The correlated product state distribution of ketene photodissociation at 308 nm

Christopher G. Morgan, Marcel Drabbels, and Alec M. Wodtke

Citation: The Journal of Chemical Physics 104, 7460 (1996); doi: 10.1063/1.471459

View online: http://dx.doi.org/10.1063/1.471459

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The correlated product state distribution of ketene photodissociation

at 308 nm

Christopher G. Morgan, Marcel Drabbels, and Alec M. Wodtke

Department of Chemistry, University of California, Santa Barbara, California 93106

͑Received 22 December 1995; accepted 16 February 1996͒

The correlated product state distribution for ketene photodissociation ͑CH₂CO→CH₂ϩCO͒ at 308

nm has been measured by using quantum-state-speciﬁc metastable time-of-ﬂight ͑TOF͒

spectroscopy. This distribution is a matrix whose elements are the probability that if CO is produced

in the dissociation with quantum-state ͉n_CO͘, CH₂will be produced with quantum-state ͉n_CH2͘. It was

found that ketene photodissociation yields CH₂in three resolved states; the ¹A₁͑000͒, and ¹A₁͑010͒

states of CH₂are the major channels, while the ³B₁state is a minor channel. In addition to this scalar

distribution, the vector correlations between the recoil velocity and the angular momentum of the

CO fragment ͑v–j correlation͒, expressed by the ␤⁰₀͑22͒ bipolar moment, have also been obtained as

a function of the kinetic energy release of the photoreaction. The correlated product state

distribution was found not to follow the predictions of phase space theory, suggesting that dynamic

hindrances exist in the photoreaction that have not been previously observed. A phase space theory

calculation with restricted impact parameter values was also performed and compared to

experiment. The impact parameter restricted phase space theory more accurately reproduced all of

the correlated product state information obtained in this work as well as previous uncorrelated

product state distributions for CH₂and CO. Both the ranges and the values of the allowed impact

parameters obtained from these restricted calculations increase as the rotational energy of CO

1

increases. Also, the values of the allowed impact parameters for A₁͑010͒ CH₂are larger than for

¹A₁͑000͒ CH₂. This strongly suggests that C–C–O bending modes are hindered at the transition

Physics. ͓S0021-9606͑96͒02719-2͔

the fragments of a photoreaction.⁶This can be seen by con-

I. INTRODUCTION

sidering the energy conservation equation of reaction ͑1͒:

Since the advent of laser spectroscopy and molecular

beam techniques, the photodissociation of small molecules

E_phh␯͒ϩE

͑CH₂CO͒ϭE_internal͑CO͒ϩE_internal͑CH₂͒

͑

internal

has been intensely studied.¹Emphasis has been placed on

investigating the applicability of statistical theories, in par-

ticular for barrierless unimolecular dissociation. Various ex-

perimental methods such as laser induced ﬂuorescence ͑LIF͒

or resonance enhanced multiphoton ionization ͑REMPI͒

have been used to determine the uncorrelated internal state

distributions of each of the products separately, for example,

the photodissociation of NCNO^2,3or HNCO.^4,5A more fun-

damental question for the experimentalist to pose would be:

What is the simultaneous product state distribution of both

fragments? For example, in the title reaction,

ϩE_transϩD₀CH ϪCO͒.

͑

2

͑2͒

In this equation, the photolysis energy, E_ph, and the bond

dissociation energy, D₀, are constant and known, and the

internal energy of ketene, E_internal͑CH₂CO͒, can be mini-

mized by using molecular beam techniques. Since

E_internal͑CO͒ is ﬁxed by the measurement process, any varia-

tion in the translational energy of CO molecules in the spe-

ciﬁc quantum state, E_trans

,

will depend solely on

E_internal͑CH₂͒. The translational energy of CO and CH₂are

related to each other by conservation of linear momentum.

There are three approaches that have been used to deter-

mine P͑n_CO,n_CH2͒. The ﬁrst approach involves careful deter-

mination of the Doppler proﬁles of individual quantum states

of one of the nascent products, and this approach has been

used for photodissociation studies of various molecules.^7–16

The limitation for velocity resolution using this method is

severe because the Doppler shift is actually dependent on the

projection of the velocity vector of the probed molecule

along the propagation direction of the laser beam. Thus, dif-

ferent speeds can produce the same Doppler shift. The sec-

ond approach to this problem is ion time-of-ﬂight ͑TOF͒

spectroscopy using REMPI.^17–19In this approach, ions pro-

CH COϩh␯ 308 nm͒→CH ϩCO,

͑1͒

͑

2

if CO is in state ͉n_CO͘, what is the probability that fragment

CH₂will be in state ͉n_CH2͘ and how can one measure this? It

might well be possible for the state distribution of one of the

products to roughly obey statistical theories even when the

correlated product state distribution shows strong dynamical

effect. In this paper, we have attempted to address this issue

for the reaction ͑1͒, which has been widely studied as one of

the prototypical examples of barrierless unimolecular disso-

ciation.

The correlated product state distribution, P͑n_CO,n_CH2͒,

can be obtained experimentally by measuring the transla-

tional energy distribution of speciﬁc internal states of one of

7460

J. Chem. Phys. 104 (19), 15 May 1996

0021-9606/96/104(19)/7460/15/$10.00

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Morgan, Drabbels, and Wodtke: Ketene photodissociation

7461

duced in a state-speciﬁc fashion by REMPI are allowed to

separate from each other as a function of their speed by

traveling several centimeters along a ﬂight path before being

detected. Variations of this method use either photofragment

imaging or ‘‘core sampling’’ techniques, in which the ions

are allowed to expand in their Newton sphere in a ﬁeld free

region.^20–23A pulsed electric ﬁeld then rapidly accelerates

the ion package onto a position sensitive detector in the case

of photofragment imaging. In the ‘‘core sampling’’ tech-

nique, the fragments are ‘‘cored out’’ by the pulsed electric

ﬁeld by allowing only the fragments traveling along a par-

ticular ﬂight path to strike the detector. Work on CH₃I ͑Ref.

24͒ and O₃͑Ref. 25͒ have shown that this method can deter-

mine the correlated product state distribution for a reaction in

which one of the fragments is an atom. A different technique

involves changing the position of the ionizing laser with re-

spect to the photolysis laser in order to probe different sec-

tions of the Newton sphere, and was used to determine the

correlated product state distribution of the NO₂photolysis.²⁶

These methods have their velocity resolution limited by

space-charge and stray ﬁeld effects.

of the data produced by these experiments is not straightfor-

ward and has been the subject of several papers.^40–45In this

paper we show the ﬁrst results where the correlation of v

with j has been measured as a function of the fragment recoil

velocity, demonstrating the high resolution of the method.

Various statistical theories have been devised in order to

explain reaction rates and product distributions of unimo-

lecular reactions, especially those in which there is no poten-

tial energy barrier to products. In phase space theory

͑PST͒,^46,47all accessible product states have equal probabil-

ity to be populated; the only restrictions are those of energy

and angular momentum conservation. Recently, an extension

of both classical⁴⁸and quantum⁴⁹PST was proposed in order

to calculate v–j correlations in the dissociation of NCCN.

Separate statistical ensembles ͑SSE͒ imposes further restric-

tions on the phase space by constraining energy ﬂow be-

tween vibration and overall rotation.⁵⁰For photolysis ener-

gies that do not allow for the formation of vibrationally

excited products, PST and SSE are identical. Another type of

constraint on the phase space can be achieved by using the

statistical adiabatic channel model ͑SACM͒,^51–54which as-

sumes that each vibrational state of the parent molecule adia-

batically correlates to a speciﬁc rovibrational state of the

fragments. This model has been used with success on the

photodissociation of HOOH.⁵⁵

The third approach uses neutral TOF methods as for ex-

ample in the photodissociation of H₂S.²⁷In this method, the

H-atom photoproducts are excited in a state-speciﬁc manner

to high-lying, long-lived Rydberg states. After substantial

ﬂight lengths, these Rydberg states can be ionized by weak

electric ﬁelds and easily detected. These methods have

Ketene is a molecule whose photochemistry has been

extensively studied both experimentally and theoretically.

Two electronic states of methylene are energetically acces-

sible in the 308 nm photolysis of ketene. Excitation occurs to

shown a resolution of 0.3% (ϭ⌬ / ), much higher than any

v v

of the previously mentioned techniques. This method has

been used in the study of H-atom photodissociations of sev-

eral organic compounds.^28–31The method of neutral meta-

stable TOF has been extended to polyatomics in this labora-

tory including CO ͑Ref. 32͒ and NO ͑Ref. 33͒. The Cameron

1

the AЉ state of ketene, followed by either internal conver-

sion to the ground state above the dissociation barrier or

intersystem crossing to the triplet manifold.^56,57The ¹A₁state

of methylene correlates to the ground state and has no barrier

3

1

bands (a ⌸←X ⌺^ϩ) of CO are ideal for this method since

these transitions: ͑1͒ have been well characterized,³⁴͑2͒ pro-

duce a metastable with an excitation energy of Ͼ6 eV, well

above the work functions of most metals, and ͑3͒ possess

enough oscillator strength, due to spin–orbit coupling to the

3

for dissociation, while the B₁state of methylene correlates

to the triplet manifold and has a small barrier that has been

measured to be 1281 cm^Ϫ1above the products.⁵⁸Photofrag-

ment translational spectroscopy has shown that the singlet

channel is the dominant one at 308 nm.⁵⁹The rotational state

distributions of both the CO and the CH₂fragment have been

determined by LIF studies in both ground and vibrationally

excited states,^60–66and these distributions have been mod-

eled with various statistical theories, including PST, SSE,

and variational-RRKM.⁶⁷Although it has been shown that

photofragment excitation spectra of singlet methylene can be

1

A ⌸ state,³⁵to excite these transitions efﬁciently. The ﬁrst

experiments using this method to measure P͑n_CH2,n_CO͒ in

the photodissociation of ketene at 308 nm were recently

reported.⁶This article presents a complete study of this sys-

tem using this method.

