10622
J. Phys. Chem. 1992, 96, 10622-10626
consistent with a fast process which may be assigned to the relaxation to an excited-state complex (the so-called pericyclic minimum) from which the system either returns back to the initial compound or undergoes photocyclization. The higher barrier obtained in solution relative to the isolated molecule can be explained by the influence of the solvent drag which hinders the motions leading to the reactive geometrical configuration. The results obtained in the supersonic free jet demonstrate the usefulness of this technique for investigating and quantifying the dynamics of reaction in the absence of a solvent environment and provide a basis for comparison with potential energy surface calculations. It should also be stressed that besides conventional fluorescence excitation techniques, the pump and probe depletion spectroscopy (hole burning) is unique in providing information about the presence or the absence of ground-state conformers in a supersonically cooled sample. In addition with pump and probe depletion spectroscopy it is possible to observe reactive vibronic levels which escape fluorescence detection. References and Notes (1) (a) De Schryver, F. C.; Boens, N.; Put, J. Adu. Photochem. 1977, 10, 359. (b) Winnik, M. A. Acc. Chem. Res. 1977, 10, 173. (2) Desvergne, J.-P.; Bitit, N.; Castellan, A.; Webb, M.; Bouas-Laurent, H. J. Chem. Soc., Perkin Trans. 2 1988, 1885,and references cited therein. (3) Bouas-Laurent, H.; Desvergne, J.-P. 4+4 Cycloaddition. In Phorochromism, Molecules and Systems; DUrr, H., Bouas-Laurent, H., Eds.; Elsevier: Amsterdam, 1990;pp 561-622. (4)Bouas-Laurent, H.;Castellan, A,; Desvergne, J.-P. Pure Appl. Chem. 1980, 2633. ( 5 ) Cowan, D. 0.;Drisko, R. L. Elements of Organic Photochemistry; Plenum Press: New York, 1976;pp 388-480. (6) (a) Gerhartz, W.; Poshusta, R. D.; Michl, J. J . Am. Chem. SOC.1976, 98, 6427. (b) Michl, J. Photochem. Phorobiol. 1977, 25, 141. (7) (a) Bergmark, W. R.; Jones, G., 11. Nouv. J . Chim. 1977, I , 271. (b) Bergmark, W. R.; Jones, G., 11; Reinhardt, T. E.; Halpern, A. H. J . Am. Chem. SOC.1978, 100, 6665.
Dynamics of the Reaction O(’D) Translational Energy Release
+ HD, H,,
(8)Livingston, R.; Kei Sin Wei. J . Am. Chem. Soc. 1967, 89, 3098. (9) Castellan, A.; Desvergne, J.-P.; Bouas-Laurent, H. Chem. Phys. Lett. 1980, 76, 390. (10)Castellan, A.; Lacoste, J.-M.; Bouas-Laurent, H. J . Chem. Soc., Perkin Trans. 2 1979,411. (11) A high ‘4s + 4%” photocyclomerization quantum yield (0.65)was recently obtained for 1,3-di(9-anthryl)propanone, but the mechanism involves the triplet state. (a) Becker, H. D.; Amin, K. A. J. Org. Chem. 1989,54,3182. (b) Becker, H. D. In Aduances in Photochemistry; Volman, D. H., Hammond, G. S.,Gollnick, K. Eds.; Wiley: New York, 1990; Vol. 15. (12) Dale, J. Tetrahedron 1974, 30, 1683. (13) Lahmani, F.; Zehnacker-Rentien, A.; Breheret, E. J . Phys. Chem. 1990, 94, 8767.
