Photodissociation dynamics of the allyl radical

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JOURNAL OF CHEMICAL PHYSICS

VOLUME 110, NUMBER 3

15 JANUARY 1999

Photodissociation dynamics of the allyl radical

a)

Hans-J u¨ rgen Deyerl, Ingo Fischer, and Peter Chen

Laboratorium f u¨ r Organische Chemie der ETH Z u¨ rich, Universit a¨ tstrasse 16, CH-8092 Z u¨ rich, Switzerland

͑

Received 31 August 1998; accepted 15 October 1998͒

The photochemistry and photodissociation dynamics of the allyl radical upon ultraviolet ͑UV͒

excitation is investigated in a molecular beam by using time- and frequency-resolved

photoionization of hydrogen atoms with Lyman-␣-radiation. The UV states of allyl decay by

internal conversion to the ground state, forming vibrationally hot radicals that lose hydrogen atoms

on a nanosecond time scale. Two channels are identiﬁed, formation of allene directly from allyl, and

isomerization from allyl to 2-propenyl, with a subsequent hydrogen loss, resulting in both allene and

propyne formation. The branching ratio is between 2:1 and 3:1, with direct formation of allene being

the dominant reaction channel. This channel is associated with site-selective loss of hydrogen from

the central carbon atom, as observed in experiments on isotopically labeled radicals. Ab initio

calculations of the reaction pathways and Rice–Ramsperger–Kassel–Marcus ͑RRKM͒ calculations

of the rates are in agreement with the mechanism and branching ratios. From the measured Doppler

proﬁles a translational energy release of 14Ϯ1 kcal/mol is calculated. The calculated value of 66

kcal/mol for the barrier to the 1,2 hydrogen shift from allyl radical to 2-propenyl is conﬁrmed by the

I. INTRODUCTION

system, with the aim of identifying the reaction products as

well as their energetics and the rate of formation.¹¹The

chemistry of the allyl system is rather complex because sev-

eral reaction channels are thermochemically accessible upon

excitation to the UV bands at an energy of 4.996 eV, corre-

sponding to 115 kcal/mol. Six important reaction channels

A detailed understanding of the chemical reactions of

organic radicals is often crucial for a realistic description of

complex chemical systems where they appear as reactive in-

termediates. This requires the identiﬁcation of the products

formed in the reactions of these radicals, as well as a deter-

mination of the reaction rates and the energetics, i.e., the

distribution of the excess energy into the product degrees of

freedom. Whenever thermochemistry permits the appearance

of several products, the relative rates for each reaction chan-

nel become important and branching ratios have to be deter-

mined. As the reactivity of any molecule depends on the

internal energy deposited in the system, experiments are best

carried out at well deﬁned excitation energies.

are summarized in Fig. 1, with the heats of formation taken

12–14

from the literature.

Three of them, formation of the

C H species cyclopropene, allene, and propyne, are associ-

3

4

ated with loss of a hydrogen atom, an enthalpically and en-

tropically favorable reaction for radicals, because a closed

shell species is formed and the reverse barriers for atom–

molecule reactions are low. Two more channels, yielding

cyclopropenylidene and propargyl, are associated with the

loss of H . Although formation of both C H isomers is

2

3

The radical we currently investigate is the allyl radical,

close in energy to the other channels, the loss of a hydrogen

molecule is expected to proceed via a high activation barrier

and is thus not considered in this study. Note that a sequen-

tial loss of two hydrogen atoms is thermochemically not pos-

sible at excitation energies around 5 eV. In principle, a reac-

tion yielding acetylene and a methyl radical would also be

thermochemically possible as the products are only higher in

energy by 49 kcal/mol. However, this reaction requires two

subsequent 1,2 hydrogen shifts before the C–C bond break-

age. As will be shown below, the reaction is kinetically dis-

favored in comparison to hydrogen loss and can be neglected

at the excess energies present in our experiments.

1

,2

C H , an important intermediate in combustion processes

3

5

and possibly in tropospheric chemistry. It is a relatively

stable radical that becomes reactive upon photochemical ex-

2

citation. The A ground state was thoroughly investigated

2

by high-resolution infrared ͑IR͒ spectroscopy, allowing an

accurate determination of the ground-state geometry.³

While relatively little is known about the structure of the

,4

2

5

lowest electronically excited B₁state, starting to absorb

around 400 nm, there is considerable information on the UV

band system to the blue of 250 nm. Several vibronic bands

were investigated by multiphonon-ionization ͑MPI͒

6

–10

2

spectroscopy

and assigned to the B A , C B , and

1 1

While a recently submitted paper gives a full account on

the early time dynamics of the system, i.e., the nonradiative

2

D B states, which are strongly coupled to each other. Ge-

2

ometries for these states were derived from partially rotation-

15

decay of the UV bands, we will here focus on the reactions

ally resolved MPI spectra.⁹

,10

occurring from the hot ground-state molecules. Detection of

hydrogen atoms by resonant MPI ͓or, alternatively, by laser

induced ﬂuorescence ͑LIF͔͒ is well suited for that investiga-

tion, ﬁrst because H loss is an important reaction channel for

radicals, and second, because of the very large cross section

Recently we started to investigate the dynamics of the

allyl radical upon photochemical excitation into the UV band

^a^͒Authors to whom correspondence should be addressed.

0021-9606/99/110(3)/1450/13/$15.00

1450

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1

J. Chem. Phys., Vol. 110, No. 3, 15 January 1999

Deyerl, Fischer, and Chen

1451

II. EXPERIMENT

The experiments were carried out in a standard molecu-

lar beam apparatus, equipped with a 1 m time-of-ﬂight mass

spectrometer. A clean beam of allyl radicals was generated

by expanding allyl iodide, obtained from Aldrich, seeded in

1

.5 bar of helium through a heated nozzle, mounted onto a

pulsed General Valve with a 0.8 mm oriﬁce. The radical

concentration obtained with this technique at the nozzle exit

is estimated to be on the order of 10¹⁴cm . The details of

the design of our supersonic jet ﬂash pyrolysis source were

given in an earlier publication.²⁴The beam passes through a

skimmer into the main chamber, where it is crossed by two

counterpropagating laser beams: one for excitation of the al-

lyl radical ͑pump͒, and one for the detection of the hydrogen

atoms ͑probe͒. We estimate a radical concentration of

Ϫ3

1

0

Ϫ3

FIG. 1. The possible reaction channels thermochemically accessible for the

allyl radical at an energy of 115 kcal/mol, corresponding to excitation of the

10 cm in the ionization region. Typical operating pres-

Ϫ6

sures were on the order of several 10 Torr in the ioniza-

tion region and 1ϫ10 Torr in the ﬂight tube.

C-state origin at 248.15 nm. The last three channels leading to the C H₃

Ϫ6

3

isomers propargyl and cyclopropenylidene and molecular hydrogen, or

acetylene and methyl, respectively, are expected to proceed via high activa-

tion barriers and thus to be irrelevant at the excess energies present in the

system.

