Chemical Dynamics of H Abstraction by OH Radicals - American

J. Phys. Chem. 1996, 100, 4853-4866

4853

Chemical Dynamics of H Abstraction by OH Radicals: Vibrational Excitation of H2O, HOD, and D2O Produced in Reactions of OH and OD with HBr and DBr N. I. Butkovskaya† and D. W. Setser* Department of Chemistry, Kansas State UniVersity, Manhattan, Kansas 66506 ReceiVed: September 25, 1995; In Final Form: December 18, 1995X

Infrared chemiluminescence from vibrationally excited H2O, HOD, and D2O molecules in the ranges 32003900 cm-1 (O-H stretch) and 2400-2900 cm-1 (O-D stretch) was observed from the reactions of OH and OD radicals with hydrogen and deuterium bromide in a fast flow reactor with 0.5-2 Torr of Ar carrier gas at 300 K. Hydroxyl radicals were produced via the H + NO2 reaction; the H atoms were generated by microwave discharge in a H2/Ar mixture. Vibrational distributions for H2O, HOD, and D2O were determined by computer simulation of the experimental emission spectra. The H2O emission from OH + HBr reaction shows inverted populations for both the collisionally coupled stretching modes and the bending mode. Inversion in the bending distribution with a maximum for V2 ) 1 is more apparent in the V1,3 ) 1 level, which is populated up to the thermochemical limit of V2 ) 5. The HOD emission from OD + HBr shows an inverted population in the O-H stretching mode with a maximum for V3 ) 2 and shows a decreasing population in the collisionally mixed O-D stretching/bending ν1,2 levels with half the molecules in the V1 ) 0 group. The distribution in ν1,2 for HOD from the OH + DBr reaction also appeared to be decreasing for V1 > 0 levels, but collisional redistribution to V3 ) 1 seems evident from the pressure dependence of the vibrational distributions. These distributions are discussed with the aid of the information theoretic analysis and compared to F atom abstraction reactions from HBr and DBr and to quantum-scattering calculations on an OH + HBr surface. The overall vibrational energy disposal is 〈fV〉 ≈ 0.6, which resembles the analogous three-body cases. However, the partitioning of the energy between stretching and bending modes raises new questions about reaction dynamics.

1. Introduction State-resolved kinetic measurements during the last two decades have provided a great advance in our understanding of the microscopic dynamical behavior for the atom plus molecule interactions as reactants undergo conversion to products.1-4 Infrared chemiluminescence was an especially powerful tool for the study of H + L-H mass combinations, since emission from HF, HCl, and OH products could be studied in great depth.4-7 Laser-induced fluorescence has also been a tool for O atom reactions giving OH.8a State-resolved measurements of bimolecular reactions producing triatomic products “represent a natural eVolution from the diatomic molecule era”.9 A central point for reactions giving diatomic products was the distribution of product vibrational states, and the energy disposal was related to the concept of a reaction coordinate and properties of the potential energy surface. Similar possibilities exist for gaining an understanding of reactions giving triatomic products, although it is complicated by the additional possibilities of energy disposal to the larger number of degrees of freedom. The distribution among the three normal modes of triatomic molecules should be especially interesting. The existing theoretical state-to-state studies have mainly concentrated on the simplest OH(OD) + diatomic reactions involving hydrogen transfer, for example, OH + H2(D2)9,10 and OH + HCl or HBr.11,12a Recently, a quantum-scattering calculation has been performed on the OH + CH4 reaction.12b Some experimental data do exist for abstraction of H by CN radicals,13 and an analogy to the dynamics of F and Cl atom reactions4-7 seemed helpful. In our laboratory we have already made the diatomic-totriatomic step in a study of the product vibrational distribution † Permanent address: Institute of Chemical Physics, Russian Academy of Sciences, 117334 Moscow, Russian Federation. X Abstract published in AdVance ACS Abstracts, March 1, 1996.

0022-3654/96/20100-4853$12.00/0

from the unimolecular decomposition of organic molecules, such as ethanol eliminating H2O, which was compared to the elimination of HF from fluoroethane.14 The contrast between the vibrational distributions of HF formed by unimolecular elimination reactions and bimolecular abstraction reactions is well established4 and has been used to identify the two types of reactions.15 In this connection, the vibrational distribution of H2O molecules produced by direct abstraction reactions vs elimination reactions will be of interest too. In this paper we present an analysis of the vibrational distributions of H2O, HOD, and D2O molecules produced in the abstraction reactions below:

OH + HBr f H2O + Br

(1)

OD + HBr f HOD + Br

(2)

OH + DBr f HOD + Br

(3)

OD + DBr f D2O + Br

(4)

The rate constant for (1) is 1.1 × 10-11 cm3 molecule-1 s-1 at 300 K,16 and the reaction has no formal potential energy barrier. The energy available to the products may be obtained from the enthalpy changes for reactions 1-4 using equation 5.

〈Eav〉 ) -∆H°0 + Ea + (7/2)RT

(5)

The thermodynamical data for reaction 1 are as follows: Ea ) 0.0 kcal mol-1 16 and -∆H°0 ) 31.5 kcal mol-1. The reaction enthalpy, -∆H°0, was calculated from the bond energies17 © 1996 American Chemical Society

4854 J. Phys. Chem., Vol. 100, No. 12, 1996 D0(HO-H) ) 118.1 kcal mol-1 and D0(H-Br) ) 86.6 kcal mol-1. Hence, the available energy in reaction 1 is equal to 〈Eav〉 ) 33.6 kcal mol-1. Consideration of the zero-point energies, which are 13.2, 11.5, and 9.7 kcal mol-1 for H2O, HOD, and D2O, 5.3 and 3.0 kcal mol-1 for OH and OD, and 3.8 and 2.7 kcal mol-1 for HBr and DBr, respectively, gives 〈Eav〉 ) 33.0, 34.2, and 33.7 kcal mol-1 for (2)-(4). This enables excitation of up to three O-H stretching vibrational quanta in H2O or HOD and up to four O-D quanta in HOD or D2O. In addition to serving as a prototype for an abstraction reaction giving a triatomic molecular product, reaction 1 is of importance for the generation of Br atoms in the atmosphere.18 Reactions 1-4 were carried out in a fast flow reactor at room temperature between 0.5 and 2 Torr of Ar carrier gas. The infrared chemiluminescence was recorded with a Fourier transform spectrometer. The vibrational distributions were determined from fitting the emission spectra of isotopic water molecules by computer simulation. The V ) 0 populations were estimated with the help of surprisal analysis; inverted distributions were obtained in the stretching modes for all reactions. Up to now, the only observation of vibrational excitation of H2O from abstraction reactions was made by time-resolved, infrared diode laser absorption/gain spectroscopy in the reaction of OH with cyclooctane.19 Population inversions were observed for the 010, 020, and 100 levels of H2O. We selected the OH + HX type of reaction in order to avoid secondary chemical reactions and to have an exoergicity comparable to the F + HX three-body reactions. The four-body case permits precise calculations of prior distributions using the informational theory analysis1b and comparison to theoretical results.11 Although the OH(OD) + HCl and OH(OD) + HI reactions will be experimentally studied in our laboratory, reactions 1-4 were chosen for an in-depth study because of the desirable exoergicity. II. Experimental Methods A detailed description of the experimental methods has been given elsewhere.20 The infrared emission spectra were recorded at 1 or 2 cm-1 resolution using a BIO-RAD FTIR spectrometer (FTS-60). The spectrometer chamber and the tube connecting the observation window with the spectrometer were continuously flushed with dry air to remove water vapor and to avoid absorption of the chemiluminescent radiation. The response of the detection system, an InSb liquid-N2-cooled detector, was calibrated with a standard black body source. Chemical reactions took place in a 4 cm diameter Pyrex flow reactor with Ar carrier gas. The flow velocity was about 130 m s-1 at a pressure of 0.5 Torr, corresponding to a reaction time of ∼0.2 ms before observation. The total pressure and reaction time could be varied with a throttling valve. The OH or OD radicals were produced via the H(D) + NO2 f OH(OD) + NO (k ) 1.5 × 10-10 cm3 molecule-1 s-1) reactions. The H(D) atoms were generated by a microwave discharge in a flowing H2(D2)/Ar mixture. The degree of the dissociation of H2(D2) was 50% as measured in ref 20b for the same apparatus. Typical hydrogen atom concentrations at 0.7 Torr were (2-3) × 1013 atoms cm-3. Nitrogen dioxide was introduced together with the main portion of the Ar flow through a perforated ring injector located just after the end of the discharge tube. Excess NO2 was used to convert the H/D atoms to OH or OD radicals. During the flow time (>2 ms) in the 30 cm long prereactor, the OH radicals were vibrationally relaxed. This was explicitly confirmed by noting the absence of the OH(V ) 1) emission. The HBr(DBr) reagent diluted in Ar was introduced into the reactor through a ring injector located 20 cm downstream of the hydrogen and NO2 inlets and 3.5 cm