(14) Dehmlow, E. W.;Schmidt, J. Tetrahedron Lett. 1976, 15. (15) (a) Chandross, E. A.; Schiebel, A. H. J . Am. Chem. Soc. 1973, 95, 611, 1671. (b) Ferguson, J.; Mau, A. W. H. Mol. Phys. 1974, 28, 1467. (16) (a) Jaff6, H.H.; Orchin, M. Theory and Applications of UItrauiolet Spectroscopy; Wiley: New York, 1962;pp 294-333. (b) Brotin, T.; Waluk, J.; Desvergne, J.-P.; Bouas-Laurent, H.; Michl, J. J . Photochem. Photobiol. 1992, 55, 349. (17) Warshaw, M.; Tinoco, I., Jr. J. Mol. Biol. 1966.20, 29,and references cited therein. Tinoco, I., Jr. J . Am. Chem. Soc. 1961, 83, 5047. (18)Dreeskamo, H.: Pabst. J. Chem. Phvs. Lett. 1979.61. 262. (19) Castellan, A.;Desvergne, J.-P.; Lesckux, R.; Soulignac; J.-C. Chem. Phys. Lett. 1984, 106, 117. (20) Birks, J. B. Photophysics of Aromatic Molecules; Wiley-Interscience: London. 1970. (21).Fox, M. A.; Britt, P. F. J . Phys. Chem. 1990, 94, 6351. (22) Syage, J. A.; Felker, P. M.; Zewail, A. H. J. Chem. Phys. 1984,81, 2233. (23) Wegewijs, B.; Hermant, R. M.; Verhoeven, J. W.; Kunst, A. G . M.; Rettschnick, R. P. H. Chem. Phys. Lett. 1987, 140, 587. (24) Lipert, R. J.; Colson, S.D. J . Phys. Chem. 1989, 93, 3894. (25) Wittmeyer, S.A.; Topp, M. R. Chem. Phys. Lett. 1989, 163, 261. (26) Wittmeyer, S. A.; Topp, M. R. Chem. Phys. Lett. 1990, 171, 29. (27)Hirayama, S.;Tanaka, F.; Shobatake, K. Chem. Phys. Lett. 1988, 1.73, 112. (28)Syage, J. A.; Felker, P. M.; Semmes, D. H.; AI Adel, F.; Zewail, A. H. J. Chem. Phys. 1985,82, 2896. (29) Fulton, R. L.; Gouterman, M. J . Chem. Phys. 1964, 41, 2280.
and D,:
Isotopic Branching Ratios and
Yutaka Matsumi,* Kenichi Tonokura, Masahiro Kawasaki, Institute for Electronic Science and the Graduate School of Environmental Earth Science, Hokkaido University, Sapporo 060, Japan
and Hong h e Kim Department of Chemistry, Kangweon National University, Chuncheon 200- 701, Korea (Received: June 8, 1992; In Final Form: September 9, 1992)
Doppler profiles of H and D atoms from the reaction of O(ID) with HD and a 1:l mixture of H2and D2have been measured by a multiphoton ionization technique as well as by a laser-induced fluorescence technique with a vacuum-ultraviolet laser. Isotopic channel branching ratios of @(OD+H)/@(OH+D)are measured in the reaction of O(’D) + HD at average collision energies EWII= 3.4 and 2.4 kcal/mol. In O(lD) + HD, the translational energy released to the OD + H product is almost twice that released to the OH D product. The measured branching ratios and translationalenergies suggest that the reaction proceeds via a short-lived complex formed by insertion.
+
Introduction An atom-diatom molecular reactive scattering is one of the fundamental elementary chemical reactions. Among them, the system
O(lD) + H2(’Z:) OH(211) + H(’S) AH = -43.5 kcal/mol +
(1)
has drawn much attention for many years because this system provides several particularly interesting features in the study of reaction dynamics. A unique combination of masses such as
heavy-light-light gives small reduced m a w in both the reactant and the product channels. A large exoergicity with the given mass combination results in unusual dynamics of the reaction. In addition, this system is mainly characterized by a deep potential minimum corresponding to H 2 0on its XiA surface that is directly associated with the reagents.’ Given these features, numerous experimental and theoretical studies have been performed to understand the dynamics of the reaction.2 Previous measurements on internal energy distributions of the OH products and the angular distributions largely support an insertion mechanism for this The very deep potential
0022-365419212096-10622%03.00/0 0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 10623
Reaction of O(ID) with HD, H2, and D2 well followed by a steep increase in potential characterized for this reaction leads to a long-lived H 2 0 complex formed by the insertion of O(lD) into H2,and the dynamics of the reaction would be governed by this complex formation. However, the detailed dynamics of the reaction are still somewhat ambiguous. There have been numerous theoretical calculations on several different potential energy surfaces. Almost all calculations, whether it was dynamical or statistical, well reproduced the experimental data.+’O Of particular importance among the measurements is the isotopic [H]/[D] branching ratio, which denotes the channel branching ratio @(OD+H)/@(OH+D)from the reaction of O(lD) with HD. The statistical calculation predicts the branching ratio less than unity (including angular momentum effects).’ A previous measurement using a laser-induced fluorescence (LIF) detection of H/D atoms with vacuum-ultraviolet (vacuum-UV) laser light at a low collision energy (EwII= 2.5 kcal/mol) reported the ratio of 1.13 f 0.08, close to what would be expected from simple statistical theory.’ l However, extensive theoretical studies and the recent measurements of the vibrational energy distribution of the OH product predict a very short-lived complex and a nonstatistical @(OD+H)/@(OH+D) ratio.2 In addition, the dynamical calculations on the different potential surfaces can be tested by the @(OD+H)/@(OH+D)ratio because the ratio is very sensitive to the shape of the surface. In this paper, we report the measurements of the [H]/[D] ratios from the reactions of O(’D) with HD and with a mixture of H2 and D2 at two different reagent collision energies using a resonance-enhanced (2 1) multiphoton ionization (REMPI) technique. The technique has high enough sensitivity to enable the measurement of the Doppler profiles of H and D in the REMPI spectra and the estimation of the average kinetic energies of the products. We also measured the [H]/[D] ratio from O(ID) + HD with a vacuum-UV LIF technique in a flow cell to compare the results with the REMPI study.
