Mechanism of the reaction, CH4+O(1D2)→CH3+OH, studied by ultrafast and state-resolved photolysis/probe spectroscopy of the CH4·O3 van der Waals complex

Mechanism of the reaction, CH 4 +O ( 1 D 2 )→ CH 3 +OH , studied by ultrafast and

state-resolved photolysis/probe spectroscopy of the CH 4 O 3 van der Waals complex

C. Cameron Miller, Roger D. van Zee, and John C. Stephenson

Citation: The Journal of Chemical Physics 114, 1214 (2001); doi: 10.1063/1.1331615

View online: http://dx.doi.org/10.1063/1.1331615

View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/114/3?ver=pdfcov

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JOURNAL OF CHEMICAL PHYSICS

VOLUME 114, NUMBER 3

15 JANUARY 2001

1

Mechanism of the reaction, CH₄¿O„ D₂…\CH₃¿OH, studied by ultrafast

and state-resolved photolysisÕprobe spectroscopy of the CH₄"O₃

van der Waals complex

C. Cameron Miller, Roger D. van Zee, and John C. Stephenson^a)

National Institute of Standards and Technology, Gaithersburg, Maryland 20899

͑Received 18 October 1999; accepted 19 October 2000͒

The mechanism of the reaction CH₄ϩO(¹D₂)→CH₃ϩOH was investigated by ultrafast,

time-resolved and state-resolved experiments. In the ultrafast experiments, short ultraviolet pulses

photolyzed ozone in the CH₄•O₃van der Waals complex to produce O(¹D₂). The ensuing reaction

with CH was monitored by measuring the appearance rate of OH( ϭ0,1;J,⍀,⌳) by laser-induced

v

4

ﬂuorescence, through the OH A X transition, using short probe pulses. These spectrally broad

pulses, centered between 307 and 316 nm, probe many different OH rovibrational states

simultaneously. At each probe wavelength, both a fast and a slow rise time were evident in the

ﬂuorescence signal, and the ratio of the fast-to-slow signal varied with probe wavelength. The

distribution of OH( ,J,⍀,⌳) states, P ( ,J,⍀,⌳), was determined by laser-induced ﬂuorescence

v

obs

using a high-resolution, tunable dye laser. The P_obs( ,J,⍀,⌳) data and the time-resolved data were

v

analyzed under the assumption that different formation times represent different reaction

mechanisms and that each mechanism produces a characteristic rovibrational distribution. The

state-resolved and the time-resolved data can be ﬁt independently using a two-mechanism model:

P_obs( ,J,⍀,⌳) can be decomposed into two components, and the appearance of OH can be ﬁt by

v

two exponential rise times. However, these independent analyses are not mutually consistent. The

time-resolved and state-resolved data can be consistently ﬁt using a three-mechanism model. The

OH appearance signals, at all probe wavelengths, were ﬁt with times ␶_fastϷ0.2 ps, ␶_interϷ0.5 ps and

␶

_slowϷ5.4 ps. The slowest of these three is the rate for dissociation of a vibrationally excited

*

methanol intermediate (CH₃OH ) predicted by statistical theory after complete intramolecular

energy redistribution following insertion of O(¹D₂) into CH₄. The P_obs( ,J,⍀,⌳) was decomposed

v

into three components, each with a linear surprisal, under the assumption that the mechanism

producing OH at a statistical rate would be characterized by a statistical prior. Dissociation of a

*

CH₄O intermediate before complete energy randomization was identiﬁed as producing OH at the

intermediate rate and was associated with a population distribution with more rovibrational energy

than the slow mechanism. The third mechanism produces OH promptly with a cold rovibrational

distribution, indicative of a collinear abstraction mechanism. After these identiﬁcations were made,

it was possible to predict the fraction of signal associated with each mechanism at different probe

wavelengths in the ultrafast experiment, and the predictions proved consistent with measured

appearance signals. This model also reconciles data from a variety of previous experiments. While

this model is the simplest that is consistent with the data, it is not deﬁnitive for several reasons. First,

the appearance signals measured in these experiments probe simultaneously many OH( ,J,⍀,⌳)

v

states, which would tend to obfuscate differences in the appearance rate of speciﬁc rovibrational

states. Second, only about half of the OH( ,J,⍀,⌳) states populated by this reaction could be

v

probed by laser-induced ﬂuorescence through the OH A X band with our apparatus. Third, the

cluster environment might inﬂuence the dynamics compared to the free bimolecular reaction.

͓DOI: 10.1063/1.1331615͔

ϭϪ15 240 cm^Ϫ1) with a rate constant close to a gas kinetic

I. INTRODUCTION

value and independent of temperature. Certain limiting, ar-

chetypical mechanisms can be envisioned for the reaction of

O atoms with CH₄, including insertion/elimination, abstrac-

tion, and stripping. In the insertion/elimination archetype, the

oxygen atom inserts into a C–H bond to form a vibrationally

The reaction between hydrocarbons and O(¹D₂) is cen-

tral to the chemistry of the upper atmosphere. As such, the

mechanism and dynamics of the major reaction channel¹

1

˜

of the simplest hydrocarbon, CH₄(X A₁)ϩO( D₂)

2

˜

→CH₃(X A₂Љ)ϩOH(X ⌸), have been extensively studied.

*

excited methanol intermediate (CH₃OH ) that undergoes

The reaction is exothermic²(⌬H₀^o_KϭϪ182 kJ mol^Ϫ1

complete intramolecular vibrational energy redistribution

͑IVR͒ before dissociating. Both the distribution of energy in

*

the fragments and the CH₃OH unimolecular dissociation

a͒

Electronic mail: john.stephenson@nist.gov

1214

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The reaction, CH₄ϩO(¹D₂)→CH₃ϩOH

1215

J. Chem. Phys., Vol. 114, No. 3, 15 January 2001

rate would be expected to follow the predictions of statistical

theory. For the abstraction mechanism, the oxygen atom

would travel towards the methane molecule along the

carbon–hydrogen bond to extract a hydrogen atom and then

recoil to form the hydroxyl radical. The reaction should be

virtually instantaneous, and the distribution of rovibrational

energy in the fragments would be colder than the statistical

expectation. In the case of a stripping mechanism, the oxy-

gen atom would ﬂy by the methane molecule, snatching a

hydrogen atom on the way. As with abstraction, a stripping

reaction should be fast, but unlike an abstraction, should re-

sult in substantial rovibrational excitation in the hydroxyl

product.

FIG. 1. A correlation diagram for the reaction between methane and atomic

oxygen. The heats of formation and barrier heights are based on Refs. 2, 89,

92–96.

Nature is not conﬁned to a single limiting case and early

work supported parallel mechanisms. Initial evidence for a

*

CH₃OH intermediate came from chemical quenching and

matrix experiments^3–5of the CH₄and O(¹D₂) reaction,

which found that as the pressure in the reaction chamber

increased, the quantum yield of CH₃OH increased. This ob-

servation was attributed to collisional stabilization of a

Although OH and CH₃are the major products ͑estimates

vary from 69%–96%͒, several minor products have also

been identiﬁed. Figure 1 shows a correlation diagram indi-

cating the energetics for various channels. Primary H atom

production has been studied by laser-induced ﬂuorescence

experiments.^19–21Whether the co-fragment was CH₃O or

CH₂OH was controversial until recent crossed molecular

beam experiments^22,23found CH₂OHϩH to be the second

most probable channel. Most of the H atom product is iso-

tropically scattered, though about a tenth is back scattered.

This ﬁnding supports parallel mechanisms for this channel

too. The beam experiments also found that H₂COϩH₂are

primary products. All the H₂was found to be isotropically

distributed, and this channel was concluded to evolve

*

CH₃OH intermediate. However, even in liquid argon some

OH was formed, suggesting that at least a fraction of the

product formed through an abstraction mechanism. Park and

Wiesenfeld⁶studied the OH rovibrational product states from

several hydrocarbons and concluded that, in the case of

methane, most of the OH was characterized by a nonstatisti-

cal distribution. They postulated, however, that all the OH

passed through a methanol intermediate, with most dissocia-

tion occurring prior to complete IVR. This conclusion was

consistent with Luntz’s earlier conjecture that most OH was

formed by the latter mechanism, although OH in low-

rotational levels was formed by an abstraction mechanism.⁷

*

through a CH₃OH intermediate after complete IVR. The

Sub-Doppler spectroscopy^8–12has shown that OH( ϭ0)

v

methoxy radical has also been reported to be a direct product

of this reaction, although this is uncertain. Because the O–H

bond is not the weakest bond in the molecule, this would

imply dissociation of an intermediate in which energy has

not fully randomized. In addition, the reaction to form

was scattered nearly isotropically in the center-of-mass

frame, but with some backward asymmetry, again suggesting

both a long-lived intermediate and a reactive complex with a

lifetime less than one rotational period. By comparison to

OH, little is known about the CH₃product. Absorption spec-

tra recorded with an infrared diode laser¹³have been used to

determine the nascent distribution of the out-of-plane bend

CH₂(˜a)ϩH₂O as minor primary products has been

reported.^23–25The observation of these minor products im-

plies that dissociation of a methanol intermediate after en-

ergy randomization is an important mechanism for reactive

collisions between CH₄and O(¹D₂).

(

). It was found that ϭ0 was the most populated level of

v

v₂

that mode, with monotonically decreasing population up to

ϭ4. This measured distribution was signiﬁcantly colder

v

We previously reported preliminary ﬁndings from ex-

periments aimed at further elucidating the mechanism of the

primary reaction channel. An ultrafast laser system was used

to measure OH production as a function of time following

ultrafast photolysis at 267 nm of the CH₄•O₃van der Waals

complex.²⁶Prompt dissociation of ozone produces O(¹D₂),

which then reacts with the neighboring CH₄to form OH.

This reaction was monitored by measuring OH laser-induced

ﬂuorescence, through the OH A(²⌺) X(²⌸) transition, as

a function of photolysis/probe delay. Initiating the reaction in

a cluster provides a clear time-zero against which to measure

the appearance of the reaction products.^27–29A single expo-

nential rise with a time constant of several picoseconds ad-

than an unconstrained, statistical prior distribution. Multi-

photon ionization spectra^14,15of the out-of-plane bend and

symmetric stretch also suggested that there was compara-

tively little vibration excitation in the CH₃fragment, though

because the Franck–Condon factors and autodissociation

rates of the excited state were unknown, no quantitative con-

clusions could be reached. An ab initio calculation¹⁶of the

potential-energy surface for the CH₄ϩO reaction suggested

that insertion-, abstraction-, and stripping-like mechanisms

were possible. Recent quasiclassical trajectory calculations

found that insertion is the dominant mechanism,^17,18though

there were distinct classes of trajectories, one being direct

and producing an inverted rovibrational distribution and the

other being indirect and producing a noninverted distribu-

tion. Although inconclusive, these investigations suggest

complicated reaction dynamics.

equately ﬁt the OH( ϭ0,J) states probed in those experi-

v

ments. This appearance rate was consistent with the rate of

*

dissociation of CH₃OH predicted by statistical rate theory.

Given the time resolution and signal-to-noise of that experi-

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1216

J. Chem. Phys., Vol. 114, No. 3, 15 January 2001

Miller, van Zee, and Stephenson

ment, we concluded that any prompt OH channel produced

less than 20% of that probed. We have also previously re-

ported the rovibrational state distributions in the cluster re-

action and found them quite similar to those of the free,

bimolecular reaction,³⁰an observation which Wada and

Obi³¹subsequently conﬁrmed and which suggests that the

cluster environment replicates the dynamics of the free bi-

molecular reaction.

Ϸ310 kPa, and the chamber pressure was Ϸ1 mPa when the

nozzle was pulsing. Under these mixture conditions, the OH

signal was linear in the methane and ozone mole fraction.

Additional evidence that the OH is formed in CH₄•O₃clus-

ters rather than larger clusters has been presented

previously.^26,29No signal was observed when either the

methane or the ozone was removed from the expansion. The

lasers, focused to a Ϸ1.5 mm diameter spot, intersected the

molecular beam 8 mm downstream from the throat of the

expansion.

The detection system was a photomultiplier tube perpen-

dicular to the laser beams with two condensing doublet

lenses to collect and image the ﬂuorescence. Colored glass

ﬁlters blocked stray photolysis light and wavelengths longer

than Ϸ400 nm. On every laser pulse, gated boxcar integra-

tors collected four channels of data: Laser-induced ﬂuores-

cence ͑LIF͒ signal, the energy of the photolysis laser, the

energy of the probe laser, and signal from the photolysis/

probe cross-correlation.

