Kinetics and dynamics in the photodissociation of the allyl radical

Article abstract of DOI:10.1063/1.474704

The direct observation of the products, kinetics and translational energy release from the photodissociation of the allyl radical, C₃H₅, upon excitation in the near-uv is reported. A statistical analysis of the data shows that they are in agreement with allene formation being the dominant H-loss reaction channel.

Full text of DOI:10.1063/1.474704

Kinetics and dynamics in the photodissociation of the allyl radical
Hans-Jürgen Deyerl, Thomas Gilbert, Ingo Fischer, and Peter Chen
Citation: The Journal of Chemical Physics 107, 3329 (1997); doi: 10.1063/1.474704
View online: http://dx.doi.org/10.1063/1.474704
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Kinetics and dynamics in the photodissociation of the allyl radical
a)
a)
Hans-J u¨ rgen Deyerl, Thomas Gilbert, Ingo Fischer, and Peter Chen
Laboratorium f u¨ r Organische Chemie, ETH Z u¨ rich, Universit a¨ tstr. 16, CH-8092 Z u¨ rich, Switzerland
͑
Received 22 May 1997; accepted 20 June 1997͒
The direct observation of the products, kinetics and translational energy release from the
photodissociation of the allyl radical, C H , upon excitation in the near-uv is reported. A statistical
3
5
analysis of the data shows that they are in agreement with allene formation being the dominant
H-loss reaction channel. © 1997 American Institute of Physics. ͓S0021-9606͑97͒02432-X͔
8
We report the direct observation of the products, kinetics
and translational energy release from the photodissociation
of the allyl radical, C H , upon excitation in the near-uv.
radicals. The isomerization to cyclopropyl has also been the
subject of several theoretical investigations.6
,9,10
Neverthe-
less, the evidence for such a reaction is inconclusive.
In our experiments a molecular beam of allyl radicals
was produced by means of supersonic jet flash pyrolysis.11
The allyl is then excited by pulsed uv-laser radiation into one
3
5
Hydrocarbon radicals appear as chemical intermediates
in many reactive environments. Of particular importance for
combustion processes or tropospheric chemistry are rela-
tively stable radicals that are converted into more reactive
species upon photochemical excitation by radiation present
in the particular environment. An example of such a system
is the allyl radical, whose spectroscopy has been the subject
2
of several vibronic bands of the C B1 state. The hydrogen
atoms formed after a variable time delay can be detected
with very high sensitivity employing Lyman-␣ radiation at
121.6 nm. If the intensity of the hydrogen signal is moni-
tored as a function of the delay time between pump and
probe laser, microcanonical reaction rates k(E) are obtained.
Product translational energy distributions can be obtained
from the Doppler profiles of the hydrogen fragment absorp-
tion spectrum. A statistical analysis of the data can then pro-
vide information that could distinguish between the two re-
action channels.
1
of earlier studies in our group. A large number of vibronic
bands between 250 and 240 nm was identified by resonant
multiphoton ionization ͑MPI͒ and assigned to the B, C, and
D states of allyl, which are strongly coupled to each other.
No fluorescence has been observed from these states despite
the very large oscillator strength of at least one of them.2
Time-resolved studies in our group have indicated lifetimes
3
The probe technique, vuv laser detection of H atoms
on the sub-100 picosecond scale for these states. Likely fast
formed in chemical reactions, has been used for roughly a
kinetic processes that would occur in competition with emis-
sion include the loss of a hydrogen atom, either prior to, or
subsequently to a radiationless transition to a lower-lying
electronic state. The elucidation of the dynamics of this re-
action is the subject of the this communication. Figure 1
shows the energy diagram for the two most important reac-
tion channels, yielding allene and cyclopropene, with data
from Refs. 4 and 5. Allene is the thermodynamically favored
product. The reaction to cyclopropene would necessarily in-
volve a cyclization to cyclopropyl radical, followed by hy-
drogen loss. This reaction would be kinetically favorable.