The experimental techniques described so far yield only

scalar observables. Other observables that also provide a

wealth of information about photodissociation reactions are

correlations between different vector quantities that exist in

the reaction. The correlation between ␮, the transition dipole

moment of the parent molecule, with v, the recoil velocity of

the fragments, can be characterized by the anisotropy param-

eter, ␤, and gives information regarding the symmetry and

lifetime of the excited electronic state produced after photon

absorption. The correlation of v with j, the angular momen-

tum of one of the fragments, gives information about the

direction of forces in the dissociating molecule. Such vector

correlation measurements have been performed using Dop-

pler proﬁles of both LIF^8,16and transient absorption

signals,^36,37and REMPI-TOF spectroscopy.^38,39The analysis

successfully

modeled

by

PST,^63,64

recent

LIF

experiments^65,66have shown that experimental CH₂distribu-

tions are colder than distributions predicted by PST for pho-

tolysis energies more than 300 cm^Ϫ1above the singlet

threshold. Doppler proﬁle measurements of transient absorp-

tion lines of singlet CH₂rotational states produced by ketene

photolysis at 308 nm represents the ﬁrst view of the corre-

lated product state distribution in this reaction.⁶⁸Doppler

proﬁles of low internal energy CH₂lines indicate that there is

2–3 times more vibrationally excited CO produced coinci-

dent with these low energy CH₂states than would be pre-

dicted from statistical calculations. An absence of any differ-

ences in the Doppler proﬁles of Q and R branches suggest

J. Chem. Phys., Vol. 104, No. 19, 15 May 1996

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7462

Morgan, Drabbels, and Wodtke: Ketene photodissociation

to pass through a quartz tube heated to 550 °C, and puriﬁed

by distilling 3ϫ from 196 to 77 K. When not in use, the

ketene was stored in a glass ampule cooled to 77 K. Prior to

use, the ketene was transferred to a stainless steel bubbler

and warmed to 200 K in a EtOH/dry ice bath. Either helium

or neon seed gas at 2 atm absolute pressure was bubbled

through the liquid ketene, and a very small amount of CO

was added to the seed gas to aid in ﬁnding CO metastable

transitions. A pulsed beam of 10% ketene was formed by

expanding this mixture using a General Valve pulsed valve

and was collimated by a 3.5 mm skimmer 3 cm downstream

of the nozzle. The pulsed current needed to run the solenoid-

driven valve was supplied by a homemade pulse-valve

driver. Both skimmer and valve were mounted on a home-

made goniometer inside a diffusion pumped vacuum cham-

ber that has a pressure of 10^Ϫ5torr when the pulsed valve

was operating. A heater and a thermocouple were also at-

tached to the pulsed valve. When neon seed gas was used in

the experiment, it was found that heating the nozzle to 50 °C

was necessary to avoid formation of clusters.

Two lasers were used in the experiment. The ﬁrst laser, a

broadband, unpolarized XeCl excimer laser ͑308 nm, 250

mJ, 40 cm^Ϫ1bandwidth͒ was used to dissociate a large per-

centage of the ketene in the beam. The second laser, ﬁred

100 ns after the ﬁrst one, was used to probe the nascent CO

in speciﬁc rovibrational states by exciting them to the spin-

3

forbidden metastable a ⌸ electronic state via the Cameron

bands. The probe light was produced by pulse amplifying the

continuous output of a single-mode ring-dye laser ͑Coherent

699 operating on Rhodamine 6G͒ in a homemade pulse dye

ampliﬁcation chain ͑operating on a mixture of Rhodamine

610 and 640͒ pumped with the second harmonic of a

Q-switched Nd:YAG laser ͑Lumonics HY600 or Continuum

7010͒. The frequency of the ring-dye laser was calibrated by

taking a small portion of its output and measuring with a

photodiode the absorption spectrum of a heated I₂cell. The

598 nm visible output of the chain was frequency doubled by

FIG. 1. ͑a͒ Diagram of experimental apparatus used to perform correlated

product state distribution. In the diagram, Aϭangle between molecular

beam and metastable ﬂight path ͑␪ in text͒, Gϭgoniometer, PVϭpulse

lab

valve, PVDϭpulse valve driver, Pϭprism, Lϭfocusing lens, Wϭwindow,

ORϭoriﬁce between the source and detector chamber, PRϭpolarization ro-

tator, BBOϭ␤-barium borate crystal, KDPϭpotassium dihydrogen phos-

phate crystal, PDACϭpulsed dye ampliﬁcation chain, RDLϭring dye laser,

I2ϭI₂absorption cell, ARϩϭArgon ion laser, Cϭcapacitive coupling,

AMP/Dϭampliﬁer/discriminator, MCSϭmultichannel scaler, 486PCϭPC

clone, and DDGϭdigital delay generator ͑b͒ diagram detailing the meta-

stable detector. In the diagram, IDϭion deﬂector, WMϭ90% transmittance

wire mesh, REPϭelectron repeller, MCPϭ3-stage microchannel plates, and

NIϭnickel surface, with 300 °C heater attached.

*

a KD P crystal, and, after polarization rotation, the doubled

and fundamental were summed in a BBO crystal to produce

199 nm light with a bandwidth of 180 MHz and a pulse

energy of 1–2 mJ. The polarization of the probe laser could

be rotated to any desired polarization state with a Berek’s

polarization compensator ͑New Focus͒. The two lasers were

counterpropagating with respect to each other, aligned so

that they cross the molecular beam on the axis of the goni-

ometer, and focused to a 0.5 mm spot size

In another chamber differentially pumped was the meta-

stable detector, which was housed in a conducting ion shield.

This diffusion-pumped chamber had a pressure of 6ϫ10^Ϫ7

torr when the pulsed valve was operating. It was connected

to the ﬁrst chamber by a 1 cm oriﬁce located 5 cm from

where the lasers and molecular beam cross. The detector

consisted of a 2.5 cm diam Ni foil target heated to 300 °C

that the CO metastables strike as they complete their ﬂight.

When they struck the foil, electrons produced in an Auger-

like process were steered by a repeller plate at Ϫ1500 V onto

a stack of three microchannel plates ͑nonimaging MCPs

#2054, from Galileo Electronics͒. The repeller plate is situ-

that there is no v–j correlation for CH₂in low rotational

states.

In this paper we present the detailed investigation of the

state-speciﬁc neutral TOF spectra obtained for 308 nm

ketene photolysis. The data lead to the most detailed infor-

mation yet available on the product energy disposal and vec-

tor correlations in this reaction. The deviations from PST are

easily observed and appear in a systematic fashion. A simple

modiﬁcation to PST is presented where exit impact param-

eter restrictions are imposed. This allowed an accurate mod-

eling of all of the product correlations. Uncorrelated state

distributions obtained in previous experiments are also more

successfully modeled using the impact parameter restrictions

obtained from this experiment.

II. EXPERIMENT

A schematic of the experimental apparatus is shown in

Fig. 1. Ketene was synthesized by allowing acetic anhydride

J. Chem. Phys., Vol. 104, No. 19, 15 May 1996

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Morgan, Drabbels, and Wodtke: Ketene photodissociation

7463

ated in the detector such that its normal is perpendicular to

the normal of the Ni foil; the MCPs are placed opposite the

repeller such that its normal is also perpendicular to the nor-

mal of the Ni foil. These MCPs ampliﬁed the electron signal

by 10⁸, and the resulting pulses were discriminated and then

time-sorted by a multichannel scaler ͑Tennelec/Nucleus Inc.

MCS-II͒. Deﬂector plates and a wire mesh were placed at the

entrance to the detector housing to prevent ions from enter-

ing the detector. The timing between the pulse-valve driver,

the Nd:YAG laser, the photolysis laser and the multichannel

scaler was coordinated with a Stanford Research Systems

DG-535 digital delay generator.

FIG. 2. Vector diagram for laboratory to center-of-mass transformation. The

diagram shows the two coordinate systems ͓(X,Y,Z) and ͑X_beam, Y_beam, and

Z_beam͔͒ used in the analysis; the detector axis is in the Z direction. Also

shown as ␧ and ␧ , the two polarization directions of the probe laser light

when it is parallel or perpendicular to the detector axis, respectively. Angles

and velocities are explained in the text.