The present article expands on our preliminary

studies,^26,30and reports important new ﬁndings. Improved

time resolution, increased signal-to-noise, and the ability to

probe more OH( ϭ0) rotational states and OH( ϭ1) made

v

these new time-resolved results possible. The appearance of

OH was measured at six probe wavelengths spanning the

OH( ϭ0,1) manifolds. The new data clearly show, in addi-

v

tion to the previously reported statistical channel, OH formed

by much faster mechanisms. We have also measured the

OH( ϭ0,1) rotational state distribution again.

v

Under the experimental conditions described above, the

LIF signal was linear in the photolysis and probe energy,

which indicates that neither the ozone nor the hydroxyl radi-

cal transitions were saturated. It also indicates that multipho-

ton processes are not a major contributor to the observed

signals. While it is conceivable that a multiphoton process

could lead to C–H bond rupture followed by reaction with

ozone to produce hydroxyl, at the intensities we used such a

process is insigniﬁcant compared to photolysis of ozone. It is

conceivable that a multiphoton process could promote ozone

to a higher electronic state, which would dissociate, presum-

ably producing a different and probably very energetic oxy-

gen atom. However, such a process would seem unlikely

because of the rapidity of ozone dissociation. Moreover, one

would expect that the product-state distribution from these

alternative reactions would be quite different from that of the

CH₄ϩO(¹D₂) reaction. In previous experiments,²⁶we deter-

II. EXPERIMENTAL APPARATUS AND PROCEDURES

A. Ultrafast experiments

The light source for the ultrafast photolysis/probe ex-

periment consisted of a passively mode-locked, titanium

doped sapphire (Ti:Al₂O₃) laser oscillator that produced

transform-limited, 70 fs pulses centered at 800 nm. The

pulses were stretched to Ͼ200 ps, ampliﬁed to 2 mJ at a

repetition rate of 20 Hz in a Ti:Al₂O₃regenerative ampliﬁer,

further ampliﬁed to 20 mJ in a Ti:Al₂O₃rod using a three

pass conﬁguration, and then compressed to 100 fs. The am-

pliﬁer rods were pumped by 10 ns, 532 nm pulses from a

Nd^3ϩ:YAG laser. The 267 nm photolysis light was generated

by ﬁrst doubling this compressed 800 nm light and then sum-

ming the resulting 400 nm light with residual 800 nm light.

The probe was generated by focusing part of the 800 nm

light into a cell containing deuterated water to create a white

light continuum, which was passed through an interference

ﬁlter to select light near 500 nm. This seed pulse was ampli-

ﬁed in three, 1 cm long dye cuvettes, which were pumped by

355 nm pulses from a second Nd^3ϩ:YAG laser. This light

was then summed with 800 nm light in a 0.5 mm

KH₂PO₄͑KDP͒ crystal to give wavelengths between 307 and

316 nm (⌬␭_FWHMϷ1.6 nm) ͓full width at half maximum

͑FWHM͔͒. The interference ﬁlter was tilted to tune the center

frequency of the transmitted light. Typically, ﬂuences were 1

mJ cm^Ϫ2for the photolysis laser and 0.75 mJ cm^Ϫ2for the

probe laser in these experiments. The orthogonally polarized

pump and probe beams were combined on a dichroic mirror

and propagated collinearly through the beam chamber.

The supersonic expansion in which the van der Waals

complexes were formed was the same as in previous

experiments.^26,30The clusters formed in a supersonic expan-

sion from reactants diluted in a 9:1 mixture of Ne:He. A 6%

mix of O₃in Ne:He ﬂowed through one calibrated ﬂow con-

troller, pure CH₄through another, and additional Ne:He

through a third. The gases mixed just upstream of the pulsed

valve, yielding a typical mix of 81% Ne, 9% He, 8% CH₄,

and 2% O₃. Prior to use, gaseous O₃was puriﬁed by distil-

lation from liquid O₃. The total stagnation pressure was

mined the OH( ,J,⍀,⌳) distribution following photolysis

v

with the ultrafast, 267 nm light and found this product-state

distribution to be indistinguishable from that measured fol-

lowing photolysis by 7 ns pulses of the same ﬂuence.³⁰

These observations suggest that the signal measured in the

appearance curves reported here arises from reaction of

CH₄ϩO(¹D₂) following single-photon dissociation of O₃.

At much higher photolysis intensities than those used here,

the signals become nonlinear, and multiphoton processes oc-

cur, as evidenced by ﬂuorescence occurring in the absence of

the probe pulse.

Proper analysis of the rise curves demands an accurate

measurement of the time of photoinitiation of the reaction.

This time was determined by measuring the photolysis/probe

cross-correlation by difference frequency mixing in a 0.1

mm KDP crystal, generating Ϸ1.9 ␮m light. To make this

measurement, the Fresnel reﬂections from the front surface

of the lithium ﬂuoride window at the chamber entrance

passed through a second lithium ﬂuoride window identical to

the chamber window. The difference frequency light was

then generated in the KDP crystal, which was located at a

point conjugate to the probe region in the chamber. The

Gaussian full-width at half-maximum of the cross correlation

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The reaction, CH₄ϩO(¹D₂)→CH₃ϩOH

1217

J. Chem. Phys., Vol. 114, No. 3, 15 January 2001

expansion and LIF detection apparatus were those used in

the ultrafast measurements. In the state-resolved experi-

ments, it was possible to vary the photolysis/probe delay

time in 10 ns steps. The signal rose sharply during the initial

20 ns after photolysis, following the integral of the temporal

cross-correlation between the photolysis and probe lasers

when pulse duration and timing jitter ͑Ϯ5 ns͒ are accounted

for. The signal remained constant for the next 50–80 ns and

then rose slowly or declined slowly, depending on the rovi-

brational state measured, as a result of collisional relaxation

of OH. The data reported here were measured with a 30 ns

delay. As in the ultrafast experiments, the LIF signal was

linear in both the photolysis and probe laser energy.

The observed spectra were normalized to variations in

the photolysis and probe laser ﬂuences and to the intensity of

the P₁₁(15), line which was remeasured after scanning 2 nm.

The normalized spectra were simulated by Lorentzian line

shapes to determine the line intensities of overlapping lines.

For hydroxyl in the A(²⌺) state, signiﬁcant autodissociation

FIG. 2. The circles are the OH LIF signal from the photolysis of H₂O₂. The

superimposed line is the photolysis/probe integrated cross correlation shifted

by 25 fs. The squares are the OH LIF signal for the CH₄•O₃cluster probed

at 316.5 nm, the probe wavelength with the fastest appearance curve. The

data are normalized so that the fast component in the cluster photolysis and

the H₂O₂signal have the same height at long time.

occurs for rotational states, Nу25 in the ϭ0 level and N

v

у15 in the ϭ1. All rotational states autodissociate for

у2. Because the diagonal bands were probed, only OH(

v

was routinely Ϸ200 fs. Accounting for the dispersion of air

͑1.0 fs cm^Ϫ1͒ and the dispersion of the KDP crystal ͑8 fs͒,

time-zero could be determined to within 5 fs. To test this

clocking apparatus, two additional experiments were carried

out. First, a second 0.1 mm KDP crystal was placed in the

vented chamber at the region of interaction, and the two

cross-correlations were compared. The cross-correlations

were aligned in time to Ϸ5 fs. Second, the LIF of OH

formed by 267 nm photodissociation of hydrogen peroxide

was measured. The ultraviolet photodissociation H₂O₂

→2OH is known to be prompt.^32–35To make these measure-

ments, vapor from a mixture of 70% H₂O₂in water ﬂowed

through the chamber at a pressure of Ϸ13 Pa. The rise curve

ϭ0,1) could be detected. In determining populations from

LIF line intensities, we corrected for the ﬂuorescence quan-

tum yield of the speciﬁc quantum levels,³⁸but do not report

populations if the correction was у50%. Division by the

Einstein B coefﬁcients³⁹converts intensities to relative popu-

lations. Results from independent measurements were then

averaged.

III. RESULTS

A. Product-state distributions

In order to understand the OH appearance measure-

ments, one must understand the form of the product-state

distribution and the extent to which the probe laser spectrum

encompasses the absorption spectrum of the product. Figure

3 shows a portion of an OH spectrum following 266 nm

photolysis of the CH₄•O₃cluster. The population distribu-

of OH( ϭ0) LIF from this reaction was indistinguishable

v

from the integral of the laser cross-correlation, except for a

shift in time attributable to the separation time of the OH

fragments. The observed shift in time for the data set with

probe laser centered at 308.9 nm is 25 fsϮ15 fs. Using a

standard approach,³⁶we calculated a shift to be 30 fs. There-

fore, the time-zero from the H₂O₂experiments was consis-

tent with the value measured using the crystal. The rise time

of OH from the prompt dissociation of H₂O₂is compared to

the fastest observed formation time of OH from the CH₄

•O₃cluster experiment in Fig. 2. This ﬁgure illustrates that

the time resolution was sufﬁcient to determine even the fast-

est OH formation rates from the cluster. To the best of our

knowledge, this represents the fastest temporal resolution

with which the dissociation of H₂O₂has been measured.³²

tion, P_obs( ,J,⍀,⌳), the probability of OH being formed in

v

a particular quantum state, was derived from the LIF spectra

such as that shown in Fig. 3. Hydroxyl has two spin–orbit

states^40,41labeled by the quantum number ⍀ϭ1/2,3/2. The

lower f₁(²⌸_3/2) and the upper f₂(²⌸_1/2) state are separated

by 126 cm^Ϫ1for the lowest rotational level. The splitting

decreases with increasing rotational excitation. Each spin–

orbit state, in turn, is split into ⌳-doublet components, la-

beled A and A , which vary by Ϸ0.2% of the rotational

Ј

Љ

energy for all rotational states probed in this experiment. As

N increases, the orbital of the unpaired electron in the A

Ј

state becomes localized in the plane of the molecular rota-

B. State-resolved experiments

tion, while for A the electron orbital becomes localized per-

Љ

For the state-resolved photolysis/probe experiments, the

fourth harmonic ͑266 nm, Ϸ1 mJ cm^Ϫ2, 7 ns͒ of a

Nd^3ϩ:YAG was used to photolyze the ozone. The second

harmonic of another Nd^3ϩ:YAG laser pumped a dye laser.

pendicular to the plane.⁴⁰Because these four unique ﬁne-

structure states are not equally populated and the

distributions may be related to the reaction mechanism, the

population distribution for each state in both ϭ0 and

v

The dye laser’s second harmonic ͑Ϸ10 ␮J cm^Ϫ2, ⌬

ϭ1 is displayed in Fig. 4.

v_FWHM

Ϸ0.3 cm^Ϫ1͒ probed the OH fragments through the ͑0,0͒ and

The populations presented in Fig. 4 agree well with

͑1,1͒ bands of the A(²⌺) X(²⌸) system.³⁷The supersonic

those that we reported earlier.³⁰A striking feature of these

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1218

J. Chem. Phys., Vol. 114, No. 3, 15 January 2001

Miller, van Zee, and Stephenson

FIG. 3. Shown here is a portion of the LIF spectrum of OH formed follow-

ing photolysis of the CH₄•O₃cluster. Superimposed on this LIF spectrum is

the power spectrum of the probe laser at 308.8 nm. The strong, low-J, Q and

FIG. 5. The dots show the measured OH LIF data for the CH₄•O₃cluster

reaction as a function of photolysis/probe delay time. The asymptotic value

was set to unity. The lines represent the optimization of Eq. ͑5͒ to the

experimental data. The wavelength probed is shown below each appearance

curve.

P branch lines and some higher-J levels of the R branch for ϭ0 are probed

v

at 308.8 nm; the P(N) and Q(N) lines decrease in frequency as N increases.

The tallest line at 32 475 cm^Ϫ1is the Q₁₁(1); the doublet at 32 444 cm^Ϫ1is

the overlap of Q₁₁(2) and P₁₁(1); the doublet at 32 355 cm^Ϫ1is the overlap

of Q₂₂(1) and Q₁₁(7).

to 20 mm downstream of the expansion nozzle, thereby, re-

ducing the number density and the collision rate by a decade.

The populations determined at 20 mm showed no difference

from the populations determined at 8 mm. These observa-

tions suggest that post-dissociation collisions do not affect

data is that the f₁and f₂levels of the lowest rotational levels

are unequally populated, with more population in the f₁

state. One conceivable explanation is that after the reaction

the OH has undergone collisions in the beam, with rotational

relaxation causing excess population in the states of lowest

energy. However, a study of the LIF from these levels as a

function of photolysis/probe delay time is consistent with the

distributions being unaffected by collisions. Additional tests

were performed by moving the laser crossing region from 8

the reported P_obs( ,J,⍀,⌳). Figure 3 also illustrates how

v

the spectrum of the ultrafast probe laser encompasses many

different rovibrational transitions. Superimposed on the

state-resolved spectra is a representation of the power spec-

trum of the probe laser at 308.8 nm, which illustrates that

many rovibrational transitions are excited at each ultrafast

probe laser wavelength. The shortest wavelengths probe only

OH( ϭ0). At 307.3 nm, the laser probes many rotational

v

levels, primarily R branch bandheads, of the f₁and f₂states.