Butkovskaya and Setser upstream of the observation window (a NaCl disk). The emission from the NaCl window was collected with a short focal length CaF2 lens and directed to the interferometer. The typical HBr(DBr) concentrations at 0.7 Torr were 2 × 1012 molecule cm-3, as determined by calibration of the reagent flow. Commercial tank grade Ar passed in succession through three molecular sieve traps cooled by acetone/dry ice mixture and liquid nitrogen to remove H2O and CO2 impurities. Tank grade H2(D2) and hydrogen bromide (Aldrich) were used without purification. The isotopic purity of the DBr (Cambridge Isotope Laboratory, 99% deuterium) was checked by comparison of the DF and HF emission in the 2200-4200 cm-1 range from the F + DBr reaction before and after the spectra were collected from the OH radical reactions. The fluorine atoms were generated by a discharge through a CF4/Ar mixture. The glass reservoir containing DBr, as well as all the inlet tubes, was treated with D2O before the DBr was loaded. The DF/HF intensity ratio improved by a factor of ∼1.5 after running the DBr/Ar mixture through the reactor for ∼2 h. The ratio usually was about 5. Taking into account that the Einstein coefficients for ∆V ) 1 transitions of HF are 3.4 times larger than that for DF,21 the [DF]/[HF] ratio was ∼17. Thus, the H2O contamination in the HOD spectra from OH + DBr was less than 6%. III. Experimental Results III.A. Chemiluminescent Spectra. The chemiluminescent spectra from reactions 1-4 were measured for 0.5, 0.7, 1.0, and 2 Torr with corresponding residence times of 0.25, 0.35, 0.50, and 1.0 ms. The average number of collisions of product molecules with Ar during the residence time for these pressures is 330, 650, 1325, and 5300, respectively. These numbers were estimated assuming molecular diameters of 2.8 Å for H2O and 3.4 Å for Ar. Raw spectra measured with 1 cm-1 resolution are shown in Figures 1-3, and each represents an average of 1024 scans of the spectrometer. All spectra are plotted with normalization to the highest observed intensity. The spectrum from reaction 1 shown in Figure 1 consists of H2O emission in the 3200-3900 cm-1 range, which includes emission from ∆V1 ) -1 (O-H symmetric stretch), the ∆V3 ) -1 (O-H asymmetric stretch), and the first overtone of the bending mode, ∆V2 ) -2 (see Table 1 for band centers). Reactions 2 and 3 (Figures 2 and 3, respectively) yield HOD emission in the ranges of 3200-3900 cm-1 (O-H stretching vibrations, ∆V3 ) -1) and 2400-2900 cm-1 (O-D stretching vibrations, ∆V1 ) -1, and ∆V2 ) -2 transitions of the bending mode). The poorer signal-to-noise ratio for the emission from reaction 3, relative to the emission from reaction 2, is a consequence of the slower rate of production of HOD owing to the isotopic effect on the rate constant. We may assume k2/k3 to be equal to the primary kinetic isotope effect,22 k1/k3 ) 3, if we neglect the secondary isotope effect. The rate constant for reaction 2 has not been reported, but the secondary isotope effect23 was insignificant for similar reactions of DCl: k(OH + HCl) ) (6.8 ( 0.25) × 10-13 and k(OD + HCl) ) (4.4 ( 0.6) × 10-13 cm3 molecule-1 s-1. The D2O emission spectrum from reaction 4 at 0.7 Torr is presented in Figure 9a. The D2O spectrum consists of symmetric, ∆V1 ) -1, asymmetric, ∆V3 ) -1, and bending overtone, ∆V2 ) -2, transitions in the 2400-3000 cm-1 range. The low intensity of the D2O emission is a consequence of the smaller Einstein coefficients and the slower reaction rate. The spectra at 0.7 and 1 Torr were practically identical and only one is shown. Because of the weak signal, D2O spectra at 0.5 and 2 Torr were not acquired. The spectra in Figures 1-3 show only small changes with an increase of pressure from 0.5 to 1.0 Torr, but differences

H Abstraction by OH Radicals

Figure 1. Raw infrared emission spectra of H2O produced by the OH + HBr reaction. The spectral resolution was 1 cm-1, and the detector response function declines by a factor of 1.6 from 3200 to 3900 cm-1. The Ar pressure and residence times in the reactor were 0.5 Torr and 0.25 ms (a), 0.7 Torr and 0.32 ms (b), 1.0 Torr and 1 ms (c), and 2 Torr and 2 ms (d). The concentrations of reagents for (b) were [HBr] ) 2.8 × 1012, [H2] ) 1.7 × 1013, and [NO2] ) 4.4 × 1013 molecule cm-3.

Figure 2. Raw infrared emission spectra of HDO produced by the OD + HBr reaction. Experimental conditions were the same as in Figure 1. The detector response function declines by a factor of 2.9 from 2400 to 3900 cm-1. The concentrations of reagents for (b) were [HBr] ) 1.5 × 1012, [D2] ) 2.4 × 1013, and [NO2] ) 4.4 × 1013 molecule cm-3.

are more noticeable for comparison of 1 and 2 Torr spectra, especially for reaction 2 (see Figure 2). This allows us to make two conclusions concerning vibrational relaxation of H2O and HOD: (i) vibrational quenching is not very important at pressures 2.7, ∼ 74, and 200 ms, respectively, confirming that deactivation from stretching vibrational levels is not important for a residence time of ∼0.2 ms. Relaxation of the 2ν2 bending mode24a-d is several times faster, (3-6) × 10-13 for M ) Ar, 3 × 10-12 for M ) H2, and 5 × 10-11 cm3 molecule-1 s-1 for M ) HCl, and Ar collisions can cause some change of ν2 state populations for our conditions. The combination levels such as ν1 + ν2 or ν3 + ν2 probably communicate efficiently24c with bending levels, like 3ν2, that are mixed by Coriolis and Fermi interactions, and the rate for relaxation of the combination level reservoir to the manifold of bending levels can be faster than the rate for the analogous relaxation of the ν1,3 stretching reservoir. Hence, some relaxation among nearly energy resonant levels (by collisions with Ar) may occur at P > 0.5 Torr, even though this is not obvious from inspection of the spectra in Figures 1-3. Fast collisional energy exchange between the O-D stretching and bending levels of HOD should take place because of the similar energies of the ν1 and 2ν2 levels. Accordingly, the (V1, V2) - (V1 - 1, V2 + 2) states will be thermally equilibrated, similar to the (V1, V3) - (V1 + 1, V3 - 1) equilibration in H2O. Unfortunately, the relaxation of population in the O-D vibrational levels of HOD could occur via the manifold of bending levels, for which deactivation rate constants in Ar are expected to be equal to or larger than for the H2O bending levels. Deactivation of the O-H stretching levels of HOD is not expected to be important. The next section presents the analyses of the spectra detected at 0.5, 0.7, and 2.0 Torr by computer simulation. Figures were selected to show fitting for the 0.7 Torr spectra because the intensity is high enough to provide a good signal-to-noise ratio, but the distributions have not been affected much by collisional deactivation. Vibrational distributions obtained from the 0.5 Torr spectra were used for the information theoretic analysis as the least relaxed distributions. Spectra measured at 2 Torr were analyzed to determine general trends for population redistribution by collisional relaxation. III.B. Modeling of H2O Spectra from the OH + HBr Reaction. The experimental spectrum from reaction 1 at 0.7 Torr, corrected for the instrumental response function, is shown in Figure 4a. The procedure for modeling the water emission spectra was described in our recent work.14,25 The ratios of the emission intensities were estimated14 to be ν3:ν1:2ν2 ) 1000: 68:1.6, so the ∆ν2 ) -2 bands can be neglected. The ∆ν1 )

4856 J. Phys. Chem., Vol. 100, No. 12, 1996

Butkovskaya and Setser

TABLE 1: Spectroscopic Constants for the Isotopic Water Moleculesa ν1 (Sv0)

2ν2 (Sv0)

ν3 (Sv0)

-x11, -x22, -x33, -x12, -x13, -x23

H2O

3657.05 (4.96 × 10-19)

3151.63 (7.57 × 10-20)

3755.93 (7.20 × 10-18)

HDO

2723.68 (6.34 × 10-22)

2782.01 (8.47 × 10-23)

D2O

2668.10

2340.38

molecule

A0

B0

C0

42.58, 16.81, 47.57 15.93, 165.82, 20.33

27.88

14.51

9.29

3707.47 (1.42 × 10-21)

43.36, 11.77, 82.88 8.60, 13.14, 20.08

23.38

9.10

6.42

2787.72

22.58, 9.18, 26.15 7.58, 87.15, 10.61

15.42

7.27

4.85

-1

a

0

-1

κ (b) -0.43 (-0.16) -0.68 (-0.087) -0.54 (-0.13)

-2

All values are in cm except the denoted values of the band sum intensity, Sv (cm /molecule cm ) and the unitless asymmetry parameters k and b. References for frequencies: 27 (H2O, HDO) and 35 (D2O). Reference for xij values: 28. References for rotational constants: 37 (H2O), 40 (HDO), and 35 (D2O).

Figure 3. Raw infrared emission spectra of HDO produced by the OH + DBr reaction. Experimental conditions were the same as in Figure 1. The concentrations of reagents for (b) were [DBr] ) 2.5 × 1012, [H2] ) 2.9 × 1013, and [NO2] ) 6.4 × 1013 molecule cm-3.

-1 bands were included in the calculations, although the emission spectrum is dominated by ∆ν3 ) -1 transitions. The available resolution gives a partly resolved rotational structure, but direct assignment of individual lines is impossible, and the spectrum will be simulated by coadding individual emission bands for 300 K rotational distributions. The basic (001)-(000) and (100)-(000) emission bands at 300 K were calculated from the corresponding absorption bands26 (also available in the HITRAN database27). An important feature of the (001)-(000) emission band is that the population of the rotational levels in H2O molecule obeys Fermi-Dirac statistics, owing to the nuclear spins of the identical hydrogen atoms, so that the statistical weights of eo and oe levels are 3 times larger than that of ee and oo levels. Since the (001)-(000) band is a pure a-branch in which only transitions between the rotational levels of different symmetry ee T eo and oo T oe are allowed, we have interchanged statistical weight of the same transition in absorption and emission. The calculated (001)-(000) emission band is shown in the bottom panel of Figure 4. The line positions of the combination and hot (V1V2V3) f (V1V2(V3 - 1)) bands can be calculated by red-shifting the centers of the basic ν3 band by ∆ν ) ν°′ - ν°, where ν°′ ) G(V1V2V3) - G(V1′V2′V3′), ν° ) G(001) - G(000), and G(V1V2V3) is given by the conventional expression for the vibrational energy levels of a nonlinear triatomic molecule.

