Crossed-beam reaction of carbon atoms with hydrocarbon molecules. I. Chemical dynamics of the propargyl radical formation, C3H3 (X2B2), from reaction of C(3Pj) with ethylene, C2H4(X1/Ag)

Article abstract of DOI:10.1063/1.472652

The reaction between ground-state carbon atoms, C(³P_j), and ethylene, C₂H₄(X¹A_g), was studied at average collision energies of 17.1 and 38.3 kJmol^-1 using the crossed molecular beams technique. Product angular distributions and time-of-flight spectra of m/e=39 were recorded. Forward-convolution fitting of the results yields a maximum energy release as well as angular distributions consistent with the formation of the propargyl radical in its X²B₂ state. Reaction dynamics inferred from the experimental data indicate two microchannels, both initiated by attack of the carbon atom to the π-orbital of the ethylene molecule via a loose, reactant like transition state located at the centrifugal barrier. Following C_s symmetry on the ground state ³A″ surface, the initially formed triplet cyclopropylidene complex rotates in a plane roughly perpendicular to the total angular momentum vector around its C-axis, undergoes ring opening to triplet allene, and decomposes via hydrogen emission through a tight transition state to the propargyl radical. The initial and final orbital angular momenta L and L′ are weakly coupled and result in an isotropic center-of-mass angular distribution. A second microchannel arises from A-like rotations of the cyclopropylidene complex, followed by ring opening and H-atom elimination. In this case, a strong L-L′ correlation leads to a forward-scattered center-of-mass angular distribution. The explicit identification of C₃H₃ under single collision conditions represents a single, one-step mechanism to build up hydrocarbon radicals. Our findings strongly demand incorporation of distinct product isomers of carbon atom-neutral reactions in reaction networks simulating chemistry in combustion processes, the interstellar medium, as well as in outflows of carbon stars, and open the search for the hitherto unobserved interstellar propargyl radical.

Full text of DOI:10.1063/1.472652

Crossedbeam reaction of carbon atoms with hydrocarbon molecules. I. Chemical
dynamics of the propargyl radical formation, C3H3 (X 2 B 2), from reaction of C(3 P j )
with ethylene, C2H4(X 1 A g )
R. I. Kaiser, Y. T. Lee, and A. G. Suits
Citation: The Journal of Chemical Physics 105, 8705 (1996); doi: 10.1063/1.472652
View online: http://dx.doi.org/10.1063/1.472652
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/105/19?ver=pdfcov
Published by the AIP Publishing
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Crossed-beam reaction of carbon atoms with hydrocarbon molecules. I.
Chemical dynamics of the propargyl radical formation, C3H3 (X2B2),
from reaction of C(3Pj) with ethylene, C2H4(X1Ag)
R. I. Kaiser, Y. T. Lee,a) and A. G. Suitsb)
Department of Chemistry, University of California, Berkeley, California 94720
and Chemical Sciences Division, Berkeley National Laboratory, Berkeley, California 94720
͑Received 28 June 1996; accepted 9 July 1996͒
The reaction between ground-state carbon atoms, C͑3Pj͒, and ethylene, C2H4(X1Ag), was studied at
average collision energies of 17.1 and 38.3 kJmolϪ1 using the crossed molecular beams technique.
Product angular distributions and time-of-flight spectra of m/eϭ39 were recorded.
Forward-convolution fitting of the results yields a maximum energy release as well as angular
distributions consistent with the formation of the propargyl radical in its X2B2 state. Reaction
dynamics inferred from the experimental data indicate two microchannels, both initiated by attack
of the carbon atom to the ␲-orbital of the ethylene molecule via a loose, reactant like transition state
3
located at the centrifugal barrier. Following Cs symmetry on the ground state AЉ surface, the
initially formed triplet cyclopropylidene complex rotates in a plane roughly perpendicular to the
total angular momentum vector around its C-axis, undergoes ring opening to triplet allene, and
decomposes via hydrogen emission through a tight transition state to the propargyl radical. The
initial and final orbital angular momenta L and LЈ are weakly coupled and result in an isotropic
center-of-mass angular distribution. A second microchannel arises from A-like rotations of the
cyclopropylidene complex, followed by ring opening and H-atom elimination. In this case, a strong
L-LЈ correlation leads to a forward-scattered center-of-mass angular distribution. The explicit
identification of C3H3 under single collision conditions represents a single, one-step mechanism to
build up hydrocarbon radicals. Our findings strongly demand incorporation of distinct product
isomers of carbon atom-neutral reactions in reaction networks simulating chemistry in combustion
processes, the interstellar medium, as well as in outflows of carbon stars, and open the search for the
hitherto unobserved interstellar propargyl radical. © 1996 American Institute of Physics.