III. RESULTS AND ANALYSIS

ʈ

Ќ

For ketene photodissociation at 308 nm, TOF data of the

CO fragment were taken in its ground vibrational state for

j_CЉ_Oϭ 0, 6, 10, 15, 20, 25, and 30 with the polarization direc-

tion of the probe laser both parallel or perpendicular to the

detector axis, and in some cases, using both Q and R transi-

tions of the Cameron system. By convention, double primes

refer to the ground electronic state quantum numbers of CO,

while primes refer to the excited electronic state. Also, for

each j_CЉ_Oand polarization direction, TOF data were taken at

various values of the lab angle between the detection axis

and the direction of the skimmed molecular beam, ␪_lab. Also,

TOF data of the CO fragment in its ﬁrst excited vibrational

state were taken for jЉ_COϭ 4, 6, and 8 at only one polarization

direction.

v³_lab

M

_keteneM_CO

I ␪_lab,t͒ϭC

͑

t

M_CH

2

Љ

v_CO

Љ

jЉ ͒S j ⍀ ,u ;jЈ ⍀ ͒

͑

Љ Ј

cm

CO CO

CO

P E

͑

trans

Ј

ϫ

͵

͉

u_cm͉

ϫN_beam

␻

͒d

d␻

v_beam

d␻_d,

beam

͑3͒

͑v_beam

beam

Ј

where C is a proportionality constant and M_iis the mass of

species i. The velocity of CO in the lab frame, _lab, can be

v

determined from the arrival time and the length of the ﬂight

The TOF spectrum for a speciﬁc rovibrational state of

CO produced by ketene photodissociation and probed by lin-

early polarized light depends on two quantities:

path, l, and will depend upon the beam velocity, _beam. The

v

transformation described by Eq. ͑3͒ above is best performed

using the forward convolution method. In this approach, the

CM quantities, e.g., translational energy distribution, are

guessed and a convolution integral is solved numerically to

predict how the guessed CM distributions will appear in the

lab frame. The guess is then reﬁned iteratively until a good

ﬁt to the entire set of data is obtained. This procedure has

been found to be far superior to direct inversion schemes

because it more accurately takes into account experimental

broadening mechanisms such as the ﬁnite distribution of mo-

lecular beam velocities.

P(E_trans, Љ , jЉ ), the CO quantum state speciﬁc kinetic en-

v_CO

CO

ergy distribution, and S(jЉ ,⍀ ,u ;jЈ ,⍀ ), the line

Љ

Ј

cm

CO

1

3

strength of the a ⌸( Ј , jЈ ,⍀ )←X ⌺^ϩ( Љ , jЉ ,⍀ )

v_CO

Љ

CO

electronic transition for a CO molecule with recoil velocity

u_cm. The ⍀ quantum number is the projection of the angular

momentum of CO on the bond axis of CO. In order to ex-

press the TOF data as a function of P(E_trans, Љ , jЉ ), a

transformation from laboratory to center-of-mass ͑CM͒ coor-

v_CO

CO

dinates is needed. The coordinates used to transform from

the laboratory and CM frame can be seen in Fig. 2. The

beam containing the ketene possesses a spatial distribution,

d␻_beam, whose maximum will depend on how much of the

beam overlaps with the lasers. The detector axis is deﬁned to

be the line connecting the center of the rotation of the goni-

ometer and the center of the Ni target. Molecules that strike

the detector will also have a solid angle distribution d␻_d,

whose maximum angle can be determined by the diameter of

the detector. The intensity I of the TOF signal at time, t, and

lab angle, ␪_lab, is given by Eq. ͑3͒,⁶⁹

The Ni target of the detector was determined to be 19.2

Ϯ0.2 cm away from the intersection of the laser and molecu-

lar beams. This distance was determined by acquiring a TOF

spectrum of a neat beam of CO, using the R₂͑0͒ transition,

with ␪_labϭ0°. The relation between the most probable ﬂight

time, t_mp, of the neat CO beam and l can be determined from

the average translational energy of a molecular beam⁷⁰and is

given by Eq. ͑4͒.

kT

lϭ

ͱ

7

t_mp

,

͑4͒

M_CO

J. Chem. Phys., Vol. 104, No. 19, 15 May 1996

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7464

Morgan, Drabbels, and Wodtke: Ketene photodissociation

FIG. 3. Time-of-ﬂight spectrum of effusive beam of pure carbon monoxide.

The probe laser is tuned to the Q₂͑7͒ transition. The dark circles are experi-

mental data, the line is a ﬁt of the data to equation ͑5͒, with parameters

lϭ19.5 cm, Tϭ297 K, and ␶ϭ10 ms. The good ﬁt shows that the metastable

detector is insensitive to the velocity of CO.

where k is the Boltzmann’s constant and T is the ambient

temperature of the pulsed valve. Using this ﬂight length.

TOF spectra of the small amount of CO doped impurity

present in the ketene beam were obtained in order to charac-

terize the velocity distribution of the ketene molecular beam.

It was assumed that no slippage between ketene and CO was

present in the beam. This TOF spectrum was ﬁt to a Gauss-

ian function, which was used as input to the forward convo-

lution program. The beam distribution N_beam

͑

v

_beam,␻

͒

beam

was assumed to be spatially isotropic over the dimension of

the laser/molecular beam crossing region.

Equation ͑3͒ is based on the assumption that all meta-

stables are detected independent of their velocity, i.e., the

metastable detector is a ﬂux detector. In order to check this

assumption, an effusive beam of CO at ␪_labϭ0° was allowed

into the vacuum chamber, and it was pumped by various

electronic transitions to the metastable state. Effusive TOF

spectra were then ﬁt to the following formula:

I t;l,T͒ϭCt^Ϫ4e

²e^Ϫt/␶

.

͑5͒

͑Ϫm/2kT͒͑l/t͒

͑

3

Here, ␶ refers to the radiative lifetime of the CO a ⌸, which

has a detectable effect on this high signal-to-noise data with

arrival times as long as 1000 ␮s. Figure 3 shows an example

of a TOF spectrum of an effusive beam. The good ﬁt con-

ﬁrms the validity of Eq. ͑3͒ above; the metastable detector is

independent of velocity and measures ﬂux.

Figure 4 shows some examples of quantum-state-speciﬁc

TOF spectra obtained in the photodissociation of ketene, all

probing j_CЉ_Oϭ 20. The data shown here were all obtained

with a 10% ketene beam seeded in neon. Data taken at

␪_labϭ4° are shown as ϩ’s while that taken at ␪_labϭ14° are

shown as ϫ’s. The shape of the TOF spectra is seen to de-

pend on: ͑1͒ the branch used for the probe transition, ͑2͒ the

polarization of the probe laser, and ͑3͒ the lab recoil angle.

The data exhibit three features arriving at ϳ100, 160, and

230 ␮s, respectively. The peaks are due to the formation of

different vibronic states of CH₂coincident with CO in jЉ_CO

FIG. 4. Time-of-ﬂight spectra for the two probed branches of jЉ_COϭ 20. The

empty circles and x’s are data points for ␪_labϭ4° and 14°, respectively. The

solid lines are simulations of the time-of-ﬂight data using the analysis

scheme described in the text.

J. Chem. Phys., Vol. 104, No. 19, 15 May 1996

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Morgan, Drabbels, and Wodtke: Ketene photodissociation

7465

͑2͒

The factor

h

ϭ1 for

Q

branch transitions and

ϭ 20, and have been previously assigned, in order from fast-

3

1

est to slowest, to B₁, A₁͑000͒ and A₁͑010͒ CH₂.⁶The

Ϫj_CЉ_O/(2jЉ_COϩ 3) for R branch transitions. From this equa-

tion one can see that the shape of the TOF is sensitive only to

terms that contain ␹_p, the angle between u_cmand the polar-

ization direction of the probe laser light ͑see Fig. 2͒. There-

fore the shape of the experimentally determined TOF spectra

is only sensitive to ␤⁰₀͑22͒ and ␤²₀͑22͒. It will be shown below

that the inﬂuence of ␤²₀͑22͒ is not observable with the present

signal to noise. Therefore, the line strengths were calculated

by considering only the effect of ␤⁰₀͑22͒, v–j correlation. One

should note that, in principle, this experimental arrangement

can be used to obtain information on any of the bipolar mo-

ments with the correct choice of geometry and control of the

polarization of both photolysis and probe lasers.

numbers in the parentheses ͑␯ ␯ ␯ ͒ refer to the vibrational

1

2 3

quantum numbers of CH₂, where ␯₁ϭsymmetric stretch,

␯₂ϭbend, and ␯₃ϭantisymmetric stretch. The solid lines of

the graphs are simulations of the TOF data and will be ex-

plained later in this section. Clearly the ﬁt to the data gener-

ated by the forward convolution program depends on the CM

ﬂux of correlated product pairs, which can be expressed as a

state speciﬁc CM translational energy distribution,

P(E_trans, Љ , jЉ ). The fact that the TOF data depend on the

v_CO

CO

probe branch and the polarization direction of the probe laser

light is a result of product v–j correlations which inﬂuence

the magnitude of S(jЉ ,⍀ ,u ;jЈ ,⍀ ) in Eq. ͑3͒. These

Љ

Ј

cm

CO

phenomena must also be included in the ﬁtting procedure

and are now discussed.