( )

G(V1V2V3) ) ∑ωi Vi + i

1

2

( )( ) ∑∑∑ ( )( )

+ ∑∑xij Vi + i

j

1

2

yijk Vi +

i

j

k

Vj +

1

2

1

+

2

Vk +

1

2

(6)

Figure 4. Simulation of the H2O emission spectrum from the OH + HBr reaction at 0.7 Torr. The experimental spectrum (a) has been corrected for response of the detection system. Q is the least-squares estimator (see text). The best fit spectrum (b) corresponds to the vibrational distribution given in Table 3. The spectrum in (d) is the fundamental emission band ∆V3 ) -1, and the band centers for combination and hot bands are indicated. The spectrum in (c) is an intermediate step of the simulation, which shows transitions from V3 ) 1 with added bending excitation (the V2 distribution is for V1,3 ) 1 in Table 3).

The frequencies, ωi, and anharmonicity coefficients, xij, were taken from ref 28 and the second-order anharmonicity constants, yijk, from ref 29. The harmonic approximation plus the frequency ratio to the third power was used to obtain Einstein coefficients for higher levels by scaling the Einstein coefficient of the (001)-(000) transition.30 Such calculations imply that the rotational energy levels are the same for each (V1V2V3) vibrational level. To improve this approximation, some line positions were determined as a difference of corresponding rovibrational levels. This was possible for the (011)-(010), (021)-(020), (031)-(030), (101)-(100), (111)-(110), (002)(001), and (012)-(011) bands because the known rovibrational energy levels of all the higher and lower vibrational states.31 In all these bands, the intensities of the rotational transitions, J′Ka′Kc′ - J′′Ka′′Kc′′, were taken to be equal to the intensities of the same transitions in the basic (001)-(000) band. Perturbations between certain rotational levels in the water molecule lead to dramatic displacements of line positions compared to the undisturbed ones. Some examples in Table 2 show a

H Abstraction by OH Radicals

J. Phys. Chem., Vol. 100, No. 12, 1996 4857

TABLE 2: Spectral Shifts for Combination Bands of H2O (cm-1) band transition V′ - V′′ (031) - (030)

J′K′aK′c J′′K′′aK′′c 212 - 313 330 - 331 413 - 514 606 - 505

approximation eq 6 45.4

TABLE 3: Vibrational Distributions for H2O from Modeling the Chemiluminescence Spectra from the OH + HBr Reaction V2

observed band observed energy levels31 centers27 48.9

(101) - (100) 212 - 313 162.2 330 - 331 413 - 514 606 - 505

163.2

(012) - (011) 212 - 313 112.5 330 - 331 413 - 514 606 - 505

87.1

49.6 63.8 54.3 49.2 162.9 158.6 161.5 166.6 86.1 87.6 87.0 89.8

comparison between the spectral shifts calculated using expression 6 and the individual energy level difference for several of the most intense transitions in the basic ∆ν3 ) -1 emission band: 330-331 (3745.09 cm-1), 413-514 (3628.35 cm-1), and 606-505 (3870.13 cm-1) in (031)-(030), (101)-(001), and (012)-(011) bands, respectively. (Note that the vibrational states (V1V2V3) are in brackets and the rotational states JKaKc are without brackets.) The discrepancy increases with rotational quantum number and may attain hundreds of cm-1 for certain transitions from J > 6. The data compilation in refs 29 and 32 provides experimentally determined values of band centers for all the (000)-(V1V2V3) absorption bands with V1 and V3 e 4, and V2 e 3, from which the required band shifts can be easily calculated (see Table 2 for some selected examples). Vibrational energy levels for V1 + V3 e 4 and V2 e 4 have been calculated, taking into account the Fermi resonance between the stretches and bends and the Darling-Dennison resonance between the stretches.33 Comparison of different approximations demonstrated that the band shifts determined from the observed band centers are satisfactory for the line positions needed in modeling of the low-resolution spectra, because the vibrational excitation in our experiments did not exceed V1,3 ) 3 and V2 ) 5. Collisional equilibration between the nearly resonant ν1 and ν3 stretching levels of H2O was assumed, and the Boltzmann population of vibrational levels within each group of (V1,3V2) states was adopted in the calculation of the model spectra. Selection of vibrational populations to fit the experimental spectrum was made using a least-squares procedure. Every (V1,3, V2) emission band, which is a combination of the thermally weighted (V1, V2, V3) ) (V1 + n, V2, V3 - n) bands with n ) 0, ..., V1,3, was considered as a vector with N ) 1452 elements corresponding to the number of measurements in one 32003900 cm-1 spectrum, separated by 0.492 cm-1. For measurements of equal accuracy, the least-squares method requires a minimization of the value of the estimator Q ) ∑(si - ∑Pjbij)2, where si is the ith measurement in the experimental spectrum, bij is the ith element of the jth basic band, and Pj are the populations of the corresponding vibrational states. The inner summation is made over the basic vectors, and the outer one is a summation over all the spectral points. The parameters Pj were found in a circular search with a step by step inclusion of additional bands. Figure 4c shows an intermediate stage of the simulation for a model spectrum containing only V1,3 ) 1 combination bands. Addition of V1,3 ) 2 and 3 transitions is required to give a satisfactory fit to the experimental spectrum. The full distribution used in the best model spectrum (Figure 4b) is given in Table 3, as well as the distributions obtained for 0.5 and 2 Torr. Taking advantage of a least-squares formalism,34 the standard deviation of the populations, σ(Pj), was

V1,3

0

1

2

3

4

5

9.0 3.4

7.2 2.5

3.9

3.0

12.4

9.7

3.9

3.0

total P1,3

P ) 0.5 Torr 0 1 2 3 Total P2b

7.7 14.6 5.6 27.9

11.4 15.3 2.7 29.4

13.8a 42.1 35.8 8.3

P ) 0.7 Torr 0 1 2 3 Total P2b

10.2 11.3 4.1 25.6

11.5 10.5 1.7 23.7

9.0 3.6

7.2 2.6

6.4

3.2

12.6

9.8

6.4

3.2

7.5 1.8

6.6 2.5

2.3

4.3

9.3

9.1

2.3

4.3

18.6a 42.1 28.1 5.8

P ) 2 Torr 0 1 2 3 Total P2b

13.0 7.0 1.7 21.7

15.8 6.3 0.8 22.9

30.3a 49.6 17.6 2.5

Obtained from the linear surprisal plot. The V2 distribution for V1,3 ) 0 is not included. The V1,3 ) 0 component would favor higher V2 levels. a

b

estimated by σ(Pi) ) [(G)-1iiQ/N]1/2, where (G)-1ii is the diagonal element of the inverse Gram’s matrix of the basic vectors bi ) (b1i, b2i, ..., bNi), i.e., Ckl ) bkTbl. For the spectrum in Figure 4, the best fit was obtained with 12 vectors included in the simulation, giving Q ) 1.68 × 106. Calculated values of (G)-1ii vary from 2.7 to 4.4 × 10-6, giving the largest magnitude of σ(Pj), which corresponds to 13% of the obtained population. This value corresponds only to the uncertainty in the simulation and does not include possible experimental errors or inaccuracy in the basic vectors. The distribution at 0.5 Torr has nearly equal population in the V1,3 ) 1 and 2 levels and an appreciable population in V1,3 ) 3 level, which is close to the thermochemical limit for reaction 1. In fact, the highest V2 energy for each V1,3 level is close to the thermochemical limit. Relaxation out of the ν1,3 levels is not important at this pressure, so this V1,3 distribution may be considered to be close to the nascent one. The overall bending distribution is only slightly inverted with the maximum in V2 ) 1; the bending inversion is more pronounced in the V1,3 ) 1 level (and presumably V1,3 ) 0). The same feature for the bending distribution in V1,3 ) 1 was found in the distributions for 0.7 and 2 Torr. The distribution from the 2 Torr spectrum shows a considerable change in stretching mode populations in accordance with energy flow from the higher vibrational levels to the lower ones. The changes with pressure suggest that populations in V1,3 ) 2 and 3 may transfer to lower stretching levels with excitation in V2. The mean fraction of vibrational energy corresponding to the distribution at 0.5 Torr was calculated as 〈fV〉 ) [∑vPvEv]/〈Eav〉, including P1,3(V1,3 ) 0) population from the surprisal analysis (below) and assuming a similar bending distribution for V1,3 ) 0 as for V1,3 ) 1 states. The result is 〈fV〉 ) 0.61, which is very close to the mean fraction of vibrational energy released to the HF product in the F + HBr (0.59) and F + HI (0.59) reactions.6 The contribution from the bending vibrational excitation is 〈fV2〉 ) 0.18, i.e., slightly less than a third of the total vibrational energy in the H2O product. Both fractions are lower limits because the P2 distribution should probably be weighted to higher V2 levels for the V1,3 ) 0 contribution and because of a small degree of possible vibrational relaxation. The scaling of the Einstein coefficients for V1,3 ) 2 and 3 probably overesti-

4858 J. Phys. Chem., Vol. 100, No. 12, 1996

Figure 5. Simulation of the O-H contribution to the HDO emission spectrum from the OD + HBr reaction at 0.7 Torr. Q is the leastsquares estimator (see text). The best fit (b) corresponds to the vibrational distribution in Table 4. The spectrum in (c) is an intermediate step of the simulation with transitions from V3 ) 1 only. The spectrum in (d) is the fundamental band ∆V3 ) -1 with indicated band centers for combination and hot bands.