Strong, low-J, Q and P branch lines and some higher-J levels

of the R branch are probed at 308.8 nm. When the probe

laser is tuned to 310.7 nm, the P and Q branch lines of

intermediate-J are probed for f₁and f₂. The other wave-

lengths probe a mixture of ϭ0 and ϭ1 levels. The frac-

v

tion of OH( ϭ1) states being probed increases with wave-

v

length, and for probe wavelengths between 308.8 and 316.5

nm, the average internal energy of the OH probed increases

uniformly.

B. Time-resolved data

The time evolution of the OH concentration following

267 nm photolysis of the CH₄•O₃van der Waals complex by

an ultrafast laser is shown in Figs. 5 and 6. The signal is

plotted as a function of photolysis/probe delay time, t_d, at

six different probe wavelengths. Figure 6 shows the early

time data on a higher resolution scale. The traces are the

averages of eight to ten scans, each of which was acquired

during about half an hour. Consecutive scans were acquired

from long to short delay time, then from short to long delay

time. The data was collected from 1 ps before reaction ini-

tiation to 80 ps after reaction initiation. The most striking

feature of the data is that both fast ͑Ͻ1 ps͒ and slow ͑Ϸ5 ps͒

formation times are obvious in the rise curves. The fraction

FIG. 4. The OH( ϭ0,1) population distributions for each lambda-doublet

and spin–orbit state. Both distributions are plotted using the same scale.

v

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The reaction, CH₄ϩO(¹D₂)→CH₃ϩOH

1219

J. Chem. Phys., Vol. 114, No. 3, 15 January 2001

almost all of the OH probed on a picosecond-time scale

comes from cluster reactions and not subsequent reactive

collisions. An upper limit on the OH formation rate, k, from

bimolecular collisions can be estimated using the formula

kϭ␳␴

,

͑1͒

_rv

where ␳, the number density of CH₄in the molecular expan-

sion is Ϸ1.4ϫ10¹⁶molecules cm^Ϫ3, the reactive cross sec-

tion, ␴ , is Ϸ0.20 nm², and the relative velocity, , is Ϸ6

v

r

ϫ10⁴cm s^Ϫ1. These numbers predict a reaction time of Ϸ0.5

␮s, about 10⁵–10⁶times slower than the rise times reported

here. Together, this evidence suggests that the time-resolved

data represent the formation rates of OH from the CH₄•O₃

complex.

Comparison of the magnitude of the ﬂuorescence from

the cluster photolysis to that from a known pressure of ﬂow-

ing H₂O₂provides an estimate of the quantum yield of for-

mation of OH from CH₄•O₃. For both experiments

FIG. 6. The dots show the measured OH LIF data for the CH₄•O₃cluster

reaction as a function of photolysis/probe delay time at short time delays.

The asymptotic value is set to unity. The dashed lines represent the optimi-

zation of Eq. ͑3͒, the two-mechanism ﬁt, and the residuals to this ﬁt are

shown at the top of each panel. The solid lines represent the optimization of

Eq. ͑5͒, the three-mechanism ﬁt, to the experimental data, and the residuals

to the three-mechanism ﬁt are shown below the two-mechanism residuals.

The wavelength probed is given below each appearance curve.

LIFϭ⌽^OH␳␴ ␭͒P

,

͑2͒

͑

detect

where ⌽^OHis the quantum yield for OH formation, ␳ is the

density of the reactants, ␴͑␭͒ is the wavelength dependent

absorption cross section of the species initiating the reaction

and P_detectis the probability of detecting the OH formed. The

value of these quantities^42–44for the hydrogen peroxide re-

action are ⌽^OHϭ1.6–2.0, ␳ϭ10¹⁵molecules cm^Ϫ3, and

␴(267 nm)ϭ9ϫ10^Ϫ20cm^Ϫ2. From the known rovibrational

distributions of OH, the relative probability of detecting the

OH from the two experiments is estimated. For H₂O₂pho-

of OH formed with the fast or slow rate depends on probe

wavelength. Different wavelengths probe different groups of

OH( ,J,⍀,⌳)

states; this shows that different

v

OH( ,J,⍀,⌳) levels have different formation rates. The ﬁt

v

of the time- and state-resolved data to particular models is

discussed below.

One possibility for different rise times is that the signal

arises from more than one reaction product. A number of

tests were undertaken to discount this possibility. First, the

lifetime of the ﬂuorescence signal was observed to decay by

a factor of e^Ϫ1in Ϸ0.8 ␮s, which is the lifetime of the OH

A(²⌺) state. Furthermore, no signal was detected when the

ultrafast probe laser was detuned from the OH A(²⌺)

X(²⌸) resonance. These observations support attribution

tolysis, all OH is formed in the ϭ0, with little ͑Ϸ1050

v

cm^Ϫ1

͒

rotational excitation.^45–50In contrast, for the

CH₄ϩO(¹D₂) reaction only about a quarter of the OH is

formed in the ϭ0 level,⁶and it is formed with about three

v

times more rotational energy than that from H₂O₂. Because

of this difference in the rovibrational distributions, when the

ultrafast laser is tuned to 310 nm, a wavelength that probes

only OH in ϭ0 with moderate J, it is ten times more likely

v

of the observed signal to ﬂuorescence from the OH X

A

to detect an OH from H₂O₂than an OH from CH₄•O₃. For

the CH₄•O₃reaction, the OH quantum yield is the quantity

to be estimated. The absorption cross section⁵¹for free

O ␴(267 nm)ϭ9ϫ10^Ϫ18cm^Ϫ2should be an adequate es-

transition. Second, the ﬂuorescence signal disappeared if ei-

ther CH₄or O₃was withheld from the plenum. The CH₄

reagent had a stated purity of 99.999%, so an impurity in that

gas seems an improbable source of the observed OH. These

observations suggest that the observed OH signal arises from

a reaction between CH₄and O. Third, the mole fractions of

CH₄and O₃were independently varied over an order of mag-

nitude while maintaining a constant backing pressure. While

the overall LIF intensity did change linearly with mole frac-

tion, the ratio of fast to slow components and the reaction

rate varied by less than ﬁve percent, the precision with which

the fast-to-slow ratio can be determined from these data. In

another test, the mole fraction of CH₄and O₃were ﬁxed as

the backing pressure was varied from 275 to 345 kPa. Again,

the ratio of fast-to-slow components and the reaction rate for

each varied by less than ﬁve percent. Both of these observa-

tions support the idea that the reaction involves the CH₄

•O₃complex, because the density of larger clusters,

(CH₄)_m(O₃)_n, would be expected to increase rapidly with

increasing reagent concentration or plenum pressure. Finally,

͓

͔

3

timate of the absorption cross section in the cluster. The

density of clusters in the beam was assumed to be Ϸ10% of

the O₃pressure (␳Ϸ4ϫ10¹⁴clusters cm^Ϫ3). This estimate is

based on previous studies of the NO dimer in this

laboratory⁵²showing that a dimer concentration greater than

10% of the monomer produced higher order clusters, causing

the signal to become nonlinear ͑i.e., deviate from the scaling

LIF signalϰ͑NO͒ϫ͑NO͒ observed at lower ͑NO͒ concentra-

tion͒. The O₃pressure in our expansion was just below that

for which the signal became nonlinear ͑i.e., deviated from

the scaling LIFϰ͑O₃͒ϫ͑CH₄͒͒, which we assume indicates a

CH₄•O₃cluster concentration of 10%. The measured signals

for both H₂O₂and CH₄•O₃photolysis were comparable and

from the quantities indicated one estimates the quantum

yield for OH production from the cluster to be Ϸ0.4 follow-

ing 267 nm photolysis. This calculation suggests that the

cluster geometry does not impose severe dynamical con-

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1220

J. Chem. Phys., Vol. 114, No. 3, 15 January 2001

Miller, van Zee, and Stephenson

straints on the reaction. Clearly, this estimate could be in

error, since we did not directly measure the concentration of

clusters.

IV. DATA ANALYSIS

Above, we saw that the rise time data clearly contained

fast and slow components, the ratio of which depended upon

the probe wavelength. The time- and state-resolved data are

analyzed in this paper with the idea that more than one re-

action mechanism produces OH, and that each mechanism

has a characteristic formation rate and population distribu-

tion. The objective of our analysis is to decompose the ob-

served population distribution into a set of distributions, and

relate these populations to the measured appearance curves.

The product decomposition must be able to predict the frac-

tion of population from each mechanism probed at each

wavelength in the ultrafast experiments.

FIG. 7. This ﬁgure shows the C^fcomponents, i.e., the fraction of ‘‘fast’’

␭

OH determined from the two-mechanism ﬁt ͓Eq. ͑3͔͒ of the time-resolved

data ͑ﬁlled circles͒ at the six ultrafast probe wavelengths of these experi-

ments. Also shown are the components derived from two-mechanism ﬁts of

the product-state data. The open and closed squares are C^fand 1ϪC^f

,

␭

respectively, using the Boltzmann-based decomposition of the product-state

A. Time-resolved data

distribution ͓Eqs. ͑6͒ and ͑10͔͒. The open and closed diamonds are C^fand

␭

1ϪC^f, respectively, using surprisal-based decomposition of the product-

␭

The simplest analysis assumes two unique appearance

time constants. The time-resolved data is taken as the sum of

two exponentials, so that at each probe wavelength, the LIF

time dependence is ﬁt to the following function:

state distribution ͓Eqs. ͑8͒ and ͑10͔͒. This comparison shows that neither the

approach of Eq. ͑6͒ nor Eq. ͑8͒ gives coefﬁcients close to those extracted

from the time-resolved data. The lines connecting the points are to guide the

eye.

LIF t ͒ϭX t ͒ꢀ C^fϫOH t ͒ϩ 1ϪC^f͒ϫOH t ͒

͑

͓

͑

s d

͔

d

␭

d

f

d

␭

͑3͒

LIF t ͒ϭX t ͒ꢀ C^fϫOH t ͒ϩCⁱ

͑

͓

͑

f d

d

␭

d

␭

where X (t_d) is the measured cross-correlation at photolysis-

␭

probe delay time t_dand probe wavelength ␭, ꢀ denotes con-

ϫOH t ͒ϩC^sϫOH t ͒ .

͑5͒

͑

s

͔

d

i

d

␭

volution, C^fis the fraction of ‘‘fast’’ OH at ␭ and (1

␭

ϪC^f) is the fraction of ‘‘slow’’ OH. The time evolution of

As before X (t_d) is the measured photolysis/probe cross-

␭

correlation, and C^f, Cⁱ, and C^sare the fractions of the fast,

the signal also is proportional to the OH number density at

␭

intermediate, and slow channel contributing at ␭, which were

time t_d:

normalized such that C^fϩCⁱϩC^sϭ1. Each channel was as-

␭

OH t ͒ϭ1ϪExp Ϫt /␶ ͒ and

͑4a͒

͑4b͒

͑

f

d

f

sumed to have a single, exponential rise as shown in Eq. ͑4͒.

The six data sets were ﬁt simultaneously by varying ﬁfteen

parameters: Twelve fractional coefﬁcients and three time

constants. The optimized values for C^f, Cⁱ, and C^sare

OH t ͒ϭ1ϪExp Ϫt /␶ ͒,

͑

s

d

s

where ␶ and ␶ are the fast and slow appearance time-

f

s

␭

constants, respectively, and OH_f/s(t_d)ϭ0 for t_dϽ0. It is as-

sumed that the appearance time-constants are ﬁxed, no mat-

ter what rovibrational state is produced. However, it is also

assumed that both the fast and slow mechanism may contrib-

ute to a speciﬁc product state. Because the ratio of popula-

tion formed by the two mechanisms may be different for

presented in Fig. 8 ͑open symbols͒. The three time constants

determined are ␶_fastϷ200 fsϮ70 fs, ␶_interϷ500 fsϮ50 fs, and

␶

_slowϷ5.4 psϮ0.3 ps. Figures 5 and 6 show the ﬁts to the

data. The residuals displayed in Fig. 6 show that the three-

channel model gives a slightly better ﬁt than the two-state

model to the fast rise of the 307.3 and 311.9 nm data and a

much better ﬁt to the 308.8 nm data, though the ﬁts at 313.3

and 316.5 nm are not signiﬁcantly improved.

each rovibrational state, the value of C^fcan be different at

each probe wavelength.