In most experiments described here, two dye lasers

͑Quanta Ray PDL 2͒ pumped independently by injection-

seeded Nd:YAG lasers ͑Quanta Ray GCR 3 and GCR 250͒

were employed, but in several later experiments an optical

parametric oscillator ͑Spectra Physics MOPO 730͒ excited

the allyl radical and induced photolysis. In most experiments

the excitation laser was not focused. A digital delay genera-

tor ͑Stanford Research DG 535͒ controlled the relative tim-

ing between the two laser pulses to an accuracy within better

than 2 ns, limited by the internal dither of the Nd:YAG la-

sers. The detection of hydrogen atoms was carried out via

resonant MPI following the approach originally developed

for the 1s-2p transition in atomic hydrogen at 121.6 nm

͑Lyman-␣͒, which makes H-atom detection an extremely

sensitive technique. The product appearance time can be ob-

tained from time-resolved detection of the H atoms, giving

microcanonical rates for product formation. Information on

the energetics of the reaction can be gained from an analysis

of the Doppler broadening in the hydrogen spectrum, which

can be detected with commercially available standard dye

lasers, due to the low mass of hydrogen. The application of

the technique to chemical problems was pioneered in the

25

by the Welge group. The output of a dye laser, operated

around 365 nm, was focused by a 150 mm lens into a cell

ﬁlled with 225 mbar of krypton in order to produce VUV

radiation around 121.6 nm. The VUV light was focused into

the ionization region by a 75 mm MgF lens at the exit of the

cell. Absorption of this wavelength excites hydrogen atoms

from the S to the P state, which is located almost exactly

at 3/4 of the ionization potential. Thus the residual funda-

mental sufﬁces to ionize the excited hydrogen atoms that are

detected in a time-of-ﬂight mass spectrometer equipped with

a dual stage Chevron-type microchannelplate detector. As

the spectrometer was operated at a static ﬁeld of 700 V/cm,

H atoms excited into Rydberg states slightly below the ion-

ization threshold were ﬁeld-ionized under our experimental

conditions. The signals were recorded in a digital storage

oscilloscope, averaged over typically 200 shots, and trans-

ferred to a computer

1

6

2

1

980’s by the groups of Welge, Kleinermanns and

1

7

18,19

20

Wolfrum, Bersohn,

and Wittig, and is by now widely

2

21

applied in experiments on elementary reaction dynamics.

While the majority of experiments was carried out in cells,

with hydrogen detection performed via LIF, some experi-

ments in molecular beams were also reported.¹

6,20,22

How-

ever, most of the work dealt with stable molecules.

As shown before by our group, a clean beam of radicals

with relatively large number densities can be generated by

supersonic jet ﬂash pyrolysis,¹

2,23

providing a way around

the problems associated with photolysis, like interfering mul-

tiphoton transitions. As we demonstrated in our earlier

1

communication, the combination of pyrolytic generation of

radicals with the detection of hydrogen atoms yields consid-

erable insight into the chemistry of hydrocarbon radicals.

In addition to the work discussed in our earlier commu-

nication, we investigated the site speciﬁcity of the hydrogen

loss by experiments on isotopically labeled compounds,

Three types of experiments were performed: ͑1͒ The ex-

citation laser was scanned in frequency with the detection

laser ﬁxed at the Lyman-␣-wavelength in order to record

resonant MPI spectra of allyl and action spectra of hydrogen,

͑2͒ the excitation laser was ﬁxed to a UV transition of the

allyl radical, while the detection laser was scanned across the

hydrogen or deuterium absorption band in order to record

Doppler proﬁles of the atomic reaction product, and ͑3͒ both

lasers were kept at a ﬁxed frequency while the relative tim-

ing between the two was changed, i.e., a time-resolved

pump–probe spectrum was recorded. The type ͑1͒ and ͑2͒

experiments were carried out at different delay times.

2-deuteroallyl and 1,1,3,3-tetradeuterioallyl, in order to gain

more insight into the mechanism of the radicals’ unimolecu-

lar decomposition. It can be assumed that allene formation

will be associated with the loss of the central hydrogen atom

in the 2-position, while cyclopropene formation should result

in the loss of one of the terminal hydrogen atoms.

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1452

J. Chem. Phys., Vol. 110, No. 3, 15 January 1999

Deyerl, Fischer, and Chen

FIG. 2. The resonant MPI spectrum of allyl ͑lower trace͒ and the action

spectrum of hydrogen atoms ͑upper trace͒, recorded simultaneously as a

function of excitation wavelength. As visible, each resonance in the allyl

spectrum is associated with a corresponding increase in the hydrogen signal.

III. RESULTS

A. C H₅

3

The results in this section were the subject of our pre-

FIG. 4. Appearance of the hydrogen signal as a function of time delay

between excitation laser and Lyman-␣ laser for initial excitation into the

1

liminary report. In a ﬁrst experiment, the excitation laser

was scanned around the C-state origin at 248.15 nm and

through the UV band from 246.5 to 245.5 nm with the probe

laser ﬁxed at the Lyman-␣ wavelength. The signal in both

mass channels, m/eϭ41 ͑allyl͒ and 1 ͑hydrogen͒, was re-

corded in parallel as a function of the excitation wavelength

at a time delay of 100 ns between the laser pulses. From the

resulting MPI spectrum depicted in Fig. 2, it is evident that

0

1

C 00 ͑lower trace͒ and C 70 state ͑upper trace͒. The solid line represents an

7

Ϫ1

exponential ﬁt, employing a rate constant of 4ϫ10 s . As the H atom is

moving out of the line of sight, the signal decays at longer delay times. Note

the deviation of the earliest data point at 10 ns from the ﬁt in both traces,

indicating the presence of a second process with a rate of approximately

8

Ϫ1

1ϫ10 s , drawn as a dashed line.

loss in the neutral. For comparison, the power dependence of

the allyl signal ͑open circles, dotted line͒ is also given in the

plot. It is well represented by a quadratic function, as it

should be for two-photon ionization, indicating that satura-

tion is not important under our conditions. Thus we conclude

that hydrogen is indeed lost from neutral allyl radicals. Fast

hydrogen atoms, originating from fragmentation in the ion,

were observed at very high excitation laser intensities. They

showed a different time dependence as well as an anisotropic

Doppler proﬁle, and could thus be easily distinguished from

the hydrogen atoms originating from the neutral. No hydro-

gen was detected when the probe laser was blocked. The

probe laser alone did produce a small hydrogen signal ͑5%͒

due to VUV photodissociation or detection of hydrogen at-

oms formed in the pyrolysis source. In all data presented

below this background was subtracted. In the following sec-

for each peak in the allyl channel a corresponding peak ap-

0

pears in the hydrogen channel. The transitions into the C 0 ,

0

1

0

1

0

C 7 , and B 9 are visible, while the hydrogen signal asso-

ciated with the B 12 band is somewhat obscured by the

1

0

smaller signal-to-noise ratio ͑S/N͒. To decide whether a hy-

drogen is lost from the neutral radical or from the allyl cat-

ion, we measured the signal’s power dependence, shown in

1

0

Fig. 3 for the C 7 band. As can be seen, the magnitude of

the hydrogen signal ͑open diamonds, full line͒ depends lin-

early on the excitation laser power, as expected for hydrogen

tions we will predominately discuss results obtained for the

0

C 0 state, because of its superior S/N ratio, but data on the

0

1

C 7 state are also given for comparison.

0

In order to obtain microcanonical rates for the hydrogen

loss, the H-atom signal was monitored as a function of the

time delay between the excitation and the detection laser.

Figure 4 shows time-delay scans for excitation of allyl into

0

1

0

the C 0 ͑lower trace͒ and C 7 ͑upper trace͒ vibronic states.

Both curves show a fast rise on the ns time scale and a slow

decay that is due to the hydrogen moving out of the detection

region, and which does not have any physical meaning. As

FIG. 3. Dependence of the signal on the pulse energy of the excitation laser.