mates the values according to comparisons to the established Einstein coefficients of HF and HCl,21 which also would lead to an underestimate of the populations in V1,3 g 2. III.C. Modeling of HOD Spectra from the OD + HBr Reaction. The O-H contribution to the HOD emission observed from reaction 2 at 0.7 Torr, corrected for the response function, is shown in Figure 5a. Since the overlap of the (001) and (100) fundamental emissions is negligible, modeling can be carried out separately for the O-H stretching emission in the 3200-3900 cm-1 range (see Figures 2 and 6. The HOD (100) fundamental and HOD (020) overtone emissions range from 2400 to 2900 cm-1. The ratio of emission strengths of the (001), (100), and (020) bands is 100:18:2.5, as obtained from the comparison of band strengths from Table 1. For H2O, the ∆ν2 ) -2 emission intensity is much less than that from ∆ν3 ) -1, but it is not negligible compared to ∆ν1 ) -1, so the ∆ν2 ) -2 transitions were included in calculations. To determine the vibrational distribution for HOD, we used a modeling method similar to the one described above for H2O. The fundamental (001), (100), and (020) absorption bands were taken from the HITRAN database.27 The calculated (001) and (100) + (020) emission spectra with a half-width of 1 cm-1 for each line are shown in Figures 5d and 6e, respectively. Since the HITRAN data for HOD are much more limited than for H2O, the shifts of band centers for combination and hot bands (V1V2V3) - (V1V2(V3 - 1)), (V1V2V3) - ((V1 - 1)V2V3), and (V1V2V3) - (V1(V2 - 2)V3) were always calculated from eq 6 with omission of cubic terms, and the fundamental frequencies and anharmonic coefficients were taken from ref 28. The near energy match between (100) and (020) vibrational states (see Figure 8) was assumed to give a thermal equilibrium between all vibrational states in a (V1 + i, V2 - 2i, V3) series, where i ) 0, 1, ..., V2/2 for even V2 and i ) (V2 - 1)/2 for odd V2. These equilibrated levels affect the simulation of both O-H and O-D parts of the spectra. For example, the 021/101, 031/ 111, 041/121/201, ... groups for V3 ) 1 and the 022/102, 032/

Butkovskaya and Setser

Figure 6. Simulation of the O-D contribution to the HDO emission spectrum from the OD + HBr (parts a and b) and OH + DBr (parts c and d) reactions at 0.7 Torr. The lower calculated curves in (b) and (d) correspond to the distributions for V3 * 0 obtained from the simulation in the 3200-3900 range; upper curves show the best fits corresponding to the vibrational distributions, including V3 ) 0 states (Tables 4 and 5). The bottom section (e) shows the bands from ∆V1 ) -1 and ∆V2 ) -2 (lower spectrum) transitions. Positions of the band centers for combination and hot bands are indicated.

Figure 7. Simulation of the O-H part of the HDO emission spectrum from the OH + DBr reaction at 0.7 Torr. The best fit (b) corresponds to the vibrational distribution in Table 5. Q is the least-squares estimator (see text).

112, ... groups for V3 ) 2 give emission in the O-H and O-D ranges and the 020/100, 030/110, 040/120/200, 050/130/210, etc. groups give emission only in the O-D range. The vibrational distributions in Table 4 were assigned in terms of the equilibrated groups of states. One advantage of this collisional mixing is that (V1V20) populations can be assigned from the ∆V1 ) -1 or ∆V2 ) -2 spectra. A major disadvantage, of course, is that neither the bending excitation nor the O-D (ν1) excitation can be assigned separately. Two steps in the simulation of the HOD ∆V3 ) -1 spectra from reaction 2 are demonstrated in Figure 5. The blue wing of the spectrum arising from the superposition of bands with only one excited quantum in ν3 stretch (see Figure 5c) is

H Abstraction by OH Radicals

Figure 8. Vibrational energy levels of HDO (V2 denotes the bending quantum number) showing the possibility of transfer from the (V1V20) manifold to the (V1′V2′1) manifold.

reproduced by the V1,2 population distribution presented in the V3 ) 1 section of Table 4. Fitting the red side of the spectrum obviously requires higher ν3 excitation. Addition of combination (V1V22) - (V1V21) and (V1V23) - (V1V22) bands with the populations given in Table 4 provides a good fit to the observed emission from OD + HBr, as shown in Figure 5b. Fitting this spectrum gives a reliable distribution for V3 g 1 and for V1,2 within V3 ) 1-3. As in case of H2O, the fitting was made with the help of a least-squares method. For the model spectra of this reaction, the values of the least-square estimators Q appeared to be approximately 2 times smaller than those for reaction 1, and the diagonal elements of the inverted Gram’s matrix for the HOD set of basic bands are also smaller, ranging from 0.6 to 3.2 × 10-6. Consequently, the fitting errors are less than 10%. The better fitting is explained by the use of a more accurate fundamental (001) emission band; some line intensities in the H2O emission fundamental band may be incorrect by a factor of 3 × 3 ) 9 because the wrong assignment of a statistical factor, g, in an initial absorption band (this kind of error for some HITRAN lines was also indicated in ref 19b). To complete the assignment, the general trends in the (V1V20) populations of HOD were obtained by a simulation carried out for the 2400-2900 cm-1 emission. In this range the intensity is much weaker (Figure 6c) and the signal-to-noise ratio is poorer than for O-H emission. The weights of the combination bands with ν3 * 0 were taken from the simulation of the ∆ν3 ) -1 emission. Transitions from the bands with V3 ) 0 were added using the absolute intensity scale for the calculated ν1, 2ν2, and ν3 fundamental emission band strengths (Figure 6d, lower curve). A least-squares procedure was used to complete the spectrum (Figure 6d, upper curve), which gave relative populations of (V1V20) states with V2 g 2 given in Table 4. The total population in the V3 ) 0 manifold of levels was determined from linear surprisal plots, and the ratio of the (000) to (010) populations was assigned by analogy to the V1,2 distribution in the V3 ) 1 manifold. The total population of the dark (000) and (010) levels was obtained as the difference between the total V3 ) 0 population and the measured (V1V20) population. The direct observation of the (V1V20) levels provides confirma-

J. Phys. Chem., Vol. 100, No. 12, 1996 4859 tion of the linear extrapolation of the surprisal. Considering all the assumptions, the P1,2 distributions must be used with caution. The vibrational distribution for the 0.5 Torr spectrum of reaction 2 is 22:33:37:6 for V3 ) 0-3, and 〈fV〉 is 0.65. The difference between the 0.5 and 0.7 Torr spectra indicates that collisional relaxation is small, but not negligible, and these are the lower limit values. The preferential contribution belongs to the O-H bond, 〈fV3〉 ) 0.40, which actually is close to the total excitation of ν1 + ν3 in H2O. Since the O-D bond is expected to be a spectator in reaction 2, most of the excitation in the ν1,2 set of levels probably was initially deposited in the bending mode. III.D. Modeling of HOD Spectra from the OH + DBr Reaction. The O-H part of the emission spectrum from reaction 3, measured at 0.7 Torr and corrected for the response function, is shown in Figure 7a, and the fitted spectrum is shown in Figure 7b. The simulation method was the same as that described in section III.C. The 6% contamination of H2O from the impurity reaction, OH + HBr, was taken into account during the simulation. The emission spectrum from reaction 3 clearly differs from that of reaction 2 (see Figure 5), and the emission from reaction 3 is mainly from V3 ) 1 with a broad distribution in V1,2. The nonmonotonic populations in the V1,2 groups (see Table 5) are noteworthy, as are changes in the V1,2 distribution of V3 ) 1 with pressure. The calculated spectrum for the O-D part of the HOD emission is shown in Figure 6b; the lower spectrum corresponds to transitions from levels with V3>0, and the top spectrum is the best simulation, including V1 and V2 excitation with V3 ) 0. The best distributions for 0.5, 0.7, and 2.0 Torr are presented in Table 5. The vibrational distribution for the lowest pressure spectrum of reaction 3 gives the mean fraction of vibrational energy as 〈fV〉 ) 0.51, with 〈fV1,2〉 ) 0.31 and 〈fV3〉 ) 0.20. At all pressures the population in the V3 ) 3 level is negligible, being less than 1% of the overall intensity. The population for V3 ) 2 is also low; the bulk of the HOD population is in V3 ) 0 and V3 ) 1 levels. The most unexpected finding is the high population in the V3 ) 1 level; the population at 0.5 Torr is even slightly higher than that for V3 ) 0. The distribution in ν1/ν2 mixed levels also contradicts the expectations for preferential release of energy into the O-D bond, since P1,2 decreases with more than 70% of molecules in the V1 ) 0 and 1 states. A likely explanation for the low 〈fV1,2〉 is the loss of ν1 excitation through collisional exchange with bending vibrational levels followed by V-T loss from the manifold of bending levels and by transfer to ν3 ) 1 (see below). The overall 〈fV〉 quoted above is a realistic lower limit to the true 〈fV〉, but the 〈fV1,2〉 and 〈fV3〉 values have probably been distorted by relaxation. This relaxation is more serious for HOD from reaction 3 than for HOD from reaction 2 because in the latter case most of the energy is initially in ν3 levels. The probable vibrational relaxation pathways of HOD can be better understood after the inspection of the vibrational energy level diagram in Figure 8. The energy difference between the collisionally coupled set of (m, n, 0) levels and the V3 ) 1 levels decreases with bending excitation and is equal to 429, 378, 327, 277, 227, 176, and 125 cm-1 for (0V20) - (0V2′1) levels with V2 ) 3-9 and V2′ ) 0-6. Thus, initially prepared (1, V2, 0), (2, V2, 0) and (3, V2, 0) levels can relax to the V3 ) 1 manifold with a modest change in the V2 quantum number or by ∆V ) 1 change in all three quantum numbers. Relaxation to V3 ) 2 is less favorable based on energy defect and change in ∆V3. The close, but lower, energy of the V3 ) 1 levels explains the abnormally low population of the V2 > 4, V3 ) 0 levels but high population of

4860 J. Phys. Chem., Vol. 100, No. 12, 1996

Butkovskaya and Setser

TABLE 4: Vibrational Distributions for HDO from Modeling the Chemiluminescence Spectra from the OD + HBr Reaction P ) 0.5 Torr V1, V2