␭

All six data sets were ﬁt to Eq. ͑3͒ simultaneously by

Fitting to four rate constants did not signiﬁcantly reduce

␹ and gave markedly increased uncertainties in the best-ﬁt

varying the six C^fcoefﬁcients, ␶_f, and ␶_s. The best-ﬁts to

2

␭

the time-resolved data and the associated residuals are dis-

parameters.

played in Fig. 6. The resulting C^fcoefﬁcients are shown in

␭

Fig. 7 ͑circles͒. The fraction of fast OH lies between 0.23

and 0.69, depending on the probe wavelength and thereby

the set of rovibrational states being probed. The slow time

constant is ␶_sϭ5.5 psϮ0.2 ps and the fast time constant is

␶_fϭ0.43 psϮ0.02 ps.

The two time-constant ﬁt adequately represents the data,

but the residuals in Fig. 6 show that some of the rise times

are not exactly ﬁt by two exponentials. To explore whether

three exponentials characterize the data better, the appear-

ance curves were ﬁt using the function

B. State-resolved data

The ultimate objective of this analysis is to relate the

observed appearance time-constants to the population distri-

bution. In this section, the decomposition of the measured

rovibrational distribution is presented. First, different ap-

proaches for decomposition of the observed distribution into

two distributions are discussed. Then, a three-channel de-

composition is presented.

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128.123.44.23 On: Fri, 19 Dec 2014 01:02:33

The reaction, CH₄ϩO(¹D₂)→CH₃ϩOH

1221

J. Chem. Phys., Vol. 114, No. 3, 15 January 2001

Another way to divide the observed population distribu-

tion into components is to carry out a surprisal analysis.⁵³

The rotational surprisal, I( ,J,⍀,⌳), deﬁned as

v

P_obs,J,⍀,⌳͒

͑v

I

,J,⍀,⌳͒ϭϪln

,

͑7͒

͑v

ͩ

ͪ

P_o,J,⍀,⌳͒

͑v

is calculated as a function of rotational energy. The two re-

action mechanisms may have characteristic and distinctly

different linear surprisals, aiding in the deconvolution of

P_obs( ,J,⍀,⌳) into P ( ,J,⍀,⌳) and P ( ,J,⍀,⌳).

v

cold

hot

To complete this analysis, the rovibrational prior distribu-

tion, P ( ,J,⍀,⌳), must be computed.

v

o

In our calculation of the prior, the production of all

FIG. 8. This ﬁgure compares the C^f/i/sdetermined from the three-

quantum states was taken as equally probable, subject only

to energy conservation. This distribution would be expected

in the absence of any dynamical constraints. The Whitten–

Rabinowitz state count was used for the vibrational states

and a classical partition function for the CH₃fragment.^54,55

An exact count was used for the hydroxyl fragment. The

prior was then taken as the product of the degeneracy of

internal states of both fragments and the translational state

density divided by total state density at the energy available

to the reaction.^56,57The prior was calculated for each

␭

mechanism ﬁtting of time-resolved data ͓Eq. ͑5͒, open symbols͔ and the

C^f/i/spredicted using the three-mechanism decomposition of the product-

␭

state distribution ͓Eqs. ͑9͒ and ͑10͒; ﬁlled symbols͔ at the six ultrafast laser

probe wavelength used in these experiments. The squares are for the fast

time-constant (C^f) and the cold distribution. The circles are the for inter-

␭

mediate time-constant (Cⁱ) and the hot distribution. The triangles are for

␭

slow time-constant and the statistical distribution. The lines connecting the

points are to guide the eye.

A simple approach is to ﬁt the observed population as

OH( ,J,⍀,⌳) level individually. The energy available in

v

the sum of two Boltzmann distributions, P_hot( ,J,⍀,⌳) and

v

the reaction was taken to be the sum of the enthalpy of the

reaction CH₄ϩO(¹D₂)→CH₃ϩOH (15 240 cm^Ϫ1) and the

average translational energy in the center-of-mass frame

͑1515 cm^Ϫ1͒. This number is correct for a free reaction, and

using it here assumes that the O₂generated in the cluster

receives the same energy as in the photodissociation of iso-

lated, gaseous O₃. The sum over rotational states,

P_cold( ,J,⍀,⌳)

v

P_obs,J,⍀,⌳͒

͑v

E_rot

ϭC_hotExp Ϫ

ͩ

ͪ

2Jϩ1

kT_hot

E_rot

ϩ 1ϪC ͒Exp Ϫ

.

͑6͒

͑

ͩ

ͪ

hot

kT_cold

⌺P ( ,J,⍀,⌳) was normalized to ⌺P ( ϭ0,1;J,⍀,⌳)

v

o

obs

A least-squares ﬁt of Eq. ͑6͒ to the ϭ0 data gave, T

ϭ4110 KϮ106 K, T_coldϭ156 KϮ7 K, and (1ϪC_hot)/C_hot

v

for each vibrational level.

Figure 10 shows the rotational surprisal for OH(

hot

v

ϭ3.5. For ϭ1, the ﬁt yielded T_hotϭ5980 KϮ80 K, T_cold

v

ϭ0,1) plotted versus the fraction of nonvibrational energy in

rotation, g_rϭf_r/(1Ϫf_v), where f_rand f_vare the fraction of

the total available energy in rotation and vibration, respec-

ϭ131 KϮ6 K, and (1ϪC_hot)/C_hotϭ3.9. These ﬁt values

represent the data well as shown in Fig. 9. The values of

(1ϪC_hot)/C_hotcorrespond to only 11% of the OH being

formed in the cold channel, while 89% is from the hot chan-

nel.

tively. If P_obs( ,J,⍀,⌳) were statistical, the data would fall

v

on a line with a slope of zero. The distribution at low g_ris

much colder than the prior distribution, while the distribution

at high g_ris hotter than the prior distribution. The surprisal

was ﬁt with the equation

P_cold,J,⍀,⌳͒ϩP

͑v

,J,⍀,⌳͒

͑v

hot

I

,J,⍀,⌳͒ϭϪln

͑v

ͫ

ͬ

P_o,J,⍀,⌳͒

͑v

ϭϪln b Exp m_coldg_r͒

͓

͑

cold

ϩb_hotExp m g ͒ .

͑8͒

͑

͔

hot

r

Least squares ﬁts gave m_coldϭϪ128Ϯ13, m_hotϭ2.6

Ϯ0.2, b_coldϭ2.53Ϯ0.38, and b_hotϭ0.56Ϯ0.03 for ϭ0; for

v

ϭ1, values m_coldϭϪ138Ϯ18, m_hotϭ4.0Ϯ0.3, b_coldϭ3.00

v

Ϯ0.61, and b_hotϭ0.51Ϯ0.03 were obtained. The data for

v

ϭ0 and 1 are well ﬁt by the sum of two linear surprisals, as

shown by the dashed lines in Fig. 10. Two population distri-

butions, P_hot( ,J,⍀,⌳) and P ( ,J,⍀,⌳), then can be

v

cold

deduced from the surprisal ﬁts.

Last, the rotational surprisals were also ﬁt to three dis-

tributions. One will be assumed to be the statistical prior,

FIG. 9. The symbols show the OH( ϭ0,1) rotational population data dis-

played as a Boltzmann plot. The lines give the two temperature Boltzmann

ﬁt via Eq. ͑6͒.

v

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1222

J. Chem. Phys., Vol. 114, No. 3, 15 January 2001

Miller, van Zee, and Stephenson

Boltzmann decomposition of the rotational populations, two

time-constants with the two-component surprisal decomposi-

tion, or three time-constants with the three-component sur-

prisal decomposition, offers the most consistent explanation

of the data.

V. DISCUSSION

A. Comparing alternatives

The principle criterion to be used in assessing which of

the alternatives is most consistent with the data will be how

well the fractional contributions ͓C^f/i/s; Eqs. ͑3͒ and ͑5͔͒

␭

determined by ﬁtting the appearance curves are predicted by

a given population decomposition. For example, if two reac-

tive channels were operative, we expect the C^ffrom the

␭

appearance curves to agree with the prediction of a two com-

ponent decomposition of the rovibrational distributions, as-

suming as usual that different formation times represent dif-

ferent reaction mechanisms and that each mechanism

produces a characteristic rovibrational distribution. Below,

we consider the two-channel alternatives ﬁrst, and then turn

to the three-channel analysis.

FIG. 10. Surprisal plots for OH( ϭ0,1) showing the surprisal as a function

v

of reduced rotational energy, g_r. The dashed lines are the optimization of

Eq. ͑8͒, the two-mechanism model, to the data. The solid lines are the

optimization of Eq. ͑9͒, the three-mechanism model.

Determining the C^f/i/scoefﬁcients from the time-

␭

resolved date is easy. They are simply the best-ﬁt coefﬁ-

cients of Eqs. ͑3͒ and ͑5͒. Determining the C^f/i/scoefﬁcients

␭

using the surprisal or Boltzmann decompositions is some-

what cumbersome, because the ultrafast probe laser spectrum

encompasses many rovibrational transitions, as illustrated in

Fig. 3. However, these coefﬁcients can be calculated by sum-

ming over all transitions excited at a particular probe laser

wavelength. Speciﬁcally, these coefﬁcients can be calculated

using the equation

which is to say the slope of its surprisal is zero. As will be

discussed further below, the observation of a component

with a slow rise time of Ϸ5 ps suggests that one of the

*

reactive channels produces OH through an CH₃OH inter-

mediate in which the energy is randomized. One might rea-

sonably expect the rovibrational energy distribution of the

products generated by this channel would be the prior distri-

bution. The surprisal parameters for the other two channels

were unconstrained in the ﬁt; one has more rotational energy

than the prior and the other less.

⌺ P

,J,⍀,⌳͒ϫB

,J ; ,J͒ϫSpec ,J ; ,J͒

͑v

v

Ј Ј

,J ; ,J͒ϫSpec ,J ; ,J͒

͔

b

c

fast

C ^fϭ

.

␭

⌺ P

͓

,J,⍀,⌳͒ϫB

͑v

v

͑v

v

Ј Ј

obs

͑10͒

Given the aforementioned assumptions, the surprisals

were ﬁt using the equation

In this expression, B( ,J ; ,J) represents the Einstein

v

Ј Ј

B-coefﬁcient for the designated transition; P_obs( ,J,⍀,⌳) is

v

I

,J,⍀,⌳͒ϭϪln b Exp m_coldg_r͒

͓ ͑

cold

͑v

the experimentally determined nascent population distribu-

tion for OH; P_fast( ,J,⍀,⌳) is the population distribution

for OH created through the fast mechanism;

v

ϩb_statExp m_statg_r͒ϩb_hotExp m g ͒ .

͑

͔

hot

r

͑9͒

Spec( ,J ; ,J) is the power spectrum of the probe pulse at

v

Ј Ј

the excitation frequency; and the sum is over rovibrational

With m_statϵ0, a least-squares ﬁt to the ϭ0 data in Fig. 10

gave m_coldϭϪ129Ϯ13, m_hotϭ6.0Ϯ0.5, b_coldϭ3.16Ϯ0.35,

v

states.

These C^fcan now be calculated for the two-Boltzmann

b

_hotϭ0.07Ϯ0.02, and b_statϭ0.67Ϯ0.03. With these values,

the population in each of the three distributions may be cal-

culated, giving 12% of the OH( ϭ0) created cold, 21% hot,

␭

decomposition of P_obs( ,J,⍀,⌳) using the best-ﬁt param-

v

eters of Eq. ͑6͒ and by associating the P_hot( ,J,⍀,⌳) of Eq.

v

͑6͒ with the P_fast( ,J,⍀,⌳) of Eq. ͑10͒. This association

v

and 67% statistical. The data for the ϭ1 level were ﬁt by

v

seems intuitive, because for a methanol intermediate one

would expect the slower evolving product to be rotationally

cooler when compared to the faster evolving product. As Fig.

assuming the statistical channel has the calculated prior

value for the ϭ1/ ϭ0 population ͑21%͒; therefore, b

v

stat

was set to a ﬁxed value of 0.15. The least-squares ﬁt to the

7 illustrates, the agreement between the time-resolved C^f

ϭ1 data gave m_coldϭϪ131Ϯ18, m_hotϭ4.7Ϯ0.3, b_cold

v

␭

and the calculated C^fis poor for this product-state decom-

ϭ3.16Ϯ0.51, and b_hotϭ0.38Ϯ0.02. This ﬁt gave 11% cold,

␭

position. It is possible, of course, that the association of the

74% hot, and 15% statistical for ϭ1. The solid lines in Fig.

v

P_hot( ,J,⍀,⌳) with P ( ,J,⍀,⌳) is incorrect. If an ab-

10 show these ﬁts to the surprisals. As would be expected,

the surprisal data are slightly better ﬁt by the three-

distribution model than by the two-distribution model.