After suitable modiﬁcation to include the effects of prod-

uct v–j alignment, the forward convolution program CM-

LAB2 of the Y. T. Lee group was used to simulate TOF

spectra using Eqs. ͑3͒ and ͑6͒ in order to determine

The accepted convention to express vector alignments in

photodissociation is that of bipolar moments.⁴²The bipolar

moment ␤⁰₀͑22͒ϭ͗P₂͑v–j͒͘, can be used to describe v–j align-

ment. Other vector correlations, namely ␮–v, ␮–j, and

v–␮–j, may be present in the photodissociation, and they will

correspond, respectively, to the bipolar moments ␤²₀͑20͒,

␤²₀͑02͒, and ␤²₀͑22͒. The proper use of these quantities in the

analysis of vector correlations in REMPI-TOF experiments

has been recently treated by Uberna et al.⁴⁵We can use the

results derived in that paper to analyze the effect of vector

correlation in our experimental setup. We must merely de-

scribe the geometry of this experiment in terms of the angles

and coordinates shown in Fig. 1 of that paper and include the

fact that the photolysis laser is unpolarized.⁴⁵When this is

accomplished, Eq. ͑1͒ of the Uberna paper can be rewritten

as

P(E_trans, Љ , jЉ ) and ␤⁰͑22,E ͒. Here, we use notation

v_CO

0

trans

CO

to indicate that the alignment parameter also depends on the

translational energy release. The input parameters to the pro-

gram include: the laboratory deﬂection angle, ␪_lab, the beam

velocity and angular distribution, the ﬂight distance, l, the

capture area of the detector, the masses of the fragments, the

rotational branch of CO probe transition, and the laser light

polarization direction.

One difﬁculty with the analysis outlined above is the

need to determine several physically signiﬁcant quantities

simultaneously,

speciﬁcally

P(E_trans, Љ , jЉ )

v_CO

and

CO

␤⁰₀͑22,E_trans͒. In order to derive information about the trans-

lational energy dependence of the ␤⁰₀͑22,E_trans͒, we approxi-

mated the beam distribution to be a single velocity vector,

i.e. the most probable one. In addition, a single laboratory

recoil direction along the detector axis is assumed. With

these approximations, Eq. ͑3͒ above can be rewritten without

the convolution integral.

Љ

Ј

CO

S j ⍀ ,u_cm;j ⍀ ͒

͑

Љ

Ј

CO

Ј

1

5

2

ϭ1ϩ ¹₂␤²20͒ϩh

␤

02͒ϩ2␤⁰22͒P cos ␹ ͒

͑2͒

͑

͓

͑

0

͑

2

p

0

ϩ ²₇␤²22͒ 1Ϫ2P cos ␹ ͒͒ .

͑6͒

͑

͔

2

p

0

v³_lab

͑

v_CO

͑

CO

P E

Љ , jЉ ͒S jЉ ,⍀ ,u ;jЈ ,⍀ ͒

M

_keteneM_CO

Љ

Ј

trans

cm

CO

Ј

I ␪_lab,t͒ϷC

.

͑7͒

͑8͒

͑

t

M_CH

u_cm

2

From this, it can be shown that

22͒Ϫ ²␤²22͒

͔

0

͑2͒

3h

␤

͓

͑

0

1

I ␻_lab,t͒ϪI_Ќ

␪_lab,t͒

_lab,t͒

͑

7

ʈ

ϭ

,

2

5

2

2ϩ␤²₀20͒ϩh

␤

02͒ϩ␤⁰22͒ϩ ²␤²22͒

͑ ͑ ͑ ͔

7

0 0 0

͑2͒

cos 2␹

␪

,t͒ I ␪_lab,t͒ϩI_Ќ

͑ ͑

lab

␪

͑

ʈ

p,

͑

͓

where I_ʈ͑␪_lab,t͒ and I_Ќ͑␪_lab,t͒ are two TOF spectra taken at a

given lab recoil angle, ␪_lab, with the probe laser’s polariza-

␹_pϭ45°. Because we have found empirically that only

␤⁰₀͑22͒ inﬂuences the data in our experiment, it is possible to

simplify Eq. ͑8͒, and this is shown in Eq. ͑9͒

ʈ

tion vector being either or Ќ to the detector axis, respec-

tively. The angle ␹ ͑␪_lab,t͒ is between the CM recoil veloc-

0

ʈ

͑

2͒

p,

3h

␤

22,E

͒

͑

0

1

I_ʈϪI

trans

^Ќϭ

.

͑9͒

ity vector ͑which varies with arrival time, t͒ and the detector

axis. Relative normalization of the I_ʈ͑␪_lab,t͒ and I_Ќ͑␪_lab,t͒ is

accomplished by setting them equal at the arrival time where

͑2͒

cos 2␹ I_ʈϩI

2ϩh

␤

22,E

͒

trans

͑

ʈ

p,

Ќ

Equation ͑9͒ allows us to use the experimental TOF spectra,

J. Chem. Phys., Vol. 104, No. 19, 15 May 1996

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7466

Morgan, Drabbels, and Wodtke: Ketene photodissociation

I_ʈ͑␪_lab,t͒ and I_Ќ͑␪_lab,t͒, to obtain ␤⁰₀͑22,E_trans͒ by direct in-

version. This is then used as the ﬁrst guessed input for the

forward convolution ﬁtting. One can then optimize both

␤⁰₀͑22,E_trans͒ and P(E_trans, jЉ , Љ ) functions until all of the

v_CO

CO

data at all values of ␪_labhave been ﬁt. The eight solid lines in

Fig. 4 which ﬁt the data for different choices of jЉ_CO, probe

branch, laser polarization and ␪ are clear evidence for the

lab

adequacy of the transformation model. In principle, if the ␤₀²

moments were important, it would be impossible to simulta-

neously ﬁt Q and R branch data for both polarizations under

the assumption that they are negligible.

To summarize what is a rather difﬁcult data analysis

task, the model used to ﬁt the quantum state speciﬁc TOF

data relies on the forward convolution method. The data ob-

tained in this work is only sensitive to the kinetic energy

probability distribution, P(E_trans, jЉ , Љ ), and the transla-

v_CO

CO

tional energy dependent v–j correlation parameter,

FIG. 5. Kinetic energy release function curve for ketene 308 nm photolysis

with the probe laser tuned on the R₂͑0͒ transition. The solid circles are the

experimentally determined probabilities of kinetic energy release,

␤⁰₀͑22,E_trans͒. Data at many lab angles, laser probe polariza-

tions and with different probe branches is all ﬁt uniquely by

P(E_trans, Љ ϭ 0,jЉ_COϭ 0). The dashed lines are theoretical P(E_trans, Љ

ϭ 0,j_CЉ_Oϭ 0)’s using phase space theory, and the solid lines are theoretical

v_CO

optimizing

the

functions,

P(E_trans, jЉ , Љ )

v_CO

and

CO

␤⁰₀͑22,E_trans͒.

P(E_trans, _CЉ_Oϭ 0,j_CЉ_Oϭ 0)’s with impact parameter restrictions to the phase

v

space theory ͑see text͒.

IV. DISCUSSION

1

A.CH₂CO˜ A₁CH₂؉ CO(v_CЉ_O

؍

0)

1. General overview of the results

cm^Ϫ1energy gap and dissociate with both ¹A₁͑010͒ CH₂and

j_CЉ_Oϭ 25.⁷²It should be noted that this hot channel is a minor

one ͑Ͻ4%͒.

An interesting observation is that for P͑E_trans, Љ

v_CO

ϭ 0,j_CЉ_Oϭ 10 and 15͒ at low kinetic energy release there is a

Previous studies of ketene photodissociation at or around

308 nm have established that the major product channel is

that which forms CO in the ground vibrational state and CH₂

in its lowest singlet state ͑¹A₁͒. Photofragment translational

spectroscopy of this photolysis has measured the maximum

translational energy release to be 6.7 kcal/mol,⁵⁹and

PHOFEX studies have shown that the fragmentation to the

singlet channel occurs via a barrierless transition.⁶³Singlet

methylene possesses an excited vibrational state with one

feature unexplained by the energy threshold arguments of the

1

previous paragraph. Since the only two A₁CH₂vibronic

states that are possible have already been accounted for, one

possible reason for the existence of this feature is that it

belongs to some vibronic state in the ³B₁CH₂manifold. This

possibility would be consistent with its absence at low j_CЉ_O

states, since triplet CH₂formation is very unlikely at low

j_CЉ_O. This will be seen when the formation of the triplet

channel from ketene photodissociation at 308 nm is dis-

cussed later in this paper. One can see from Fig. 6 that for

j_CЉ_Oϭ 10, this feature appears with ϳ0.5 kcal/mol of transla-

1

quantum in the bending mode, A₁͑010͒, with 3.9 kcal/mol

of energy above the ground vibrational state, ¹A₁͑000͒,⁷¹and

is therefore energetically accessible by 308 nm photolysis.

