Product State Distributions and Angular Differential Cross Sections

J. Phys. Chem. 1995, 99, 9843-9853

9843

Product State Distributions and Angular Differential Cross Sections from Photoinitiated Reactions of Chlorine Atoms with Small Hydrocarbons David F. Varley and Paul J. Dagdigian" Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218-2685 Received: January 24, 1995; In Final Form: April 3, 1995@

The internal state distributions of HCl products from the reactions of C1 atoms with methane, propane, and isobutane are reported. These measurements were carried out using state-selective detection of the HCl(v,J) vibration-rotation states by resonance-enhanced multiphoton ionization (REMPI) in a time-of-flight mass spectrometer. The reactions were initiated in a crossed, pulsed-flow of the reagents by 355 nm photolysis of Clz to produce the C1 atom reagents. The rotational state distributions in the observed HCl(v = 0 and 1) vibrational levels were found to be quite cold. The relative intensities of REMPI signals for the detection of v = 0 and 1 products were compared in order to gain a measure of the degree of vibrational excitation. Because of the known speed and angular distribution of the C1 reagents, it was possible to obtain information on the product center-of-mass angular distribution from measurement of the product laboratory velocity distribution; the latter could be derived from the observed mass 36 time-of-arrival profile. The HCl(v = 0) product from the C1 isobutane reaction was found to be mainly backward scattered with respect to the incoming C1 atom. These observations of the product intemal state distributions and angular distribution are consistent with a mechanism involving abstraction of hydrogen atoms from the hydrocarbon reagent through a collinear C1-H-R geometry.

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1. Introduction In contrast to the extensive number of studies of the dynamics atoms with saturated of reactions of fluorine' and hydrocarbons, there have been relatively few dynamical investigations of the corresponding reactions involving chlorine atoms. The latter class of reactions have, however, been extensively studied in kinetics experiments6-l0 because of their importance as a temporary sink for chlorine atoms in the stratosphere." Park et a1.I2have detected the DCl product from the reaction of C1 with deuterated cyclohexane by infrared absorption spectroscopy and have derived the nascent rovibrational state distribution. They also derived information on the product translational energy release from Doppler spectroscopy. Simpson et al.I3 have used resonance-enhanced multiphoton ionization (REMPI) in a time-of-flight mass spectrometer ( T O M S ) to observe HCl(v = 1) products from the reaction of C1 atoms with vibrationally excited CHq (v3 = 1). From analysis of the mass 36 time-of-arrival profile, they were able to characterize the center-of-mass (c.m.) angular differential cross section of the HCl product. Yen et al.I4 have also used REMPI detection in a T O M S in order to study the reaction of C1 atoms with selectively deuterated propane isotopomers, in order to probe the relative reactivity of specific sites in the hydrocarbon reagent. Because of the near equality of the OH and HCl bond dissociation energies,I5 the exothermicities of the analogous oxygen and chlorine atom reactions are very similar, and they should have similar kinematics since they involve approximately the same combination of masses (heavy light-heavy heavylight heavy reaction). Nevertheless, the activation energies for the O(3P) hydrocarbon reactionsI6-l9 are considerably higher than those of the corresponding C1 hydrocarbon reactions.6-8.'0 Both classes of reactions are believed to proceed by direct dynamics. A linear 0-H-CH3 transition state has been calculated for the O(3P) CH4 reaction,20and similarly

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Abstract published in Advance ACS Absrracts, June 1, 1995.

0022-3654/95/2099-9843$09.00/0

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for C1 CH4.21-23A linear transition state is consistent with the results from a number of studies of the nascent OH product internal state distribution from the reaction of O(3P) with saturated hydrocarbons and other classes of organic molecule^?^^^^^-^^ For these reactions, the product vibrational excitation was found to increase with increasing reaction exothermicity, while in all cases very little of the available energy appears as product rotational excitation. These observations were reconciled with classical trajectory calculations on model potential energy

surface^.^ The observations of Park et a1.I2 present a similar picture for the dynamics of the C1 c - C ~ D Ireaction Z as that described above for the O(3P)reactions and are consistent with a collinear C1-D-R recoil. They found that little of the available energy in the C1 C-cgD12reaction appeared as DC1 product rotational excitation. Moreover, much of the available energy is released as product translational energy. In the study of Yen et a1.,I4 differences in the reactivity of primary vs secondary hydrogen atoms were explored. For the reaction of O(3P) atoms with hydrocarbons, it has been possible to correlate approximately the entropy of reaction and the activation energy with the number of different types of hydrogen atoms in the hydrocarbon reagent and to describe the rate constants by an additivity r e l a t i ~ n . ~Such ~ , ~ a~ correlation is less successful with the reactions of C1 atoms, in part because of the smaller activation energies for these reactions.8 Nevertheless, Yen et al.I4 find for the reaction of C1 with propane that abstraction of a secondary hydrogen atom is favored over primary hydrogen abstraction, presumably because of the greater exothermicity for the former pathway.'0.31 There has been considerable recent interest in the utilization of photoinitiated reactions in a bulb for the determination of product c.m. angular distributions and vector correlations for specific intemal Here, one takes advantage of the anisotropy of the angular distribution of the photolytically prepared reagent to generate an anisotropic distribution of reaction products. Shafer et al.37 showed that in favorable

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0 1995 American Chemical Society

Varley and Dagdigian

9844 J. Phys. Chem., Vol. 99, No. 24, 1995 kinematic cases it is possible to extract the c.m. angular distribution from measurement of the product laboratory velocity di~tribution.,~Thus, it is possible to determine angular distributions of products in specific internal states in a bulb experiment. In this way, Simpson et al." have derived the c.m. angular distribution for HCl(v = 1) products in several rotational levels for the C1 CH4(v3 = 1) reaction, with the atomic reagent formed by photolysis of Cl?. In this experiment, a vibrationally excited CH4 reagent was prepared by infrared excitation with an optical parametric oscillator. Their results present a very different picture for the dynamics of the reaction of C1 atoms with vibrationally excited methane. They find that the vibrationally excited HCI products are scattered predominantly in the forward direction with respect to the C1 reagent. In addition, the remaining available energy is channeled primarily into product recoil, rather than internal excitation of the CH, product. Thus, the dynamics of this reaction pathway is different from that deduced for the reaction of O(3P)with hydrocarbons. In view of the relatively sparse number of experiments probing the dynamics of the reactions of C1 atoms with hydrocarbons, we have also undertaken experiments to probe the dynamics of these reactions. In this paper, we report the nascent HCl product internal state distribution from the reaction of C1 atoms with an homologous series of alkanes, namely, methane, propane, and isobutane, all in their ground vibrational states. The exothermicities of these reactions vary considerably.'() The C1 CH4 reaction is slightly endothermic:

(a)

mirror

lens

+

+

C1+ CH4

-

HCI

+ CH,,

AHo = +7.2 kJ mol-'

(1)

Truong et al.?' calculate the ground vibrationally adiabatic barrier height of reaction 1 to be 14.6 kJ mol-', which is consistent with the measured temperature dependence of the thermal rate constant.'" In the reactions involving propane and isobutane, there are two reaction pathways, with considerably different exothermicities:

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+ n-C3H7, AW = -8.4 kJ mol-' (2a) - HCI + i-C,H7, AW = -20.1 kJ mol-' (2b) C1 + i-C4Hlo- HCI + i-C4H9, AHo = -8.4 kJ mol-'

C1+ C3Hx

HCI

-

HCI

+ r-C4H9,

AW = -29.4 kJ mol-' (3b)

The exothermicities of reactions 2a and 2b were taken from a recent compilation of rate constants of atmospherically relevant reactions.'() The exothermicity of reaction 3b was calculated using the recently established heat of formation of the rerrbutyl radical;3xthe exothermicity of reaction 3a was assumed to be equal to that for reaction 2a since both involve the abstraction of a primary hydrogen atom. The baniers to reaction for the C1 C3Hx and i-C4H10 reactions are small since the rate constants for both have only a small (and slightly negative) temperature dependence.x The considerable differences in reaction exothermicities and activation barriers suggest that a probe of collision dynamics through the measurement of product HCl internal state distributions would provide insight into specific reaction mechanisms.