V3 ) 0

00 01 02/10 03/11 04/12/20 05/13/21 06/14/22/30 07/15/23/31 Total P3

2.6b 2.3b 3.7 6.1 2.0 3.5 0.9 0.3 21.7a

V3 ) 1

P ) 0.7 Torr

V3 ) 2

6.7 5.9 6.3 4.9 4.1 2.6 1.7 0.8 33.0

V3 ) 3

12.5 9.7 7.1 4.9 2.3 0.8

2.9 2.8 0.1

37.3

a

P1,2

V3 ) 0

24.7 20.7 17.2 15.9 8.4 6.9 2.6 1.1

6.2b

5.8

V3 ) 1

6.4b 5.7 8.3 1.6 0.7 1.2 0 30.1a

V3 ) 2

6.7 5.9 6.0 4.8 4.3 2.9 2.2 1.5 34.9

P ) 2.0 Torr V3 ) 3

9.4 6.4 5.4 3.6 2.2 1.3

1.8 1.1

29.4

2.9

P1,2

V3 ) 0

V3 ) 1

V3 ) 2

V3 ) 3

P1,2

24.1 19.8 17.1 16.7 8.1 4.9 3.4 1.5

23.9b

13.0 6.3 5.7 2.2 3.9 2.7 1.7

4.9 2.4 1.7 0.7

0.7

42.5 19.9 17.5 8.6 5.4 2.9 2.1 0.9

35.5

9.7

0.7

11.2b 10.1 5.7 1.5 0.2 0.4 0.9 53.9a

b

Evaluated from surprisal linear plots. The population of the dark (000) and (010) levels was calculated as a difference between the linear surprisal value for V3 ) 0 and the measured population (see text) for the emitting V3 ) 0 states. This population was shared between the V2 ) 0 and V2 ) 1 states by analogy to the V3 ) 1 distribution.

TABLE 5: Vibrational Distributions for HDO from Modeling the Chemiluminescence Spectra from the OH + DBr Reaction P ) 0.5 Torr V1,V2

V3 ) 0

00 01 02/10 03/11 04/12/20 05/13/21 06/14/22/30 07/15/23/31 08/16/24/32/40 Total P3

2.5a

a

2.5a 9.8 8.4 3.3 0.7 3.5 0.7 2.5 33.9

V3 ) 1

V3 ) 2

P ) 0.7 Torr V3 ) 3

6.8 10.3 9.8 5.4 12.5 4.0 3.9 1.0

3.0 2.8 2.3 1.4

0.5 0.4

53.7

9.5

0.9

P1,2

V3 ) 0

12.8 16.0 21.9 15.2 15.8 4.7 7.4 1.7 2.5

5.4a 5.4a 17.8 17.2 1.6 0.9 0.5 0.2 0.3 49.3

V3 ) 1

V3 ) 2

P ) 2.0 Torr V3 ) 3

3.1 2.0 5.5 3.0 11.4 8.4 7.8 1.9

0.6 1.7 1.9 0.9

1.0 0.6

43.1

5.1

1.6

P1,2

V3 ) 0

V3 ) 1

V3 ) 2

V3 ) 3

P1,2

10.1 9.7 25.2 21.1 13.0 9.3 8.3 2.1 0.3

13.3a

8.6 5.6 5.5 3.1 6.1 4.4 3.3 0.9

0.3 0.8 0.7 0.1

0.3 0.6

22.5 20.3 22.3 14.2 9.0 6.1 3.9 1.1 0.7

37.5

1.9

0.9

13.3a 16.1 11.0 2.9 1.7 0.6 0.2 0.7 59.8

Estimated by comparison of the populations assigned by simulation and linear surprisal plot extrapolation (see text).

Figure 9. Simulation of the D2O emission spectrum from the OD + DBr reaction. The infrared spectrum (a) was taken at 0.7 Torr for [DBr] ) 1.8 × 1012, [D2] ) 2.9 × 1013, and [NO2] ) 5.1 × 1013 molecule cm-3 and has been corrected for response of the detection system. The best fit simulated spectrum (b) corresponds to the vibrational distribution in Table 6, and (c) is the fundamental emission band ∆V3 ) -1. Positions of the band centers for combination and hot bands are indicated.

V3 ) 1 levels from reaction 3. The overpopulation of the (041), (121), and (201) set of levels is especially noticeable, and this can be explained as transfer from the (V1V20) set of levels near 9400 cm-1, which would be expected to receive a significant population from reaction 3. III.E. Modeling of D2O Emission from the OD + DBr Reaction. The emission observed from reaction 4 at 0.7 Torr, corrected for the response function, is shown in Figure 9a and compared to the simulated spectrum in Figure 9b. The positions of the band centers for several bands are shown in Figure 9c.

The wavelengths of the (100), (020), and (001) bands, which were needed for the model calculation, were taken from the absorption spectra.35 Corrections to the intensities of the saturated lines in (001) band were made with the help of the tables for transition strengths for rotational transitions of an asymmetric rotor.36 Although the accuracy of calculated intensities may not be high, we had to use this approximation, since the only published D2O (001)-(000) absorption spectrum28 does not contain complete assignments of the rotational lines. Assignment of transitions is necessary for calculation of the (001) fundamental emission band in order to take into account the nuclear spin statistics of the rotational levels; in this case the ratio of the statistical weights of ee and oo levels to those of eo and oe levels is 2:1. The calculated (001) emission band is shown in the bottom panel of Figure 8 together with the symmetric band (100). The integrated emission intensities for the three bands are (001):(100):(020) ) 1000:119:15; the intensity from the bending overtone emission can be neglected. As in the case of H2O, the energies of the ν1 and ν3 levels are close together and equilibration of populations between states with a given stretching number was assumed. The band centers for combination bands were calculated using expression 6, without cubic terms, with molecular constants from ref 28. Contamination of HOD emission formed from the HBr impurity was taken into account in the simulation. The assigned distribution for the 0.7 Torr spectrum is presented in Table 6. The vibrational levels of D2O are populated up to the energetic limit (V1,3, V2) ) (4, 1) and nearly to the limit for (3, 3) and (2, 5). According to a surprisal plot (not shown), an inversion exists with the V1,3 ) 1 level having the largest population. The vibrational distribution for the 0.7 Torr spectrum of reaction 4 gives 〈fV〉 ) 0.54, with a bending contribution of 〈fV2〉 ) 0.16. The ratio of the bend-to-stretch excitation is nearly the same as that for H2O. The overall smaller 〈fV〉 could be a consequence of relaxation, since the D2O distribution was assigned from 0.7 Torr data and since 2 times

H Abstraction by OH Radicals

J. Phys. Chem., Vol. 100, No. 12, 1996 4861

TABLE 6: Vibrational Distribution for D2O from Modeling the Chemiluminescence Spectra from the OD + DBr Reaction at 0.7 Torr V2 V1,3

0

1

2

3

4

5

6

7

0 1 2 3 4 Total P2

8.8 6.5 4.4 3.0 26.0

8.8 6.6 5.8 1.6 26.1

5.3 6.9 5.0 0 19.2

5.7 3.7 3.7 0 15.2

5.9 1.8 0 0 9.9

0.6 0.6 0 0 1.4

0.9 0 0 0 1.2

0.7 0 0 0 0.9

a

total P1,3 13.6a 36.6 26.2 19.0 4.6

Obtained from the linear surprisal plot.

more collisions occurred for D2O compared to H2O at 0.5 Torr. The 0.7 Torr distribution for H2O from Table 3 gives 〈fV〉 ) 0.58 and 〈fV2〉 ) 0.20.

The vibrational states are represented by two quantum numbers V1,3 and V2, denoting stretching and bending vibrations. This is required, since collisional equilibration between the ν1 and ν3 stretching modes makes it impossible to observe individual V1 and V3 populations. Formula 10 gives the prior distribution for vibrational states V1,3, V2. The prior P0(V1,3, V2, J) needs summation over 2J + 1 sublevels because of the asymmetry splitting. Commonly used notation for these states is J, τ, where τ ) Ka - Kc, and τ accepts values from -J to J.36,37 For convenience of computation, we used the notation τ′ ) τ + J so that τ′ varies from 0 to 2J. A large energy difference between stretching and bending vibrations allows us to consider bending vibrations as a degree of freedom intermediate between the stretching vibrations and rotation and to obtain the prior for the stretching vibrations as V*2(V1,3)

IV. Information-Theoretical Analysis IV.A. Vibrational Surprisal Analysis of H2O(W1,3, W2) from the OH + HBr Reaction. Vibrational surprisal plots from information theory1 have been widely used for analysis of distributions from H + L-H reaction dynamics,1,2 and the linear plots have been very helpful in correlation of the data from many different reactions. The theory is based on comparison of the experimentally determined vibrational distribution of the products, P(V), to the prior distribution, P0(V), calculated with the assumption of equal probability for all the energetically possible quantum states of the products. The surprisal of the observed population distribution is defined as

I(V) ) -ln[P(V)/P (V)] 0

(7)

For a diatomic + atom product, P0(V) is calculated from eq 8, using the formalism developed in ref 1,

∑

P0(V, J)

(8)

J)0

where J*(V) is the highest allowed rotational level for vibrational level V and P0(V, J) is given by eq 9.