The hydrogen signal ͑open diamonds, full line͒ increases linearly with the

pulse energy, as expected for H loss from neutral allyl radicals, while the

allyl signal ͑open circles, dotted line͒ shows an approximately quadratic

energy dependence.

discussed elsewhere, the initially excited UV states decay

within 20 ps or less,¹

5,26

in agreement with the absence of

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J. Chem. Phys., Vol. 110, No. 3, 15 January 1999

Deyerl, Fischer, and Chen

1453

ﬂuorescence reported earlier. Thus we conclude that hydro-

gen is not lost directly from the initially excited UV states,

but rather from hot ground-state molecules produced by fast

internal conversion of the initially excited states. The hot

ground-state allyl subsequently dissociates on a ns time scale

27

into C H ϩH. Following Bersohn, the curves were ﬁtted

3

4

by the expression

S_H₁_,₂͑t͒ϭN͓exp͑Ϫk t͒Ϫexp͑Ϫk_H₁_,₂t͔͒,

͑1͒

2

with S_H₁_,₂(t) being the atomic hydrogen signal, k_H₁_,₂the

unimolecular rate constant for hydrogen loss from allyl, and

k accounting for the decay of the signal. From this expres-

2

7

Ϫ1

sion we derived a rate constant of k ϭ4ϫ10 s for ini-

tial excitation into the C 0 state. The resulting ﬁt is depicted

as a solid line in Fig. 4, and also ﬁts the C 7 state, given in

H1

0

1

0

the upper trace, well. Note that the signal-to-noise ratio is

0

signiﬁcantly better for the C 0 state, as shown in the exci-

tation scan, Fig. 2. Since the excess energy available for the

reaction is different for all initially excited UV states, the

reaction should become faster with increasing excitation en-

ergy. However, this difference is too small to be observed in

our experiments. The time scale for dissociation is long

enough to assume complete randomization of energy, per-

mitting us to treat the data within the framework of statistical

theories. Interestingly, in both curves there appears reproduc-

ibly an early data point at around 10 ns, which does not fall

onto the ﬁtting curve. Although one might be tempted to

regard the deviation of this point from the ﬁt to be within the

experimental error bars, we believe, in light of our work

described in the latter sections, that this deviation is real. We

interpret it as being due to the existence of two different

reaction channels, as will be discussed below, and assign a

0

FIG. 5. H-atom Doppler proﬁles after excitation into the C 0 ͑lower trace͒

0

1

and C 7 state ͑upper trace͒. A Gaussian ﬁt ͑full line͒ yields an expectation

0

value of 14Ϯ1 kcal/mol for the translational energy release.

^f^r^o^m^w^hⁱ^c^h^w^e^o^b^t^aⁱⁿ^t^h^e^t^r^aⁿ^s^l^a^tⁱ^oⁿ^a^l^eⁿ^e^r^g^y^Etrans

ϭ3/2 kT. This approach implicitly assumes a Boltzmann-

^lⁱ^k^e^dⁱ^s^t^rⁱ^b^u^tⁱ^oⁿ^o^f^Etrans . In principle, the Doppler proﬁle of

hydrogen consists of two ﬁne structure lines due to the j

ϭ1/2 and jϭ3/2 states, separated by 0.4 cm , that are both

broadened by the laser linewidth of 0.5 cm , requiring a

proper deconvolution. Experiments on a beam of H atoms

produced from H at a hot ﬁlament resulted in a Gaussian

Doppler proﬁle with a FWHM of 1 cm . Employing this

value in the deconvolution we arrive at a linewidth of 4.0

cm , corresponding to a translational temperature of

roughly 4600 K and an expectation value for the translational

energy release of 14Ϯ1 kcal/mol, if an uncertainty of 0.1

Ϫ1

8

Ϫ1

tentative rate of k_H₂ϭ1ϫ10 s to it ͑dashed line͒.

In the dissociation process, part of the excess energy will

be released as translational energy. Conservation of momen-

tum requires that most of the translational energy will be

carried away by the hydrogen atom, leading to a Doppler

broadening of the absorption line. From the Doppler proﬁle,

information on the dissociation mechanism can be obtained.

In a rapid dissociation process there is no time to redistribute

the excess energy between the internal degrees of freedom,

leading to a large, but anisotropic translational energy release

and structured Doppler proﬁles. On the other hand, a com-

plete redistribution of the internal energy before the dissocia-

tion, as required for the application of statistical theories,

will lead to an isotropic energy distribution and unstructured

Doppler proﬁles that are peaked in the center and can be

approximately described by a Gaussian. In Fig. 5, Doppler

proﬁles recorded for H atoms originating from initial excita-

2

Ϫ1

cm for the determination of the FWHM is taken into ac-

count.

If allene were the reaction product, 24% of the excess

energy of around 59 kcal/mol would be released as transla-

tion. For propyne formation a similar value of 23% is calcu-

lated, while cyclopropene formation would be associated

with 37% of the excess energy being released as translation.

Typically, for hydrogen loss from unsaturated hydrocarbons,

translational energy releases between 10% and 20% of the

excess energy have been reported.¹

8,19,27

The values deter-

0

1

0

mined for allene and propyne formation are within this

range, although at the upper limit, the value for cyclopropene

formation is clearly outside the range expected for this type

of reaction.

While the expectation value for the translational energy

release can be obtained from such a simple analysis of a

Doppler proﬁle, one is often interested in the details that a

knowledge of the complete distribution of the translational

energy provides. In an ideal case, the product translational

energy distribution can be calculated by utilizing simple

tion into the C 0 ͑lower trace͒ and C 7 ͑upper trace͒ are

given, which can both be well ﬁtted by a Gaussian with a full

Ϫ1

width at half maximum ͑FWHM͒ of 4.1 cm , in agreement

with a statistical dissociation process. ͑We are aware that a

Gaussian Doppler proﬁle is in itself not sufﬁcient proof of

statistical behavior.͒

From the half-width of the Doppler proﬁle, a transla-

tional temperature can be derived via the expression

␦

␻ ϭ͑␻ /c͒

ͱ

8kT ln 2/m_H,

͑2͒

D

0

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1454

J. Chem. Phys., Vol. 110, No. 3, 15 January 1999

Deyerl, Fischer, and Chen

28

models, like the prior distribution approach or RRKM

2

9,30

calculations,

assuming that the energy in the reaction co-

ordinate is released as translation. In either case, the distri-

1

/2

bution P(E_t_r_a_n_s) is proportional to E

, yielding an expec-

trans

tation value of Ϸ7 kcal/mol, signiﬁcantly less than the

experimental value determined from the Doppler proﬁle.

However, this simple model does not take the energy of the

reverse activation barrier into account, restricting its applica-

bility to reactions with a loose transition state. As we have

calculated reverse barriers of several kcal/mol for all reaction

pathways ͑see below͒, those approaches are inappropriate.

More recent models³

1,32

deal with the reverse barrier by di-

viding the total energy available to the products into two

reservoirs, the statistical reservoir, deﬁned as the difference

between the total energy and the zero-point energy of the

transition state, and a so-called impulsive reservoir that con-

tains the energy difference between the zero-point energy of

the product and the transition state, i.e., the reverse activation

barrier. For the latter, one assumes that the distribution onto

FIG. 6. Doppler proﬁles for the 2-deuterioallyl at different time delays. The

H signal is given by open circles, the D signal by full diamonds. The solid

line constitutes a Gaussian ﬁt. At early times there is a clear preference for

deuterium loss in the dissociation, but interestingly the relative ratios be-

tween H and D change with time.

the different product degrees of freedom can be treated by

the impulsive model³

3,34

which is in general used for the

description of direct dissociation processes. Typically, in the

impulsive model most of the energy is released as transla-

tion. For several examples, correct expectation values for the

translational energy release were calculated this way.³¹^,³²As

shown below, in the case of allyl, the large Doppler shift can

also be explained by assuming that most of the reverse acti-

vation barrier is released as translation. However, the treat-

ment of the reverse barrier in the framework of the impulsive

model leads to ﬂat top Doppler proﬁles, indicating that this

model does not describe the physics of the dissociation pro-

cess properly.

_i_n_g_a_n_y_s_e_l_e_c_t_i_v_i_t_y_,35 there are also cases of unimolecular

dissociations, where such site speciﬁcity has been

35

observed.

However, one has to consider that in experiments on

isotopically labeled compounds, a regular kinetic isotope ef-

36

fect will be present. Replacement of hydrogen with deute-

rium will change the zero-point energies as well as the den-

sity of states, due to the lower frequency of -X-D as

compared to -X-H vibrations. As a result, reaction rates will

in general decrease upon deuteration of the C–H bond that is

broken.