͓S0021-9606͑96͒00639-3͔
ϩ
g
1
2
2
CH a1A ͒ϩC H X ⌺ ͒→C H X B ͒ϩH S ͒, ͑1͒
I. INTRODUCTION
͑
͑
2
͑
3
͑
2
1
2
3
2
1/2
2
The propargyl radical in its B2 electronic ground state
holds the global minimum on the C3H3 potential energy sur-
face ͑PES͒ and has received considerable attention due to its
potential importance in interstellar and planetary
chemistry1–2 and contribution to combustion processes.3–7
High propargyl concentrations are predicted in oxygen rich
hydrocarbon flames due to a partial delocalization of the un-
paired B2 electron and an inherent low reaction rate constant
of k͑295 K͒ϭ5ϫ10Ϫ14 cm3 sϪ1 with O2.8 Current combus-
tion models postulate that soot formation and synthesis of
polycyclic aromatic hydrocarbons ͑PAHs͒ are strongly cor-
related and initiated by recombination of two C3H3 radicals
to C6H6 isomers ͓k͑295 K͒ϭ1.2ϫ10Ϫ10 cm3 sϪ1͔ followed
by stepwise ring growth to larger PAHs.9 However, little is
known on the synthesis of the propargyl radical in hydrocar-
bon flames. Adamson investigated the reaction of singlet me-
thylcarbene with acetylene, reaction ͑1͒, as a potential
pathway,10 whereas a unimolecular decomposition of vibra-
tionally excited singlet allene or methylacetylene, C3H4 via
C–H bond rupture, is suggested as a propargyl source, reac-
C H X1A ͒→C H X B ͒ϩH S ͒,
͑2͒
2
2
͑
4
͑
3
͑
3
1
3
2
1/2
CH CCH X1A ͒→C H X B ͒ϩH S ͒.
͑3͒
2
2
͑
͑
͑
3
1
3
3
2
1/2
Besides its relevance in combustion chemistry, the pro-
pargyl isomer is expected to exist in interstellar and plan-
etary environments. Its potential ethylene precursor has been
widely incorporated into photochemical models of the strato-
sphere of Jupiter, Saturn, Uranus, Neptune, and Titan,12 as
well as into sophisticated ion-molecule networks of the Jo-
vian ionosphere.13 The very first detection of ethylene out-
side our solar system in circumstellar shells14 fueled Herbst
et al. to include the reaction of C͑3Pj͒ with C2H4 in a generic
chemical model of the circumstellar envelope surrounding
IRCϩ10216, postulating the existence of C3H3 products.15
Since the reaction network was based simply on spin-
conservation and thermochemistry without investigation of
the chemical dynamics, the explicit identification of any hith-
erto unobserved interstellar C3H3 isomer remains to be re-
solved, cf. Fig. 1.
11
tions ͑2͒ and ͑3͒
Previous mechanistic information on the C/C2H4-system
was derived from radioactive tracer studies of suprathermal
11C͑3Pj͒ and 11C͑1D2͒ recoil atom reactions with
C2H4,C2D4,C2H4/O2, as well as C2H4/Ne-mixtures under
a͒
Present address: Academia Sinica, Nankang, Taipei, 11529, Taiwan.
Author to whom correspondence should be addressed.
b͒
J. Chem. Phys. 105 (19), 15 November 1996
0021-9606/96/105(19)/8705/16/$10.00
© 1996 American Institute of Physics
8705
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8706
Kaiser, Lee, and Suits: Reaction of carbon atoms with hydrocarbons. I.
body collision, undergoes 1,3-hydrogen migration to methy-
lacetylene ͑3͒ prior to its collisional deactivation, or is as-
sumed to fragment to hydrogen and C3H3 radicals. To a mi-
nor amount, hot 11C͑1D2͒ inserts in a C–H bond to singlet
vinylcarbene ͑4͒. Intermediate ͑4͒ undergoes 1,2- or 2,3-H
migration to singlet allene ͑2͒, or methylacetylene ͑3͒, re-
spectively, before a third body deactivation takes place.
Thermal 11C͑1D2͒ atoms, however, are found to add exclu-
sively to the ethylene ␲-bond.