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2. Experimental Section

In this study, the hydrocarbon reagents are allowed to react with chlorine atoms, prepared by 355 nm photolysis of Clz. We

4ind.p. 6ind.p.

(b) dual MCP detector

einzel outer kV)

fli ht tube ( - f 7 kv)

accel. 2

/ ; I einzel deflectors inner accel. i G1 ' G4 (adi.) (-250 V)

CI2 pulsed valve

probe 238-247laser n

hydrocarbon pulsed valve w time-of-flight axis

photolysis laser 355 nm

outer guard electrode (G4)

Figure 1. (a) Schematic diagram of the experimental apparatus; (b) detail of the electrode structure in the time-of-flight mass spectrometer; (c) detail of the configuration of the two beam sources within the ionization-extraction region of the TOFMS. The ions are formed at the focus of the lasers, denoted I in panel b. The flight tube and einzel lens lengths (shown not to scale in panel b) are 0.74and 0.25 m, respectively. The cross-hatched centers of the electrodes represent high-transmission meshes over the openings.

probe HCl products in specific vibration-rotation states by 2 1 REMPI detection. The reaction takes place in the ionization-extraction region of a newly constructed TOFMS. The general arrangement of the apparatus, which consists of a differentially pumped vacuum system, TOFMS, reagent injection system, and copropagating laser beams, is illustrated in Figure la. The vacuum system has two chambers, housing the ionization-extraction region (reaction chamber) and the flight tube, both evacuated by trapped oil diffusion pumps. The reaction chamber is pumped by a cold trapped (-50 OC) 6 in. diffusion pump, and the flight tube chamber is pumped by a 4 in. liquid nitrogen trapped diffusion pump. The two chambers are separated by a differential pumping wall with a 1.2 cm diameter aperture. The base pressure in both chambers is (510) x Torr. The typical pressure in the source chamber when the reagents are being admitted is (2-5) x Torr. Under these conditions, the pressure in the flight tube does not exceed 8 x Torr. The experiment is operated at a 10 Hz repetition rate. The TOFMS constructed for this experiment is a WileyMcLaren type,39 with two acceleration regions. Figure 1b presents a schematic diagram of the TOFMS, with typical electrode voltages indicated. Following the ionization-extraction region, we employ two sets of deflection electrodes for beam steering and an einzel lens for beam collimation. The ions then enter a field-free region and finally strike a dual microchannel plate (Galileo type N, with 2.54 cm diameter), whose output is monitored with either a digital oscilloscope (LeCroy Model 9360, 300 MHz analog bandwidth input employed, maximum sampling rate 5 Gsh) or a gated integrator (Stanford Research Systems Model SRS250). The output of the gated integrator was digitized and accumulated by a laboratory computer, and the data were stored on magnetic media for subsequent analysis. Likewise, waveforms ac-

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Photoinitiated Reactions of Chlorine Atoms cumulated with the digital oscilloscope were saved on magnetic media. In this way, either the mass spectrum or the time profile of a given mass channel can be recorded. The total ion flight path in the TOFMS was 1.03 m. We have also added the provision for pulsing an electrode for mass gating>0.4'but this feature was not required for the experiments described in this paper. All electrode potentials were set so that the T O W S operated under near space-focusing conditions. While we have not undertaken an exhaustive study of the instrument resolution, we obtain a time separation of 140 ns between masses 35 and 36, and we can easily discriminate against C1+ ions from the Cl2 precursor and selectively detect HCl+ ions. The reactions take place in the ionization-extraction region of the TOFMS. In our original set of experiments, the Clz photolytic precursor for C1 atoms and the hydrocarbon reagent were premixed and injected into the TOFMS with a pulsed valve. Simpson et al.'? and Yen et al.I4 employed an analogous injection scheme. While this injection method is simple mechanically and offers advantage^'^ in the determination of c.m. angular distributions from the experimental data (because of a reduction in the relative velocities of the Cl2 and hydrocarbon species), prereaction of the reagents can limit observation of the products of the photoinitiated reaction. Indeed, preliminary experiments with our apparatus indicated that prereaction was a significant problem. Accordingly, we have separated the reagents and in later sets of experiments injected them into the TOFMS through two separate pulsed valves. This ,arrangement adds significant complexity over a one-valve source but allows much greater flexibility in the choice of reagents. While the C12 and hydrocarbon reagents suffer from a "mild" chemical incompatibility, our two-valve arrangement will allow the study of reactions of species which have a more vigorous interaction if premixed. Our reagent injection system is located in the center of the 3 cm long ionization-extraction region and is illustrated in Figure IC. Each valve (General Valve series 9) is mounted 45" from the vertical so that the reagent expansions intersect at 90". The valve orifices (0.5 mm diameter) are located 1 cm from the TOFMS axis. To prevent discharges inside the reagent sources, the pulsed valves and orifice mounts (stainless steel) are all kept at ground potential. We estimate the interaction volume to be 0.5-1 cm3. The copropagating photolysis and probe lasers intersect the gas flow on the TOFMS axis. Since the operation of a TOFMS relies on a homogeneous acceleration field across the ionization region, we have added four adjustable guard electrodes (Gl, G2, G3, and G4 in Figure lb) in the ionization region to ensure that the equipotential lines experience minimal distortion from the source assembly. A uniform field is also required for the extraction of translational energy distributions from mass peak profiles. The voltages on the guard electrodes were initially set to values appropriate in the absence of the pulsed valves. Under typical experimental conditions, the guard electrodes must be varied by only a small amount from these ideal values. We find that G1 and G4 require little adjustment, while G2 and G3 need some adjustment in an experiment. The good performance of the TOFMS and the agreement of the observed and calculated mass 35 and 36 time separations indicate that our guard electrode arrangement corrects for the perturbation in the first accelerationfield induced by the source assembly. We also monitor the performance of the TOFMS by REMPI detection42of the C1 products from the photolysis of C12. With the guard electrodes properly adjusted, the mass 35 peak profile has the shape expected for the

