling.
Introduction The thermal decomposition of (ordinary) formaldehyde has been the subject of a recent publication' in which it was shown that both thermal and photochemical data on formaldehyde decomposition are mutually compatible if tunneling is invoked for the molecular channel H 2 C 0 H2 CO (1) and a very loose transition state for the radical channel H2CO H HCO (2) If we assume that the above interpretation is correct, it is now of some interest what the consequences are for the decomposition of the analogous fully deuterated compound D2C0. Specifically, we shall assume that the same parameters apply to the HzCO and DzCO decomposition, except those that depend on the masses of the atoms; in other words, we shall investigate the isotope effect. Given that the D2C0 model is derived from the H2C0 model, it shares with it all the assumptions, defects, and virtues discussed a t some length in ref 1. Since few experimental data are available for D2C0,the calculations reported below represent, for the most part, predictions to be confirmed or invalidated by experiment at some later date.
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Molecular Parameters The vibrational frequencies of D,CO and its transition states are shown in Table I. The molecular channel transition-state frequencies were taken from Miller? based on the calculations of Goddard and S~haefer.~ The radical channel transition-state frequencies are those of the same extreme loose model used in ref 1,reduced by a factor of 1.35 for the stretches (2200 1630 cm-l) and by a factor of 1.25 for the bend (1000 800 cm-l). These are reductions actually observed in D2C0 with respect to H2C0 for the same type of vibrations, and the assumption here is that the same reductions would apply in the transition state. (If only light and heavy hydrogens were involved, the reduction factor would be 2'i2 = 1.4.) The rotational constant B of the two free rotors is obtained by taking the average of the two smallest rotational constants in D&O, which is the same procedure used in the case of H2C0. The value of the critical energy for decomposition of HzCO into the molecular channel required to fit experimental data was found to be' 81 kcal/mol, which corresponds to a bare barrier height V, = 86 kcal/mol since the zero-point energies of reactant (E,) and the transition state
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(1) W. Forst, J . Phys. Chem., in press. (2) W. H. Miller, J. Am. Chem. SOC., 101, 6810 (1979). (3) J. D. Gcddai-d and H. F. Schaefer, J. Chem. Phys., 70,5117 (1979).
TABLE I: Vibrational Freauencies' of D-CO in cm'' transition states moleculeb 2056 1700 1106 2160 990 938
radical channeld
molecular channelC 2186 1503 820 7 24 505
1630 (2) 800
e
B = 0.98 cm-'
a Degeneracies in brackets if different from 1. Reference 10. Reference 2. This work. = Plus two onedimensional rotors.
(E,*) are, in the case of H2C0,E, = 16.8 kcal/mol and E,* = 11.8 kcal/mol (Figure 1). For D&O, it follows from Table I that E, = 12.8 kcal/mol and E,* = 8.2 kcal/mol, so that, for the same bare barrier height, the critical energy for decomposition of D2C0 into the molecular channel D2CO D2 + CO (1') is E, = V , + E,* -E, = 81.4 kcal/mol. In a similar manner, one calculates from the H2C0 data' that the bare barrier height for the radical channel decomposition is V , = 95.1 kcal/mol, which coresponds to a critical energy Eo = 88.1 kcal/mol for the process DzCO D DCO (2') It will be assumed that there is no reverse activation energy for this process, in accordance with a similar assumption made in the case of H2C0. As before,' the D2C0 molecular channel barrier E, will be taken to be the symmetrical one-dimensional Eckart barrier
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where x is the distance along the reaction coordinate, p is the reduced mass of the tunneling particles, and D = 101.1 is a parameter which determines the tunneling probability (eq 20 in ref 1). D is obtained from the calculated2 imaginary frequency hv* (= 19OOi cm-' in the case of D2CO) of the transition-state oscillator undergoing diss~ciation.~ Compared with H2C0, the molecular channel barrier (E,) in D2C0 is almost of the same height but the parameter D is larger, causing the tunneling probability to be smaller; the radical channel barrier in D2C0 is about 2 kcal/mol higher than in H2C0. (4) The relation is D = P.lrE,,/Ihv*I;since hv* was calculated in ref 2 and 3 for a bare barrier of 92 kcal/mol, one has to use here, for consistency, Eo = 87.4 kcal/mol.
0 1983 American Chemical Society 0022-~654/83/2087-5234$01.50/0
The Journal of Physical Chemistry, Vol. 87, No. 25, 1983 5235
Tunneling in Thermal Unimolecular Reaction
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molecule
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,'
transition stote
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Flgure 1. Relation of bare barrier height V o to critical energy Eo. E , is the zero-point energy. 100
90
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'
120
110
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130
100
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140
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120
130
140
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Flgure 3. Calculated energy dependence of branching ratio k(E)(radical channel)lk(E)(molecular channel) in H,CO and D,CO. Same energy zero as in Figure 2.