Other possible reactions include the formation of 1-propyne,
which is expected to have a higher activation barrier due to
an additional, less likely hydrogen shift, or concerted H2
loss, forming cyclopropenyl radical. They will not be consid-
ered in this communication.
decade.1
2,13
It has been applied mostly to reactions of stable
molecules in cells, although some studies on saturated hydro-
carbon radicals have been reported.14 In those studies, how-
ever, the radicals were produced by photolysis, complicating
the experiment through interference by higher-order multi-
photon processes. Alternatively, photofragment translational
spectroscopy has been successfully applied to radical
reactions.15 In the next sections, we show that a combination
of H-atom detection with pyrolytic production of radicals
yields an amount and quality of information equal to that
available from experiments on stable molecules, and permits
a study of the photochemistry of medium-sized organic radi-
cals in molecular beams.
The experiment was carried out in a molecular beam
machine equipped with a time-of-flight ͑TOF͒ mass spec-
trometer. The details of the experimental setup will be de-
scribed in a future publication, the supersonic jet flash py-
rolysis source and the formation of the allyl radical have
been described previously. Two Nd:YAG pumped dye laser
systems were employed, synchronized externally to within
better than 2 ns. The first laser excited the allyl radical and
induced photolysis. The hydrogen detection was carried out
The photochemistry of the allyl radical has already at-
tracted some interest due to its importance as a model sys-
tem, with most prior studies performed in rare gas matrices.
When allyl was irradiated with blue light, bands appeared
that were assigned to the cyclopropyl radical.6 Irradiation at
16
1
,7
2
54 nm in the presence of bromine atoms, on the other hand,
7
yielded allene, propyne and some smaller fragments. The
gas-phase resonance Raman spectrum of the C B state at
17
as described by Welge and co-workers. A second laser was
2
1
frequency tripled in 225 mTorr of Kr to produce Lyman-␣
radiation around 121.6 nm, exciting H atoms into the 2p
state. They were ionized by the 364.7 nm dye laser funda-
mental and detected in the TOF spectrometer. Typically each
225 nm was consistent with isomerization to cyclopropyl
a͒Authors to whom correspondence should be addressed.
J. Chem. Phys. 107 (8), 22 August 1997
0021-9606/97/107(8)/3329/4/$10.00
© 1997 American Institute of Physics
3329
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3330
Letters to the Editor
FIG. 1. Schematic diagram of the energetics of the allyl radical for the two
most important reaction channels, leading to allene and cyclopropene
FIG. 3. Growth curve of the hydrogen signal as a function of the delay time
between excitation laser and Lyman-␣ laser. The curve is fitted with a rise-
7
Ϫ1
time of 25 ns, corresponding to a rate k(E)ϭ4ϫ10 s . The exponential
decay is due to the motion of the hydrogen out of the observation region.
data point represents an average of 200 shots.
In Fig. 2, a resonant MPI spectrum of the allyl radical is
given, showing the region around the C B1 state origin.
While the pump laser was scanned, the probe laser was kept
2
C-state bands visible in Fig. 1 were studied in detail, we will
0
concentrate exclusively on the C 0 band.
0
A microcanonical rate for the H loss can be obtained
when the appearance of the hydrogen signal is monitored as
a function of the pump–probe delay. Such a delay scan is
given in Fig. 3. The hydrogen signal shows a fast risetime, a
short plateau around 100 ns, and a decay at longer delay
times. The decay is due to the motion of the hydrogen atoms
out of the detection region and does not have any physical
significance. The rate can be extracted from a fit of the rising
edge of the curve. The time constant is 25 ns, yielding
fixed at 121.6 nm. The masses 41 ͑allyl, lower trace͒ and 1
͑hydrogen, upper trace͒ were recorded simultaneously. The
spectrum was not corrected for laser power. For each peak in
the allyl channel there is a corresponding peak in the hydro-
gen channel. The transitions into the C-state origin band, as
1
0
1
0
well as into the B 9 and the C 7 bands, can be identified.