+
Experiment Reso~mceEnbsacedMultiphoton Ionization Measurement. The experimental setup used was almost the same as our previous studies.I2J3 O3(2 Torr)/HD (2 Torr) or O3 (2 Torr)/[Hz D2 1:1 mixture] (2 Torr) were mixed just before passing through a pulsed nozzle (General Valve, time width 0.8 ms) into a vacuum chamber. Pressures of the reaction and detection chambers and 1 X lod TOK,respectively. pumped separately were 5 X A KrF excimer laser light at 248 nm (-2 mJ/pulse, 10 Hz) dissociated O3 and produced translationally hot O(lD) atoms. When N20was used for the O(lD) atom source, the excimer laser was operated with ArF (193 nm). One hundred nanoseconds after the photolysis laser pulse, a probe UV laser (-0.2 mJ/pulse) was fired to detect H and D atoms produced from the reaction using REMPI technique. For the probe light, the output of a tunable dye laser pumped by a XeCl excimer laser was frequency doulbed with a BBO crystal and focused with a lens (f = 200 mm). The dissociation and probe laser beams were collinearly counterpropagated at right angles to the molecular beam. The spectra of H and D atoms were measured by (2 1) REMPI at 243.135 and 243.069 nm, respectively. Resulting H and D ions were detected by an electron multiplier. The log-log plot of the MPI signal intensity versus the probe laser intensity was found to have a slope of 2.0 f 0.1 for both H and D. The probe laser intensity was almost constant around the H and D resonance wavelengths. The isotopic [HI/ [D] branching ratios are calculated from the measured areas under the peaks in the spectra after the spectra were divided by the square of the probe laser power. Detection sensitivity of our REMPI system was checked by the measurements of H and D atoms from a microwave discharge of a 1:l mixture of H2 and D2, which was 1.0 f 0.1. In the experiments for measurement of the spatial distribution of the H atom velocity, the output of the photolysis laser was polarized with a pile-of-plates polarizer, and the two laser beams of the photolysis and probe were perpendicularly crossed with each other. Dogpler pTofileswere matured in the two configurations of Ed // k, and Ed I Kp,where Ed is the polarization vector of
+
+
the dissociation laser and i, is the propagation direction of the probe laser. Since the beam diameter of the photolysis laser was large enough (2 mm), within a 100-ns delay the reactions were presumed to proceed homogeneously in the probing region, and escape of the products from the veiwing zone could be ignored. Therefore, the measured concentration ratios [H]/[D] are equal to the channel branching ratios of the reaction @(OD+H)/@(OH+D) for the reaction with HD. The experiment with crossed molecular beam configuration was also performed, where O3and HD gases were introduced into the chamber through two pulsed nozzles independently, to make sure that we were observing the products from reaction 1. The crossed molecular beam experiment gave the same results with the single beam experiment. Laser-Induced Fluorescence Measurement. The [H]/[D] ratios and Doppler profiles from O(lD) + HD were also measured with a LIF method. O3and HD gas were mixed and introduced into a reaction cell. The size of the cell was 60 X 60 X 60 mm3 and pumped by a rotary pump with a liquid nitrogen trap. The pressures of O3and HD in the reaction cell were 8 and 60 mTorr, respectively. O(lD) atoms were produced by the photolysis of O3at 248 nm. The probe light for H and D atoms around 121.6 nm was generated by the four-wave mixing of a 2wl - w2 scheme in a Kr gas celIl4with two tunable dye lasers pumped by a XeCl excimer laser (308 nm, 200 mJ/pulse). The output of the vacuum-UV light going through the reaction cell was monitored with a vacuum-UV monochromator and a solar-blind photomultiplier. The laser-induced fluorescence was observed by another solar-blind photomultiplier at right angles to both the photolysis and probe laser through a LiF window and a band-pass filter (Acton Research, X = 120 nm, AA = 12 nm). The delay (20-1000 ns) between the photolysis and probe light pulses was controlled with a time jitter of about 10 ns. Estimation of the Average Collision Energies. The average center-of-mass (CM) collision energies EwIIfor the O(lD) AB reaction (AB = Hz, D2, or HD) are calculated with the following equationI5 @,Id = 2 -kT] 3 - m(AB) m(o) L ( E f A B ( 0 ) ) + (2) 2 m(AB) + m(0) m(0) m(AB) 2