The solid circles with error bars shown in Fig. 5 are the

P(E_trans, Љ ϭ0,jЉ ϭ0), and the two features of the graph

v_CO

CO

are assigned, in order of increasing translational energy re-

1

lease, to formation of the A₁͑010͒ and A₁͑000͒ vibronic

levels of CH₂based on the energy considerations just de-

scribed. The ﬁgure also shows with arrows the expected ki-

netic energies of these levels if there were no rotational ex-

citation of CH₂. One can see a clear correlation between the

onset of each singlet feature and these arrows. This correla-

tion is also seen in the experimentally determined

tional energy. By j_CO

Љ ϭ 15 in Fig. 7, it is appearing with just

slightly more than zero kinetic energy. For higher values of

j_CЉ_O, this feature may not be energetically allowed. This fea-

ture is consistent with bands in the triplet vibronic manifold

at 5000Ϯ100 cm^Ϫ1of energy above the triplet origin.⁷³

These bands have been observed to perturb the ¹A₁͑010͒ CH₂

states near them, and these perturbations, which would lead

to greater singlet character in these triplet states, may explain

why there is an increase in the probability that these triplet

states are formed in the photolysis of ketene at these wave-

P(E_trans, Љ ϭ0,jЉ ) graphs of Figs. 6–8, thereby conﬁrm-

v_CO

CO

ing our assignment. The solid and dashed lines will be dis-

cussed later. The exception to this is P(E_trans, Љ ϭ0,jЉ

v_CO

CO

ϭ 25), in which a peak appears at 0.2 kcal/mol kinetic energy

release. The A₁͑010͒ state of CH₂is energetically inacces-

lengths. For both j_CO

feature is ϳ5%.

Љ

ϭ 10 and 15, the contribution of this

1

sible when the CO fragment has that much internal energy,

therefore it is believed that this feature is due the formation

of A₁͑010͒ CH₂produced from the dissociation of vibra-

tionally hot ketene. Several low frequency modes of ketene

have enough energy so that the CO can overcome a 254

Also shown in Figs. 6–8 are the translational energy

release dependent ␤⁰₀͑22͒ parameters derived from this ex-

periment. These parameters indicate that there is a strong

perpendicular ͑vЌj,␤₀⁰͑22͒р0͒ alignment of jЉ_COfor low

j-states of CH₂, and decreasing perpendicular alignment as

1

J. Chem. Phys., Vol. 104, No. 19, 15 May 1996

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Morgan, Drabbels, and Wodtke: Ketene photodissociation

7467

FIG. 6. ͑a͒ The state-speciﬁc kinetic energy release function curves for ketene 308 nm photolysis probing the ground vibrational state of CO with jЉ_COϭ 6. The

solid circles are the experimentally determined probabilities of kinetic energy release, P(E_trans, Љ ϭ 0,j_CЉ_Oϭ 6). The dashed lines are theoretical

v_CO

P(E_trans, _CЉ_Oϭ 0,j_CЉ_Oϭ 6)’s with impact parameter restrictions to the phase space theory ͑see text͒. Also shown, with arrows, are the energy thresholds for the

v

1

3

¹A₁͑000͒ and the A₁͑010͒ CH₂channels; kinetic energy release above the singlet threshold is attributed to the formation of B₁CH₂. ͑b͒ The ␤₀⁰͑22,E_trans

͒

parameter for ketene 308 nm photolysis probing the ground vibrational state of CO with jЉ_COϭ 6. The empty circles are the experimentally determined

␤₀⁰͑22,E_trans͒. The dashed lines are theoretical ␤⁰₀͑22,E_trans͒ using phase space theory, and the solid lines are theoretical ␤₀⁰͑22,E_trans͒ with impact parameter

restrictions to the phase space theory ͑see text͒. ͑c͒ The state-speciﬁc kinetic energy release function curves for ketene 308 nm photolysis probing the ground

vibrational state of CO with jЉ_COϭ 10. For further details, see the caption to ͑a͒. ͑d͒ The ␤⁰₀͑22,E_trans͒ parameter for ketene 308 nm photolysis probing the

ground vibrational state of CO with jЉ_COϭ 10. For further details, see the caption to ͑b͒.

uted amongst more j states in CO than in CH₂, especially at

j_CH, the total rotational quantum number of CH₂, increases.

2

high kinetic energy release. Since low j_CHstates are more

Another observation is that as jЉ_COincreases, there is a cor-

responding increase in this perpendicular alignment. Previ-

ous studies have found no evidence of v–j alignment in low

rotational states of CH₂,⁶⁸and although at ﬁrst glance this

may seem contradictory to the results of our experiments, it

is consistent and is actually predicted by the classical phase

space calculations of the ␤⁰₀͑22͒ parameters of Klippenstein

and Cline⁴⁸and quantum phase space calculations of North

2

likely to be populated, low ␭

states are more likely to be

CH

2

populated, even if the distribution over all ␭

is an isotro-

CH

2

pic one. This corresponds to low ␭

states being more

CO

likely to be populated. Therefore, the ␭ states are limited

CO

by the j_CHstates, and since CO states are more likely to be

2

in high rotational states than CH₂, the net effect is a perpen-

dicular alignment of jЉ_COwith respect to the recoil velocity.

At low j_CЉ_O, the average rotational number of CH₂is equal or

greater than jЉ_CO, so the perpendicular alignment is very

small unless E_transis high. This can be seen in the jЉ_COϭ 6

and j_CЉ_Oϭ 10 graphs of Fig. 6. The perpendicular alignment

becomes larger as jЉ_COincreases because less energy can be

partitioned into CH₂rotations, and therefore even fewer

and Hall.⁴⁹By conservation of angular momentum, J ϭ j_CH

2

ϩ j_CЉ_Oϩ l, where J is the total angular momentum of ketene

and l is the orbital angular momentum. The projection quan-

tum numbers of angular momenta j_CH, j_CЉ_Oand l on the

2

recoil velocity axis, also known as the helicity quantum

numbers, are ␭ , ␭_CO, and ␭_l, respectively. For molecular

CH

2

beam experiments, the total angular momentum of the parent

j_CHare populated. A problem with this whole interpretation

2

will be small, and by deﬁnition, ␭ ϭ0; therefore, ␭

Ϸ

might be that one should expect the kinetic energy releases

CO

l

corresponding to ¹A₁͑010͒ to have a more perpendicular

Ϫ ␭ . The rotational constants for CH₂are larger than for

CH

2

1

CO, therefore energy earmarked for rotation can be distrib-

alignment than those corresponding to A₁͑000͒, since the

J. Chem. Phys., Vol. 104, No. 19, 15 May 1996

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7468

Morgan, Drabbels, and Wodtke: Ketene photodissociation

FIG. 7. ͑a͒ The state-speciﬁc kinetic energy release function curves for

ketene 308 nm photolysis probing the ground vibrational state of CO with

j_CЉ_Oϭ 15. ͑b͒ The ␤⁰₀͑22,E_trans͒ parameter for ketene 308 nm photolysis prob-

ing the ground vibrational state of CO with jЉ_COϭ 15. ͑c͒ The state-speciﬁc

kinetic energy release function curves for ketene 308 nm photolysis probing

the ground vibrational state of CO with jЉ_COϭ 20. ͑d͒ The ␤⁰₀͑22,E_trans͒ pa-

rameter for ketene 308 nm photolysis probing the ground vibrational state of

CO with j_CЉ_Oϭ 20. A more complete explanation of the ﬁgure can be found

in the caption to Fig. 6.

FIG. 8. ͑a͒ The state-speciﬁc kinetic energy release function curves for

ketene 308 nm photolysis probing the ground vibrational state of CO with

j_CЉ_Oϭ 25. ͑b͒ The ␤⁰₀͑22,E_trans͒ parameter for ketene 308 nm photolysis prob-

ing the ground vibrational state of CO with jЉ_COϭ 25. ͑c͒ The state-speciﬁc

kinetic energy release function curves for ketene 308 nm photolysis probing

the ground vibrational state of CO with jЉ_COϭ 30. ͑d͒ The ␤⁰₀͑22,E_trans͒ pa-

rameter for ketene 308 nm photolysis probing the ground vibrational state of

CO with j_CЉ_Oϭ 30. A more complete explanation of the ﬁgure can be found

in the caption to Fig. 6.

1

2. Modeling results with PST

average j_CHfor A₁͑010͒ is less than for A₁͑000͒. The rea-

2

A series of PST calculations was performed in an at-

tempt to model the kinetic energy release functions attributed

to ¹A₁CH₂formation for each rovibrational state of CO

probed in our experiment. According to PST, the probability,

son this is not so is that for E_trans, corresponding to low j

states of CH₂¹A₁͑010͒, there is still contribution to the signal

from high j states of CH₂¹A₁͑000͒. This high j-state contri-

bution will have the effect of dampening the alignment of

CO at these E_trans

.