J. Phys. Chem., Vol. 99, No. 24, 1995 9845

perpendicular @ = -1) dissociative transition in c12>3 as discussed in detail in section 3.2. Chlorine atomic reagents, predominantly in their ground 2P3/2 spin-orbit are produced by 355 nm photolysis of Cl2 with the third harmonic output from a Continuum NY81C Nd: YAG laser. The frequency-doubled output of a XeCl excimer laser pumped dye laser (Lambda Physik EMGlOlMSC and FL3002) is employed as the probe laser and is used for REMPI detection of the C1 reagents and HC1 products. The photolysis and probe laser beams (1 and 0.2 cm diameter, respectively) are combined with a dichroic beam splitter and are focused into the center of the TOFMS ionization-extraction region with a 40 cm focal length fused silica lens. The pulse energies of the laser beams are typically 35 and 0.5 d, respectively, and their estimated respective focused spot sizes are 0.1 and 0.02 cm diameter. The timing of the experiment is controlled with an extemal master oscillator (Stanford Research Systems DG535 digital delay generator). The pulsed valves are first fired. The 355 nm photolysis laser pulse is delayed by ca. 1 ms to allow for the opening of the pulsed valves. After a variable delay (100200 ns), the probe laser is fired to ionize the HC1 reaction products. As discussed in detail in the next section, either mass 1 (H+) or 36 (HCl+) is employed in the REMPI detection of the HC1 products. The dependence of the REMPI signals on the photolysis-probe delay was found to be essentially identical for all product HCl rotational levels for a given reaction. For the determination of HC1 product internal state distributions, the photolysis-probe laser delay was set to the time (120- 140 ns) approximately corresponding to that yielding maximum signal. The product REMPI signal were recorded in two ways. In some experiments, the probe laser wavelength was scanned over the HCl REMPI transitions. This did not lead to the most accurate measurement of HC1 internal state populations since there was still some HC1 contaminant in our apparatus. Altematively, the probe laser was fixed at the wavelength of a transition out of a given HC1 state, and the signal monitored while photolysis laser was tumed on and off. The signal due to the HCl reaction product was taken as the difference of these two signals. In some runs, mass peak profiles for the reaction products were obtained by taking difference of the waveforms accumulated over many laser shots with the photolysis laser on and off. Typical mass peak profiles require 2000-3000 shots to obtain adequate signal-to-noise ratios. As mentioned above, a dual reagent injection system was constructed to suppress the formation of HCl background. We have also found it necessary to purify the C12 reagent. For this purpose, we have constructed a glass vacuum manifold for the purification and handling of the Clz reagent. All glass bulbs used for handling C12 were evacuated to 5 x lop6 Torr. Chlorine was obtained from Matheson (UHP Grade, 99.9%) and was purified in the following manner. A sample was first condensed with liquid nitrogen and pumped on to remove noncondensable species. It was then warmed to -131 OC (npentane slush) and pumped on to remove HC1; at this temperature, the vapor pressure of HC1 is 40 times larger than that of C12.44 Gaseous samples of Cl2 were then prepared (7-10% diluted in helium, at a total pressure of 900 Torr) in glass bulbs shielded from room lights; the glass bulbs were connected to the pulsed valve with Teflon PFA tubing. Methane (Airco prepurified grade, 99%), propane (Matheson instrument grade, 99.5%), and isobutane (Matheson instrument grade, 99.5%) were used without further purification. Methane was employed in the pulsed valve in a neat expansion, while

9846 J. Phys. Chem., Vol. 99, No. 24, 1995


the heavier hydrocarbons were diluted 70:30 with helium. Typical backing pressure in the pulsed valve was 700-900 Torr. The hydrocarbon gas handling system was also evacuated to a base pressure of Torr.

3. Results 3.1. Determination of Product HCl Internal State Distributions. The E'Z+-X'E+ and F'A-X'Zf band systems, which can be excited in the wavelength range 238-247 nm, were employed for 2 1 REMPI detection of the HCl products of reactions 1-3. The REMPI spectrum of HCl has been extensively studied by G ~ r d o n : ~ ,Wallace$6 ~~ Chandler:7,48 and their co-workers. These two band systems are among the strongest HCl two-photon transitions and offer complementary advantages for the detection of the HCl reaction products. Unfortunately, the E ' F and F'A electronic states are both significantly perturbed, as evidenced by anomalous variations of vibrational level spacings and rotational constants with the vibrational quantum number v'!~ Additionally, 2 1 REMPI detection through the E'C+ state is found to yield both the parent HCl+ ion, as well as fragment ions.45,47,48 The spectroscopic perturbations in these excited states also lead to variations in the ion yield for excitation through various excited rovibronic levels. Hence, the ion signals are not directly proportional to the two-photon line strengths for excitation, and an experimentalcalibration procedure is the most straightforward way to relate the signals to the HCl(X'Z+,v,J) populations. Such a procedure has been employed to determine calibration factors for detection of HC1 rotational levels through several bands in the E-X and F-X band s y ~ t e m s . ~Both ~ . ~Spiglanin ~ et al.47 and Xie et al.45 find that the REMPI intensities drop off with increasing J in the E-X(0,O) band, while the parent to fragment ion intensity ratio is constant with J. The Q branch lines are by far the strongest transitions in this band system; this indicates that the two-photon E X electronic transition is dominated by the zero-rank absorption tensor. Xie et al.45have determined calibration factors for various rotational transitions within the (0,O) and (1,O) F-X bands. They find that the REMPI intensities are depressed in the former band for 3 J' < 10 and for J' > 5 in the latter band. Thus, the E-X(0,O) band is useful for detection of HCl(v = 0) rotational levels of low J , while the F-X(0,O) band is advantageous for detection of high J levels. We have employed the calibration factors measured by Rohlfing et aL4*for the E-X(0,O) and (0,l) bands and those measured by Xie et al.45for the F-X(0,O) and (1,O) bands for the conversion of ion signals to relative rotational populations. We have taken the correction factors for the F-X (1,l) band to be the same as for the (1,O) band, as Gordon and c o - ~ o r k e r s ~ ~ have also assumed. The determination of HC1 vibrational population ratios is more problematic. Because of the perturbed nature of the excited states, calculation of the strengths of various (v', v) bands is not expected to be reliable. For H2 and its isotopomers, Zare and c o - w ~ r k e r shave ~ ~ employed a high-temperature oven for the calibration of REMPI intensities for detection of various vibrational levels. A similar experimental calibration for REMPI measurement of relative HC1 vibrational populations will be required. In our initial experiments for the determination of HC1 rotational populations in the v = 0 vibrational level, we employed the E-X(0,O) band for REMPI detection. Figure 2(a) presents representative scans over this band. We employed the E-X(0,l) band for detection of rotational levels within the v = 1 vibrational level. A scan over this band is presented in Figure 2b. Since both these transitions have been observed through detection of the H+ ion signal, both H 3 T l and H37Cl

(4

~ 3 5 E~- 1 x ~

5

4

3

(o,o) Q 2

1 0

+

83675 83700 83725 83750 83775

+

+ -

two-photon wavenumber (cm-') Figure 2. REMPI spectrum of the H35Clproduct from the reaction of C1 atoms with (a) isobutane and (b) propane at a photolysis-probe delay of 140 ns. The plots show the mle = 1 signal as a function of the two-photon laser wavenumber. Assignments of rotational lines in the (a) (0,O) and (b) (0,I) bands of the H 3 T l E'Z+-X'X+ transition are marked.