The question remains as to which of the alternatives ap-

proaches, two appearance time-constants with a two-

v

fast

straction reaction were operative, for example, one might

expect the fastest mechanism to produce the rotationally

coldest product. In this case, the time-resolved C^fwould

␭

correspond to (1ϪC^f), where the latter C^fis the product-

␭

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The reaction, CH₄ϩO(¹D₂)→CH₃ϩOH

1223

J. Chem. Phys., Vol. 114, No. 3, 15 January 2001

state prediction. This quantity is also shown in Fig. 7 and

also agrees poorly with the time-resolved C^f. This observa-

␭

tion is perhaps not surprising, inasmuch as there is no gen-

eral justiﬁcation for products having thermal distributions,⁵⁸

because the available energy is limited by the sum of the

enthalpy for the reaction CH₄ϩO₃→CH₃ϩOHϩO₂and the

energy of the photolysis photon.

The comparison can be repeated using the surprisal-

based decomposition of P_obs( ,J,⍀,⌳). Using the best-ﬁt

v

parameters to Eq. ͑8͒, the C^fwere again calculated. Again,

␭

for a two-mechanism model to be valid, either the calculated

C^for (1ϪC^f) must agree with the best-ﬁt values of the

␭

two-exponential appearance model. Again, Fig. 7 shows that

agreement is poor.

It appears that the time-resolved and state-resolved data

cannot be simultaneously ﬁt with a two-mechanism model.

FIG. 11. The fraction of the OH( ϭ0,1) rotational state populations popu-

lated through the three mechanisms: Fast mechanism ͑squares͒, dissociation

v

*

͔

of CH O before complete IVR ͑circles͒, and dissociation of a methanol

͓

4

The P_obs( ,J,⍀,⌳) data can be decomposed into two

v

intermediate after IVR ͑triangles͒. The fractions were calculated using the

best-ﬁt parameters given in the text.

unique components. The time-resolved data are adequately

ﬁt by the sum of two exponential OH rise times. However,

the amplitudes of fast and slow components do not match the

amplitudes of the hot and cold distributions for the decom-

positions considered here. This leaves the three-channel

model to be considered.

ﬁtting parameters of Eq. ͑9͒, e.g., P_hot( ,J,⍀,⌳)

ϭ b_hotExp(m_hotg_R) / (b_hotExp(m_hotg_R) ϩ b_coldExp(m_coldg_R)

v

ϩb_stat) P_obs( ,J,⍀,⌳) while using Eq. ͑6͒ to represent the

v

With the aid of formulas analogous to Eq. ͑10͒, coefﬁ-

values of P_obs( ,J,⍀,⌳).

v

cients C^f/i/sfor the six probe wavelengths may be calculated

␭

from the surprisal analysis and the decomposition of Eq. ͑9͒.

Figure 8 compares the C^f/i/sfor the three mechanisms that ﬁt

B. Mechanism assignments

␭

the time-resolved data ͑open symbols͒ to the C^f/i/scalculated

The long time constant is almost surely the dissociation

of a methanol intermediate after essentially complete IVR

according to a statistical theory, such as the Rice–

Ramsburger–Kassel–Marcus ͑RRKM͒ theory.⁵⁹RRKM rate

calculations,⁶⁰consistent with thermal rate coefﬁcients and

␭

from the state-resolved data ͑ﬁlled symbols͒. For all wave-

lengths, there is close agreement, if the following identiﬁca-

tion is made: Associate the OH formed fastest with OH

formed in the lowest

N

levels ͓␶_fastϷ0.2 ps and

P_cold( ,J,⍀,⌳)͔, the OH formed at the intermediate rate

v

*

assuming reasonable values for the CH₃OH transition

state,⁶¹ﬁt both the time scale ͑Ϸ10 ns͒ for dissociation in

infrared multiphoton dissociation experiments⁶²of the disso-

ciation of CH₃OH and the time scale ͑Ϸ5 ps͒ for dissociation

at the 16 700 cm^Ϫ1energy in the cluster photolysis experi-

ments. This supports the statistical assignment, because one

expects the RRKM rate to scale correctly with internal en-

ergy, even though exact agreement is usually achieved only

if the transition state is selected to ﬁt a particular microca-

nonical rate. Statistical adiabatic channel model

calculations⁶³predict lifetimes of 10 ps for the reaction of

with the hot distribution ͓␶_interϷ0.5 ps and P_hot( ,J,⍀,⌳)͔,

v

and the OH formed slowest with the statistical channel

͓␶_slowϷ5.4 ps and P_stat( ,J,⍀,⌳)͔. This three-mechanism

v

model is internally consistent. It must be noted that the three

rovibrational distributions are not unique, because there are

other distributions with nonlinear surprisals which also ﬁt the

data. Improved agreement between the coefﬁcients calcu-

lated from time- and state-resolved data can be achieved by

varying the ﬁtting parameters slightly from their best ﬁt val-

ues. We reiterate that the analysis in terms of three mecha-

nisms arises from our conceptual requirement that each com-

thermal CH₄ϩO( D₂)→CH₃OH at an energy 1300 cm^Ϫ1

1

*

ponent of P_obs( ,J,⍀,⌳) characterized by a linear surprisal

less than our hot O(¹D₂) experiments, and 1.6 ps for O(¹D₂)

atoms from N₂O photodissociation at 193 nm, providing

7700 cm^Ϫ1more available energy than in our experiments.

v

must have a unique appearance time-constant and that one of

the components of the product-state distribution has a sur-

prisal of zero-slope. The curves in Fig. 11 show the fraction

of cold, statistical, and hot product as a function of internal

energy calculated from the three-distribution ﬁt parameters.

One sees that the cold distribution only contributes signiﬁ-

cantly to the four, lowest rotational levels. The statistical

distribution contributes to the majority of the probed levels,

*

These estimates of the lifetime of CH₃OH are also in agree-

ment with the value of 5.4 ps observed for the slow compo-

nent, which is also the slowest rise time measured. No inter-

mediate should dissociate more slowly than that following

complete IVR. If IVR is complete within picoseconds—and

the contrary would be unexpected at this energy⁶⁴—the long-

est formation time is, by default, the statistical lifetime.

These observations argue for identifying the slow channel

at least for ϭ0, while the hot distribution contributes pri-

v

marily to OH with an internal energy у4000 cm^Ϫ1. Though

*

we have data only for ϭ0 and ϭ1, this model predicts

with the statistical dissociation of a CH₃OH intermediate.

v

that the statistical mechanism makes a negligible contribu-

The intermediate formation time of 0.5 ps is ascribed to

*

tion to vibrational levels у2. If one desires analytic expres-

dissociation of a CH₄O intermediate before complete IVR

sions for the three P( ,J,⍀,⌳), one may use the

and associated with the high-J fraction of OH arising from

v

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128.123.44.23 On: Fri, 19 Dec 2014 01:02:33

1224

J. Chem. Phys., Vol. 114, No. 3, 15 January 2001

Miller, van Zee, and Stephenson

this reaction. According to our three-state decomposition of

P_obs( ,J,⍀,⌳), this component accounts for about 21% of

though clearly this is not deﬁnitive. This alternative is dis-

cussed in more detail in the Appendix.

v

Although our three-mechanism model ﬁts our present

data, a crucial question is: Does this model also ﬁt the vast

amount of data already available on the CH₄ϩO(¹D₂)

→CH₃ϩOH reaction? If the answer is clearly ‘‘No,’’ then it

is possible that our data or its interpretation is wrong, or our

premise that the cluster reaction is similar to the bimolecular

reaction is wrong. This question is systematically addressed

in the Appendix, where we compare our data and its inter-

pretation to other experimental and theoretical research on

OϩCH₄. Speciﬁcally, we show that our present work is con-

sistent with time scales deduced from chemical quenching

experiments, from Doppler spectroscopy, and from angular

distributions measured in molecular beam experiments. Our

state-resolved measurements are in reasonable agreement

with most, but not all, previous gas phase results using sev-

eral sources of O atoms and different experimental condi-

the population in ϭ0, 74% for ϭ1, and presumably most

v

of the population in ϭ2 to ϭ4. At least three observa-

v

tions bolster this assignment. First, evidence overwhelmingly

suggests that O(¹D₂) insertion is the predominant reaction

mechanism,^{3–7,17,18,24,65,66}pointing to nonstatistical dissocia-

*

tion of CH₄O . Second, and related, a 0.5 ps rise time seems

too long to be a stripping of a H atom by fast O ͑forward

scattering limit͒ or a collinear abstraction by fast O ͑back-

ward scattering limit͒. The attacking oxygen atom initially

moves with an average speed⁶⁷of Ϸ2.1 nm ps^Ϫ1and hence

would travel the 0.3–0.4 nm necessary for a simple stripping

reaction in much less than 0.5 ps. The product OH would

presumably gain additional translational energy from the re-

action exothermicity, which, in the absence of complex for-

mation, would further decrease the estimated time for a strip-

ping reaction. Last, the OH product is too hot to be the

statistical channel. Together, these observations suggest dis-

tions. We show that the P_obs( ,J,⍀,⌳) plots of others could

v

be well ﬁt by our three mechanism model, although earlier

authors did not do this. The possibility that O(³P) atoms are

signiﬁcantly inﬂuencing the low-N OH in our experiments is

examined in detail by reference to theoretical and experimen-

tal studies of this speciﬁc channel ͑we argue against it͒. The

inﬂuence of the minor channels ͑e.g., H₂ϩH₂CO͒ on our

time-dependent results is discussed. The overall conclusion

of the Appendix is that our experimental results and the

model we use to interpret them are consistent with a great

body of data, and that the present approach provides a uni-

fying framework for its understanding. We have put the

comparison to previous work, which is extremely important,

into an Appendix in order to focus the main part of the paper

on our new data and its analysis.

*

sociation through a CH₄O intermediate before IVR.

The most tenuous part of the present data analysis is the

very fast time ͑0.2 ps͒ associated with OH in low-J states.

This OH accounts for about 11% of the population in both

ϭ0 and ϭ1 levels. Fast OH could be formed by O mov-

v

ing perpendicular to a C–H bond and stripping off a H atom

at impact parameters sufﬁciently large to avoid being trapped

in the CH₃OH well. Such trajectories presumably would give

rise to forward-scattered OH in high, rather than low, rota-

tional states. Collinear attack followed by prompt back-

scattered OH could give rise to OH in the low-J levels that

seem to be correlated with the shortest time constant. The

saddle point on the O(¹D₂) potential surface¹⁶shows such a

collinear C–H–O reaction. Some abstraction component

seems consistent with the Doppler spectroscopy results^8–12

which show a slight preference for backward scattering for

VI. STRENGTHS AND WEAKNESSES OF THE

PRESENT EXPERIMENT AND ANALYSIS

the OH( ϭ0, Nϭ5 and 8). Our decomposition shows that

v

Several elements of this experiment and its analysis

complicate the interpretation of our results. This section dis-

cusses these factors and outlines experimental strategies for

circumventing these difﬁculties.

the prompt component contributes mostly to the four lowest

f₁rotational states and predicts that these states would show

pronounced backward scattering.

A conceivable explanation for the fast OH in low-J, f₁

levels is reaction of O(³P_j) formed in about 10% yield in O₃

photolysis with 266 nm light. A large percentage of these

atoms have enough energy to surmount the barrier to

reaction.⁶⁷Additional O(³P_j) might also evolve through

O(¹D₂)/O(³P_j) curve crossing in the entrance channel. Be-

cause reactions of O(³P_j) are typically abstractions, the ro-

tationally cold and fast appearing OH may indeed be from

reaction with O(³P_j). On the other hand, low-J, f₁OH was

also preferentially populated in the photolysis of the CH₄

•N₂O cluster,³¹and no O(³P_j) atoms are formed directly in

N₂O photolysis. Also, the low-J population is observed for

In these experiments, the appearance rate for most of the

product states has not been measured. The free reaction⁶and

the cluster reaction³⁰between CH₄and O(¹D₂) produces

about half of the OH in vibrational levels у1, with ϭ2

v

the most probable and levels up to ϭ4 populated.⁶The

v

experiment reported here investigated no levels above

v

ϭ1. Moreover, the highest rotational states even for these

two vibrational states were not monitored, because of the

autodissociation of OH(A). Therefore, the conclusions

drawn here are based on probing somewhat less than half the

OH product from the reaction. In our preliminary

experiments²⁶only OH( ϭ0,J), formed predominantly

v

both the ϭ0 and ϭ1 product, which is different than

v

through the statistical channel, was probed. As a result, we

failed to discover the fast components discussed here. This

earlier failure highlights the desirability of obtaining more

comprehensive data.