P(

, j_CH,k ,k ; Љ , jЉ ), that the CH fragment will

v_CO

v_CH

A

C

2

CO

2

J. Chem. Phys., Vol. 104, No. 19, 15 May 1996

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Morgan, Drabbels, and Wodtke: Ketene photodissociation

7469

and Hall,⁴⁹there are procedures that can be employed in

order to eliminate the need to calculate many of these

Clebsch–Gordon coefﬁcients and thus reduce the time

needed to determine ␤⁰₀͑22,E_trans͒.

be produced with vibrational quantum number

and

v_CH

2

rotational quantum numbers j_CH, k_A, and k_Ccoincident

2

with CO produced with Љ and jЉ_COis equal to the number

v_CO

of accessible states with these quantum numbers,

A convolution over the rotational states of ketene, using

N(

, j_CH,k ,k ; Љ , jЉ ,E,J,K ),

v_CO

divided

by

v_CH

A

C

a

71

CO

2

a prolate top model ͑␬_keteneϭϪ0.997͒ for the rotational en-

N( Љ , jЉ ,E,J,K ), the total number of accessible states

v_CO

with quantum numbers Љ and jЉ . The numbers J and K

a

CO

ergy distribution, assuming that the rotational temperature of

the ketene in the beam is 20 K, and a convolution over the

photolysis laser photon-energy proﬁle were done in order to

v_CO

a

CO

are the total angular momentum quantum number and the

body-ﬁxed projection angular momentum quantum number

͑prolate top limit͒ of the ketene molecule, respectively. The

generate a theoretical P(E_trans, jЉ , Љ ) and ␤⁰͑22,E

͒

v_CO

0

trans

CO

for each probed state of CO. The rotational energy distribu-

tion of CH₂was calculated using an asymmetric top Hamil-

tonian using recently measured rotational constants.⁷³The

maximum impact parameter b_maxwas estimated to be 4 Å

from the ab initio potential surface of Yu and Klippenstein.⁷⁴

Clebsch–Gordon coefﬁcients can be calculated using an al-

gorithm found in a standard reference on the subject.⁷⁵

As seen in the dashed lines in Figs. 5–8, the

quantity N( Љ , jЉ ,E,J,K ) has been succinctly expressed

v_CO

a

by Klippenstein:⁶⁷^CO

N

Љ , jЉ ,E,J,K ͒

a

CO

͑v_CO

ϭ

⌰ EϪE

͓

CO͒

͑

internal

͚

V

, j ,k ,k ,l, j,M

CH CH a c J

2 2

*

ϪE_internalCH ͒ϪE

l͒ ⌬ J, j,l͒⌬ j, j , j_CO͒.

͔ ͑

͑

cent

͑

P(E_trans, Љ ϭ 0,jЉ ) of the two singlet CH vibronic chan-

v_CO

2

CH

2

CO

1

nels A₁͑000͒ and A₁͑010͒ are not successfully modeled by

PST. In general the predicted distributions are too wide and

they increase to a maximum near zero kinetic energy release,

unlike the experimental results. In particular, PST overesti-

͑10͒

Here, ⌰ is the Heaviside function and ⌬ is the triangle in-

equality. The quantum numbers j, l, and M_Jare the quantum

numbers for the total angular momentum of the fragments,

the orbital angular momentum of the dissociation, and the

space-ﬁxed projection of the total angular momentum, re-

spectively. The energy at the top of the centrifugal barrier,

E_cent(l), can be written as a function of b_max, the maximum

allowed impact parameter and ␮, the reduced mass of the

fragments:⁶³

mates the amount of singlet CH₂produced with low j_CH

2

coincident with a particular state of CO. This overestimate

diminishes with higher j_CЉ_O. Furthermore PST overestimates

the amount of singlet CH₂produced with high j_CHcoinci-

2

dent with a particular state of CO. This does not diminish

with higher jЉ_CO. Finally, PST underestimates the amount of

1

singlet CH₂produced in the A₁͑010͒ state. This underesti-

ប²l lϩ1͒

2␮b²_max

Љ

͑

mate increases with higher j_CO. All of this suggests that

there are further restrictions to the dissociation phase space

than just energy and total angular momentum conservation.

As can be seen in Figs. 6–8, there is qualitative agree-

ment between PST and our experimental results for the

␤⁰₀͑22,E_trans͒ parameter, especially at high j_CЉ_O. At jЉ_COр 15,

there are noticeable deviations between PST and experiment,

speciﬁcally, PST tends to underestimate the amount of per-

pendicular alignment in the v–j correlation. This underesti-

mate suggests that there is an overcounting of states by PST,

especially those which would contribute to a more isotropic

distribution of jЉ_CO. This overcounting of states will have less

of an effect as jЉ_COincreases.

E_centl͒ϭ

.

͑11͒

͑

The ␤⁰₀͑22͒ parameter as a function of kinetic energy

release can also be modeled by PST calculations.⁴⁹The

method employed to do this uses a transformation from the

͉

jl basis set to the

͘

͉

␭

_CO,␭

helicity basis set according

͘

CH

2

to the following equation:

2lϩ1

2

͉

jl ϭ

͘

j

␭

_CO, j_CH

␭

͉j⌳

͘

CH

2

͗

ͩ

ͪ

͚

CO

2

2Jϩ1

␭

,␭

jCO jCH

2

ϫ j⌳,l0

͉

J⌳

͉

␭

,

͑12͒

͗

͘

CO CH

2

where ͗..,..͉..͘ are Clebsch–Gordon coefﬁcients and ⌳ is the

total helicity. Summing over all j, l, and ␭ states for a

CH

3. Restricted PST calculations

2

particular ␭ state will yield p͑␭_CO,E_trans͒, the probability

CO

Even for a molecule like this one where we expect fast

intramolecular vibrational energy transfer and the possible

applicability of statistical unimolecular dissociation theories,

the reaction has a well deﬁned transition state, albeit perhaps

a ‘‘loose’’ one. In PST all exit impact parameters are al-

lowed as long as the ﬁnal product states conserve angular

momentum and energy, and no information need be included

regarding the nature of this transition state. Since we see

narrower rotational energy distributions for CH₂, it appears

likely that the allowed range of impact parameters of the

dissociation is restricted by more than just angular momen-

tum conservation and centrifugal energy considerations. Al-

that ␭ with kinetic energy release E_transwill be populated.

CO

These probabilities can then be used to calculate a theoretical

␤⁰₀͑22,E_trans͒ parameter as a function of kinetic energy release

using the following formula,

␭

jCO

0

␤

22͒ϭ

p ␭ ͒P₂

,

͑13͒

͑

͚

jCO

ͩ

ͪ

␭

ͱ_j

͑

j

_COϩ1͒

jCO

CO

where P₂(x)ϭ1/2(3x²Ϫ1), the second Legendre moment.

This method involves the calculation of an enormous number

of Clebsch–Gordon coefﬁcients, which requires a great

amount of computer time. Fortunately, as described by North

J. Chem. Phys., Vol. 104, No. 19, 15 May 1996

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7470

Morgan, Drabbels, and Wodtke: Ketene photodissociation

though the C–C bond cleavage has no barrier and thus has

no dynamical restrictions, there are other molecular coordi-

nates and oscillations involved in the dissociation that could

lead to a more deﬁned transition state. These are the ‘‘disap-

pearing’’ oscillators, i.e., vibrational modes in the parent

molecule that become rotations and translations in the frag-

ments. In ketene these modes include the in-plane and out-

of-plane C–C–O bend and CH₂wag.⁷²Let us say that some

or all of these ‘‘disappearing’’ oscillators are bound at the

transition state; one effect of this would be that the allowed

range of impact parameters for a dissociation producing CO

with a speciﬁc rotational energy will be restricted. Given

these considerations, it was decided to modify the PST cal-

culations in order to constrain the impact parameters to a

certain range of values so that a ﬁrst-order approximation

can be made on what effects these restrictions would have on

the calculated P(E_trans, jЉ , Љ )’s and ␤⁰͑22,E ͒ param-

v_CO

0

trans

CO

eters. For a dissociation channel with orbital angular momen-

tum l, and kinetic energy release E_trans, the impact param-

eter, b, can be calculated semiclassically to be

l lϩ1͒ប²

͑

bϭ

ͱ

.

͑14͒

2␮E_trans

An opacity function can be included in the PST calculation

such that

f b ;b_min,i,b_max,i͒ϭ1

if b_min,iрb_iрb_max,i

͑

i

ϭ0 otherwise,

͑15͒

where the index i, refers to the vibrational state of the singlet

CH₂. When these impact parameter restrictions were in-

cluded, it was found that, with adjustments to b_min,iand

b_max,ifor both the ͑0,0,0͒ and ͑0,1,0͒ channel, these restricted

PST ͑RPST͒ calculations made predictions of the

FIG. 9. ͑a͒ Probability of CO produced by ketene photolysis being formed

in its ground vibrational state with rotational quantum number jЉ_CO. The

solid circles are probabilities of CO being formed in the ground vibrational

state from ketene photodissociation with jЉ_CO. These points were experimen-

tally determined by Kim et al. ͑Ref. 62͒ with the photolysis light being 2500

cm^Ϫ1above the dissociation barrier. The dashed line is the theoretically

determined probability curve of ground vibrational state CO being formed

from ketene photodissociation at 308 nm with jЉ_COusing phase space theory,

and the solid line is the theoretically determined probability curve of CO

being formed from ketene photodissociation at 308 nm with jЉ_COincluding

impact parameter restrictions to phase space theory. ͑b͒ Probability of CO

produced by ketene photolysis being formed in the ﬁrst excited vibrational

state with rotational quantum number jЉ_CO. See above for a complete expla-

nation of the ﬁgure. It should be noted that the probabilities shown in ͑a͒ and

͑b͒ have been normalized with respect to one another.

P(E_trans, jЉ , Љ ) that more closely matched the experimen-

v_CO

CO

tal data for the j_COstates probed. The results of this model

calculation are shown as solid lines in Figs. 5–8. The RPST

calculations make predictions for the ␤⁰₀͑22,E_trans͒ parameter

similar to the unrestricted calculation, as can be seen in Fig.