products are detected. The E-X(0,O) band displays an isotope splitting (2.1 cm-' 46,5') which is easily resolved under our experimental conditions. However, the E-X(0,l) band lacks isotopic fine structure, as noted previously by Rohlfing et al.48 Although we have not so indicated in Figure 2b, the VIE+X'z1+(6,0) band falls within the same spectral region as the E-X(0,l) and the Q(1) and Q(2) lines of the former overlap the Q(0) and Q(1) lines, respectively, of the latter. However, the V-X band is considerably weaker than the E-X band48and is not discernible in our spectra. The former band would show a 2.6 cm-' isotope which we do not observe. Figure 3 presents scans over the F-X(0,O) band. The survey scan in panel (a) around the origin of the band dramatically illustrates the effect of the perturbations on the intensities of individual rotational transitions. We see a sharp drop in the intensities of lines in the R branch; the signal on the R(3) line is quite. small compared to that on the R(2) line. Comparison of the rotational intensities in this band and the E-X(0,O) band shows that this drop is not the result of a low J = 3 population; rather, it is a result of the perturbations in the F state. The Q branch of this band, shown in Figure 3b, provides a convenient probe, over a spectrally compact region, of the populations of high-J rotational levels. The intensities of the Q( 10) and Q( 11) lines appear to be enhanced compared to the intensities of the lower-J Q lines. This enhancement results from the reduction in the REMPI intensity factors for the latter lines.45 We have employed the E-X and F-X bands to derive rotational state distributions of the HC1 products in the v = 0 and 1 vibrational levels for reactions 1-3. Specifically, the E-X(0,O) band was used to determine the relative populations of rotational levels J 5 6 in the v = 0 vibrational level, while

Photoinitiated Reactions of Chlorine Atoms

(4 R l

F-X(0,O)

1

J. Phys. Chem., Vol. 99, No. 24, 1995 9847

SI 0

1

2

3

4

2 3 E?a

i

Q J

.? Y

m

e

g

."6 Y

m 1

e

3 a

:

.I

Y

m

3

g rotational level J 82820

82830

82840

Figure 5. Measured rotational state distributions for HCI products in the (a) v = 0 and (b) v = 1 vibrational levels from the reaction of C1 atoms with propane. The distributions are normalized so that the sum of the rotational populations is unity for each vibrational level.

82850

two-photon w a v e n u m b e r (cm-') Figure 3. REMPI spectrum of the HC1 product from the reaction of CI atoms with isobutane at a photolysis-probe delay of 140 ns. The plots show the mle = 36 signal as a function of the 2-photon laser wavenumber. Panel (a) shows a survey scan over the region around the origin of the HC1 P A - X ' F (0,O) band, while panel (b) displays a detailed scan through the Q branch of this band. Assignments of rotational lines in this band, as well as the V'X+-XIP (9,O) band, are given.

0.5

(a)

0.3

1

1

1

0.2 I 0

1 0

I

I

1

2 3 4 5 6 rotational level J

1

I

I

I

I

i

7

8

Figure 4. Measured rotational state distribution for HC1 products in the v = 0 vibrational level from the reaction of C1 atoms with methane. The distribution is normalized so that the sum of the rotational populations is unity. The estimated experimental uncertainties are indicated.

T

I

1

0

1 0

2

4

6

8

1

0

1

2

rotational level J Figure 6. Measured rotational state distributions for HCI products in

the high-J tail was determined from the intensities of lines in the Q branch of the F-X(0,O) band. The E-X(0,l) band was used to determine rotational populations within the v = 1 level. We note that we have used the H+ fragment ion to monitor REMPI transitions through the E state. Previous work4' has demonstrated that the fragmentation pattern is independent of the rotational level of the intermediate excited state. Figures 4-6 display the derived nascent product HCl(v, s) populations for reactions 1-3. All of the distributions are

the (a) v = 0 and (b) v = 1 vibrational levels from the reaction of C1 atoms with isobutane. The distributions are normalized so that the sum of the rotational populations is unity for each vibrational level.

normalized so that the sum of the rotational populations is unity for each vibrational level of a given reaction. For the C1 f C& reaction (see Figure 4),we were able to observe HCl(v = 0) products only for J 5 4. This state distribution was the most difficult to determine since the HCl product signals


9848 J. Phys. Chem., Vol. 99, No. 24, 1995 from this reaction were approximately an order of magnitude smaller than those from the more exothermic reactions 2 and 3. It can be seen that the product rotational state distribution for reaction 1 is quite cold; the average rotational excitation is 0.7 W mol-'. We observed HC1 products in both the v = 0 and 1 vibrational levels for reactions 2 and 3. Comparison of Figures 4 and 5 shows that the product rotational excitation is significantly greater for the reaction with propane vs methane. For the C1 C3Hg reaction, the rotational state distribution is quite similar for v = 0 and 1, with the most probable J = 1 for both vibrational levels. The major difference is that the high-J tail in the v = 1 distribution appears to cut off at J % 6, while the tail for v = 0 extends to slightly higher J. The average rotational excitation is 1.4 and 1.0 kJ mol-' for the v = 0 and 1 products, respectively, from reaction 2. We see from Figure 6 that the product rotational state distribution for the C1 i-CdH10reaction is significantly hotter and extends to high values of J ( ~ 1 2 ) than for the reactions of the smaller hydrocarbons. We also observe that the high-J tail cuts off at J x 7 for v = 1 and the degree of rotational excitation is less for products in the v = 1 vibrational level than for v = 0: the average rotational excitation for v = 0 and 1 products is 2.1 and 1.3 kJ mol-', respectively. As discussed previously, the relevant ratios of REMPI line strengths are not yet available for the determination of ratios of HCl product populations in the v = 0 and 1 vibrational levels. Since the F-X(0,O) and (1,l) bands appear to be the most convenient bands for measuring this population ratio, we have measured relative REMPI intensities for detection of HCl(v = 0 and 1) products, in the same rotational level J, from reaction 2 and 3. Since the rotational constants for the X'C+ and F ' A states are very similar in magnitude,46we might expect the (0,O) and (1,l) Franck-Condon factors, and hence band strengths, to be similar, provided that state mixing effects are not large. When the relevant intensity factors become available, it will then become possible to convert our measured intensities to relative populations. At the present time, we arbitrarily assume that the relationship between REMPI intensity and rotational population is the same for excitation in the (0,O) and (1,l) bands, Le., that the band strengths are the same. This allows us to compute the ratio of the population in the (v = 0, J) and (v = 1, J) levels, for the particular level J interrogated in both bands. With our knowledge of the rotational distributions in both vibrational levels, we can then derive the ratio of vibrational populations. For the C1 f C3Hg reaction, we have compared the REMPI intensities for excitation of both the R( 1) and the R(2) lines in both bands and obtain the same ratio (0.13 f 0.02) of v = 1 to v = 0 vibrational populations (summed over all rotational levels) with these transitions. We have employed the R(1), R(2), and Q(2) lines in the (0,O)and (1,l) bands for the determination of the HC1 product vibrational populations for the C1 i-C4H10 reaction. For this reaction, we derive a v = 1 to v = 0 population ratio of 0.10 f 0.02, independent of the lines employed. When the relative intensity factors relating REMPI signal strengths to vibrational populations become available, these quoted apparent population ratios can be converted to true population ratios. For the interpretation of our measured product internal state distributions, it is of great interest to calculate E,,, the total energy available to the products. The Appendix presents calculations of the initial relative translational energy distributions for the three reactions studied. Unfortunately, photolytic preparation of the C1 atom reagent in our two-beam experimental

l

+

+

+

-120

"

l

"

l

-60

"

l

"