Power studies revealed a quadratic dependence on the pump
laser energy for the allyl signal, but a linear dependence for
the hydrogen signal, indicating that the hydrogen originates
from dissociation of the neutral excited allyl radical rather
than from the cation. When the probe laser was blocked no
hydrogen was detected. However, the probe laser alone did
produce a small background signal, attributable either to hy-
drogen produced in the pyrolysis source or to photodissocia-
tion induced by the vuv light, that was subtracted in the
Doppler-spectra discussed below. Although both of the
7
Ϫ1
k(E)ϭ4ϫ10 s . This is close to the limits of the time
resolution of our laser system. As mentioned above, time-
resolved studies indicate lifetimes of less than 100 ps for the
states excited in the present experiments. As we observe hy-
drogen loss on a nanosecond timescale we conclude that hy-
drogen is not lost directly from the C state. Presumably, the
C state decays via an internal conversion, forming very hot
ground state molecules or allyl radicals in the A state. In
either case, the timescale of dissociation is long enough to
assume that the allyl is completely thermalized before the
reaction occurs, and that statistical theories can be applied.
RRKM calculations, including rotation, for both the di-
rect loss of hydrogen from hot allyl radicals, and H loss
subsequently to cyclization were performed. For the pathway
yielding cyclopropene, we assumed that cyclization occurs
fast and that hydrogen loss is the rate determining step. From
a statistical viewpoint, this assumption is justified by the
large amount of excess energy available for the reaction. The
activation energies EA were calculated from the thermo-
chemical data given in Fig. 1, assuming reverse barriers
of ϳ5 kcal/mol. All frequencies were calculated with
the aid of the GAUSSIAN1 94 program package18 on the
MP4͑SDQ͒ 6-31 G* level. 9 The frequencies were scaled by
a factor of 0.94 in order to match the experimentally known
FIG. 2. Resonant MPI spectrum of the allyl radical ͑lower trace͒. The signal
recorded simultaneously in the hydrogen mass channel is given in the upper
trace. For each resonance in the allyl spectrum there is a corresponding
increase in the hydrogen signal.
8
frequencies of the allyl radical. The details of the calcula-
tion will be reported in a full account of this work. This
9
Ϫ1
procedure yielded rate constants of k(E)ϭ2.6ϫ10 s for
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Letters to the Editor
3331
9
Ϫ1
the reaction from allyl→allene, and 6ϫ10 s for the reac-
tion from cyclopropyl→cyclopropene, both calculated rates
overshooting the experimentally observed reaction rates con-
siderably. However, under our conditions there would be ex-
cess energies of 59.1 and 36.6 kcal/mol for the allyl→allene
and cyclopropyl→cyclopropene reaction present in the sys-
tem, making the effect of anharmonicity non-negligible. In
order to mimic the effect of anharmonicity, we employed an
additional scaling factor obtained in the following way: Ab
initio frequencies were used to calculate heat capacities Cp
of allene and propene. The calculated values were then com-
pared to data obtained from an extrapolation of experimental
2
0
values. When the molecular frequencies were scaled by an
additional factor of 0.71, a good fit to the extrapolated Cp
data around 3000 K was obtained. As will be discussed be-
low, the vibrational temperature of the allyl radical can be
calculated to be around 4000 K. However, experimental data
to check the extrapolation are only reported up to 1500 K,
leading probably to unreliable predictions at temperatures
higher than 3000 K. Nevertheless, another set of RRKM cal-
culations was then performed in which the ab initio frequen-
cies were multiplied by an additional factor of 0.71 to simu-
late the effects of anharmonicity. Under these conditions rate
0
FIG. 4. Doppler profile of the hydrogen atom after excitation into the C
0
band of allyl. The full line represents a Gaussian fit with a FWHM of
4 cm after deconvolution. This corresponds to an expectation value of
Ϫ1
13.6 kcal/mol for the translational energy release.
both reaction channels, the hydrocarbon fragment would
contain a large amount of internal excitation, in agreement
with an indirect dissociation process in which the molecule
undergoes a large geometry change before entering the exit
7
Ϫ1
8
Ϫ1
constants k(E)ϭ9.5ϫ10 s
and 8ϫ10 s
for the
allyl→allene and cyclopropyl→cyclopropene reaction were
obtained. A RRKM calculation for the isomerization of allyl
to cyclopropyl, assuming a reverse barrier of 16.6 kcal/mol
25
channel. This geometry change is certainly more pro-
nounced for the formation of the cyclic product, cyclopro-
pene, making it surprising if the formation of cyclopropene
were to be accompanied by a translational energy release
about twice as high as is typical for similar compounds.