Another limitation of the data presented here is that each

appearance curve represents a complicated superposition of

many rovibrational states, because of the inherently broad

what has been observed for the reaction between CH₄and

O(³P_j) where no ϭ1 has been observed. Moreover, ab

v

initio calculations of the singlet surfaces do not preclude

abstraction trajectories, which would produce rotationally

cold products quickly.^16–18Together, we feel these facts ar-

gue against attributing this channel to reaction with O(³P_j),

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The reaction, CH₄ϩO(¹D₂)→CH₃ϩOH

1225

J. Chem. Phys., Vol. 114, No. 3, 15 January 2001

spectrum of short pulses compared to the spacing of indi-

vidual OH transitions. This averaging process will tend to

obfuscate different appearance rates of speciﬁc product

states. Although three rise times adequately represented our

LIF data within the present signal-to-noise, the idea that

there are three distinct OH formation mechanisms, each

characterized by a distinct distribution, is presumably overly

simple. An absorption experiment could allow measurement

energy surface for this van der Waals complex would be

helpful. The dissociation of gaseous O₃has been studied and

the dynamics of forming O(¹D₂) and O₂are fairly well un-

derstood. Presumably, complexation does not signiﬁcantly

alter this dissociation process. There is almost complete dis-

sociation within 70 fs.^74–76While this dissociation is very

fast, it is not a negligible fraction of the fastest time-constant

measured in these experiments and may limit the time-

resolution in these experiments. The average asymptotic

velocity⁶⁷of the O(¹D₂) is Ϸ2.1 nm ps^Ϫ1, directed along the

initial O₂–O bond,⁷⁷and the O₂travels Ϸ1.1 nm ps^Ϫ1. The

of the appearance of individual OH( ,J,⍀,⌳) states. Fol-

v

lowing photolysis, spectrally broad ultrafast pulses could

probe the OH, and a spectrometer could disperse the trans-

mitted light onto a multichannel detector. With this ap-

proach, the experimental time resolution is limited by the

laser pulse duration, the experimental spectral resolution by

the spectrometer, and the observed linewidths by the sample

dephasing time.⁶⁸This approach might also permit probing

the OH close to the transition state,^69,70where the OH(X)

and OH(A) potentials are perturbed by the CH₃or O₂frag-

ments. Such information, combined with sub-Doppler spec-

tra of individual rovibrational states, would yield a more

complete picture of the dynamics of this reaction. In the

absorption experiment considered above, one would measure

the absorption spectrum as a function of time for each

*

O₂molecule should not alter the long-lived CH₃OH disso-

ciation, because the diatom would be on average Ϸ6 nm

away from the dissociating methanol. Our RRKM calcula-

tions and calculations of the statistical prior energy distribu-

tions for the OH and CH₃products assumed the energetics of

the free reaction, i.e., the energy carried by the O₂molecule

was assumed to be unaffected by the complex, an idea which

is supported by the similarity between the OH energy distri-

butions for free and cluster reactions.

Since submission of this manuscript, the geometry of a

CH₄•O₃cluster has been determined by another group at

NIST,⁷³using microwave spectroscopy. This study found the

methane moiety to be freely rotating and located atop the

ozone molecule. The angle between the line formed by the

center-of-mass of the two molecular components and the

plane of the ozone molecule was 118.2° and the closest oxy-

gen to carbon internuclear distance was 0.36 nm for the equi-

librium structure. If the O(¹D₂) recoils along the O–O

bond,⁷⁷it would seem unlikely to react, since the dissociat-

ing O is not initially pointed at a H atom; hence this structure

seems hard to reconcile with our estimate of a large ͑Ϸ40%͒

quantum yield for OH formation. However, as noted above,

the OH LIF signal scaled with the pressure of the reactants

and carrier gases as expected for the CH₄•O₃complex. Also,

the OH rovibrational distributions are similar to the free

reaction.³⁰These observations strongly suggest that the reac-

tion is taking place in a CH₄•O₃cluster, rather than some

larger (CH₄)_m•(O₃)_ncluster. It is possible that the CH₄•O₃

producing OH in our dynamics experiments has a different

geometry from that identiﬁed by microwave spectroscopy.

Different expansion conditions and apparatus could produce

clusters in different geometries. It is also quite possible, as

discussed above, that our estimate of a 40% quantum yield is

signiﬁcantly in error due to one assumption we had to make

in its derivation. A deep methanol minimum dominates the

CH₄–O potential^16–18and could alter the O(¹D₂) recoil di-

rection, so that reaction occurs despite an unfavorable initial

geometry.

OH( ,J,⍀,⌳) state, each of which might have a different

v

and complex time dependence. This approach has previously

been used to study photodissociation reactions.⁶⁸Also, an

absorption experiment could probe OH( Ͼ1) using strong

v

A(²⌺) X(²⌸) absorptions that could not be used in ﬂuo-

rescence due to autodissociation that competes with the 0.8

␮s ﬂuorescence lifetime.

The product state distributions were decomposed subject

to the condition that one of the three distributions was an

unconstrained prior. This restriction was imposed, in part,

because infrared multiphoton dissociation studies⁶²of

CH₃OH showed good agreement between an unconstrained

prior and the product state distribution measured in those

experiments and between the dissociation rate and RRKM

predictions. It should be noted, however, that those experi-

ments were only 2000–3000 cm^Ϫ1above threshold, while

the experiments reported here are Ͼ16 000 cm^Ϫ1above

threshold. For reactions without a large barrier, there is evi-

dence that as energy increases, the product-state distributions

may become nonstatistical.^71,72Clearly, if this were true for

*

the CH₃OH dissociation, our decomposition of the product-

state distribution could be incorrect.

Throughout this paper we compared free and cluster re-

action results with the unstated assumption that the reaction

mechanisms are similar. However it is important to question

whether the trajectories of O(¹D₂) attacking CH₄in the clus-

ter resemble the trajectories in the free, gas phase reaction.

In this paper we used complimentary data, product-

appearance curves and product-state distributions, to learn

about the mechanisms of the elementary reaction

CH₄ϩO(¹D₂)→CH₃ϩOH, which has rich and interesting

dynamics. The data were analyzed under the assumption that

each mechanism was characterized by a unique appearance

time-constant and that each mechanism produced a unique

We observed that the OH ϭ1/ ϭ0 ratio for the cluster was

v

the same as for the free reaction and that the rotational state

distributions were generally similar ͓e.g., excluding the low-

est N, T ( ϭ0,1)Ϸ7000 K for the bulb reaction and Ϸ5000

v

rot

30

K for the cluster reaction͔ As we have discussed before,

these observations suggest, but do not prove, that reaction

mechanisms in the cluster are similar to those for the free

reaction. The CH₄•O₃cluster environment⁷³could have a

signiﬁcant impact on the observed dynamics, and a potential-

OH( ,J,⍀,⌳) energy distribution. For the data reported in

v

this manuscript, it was found that a three-channel model ͑for-

mation times of 0.2, 0.5, and 5.4 ps͒ best described the data.

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1226

J. Chem. Phys., Vol. 114, No. 3, 15 January 2001

Miller, van Zee, and Stephenson

An improved experimental approach ͓e.g., ultrafast ultravio-

let absorption rather than LIF͔ and more comprehensive data

would be likely to uncover even more complex reaction dy-

namics. We hope these studies will motivate a rigorous the-

oretical investigation of the dynamics of this reaction.

zed. This generation process gave Ϸ20% uncertainty in the

total available energy. The value of 0.8 ps was calculated

from the slope-to-intercept ratio ͑the intercept value being an

extrapolation from ﬁnite to zero pressures͒ of a plot of the

ratio of the concentration of methanol to the pressure of the

cooling gas as a function of methane concentration. While

our experiments probe a limited subset of the total product

states, the 0.8 ps value is nevertheless similar to the

population-weighted average of the rise times that we mea-

sured directly. Olzmann⁶³has also noted that Lin and De-

More used a strong-collision model in analyzing the chemi-

cal timing data, and if one assumes that the collisional

cooling rate is different than gas kinetic, a somewhat differ-

ent lifetime can be extracted from these experiments. Given

the experimental uncertainties and differences between the

experiments of DeMore and co-workers and the data pre-

sented here, we believe that the two lifetime measurements

are in remarkable agreement.

ACKNOWLEDGMENT

C. Cameron Miller acknowledges the receipt of an

NIST/NRC Postdoctoral Associateship.

APPENDIX: COMPARISON OF THE CH₄"O₃RESULTS

TO PREVIOUS STUDIES OF REACTIVE

COLLISIONS BETWEEN CH₄AND O

As highlighted in the introduction, the literature contains

a wealth of information concerning the thermodynamics,

chemical kinetics, and molecular dynamics of the reaction

between CH₄ϩO(¹D₂). In this Appendix, we critically com-

pare this literature to our results. The objective of this com-

parison is to look for evidence in the literature that will test

the mechanistic assignment of this paper and to help unify

this sizable literature into a comprehensive understanding of

the dynamics of the title reaction.

To answer whether formation of CH₃and OH from

CH₄ϩO(¹D₂) in liquid argon requires an abstraction chan-

nel, one may compare the vibrational relaxation time of

*

CH₃OH in liquid argon to the dissociation time of

*

CH₃OH . The collisional stabilization time, ␶_vr, can be es-

timated as

^Ϫ1ϭk ␳g r͒.

͑A1͒

A. Matrix and chemical timing experiments

␶

͑

vr

Much of our intuition about the reactions between

atomic oxygen and hydrocarbons is derived from the early

work of Cvetanovic and co-workers⁶⁶and DeMore and

co-workers.^3–5Cvetanovic and co-workers⁶⁶proposed three

distinct mechanisms: Insertion and fragmentation to form

OH, abstraction to form OH, and elimination of molecular

hydrogen. In experiments carried out in liquid argon aimed

at further elucidating the role of the these proposed mecha-

nisms, DeMore and Raper⁴identiﬁed three products for the

reaction with methane,

In this expression, k_vrrepresents the vibrational relaxation

*

rate constant of CH₃OH in liquid argon at a temperature of

87 K, ␳ is the density of the liquid argon, and g(r) is the

radial distribution function evaluated at the Lennard-Jones

diameter.⁷⁸The exact value for k_vris not known, but it is

likely to be slightly less than the gas kinetic rate, and we

assume it to be Ϸ10^Ϫ10cm³s^Ϫ1. The argon density is

Ϸ2.3ϫ10²²cm^Ϫ3. The value of the radial distribution is also

unknown, though in general it lies between 1 and 3, and we

will take a value of 2. Using these numbers in the Eq. ͑A1͒

1

gives a ␶ _rϷ0.2 ps. If we take the dissociation time, ␶, to be

CH ϩO D ͒→CH OH 53%,

͑

v

4

2

3

0.5 ps ͑the dissociation time we have assigned to the incom-

plete IVR mechanism͒, then the probability of the interme-

diate dissociating prior to vibrational relaxation is 1

→H₂COϩH₂7%,

→CH₃ϩOH 40%.

*

Ϫexp(Ϫ␶_vr/␶)Ϸ0.33. That is, one-third of the CH₃OH

5

*

From this work, DeMore speculated that CH₃OH might be

common to all these reaction paths. However, subsequent

studies of the free, gas-phase reaction at room temperature

lead Lin and DeMore³to conclude that about half of the total

would have dissociated into CH₃and OH prior to stabiliza-

*

tion of CH₃OH . This number lies very close to 40% re-

ported for the reaction in liquid Ar. This estimate suggests

*

that the collision stabilization of CH₃OH , even in liquid

*

CH₃and OH produced passed through a CH₃OH interme-

argon, is unlikely to be much faster than the rate of OH

formation. Therefore, observation of OH does not necessar-

ily suggest an abstraction mechanism against an insertion/

elimination mechanism. It should be noted that photolysis of

O₃–CH₄mixtures in solid argon at 20 K reportedly gives

only CH₃OH.⁷⁹This may be because IVR is faster in solid

than liquid argon, or more likely, that the fragments are

trapped so that geminate recombination occurs.

diate, which they estimated to have a lifetime of about 0.8

ps. Production of the other half was attributed to a different

prompt mechanism. The production of methyl and hydroxyl

radicals at high pressures and even in liquid argon is fre-

quently cited as evidence for an abstraction mechanism that

does not involve a methanol-like intermediate. The results of

DeMore and co-workers pose two questions. First, is the 0.8

ps consistent with the lifetimes measured in our experi-

ments? Second, does production of methyl and hydroxyl

radicals even in liquid argon demand an abstraction channel?

To answer the ﬁrst question, it is important to understand

how the 0.8 ps lifetime was determined. The O(¹D₂) was

generated by 184.9 nm photolysis of nitrous oxide, and the

translational energy was neither nascent nor fully thermali-

B. State-resolved measurements

In his pioneering studies of this reaction, Luntz⁷photo-

lyzed ozone at 266 nm in a dilute gaseous Ar–O₃–CH₄mix-

ture and probed OH( ϭ0,1). The experiments were carried

v

out at a density of 6ϫ10¹⁶cm^Ϫ3and a photolysis/probe time

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The reaction, CH₄ϩO(¹D₂)→CH₃ϩOH

1227

J. Chem. Phys., Vol. 114, No. 3, 15 January 2001

delay of 0.5 ␮s, presumably ensuring that the hot oxygen

atoms formed in the photolysis were thermalized prior to

reaction. As a result of this thermalization, the O(¹D₂) car-

ried Ϸ1200 cm^Ϫ1less energy; moreover, the O(³P_j) atoms

lacked sufﬁcient translational energy to surmount the barrier

for reaction. However, the long photolysis/probe delay and

the relatively high pressures opened the possibility of colli-

PW ϭ0 data for states with internal energies Ͻ3000 cm^Ϫ1

v

lie very close to a linear surprisal with zero-slope. It is likely

that if the PW data were analyzed by the three state model

above ͑one channel to be characterized by an unconstrained

prior͒, a statistical channel greater than 18% would be de-

duced.