P (V, J) )

(2J+1)(E - EI)1/2

0

V* J*(V)

(9)

(2J + 1)(E - EI)1/2 ∑ ∑ V)0 J)0 The internal energy of the product is EI ) Ev + ER and V* is the highest accessible vibrational level. The dependence of I(V) upon V can reveal the specificity of the vibrational energy disposal. To extend the formalism to H2O with vibrational and rotational states described by V ) V1V2V3 and J ) JKaKc, we replace eqs 8 and 9 by 10 and 11. J*(V)

P0(V1,3, V2) )

P0(V1,3, V2, J) ∑ J)0

(10)

τ*(J)

P0(V1,3, V2, J) )

(2J + 1)(E - EI)1/2 ∑ τ′)0

* V1,3

V2*

1,3

2

(11) J*(V) τ*(J)

(2J + 1)(E - EI)1/2 ∑ ∑ ∑ ∑ V )0 V )0 J)0 τ′)0

∑ V )0

P0(V1,3, V2)

(12)

2

where V2* is the highest bending vibration allowed for a given V1,3 stretching vibrational state. The vibrational energy for every V1,3 state was calculated according to the expression i)V1,3

Ev ) Ev(V1,3, V2) )

∑ i)0

keq[G(V1,3 - i, V2, i) - G(000)] (13)

where keq is the Boltzmann weight of an individual (V1V2V3) state in a given (V1,3, V2) manifold and G(V1V2V3) is determined by expression 6. Rotational energy levels36,37 for an asymmetric top are given by eq 14,

ER )

J*(V)

P0(V) )

P (V1,3) ) 0

B+C B+C W(J, τ) J(J + 1) + A 2 2

[

]

(14)

where A, B, and C are the rotational constants. The term W(J, τ) depends upon the asymmetry parameter, which may be expressed as b ) (C - B)/2[A - 1/2(B + C)]. Although H2O is a rather strongly asymmetric top with b ) -0.16, we used an expansion37a of W into a power series of b and J(J + 1) up to b4 and J3(J + 1)3. Centrifugal effects were taken into account.37b The distortion parameters DJ, DJK, DK, D1, D2, and D3 were obtained by using the experimental data for the quartic distortion constants38 and the relations given in ref 39 between vibrational force constants and distortion constants. The values of rotational constants can vary significantly for different vibrational levels, and we have tested that the calculated vibrational prior distributions were not sensitive to these variations. It was shown that the use of the specific values of A, B, and C constants for each vibrational level, which were obtained from the low J rotational energies or extrapolation of the existing data, resulted in less than a 1% deviation from the populations corresponding to the ground-state values. Since sets of all the rotational constants for different vibrational states are not available, we used the ground-state constants without an appreciable loss of accuracy in the calculations. The results from eqs 10-12 are presented in Figure 10a. The prior distribution P0(V1,3), shown as the dashed curve, is a decreasing function of V1,3 falling nearly to zero at V1,3 ) 3. The experimental distribution, shown as squares connected by solid lines, is for the 0.5 Torr distribution from Table 3. The linear surprisal plot for P1,3 (with fV1,3 as the variable) is shown in Figure 10b. Since the vibrational surprisal plot is linear, the

4862 J. Phys. Chem., Vol. 100, No. 12, 1996

Butkovskaya and Setser

Figure 10. (a) Comparison of the observed P1,3 distribution for H2O from the OH + HBr reaction (0) and the prior distribution (- - -). (b) Surprisal plot for the P1,3 distribution vs the variable fV1,3; the P1,3(0) value was obtained from linear extrapolation.

V1,3 vibrational distribution can be expressed by eq 15: 0 ln I(fV1,3) ) λ1,3 + λV1,3fV1,3′

(15)

where fV1,3 ) Ev(V1,3, V2 ) 0)/〈Eav〉 is the fraction of vibrational energy in the V1,3 levels. The plot is linear with λ01,3 ) -1.2 and λV1,3 ) -4.5, and the intercept gives an estimate of the relative population in the V1,3 ) 0 level of 0.14, indicating an inverted distribution for V1,3. The magnitude of λV1,3 is a global measure of the deviation of the experimental stretching distribution from the statistical prior distribution. The overall bending distribution, i.e., the bending populations for V1,3 ) 1, 2, and 3 levels, is rather close to the statistical one (Figure 11a). The bending distribution in the V1,3 ) 0 stretching state is unknown, but taking into account its low contribution, the V2 distribution in V1,3 ) 0 cannot change the general picture. The reduced variable, analogous to fV1,3 of the previous paragraph, which indicates the fraction of the available energy in product bending, is gV2 ) fV2/(1 - fV1,3). The corresponding surprisal for the complete distribution (Figure 11c, open circles) constitutes nearly a horizontal line, which means that the experimental and prior distributions are nearly the same. The small deviation is due mainly to the bending population in the V1,3 ) 1 stretching state, which shows a slight inversion in V2 ) 1. To apply surprisal analysis to the bending distribution of a given stretching level, we need to examine the conditional surprisal

I(fV2|fV1,3) ) -ln [P(fV2|fV1,3)/P0(fV2|fV1,3)]

Figure 11. Comparison of the prior (- - -) and observed (s) bending distributions for H2O from the OH + HBr reaction: (a) complete P2 distribution (O); (b) conditional P2 distribution for V1,3 ) 1 (4); (c) surprisal plots (O) for the complete P2 distribution and (4) for the bending distribution of V1,3 ) 1.

because the simulated population has a large uncertainty due to the overlaping with the strong V3 ) 2 hot band and because the prior distributions for the highest vibrational states are very sensitive to the exact magnitude of the available energy. The negative value for λV2 indicates the release of more than the statistical energy to ν2 for V1,3 ) 1. IV.B. Vibrational Surprisal Analysis for HOD. The ν1 (OD stretch) populations of HOD are coupled to the populations in the ν2 (bending) levels, and we consider only two vibrational degrees of freedom, which are ν3, OH stretch, and ν1,2, the OD stretch + bending reservoir. The energy of every vibrational state is determined by

Ev ) Ev(V1,2, V3) ) ∑keq[G(V1 + i, V2 - 2i, V3) - G(000)] i

where keq is the Boltzmann weight of an individual (V1, V2, V3) state in a given (V1,2, V3) set. This causes no difficulty in performing a surprisal analysis for reaction 2, since excitation of the OH mode is of interest, and the prior distribution for ν3 excitation can be calculated using a transformed eq 12, V*1,2(V3)

P (V3) ) 0

(16)

with the prior P0(fV2|fV1,3) defined by formula 10. Figure 11b shows the dependence of the bending population of the V1,3 ) 1 level and the calculated prior P0(fV2|V1,3 ) 1) on the quantum number V2. The triangle points in Figure 11c show the surprisal I(fV2|V1,3 ) 1) vs the variable gV2 ) fV2/[1 - Ev(1,0)/Eav]. For a linear representation, I(fV2|fV1,3) ) λ02 + λV2gV2, the best fit gives λV2 ) -2.5. We excluded the V2 ) 5 point from the analysis

(17)

P0(V1,2, V3) ∑ V )0

(18)

1,2

and similarly transformed eqs 10 and 11. Quartic distortion constants40 were included in the calculated prior V3 distribution for HOD. We can sum over the ν1,2 states for each V3 level and obtain total relative populations for V3 ) 1, 2, and 3 states as 33, 38, and 6, respectively, for 0.5 Torr (see Table 4). The experimental and statistical distributions are compared in Figure 12a, and the corresponding surprisal plot with fV3 ) [∑V1,2keq-

H Abstraction by OH Radicals

Figure 12. (a) Observed P3 (O-H stretch) distribution for HDO from the OD + HBr reaction (0) and the prior distribution (- - -). (b) Surprisal plot for P3 distribution; the P3(0) was obtained by the linear extrapolation.

(V1,2)E(V1,2, V3)]/〈Eav〉 shown in Figure 12b is remarkably linear. The intercept gives the total population of the V3 ) 0 states, and the difference in the assigned population for V3 ) 0, V2 > 1 (see Table 4) allows an estimate of the population of the “dark” (000) and (010) vibrational levels. For the distribution under consideration λ03 ) -1.2, from which the total V3 ) 0 population is 22% and the population of the dark states is about 5%. The λV3 ) -6.1 value is substantially higher than the slope of the surprisal for H2O distribution, λV1,3 ) -4.5, which is mainly a consequence of different statistics for the two priors. We made an analysis of HOD from reaction 3 by summation of the ν1,2 states related to a given V1 number over V3 ) 0-3, (i.e., the sum ∑(00V3 + 01V3) corresponds to V1 ) 0, the sum ∑(02V3 + 03V3) corresponds to V1 ) 1, etc.). The 0.5 Torr distribution from Table 5 gives 37, 21, 9, and 3 for the V1 ) 1-4 populations, and these are compared to the prior in Figure 13a. The corresponding surprisals (not shown) are -0.03, -0.06, -0.13, 0.04, and 1.07. Within the uncertainty limits, the distribution as a whole shows no deviation from the calculated prior distribution, only the population of the highest possible level V1 ) 4 is “surprising”, which can be explained by the high sensitivity of the prior for the level close to the thermodynamical limit. A comparison of the experimental and prior distributions for ν3 in Figure 13a shows that the P3(1) level is strongly overpopulated. This overpopulation and the apparent statistical distribution of P1 is explained by collisional coupling between the V3 ) 0 and V3 ) 1 manifolds (see section III.D and Figure 8). The collisional transfer from high V1,2V3 ) 0 levels to V3 ) 1 levels with reduction of the bending quantum number by 3 may occur. Adding populations of the V2, V3 ) 1 states to populations of the V2 + 3, V3 ) 0 states, we obtain P1 - P4 ) 27, 26, 30, 15 as an estimate of the initial distribution in V1 levels. This distribution gives the surprisal plot in Figure 13b. The best linear fit gives λV1 ) -5.1 and λ01 = -2.0, which gives about 5% of molecules in the (000) and (010) states. We do not attach much importance to the λV1

J. Phys. Chem., Vol. 100, No. 12, 1996 4863

Figure 13. (a) Observed (s) and the prior (- - -) distributions for HDO from the OH + DBr reaction. Squares correspond to O-H stretch, and triangles correspond to mixed O-D stretch and bending vibrations. The experimental PV1,2 is nearly statistical. (b) Surprisal plot for the P1 distribution after adjustment for collisional redistribution (see text).