For the isotopically labeled compounds, neither excita-

tion and action spectra nor power dependencies were re-

corded, due to the small amount of substance available. As

the NMR spectra of the labeled compounds³⁷indicated the

presence of CH I and (CH ͒ SiOH, we ensured that neither

B. Isotopically labeled compounds

Substituting hydrogen with deuterium allows for an in-

vestigation of the site selectivity of the reaction. For a disso-

ciation forming allene, one would expect a loss of the hydro-

gen atom connected to the central carbon in allyl. Upon

cyclization, on the other hand, one of the terminal C–H

bonds should be cleaved. And ﬁnally, propyne formation,

requiring a 1,2 hydrogen shift, might give rise to isotopic

scrambling. Probing the site speciﬁcity of the reaction by

partially deuterating the parent molecule in either the central

or all terminal positions should thus aid the identiﬁcation of

the reaction products. The 1s-2p Lyman-␣ transition in D is

3

3 3

of the two contaminants gave rise to hydrogen signals under

0

our conditions. The labeled species were excited to the C 0₀

band¹⁰at 248.22 ͑monodeuterated͒ and 248.21 nm ͑tetradeu-

terated͒ under conditions similar to those employed in the

C H experiments.

3

5

Three such Doppler scans for the monodeuterated allyl

radical, recorded at pump–probe delay times of 10, 40, and

100 ns are presented in Fig. 6, together with the relative ratio

of hydrogen ͑open circles͒ and deuterium ͑full diamonds͒, as

obtained from the integral under the Gaussian used to ﬁt the

Doppler proﬁles. The H/D ratio is around 1.7:1 at the early

delay times and reaches 4:1 at a delay of 100 ns. Note that it

is not possible to measure the relative ratio at substantially

longer delay times, because the hydrogen atoms leave the

observation region faster than the deuterium atoms. The

Ϫ1

blue shifted only by 22.4 cm with respect to H, so a Dop-

pler proﬁle can be recorded in a very similar manner. Due to

the closeness of the two transitions we assume that the num-

ber of VUV photons produced in the tripling process is con-

stant over the whole range. Assuming, in addition, that the

absorption and ionization cross sections for H and D are

similar, we can compare the area under the hydrogen and

deuterium peaks in the spectra without any further correction

and assume that they are directly proportional to the relative

number of H and D lost from the parent at a given time.

Although there are examples for isotopic scrambling obscur-

width of the Doppler proﬁles is considerably smaller for deu-

Ϫ1/2

terium because of its m

dependence. The FWHM of 2.8

Ϫ1

cm after deconvolution yields the same translational en-

ergy release of 14 kcal/mol as for the hydrogen atoms, how-

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J. Chem. Phys., Vol. 110, No. 3, 15 January 1999

Deyerl, Fischer, and Chen

1455

FIG. 8. Doppler proﬁles for tetradeuterioallyl at different time delays, dem-

onstrating the preference for H loss, and thus allene formation. The H signal

is again given by open circles, the D signal by full diamonds. The solid line

constitutes a Gaussian ﬁt.

FIG. 7. Rates for H ͑upper trace, open circles͒ and D loss ͑lower trace, open

diamonds͒ from 2-deuterioallyl. There are two rates present in the D-loss

channel, in agreement with the change in H/D ratio as observed in the

Doppler proﬁles, Fig. 6.

Although there is only a single hydrogen present in the mol-

ecules, the spectrum at 10 ns is clearly dominated by the

hydrogen signal, the H/D ratio being 15:1. At later delay

times the relative ratio decreases, but hydrogen loss is still

the dominating process. Interestingly, the relative amount of

deuterium is largest at 40 ns ͑H/Dϭ7:1͒, but decreases again,

reaching H/Dϭ10:1 at 100 ns delay.

ever, with slightly larger error bars. Using similar arguments

as before, they are in good agreement with allene and pro-

pyne formation, but not with cyclopropene formation.

Two interesting results are apparent from the scans given

in Fig. 6: ﬁrst, deuterium is lost more rapidly than hydrogen.

This is in contrast to the expected kinetic isotope effect and

thus indicates a preference for allene formation. Second, the

relative ratio between H and D changes with time. In order to

obtain a change in the relative ratio with time, two different

species have to be involved, because a loss of H and D from

the same precursor would yield a time-independent ratio.

Thus only the assumption of two different reaction channels

originating from two different, but chemically related, spe-

cies can explain the change in relative intensity of the Dop-

pler proﬁles.

Again we recorded time-delay scans in order to get ac-

cess to the rates for the processes, which are given in Fig. 9.

Another striking feature is the almost constant H/D ratio

at 10 and 40 ns. If one records the H ͑upper trace͒ and D

͑lower trace͒ signal, respectively, as a function of the pump–

probe delay, the curves given in Fig. 7 are obtained. Inter-

estingly, there is a plateau at 40 ns in the graph describing

deuterium formation, in agreement with the constant H/D

ratio at 10 and 40 ns, and resembling the early data points in

the time-delay scans for the fully hydrogenated compound in

Fig. 4. We can thus extract two rate constants from the time

8

Ϫ1

delay scan, k у1ϫ10 s

for the faster process, and

D1

Ϫ1

7

k_D₂ϭ2.5ϫ10 s for the slower one. Hydrogen loss, on the

other hand, can be described well by a smooth curve with a

7

Ϫ1

rate constant k ϭ6ϫ10 s , indicating the existence of

H

two channels for deuterium formation and one channel for

hydrogen formation.

In order to check for internal consistency, the same ex-

periments were conducted on the isotopic mirror image,

FIG. 9. Rates for H ͑upper trace͒ and D loss ͑lower trace͒ from tetradeute-

rioallyl. This time there are two rates present in the H-loss channel. Due to

the small amount of D loss ͑see Fig. 8͒ the signal-to-noise ratio in the D

channel is rather poor.

C HD , with the hydrogen attached to the central carbon

3

4

atom. The resulting Doppler proﬁles are given in Fig. 8.

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1

1456

J. Chem. Phys., Vol. 110, No. 3, 15 January 1999

Deyerl, Fischer, and Chen

The curve for hydrogen loss ͑upper trace͒, showing a very

fast rise with a maximum at 10 ns, followed by a slight

decrease and a second rise, is again in agreement with the

picture developed above, a loss channel directly from allyl,

and a second channel via a high energy intermediate. We can

8

Ϫ1

7 Ϫ1

derive rate constants k_H₁у1ϫ10 s and k_H₂ϭ5ϫ10 s

.

The curve for deuterium loss, given in the lower trace, is

somewhat ambiguous due to the small overall signal magni-

tude and the subsequently higher signal-to-noise ratio. The

solid line represents a tentative ﬁt with a rate constant of

7

Ϫ1

k ϭ4ϫ10 s . We note that we had to restrict ourselves to

D

a relatively small number of experiments because the isoto-

pically labeled precursors were only available in small

amounts. For that reason, the time-delay scans given in Figs.

FIG. 10. Computed reaction coordinate for the pathways leading from allyl

to cyclopropene ͑left-hand side͒ and allene ͑right-hand side͒. The values in

brackets represent the experimentally known heats of formation for the re-

action products.

7

and 9 were not reproduced.

The qualitative behavior is in agreement with the picture

derived from the experiments on the monodeuterated com-

pound. The H or D atom, respectively, that is connected to

the central carbon atom, is lost faster than the atoms con-

nected to the terminal carbons, indicating a preference for

allene formation. For CD CHCD , the intrinsic preference

shift, leading to the 2-propenyl radical, constitutes an alter-

native pathway, depicted in Fig. 11. Hydrogen loss from

2

-propenyl can either lead to the formation of propyne

2

͑lower trace͒ or allene ͑upper trace͒. All energies are relative

for cleavage at the 2-position is reinforced by the isotope

effect, while for CH CDCH , the two effects work in oppo-

with respect to the electronic energy of the allyl radical,

which was chosen as the reference point. The calculated en-

ergies are zero-point corrected, using the calculated frequen-

2

site directions.