Wada and Obi ͑WO͒ have reported P_obs

(

v

sional relaxation of OH( ,J,⍀,⌳) that would alter the na-

ϭ0,1;J,⍀,⌳) of OH from CH₄ϩO(¹D₂) both for the free

reaction and for the CH₄•N₂O cluster.³¹Photolysis of N₂O at

193 nm produced O(¹D₂) with an average total energy for

the reaction of about 18 400 cm^Ϫ1. For the free reaction, a

v

scent distribution, though Luntz maintained that the distribu-

tions were close to nascent. Luntz reported that ϭ0 and

v

ϭ1 were comparably populated and had similar rotational

state distributions. The f₁and f₂spin–orbit states were

equally populated, and the ⌳-doublet ratio increased from

unity at low-N to Ϸ1.7 at Nϭ19. A surprisal analysis was

done for the rotational distribution. Luntz decomposed this

surprisal into two regions. Levels for NϾ6 were well ﬁt by a

line of slope Ϸ6.5, whereas states for NϽ6 were much

colder, and deviated greatly from a linear surprisal. From the

data in Luntz’s Fig. 2, the cold component can be estimated

ϭ1/ ϭ0 ratio of 1.1 was measured. For both ϭ0 and

v

ϭ1 the high-N levels are characterized by a temperature of

Ϸ13 000 K and for the low-N states a temperature of Ϸ1000

K. WO found the average f /f ratio to be 1.1 for ϭ0 and

v

1

2

ϭ1. The average value of A /A was 1.9 for ϭ0 and 1.3

v

Ј

Љ

for ϭ1. For the cluster reaction, they found the same

v

ϭ1/ ϭ0 ratio and comparable rotational distributions and

v

A /A ratios. Notably, the f /f ratio at low N was larger for

Ј

Љ

1

2

to be Ϸ7% of the total population. The P_obs( ,J,⍀,⌳)

the cluster than for the free reaction and resembles the

v

peaks at g_rϷ0.3. Luntz attributed the population character-

CH₄•O₃cluster data in Fig. 4. The high-N cluster data gave a

*

ized by the linear surprisal as product from a CH₃OH in-

linear surprisal, with a slope of 6.9 for both ϭ0 and

v v

termediate before complete IVR. The minor, cold OH was

from an in-line collision at low impact parameter giving ro-

tationally unexcited product. Our analysis of the data from

these experiments is consonant with his interpretation of the

distribution for high-N. However, we believe there is a sig-

niﬁcant contribution from a statistical channel that contrib-

utes to OH at both intermediate- and low-N, which would be

identiﬁed if our three-mechanism model were used to ana-

lyze Luntz’s data.

ϭ1. They deduce the cold, low-N population to be 24% of

the total for ϭ0 and 7% for ϭ1 for the cluster, and 16%

v

and 5% for the free reaction. They assigned the colder OH to

*

the dissociation of CH₃OH after complete energy redistri-

bution and the hotter, high-N to insertion of O(¹D₂), fol-

´

lowed by dissociation prior to complete IVR. Gonzalez

et al.¹⁸have also measured the rovibrational distribution of

the OH fragment using 193 nm photolysis of N₂O, and re-

port very similar distributions for the free reaction.

In a similar set of experiments, Park and Wiesenfeld⁶

The WO ﬁts to their P_obs( ,J,⍀,⌳) results are quanti-

v

͑PW͒ probed OH( ϭ0,1,2,3,4) following 248 nm photolysis

tatively different from our results, although we believe that

different approaches to data analysis account for some of the

apparent discrepancy. WO give much hotter values for the

rotational temperature at high-N ͑13 000 K compared to our

result of 4100 K for ϭ0 and 6000 K for ϭ1͒. The differ-

v

of ozone in a Ne–CH₄–O₃mixture. A density of 5

ϫ10¹⁵cm^Ϫ3and a delay time of 0.2 ␮s were used, which

should make the P_obs( ,J,⍀,⌳) close to nascent, though the

v

cooling of the hot O(³P_j) before a reactive collision would

v

be incomplete. The fractional population in vibrational levels

ences seem greater than can be accounted for by the 11%

ϭ0–4 was reported to be 0.25, 0.25, 0.33, 0.12, and 0.05,

higher available energy in the CH₄•N₂O photolysis. How-

v

respectively. These vibrational populations are in fair agree-

ever, while the WO data for the ϭ1 level has a great deal

v

ment with those from an infrared chemiluminescence study⁸⁰

of scatter, it does appears to overlap our

ϭ1

v

͑which could not probe ϭ0͒ and a LIF study that probed

P_obs( ,J,⍀,⌳) plots almost exactly. Perhaps some differ-

v

rotationally relaxed OH( ϭ0,1,2).⁸¹PW found that a rota-

ence in the temperature determinations accounts for these

apparent differences, or perhaps the derived values overlap

within the associated uncertainties. The value of the surprisal

slope of 6.9 may be compared to our value of 5.5 in our

three-state ﬁt. It appears from WO’s Fig. 6 that much of the

data for g_rϽ0.2 could be ﬁt by a linear surprisal of slope

zero. It is likely that if the WO data were analyzed using a

three state model, a statistical channel greater than 24% for

v

tional temperature of Ϸ7000

K characterizes P_obs(

v

ϭ0,J,⍀,⌳) well within the range 1000–10 000 cm^Ϫ1. At

lower-N, a second, almost thermal component was observed,

though PW did not give a characteristic temperature. They

reported near-equal population of the two spin–orbit states

and an average A /A ratio of Ϸ1.6, which increased with N.

Ј

Љ

Both the ϭ0 and ϭ1 surprisals were linear between g of

v

r

0.17 and 0.7, with a slope of Ϸ5.5. The surprisal of the

ϭ0 and 5% for ϭ1 would be deduced, bringing their

v

ϭ0 data, shown in Fig. 12 of their paper, is linear with a

slope near zero for rotational levels g_rϽ0.17. PW interpret

the high-N population producing the linear surprisal as aris-

ing from insertion and elimination before energy randomiza-

conclusions closer to ours.

Naaman and co-workers^82,83measured P_obs( ,J,⍀,⌳)

v

after initiating the reaction by 266 nm photolysis of O₃in a

crossed beam experiment. The rotational distribution for

v

*

tion. The colder OH was ascribed to dissociation of CH₃OH

ϭ0 and ϭ1 were reported for NϽ14. For ϭ0, these dis-

v v

after energy randomization. PW reported that fraction of the

rotational population arising from this second channel to be

tributions are hotter than our cluster results and cooler than

those of PW. An f₁/f₂ratio of Ϸ2.4 and Ϸ1.3 was reported

18% and 6% for ϭ0 and ϭ1, respectively. It appears the

for the low-N levels of ϭ0 and ϭ1, respectively; other

v v

v

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128.123.44.23 On: Fri, 19 Dec 2014 01:02:33

1228

J. Chem. Phys., Vol. 114, No. 3, 15 January 2001

Miller, van Zee, and Stephenson

rotational levels appear to have ratios near unity. The authors

stated that there is a slight preference for the f₁spin–orbit

state after correcting for the 2Jϩ1ϭN/Nϩ1 statistical

weight. Naaman and co-workers report that the A /A ratio

respect to the rotational time of the complex forming the OH

state probed. To reconcile the asymmetry in the differential

scattering cross sections to our earlier report of only long-

lived statistical formation of OH( ϭ0), Simons and co-

v

Ј

Љ

for OH( ϭ1) increases from Ϸ2 to Ϸ10 between N

workers postulated a correlation between the impact param-

v

*

ϭ1–13. This unusually large propensity of the A state was

eter ͑the rotational period of the CH₃OH intermediate is

Ј

attributed to the cold temperatures of the beam. A similar

propensity has not been observed in reactions initiated in van

der Waals clusters, where one might reasonably presume the

rotational temperature of reactants to be comparable to those

in a crossed beam experiment. The OH velocity distribution

was also measured in the crossed-beam experiments and re-

ported to have an average value of Ϸ6ϫ10⁵cm s^Ϫ1. Be-

cause this value would correspond to a total translational

energy release to both fragments of about 60 000 cm^Ϫ1, as

compared to Ϸ22 100 cm^Ϫ1available, we presume it to be

incorrect. In any event, the rotational distribution at low-N,

spin–orbit ratio, ⌳-doublet ratio, and velocity distribution

reported for these crossed beam experiments are quite differ-

ent from the results reported by Luntz,⁷Park and

Wiesenfeld,⁶Wada and Obi,³¹and our laboratory.³⁰Indeed,

there is a strong congruence in this latter group of experi-

ments. The surprising uniqueness in the data reported by

Naaman and co-workers perhaps suggests that there are not-

yet-understood differences between the data from the mo-

lecular beam environment and the cluster and gas cell envi-

ronments.

inversely proportional to the impact parameter͒ and scatter-

ing angle. Indeed, such a correlation may be associated with

distinct mechanisms we have identiﬁed. In light of our

present ﬁndings, however, it is likely that at least two reac-

tion mechanisms contribute to each of the OH( ϭ0,N), so

v

the observed distribution would be a superposition of an

asymmetrical scattering distribution from a short-lived com-

ponent and a symmetric distribution from the statistical

channel. Our deconvolution of the population distribution

into three components allows us to estimate that for the

OH( ϭ0,Nϭ5,8) levels about 80% of the population was

v

from the statistical channel, and about 20% from the inter-

mediate channel ͑cf. Fig. 11͒, which is comparable to the

fraction back-scattering products deduced from Doppler pro-

ﬁles.

D. Theory

Arai, Kato, and Koda have calculated potential-energy

surfaces for CH₄–O(¹D), subject to some geometrical

restrictions.¹⁶The minimum energy path for the reaction

travels along a narrow valley, with the O atom collinearly

approaching the C–H bond, to a saddle-point with a collinear

C–H–O structure. At this saddle-point the C–H bond length

͑110 pm͒ is close to the CH₄equilibrium value, and the OH

bond length is 166 pm, as compared to 97 pm for OH(X).

The electronic energy of the saddle-point is only slightly

higher than the separated reactants. From this transition state,

the minimum energy path leads directly to CH₃OH in its

equilibrium geometry. The exit channel leading to CH₃ϩOH

is broad and extends nearly up to the saddle point. This ob-

servation lead Arai et al.¹⁶to suggest that the reaction might

proceed through abstraction-like trajectories directly from

the saddle-point without ever passing through a methanol-

like geometry.

C. Doppler spectroscopy

Simons and colleagues have studied the free reaction

between CH₄ϩO(¹D₂) using Doppler spectroscopy.^8–12

These investigations probed OH( ϭ0,Nϭ5,8,19) and the

v

very minor product OH͑4, 8͒. The O(¹D₂) in the Doppler

experiments was from photolysis of N₂O at 193 nm and, as

noted above, the reaction had substantially more translational

energy than experiments using ozone photolysis. Neverthe-

less, this is still small compared to the reaction enthalpy and

probably changes the lifetime of the statistical channel only

slightly, though it is difﬁcult to assess how the changed col-

lision energy might alter the lifetime of the nonstatistical

channels.

Gonzalez et al.¹⁸have recently calculated another ab ini-

´

tio potential. They ﬁt this potential, treating the methyl moi-

ety as a pseudoatom. This parameterized potential was then

used to run quasiclassical trajectory calculations for several

collision energies.^17,18The calculated OH rovibrational dis-

tribution was found to be in good agreement with the mea-

sured distributions.^6,18,31At a collision energy of 1710 cm^Ϫ1

͑0.212 eV, corresponding to O(¹D₂) from photolysis of

ozone͒, all reactive trajectories involved insertion into a C–H

bond. There were, however, two classes of these trajectories.

Two conclusions from these Doppler proﬁles pertain

to our experiments. First, for OH͑0,5,f ,A and A ͒ and

Ј

Љ

1

OH͑0,8,f ,A ) Doppler proﬁles showed the average transla-

Ј

1

tional energy was about a quarter of the available energy ͓cf.