+
[
where m(i) refers to a mass of the i reactant and T is room temperature. (EkAB(0))is the average translational energies in the laboratory frame (LAB) for the O(lD) atoms which are produced in the photolysis of NzO at 193 nm or O3at 248 nm. The average kinetic energy of O(lD) from N20 at 193 nm has been reported by Felder et a1.I6 The vibrational distribution of O#A) from the photodissociation of O3at 266 nm was reported by Sparks et al.” Based on their results, the fraction of the available energy that is released into translation is estimated to be 0.68. Assuming that this same fraction holds at 248 nm, the collision energies are calculated. The estimated collision energies are shown in Table I. Results [Hl/[D] Ratio Measurement by REMPI aod LIF Methods The typical REMPI spectra of the H and D atoms produced from the reactions are shown in Figure 1, when O( ‘D) is produced from the photodissociation of O3at 248 nm and the REMPI signal was measured at 100-ns delay. Figure la shows the spectrum of H and D atoms from the reaction of O(lD) with the 1:l mixture of H2 and D2, and Figure l b shows the spectra from O(lD) HD. The isotopic ratio [H]/[D] is calculated to be 1.3 f 0.2 for H2 D2 and 1.5 f 0.2 for HD from the obtained spectra and listed in Table 11. Even when the O(lD) source was changed from photolysis of O3at 248 nm to N 2 0 at 193 nm, the isotopic ratios [H]/[D] were 1.4 f 0.2 for both H2 + O2and HD, which are almost identical with the ratios (1 -3-1 - 5 ) for the O3photolysis case. By the vacuum-UV LIF technique, the H and D atoms from O(lD) + HD with the photolysis of O3 at 248 nm were also
+
+
Matsumi et al.
10624 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 TABLE I: Isotopic Branching Ratio8 for O('D) + HD or (H2+ D2) ( E,II)/kcal m o P O(lD) sourcea N 2 0 (193 nm) O3(248 nm)
H2 2.6 1.9
HD 3.4 2.4
4.1 2.8
0.5
0.5
theoryg
D2
0.5
5.0 0.58 5.8
[Hl/[DIC HD H 2 + D2d 1.4(0.2) 1.4 (0.2) 1.5 (0.2) 1.3 (0.2) 1.3 (0.1) 1.1 (0.1) 1.13 (0.08) 1.3 (0.2) 1.08 (0.06) 1.02 1.8 I .07 1.09 (0.06) 1.4 2.28 (0.32) 1.77 (0.25)
ref this work this work this work
remarks
e e
f f
11, 18
h
6 6 6 6 8 8
i
h i
a Molecules and photodissociation wavelength used for the generation of translationally hot O(lD) atoms. bAverage center-of-mass collision energy for the reaction of O(ID) with each reactant, H2, HD, or D2. CMeasured [H]/[D] product concentration ratios. The values for HI>correspond to isotopic channel ratios (P(OD+H)/+(OH+D), while those for H z + D2 correspond to reaction rate constant ratios k(O+H2)/k(O+D2). Numbers in parentheses are errors (one sigma). dReaction between O(lD) and 1:l mixture of H2 and D2. CMeasurcdusing multiphoton ionization technique. JMeasurcd using vacuum-ultraviolet laser-induced fluorescence technique. 8 Results of quasi-classical trajectory (QCT) calculations. QCT calculations on a Murrell-Carter surface. QCT calculations on Schinke-Lester surfaces.
*
'
1.5 1
VUV Wavenumber / cm-l 82280 82260 I
1
I
I
I
' 1 ' "
-.
I
-2a Y
1.0-
0.5 0D
400
800
o
3:
Time delay / ns I
I
I
~ 4 3 0. 5 243.1 2 4 3 . 15 Probe Laser Wavelength / nm Figure 1. Typical REMPI spectra of H and D atoms produced from the reaction of O(lD) with (a) 1:l mixture of H2 and D2 and (b) HD, when the O(lD) atoms are produced by the photodissociation of O3at 248 nm. Numbers in the spectra are values of full width at half-maximum in cm-I in vacuum-UV resonance wavenumber.