Suprathermal 11C͑3Pj͒ inserts into C–H bonds yielding
triplet vinylcarbene ͑5͒ and adds to olefinic double bonds to
triplet cyclopropylidene ͑6͒. The yield of C–H insertion
products is reduced with increasing thermalization of the hot
11C͑3Pj͒ atoms. Both triplet intermediates ͑5͒ and ͑6͒ are
postulated to lose H to form C3H3 radicals with subsequent
attack of
a
second ethylene molecule, producing
FIG. 1. Point groups, electronic ground states, and enthalpy of formations of
C3H3 isomers relative to the propargyl radical: ͑1͒ propargyl ͑C2v,
2B2 , 0
1-propyneyl-5 ͑7͒ and 1,2-pentadienyl-5 ͑8͒. Internally ex-
cited ͑7͒ and ͑8͒ abstract hydrogen atoms yielding 1-propyne
͑9͒ and 1,2-pentadiene ͑10͒. Vinylacetylene is assumed to be
generated via reaction of C2Hx radicals with ethylene mol-
ecules. The diminished concentration of vinylacetylene and
acetylene goes hand in hand with a decreasing internal exci-
tation of triplet C3H4 intermediates, suggesting C2H2 as a
fragmentation product via CϭC bond rupture in ͑5͒ or indi-
rectly via vinylidenecarbene ͑11͒ after ring cleavage of ͑6͒
and 1,2-H-migration. Postulated cyclopropylidene intermedi-
ates were trapped as dimethyl-spiranes ͑12͒ as reaction prod-
ucts of carbon recoils with 2-butene.
2
kJ molϪ1͒; ͑2͒ cyclopropen-1-yl ͑D3h, E , 100Ϯ25 kJ molϪ1͒; ͑3͒ propyn-
Љ
1-yl ͑D3h, 2E, 147 kJ molϪ1͒; ͑4͒ cyclopropen-2-yl ͑C , 2A , 233 kJ molϪ1͒;
Ј
s
2
͑5͒ allenyl ͑C1 , A, 270 kJ molϪ1͒. Absolute enthalpy of formations of ͑1͒
and ͑2͒ were taken from Ref. 26.
bulk conditions.16–25 Four product classes were identified:
C2H2 ͑class 1͒, C5Hx products ͑class 2͒, vinylacetylene ͑class
3͒, and allene/methylacetylene ͑class 4͒. Suprathermal
11C͑1D2͒ atoms add to the olefinic double bond to singlet
cyclopropylidene ͑1, Fig. 2͒ followed by insertion between
the previously joined carbon atoms to singlet allene ͑2͒. The
vibrationally excited molecule could be stabilized via a third
Here, we investigate the detailed chemical dynamics of
FIG. 2. Postulated reaction mechanisms and detected products in the C/C2H4 system as derived from bulk experiments of suprathermal 11C͑3Pj͒ and 11C͑1Dj͒
recoil atoms with C2H4 , C2D4 , C2H4/O2 , and C2H4/Ne mixtures.
J. Chem. Phys., Vol. 105, No. 19, 15 November 1996
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Kaiser, Lee, and Suits: Reaction of carbon atoms with hydrocarbons. I.
8707
TABLE I. Experimental beam conditions and 1␴ errors: Most probable velocity 0 , speed ratio S, most
v
probable relative collision energy with the ethylene molecules, Ecoll , center-of-mass angle, ␪CM , composition of
the carbon beam, and flux factor fv in relative units, cf. Sec. IV A.