value, but use this approach to estimate the population of the dark states, which do not participate in collisional redistribution. IV.C. Surprisal Analysis for D2O. We followed the calculation scheme developed for H2O for the surprisal analysis of D2O. To calculate the prior V1,3 distribution, the experimental values for D2O quartic distortion constants35 were used. Prior and experimental distributions were compared. The linear surprisal gave λ01,3 ) -0.8 and λV1,3 ) -3.4. The intercept with λ01,3 gives a relative population of the V1,3 ) 0 level of about 14%, similar to that for H2O. As was already mentioned, data for D2O could be acquired only for 0.7 Torr and the experimantal distribution is partially relaxed, and the 〈fV〉 and |λV1,3| values consequently are lower than for H2O. V. Discussion V.A. State-Resolved Product Kinetics from H2O and HOD Infrared Chemiluminescence. The formation of water via H abstraction by OH radicals is an important reaction in a variety of environments. The measurement of these rate constants vs temperature and the development of state-of-theart transition-state theory models are active research areas. The present work has shown that infrared chemiluminescence for short reaction times in 0.5 Torr of Ar buffer gas provides a new tool for measuring H2O, HOD, and D2O vibrational distributions when combined with spectral simulation. It seems likely that time-resolved infrared chemiluminescence from a photolytic pulsed source of OH radicals would provide complementary information, and perhaps results could be obtained under conditions such that rotational relaxation could also be partly arrested. Since the ν1 and ν3 normal modes of H2O and D2O are linear combinations of local modes, the energy released to one bond would appear as ν1 and ν3 excitation, so the collisional coupling of the ν1 and ν3 levels is not a serious flaw in the method. The rapid equilibration in the ν1 and ν2 levels of HOD does result in loss of information. The normal modes of HOD are nearly pure local modes, and the nascent distribution in HOD could provide a more intimate view of the reaction

4864 J. Phys. Chem., Vol. 100, No. 12, 1996

Butkovskaya and Setser

TABLE 7: Summary of Energy Disposala and Comparison to Atom-Diatom Reactions reaction

〈Eav〉 kcal/mol

〈fV〉

〈fV2〉

〈fV〉/〈fV〉st

〈fV2〉/〈fV2〉st

〈fV1,3〉/〈fV1,3〉st

-λV1,3

ref

OH + HBr a H2O + Br OD + DBr a D2O + Brb

33.7 33.8

0.61 0.54

0.18 0.16

1.85 1.46

1.20 1.00

2.39 1.81

4.5

this work

reaction

〈Eav〉 kcal/mol

〈fV〉

〈fV1,2〉

〈fV〉/〈fV〉st

〈fV1,2〉/〈fV1,2〉st

〈fV3〉/〈fV3〉st

-λV3

ref

OD + HBr a HDO + Br OH + DBr a HDO + Br

33.1 34.3

0.65 0.57

0.25 0.34

1.81 1.58

0.93 1.26

4.60 2.64

6.1

this work

reaction

〈Eav〉 kcal/mol

〈fV〉

〈frot〉

O( P) + HBr a OH + Br F + HBr a HF + Br F + HCl a HF + Cl F + DBr a DF + Br F + DCl a DF + Cl F + HI a HF + I Cl + HI a HCl + I Cl + DI a DCl + I

22.0 51.0 36.3 51.5 37.0 67.2 34 34

0.51 0.59 0.51 0.58 0.52 0.59 0.70 0.69

0.24 0.13 0.18

3

0.12 0.13 0.13

-λV 5.4 5.5 5.4 5.5 4.5 8.0 8.0

ref 8 6

41

a 〈fV2〉 is the fraction of energy in bending vibrations and -λV1,3 is the surprisal slope for P1,3 stretching distribution. 〈fV1,2〉 is the sum fraction of energy in O-D stretching and bending vibrations, and -λV3 is the surprisal slope for O-H stretching distribution. 〈fV3〉 is the fraction of energy in the O-H stretching mode. b A partially relaxed vibrational distribution was used for analysis of this reaction.

dynamics. Fortunately, the relaxation rates for ν3 levels of HOD are slower than those in the ν1 + ν2 manifold, and the nascent distribution in ν3 from HOD formed by OD + HR reactions can be obtained by our experimental technique. A combination of the information from reactions 1 and 2 provides an overview of the energy disposal. One advantage of the HOD molecule is that both OH(ν3) and OD(ν1) emission can be analyzed to obtain estimates for (V1V2(V3 * 0)) and ((V1 * 0)V20) distributions. These distributions confirmed the linear surprisal extrapolation for the populations in the V3 ) 0 or V1 ) 0 levels from the HBr reactions. The O(3P) + HBr and F + HBr reactions have a minor channel yielding electronically excited Br*(2P1/2) with a branching ratio of about 0.06 relative to the formation of the ground state, Br(2P3/2).8a,42 Since the exoergicities of reactions 1-4 are within the range of the O + HBr and F + HBr reactions, a similar Br*/Br ratio might be expected. Inspection of the emission spectra gave no evidence for the Br* emission line at 3685 cm-1, but a 6% contribution probably would not have been observable. The available energy on the electronically excited potential surface, about 23 kcal/mol, is similar to that of the ground-state channel of the O + HBr reaction, and by analogy, the population would probably go to one quanta of O-H stretch. In any case, a 6% contribution to V1,3 or V3 ) 1 levels would not have an appreciable effect on the vibrational energy disposals for reactions 1-4, and we will assume that reactions 1-4 represent the interaction of OH radicals with HBr on the groundstate potential surface. The energy released to the vibrational modes is compared to the statistical expectation in Table 7. Reactions 1 and 2 give a mean vibrational energy of 〈fV〉 ) 0.61 and 0.65, respectively, and, hence, similar values of 〈fV〉/〈fV〉st equal to 1.85 and 1.81, respectively. Qualitative models and the analogy to X + HR reactions suggest that reactions should favor release of energy to the newly formed bond. Since the local mode description matches the normal modes for HDO, this qualitative view can be tested. The HDO molecules formed in reaction 2 should bear more energy in the O-H mode than in reaction 3, whereas the O-D mode is expected to be preferentially excited in reaction 3. Such a model does not provide insight into ν2 excitation. The excess energy in ν3 for OD + HBr over the

statistical is 〈fV3〉/〈fV3〉st ) 4.60. The rest of the vibrational energy is in the collisionally mixed manifold of O-D stretch + bending vibrations and does not differ much from the statistical energy 〈fV1,2〉/〈fV1,2〉st ) 0.93. The delocalization following excitation of a single O-H bond in H2O should lead to a predictable distribution between ν1 and ν3 normal modes, which, unfortunately, cannot be observed by our technique because of collisional mixing. Instead, we measure a common energy of the ν1,3 manifold that exceeds the statistical value by a factor of 〈fV1,3〉/〈fV1,3〉st ) 2.39. This value is quite consistent with the factor of 4.6 obtained for local O-H excitation, since the local mode in H2O is an equal mixture of the ν1 and ν3 normal modes,43 so that the statistically expected excitation in a local mode is one-half the statistical energy in ν1,3. These results confirm the concept of a “spectator” bond, suggested by Schatz in the quasiclassical trajectory study of the OH + H2 and OH + D2 reactions.9 In reaction 1 the excess energy in bending over statistical is 20%. Since these are direct reactions, some specific dynamics are necessary to produce bending excitation up to V2 ) 5. The excess vibrational energy of D2O over the statistical value is about 20% less than that for H2O, and the reduction in 〈fV2〉 and 〈fV1,3〉 are similar. Although we did not make a surprisal analysis of bending excitation for D2O, this energy is equal to the statistical value. The apparent reduced vibrational energy release to D2O relative to H2O is probably a consequence of some relaxation in the 0.7 Torr D2O experiment, and it is not an isotope effect on the energy disposal. For the OH + DBr reaction, we expect ν3 to behave as a “spectator” degree of freedom, but the energy in ν3 actually exceeded the statistical expectation by a factor of 〈fV3〉/〈fV3〉st ) 2.6. At the same time, the energy in the mixed ν1 and ν2 vibrations only slightly exceeded the statistical expectation, 〈fV1,2〉/ 〈fV1,2〉st ) 1.3. The unexpectedly low 〈fV1,2〉/〈fV1,2〉st and high 〈fV3〉/ 〈fV3〉st suggest that collisional redistribution of vibrational energy has occurred. The study of D abstraction reactions by OH or OD appears to be less useful than abstraction of H for purposes of assigning nascent product distributions. One of the reasons is that a large kinetic isotope effect and the reduced Einstein coefficient for OD emission requires experiments at elevated concentrations of reagents and longer reaction times, which enhances vibrational relaxation.