6–8. In fact, for jЉ_COϭ 10 and 15 RPST does a better job of

modeling the data than unrestricted PST. The exception is

the ␤⁰₀͑22,E_trans͒ calculation for j_CЉ_Oϭ 6, in which RPST pre-

dicts a positive ␤⁰₀͑22͒ parameter for certain kinetic energy

releases; this is not seen at all in the experimental results.

It was also found that the restricted calculation makes a

better prediction of the total rotational population of CO,

¹A₁͑000͒ and ¹A₁͑010͒ CH₂than the unrestricted calculation,

There have been no measurements of either the nascent CH₂

or CO rotational state distributions produced by 308 nm pho-

tolysis of ketene in a molecular beam. Nesbitt et al.⁶⁰mea-

sured CO rotational state distributions of 308 nm photolysis

of ketene in a cell, while Kim et al.⁶²used molecule beam

methods with photolysis light at 306.6 nm to measure the

rotational state distribution. Since the Kim experiment was

closest to our conditions, it was decided to compare their

results to our calculations. As can be seen in Fig. 9͑a͒, the

RPST gives a better ﬁt to the experimental data, although

this effect is slight. Peeters et al.⁶¹have deduced a rotational

temperature of 800Ϯ200 K for nascent ¹A₁͑000͒ CH₂

through LIF studies of room temperature ketene photolyzed

by 308 nm light. Garcia-Moreno et al.^65,66also have per-

1

formed LIF studies of both A₁͑000͒ and A₁͑010͒ CH₂pro-

duced from photolysis at various wavelengths of rotationally

cold ketene. Their data shows that for both vibronic states,

the rotational temperature of the CH₂increases linearly with

an increase in the energy of the photolysis light. From this,

one can obtain an extrapolated rotational temperature for

CH₂produced from photolysis by 308 nm light of rotation-

1

ally cold ketene. For both the A₁͑000͒ and A₁͑010͒ CH₂,

the RPST calculation gives a better ﬁt of the experimental

data than the unrestricted calculation, as seen in Fig. 10.

J. Chem. Phys., Vol. 104, No. 19, 15 May 1996

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Morgan, Drabbels, and Wodtke: Ketene photodissociation

7471

FIG. 11. The impact parameter opacity functions plotted as a function of the

rotational energy of CO. The extrema of the error bars are the maximum and

minimum allowed impact parameters ͑b_minand b_max, respectively͒ used in

Eq. ͑16͒. The data points are the average values of the allowed impact

parameters for each energy-accessible vibrational state of ¹A₁CH₂

͓ᮀϭ¹A₁͑0,0,0͒ and ᭝ϭ¹A₁͑0,1,0͔͒ produced in the 308 nm photolysis.

1

¹A₁͑000͒ and A₁͑010͒ apparently do not occur from identi-

cal transition state geometries. The reason for this behavior

can be understood by considering another aspect of the

model. The model shows differing slopes of the impact pa-

rameter as a function of j_CЉ_O₁, dependent upon which state of

1

CH₂is formed, A₁͑000͒ or A₁͑010͒. This is due to the fact

1

that the A₁͑010͒ CH₂is always formed with less transla-

tional energy than is ¹A₁͑000͒ CH₂, since there is always less

energy available for translation when a vibrationally excited

product is formed. Consequently, in order to form a given

FIG. 10. Probability of CH₂produced by ketene photolysis being formed

with rotational energy E_rot͑CH₂͒. The solid circles in ͑a͒ are the probabilities

of rotational energy for CH₂¹A₁͑000͒ with rotational temperature 662Ϯ160

K. The solid circles in ͑b͒ are the probabilities of rotational energies for

CH₂¹A₁͑010͒ with rotational temperatures 309Ϯ60 K. These are the esti-

mated rotational temperatures for CH₂produced by 308 nm photolysis of

ketene in a molecular beam, and they were extrapolated from experimental

work of Garcia-Moreno et al. ͑Refs. 65 and 66, see text͒. The dashed line is

the theoretically determined probability curve of CH₂being formed from

ketene photodissociation at 308 nm with E_rot͑CH₂͒ using phase space

theory, and the solid line is the theoretically determined probability curve of

CH₂being formed from ketene photodissociation at 308 nm with E_rot͑CH₂͒

including impact parameter restrictions to phase space theory.

1

j_CЉ_O, a larger impact parameter is required for A₁͑010͒ CH₂

1

relative to A₁͑000͒ CH₂, since the relative recoil velocity

will be smaller. This effect disappears as jЉ_COgoes to zero,

where one sees in Fig. 11 that the impact parameter for for-

1

mation of A₁͑010͒ CH₂and A₁͑000͒ CH₂are nearly iden-

tical. Figure 11 also shows that the width of the opacity

function increases as rotational energy increases. This effect

can be attributed to an increase in the amplitude of the

C–C–O bending mode, which will cause a wider range of

transition state geometries to be accessed and at the same

time give more rotational energy to CO.

It should be noted that there is a consistent deviation

Given the good agreement between observation and

model, it is intriguing to investigate the model’s predictions.

Figure 11 shows a plot of the opacity functions used to ﬁt the

between RPST calculation and experiment. For j_CO

Љ

р 20,

RPST tends to overcount the low rotational energy states of

CH₂, while undercounting the rotational states which lead to

a peak in the experimental P͑E_trans͒. In other words, the CH₂

rotational distribution predicted by RPST is still much

broader than the distribution that was experimentally deter-

P(E_trans, jЉ , Љ ) as a function of the rotational energy of

v_CO

CO

CO. The upper and lower extrema of the ‘‘error bars’’ are

b_maxand b_min, respectively, and the open squares ͑¹A₁͑000͒

CH₂͒ and open triangles ͑¹A₁͑010͒ CH₂͒ are the midpoints of

the opacity functions. As a reference point, the most prob-

able rotational energy for CO is 0.93 kcal/mol. Therefore,

the model predicts that the most probable impact parameter

mined. This is especially true for P(E_trans,v_CO

Љ ϭ 0,jЉ ϭ 6)

CO

which, although RPST models the experimental results better

than the unrestricted calculation, does not produce a good ﬁt

to the data.

Restricting the values of the impact parameter only takes

into consideration possible hindrances to the C–C–O bend-

ing modes and limitations on the value of the angle between

1

is 0.58 Å for formation of A₁͑000͒ CH₂and 0.82 Å for

1

formation of A₁͑010͒ CH₂. Since the appearance of prod-

ucts with different impact parameters indirectly reﬂects the

structure of ketene at the transition state, formation of CH₂in

J. Chem. Phys., Vol. 104, No. 19, 15 May 1996

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7472

Morgan, Drabbels, and Wodtke: Ketene photodissociation

TABLE I. Relative populations of the vibronic states of CH₂produced from

ketene photolysis at 308 nm.

the recoil velocity and the C–C bond axis. The contribution

of the CH₂moiety to the impact parameter will be small.

One still must consider that hindrances to the CH₂wagging

j_cЉ_orelative

population

¹A₁͑0,0,0͒ ¹A₁͑0,1,0͒

modes will affect the P(E_trans, Љ , jЉ ) in some way. These

v_CO

CO

j_CЉ_O

³B₁CH₂

CH₂

͑Ref. 62͒

modes correlate in the dissociation to the A and C rotational

constants of singlet CH₂, and by placing restrictions on the

k_Aand k_Crotational quantum numbers of CH₂, one might be

able to provide a better model of our results. Putting restric-

tions on these quantum numbers may entail more sophisti-

cated theoretical treatments than the crude approximations

we employed on our impact parameters restricted calcula-

tions. These could be done by either classical trajectory

calculations⁷⁶or employing the pseudospectral algorithm

method that uses body-ﬁxed Wigner functions as the basis

set, which has been devised by Smith for looking at product

state distributions of photodissociations.⁷⁷

0

6

0

0.57Ϯ0.07

0.54Ϯ0.08

0.58Ϯ0.12

0.64Ϯ0.13

0.83Ϯ0.10

0.83Ϯ0.14

0.78Ϯ0.05

0.43Ϯ0.05

0.38Ϯ0.07

0.32Ϯ0.06

0.11Ϯ0.02

0.05Ϯ0.01

0

0.02Ϯ0.01

0.18Ϯ0.02

0.22Ϯ0.03

0.23Ϯ0.03

0.18Ϯ0.03

0.12Ϯ0.02

0.05Ϯ0.01

0.03Ϯ0.01

0.04Ϯ0.01

0.06Ϯ0.01

0.12Ϯ0.01

0.22Ϯ0.01

10

15

20

25

30

Total relative

population of

CH₂state

0.06Ϯ0.02

0.67Ϯ0.21

0.27Ϯ0.09

Ͼ0.10

͑Ref. 59͒

0.74Ϯ0.05

͑Ref. 66͒

0.20Ϯ0.05

͑Ref. 66͒

In summary to this section, by placing restrictions on the

impact parameters of the photodissociation of ketene, it was

found that phase space theory can make a better prediction of

both the correlated product state distribution and the kinetic

energy dependent ␤⁰₀͑22͒ parameter. The opacity functions

that were used to ﬁt the data are consistent with our assump-

tions about the inability of PST to successfully model our

data, and they give a physically reasonable picture of ketene

photodissociation. It is clear that we are now able to observe

the effects that hindrances to the C–C–O bending modes

CH₂. The reliability of this data can also be checked by

comparison of the previously reported branching ratio of

1

¹A₁͑010͒ CH₂and A₁͑000͒ CH₂with the present experi-

ment, as shown in Table I. We calculate a total probability of

triplet formation to be 0.06 at 308 nm, which is below the

upper limit set in the photofragment translational spectros-

copy experiment of Hayden et al.⁵⁹Kim et al.⁶²estimated

the singlet/triplet branching ratio at 2500 cm^Ϫ1of excess

energy by assuming that the rotational state distribution of

CO produced coincidentally with singlet CH₂could be mod-

eled by PST, and that any discrepancy between model and

experiment was due to CO being produced coincidentally

with triplet CH₂. They estimated that the triplet CH₂contri-

bution to the CO rotational distribution was Gaussian in

shape, peaking at jЉ_COϭ 20. Their estimated triplet probability

was 0.20Ϯ0.10, well above the value obtained in this work.