detected. Figure 2 shows LIF signal intensity of the H atom and [H]/[D] ratios as a function of delay between the photolysis (248 nm) and probe vacuum-UV laser pulses at the pressures of O3 (8 mTorr) and HD (60 mTorr). The LIF signal intensity of the H atoms rose with the increase of the delay time. The rise time is about 250 ns. It was found that the ratio of [H]/[D] was constant at the delay time of 100-300 ns, which was 1.3 f 0.1. This value can be considered to be the nascent [H]/[D] ratio from the reaction of O(lD) + HD, since the isotopic scrambling by reactions such as H HD H2 D are negligible in the time scale 100-300 ns. The [H]/[D] ratios from O('D) + HD measured with the MPI and LIF techniques are in agreement with each other within experimental errors. The obtained valuca of the [HI/ [D] ratio are also in agreement with the earlier measurementsll.l8within experimental errors (see Table I). Doppler Profile Measuremeat. Figure 1 shows the measured Doppler curves of H and D atoms in the MPI spectra in wavenumber scales. The ratio of the full width at half-maximum (fwhm) for the D peaks to H peaks are different between the O(lD) + H2, D2 and O(lD) + HD reaction systems; that is, fwhm(H)/fwhm(D) = 1.3 for O(lD) + H2/D2and 1.9 for O(ID) + HD. In order to discuss the energy release more quantitatively, the average kinetic energies of the H and D atoms in the laboratory frame were calculated from the second moment (u2)I o,f the ?bserved Doppler profiles for the collinear configuration (Ed I b)and then converted to the total kinetic energy released to the The second moment of the products in the CM frame (E',),13*19
-
+
+
Figure 2. Temporal profiles of isotopic concentration ratio of [H]/[D] and laser-induced fluorescence signal intensity of H atoms in the reaction of O(lD) HD. Photolysis of O3at 248 nm is used as the source of O(ID). Solid curve has a rise of 250 11s. The vertical bars for [H]/[D] are one standard deviation. Pressures of O3and HD are 8 and 60 mTorr, respectively.
+
Doppler spectra of the H (D) atom is given by the following equation for the collinear configuration ( u 2 ) , = (1/2)m(H)ZJ+[(v -m
- vo)/%I2g(4 dv
(3)
where g(v) is the normalized Doppler profile, v is the frequency of the probe laser, and vo is the rwonance center frequency. With the polarized photolysis laser, the measured Doppler profiles of the H and D a t p s wpre ideniical for the two polarization configurations of Ed // k and Ed I k,. This indicates that the velocity distribution ofthe H and D atoms are isotropic in the laboratory frame. Therefore, we assumed an isotropic velocity distribution for the H and D atoms in the LAB frame. The average translational energy released to the products in the CM frame, ( E : ) , can be calculated from the average translational energy of the H atoms in the LAB frame, EFAB(H)), from the following equation WYW) = ( ~ M - ~ ~ ) ( u z ( IH ) ) H
(E't)m(OH)/m(HzO) + (EkAB(H20))m(H)/m(H20) (4)
for the O(lD) + H2 reaction system, where (Ef.AB(H20)) is the kinetic energy for the center of mass of the reaction system in the LAB frame. (EFAB(H20))is given by (EtAB(H20))= (EtAB(O))m(O)/m(H@) + (Et.AB(H2))m(H~)/lll(H~0) (5)
The values of (E:AB(H20))m(H)/m(H20) in q 4, which correspond to the contribution of the motion of the center of mass, are less than 0.3 kcal/mol and negligibly small compared with
Reaction of O(lD) with HD, H2, and D2
The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 10625
TABLE II: Translational Energies (kcal mol-') for O('D)
D,
--
O(lD) source' reaction (193 nm) O('D) HD OD + H OOD) HD OH + D O(lD) + H2 OH + H O('D) + D2 OD + D O3(248 nm) O(lD) + HD OD + H O(lD) HD OH + D O(lD) + H 2 OH + H O('D) + D2 OD + D
+ +
N,O
+
----
46.4 47.8 46.1 48.0 45.4 46.8 45.4 46.7
+ HD, H2,and
(E;)'
V't)d
19 (4) 9 (2) 16 (3) 14 (2) 21 (4) 11 (2) 14 (2) 14 (3)
0.41 (0.09) 0.19 (0.04) 0.35 (0.07) 0.29 (0.04) 0.46 (0.09) 0.24 (0.04) 0.31 (0.04) 0.30 (0.07)
"Same as Table I. bAveraged available energy, (Ecoll)+ AH. Averaged center-of-mass translational energy released to the product, which is obtained from the second moment of the Doppler profile of H or D atoms. Numbers in parentheses are errors (one sigma). "Fraction of the translational energy to the total available energy: Cr;) = (E\)/(Eavl).
the obtained (EkAB(H))= 10-20 kcal/mol. The obtained values of (E',) are listed in Table I1 with the fraction of the total availableenergy released into translation, (ft). The fraction (f'J for O(lD) + H2 with O3photolysis at 248 nm is 0.3 1 f 0.07, which is in good agreement with the estimation (0.29) from the recent LIF measurements of ro-vibronic distribution of OH products.20 The (E',) values are almost equal between the reactions with H2 and D2 in both experiments with the O3and N 2 0photolysis. On the other hand, in the reaction of O(lD) HD, the ( E : ) values for the OD H product channel are almost a factor of 2 higher than those for the OH D channel. In addition, it should be noticed that the sum of (E',) over the OD + H and OH + D channels is almost double the value of ( E ; ) for either the O(lD) + H2 or O(ID) + D2 reaction.