C. Electronic structure calculations

To aid the analysis of our experimental data, ab initio

calculations were performed, using the GAUSSIAN 94 program

3

8

package. The main goal was the calculation of data neces-

sary for a statistical analysis, in particular reliable vibrational

frequencies for the transition states of the different reaction

channels and activation barriers, which are both needed for

RRKM calculations. In a ﬁrst step, we performed a geometry

optimization by fourth-order perturbation theory ͑MP4͒ in-

cluding single, double, and quadruple excitations, employing

a 6-31 G* basis set. These calculations yielded a good de-

scription of the reaction path for all channels, including the

geometries for the transition states. Subsequently, a vibra-

tional frequency analysis was performed at all stationary

points on the MP4 level. By comparing the frequencies cal-

culated for the allyl radical with the experimentally deter-

3

9,40

mined values,

a scaling factor of 0.945 was derived,

which was employed for the transition state frequencies as

well.

In order to achieve high accuracy in the determination of

the activation barriers, we performed single point CCSD͑T͒

coupled cluster calculations at the geometries optimized at

the MP4 level for the stationary points ͑educt, transition

state, and product͒ for every reaction channel. Here we em-

ployed the correlation consistent valence triple zeta basis set

4

1

͑

cc-pVTZ͒,

ϫ͓4s3p2d1f ͔ contraction on each carbon atom and a

3s2p1d͔ contraction on each hydrogen. While the carbon

s orbitals were frozen on the UHF level, all other electrons

which consists of

a

(10s5p2d1f)

͓

1

FIG. 11. Computed reaction coordinate for the pathways proceeding via the

2-propenyl intermediate. The barrier for the 1,2, hydrogen shift is compa-

rable to the barrier to allene formation. From 2-propenyl, two product chan-

nels are accessible, propyne ͑lower trace͒ and allene ͑upper trace͒. The

calculations indicate that propyne should be preferentially formed from me-

thylvinyl due to the lower barrier. All electronic energies given in the ﬁgure

are zero-point corrected.

were included in the calculation of the correlation energy.

The details of all calculations can be obtained from the

_s_u_p_p_l_e_m_e_n_t_a_r_y_m_a_t_e_r_i_a_l_.₃7

The energetics for the reaction pathways leading to al-

lene and cyclopropene are given in Fig. 10. A 1,2 hydrogen

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1

J. Chem. Phys., Vol. 110, No. 3, 15 January 1999

Deyerl, Fischer, and Chen

1457

cies multiplied by 0.945. The experimental values for H are

It was shown in electron spin resonance ͑ESR͒ experi-

f

given in brackets below the calculated electronic energies

ments several years ago that the barrier to rotation around the

C–C bond in the allyl radical is only 15.7Ϯ1 kcal/mol.

whenever they are known.¹

2,13

They agree within Ϯ2 kcal/

45

mol with the ab initio electronic energies. In calculations of

activation barriers it is very hard to obtain chemical accu-

racy, so it is reasonable to assume at least the same error

bars. For the reaction yielding allene, we calculated a reverse

barrier of 7.9 kcal/mol, resulting in a total activation barrier

of 63.3 kcal/mol. Assuming that most of the energy in the

reverse barrier is released as translation in the reaction, we

can thus, in principle, account completely for the 6–8 kcal/

mol difference between the observed expectation value for

the translational energy release of 14 and the 7 kcal/mol

obtained from RRKM calculations or a prior distribution ap-

proach. The reaction to cyclopropene proceeds via the cyclo-

propyl radical that is only 27 kcal/mol higher in energy than

allyl itself. The activation barrier of 52.7 kcal/mol for cy-

clization is in good agreement with both earlier

Thus the methylene groups have to be regarded as free rotors

at the high excess energies present in our experiment. Good

agreement between experimental and calculated values was

achieved when both of the torsional frequencies of 525 and

Ϫ1

545 cm were replaced in the RRKM calculations by 100

Ϫ1

cm . We did not correct the frequencies in the transition

state, because the ab initio geometries did not indicate the

presence of hindered rotors. The transition states for the ma-

jor reaction channels were calculated to be of C symmetry

s

or lower,³⁷so a symmetry number of 2 was employed in the

RRKM calculations.

Formation of allene by direct hydrogen loss from allyl,

as depicted in Fig. 10, represents the ideal case of a unimo-

lecular dissociation that can be described by a single rate

8

Ϫ1

constant. A rate of 4.2ϫ10 s was calculated, on the order

of the experimentally observed value. Without correcting for

the free internal rotation, i.e., employing torsional frequen-

4

2

43

calculations and the experimental value of 49.4 kcal/mol.

However, the barrier to cyclopropene formation is almost 82

kcal/mol, the highest of all channels investigated. We also

calculated the barrier to 1,2 hydrogen shift within the cyclo-

propyl radical, which is as high as 75 kcal/mol relative to

allyl, and thus unimportant under our conditions. On the

other hand, a barrier of 66.0 kcal/mol was calculated for

isomerization to 2-propenyl via a 1,2 hydrogen shift, only

slightly higher than the barrier to allene formation. The cal-

culated transition state geometry indicates an almost triangu-

lar conﬁguration, the H-atom being in between the two car-

bon atoms. In conclusion, from the computations it can be

expected that both pathways, allene formation from allyl and

isomerization to 2-propenyl, are important.

Ϫ1

cies of 525 and 545 cm , the rate constant became one

order of magnitude faster.

As visible from Figs. 10 and 11, both cyclopropene and

propyne formation are two-step processes via a high energy

intermediate. In this situation, one of the basic assumptions

of RRKM theory, that the rate depends only on the energy

and not on the mechanism, becomes questionable. However,

the situation simpliﬁes considerably for the pathway leading

to cyclopropene. Cyclization of allyl will yield in a ﬁrst step

a cyclopropyl radical with an activation barrier of 52.7

kcal/mol. At the energies present in the molecule, cyclopro-

pyl loses an H atom to form cyclopropene, via a transition

state that lies about 82 kcal/mol above the ground state of

allyl. Thus at the large amount of excess energy present in

the system, the cyclization will be very rapid, so we can

ignore the cyclopropyl intermediate and describe the overall

process by a single rate constant, k_c_y_c. This is the well-

known Curtin–Hammett principle. For the RRKM calcula-

tions of k_c_y_c, the density of states of the allyl radical was

employed in the numerator, while the number of states at the

transition state of the cyclopropyl–cyclopropene reaction ap-

We also calculated the pathway for a second consecutive

1,2 hydrogen shift within 2-propenyl, with one of the meth-

ylenic hydrogens moving to the central carbon. This leads to

the 1-propenyl isomer, with the radical center located at the

terminal carbon atom. We found an electronic energy of 24.6

kcal/mol relative to allyl for this radical, and a barrier of 68.3

kcal/mol for isomerization between the two propenyl

isomeres. Thus a second 1,2 H shift is unfavorable compared

to dissociation. This also indicates that cleavage of the C–C

bond into acetylene and methyl, a pathway that requires a

sequence of two 1,2 H shifts and is expected to have a re-

verse barrier signiﬁcantly higher than an atom–molecule re-

action, is unlikely to occur under our conditions on kinetic

grounds. However, at higher excess energies it might consti-

tute an important reaction channel.

6

Ϫ1

pears in the denominator. A rate constant of 4ϫ10 s was

calculated for cyclopropene formation, about two orders of

magnitude slower than allene formation. This conﬁrms that

cyclopropene formation is not important under our condi-

8

Ϫ1

tions. Any allyl that ring closes (k_c_l_o_s_eϭ8ϫ10 s ) will ring

10 Ϫ1

open back to allyl again (k_o_p_e_nϭ1.4ϫ10

s

) before it can

lose an H atom.