1
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b
160
'
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'
130 '
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Flgure 2. Calculated energy dependence of isotope effect on microcanonical rate constants k ( E ) in formaldehyde decomposition: (a) molecular channel; (b) radical channel. Insert: molecular channel with magnified vertical scale. The appropriate rate constant in H,CO decomposition is designated as k H ( E ) in , D,CO decomposition as k D ( € ) . The zero of energy is ground state H,CO and D,CO for k H ( € )and kd(€), respectively.
Results Once the various parameters characterizing the DzCO system have been determined, the calculations then proceed exactly as described in sections 3 and 5 of ref 1, so the details may be dispensed with and only the results will be presented. Figure 2 shows the calculated isotope effect on the specific-energy (microcanonical) rate constants k ( E ) for the molecular and radical channels. The molecular channel k(E) (Figure 2a) is assumed to proceed by tunneling below threshold and shows the expected large rise in the ratio kH(E)/kD(E) as the energy drops below threshold due to the smaller tunneling probability of the heavier isotope, but a t higher energies the ratio becomes almost constant a t slightly below unity. The radical channel k ( E ) ,which is obtained by standard RRKM calculations, is an example of the primary isotope e f f e ~ twhere ,~ again the rate constant for the lighter isotope is expected to be larger, as confimed by Figure 2b. The combined result of these effects is that the ratio k(E)(radical channel)/k(E)(molecular channel) is smaller in DzCO than in HzCO (Figure 3). The results of coupled-channel calculations of the thermal rate constants a t 2000 K are given in Table 11. Since the radical channel k(E)in HzCO is always larger than in DzCO (Figure 2b), we find a t the high-pressure limit kmH > kmD;for the molecular channel, by contrast, kD(E)> k H ( E )a t higher energies (insert in Figure 2), so that as a result k m D > kmH. In the falloff region, the rate constants for both isotopes in a given channel are very similar (compare the second-order rate constants k in (5) W. Forst, "Theory of Unimolecular Reactions", Academic Press, New York, 1973, p 350.
,
1
j/
loglo mo1/cm3 Figure 4. Calculated falloff of thermal unimolecular rate constant k,,, (upper panel) and activation energy E , (lower panel) at 2000 K for coupled-channel formaldehyde decomposition: curve 1, radical channel: curve 2, molecular channel; full line, D,CO; dotted line H,CO. Assumed collision efficiency X = 0.1.
TABLE 11: Comparison of Calculated Thermal Rate Constants a t 2000 K in Argona H,CO
km k
k, k
D,CO
Molecular Channel 1 . 2 2 x 1014 x 1.90 x 1014 x exp(-83.7/RT) = exp(-84.3/RT) = 8.7 X l o 4 1 . 1 6 x 105 7.81 x 1015 x 1 . 1 6 X 10l6 X exp(-71.2/RT) = exp(-71.2/RT) = 1 . 2 9 X lo* 1 . 9 0 x 10s Radical Channel 3.39 x 10l6 x exp(- 8 8 . 3 / R T ) = 7.57 x l o 6 3.41 X 10l6 X exp(-81.4/TT) = 4.33 x 107
2 . 3 5 X 10l6 X exp(-89.G/RT) = 3.85 X l o 6 3.97 x 10'6 x exp(-81.7/RT) = 4.72 x 1 0 7
a Activation energies are in kcal/mol, k , is in s-l, and k in c m 3 / ( m o ls ) , calculated a t mol/cm3 assuming collision efficiency h = 0.1.
Table 11) to the point where the usual double logarithmic falloff curves of both isotopes are indistinguishable except near the high-pressure limit (Figure 4,upper panel). As
5236
J. Phys. Chem. 1983,87,5236-5240
usual, activation energy (E,) falloff is a more sensitive reflection of the energy dependence of the corresponding k(E), and even here the difference between the two isotopes is small (Figure 4,lower panel). The reason is that, whereas a t the high-pressure limit the two channels do not interact, they do in the falloff region, where isotopic substitution tends to increase the rate in one channel and decrease it simultaneously in the other (at high energies, from which comes the bulk of the contribution to the thermal rate constant at high temperature), with the result that the isotope effect becomes very small.