+
+
+
Discussion [H]/[D] Ratio and Reaction Mechanism. We have measured the [H]/[D] branching ratio from the reaction of O(lD) with HD molecules for two different O('D) sources by using the two O(lD) sources, that is, the photolysis of N20and O3at 193 and 248 nm, and the measured respectively. The collision energies, ( EmII), [H]/[D] ratios are summarized in Table I. Table I includes the theoretical [H]/[D] ratios from trajectory calculationson different potential energy surfaces. The measured [H]/[D] ratios from both HD and the 1:l mixture of H2 and D2 mixtures with the REMPI are almost independent of the collision energies because the difference in collision energy is only about 1 kcal/mol and is smeared out by the large exoergicity of the insertion reaction. In a classical sense, when the abstraction dominates, the incoming O(ID) atom sees H with higher probability because the center of mass is closer to D and H moves with a larger volume. This results in the [H]/[D] ratio less than unity.21 On the other hand, when the insertion dominates, the O(lD) atom forms a complex with HD. Since H leaves the complex with higher probability due to its lighter mass, an [H]/[D] ratio larger than unity would be expected. Several quasiclassical trajectory calculations on different potential surfaces also predicted an [H]/[D] ratio larger than unity for the insertion.6.8*22Our measured [HI / [D] ratio generally supports the insertion mechanism. The detailed dynamics of the reaction can be understood by the internal energy and the angular distribution of the products. The deep potential well followed by a steep increase in the potential energy along the reaction coordinate favors the long-lived complex and a statistical energy distribution among the degrees of freedom of the products. However, the previously measured internal and angular distributions could not predict the lifetime of the complex unambiguously. The insertion mechanism makes the forward and backward scattered products which are unusually ascribed to the long-lived complex independent of the complex lifetimeO5The inverted rotational distribution may be explained by just the angular momentum constraints.I0 However, our measured [H]/[D] ratio clearly indicates the lifetime of the complex to be very short compared to the statistical calculation with the angular momentum constraints ([H]/[D] = 0.8).' Most of the recent trajectory calculations predict a very short lifetime of the complex, shorter than one or two bending vibrational periods of the H 2 0
complex. The short lifetime of the complex would be expected because the system has relatively small reduced mass upon which a large impulsive force is applied. Isotopic Effect on Kinetic Energy Release. As shown in Table 11, the kinetic energy released to the OD H channel is almost 2 times larger than that to the OH + D channel in the O(lD) + HD reaction. This results in the higher rotational excitation of OH than OD as observed by Wiesenfeld and c o - ~ o r k e r s . ~ Fitzcharles and Schatz6 found in their trajectory calculations that the average rotational energy ( E L t )of OH produced by O(lD) + HD is hotter than that from O(lD) + Ha, while (E;ot) of OD from O('D) + HD is colder than that from O(lD) + D2. They presented a simple kinetic model as follows. The O(lD) atom preferably approaches at right angles to the HD molecular axis, and the insertion takes place. The bending mode in the HDO complex is strongly excited. Before the vibrational energy in the bending mode is redistributed among other modes, a hard collision between the H and D atoms causes dissociation of the complex and the lighter H atom escapes the complex with higher probability. Kinematically, in the reaction of O(ID) + H2, the translational energy released to H + OH is simply given by E', = p2/2p(HOH), while the rotational energy released to OH is given by = p2/2p(H-O), where p(a-b) is a reduced mass of mamb/(ma+ mb) and p is the momentum of the impulse of the collision between the two hydrogen atoms in the complex. Because of p(H-OH) = p(H-0) and p(D-OD) p(D-O), the available energy (in excess of product vibrational energy) is equipartitioned into E', and E; in the cases of O(ID) + H2 and O(ID) D2. Therefore, E',(OH+H) is