D. RRKM calculations

For propyne formation, a reaction that proceeds via the

2-propenyl radical, the situation is more difﬁcult. As de-

picted in the ﬁgures, the barrier to isomerization is compa-

rable to the barrier to dissociation. Although strictly speaking

the barrier to 2-propenyl constitutes a bottleneck in phase

space that prevents the system from full equilibration before

dissociation, we can try to treat it as a series of two unimo-

lecular processes, an isomerization and a dissociation. To

complicate matters further, the 2-propenyl route provides ac-

cess to two products. Upon loss of a hydrogen atom at the

In order to calculate reaction rates for the different path-

ways, RRKM calculations were performed for all three reac-

tion channels, allene, propyne, and cyclopropene formation.

All rates presented below were obtained employing direct

vibrational state count,⁴⁴but a program utilizing the

30

Whitten–Rabinovich algorithm yielded identical results.

3

7

All frequencies, scaled by 0.945 in order to match the ex-

perimentally known frequencies of the allyl radical, and the

reverse activation barriers were obtained from ab initio cal-

culations as described above.

CH group, propyne is formed, whereas hydrogen loss from

2

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1458

J. Chem. Phys., Vol. 110, No. 3, 15 January 1999

Deyerl, Fischer, and Chen

In two earlier communications on the photodissociation

dynamics, we demonstrated that the dynamics upon UV ex-

citation is governed by two different time scales. The ini-

tially prepared states decay nonradiatively within 20 ps or

the ϪCH group in 2-propenyl will yield allene. As the bar-

3

rier to allene formation was calculated to be Ϸ2 kcal/mol

higher in energy than the barrier to propyne formation, the

latter channel is expected to dominate. In any case, due to the

higher barrier, the isomerization to 2-propenyl is the rate-

less, as shown by ps time-resolved photoelectron

8

Ϫ1

15,26

determining step, calculated to be 1.9ϫ10 s , while the

spectroscopy,

forming hot ground-state molecules. The

hydrogen loss to propyne was calculated to be 3

hot allyl subsequently loses a hydrogen atom on a nanosec-

ond time scale, which was detected by resonant MPI

1

Ϫ1

ϫ10

s

. Thus the experimental rates give the rate for the

10

Ϫ1

11

7

Ϫ1

isomerization. We also calculated a rate of 1.7ϫ10

s

for

spectroscopy. We found a rate of k(E)ϭ4ϫ10 s for

the hydrogen loss and a translational energy release of 13.6

kcal/mol, and showed that a statistical analysis of the data is

in agreement with allene being the dominant reaction chan-

nel, while cyclopropene formation is unlikely to be impor-

tant. The data presented here indicate that propyne formation

has to be considered as a reaction channel as well, because

the measured rates and translational energy releases are in

agreement with both allene and propyne, and the calculated

activation barriers for both channels are comparable.

From a ﬁrst qualitative analysis of the experiments on

isotopically labeled allyl radicals, two conclusions can al-

ready be derived: ͑1͒ There is a clear preference for loss of

the central hydrogen or deuterium atom, respectively. This

channel is associated with allene being the molecular frag-

ment. ͑2͒ The relative rates of hydrogen and deuterium for-

mation change with time. Thus there has to be a second

hydrogen loss reaction, originating from a chemically differ-

ent molecule. If both loss channels would originate from

allyl, the relative rate could not change with time, because a

reaction that yields a certain branching ratio at early delay

times will yield the same branching ratio at late delay times.

On the other hand, an isomerization process that competes

the reaction back to allyl. This means that less than one out

of ten 2-propenyl radicals formed will react back to allyl

instead of dissociating.

The RRKM calculations for the deuterated species

yielded only a small rate decrease by typically a factor of 2

͑

primary͒ or less ͑secondary͒. For the reaction from allyl to

8

Ϫ1

allene a rate of 1.9ϫ10 s was calculated for D loss from

C H D, compared to 4.2ϫ10 s for H loss from C H .

8

Ϫ1

3

4

3

5

For H loss from C D H, the rate decrease was even smaller,

3

4

8

Ϫ1

from 4.2 to 3.8ϫ10 s . Such small isotope effects are not

uncommon for reactions carried out at high excess energies.

In experiments on partially deuterated ethylenes, for ex-

ample, kinetic isotope effects ranging from 1.1 to 2.4 were

1

9

reported.

For the 1,2 hydrogen shift in 1,1,3,3-

8

Ϫ1

tetradeuterioallyl, we calculated a rate of 1.7ϫ10 s

,

slower by a factor of 2.3 as compared to direct formation of

allene from this precursor, while for the 2-deuterioallyl the

8

Ϫ1

calculated rate of 1.1ϫ10 s was slower only by a factor

of 1.6. This is in agreement with the measured Doppler pro-

ﬁles ͑see Figs. 6 and 8͒, which show a more pronounced site

selectivity, i.e., preference for allene formation, in the case of

1,1,3,3-tetradeuterioallyl.

with dissociation, yielding a C H₅isomer, which subse-

3

quently loses both hydrogen and deuterium atoms, could ex-

plain this time dependence. In the case of the monodeuter-

IV. DISCUSSION

^a^t^e^d^C^H^C^D^C^H2 such a scenario would lead to two

The photochemistry of the allyl radical was already ad-

dressed in several earlier studies, but the results are still am-

biguous. Matrix-isolated allyl radicals,⁴⁶as well as substi-

tuted allyl radicals grafted onto a silica surface,⁴⁷are

reported to cyclize upon irradiation at 400 nm. Irradiation in

matrices at 254 nm, on the other hand, produced a mixture of

2

chemically distinct species, one losing only D atoms, the

other one losing H and D atoms, and subsequently three

rates, the fastest one being the selective loss of deuterium

from allyl radicals, resulting in the formation of allene. The

second slower channel should yield both hydrogen and deu-

terium.

4

8

products, including allene and propyne. The gas-phase

39

resonance Raman spectrum recorded at 225 nm showed

In principle there are two isotopic species that might

account for this second reaction channel, cyclopropyl radical

and 2-propenyl. As discussed above, there is no indication of

cyclopropene formation in our experiments, which would be

expected if hydrogen loss from cyclopropyl constituted an

important reaction channel. H loss from a 2-propenyl inter-

mediate, on the other hand, could lead to allene and propyne

formation, both being in agreement with the statistical analy-

sis of the rates and the Doppler proﬁles of both hydrogen and

deuterium. In addition, our ab initio calculations indicate that

isomerization to 2-propenyl is energetically similar to direct

allene formation, so a competition can be expected.

In light of the data obtained for the deuterated allyl, we

can now explain the time delay scan obtained for C H . We

enhancement for the ␯₁₂CH torsional mode, in agreement

2

with a disrotatory isomerization to cyclopropyl radical. This

isomerization process can be regarded as the ﬁrst step in the

formation of cyclopropene, because at the excitation energies

employed, the internal energy that would be present in the

cyclopropyl radical would sufﬁce for dissociation. The cy-

clization process was also the subject of several computa-

4

2,49,50

tional studies,

while the other reaction channels, to the

best of our knowledge, were not yet investigated theoreti-

cally. The ﬁrst examples of monitoring the dissociation of

organic radicals via H-atom detection were reported by Ko-

plitz and co-workers,³who investigated the site speciﬁcity

of hydrogen loss in alkyl radicals. As they generated their

radicals by photolysis, multiphoton processes complicated

the analysis of the data. In the work presented here, H-atom

detection was combined with pyrolytic generation of

radicals.