1

~

0 60 time (ns)

120

Figure 7. Measured mass 35 peak profile for REMPI detection of C1 atoms from the 355 nm photodissociation of Clz. The photolysis laser polarization is perpendicular to the TOFMS axis, and the photolysis and probe lasers coincide in time. The dashed line is a simulation of the profile which takes into account the finite time response of the apparatus (modeled as a Gaussian with 20 ns fwhm) and the Doppler velocity selection by the finite bandwidth of the probe laser (modelled as 0.6 cm-' at the 2-photon wavenumber).

arrangement results in a very broad distribution of incident kinetic energies. 3.2. Preliminary Product Angular Distributions. As discussed in the Introduction, several groups have shown that it is possible for a photoinitiated reaction to extract information on the product c.m. angular distribution from measurements of the product laboratory velocity distributions, as obtained, for example, from Doppler profile^.^*.^^,^' Zare and c o - ~ o r k e r s ~ ~ have shown that the extraction of the c.m. product angular distribution is greatly simplified if the parent velocities can be neglected compared to the velocity of the photolytic reagent and have derived equations relating the c.m. angular distribution to the laboratory velocity distribution. As with Doppler velocity analysis with laser fluorescence detection, the mass peak profiles in REMPI detection with a TOFMS can provide a onedimensional velocity d i s t r i b ~ t i o n . ' ~ .We ~ ~ -have ~ ~ measured mass peak profiles for REMPI detection of the HCl product for reaction 3 and have derived a coarse c.m. angular distribution. To check the performance of the TOFMS, we have taken mass peak profiles for C1 atoms produced in the 355 nm photodissociation of Clz, for which the recoil anisotropy parameter is well known = - l).43 The C1 atoms were probed 1 REMPI detection on the 4Di,,-2P;,, transition, at a by 2 two-photon wavenumber of 84 127 ~ m - ' . ~Figure , 7 displays the mass peak profile obtained with the photolysis laser polarization perpendicular to the TOFMS axis and no delay between the photolysis and probe lasers. We find that an essentially identical profile for a photolysis-probe delay of 120 ns; this indicates that flyout effects are negligible. The profile in Figure 7 has the expected double-peaked form for a one-dimensional velocity distribution for this polarization geometry.56 In the absence of blurring by the finite time response of the apparatus, the peak-to-valley ratio should be 2. It can be seen that the ratio for the profile displayed in Figure 7 is larger than this. The depressed intensity at the center of the profile results from a slight Doppler velocity selection by the probe laser because of its finite bandwidth and the large recoil speed of the C1 atoms. At the center of the profile, the atoms have the largest velocity projection v l perpendicular to the TOFh4S axis and along the laser propagation axis. Alternatively, the loss of intensity from the center of the profile could arise from incomplete collection of the ions by the microchannel plate because the large velocity component VI at the center of the profile.55 However, we have adjusted the einzel lens so as to collect ions irrespective of the magnitude of VI. In addition,

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J. Phys. Chem., Vol. 99, No. 24, 1995 9849

the C1 atom profile was found to be independent of the einzel lens focusing over a wide range of voltages. To model the Doppler velocity by the probe laser, we first ignore the apparatus time response and write the intensity as a function of the velocity projection v; along the TOFMS axis as

where the definitions of the axes and the fragment recoil velocity distributionAvA) are given in the Appendix. The probe laser Doppler resolution function D(v,) is taken as a Gaussian with an effective 2-photon linewidth. The two-dimensional integral in eq 4 can be reduced to a one-dimensional quadrature. Using the relationship At = mv,/qE, where E is the electric field in the ionization region,54 we can convert the velocity profile in eq 4 into a time profile, which is finally convoluted over the time response of the apparatus: S(t) = JZ(qEt’/m) T(t - t’) dt’

(5 1

Our apparatus time response function T(t - t‘) is approximated by a Gaussian with 20 ns fwhm. This width arises, in part, from the probe laser pulse width ( ~ 1 ns). 0 It can be seen from Figure 7 that the calculated profile reproduces well the measured C1 atom mass peak profile. Since the recoil speed of the C1 atoms is known (1.67 x IO5 c d s ) from the dissociation energetic^,^^ the width of the profile provides a calibration of the electric field. The width of the profile in Figure 7 corresponds to E = 74 Vlcm, which is close to the nominal field strength calculated from the voltage differences between the plates denoted “accel. 1” and “0 V” in Figure lb. The angular distribution of the C1 atoms is also crucial in deducing the product c.m. angular distribution from HCl mass peak profiles. While the elegant analysis of Zare and c o - ~ o r k e r to s ~deduce ~ the product c.m. angular distribution does not strictly apply to the present experimental conditions since the spread of initial relative translational energies is large (see Appendix), we have nevertheless measured HCl product mass profiles for reaction 3 in order to carry out a preliminary investigation of the c.m. product angular distribution. We have carried out Monte Carlo simulations of the expected mass peak profiles for the C1 isobutane reaction and find that these are only slightly broader (differences comparable to our apparatus time resolution) than for the idealized case (negligible parent velocities) described by Zare and c o - ~ o r k e r s .The ~ ~ principal broadening mechanism of the mass peak profiles arises from the vectorial addition of the photofragment reagent velocities, which have a wide angular distribution, with the parent velocities. As discussed in the Appendix, the spread in the incident relative translational energy distribution in our experimental geometry can be considerably reduced by decreasing the intersection angle of the two beams. We plan to make further measurements of product mass peak profiles for a range of internal states in all three reactions after we have made this modification to our apparatus. Figure 8a presents a measured mass 36 profile for HCl (v = 0, J = 1) from reaction 3, obtained by 2-photon excitation on the F-X(0,O) R(1) line. To remove the HCl background, the profile in Figure 8 was obtained by taking the difference in the signal with the photolysis laser on vs off. We note in passing that the width of the HCl background peak is consistent with our estimated 20 ns apparatus time response. We have also taken mass peak profiles of several other HCl(v = 0) product rotational levels for reaction 3. These display a profile very similar to that shown in Figure 8a and were not considered further here. We have also investigated whether the formation

+

:.I

..-.,......................\... , .

time(ns) Figure 8. (a) Measured mass 36 peak profile for REMPI detection through the F-X R(l) line of HCl(v = 0, J = 1) products from the reaction of C1 atoms with isobutane. This profile was taken with perpendicular photolysis laser polarization and a photolysis-probe delay of 140 ns. The dashed line shows a best fit as described in the text using the basis functions displayed in panel (c) below. (b) Basis functions S,(t) obtained with the recoil speed calculated from the full exothermicity A&, of reaction 3b. The solid, dashed, dot-dashed, and dot-dot-dashed lines represent the contributions to the profile from scattering into the c.m. angular ranges cos 8, (-1, -0.5), (-0.5, 0), (0, O S ) , and (0.5, l), respectively. (c) Basis functions S,(t) obtained with the recoil speed calculated from hH3b - 20 kJ mol-’.