Beam
0 , msϪ1
S
Ecoll , kJ molϪ1
␪
C1 :C2 :C3
fv
v
CM
C͑3Pj͒/Ne
C͑3Pj͒/He
C2H4
1850Ϯ30
2900Ϯ80
840Ϯ40
4.5Ϯ0.3
4.0Ϯ0.2
8.3Ϯ0.2
17.1Ϯ0.7
38.3Ϯ2.1
•••
45.3Ϯ0.8
34.1Ϯ1.6
•••
1:0.6:1.8
1:0.2:0.3
•••
1.0
5.6Ϯ1.1
•••
the atom-neutral reaction of C͑3Pj͒ with C2H4(X1Ag) under
single collision conditions at relative collision energies of
17.1 and 38.3 kJmolϪ1 as provided in crossed molecular
beam experiments.27 The detailed information on the reac-
tion dynamics disclose the nature of the triplet C3H4 PES, the
formation of C3H3 isomers in interstellar environments and
hydrocarbon flames, reaction intermediates postulated in
bulk experiments, and offer a valuable comparison to the
O͑3Pj͒ϩC2H4(X1Ag) reaction studied recently in our
group.28
III. DATA ANALYSIS
A. Velocity and speed ratio of the parent beams
The velocity distribution of each supersonic parent beam
is defined by
2
␯
N ␯͒ϭ␯ exp Ϫ 0ϪS
,
͑4͒
2
0
͑
ͩ ͩ
ͪ ͪ
␣
with the velocity 0, the speed ratio S, and ␣ϭm/2RT, mass
v
of the molecule ͑atom͒ m, the temperature of the beam T and
the ideal gas constant R. A transformation from the velocity
to time domain yields
II. EXPERIMENT
2
L3
t4
L
N t͒ϭ
exp Ϫ
ϪS
,
͑5͒
͑
ͩ ͩ
ͪ ͪ
The reactive scattering experiments are performed in a
universal crossed molecular beam apparatus described in
Ref. 29. A pulsed supersonic carbon beam was generated via
laser ablation of graphite at 266 nm.30 The 50/30 Hz, 35–40
mJ output of a Spectra Physics GCR-270-50/30 Nd:YAG
laser is focused onto a rotating carbon rod. Ablated carbon
atoms are seeded into neon ͑99.999%, Bay Area Gas͒ ͑ex-
periment 1͒ or helium ͑99.999%, Bay Area Gas͒ ͑experiment
2͒ released by a Proch–Trickl pulsed valve operating at 100
Hz or 60 Hz, 80 ␮s pulses, and 4 atm backing pressure. A
four slot chopper wheel mounted 40 mm after the ablation
zone selects a 9.0/7.5 ␮s segment of the seeded carbon beam.
Table I compiles the experimental beam conditions. The
pulsed carbon beam and a continuous ethylene ͑99.99%,
Matheson͒ beam with 584Ϯ10 Torr backing pressure pass
through skimmers with apertures of 1.0 and 0.58 mm, and
cross at 90° with divergences of 3.0° and 4.7° in the interac-
tion region of the scattering chamber at relative collision
energies of 17.1 and 38.3 kJmolϪ1. The reactively scattered
products were detected in the plane of the beams using a
rotatable detector consisting of a Brink-type electron-impact
ionizer,31 quadrupole mass filter, and a Daly ion detector32 at
different laboratory angles between 5.00 and 60.00 with re-
spect to the carbon beam in 2.50–5.00 steps. The velocity
distribution of the products was determined using the time-
of-flight ͑TOF͒ technique33 choosing a channel width of 10
␮s. Counting times ranged from 0.5–5 h, averaged over sev-
eral angular scans. The velocity of the supersonic carbon
beam was monitored frequently after taking the data for 2–4
angles and minor velocity drifts corrected by adjusting the
laser pulse delay within Ϯ1 ␮s.30 Reference angles were
chosen at 350 and 47.50, respectively, to calibrate fluctuating
carbon beam intensities and mass dial settings at the quadru-
pole controller.
␣t
where L is the neutral flight length. The most probable ve-
locity and speed ratio are fitted after convolution over the
ionizer length and the shutter function of the chopper wheel
͑Table I͒.
B. TOF spectra and laboratory angular distribution
Information on the velocity and angular distributions of
products in the center-of-mass coordinate system was ob-
tained by fitting the TOF spectra and the product angular
distribution in the laboratory frame using a forward-
convolution routine.34,35 This iterative approach initially
guesses the angular flux distribution T͑␪͒ and the transla-
tional energy flux distribution P(ET) in the center-of-mass
system ͑CM͒ which are assumed to be independent of each
other. Since neither of the reactants is polarized, the cylin-
drical symmetry of the scattering process around the relative
velocity vector in the CM-system restricts the angular depen-
dence to ␪, the scattering angle in the center-of-mass coordi-
nate system measured from the direction of the carbon beam.
The P(ET) is chosen as a parameterized function
P E ͒ϭ E ϪB͒pϫ EavϪET͒q.