5,51

3

5

interpret it as a convolution of two rates, a fast process, site-

selective loss of the central H atom yielding allene, in com-

petition with an isomerization to 2-propenyl with a subse-

quent H loss leading either to propyne or allene. The early

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J. Chem. Phys., Vol. 110, No. 3, 15 January 1999

Deyerl, Fischer, and Chen

1459

data point visible in Fig. 4 that does not fall on the solid

curve is due to the fast process. While the rate constant of

tion of propyne from the 2-propenyl intermediate is associ-

ated with deuterium loss, while allene formation can proceed

via hydrogen loss and is thus ampliﬁed by the kinetic isotope

effect. Assuming equal transition state energies for the reac-

tions from 2-propenyl to propyne and allene, allene forma-

tion should now be favored, in agreement with the very small

deuterium signals observed ͑see Figs. 8 and 9͒. The small

signals and the correspondingly low signal-to-noise ratio

make it difﬁcult to extract reliable H/D ratios. Nevertheless,

two rates are visible in the hydrogen channel,

7

Ϫ1

4

ϫ10 s is assigned to 2-propenyl formation, the rate for

allene formation is at the limit of the time resolution for our

experiment and can only be estimated to be around 1

8

Ϫ1

ϫ10 s or faster.

From the computational results discussed above, the

pathway via the 2-propenyl radical should lead predomi-

nately to propyne formation, because of the 2 kcal/mol lower

activation barrier as compared to allene formation. For

8

Ϫ1

7 Ϫ1

2-deuteroallyl, one would thus expect the shifted deuterium

k_H₁у1ϫ10 s ͑allene-formation͒ and k_H₂ϭ5ϫ10 s ͑re-

action via 2-propenyl͒, different by approximately a factor of

two. The rate for deuterium loss from 2-propenyl is around

to become part of the methyl group in propyne, i.e., loss of a

hydrogen atom from the methylene group in 2-propenyl and

7

Ϫ1

formation of HCCCH D. In addition, this reaction should be

k Ϸ4ϫ10 s , showing no signiﬁcant kinetic isotope ef-

2

D

favored over deuterium loss because of the kinetic isotope

effect. However, the presence of two rates in the D-loss

channel is evident from both the time-delay scans given in

Fig. 7, as well as the Doppler proﬁles given in Fig. 6. We

thus have to ﬁnd the origin of the second D-loss channel

originating from the 2-propenyl intermediate.

fect, as expected from the discussion above.

Another issue of interest is the experimental veriﬁcation

of the barrier to 1,2 hydrogen shift in an organic radical. A

signiﬁcantly lower barrier would lead to complete isotopic

scrambling, inconsistent with the observation of any site se-

lectivity. A signiﬁcantly higher barrier, on the other hand,

would reduce the rate to isomerization to such an extent that

this reaction channel could not be observed. We calculated

rates for the isomerization, varying the calculated barrier of

66.0 over a Ϯ3 kcal/mol range. A reduction to 63 kcal/mol

brings the RRKM rate for isomerization up to 3.6

There are several possible explanations for the loss of

deuterium from 2-propenyl. The most likely reason for a

difference between observed and calculated rates is an error

in the activation barriers, because it is hard to calculate tran-

sition state energies to within better than Ϯ2 kcal/mol. To

our mind the best explanation is that in contrast to the ab

initio results, the barriers to allene and propyne formation are

approximately equal in magnitude, so there is no preference

for either product. As the isomerization is the rate-

determining step, the two reactions cannot be distinguished

in the case of a fully hydrogenated allyl, but they can for the

deuterated radicals. Another explanation could be that the

barrier for the 1,2 hydrogen shift is lower than calculated. In

this case, a higher fraction of 2-propenyl would isomerize

back to allyl and lead to partial isotopic scrambling. As will

be discussed below, a signiﬁcantly lower activation barrier

would be incompatible with the experimental observations.

In principle, one could imagine that the dissociation of

the 2-propenyl intermediate is so fast that the energy is not

8

Ϫ1

ϫ10 s , close to the rate for direct formation of allene.

The two rates are even closer for the monodeuterated allyl, in

contrast to the observed site selectivity. A barrier higher by 3

kcal/mol, on the other hand, leads to a rate decrease by a

factor of two, which is outside the experimental error bars.

Varying the barrier height within Ϯ1 kcal/mol of the ab

initio value yields good agreement with the experimental

rates for C H as well as for the deuterated compounds. Thus

3

5

we conclude that the calculated barrier for the 1,2 H shift is

conﬁrmed by the observed rates.

Isomerization of the reaction products might pose prob-

lems for the data interpretation. It was found that cyclopro-

pene is an intermediate in the reaction from allene to

propyne.⁵²However, the barriers of 68.4 and 64.1 kcal/mol

found for the allene→cyclopropene and propyne

→cyclopropene reaction, respectively, are not accessible in

the experiments described here.

fully equilibrated, prohibiting the application of statistical

theories for this step. Indeed, a rate of 3ϫ10¹¹

s

Ϫ1

is calcu-

lated for the reaction from 2-propenyl to propyne, corre-

sponding to a reaction time of 30 ps, which might be too

short to ensure complete energy randomization. However,

we prefer the ﬁrst explanation, inaccuracies in the calculation

of the barriers to hydrogen loss from 2-propenyl, since it

permits one to explain all observations within the framework

of statistical theories.

Figure 12 summarizes the results obtained from the

analysis of the kinetics. When we compare the experimental

rates, given above the arrow, with the RRKM values, given

8

Ϫ1

in brackets below the arrows, of 4.2ϫ10 s ͑allene forma-

7

Ϫ1

tion͒ and 1.9ϫ10 s

͑2-propenyl formation͒, we realize

that the calculated rates are on the same order of magnitude,

but slightly faster, and that the relative ratios match quite

The experimental rate for hydrogen loss from the

2

-propenyl isomer of C H D should be similar to deuterium

well, yielding k ϭk

/k_p_r_o_p_e_n_y_lϭ2.3 from the calculations

3

4

rel

allene

loss, because the rate-determining step is identical. Both

should also be slightly slower than the isomerization rate in

C H . In looking at the hydrogen channel, we observe a

and 2.5 from the experiment.

With the kinetic data we can now extract branching ra-

tios. Considering the error bars of experiment and calcula-

tions, we assume that k Ϸ2.5, but not smaller than k

3

5

7

Ϫ1

small increase, from 4ϫ10 to 6ϫ10 s , looking at the

rel

deuterium channel we ﬁnd the expected decrease to 2.5

ϭ2. The upper limit is not well deﬁned, because the accu-

racy in the determination of the fast rate is limited by the

time resolution of our setup. The agreement between the

measured and calculated ratios for C H D, however, seems

7

Ϫ1

ϫ10 s . To our mind, this difference gives an idea of the

error bars in the experiments on the deuterated species.

For the 1,1,3,3-tetradeuterioallyl, the appearance of two

different rates for hydrogen loss is understandable. Forma-

3

4

to conﬁrm this branching ratio. In addition, a signiﬁcant frac-

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1460

J. Chem. Phys., Vol. 110, No. 3, 15 January 1999

Deyerl, Fischer, and Chen

FIG. 12. Summary of the unimolecular chemistry of the allyl radical at 115 kcal/mol. Two competing pathways, formation of allene, and isomerization to

-propenyl with subsequent hydrogen loss can be observed. The experimental rates, as well as the RRKM rates ͑italic, in brackets͒ are given in the ﬁgure. As

2

visible, formation of allene is the faster, and thus dominating, channel.

tion of the 2-propenyl isomer will also dissociate into allene

so that the overall product ratio allene/propyne is higher,

probably between 3/1 and 4/1. Formation of cyclopropene or

C–C bond cleavage to acetylene and methyl are considered

to be of minor importance.

supersonic jet ﬂash pyrolysis of allyl iodide, C H I, seeded

3

5

in helium. Action spectra showed that each UV resonance is

associated with a hydrogen signal. The linear power depen-

dence of the H signal on the excitation laser conﬁrmed that

hydrogen is lost from neutral allyl. Time-delay scans yielded

an appearance time of several nanoseconds for the hydrogen

atoms. Interestingly, they can be ﬁtted best under the as-

sumption of two processes with two different rates contrib-

uting to the signal. As picosecond lifetimes for the excited

state were reported in earlier time-resolved experiments, we

conclude that hydrogen is not lost from the excited states

directly, but rather from the hot ground state, populated by

internal conversion.