H Abstraction by OH Radicals V.B. Comparison to Dynamics for H Abstraction by Halogen or Oxygen Atoms. The distinctive features associated with the dynamics of the H + L-H reaction systems are also exhibited by reactions 1-4. As summarized in ref 2, these systems are characterized by a large release to product vibrational energy, 〈fV〉 ∼ 0.5-0.7, and the fraction of the energy, 1 - fV, available to each V level, is almost statistically shared between rotational and translational energy. The highest possible vibrational levels permitted by the thermochemical limit are experimentally observed in atom-diatom reactions. Furthermore, the rotational level populations for each V extend nearly to the limit of the available energy, i.e., an inverse correlation between EV and ER exists. A significant population in the highest available vibrational stretch levels of water was also found for reaction 1 (about 8%), reaction 2 (about 6%), and reaction 4 (about 5%). Bending excitation as high as V2 ) 5 for H2O from reaction 1 and V2 ) 7 for D2O from reaction 4 was observed in the V1,3 ) 1 stretch level, which approaches the thermochemical limit. These general properties related to the mixed energy release mechanism associated with the motion of the light mass of the transferred atom hold for reactions of both halogen atoms and OH radicals. A comparison of the vibrational energy release for OH(D) + H(D)Br reactions to the atom-diatom H + L-H reaction systems in Table 7 shows the detailed similarity. No significant difference was observed for D vs H transfer in the vibrational distributions for F + HBr and F + DBr reactions, giving 〈fV〉 ) 0.59 and 0.58, nor for F + HCl and F + DCl reactions with 〈fV〉 ) 0.51 and 0.52. These values are close to the mean vibrational energy of triatomic products from reactions 1-4. Surprisal plots for F atom reactions are linear with equal slopes for isotopic species, λV ) -5.4 for HBr and DBr and λV ) -5.5 for HCl and DCl, which are close to λV3 ) -6.1 for HDO from reaction 2. The λV1,3 values for H2O is substantially lower, but this is a result of different statistics for fV, which is a single degree of freedom, and fV1,3, which is the fraction for the mixed modes. In the present work we also do not observe any substantial difference between the fractional vibrational energy for D atom transfer by the OH + DBr reaction compared to H atom transfer by the OH + HBr reaction. The apparent difference for the OD reactions was explained by the partially relaxed distributions for D2O and HOD. The O(3P) + HBr reaction was studied by LIF measurements of O-H product state distributions and by quasiclassical trajectory calculations using a LEPS potential energy surface.8 The experimental distribution for OH is strongly inverted with ∼90% of the molecules in the V ) 1 state, and the rotational excitation extended to the limit of available energy. Very good agreement was obtained between the experimental and calculated fractional energy release to the vibrational and rotational degrees of freedom, although the calculation failed to reproduce the experimental observation of ∼10% population in V ) 2. A transition state with a low-bending frequency was required to fit the rotational distribution. The bending frequency of the transition state seems to be an important factor in the partitioning of energy between translational and rotational degrees of freedom for the H + L-H system.8b Clary’s potential for OH + HBr was built from a LEPS description of the O + HBr reactive interaction plus a switching function to include the interactions of the hydroxy H atom. Clary’s potential fits the general properties of reaction 1 in that no formal potential barrier exists and the asymptotic properties are correct. In the future we will compare quasi-classical trajectory results on this surface to our experimental data. The preliminary results already show that the H + L-H kinematics

J. Phys. Chem., Vol. 100, No. 12, 1996 4865 dominates the dynamics for release of vibrational energy just as the empirical comparison in Table 7 suggests. However, additional considerations are needed to explain the partitioning of energy between the stretch and bending modes and the role of product and reactant rotational energy. V.C. Comparison to a Quantum Model for the OH + HBr Reaction. The vibrational distribution for H2O from reaction 1 is in general agreement with the results of the theoretical study of Clary et al.,11 where the rotating bond approximation was used in quantum-scattering calculations of the specific cross sections for the OH(j, K) + HBr(V ) 0) f H2O(m, n) + Br reaction, where j is the OH rotational angular momentum, K is its projection along the intermolecular axis, and m and n are the bending and local stretching vibrational quantum numbers, respectively. For the OH(j, K) + HBr reaction at thermal energies, the most probable product vibrational state of H2O was the combination level that has one quantum of energy in the H2O bending mode and one quantum in the local OH stretching mode. This finding suggests that the most likely product states of H2O will be the (1, 1, 0) and (0, 1, 1) vibrations in the triatomic normal mode notation or (1, 1) in our (V1,3, V2) representation. The favorable population of this state was explained by the avoided crossing of the OH(j, K ) j) + HBr and Br + H2O(1, 1) adiabats in the region of the potential ridge combined with the fact that the reaction cross section is large for the OH(j, K ) j) states and much smaller for j > |K| ones. Besides, they showed that other vibrational states of H2O, such as (1,2), (2,0), and (2,1), are quite close to the crossing point of the OH(0, 0) + HBr adiabat with the Br + H2O(m, n) surface, and these product states would be also populated. Our experimental results suggest that the bending excitation is relatively probable and that another mechanism in addition to the correlation with OH rotational states needs to be sought. Our results also confirm features found for the exothermic OH + H2, OH + D2, and H2+ + H2 direct reactions in the quasi-classical trajectory study of Schatz;9 excitation of stretch modes is accompanied by significant excitation of the bend mode and none of the vibrational distributions are statistical. Identification of the dynamics that specifically releases energy to bending modes of triatomic molecules will require a systematic investigation of model potentials. VI. Conclusions Infrared chemiluminescence from H2O, HOD, and D2O can help in the elucidation of the dynamics of H atom abstraction reactions by OH or OD, as illustrated by the current study with HBr and DBr. Product vibrational distributions were obtained by development of simulation methods to fit the experimental spectra. The rotational distributions were assumed to be 300 K Boltzmann. Spectra from H2O levels extending to 12 200 cm-1 of energy were required for analysis of the HBr reaction. The reliability of the modeling strongly depends upon the data base of transition frequencies and strengths for the absorption bands of the isotopic water molecules. The lack of knowledge about bands with bending excitation V2 > 3 restricts the reliability of the assignment of distributions for bending excitation in H2O. A better knowledge of band center positions and integral intensities for combination bands up to 18 000 cm-1 is desirable for extending the method to reactions with higher exoergicity, for example, the OH(OD) + HI reaction. Because of rapid equilibration of nearly isoenergetic ν1 and ν3 levels of H2O (and D2O), only the vibrational distribution, P1,3, and bending distributions, P2(V1,3), can be obtained for H2O and D2O molecules. The equilibration of ν1 and 2ν2 levels of HOD gives the mixed stretch-bend distribution, P1,2, for the

4866 J. Phys. Chem., Vol. 100, No. 12, 1996 HOD molecule, but the larger vibrational quanta for the OH stretching mode in HDO allow measurement of the distribution in the O-H bond, P3. Hence, the OH + HR and OD + HR reactions complement each other, the former giving a clear insight into the product bending excitation and the latter providing data on the local excitation in the new bond. The D atom abstraction reactions are less useful in the present experimental apparatus because of the lower rate constants, smaller Einstein coefficients, and faster relaxation of O-D (V1) levels in HDO. The experimental measurements give steadystate vibrational distributions. However, we argue that the vibrational distributions assigned from the 0.5 Torr spectra are nearly unrelaxed, except for the nearly isoenergetic levels mentioned above. The vibrational energy disposal for the OH + HBr f H2O + Br and analogous deutero reactions agrees with the principal dynamical features found for H + L-H atom-diatom reactions. The overall 〈fV〉 is ∼0.6 with 〈fV3〉 = 0.4 and 〈fV2〉 = 0.2, and the vibrational surprisal plots are linear. Linear extrapolations of surprisal plots were used to determine V3 ) 0 and V1,3 ) 0 contributions. This method was confirmed by analysis of the OD emission (V1 g 1) from HOD. A new finding, specific for triatomic products, is that high excitation in stretching vibrations is accompanied by bending mode excitation, which extends to the thermochemical energy limit. The implication is that the dynamics associated with rotational energy released to H2O may differ from that of the F + HBr generic class of reaction. The release of ∼60% of the available energy into H2O or HOD vibrations is consistent with the requirement of vibrational excitation of H2O or HOD to drive the reverse reaction, as has been found for the Cl + H2O(HOD) reaction.44 Acknowledgment. This work was supported by the National Science Foundation, CHE-9505032. N.I.B. is particularly thankful to the Russian Foundation for Fundamental Research for support that aided development of the spectral simulation methods. The authors thank Mr. Gerald Manke II for valuable help with some experimental work. References and Notes (1) (a) Levine, R. D.; Bernstein, R. B. Molecular Reaction Dynamics and Chemical ReactiVity; Oxford University Press: New York, 1987. (b) Bernstein, R. B.; Levine, R. D. Role of Energy in ReactiVe Molecular Scattering: An Information-Theoretic Approach; Bates, D. R., Ed.; Advances in Atomic and Molecular Physics, Vol. 11; Academic Press: New York, 1975; p 216. (2) Holmes, B. E.; Setser, D. W. In Physical Chemistry of Fast Reactions; Smith, I. W. M., Ed.; Plenum: New York, 1980; Vol. 23, p 83. (3) (a) Sloan, J. J. J. Phys. Chem. 1988, 92, 18. (b) Alagia, M.; Balucani, N.; Casevecchia, P.; Stranges, D.; Volpi, A. A. J. Chem. Soc., Faraday Trans. 1995, 91, 575. (4) Agrawalla, B. S.; Setser, D. W. In Gas Phase Chemiluminescence and Chemiionization; Fontijn, A., Ed.; Elsevier: Amsterdam, 1985. (5) (a) Agrawalla, B. S.; Setser, D. W. J. Phys. Chem. 1986, 90, 2450. (b) Agrawalla, B. S.; Setser, D. W. J. Chem. Phys. 1987, 86, 5421. (6) Tamagake, K.; Setser, D. W.; Sung, J. P. J. Chem. Phys. 1980, 73, 2203. (7) Kruss, E. J.; Niefer, B. I.; Sloan, J. J. J. Chem. Phys. 1988, 88, 985. (8) (a) McKendrick, K. G.; Rakestraw, D. I.; Zhang, R.; Zare, R. H. J. Phys. Chem. 1988, 92, 5530. (b) Persky, A.; Kornweitz, H. Chem. Phys. 1989, 133, 415. (9) Schatz, G. C. J. Phys. Chem. 1995, 99, 516. (10) Neuhauser, N. J. Chem. Phys. 1994, 100, 9272. (11) Clary, D. C.; Nyman, G.; Hernandez, R. J. Chem. Phys. 1994, 101, 3704. (12) (a) Nyman, G.; Clary, D. C. J. Chem. Phys. 1994, 100, 3556. (b) Nyman, G.; Clary, D. C. J. Chem.Phys. 1994, 101, 5756.

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