of fragment ions with REMPI detection in the E-X band system45,46,48 affects the mass 36 (HCl+) profiles. We find that these are essentially identical to those obtained with F-X transitions. Our analysis of the HC1 mass peak profile proceeds from the expression for the product laboratory velocity distribution AVAB)derived by Shafer et al.37(eqs 10-12). We assume that the products have a single c.m. recoil speed UAB. Initially, we calculate this speed by assuming that reaction 3 proceeds only by abstraction of the tertiary hydrogen atom [pathway 3b], with no internal excitation of the product alkyl radical. We express the normalized c.m. angular differential cross section as a series of equally spaced steps vs the cosine of the c.m. scattering angle 8,: . . where u(x) is the unit step function and xi = -1 2ilN. The signal due to each slice i of the differential cross section is denoted as Si(t) and is obtained by integrating the contribution t O A V A B ) from this slice over the perpendicular velocities v, and vy, converting to flight time, and finally convoluting over the apparatus response function [cf. eqs 4 and 5 above]. We note

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9850 J. Phys. Chem., Vol. 99, No. 24, 1995

5

0.5


7

TABLE 1: Highest Energetically Accessible Vibrational and Rotational States of the HCl Product of Reactions 1-3

reaction C1 + CH4- HCI + CH3 C1+ CjHs HCI n-C,Hj HC1+ i-C3H7 CI + i-C4Hj0 HC1+ n-CdH9 HCl + t-CdH9

---

0.25 m .-U C

+

Em. u mol-‘

23 53 65 57 78

a

Vmax

Jmaxb

0

13 20

1 1 1 2

22

20 24

E,,, includes the reaction exothermicity and the average initial relative translational energy in our experimental configuration. Highest rotational level in the v = 0 vibrational level.

2 0 -1

0 coser

1

Figure 9. Derived c.m. differential cross section from the fit to the HCI mass peak profile displayed in Figure 8a. The error bars represent 3 standard deviations.

parenthetically that the two-dimensional integration over v, and v? is best done by transforming first to polar coordinates because of the near cylindrical symmetry of ~ ( v A B ) . The measured product mass peak profile can then be expressed as a linear combination of the basis functions S;(t), with weighting factors ai. We then determine the product c.m. angular distribution by a singular-value decomposition linear least squares procedure5* to determine the factors ai which govern the contribution to the scattering from each c.m. angular slice. Since the hwhm of the mass peak profile is ~ 8 ns, 0 or about four time-resolution widths, we have chosen to analyze the profile with only four slices (N = 4, in eq 6). We have investigated fitting the experimental profile with N larger but find strong correlations between the derived values of ai from adjacent slices and marginally improved overall fits. Figure 8b presents the computed basis functions for the least squares fit when we calculate the c.m. recoil speed as described above, Le., with the full exothermicity of reaction 3b and assuming no excitation of the alkyl radical. Comparison of these calculations with the experimental profile in Figure 8a indicates that the products are predominantly backward scattered with respect to the C1 reagent. It can also be seen that the calculated width from the backwardmost slice (i = 1) of the differential cross sections is significantly larger than the width of the experimental profile. This suggests that the energy available to product recoil energy is less than has been assumed. We have carried out least squares fits with the basis functions shown in Figure 8b and with those calculated assuming the energy available for translational energy of the products is 10 and 20 kJ mol-’ less; basis functions calculated with the latter available energy are shown in Figure 8c. We find that the fit to the experimental profile is the best with the assumption that the available energy is 20 kJ mol-’ less than the full exothermicity of reaction 3b. Figure 8a compares the experimental and fitted profiles, and Figure 9 displays the derived c.m. differential cross section. We see from Figure 9 that there is a definite propensity for the HCI products from reaction 3 to be backward scattered with respect to the incoming C1 reagent. This propensity was found in all the fits, regardless of the assumed available energy. From the differential cross section presented in Figure 9, we deduce that the ratio of the cross section for backward scattering [- 1 5 cos 8,. 9 01 to that for forward scattering [-1 I cos 8, 5 01 is 2.5 i0.2. Our fits also seem to suggest that the translational energy released in reaction 3 is considerably less than the full exothermicity of the presumed favored pathway for this reaction, namely abstraction of the tertiary hydrogen to form the r-C4H9 alkyl radical product.

4. Discussion

As discussed in the Introduction, reactions 1-3 are examples of a class of kinematically constrained reactions involving the transfer of a light atom between two heavier species. The dynamics of this class of reactions has been extensively studied. It has been found in both e ~ p e r i m e n t a and l ~ ~ theoretica160s6’ studies of many atom diatom reactions with the heavy light-heavy mass combination that reagent translational energy is preferentially converted into product translational energy. Andresen and Luntz* and Park et a1.’* observed that the OH and HCl products from the reactions of 0 and C1 atoms, respectively, with cyclohexane were essentially independent of the incident relative translational energy. Moreover, Park et al. found that increasing reagent translational energy was funneled into product translational energy, as expected for this mass combination. Thus, if this propensity applies to the C1 hydrocarbon reactions, our large spread of incident relative translational energy should not strongly affect the HC1 product internal state distribution. For the calculation of Et,,, we arbitrarily take the average initial relative translational energy, which equals 30, 45, and 49 M mol-’ for reactions 1-3, respectively. Table 1 presents calculated values of E,,, and the highest accessible HC1 vibrational level vmaxand the highest rotational level J,,, within the ground vibrational level if all the available energy were channeled into internal excitation of the HC1 product. It should be noted that the Cl CH, reaction is slightly endothermic, and reaction is enabled only by the availability of reagent translational energy. As discussed in the Introduction, there are two distinct chemical pathways for the reactions with the larger hydrocarbons, wherein the abstracted atom can be a primary hydrogen, or a secondary or tertiary hydrogen for reactions 2 and 3, respectively. For HC1 product internal states energetically accessible from the abstraction of either type of hydrogen atom, these pathways can, in principle, be distinguished by measurement of the product relative translational energy disposal, provided that the alkyl radical does not possess significant internal excitation. Comparison of the values of J,,, presented in Table 1 with the rotational state distributions displayed in Figures 4-6 show that the range of product HCI rotational states populated is considerably less than that allowed by energy conservation. In this regard, the dynamics of the C1 hydrocarbon reactions appear to be quite similar to that of the extensively studied corresponding 0 atom reactions.’,4.’8 A careful comparison of product HCl and OH distributions from these reactions with similar E,,, reveals that the HCl product from the C1 atom reaction possesses marginally more rotational excitation than the OH product from a comparable 0 atom reaction. In the case of the isobutane reaction, we can compare directly with the results of Andresen and Luntz.? They find the OH(v = 1) product rotational state distribution extends out to N = 6 in the F I(’I&,?) spin-orbit manifold, with an average rotational