In applications there is often interest in the canonical

rate constant, k , at a given temperature, rather than the

T

microcanonical constant k . When the energy distribution is

E

adequately described by a Boltzmann distribution, the rela-

3

4

tion becomes

Eϭϱ

Ϫ1

k_TϭQ^Ϫ¹

k_E␳͑E͒e

ϪE ͑kT͒

i

dE,

͑3͒

͵

EϭE

A

with Q^Ϫ¹being the vibrational partition function and ␳(E)

being the density of states, corresponding to the degeneracy

factor. We calculated k_Tfor the allyl→allene reaction for

Partially deuterated precursors were employed in order

to investigate the site selectivity of the hydrogen loss. Ex-

periments on both C H D and C HD showed a marked pref-

3

4

3

4

two temperatures, Tϭ4300 K, the vibrational temperature of

_a_l_l_y_l_,_a_s_d_e_r_i_v_e_d_b_e_f_o_r_e_,₁1 and Tϭ4600 K, the observed

erence for hydrogen loss from the central carbon atom, re-

sulting in allene formation being the major product channel.

However, in addition, a second process was observed, that

led to a change of the relative ratios between hydrogen and

deuterium with delay time. This channel is assigned to

isomerization to the 2-propenyl radical via a 1,2 hydrogen

shift. 2-propenyl subsequently loses a hydrogen atom to form

either allene or propyne. Ab initio calculations on the

coupled cluster level showed that the barriers from allyl to

allene and to 2-propenyl are comparable and that a competi-

tion between the two channels can be expected. From the

translational temperature for the hydrogen atom, and ob-

tained values of k_T_ϭ₄₃₀₀_ϭ₉_.₅_ϫ₁₀7 and k_T_ϭ₄₆₀₀

ϭ

7

Ϫ1

9

.6ϫ10 s . For the allyl→2-propenyl isomerization, we

7 7 Ϫ1

obtain k_T_ϭ₄₃₀₀ϭ3.8ϫ10 and k

ϭ3.9ϫ10 s

Tϭ4600

.

It is worthwhile to compare our approach to other tech-

niques employed to study the dynamics of radicals. An in-

teresting alternative is photofragment translational spectros-

copy, developed by the Neumark group⁵

3–55

Here the

radicals are produced by photodetachment in a fast beam of

the corresponding mass selected anions. After excitation into

dissociative or predissociative states by a tunable laser, the

different fragments are detected in coincidence. This tech-

nique is general and provides a considerable amount of in-

formation; however, it is difﬁcult to apply when the frag-

ments are very different in mass, in particular when a

hydrogen atom is lost. In addition, reaction rates can only be

obtained indirectly. An extension of this technique was in-

troduced by Continetti and co-workers, who detect the pho-

8

Ϫ1

time-delay scans, rate constants of Ͼ1ϫ10 s for allene

7

Ϫ1

formation and 4ϫ10 s

for isomerization to 2-propenyl

were determined, corresponding to a branching ratio of 2.5:1.

RRKM calculations yielded a similar ratio of 2.3:1 for the

two rate constants. Thus we conclude that the relative

branching ratio for the two processes lies between 2:1 and

3

:1 in favor of direct allene formation from allyl. From the

experimental rates an activation barrier of 66Ϯ1 kcal/mol for

the 1,2 hydrogen shift to 2-propenyl is deduced, in agree-

ment with the ab initio value.

From the FWHM of the measured Doppler proﬁles, a

translational energy release of 14Ϯ1 kcal/mol is calculated.

For allene this corresponds to 24% of the excess energy be-

ing released as translation, for propyne this corresponds to

toelectrons generated in the detachment step in coincidence

with the neutral radicals or fragments.⁵

6,57

In contrast, Dop-

pler spectroscopy, as applied by us, works best for small

fragments. Thus both techniques complement each other

very well.

V. CONCLUSION

2

3%. This is substantially larger than expected from a prior

In this paper we investigated the photochemistry and

photodissociation dynamics of the allyl radical, C H , upon

excitation into the UV bands to the blue of 250 nm. A clean

and cold molecular beam of allyl radicals was generated by

distribution or RRKM calculations, but can be explained by

the relatively large reverse activation barrier of 7 kcal/mol

for the allyl→allene reaction. The energy of the reverse bar-

rier will be preferentially released as translation.

3

5

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J. Chem. Phys., Vol. 110, No. 3, 15 January 1999

Deyerl, Fischer, and Chen

1461

ACKNOWLEDGMENTS

͑5͒ 1,1,3,3-tetradeuterio-1-iodoprop-2-ene: The alcohol was

converted to the iodide by a modiﬁcation of the Land-

auer and Rydon procedure. 5.1 g of the alcohol were

We would like to thank Thomas Gilbert for his contri-

butions to the early part of this work and for working out the

synthesis of the tetradeuterioallyliodide. Financial support

from the Schweizerische Nationalfonds and the ETH Z u¨ rich

58

stirred with 17.7 g CH I in 25.5 g triphenylphosphit for

3

one day under Ar at 75°, generating the 1,1,3,3 D al-

4

lyliodide. This was distilled off at 120 Torr/32–34°

yielding around 4.2 g ͑17% yield͒ of the precursor for

our experiments.

is gratefully acknowledged.

APPENDIX: SYNTHESIS OF THE DEUTERATED

PRECURSORS

For all substances NMR spectra were recorded that are

available as supplementary material.³⁷

For the experiments investigating the site speciﬁcity of

the hydrogen loss, two different isotopically labeled precur-

sors were employed. 2-deuterioallyliodide was synthesized

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from propargyl alcohol and LiAlD , following the procedure

2

4

1

0

described before.

,1,3,3 tetradeuterioallyliodide was synthesized in the

3

1

4

following way: Please note that the ﬁrst three steps were

repeated several times before the fourth reaction was carried

out.

5

6

7

8

9

͑1͒ 1,1-dideuterioprop-2-yn-1-ol: A solution of 47.1 g ethyl

1

0

1

propriolate in 300 ml of ether was added dropwise to 15

g LiAlD in 600 ml diethylether at Ϫ78° over a period

4

͑

1997͒.

of 4 h. The mixture was stirred overnight. After adding

12

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5 ml H O dropwise, the mixture was brought to room

2

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temperature. 15 ml of a 15% NaOH solution and then 45

ml of H O were added. The precipitate was ﬁltered off

14

2

H. Clauberg, D. W. Minsek, and P. Chen, J. Am. Chem. Soc. 114, 99

and washed with ether. The combined ethereal fractions

were evaporated and distilled, yielding 28 g of 1,1-

dideuterioprop-2-yn-1-ol, 1, at 91-101° at 1 atm.

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ATM, 5.4 g of 3 were obtained.

͑

4͒ 1,1,3,3-tetradeuterioprop-2-enol: In the next step, 11.4 g

29

of 3 in 100 ml of ether were added drowse to 8.9 g

3

0

1

LiAlH in 400 ml of ether under Ar atmosphere at 0°.

4

The mixture was subsequently reﬂuxed for 18 h. Then

4

5.6 g D O were added at room temperature. The lithium

32

2

salt formed in the reaction was ﬁltered off and washed

with ether. The combined ethereal fractions were evapo-

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g

of 1,1,3,3-

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Photodissociation dynamics of the allyl radical

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