almost equal to E',(OD+D), while in the case of O(lD) + HD, p ( D 4 H ) 2p(H-O) and 2p(H-OD) p(0-D) lead to E',(OD+H) 2E',(OH+D), which is consistent with our experimental results. The [H]/[D] ratio measured for O('D) + H2, D2 (1:l mixture) with O3 photolysis at 248 nm is in good agreement with that reported by Satyapal et a1.I8 as shown in Table I. The measured [H]/[D] ratios correspond to the ratios of rate constants k(O+H2)/k(O+D2). The rate constants are approximated by k = (urel)u,where (urel) is the average relative velocity between O(lD) and H2/D2and u is the reaction cross section. The ratio of the relative velocity u,l(O+H2)/urel(O+D2)is calculated to be about 1.1 for both the O3and N20 sources. The quasiclassical trajectory (QCT) calculations6 indicated that the ratio of u(O+H2)/u(O+D2) is 1.02-1.07 at EmI1= 0.5 kcal/mol. The collision energy for O(lD) D2 is larger than that of O(lD) H2 with the same O(ID) atom source due to the mass ratio as listed in Table I. The QCT trajectory calculations6also showed that the cross section of the O(ID) + H2 reaction decreases with collision energies, as expected for exothermic reactions without entrance barriers. These factors larger than unity explain the values of 1.l-1.4 for k(O+H2)/k(O+D2)obtained experimentally. In summary, the measured [HI / [D] branching ratios are in good agreement with previously reported ones by Tsukiyama et al.ll The translational energies of the products suggest that the reaction O('D) H2 is not a simple abstraction and that insertion is involved. The dissociation may occur by hard collision between the H (D) atoms in the complex as proposed by Badenhoop et a1.9 Acknowledgment. The authors thank Prof. Richard Bersohn for fruitful discussions. This work is supported by the Grant-in-Aid from the Ministry of Education of Japan, the Korea Science and Engineering Foundation, and Japan Society for Promotion of Science (JSPS)for the joint programs with KOSEF and NSF. K.T. thanks JSPS Fellowships for Japanese Junior Scientists. Registry No. Atomic oxygen, 17778-80-2; H2,1333-74-0; D2, 778239-0; HD, 13983-20-5. References and Notes (1) Whitlock, P. A.; Muckerman, J. T.; Fisher, E. R.J . Chem. Phys. 1982,
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76, 4468. (2) Sloan, J. J. J . Phys. Chem. 1988, 92, 18. (3) Butler, J. E.; Jursich, G. M.; Watson, I. A.; Wiesenfeld, J. R.J. Chem. Phys. 1986,84, 5365.
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(4) Cleveland, C. B.; Jursich, G. M.; Trolier, M.; Wiesenfeld, J. R. J . Chem. Phys. 1987,86, 3253. ( 5 ) Buss, R. J.; Casavecchia, P.; Hirooka, T.; Sibener, S.J.; Lee, Y. T. Chem. Phys. Lett. 1981,82, 386. (6) Fitzcharles, M. S.;Schatz, G. C. J . Phys. Chem. 1986, 90, 3634. ( 7 ) Kuntz, P. J.; Niefer, B. I.; Sloan, J. J. J . Chem. Phys. 1988,88, 3629. (8) Dunne, L. J. Chem. Phys. Lett. 1989, 158, 535. (9) Badenhoop, J. K.; Koizumi, H.; Schatz, G. C. J . Chem. Phys. 1989, 91, 142. (10) Rynefors, K.; Elofson, P. A.; Holmlid, L. Chem. Phys. 1985,100, 53. (1 1) Tsukivama. K.: Katz. B.: Bersohn. R. J . Chem. Phws. 1985.83.2889. (12j T o n o h a , K.;'Matsumi; Y.; Kawasaki, M.; Kasatani, K:J. Chem. Phys. 1991, 95, 5065. (13) Matsumi, Y.; Shafer, N.; Tonokura, K.; Kawasaki, M.; Kim, H. L. J . Chem. Phys. 1991, 95, 4972. (14) Hilber, G.; Largo, A,; Wallenstein, R. J . Opt. SOC.Am. 1987, 8 4 , 1753.
(15) Marinero, E. E.; Rettner, C. T.; &re, R. N.J. Chem. Phys. 1984. 80,4142. (16) Felder, P.; Haas, B. M.; Huber, J. R. Chem. Phys. Lett. 1991,186, 177. (17) Sparks, R. K.; Carlson, L. R.; Shobatake, K.; Kowalnyk, M. L.; Lee, Y. T. J. Chem. Phys. 1980, 72, 1401. (18) Satyapal, S.;Park, J.; Bersohn, R.; Katz, B. J. Chem. Phys. 1989,91, 6873. (19) Shafer, N.; Tonokura, K.; Matsumi, Y.; Tasaki, S.;Kawasaki, M. J . Chem. Phys. 1991, 95, 6218. (20) Park, C. R.; Wicscnfeld, J. R. Chem. Phys. L r t . 1989, 163, 230. (21) Johnston, G. W.; Kornweitz, H.; Schechter, 1.; Persky, A.; Katz, B.; Bersohn, R.;Levine, R. D. J . Chem. Phys. 1991, 94, 2749. (22) Whitlock, P. A.; Muckerman, J. T.; Kroger, P. M. In Potential Energy Surfaces and Dynamic Calculationsfor Chemical Reactions and Molecular Energy Transfer; Truhlar, D. G., Ed.; Plenum: New York, 1981, p 551.