1

have on the ketene molecule as it fragments into A₁CH₂

and CO in its ground vibrational state, and thereby add a new

dimension to molecular dynamics.

3

B.CH₂CO˜ B₁CH₂؉CO(v_CЉ_O

؍

0)

Up to now we have focused on the kinetic energy distri-

1

bution of the dominant A₁CH₂channel. The appearance of

a small yet broad feature in the P(E_trans, Љ ϭ 0,j_CЉ_O) with

v_CO

translational energies above the limit for singlet CH₂forma-

tion has been attributed to formation of the lower energy ³B₁

state of methylene. The singlet–triplet splitting in methylene

is 9.0 kcal/mol,⁷⁸which means that there is a maximum of

15.7 kcal/mol of available energy for the triplet channel.

There exists an energy barrier to formation of triplet meth-

ylene from ketene which is 3.7 kcal/mol in height.⁵⁸Disso-

ciations with a barrier generally give kinetic energy release

spectra which do not exhibit a maximum at zero kinetic en-

ergy release. The features that appear in P͑E_trans͒ above the

1

C.CH₂CO˜ A₁CH₂؉CO(v_CЉ_O

؍

1)

The P(E_trans, Љ ϭ 1,jЉ ) for CO in its ﬁrst excited vi-

v_CO

CO

brational state from ketene photodissociation at 308 nm is

shown in Fig. 12. Only the ground vibrational state of

¹A₁CH₂is energetically accessible when CO is formed co-

incidentally in its ﬁrst excited vibrational state. Also shown

are PST calculations, which do a fairly reasonable job of

modeling experiment. Because of this, RPST calculations

were not attempted for this set of data. However, these cal-

culations tend to underestimate the amount of singlet CH₂

produced with high kinetic energy release ͑low internal en-

ergy of CH₂͒, and overestimate the amount produced with

low kinetic energy release ͑high internal energy of CH₂͒. In

1

kinetic energy limit for A₁͑000͒ CH₂formation have these

3

properties and can only be due to B₁CH₂.

3

1

Table I shows the relative populations of B₁, A₁͑000͒

1

and A₁͑010͒ CH₂as a function of j_CЉ_O. The triplet yield

increases as a function of j_CЉ_O. This is strongly suggestive of

the bent transition state predicted by the ab initio calcula-

tions of Allen and Schaefer.⁵⁷The ␤⁰₀͑22͒ parameter for the

triplet channel was found to become more negative as j_CЉ_O

increased, varying from 0 for jЉ_COϭ 6 to Ϫ0.4 for j_CЉ_Oϭ 30,

also suggesting a strongly bent transition. The jЉ_CO-state spe-

ciﬁc branching ratios were convoluted over the measured

rotational distribution of CO formed in the photolysis of a

molecular beam of ketene in order to determine the total

probability of formation for each accessible vibronic state of

the P(E_trans, Љ ϭ 1,jЉ_CO), a shoulder is seen at kinetic en-

v_CO

ergy release above the limit for singlet formation, which can

be either due to triplet CH₂formation or signal from the

dissociation of vibrationally hot ketene. Triplet CH₂forma-

tion coincident with v_CO

Љ ϭ 1 formation had been postulated

for LIF photodissociation experiments of ketene in which the

rotational distribution of Љ ϭ 1 had been detected.⁷⁹

v_CO

J. Chem. Phys., Vol. 104, No. 19, 15 May 1996

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Morgan, Drabbels, and Wodtke: Ketene photodissociation

7473

PST to model the CO in its ﬁrst excited vibrational state.

Phase space theory underestimates the amount of vibra-

tionally hot CO produced in this reaction. As is seen in Fig.

9͑b͒, using RPST to model the ground vibrational state dis-

tribution of CO provides a better ﬁt for the ﬁrst excited state

data.

V. CONCLUSIONS

Correlated product state distribution have been measured

for the ketene photodissociation at 308 nm. It has been found

1

that the two major vibronic channels of CH₂are A₁͑000͒

and ¹A₁͑010͒. Triplet CH₂production at this photolysis

wavelength has also been found, and its branching ratio has

been measured as a function of its correlation to a speciﬁc

rovibrational state of CO. Comparisons between experimen-

tal data and phase space theory calculations have shown that

PST does not predict accurately the internal state distribution

of CH₂produced simultaneously with a speciﬁc rovibrational

state of CO for this photodissociation. A modiﬁcation to the

PST calculation was made in which the impact parameter of

the dissociation was limited. This ‘‘restricted’’ PST, or

RPST, was found to provide a better description of the cor-

related product state distribution. Vector correlations be-

tween the recoil velocity and the angular momentum of the

CO fragment have also been measured in this experiment by

changing the polarization direction of the probing laser rela-

tive to the ﬂight path. Bipolar moments analysis can then be

used to obtain the alignment between the recoil velocity and

the angular momentum of the CO fragment. Phase space

theory was also used to predict the vector correlations, and

experimental and theoretical ␤⁰₀͑22͒ parameters curves plot-

ted as a function of kinetic energy release have been shown

to exhibit the same general behavior. The restricted phase

space calculation of the ␤⁰₀͑22͒ parameters as a function of

kinetic energy release has been found to give a marginally

better ﬁt to experimental data than unrestricted PST, though

they are both fairly good. The total rotational state distribu-

tions of both the CO and CH₂fragments in their ground and

ﬁrst excited vibrational states were also calculated using PST

and RPST, and it was found that RPST produced a better

model to all of the available data.

This work points out a shortcoming of statistical phase

space theory. Since PST considers only conservation of en-

ergy and angular momentum, it may end up including many

dissociation events which result from unrealistically large or

small impact parameters. These impact parameters may be

restricted not only by centrifugal effects but by the potential

energy surface of bending modes associated with the frag-

mentation. Our calculations give strong evidence that

C–C–O bending modes in ketene may be hindered in some

way at the molecule’s transition state, causing the rejection

of many impact parameters that might otherwise be allowed

to contribute to dissociation. With the method of state-

speciﬁc neutral TOF spectroscopy, we are now able to ob-

serve the effects of a multidimensional potential energy sur-

face on the dynamics of photodissociation.

FIG. 12. Parts ͑a͒–͑c͒ are state-speciﬁc kinetic energy release function

curves for ketene 308 nm photolysis probing the ﬁrst excited vibrational

state of CO with jЉ_COϭ 4, 6, and 8, respectively. The solid circles are the

experimentally determined probabilities of kinetic energy release,

P(E_trans, Љ

v_CO

ϭ

1,jЉ ). The dashed lines are theoretical P(E_trans, Љ

v_CO

CO

ϭ 1,j_CЉ_O)’s using phase space theory.

The probability of these rovibrational states occurring is

plotted in Fig. 9͑b͒. As in Fig. 9͑a͒, the solid circles are

experimentally determined probabilities.⁶²The dashed line

describes theoretically determined probabilities using the

PST model for all CO states probed, and the solid line de-

scribes theoretically determined probabilities using RPST to

model the CO distribution in its ground vibrational state and

J. Chem. Phys., Vol. 104, No. 19, 15 May 1996

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7474

Morgan, Drabbels, and Wodtke: Ketene photodissociation

³⁰D. H. Mordaunt, I. R. Lambert, G. P. Morley, M. N. R. Ashfold, R. N.

ACKNOWLEDGMENTS

Dixon, C. M. Western, L. Schnieder, and K. H. Welge, J. Chem. Phys. 98,

2054 ͑1993͒.

The authors wish to thank Dr. Joe Cline and Dr. Gregory

E. Hall for providing important preprints of their work and

for providing many helpful discussions. Their patience in

explaining many of the concepts vital to this paper is greatly

appreciated. The authors also wish to thank Dr. William

Green, Jr. for helpful advice about ketene synthesis, and to

Professor Seung Koo Shin for checking the purity of our

ketene with his mass spectrometer. Professor C. B. Moore

and Elisabeth Wade are also thanked for sharing some pre-

liminary results with us. This work was supported by the

National Science Foundation under Grant No. CHE-

9318885, and the National Science Foundation Chemistry

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