Discussion The calculated critical energy Eo = 88.1 kcal/mol for the radical channel is in agreement with the observation of Clark et a1.6 that radical formation in the UV photolysis of DzCO begins between 87.6 and 89.4 kcal/mol above ground state. From infrared multiphoton dissociation (IR MPD) data, Berman' deduced that the molecular channel critical energy Eo in D2C0 should be 3.6 f 2 kcal/mol below the radical channel E3, i.e., between 82.5 and 86.5 kcal/mol, which at its low end is only slightly higher than the Eo = 81.4 kcal/mol used here. This is not a significant difference given the approximate nature of the model used in the calculations. There are no actual rate data available for D2C0. Berman7 found a 10% radical yield in IR MPD, but this cannot be easily translated into rate constants without an assumption as to the energy distribution'following photon absorption and the colision-induced dissociation and deactivation probabilities. Above the radical threshold, (6) J. H. Clark, C. B. Moore, and N. S. Nogar, J. Chem. Phys., 68,1264 (1978).
(7) M. R. Berman, Ph.D. Thesis, University of California, Berkeley,
1981.
Clark et a1.6 have observed a constant 2:3 ratio of radical to molecular (@Jam) quantum yields, which would seem to indicate k(E),,d 2 / 3 k(E)molecde.However, Lee et a1.8 have shown that quantum yields are not reliable indicators of rates, probably because of collisional effects, because they determined under collisionless conditions k.(E)rad k 10k(E)mo~ecu~e in H2C0, although @.,/am 2 in this case if one takes the mean of several (not always concordant) determinations. The best that can be said is that the quantum yield ratio @r/@m appears to be smaller in D,CO, suggesting a smaller k(E)rad/k(E)molecule relative to H,CO, which is also the result of the present calculations (Figure 3). There are no thermal data on D2C0 decomposition, beyond the brief observation of Gay et al.9 that isotopic mixing occurs in H2CO-D2C0 mixtures between 1500 and 2000 K. The present calculations show that a t high temperatures the isotope effect in formaldehyde is so small as to be most probably lost in experimental error, making shock tube determinations unprofitable in this respect. The problem in thermal systems is that, on the basis of the present model, the isotope effect becomes appreciable only a t temperatures so low that the decomposition is probably too slow to be measured.
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Acknowledgment. This work has received financial support from the National Sciences and Engineering Council of Canada. Registry No. Formaldehyde, 50-00-0;deuterium, 7782-39-0. (8) P. Ho, D. J. Bamford, R. J. Buss, Y. T. Lee, and C. B. Moore, J . Chem. Phvs.. 76. 3630 (1982). (9) I. D : Giay,'G. P. Glass,'G. B. Kistiakowsky, and H. Niki, J . Chem. Phys., 43, 4017 (1965). (10) T. Shimanouchi, Natl. Stand. Ref. Data Ser., Natl. Bur. Stand., no. 39 (1972).
Effect of Interfacial Electric Charge on Photoionization Yields in Micellar Systems D. Grand,' S. Hautecloque, A. Bernas, and A. Petit E.R.A. 718, Universit6 Paris-Sud, B8t. 350, 91405 Orsay, France (Received: July 22, 1982; I n Final Form: October 19, 1982)
The effect of the electric charge at the lipid-water interface on the ionization threshold energy and photoionization efficiency curves (& vs. A,,) has been examined. Perylene (Pe) was used as an easily photoionizable solute and the following systems have been investigated and compared: Pe in neutral micelles (Brij 35); Pe in anionic micelles (sodium lauryl sulfate (NaLS))in the presence of various salts or alcohols. The one-photon ionization of Pe has been evidenced by hydrated-electron scavenging by NO3-. The main conclusion of the present study is twofold: (1)The interfacial electric potential does not appreciably affect the magnitude of the ionization threshold of Pe. (2) For a given surfactant, increasing the interfacial negative charge allows a higher solubilizate ionization yield to be reached. The steeper slope obtained, reminiscent of gas-phase photoionization cross-section curves, may reasonably be correlated with an increased probability for the photoejected electron to escape from geminate recombination.
Introduction Various authors have compared the photophysical and photochemical behavior of systems in which the chromophore is either sequestered in micellar assemblies or dispersed in homogeneous liquid solutions. In the particular case of photoelectron transfer it was repeatedly ob~ervedl-~ that incorporation of solute mole(1)S. C. Wallace, and M. Gratzel, and J. K. Thomas, Chem. Phys. Lett., 23, 359 (1973).
cules into anionic micelles drastically increases the solvated-electron yield, the neutralization back-reaction being presumably inhibited by the electrostatic barrier a t the lipid-water interface. (2) M. Gratzel and J. K. Thomas, J . Phys. Chem., 78, 2248 (1974). (3) S.A. Alkaitis, G. Beck, and M. Gratzel, J. Am. Chem. SOC., 97, 5723 (1975). (4) S. A. Alkaitis, and M. Gratzel, and A. Henglein, Ber. Bunsenges, Phys. Chem., 79, 54 (1975). (5) S.A. Alkaitis and M. Gratzel, J. Am. Chem. SOC.,98,3549 (1970).
0022-3654/83/2087-5236$01.50/00 I983 American Chemical Society