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J. Phys. Chem., Vol. 99, No. 24, 1995 9851

excitation of 0.7 kJ mol-'. (It should be noted that the rotational constant for OH is much larger than that of HCl,I5 so that lower rotational quantum levels are populated in the former.) Our derived HCl(v = 1) rotational state distribution for reaction 3 corresponds to an average rotational excitation of 1.3 kJ mol-'. For the C1+ CHq reaction, a low degree of product rotational excitation is consistent with the ab initio calculated linear C1H-CH3 transition With this transition state geometry, we expect a expect a bias toward linear C1-H.. CH3 recoil and hence little torque exerted on the departing HCl product. We also observe little HC1 rotational excitation in the reactions of C1 atoms with propane and isobutane. Indeed, for three reactions studied here, the fraction of E,,, which appears as HCl product rotational excitation is 3% or less. Similarly, Park et a1.I2find little product DC1 rotational excitation in the reaction of C1 with c-C6D12. Thermal rate data for the reactions of C1 with the heavier hydrocarbons8.l0indicates that the activation barriers for these reactions are much lower than for C1 CH4. We might infer from this that there would be a less strong constraint for linear Cl-H-R geometries at the transition state, Le., that the potential energy does not increase as strongly as the ClHR bending angle decreases from 180°, as in the C1 CHq reaction. However, we see a similar low degree of product HCl rotational excitation in all three reactions, although the average rotational excitation is slightly higher for reactions 2 and 3 than for reaction 1. Park et a1.I2have reconciled the low observed DC1 rotational excitation with a small activation barrier for C1 c-C& by invoking the role of zero-point CD2 bending vibrations in the dynamics. As discussed above, the reactions of C1 with propane and isobutane can proceed by two different pathways, involving the abstraction of different types of hydrogen atoms. Because of the larger exothermicity for the abstraction of a secondary or tertiary hydrogen in reactions 2 and 3, respectively, than for the removal of a primary hydrogen, we might expect the former pathways to dominate the dynamics. However, in contrast to the C1 CHq reaction, we see that abstraction of a primary hydrogen is also an exothermic pathway for the reaction of C1 with both C3H8 and I'-C~HIO. In addition, since this study was carried out with significant initial relative translational energy, we cannot distinguish between the two reaction pathways without isotopic labelling, even for the formation of HCl(v = 1) products. Because of the lack of appropriate intensity calibration of REMPI signals for detection of HCl(v = 0 and 1) vibrational levels, we are unable to derive the absolute ratio of the vibrational populations in the HC1 product. We have, nevertheless, measured ratios of REMPI intensities for excitation in the F-X(0,O) and (1,l) bands. When appropriate calibration factors become available, these intensity ratios can be converted to vibrational population ratios. Even without this calibration, we can still draw preliminary conclusions from our measurements. We find that the HC1 product v = 1 to v = 0 vibrational population ratio is essentially the same for the C1 C3H8 and i-C4Hlo reactions, where the favored reaction pathways involve abstraction of a secondary and tertiary hydrogen, respectively. By contrast, Andresen and LuntzZ found a strong dependence of the OH v = 1 to v = 0 population ratio on the type of hydrogen abstracted in the reactions of O(3P)with hydrocarbons. Indeed, they found a population inversion in the OH products of the O(3P) i-C4Hlo reaction. Their observations were explained3 through trajectory calculations on model potential energy surfaces which had different activation barriers and for which the C-H bond is broken earlier along the reaction coordinate for abstraction of a tertiary hydrogen, as compared

+

+

+

+

+

+

to abstraction of a secondary or primary hydrogen. For the C1 hydrocarbon reactions, the thermal kinetic data8 indicate that the activation barriers for the reactions of propane and isobutane are similar and are quite small. This suggests that the C-H bond is broken at a similar point along the reaction coordinate in these reactions. This would explain the similar observed degree of HCl product vibrational excitation. From the preliminary product HCl mass peak profiles recorded in this study, we have deduced, at least for the C1 isobutane reaction, that the products are scattered predominantly backward with respect to the incoming C1 atom. While the angular resolution of our derived c.m. differential cross section is not high, we have obtained sufficient information so as to be able to draw inferences about the reaction dynamics. Our observations are consistent with the mechanism previously developed by Luntz and Andresen3 to explain the dynamics of reactions of O(3P)atoms with hydrocarbons. Classical trajectory calculations on model potential energy surfaces, with the collinear transition-state geometry, predict that the hydride product is preferentially backward scattered with respect to the incoming atom. This also implies that it is primarily low impact parameters collisions that are responsible for the reaction. This model would seem to apply to the C1 isobutane reaction. An intriguing preliminary result from our mass peak profile measurements is that the translational energy release is considerably smaller than that allowed by energy conservation for reaction 3b. This could be due to the significant participation of the less exothermic pathway 3a, or a significant excitation of the alkyl radical in pathway 3b. We intend in future experiments to resolve this question by measuring mass peak profiles with a reduced spread of initial relative translational energies and also with selectively deuterated isobutane reagent. The latter experiment will allow us to distinguish between tertiary and primary hydrogen abstraction, as well as to measure the translational energy release for these pathways separately. The present study of the reactions of C1 atoms with small hydrocarbons suggests that the dynamics of these reactions are quite similar to those of the corresponding 0 atom reactions. The abstraction of a hydrogen atom to form the hydride product is governed by a linear transition state, and the products are formed with little rotational excitation. Our observation of predominantly backward scattering of the HCl product in the C1 isobutane reaction also suggests that the reaction occurs mainly in low impact parameter collisions. In future experiments with a reduced spread of initial relative translational energies and selectively deuterated hydrocarbon reagents, we hope to uncover further details of the dynamics, such as differences between the abstraction of primary vs secondary or tertiary hydrogens and differences in the c.m. angular distributions for v = 0 and 1 products. The recent experiment of Simpson et al.I3 on the reaction of C1 atoms with vibrationally excited methane has revealed a distinctly different dynamics for reactions involving vibrationally excited reagents. It will also be interesting to develop a global picture of the dynamics of reactions of simple hydrocarbons in both their ground and excited vibrational levels.

+

+

+

+

Acknowledgment. We are very grateful to W. R. Simpson and R. N. Zare for several conversations about their experiments and for sharing of unpublished results with us, to R. J. Gordon for providing unpublished tables of correction factors relating HC1 F-X REMPI intensities to rotational populations, to C. A. Wight for advice about the purification of Clz by fractional

9852

J. Phys. Chem., Vol. 99, No. 24, 1995

I

V


'AX

/

TOFMS axis z

BC

Figure 10. Velocity diagram for our experimental two-beam arrangement. The velocities of the C1 atom precursor and the hydrocarbon reagent are denoted VAX and VBC. respectively, while the velocity of the photolytic fragment A in the c.m. frame of AX is denoted V A . The polarization of the photolysis laser is denoted as &pol.

distillation, and to G. E. Hall for an illuminating conversation about Monte Carlo integration. We also gratefully acknowledge conversations with S. Rosenwaks and I. Bar about reactions of atoms with hydrocarbons. This research was supported by the National Science Foundation, under Grant No. CHE-93 13722, and the U.S. Army Research Office, under Grant No. DAAL03-91-G-0129. Finally, we acknowledge travel support from the U. S.-Israel Binational Science Foundation.