An approach to calculate the product translational en-
21
obtained from ab initio calculations, yielded a value of
1
0
Ϫ1
k(E)ϭ2ϫ10
s , confirming the assumption that hydro-
gen loss is the rate determining step. We note that the value
for allene formation is within a factor of 2 of the experimen-
tal data, while the rate calculated for cyclopropene formation
is too fast by a factor of 30.
Information on the product energy distribution can be
obtained from Doppler profiles of the hydrogen spectrum. A
representative Doppler profile, recorded at a pump–probe
delay of 100 ns, is depicted in Fig. 4. It is fitted well by a
26
ergy release was described by Quack. He suggested the use
of a distribution function
n
T
P͑E ͒ϭC␳ ͑EϪE ͒E
͑1͒
T
p
T
with n being an adjustable parameter, 0ϽnϽ3, ␳ being the
p
rovibrational density of states of the product and C a nor-
malization constant, to mimic the more accurate phase space
and adiabatic channel model behavior. The parameter n re-
flects to some extent the tightness of the transition state as
well as the extent to which the reaction behaves statistically.
We employed the following simplified procedure: The ex-
pression
Gaussian with a full width at half maximum ͑FWHM͒ of
Ϫ1
4
.1 cm , implying a speed distribution which is close to
Maxwellian. Part of the halfwidth is due to the laser band-
Ϫ1
width of 0.4 cm in the vuv and the fine-structure splitting
of the P3/2 and the 2P1/2 states of hydrogen, which are
2
Ϫ1
0
.4 cm apart. A deconvolution of the band yielded a Dop-
Ϫ1
pler broadening ␦␯ of 4.0 cm . From the formula given in
the literature a translational temperature T ϭ4583 K is cal-
E
nϩ1
2
2
E
͐
␳ ͑EϪE ͒E
dET
0
p
T
T
T
͗
ET
͘
ϭ
͵
E P͑E ͒dEϭ
͑2͒
T
T
E
n
ET
͗ ͘
culated. Using the expression ϭ3/2 RT and correcting
0
͐
␳ ͑EϪE ͒E dE
p
T
T
0
T
for the mass of the hydrogen fragment, a corresponding
translational energy release of 13.9 kcal/mol is obtained. For
the reaction forming allene, the excess energy is 59.1 kcal/
mol, meaning that 23% would have been released as trans-
lational energy if this channel were to be dominant. This is
within the range of values typical for predissociative hydro-
gen loss in unsaturated hydrocarbons, if compared with, e.g.,
with the denominator being the normalization constant, was
used to find a value for n that could reproduce our experi-
mentally derived ET of 13.9 kcal/mol. We found n to be
͗ ͘
around 2.4 for the allyl→allene reaction, and 4.5 for the
cyclopropyl→cyclopropene reaction. With scaled frequen-
cies (ϫ0.71) the n values increases to nϭ2.7 and nϭ5.3,
respectively. Thus the value of n necessary to fit the experi-
mentally observed translational energy release for the reac-
tion leading to cyclopropene is well outside the range ob-
served to be consistent with statistical behavior.26 For
comparison, we calculated n values for hydrogen-loss from
2
3
ethylene ͑18%͒ or methyl substituted benzenes and pyra-
zines ͑10%–15%͒.24 For a reaction forming cyclopropene,
the lower excess energy of 36.6 kcal/mol would mean that
37% is released as translational energy, a fraction signifi-
cantly higher than in the above mentioned examples. For
J. Chem. Phys., Vol. 107, No. 8, 22 August 1997
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3332
Letters to the Editor
cycloheptatriene and substituted benzenes,13,24 forming ͑sub-
stituted͒ benzyl radicals, and obtained values of nϷ2.
In their work on the decomposition of toluene into ben-
6
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scaled frequencies are employed the Tvib come out about 200
K lower. Under the assumption that the principle of detailed
balance is valid for our system, the translational temperature
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the vibrational temperature expected for the allyl→allene re-
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contributions of the reverse barrier. The agreement is less
satisfying for the cyclopropyl→cyclopropene reaction.
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comes from hydrogen loss at the central carbon atom, while
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J. Chem. Phys., Vol. 107, No. 8, 22 August 1997
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