Overtone-Induced Unimoiecuiar Decomposition of Poiyatomic Molecules in Rare Gas Clusters: A Classical Trajectory Study of H202-Ar,3 Lisa M. Finney and Craig C. Martens* Department of Chemistry, University of California, Imine, Imine, California 9271 7 (Received: July 16, 1992; In Final Form: September 24, 1992)
The effects of intermolecular interactions on the dynamics of intramolecular energy transfer and unimolecular dissociation are studied by considering the overtone-induced unimolecular decomposition of a polyatomic molecule embedded in a rare gas cluster. The system studied is H202-Ar13.Classical trajectory calculations are performed on both the isolated molecule and the molecule-cluster complex. The rates and mechanisms of intramolecular energy transfer and molecular decomposition of the complex are investigated and compared with the behavior of isolated H202 Three main mechanisms leading to pronounced differences in the intramolecular dynamics and unimolecular decay rates are identified: vibrational deactivation of the excited molecule, modification of intramolecular vibrational energy redistribution (IVR)pathways by molecule-cluster interactions, and recombination of the nascent OH fragments induced by binding to the cluster and subsequent diffusion on its surface.
I. Introduction The dynamics of intramolecular energy redistribution and unimolecular dissociation of highly excited molecules are currently the subjects of great interest and research activity. Significant progress has been made in recent years in understanding the detailed dynamics of chemical processes, particularly for isolated polyatomic molecules in the gas phase.14 Here, modern experimental methods such as supersonic molecular beam technology and time- and frequency-resolved laser spectroscopy have allowed detailed measurements to be made on molecular systems in the absence of external perturbations. In the simplest cases, the small number of coupled degrees of freedom and the level of detail supplied by experiments allow a close comparison to be made with first-principles theory . Although the study of gas-phase chemical dynamics has led to important advances, much chemistry of practical significance occurs in condensed phases. Here, the chemical dynamics of polyatomic molecules can be strongly influenced by the perturbing effects of the solvent, and the outcome of a chemical reaction in solution is dictated by energy-transfer processes involving both intramolecular and intermolecular coupling. Thermal activation of the reactant species, energy redistribution within reactant molecules, crossing (and recrossing) of the transition state in the presence of solvent perturbations, and energy relaxation from excited product species into the bath are all key steps in the overall chemical process, and all involve energy transfer between the relevant molecular and solvent degrees of freedom.5 In this paper, we investigate the effects of solvent interactions on the dynamics of energy transfer and unimolecular reaction of Author to whom correspondence should be addressed.
polyatomic molecules. We consider the unimolecular dissociation dynamics of hydrogen peroxide resulting from l o c a l i i overtone excitation of an OH bond. The "solvent" is represented by an associated rare gas cluster. Finite clusters provide an intermediate case between isolated molecules and true c o n d d - p h a s e systems. The method of classical trajectory integration is employed to model the unimolecular decomposition of H202embedded in an Ar13 cluster, and, for comparison, the dynamics of the isolated molecule on the same intramolecular potential surface and with the same molecular initial conditions. Ensembles of trajectories are integrated and the unimolecular lifetimes an determined as a function of the initial OH excitation energy. Individual trajectories are also examined, in order to reveal the dynamical mechanisms at work in determining the overall rates of reaction and the role played by the cluster in modifying the behavior of the isolated hydrogen peroxide molecule. Overtone-induced proctsses in hydrogen peroxide have been the subject of extensive experimental2vWand theoretical'*ls investigation. Crim and co-workers measured the overtone spectra of hydrogen peroxide at room temperature using laser-induced fluorescence and compared the unimolecular rate implied by the overtone line width and productstate distributionswith statistical models.2-6 Butler et al. measured the overtone spectra in a molecular beam, yielding a lower limit of 3.5 p for the unimolecular lifetime of the v = 6 overtone level.' Scherer et al. used timeresolved photofragment spa%mcopy to study the avertoneinduced decomposition of hydrogen peroxide! Rizzo and *workers have applied double resonance techniques to investigate the intramolecular dynamics and unimolecular decomposition of H2OP9 A number of groups have employed the method of classical trajectory simulation and concepts from nonlinear dynamid6 to investigate the detailed mechanisms of intramolecular energy
0022-3654/92/2096-10626%03.00/0 @ 1992 American Chemical Society