Appendix As Zare and co-workers have discussed, the initial relative translational energy distribution is quite narrow when premixed reagents in a supersonic beam are employed for the study of photoinitiated reactions.13x37In our two-beam configuration,the initial velocities of the photolytic precursor and the hydrocarbon reagent can lead to a substantial spread in the translational energy distribution. The effect of the motion of the reagents on the reagent translational energy distributiod2 and the product velocity d i s t r i b ~ t i o n ~ ~has - ~been ~ s ~ considered ~ for photoinitiated reactions in a bulb. In this Appendix, we calculate the initial relative translational energy distribution for a general A BC AB C chemical reaction appropriate to our experimental configuration. Figure 10 defines the geometry of our reagent beams. The photolytic precursor of A is denoted AX. The reagent beams lie in the xy plane, which is perpendicular to the TOFMS axis. The photolysis laser propagates along the y axis, with polarization direction perpendicular to the plane defined by the laser beam and TOFMS axes. We ignore the angular and velocity spreads of the beams here. The velocity of reagent A in the c.m. frame of AX is denoted VA. It is well-known56that the distribution of velocities of a photolytic fragment can be written as

+

-

+

E (ev) Figure 11. Calculated initial relative translational energy distributions for the reaction of photolytically preapred C1 atoms with (a) methane, (b) propane, and (c) isobutane for our experimental geometry.

In the second line of eq A2, we have substituted for the relative velocity vrel and carried out the trivial integration over V A . Here, the parameters

V,

= vAXsin e,, - vBC sin OB,

(A4)

are the x and y components of VAX - VBC. In our geometry, 8AX = ~ B = C 45" and hence v, %z0 for similar reagent beam velocities. We can readily evaluate eq A2 for the limiting case vX = 0. From the vector addition of VA and v), we see that p ( E ) is nonzero only for the range ' / @ ( v o - v , ) I ~ E 5 '/@(vo v , ) ~ . We first carry out the integration over @A. The integrand is nonzero only for the 2 values @I in the domain (0,2n),where

+

where vo is the c.m. speed of the fragment and O*Ep,l = cos&, (see Figure 10). The distribution of relative translational energies E can be written as

GI = cos-'

+ ~v,[v, e, + vy sin 8, cos 4,] +:v + vy - (2E/p))[1+

= (2/p)JJs(~,?

COS

2

pP,(COS 6,)](4n)-'

d(cos 6,) d@A (A2)

The integral over the relationship@

2v0v, sin 8,

045)

can then be carried out with the help of


J. Phys. Chem., Vol. 99, No. 24, 1995 9853

where g(xn) = 0. Equation A2 then becomes

(22) Gonzalez-Lafont, A.; Truong, T. N.; Truhlar, D. G. J. Chem. Phys. 1991, 95, 8875-8894.

p ( ~=) (np)-1J+xm[4v,?v,? -x,,, sin2 e, -

+

( ( 2 ~ 4 . 4- v,? - vy2}2]-112[i ~ P , ( C O S e,)] q c o s

e,)

(A7) where x, = [I - {(2E/p) - VA* - V~}2/(4VA2V~)]1'2. Performing the integration over COseA, we obtain p(E) = (2pvAvy>{(1 - p/2) + (3p/2)[{(2E/p) - v,? - v,2}*/(4vA2V,?)]} (A8) The near-UV photolysis of C12 involves a perpendicular transition, with p = - 1.43 In this case, p(E) has its maximum at the lower and upper limits on E, Le., '/@(vo f v,.)~,and its minimum at the approximate midpoint '/p(vo2 v),: analogous to the form of the projection of the velocity distribution of a photolytic fragment along a direction perpendicular to With the exception of the C1 C& system, the velocities of the C1 and RH reagents are not equal, so that both v, and v,. (eqs A3 and A4) are nonzero. For this general case, we evaluate eq A2 by Monte Carlo i n t e g r a t i ~ n . Figure ~~ 11 displays the calculated initial relative translational energy distributions for the three reactions studied. It can be seen that these are double peaked, as expected from eq A8. We also see that there is a large spread in the energy distributions, reflecting the fact that vo and v,. are of comparable magnitude. This is the major disadvantage of the two-beam configuration adopted here to avoid prereaction of the reagents. This spread can be significantly reduced in our geometry by reducing the beam intersection angle ( e A X &C) and adjusting the reagent seed gas mixture so that V A X x VBC. In this way, vv can be made small. We are presently modifying our experimental apparatus to reduce the intersection angle between the two reagent beams.

+

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References and Notes (1) Bogan, D.; Setser, D. W. ACS Symp. Ser. 1978, 66, 237-280. (2) Andresen, P.; Luntz, A. C. J. Chem. Phys. 1980, 71, 5842-5850. (3) Luntz, A. C.; Andresen, P. J. Chem. Phys. 1980, 72, 5851-5856. (4) Dutton, N. J.; Fletcher, I. W.; Whitehead, J. C. Mol. Phys. 1984, 52, 475-483. ( 5 ) Park, C. R.; Wiesenfeld, J. R. J. Chem. Phys. 1991, 95, 81668177. (6) Zahniser, M. S.; Berquist, B. M.; Kaufman, F. lnt. J. Chem. Kinet. 1978, 10, 15-29. (7) Ravishankara, A. R.; Wine, P. H. J. Chem. Phys. 1980, 72, 2530. (8) Lewis, R. S.; Sander, S. P.; Wagner, S.; Watson, R. T. J. Phys. Chem. 1980, 84, 2009-2015. (9) Heneghan, S. P.; Knoot, P. A.; Benson, S. W. Int. J. Chem. Kinet. 1981, 13, 677-691. ( I O ) Atkinson, R.; Baulch, D. L.; Cox, R. A,; Hampson, R. F.; Kerr, J. A,; Troe, J. J. Phys. Chem. Ref Data 1992, 21, 1125-1568. (11) Rowland, F. S.; Molina, M. J. Rev. Geophys. Space Phys. 1975, 13, 1-35. (12) Park, J.; Lee, Y.; Herschberger, J. F.; Hossenlopp, J. M.; Flynn, G. W. J. Phys. Chem. 1992, 114, 58-63. (13) Simpson, W. R.; Orr-Ewing, A. J.; Zare, R. N. Chem. Phys. Lett. 1993, 212, 163-171. (14) Yen, Y.-F.; Wang, Z.; Xue, B.; Koplitz, B. J. Phys. Chem. 1994, 98, 4-7. (15) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules; Van Nostrand Reinhold: New York, 1979. (16) Herron, J. T. J . Phys. Chem. Ref Data 1988, 17, 967-1026. (17) Tsang, W.; Hampson, R. F. J. Phys. Chem. Ref Data 1986, 15, 1087- 1279. (18) Tsang, W. J. Phys. Chem. Refi Data 1988, 17, 887-951. (19) Tsang, W. J. Phys. Chem. Ref Data 1990, 19, 1-68. (20) Walch, S . P.; Dunning Jr., T. H. J. Chem. Phys. 1980, 72, 32213227. (21) Truong, T. N.; Truhlar, D. G.; Baldridge, K. K.; Gordon, M. S . ; Steckler, R. J. Chem. Phys. 1989, 90, 7137-7142.

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