Figs. 1͑d͒, 2͑d͒, and 3͑d͒ of Ref. 8͔. The observed fraction of

energy in translations compares well to 20% predicted by our

prior calculations described above. Second, the differential

scattering cross sections deduced from the detailed shape of

the Doppler proﬁles OH͑0,19͒ showed backwards

scattering,¹⁰with the most probable center-of-mass scatter-

ing angle of 115 ° with a FWHM of 70 °. Similarly, for

*

One of these was a direct mechanism. The CH₃OH inter-

mediate had a negligible lifetime. The OH rovibrational dis-

tribution for these trajectories was inverted, with ϭ2 being

v

*

the most probable state. The other class involved a CH₃OH

OH( ϭ0,Nϭ5,8) about a quarter to one-third of the product

v

was scattered backward in a 40 ° cone about the line-of-

impact ͑cf. Figs. 2 and 3 of Ref. 8͒. Neither of these scatter-

ing patterns is what would be expected for a long-lived com-

plex.

intermediate that existed for several vibrational periods. The

lifetime of this intermediate ranged from 40 fs to 2 ps, with

0.2 ps being the average value.¹⁷The rovibrational distribu-

tion arising from these trajectories was not inverted, and

v

In the Doppler experiments ‘‘long-lived’’ means with

ϭ0 was the most probable vibrational state. There was es-

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128.123.44.23 On: Fri, 19 Dec 2014 01:02:33

The reaction, CH₄ϩO(¹D₂)→CH₃ϩOH

1229

J. Chem. Phys., Vol. 114, No. 3, 15 January 2001

sentially equal probably for a trajectory to be direct or indi-

rect. A small but clear dependence of the lifetime of the

intermediate was observed with varying collision energy,¹⁸

and the rovibrational distributions changed with changing

collision energy. While less than 1% of the total number of

reactive trajectories at 1710 cm^Ϫ1, abstraction-like trajecto-

ries were observed, and contributed to 8.3% of all trajecto-

ries at 6450 cm^Ϫ1͑0.8 eV͒. It is important to note that the

lifetimes obtained in these calculations are probably lower

limits. By treating the methyl moiety as an atom, many vi-

brational modes are eliminated and presumably these extra

degrees of freedom into which energy could ﬂow would tend

to slow the reaction time. Despite the imperfect agreement

between the appearance times measured in these experiments

and the reaction times from these calculation, it is suggestive

that an insertion complex was seen to give product on two

distinct time scales and that there were a few abstraction

trajectories. This ﬁnding is not unlike what is reported here.

All theoretical calculations^87–90have found the mini-

mum energy path has a high barrier along the O–H–CH₃

co-ordinate, and the minimum-energy conﬁguration atop the

barrier is a collinear C–H–O geometry. At this transition

state, however, a 20° bend of the C–H–O angle costs only

Ϸ350 cm^Ϫ1, which makes this potential more like a funnel

than a tunnel.⁸⁹

Let us now compare what is known about the reaction

CH₄ϩO(³P_j)→CH₃ϩOH and the cold and fast OH ob-

served in these experiments. The two-Boltzmann ﬁt to our

data gave a OH͑ ϭ0, low-N͒ distribution characterized by

v

Ϸ150 K; and the three-channel model, the average energy

for OH( ϭ0,f ) for the cold distribution is 86 cm^Ϫ1, corre-

v

1

sponding to only 2% of the available energy. This distribu-

tion is signiﬁcantly colder than the measured and calculated

distribution for reaction with O(³P_j). However, the energy

available in both experiments is both uncertain and broad,

and this difference might reﬂect different energetics. More

importantly, we observe this preferential population of the f₁

3

E. The reaction of CH₄¿O„ P_j…

level both in ϭ0 and ϭ1, and the fractional population

v

Because ozone photolysis near 266 nm has a O(³P_j)

quantum yield⁶⁷of Ϸ10%, the possibility of O(³P_j) reac-

attributed to the fast/cold mechanism is the same ͑Ϸ11%͒ for

both vibrational levels. This contrasts with the experiment

and theoretical ﬁnding that reaction with O(³P_j) gives little

tions must be considered. A high barrier ͑3300–3600 cm^Ϫ1

͒

to the reaction of O(³P_j) with CH₄exists so substantial en-

ergy is necessary to promote this slightly endothermic

reaction²(⌬H₀^o_Kϭ7.5 kJ mol^Ϫ1ϭ630 cm^Ϫ1͒. The distribu-

tion of translational energy in the O(³P_j) generated by ozone

photolysis is broad,⁶⁷but most atoms carry enough transla-

tional energy to overcome the barrier. On average there is

Ϸ6400 cm^Ϫ1of translational energy available in the

O(³P_j)–CH₄center-of-mass frame. To assess whether

O(³P_j) reactions are contributing to the time-resolved mea-

surements reported here, we turn to what is known about the

free, bimolecular reaction between O(³P_j) and methane.

The rovibrational energy distribution in the hydroxyl

product has been measured, and the potential surface of the

O(³P_j) has been extensively studied. The most recent and

comprehensive of these experiments used O(³P_j) generated

by photolysis of NO₂to study the reaction with methane.⁸⁴

The translational energy distribution of the O(³P_j) generated

is broad,⁸⁵and the most-probable translational energy is

Ϸ9990 cm^Ϫ1, giving about Ϸ4900 cm^Ϫ1of available energy

in the CH₄–O(³P_j) frame. For methane, the rotational dis-

tribution may be roughly characterized by a temperature be-

population in Ͼ0. Another point worth noting is that in the

v

CH₄•N₂O cluster experiments—but not in the cell experi-

ments using N₂O—a high f₁/f₂ratio for low-N was also

observed, and O(³P_j) is not produced in the photolysis of

N₂O.

For the data presented here, the preferential population

of f₁at low-J could arise from reaction of nascent O(³P_j)

formed in the photolysis of ozone. However, the observation

that the rotational distribution is much colder than that for

reaction with O(³P_j), the observation that this component is

in both ϭ0 and ϭ1, and the observation that a similar

v

cold component for reactions in the CH₄•N₂O cluster sug-

gests to us that this population does not arise from an O(³P_j)

reaction. It might also be possible that the unusually large

population in low-J f₁states is an effect unique to the clus-

ter, perhaps involving the adjacent N₂or O₂molecule, an

orientation effect of the reactants in the cluster, or a curve-

crossing.

tween 800 and 1100 K. The OH( ϭ0,Nϭ1–7,f ) states

v

1

were found to have an average rotational energy of 580

cm^Ϫ1, Ϸ12% of the available energy. No OH( ϭ1) could

F. Other channels

v

be detected and the rotational-state averaged ⌳-doublet ratio

was reported to be near unity. The f₁/f₂ϫ(N/Nϩ1) ratio

Although formation of CH₃ϩOH is the primary channel

in the bimolecular reaction between CH₄ϩO(¹D₂), it is not

the only channel. The reported contributions of the various

channels have varied greatly. For example, estimates of the

contribution of the principal channel have spanned 69%–

96%. Lee and co-workers²³recently critically reviewed the

work of Hack and Theismann,²⁴Brownsword et al.,¹⁹Satya-

pal et al.,²¹and their own crossed-beam experiments^22,23,91

and recommend the branching ratios listed below, which are

given along with the standard enthalpies of reaction at 0 K.

varied between 1.5 and 2 for OH( ϭ0, NϽ5). It has often

v

been suggested that the origin of the high spin–orbit ratio

points to an adiabatic reaction co-ordinate, inasmuch as only

speciﬁc spin states ͑j͒ correlate to particular OH spin–orbit

levels. However, strict adiabatic correlation gives a spin–

orbit ratio larger than observed. This lead to the conclusion

that a combination of angular momentum mixing in the en-

trance channel and spin–orbit coupling in the exit channel is

the best explanation for the observed f₁/f₂ratio.⁸⁶

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128.123.44.23 On: Fri, 19 Dec 2014 01:02:33

1230

J. Chem. Phys., Vol. 114, No. 3, 15 January 2001

Miller, van Zee, and Stephenson

This overview shows not only that there are several competi-

tive channels, but also that production of CH₃ϩOH is not the

lowest energy channel. This is also illustrated in Fig. 1,

which is based on the best experimental data and theoretical

calculations presently available.^2,89,92–96Figure 1 illustrates

that one reason the lower energy products are not favored is

the presence of signiﬁcant potential-energy barriers separat-

ing the methanol well from these lower energy asymptotes.

Lee and co-workers^22,23also studied the atomic and mo-

lecular hydrogen channels in crossed molecular beams. They

found that the H₂product was isotropically distributed, sug-

gesting that this channel is likely to be formed in a statistical

process. For the atomic hydrogen channel about 90% of the

product was isotropically spread, which again supports an

intermediate in which energy is randomized prior to disso-

ciation. However, the remaining 10% was back scattered,

suggesting that a fast mechanism operates in parallel. They

also concluded that the partner species for this channel was

more likely to be hydroxymethyl (CH₂OH) rather than the

methoxy radical (CH₃O͒. This ﬁnding further provides evi-

dence for a long-lived intermediate, because although the

former is Ϸ36 kJ mol^Ϫ1lower in energy than the latter, to

OH is formed via the RRKM intermediate. Therefore, 0.69

ϫ0.21Ϸ14% of the total reactive collisions result in forma-

*

tion of CH₃OH followed by statistical dissociation to

CH₃ϩOH. According to work mentioned in the preceding

paragraph,²³23% of the reactive scattering gives

CH₂OHϩH, of which 90% is isotropically scattered, repre-

senting decay of a long-lived intermediate. This implies that

*

Ϸ21% of reactive collisions result in formation of CH₃OH

followed by statistical dissociation to CH₂OHϩH. An addi-

*

tional 5% is ascribed to CH₃OH →H₂COϩH₂, and 1.5% to

*

˜a)ϩH₂O. Is the decay of CH₃OH into

CH₃OH →CH₂(

these four channels in the ratio 14/21/5/1.5 reasonable? One

expects loose, barrierless transition states for the two simple

bond-breaking channels. The CH₃ϩOH channel is favored

by a slightly lower energy than CH₂OHϩH, and one expects

it to be Ϸ50% faster on that basis. However, the latter chan-

nel is triply degenerate, favoring it by a factor of 3. The net

*

expectation for decay of CH₃OH is close to the 14/21 ratio

deduced from the experiments. The CH₂(a)ϩH₂O channel,

˜

although essentially isoenergetic with the OH channel, ap-

pears to require an unlikely transition state ͑low Arrhenius

A-factor͒, resulting in its much lower branching ratio. Pre-

sumably this is also the reason for the low yield of H₂, de-

spite its being much lower in energy than the other three

channels. Therefore, one may plausibly ascribe the indicated

fractions of these four different reactions to statistical decay

*

form CH₂OH the CH₃OH complex must live long enough

for energy to migrate to the C–H bond. Satyapal et al.²¹

measured Doppler spectra of the H atom. They measured that

about 20%–23% of the available energy appears in transla-

tion. They also concluded from comparing H atoms for pho-

tolysis of methanol and Doppler spectra of nascent H from

reaction of CH₄ϩO(¹D₂), that an intermediate existed. Sa-

tyapal et al.²¹estimated that its lifetime was Ϸ0.8 ps. This

lifetime is commensurate with the 0.5 ps that we have as-

*

of a CH₃OH intermediate. An implication of this is that the

slow OH formation time we determined (␶_slowϷ5.4 ps

*

Ϯ0.3 ps) is the total decay time of the CH₃OH precursor to

the four reactive channels. One would predict that if H,

CH₂(

would be found. If so, then the identiﬁcation could be made:

_uniϭ(5.4 ps)^Ϫ1ϭk͑OH͒ϩk͑H͒ϩk(CH₂(

a))ϩk͑H₂͒, where

the ratio of unimolecular rate constants ͑at Ϸ50 000 cm^Ϫ1in

˜a), or H₂, were probed, the same 5.4 ps formation time

*

signed to the dissociation of a CH₄O intermediate. While it

k

˜

is clear that further studies will be needed to fully elucidate

the dynamics of these minor channels, the data support our

identiﬁcation of an intermediate species following insertion

as the principle mechanism.

*

the CH₃OH ͒ is in the ratio 14/21/5/1.5 deduced above.

*

Evidence suggests that a CH₃OH intermediate dissoci-

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CH₂(

quantum yields are consistent with this idea. Our results sug-

gest that 67% of OH( ϭ0), 15% of OH( ϭ1), and 3% of

˜a)ϩH₂O, which begs the question of whether the

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v

OH( ϭ2) are formed by decay of such an intermediate.

v

These percentages and the measured ratios⁶

ϭ0)/(1)/(2)ϭ0.25/0.25/0.33 imply that Ϸ21% of the total

(

v

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Article Doi

Mechanism of the reaction, CH4+O(1D2)→CH3+OH, studied by ultrafast and state-resolved photolysis/probe spectroscopy of the CH4·O3 van der Waals complex

DOI: 10.1063/1.1331615

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Article abstract of DOI:10.1063/1.1331615

Full text of DOI:10.1063/1.1331615

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