͑6͒
͑
͑
͑
T
T
The B-parameter is related to the exit barrier with Bϭ0 for a
simple bond rupture without an exit-barrier. Peaking at a
finite value EP and for BÞ0, the first argument in Eq. ͑6͒
governs the energy difference of EP and the low energy tail
where ET→0, whereas the second argument describes a de-
caying function from EP to the high energy tail. Likewise,
T͑␪͒ is defined as a sum of up to five Legendre-polynomials
P1͑cos ␪͒ with coefficients a1
J. Chem. Phys., Vol. 105, No. 19, 15 November 1996
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8708
Kaiser, Lee, and Suits: Reaction of carbon atoms with hydrocarbons. I.
TABLE II. Thermochemistry of the reaction C͑3Pj͒ϩC2H4(X 1Ag). Enthal-
5
pies of formations were taken from Refs. 26, 36–38 ͑channels 12–13͒. The
designation of the C3H3 isomers ͑channels 1–5͒ follows Fig. 1. C3H2 iso-
mers ͑channels 6–11͒ are cyclopropenylidene ͑c-C3H2͒, propargylene
͑HCCCH͒, and vinylidenecarbene ͑CCCH2͒.
T ␪͒ϭ
a ϫP cos ␪͒.
͑7͒
͑
͑
͚
l
l
lϭ0
Laboratory TOF spectra and the laboratory angular dis-
tribution ͑LAB͒ were calculated from the T͑␪͒ and P(ET)
distributions, and averaged over a grid of Newton diagrams
defining the velocity and angular spread of each beam, de-
tector acceptance angle, and the ionizer length. Best fits were
obtained by iteratively refining the Legendre-coefficients and
adjustable P(ET) parameters.
Reaction enthalpy at 0 K,
#
Exit channel
⌬RH͑0 K͒, kJ molϪ1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
H2CCCH(X 2B2)ϩH͑2S1/2
͒
Ϫ215.5Ϯ8.4
Ϫ115Ϯ25
Ϫ69Ϯ10
ϩ17Ϯ23
ϩ56Ϯ25
Ϫ284.2Ϯ10
Ϫ222Ϯ20
Ϫ194Ϯ10
Ϫ157Ϯ25
Ϫ67Ϯ10
Ϫ46Ϯ10
ϩ154Ϯ15
ϩ143.8Ϯ15
ϩ39.3Ϯ0.5
ϩ241.3Ϯ0.5
ϩ118.5
c-C3H3͑X 2E ͒ϩH͑2S
͒
͒
Љ
1/2
CCCH3(X 2E)ϩH͑2S1/2
c -C H ͑X 2A ͒ϩH͑2S
͒
Ј
Ј
3
3
1/2
HCCCH2(X 2A1)ϩH͑2S1/2
͒
Collision energy dependent relative cross sections are
computed by integrating T͑␪͒ and P(ET):
c-C3H2(X 1A1)ϩH2(X
⌺
)
1
ϩ
g
3
1
ϩ
HCCCH͑X B͒ϩH2(X
⌺
)
g
ϱ
2␲
␲
CCCH2(X 1A1)ϩH2(X
⌺
⌺
⌺
⌺
)
)
1
ϩ
g
␴
E͒ϭ
P E ͒T ␪͒sin ␪d␪d␸dE .
͑8͒
͑
͑
͑
Ј
͵ ͵ ͵
1
1
ϩ
g
T
T
HCCCH͑a A1͒ϩH2(X
0
0
0
c-C3H2(a 3A1)ϩH2(X
)
1
1
ϩ
g
CCCH2(a 3B1)ϩH2(X
)
ϩ
g
Since the product yield under single collision conditions fol-
l-C3H͑X ⌸1/2͒ϩH͑2S1/2͒ϩH2(X
⌺
⌺
)
)
2
1
ϩ
g
ϩ
g
lows Eq. ͑9͒ with the number density of the ith reactant ni
c-C3H(X 2B2)ϩH͑2S1/2͒ϩH2(X
1
and the relative velocity r , ␴Ј has to be scaled by the flux
v
1
1
ϩ
C3(X
⌺
ϩg )ϩ2H2(X
⌺
)
g
C3(a 3⌸u)ϩ2H2(X
⌺
)
1
ϩ
factor fv ͑Table I͒:
g
C2H3͑X 2A ͒ϩCH(X 2⌸j)
Ј
dn /dtϭ␴ϫn C͒ϫn C H ͒ϫ ϭ␴ ϫf .
vr
͑9͒
͑
͑
Ј
p
2
4
v
1
C2H2(X
C2H(X
C2(X
⌺
ϩg )ϩCH2(X 3B2)
Ϫ159
Ϫ60Ϯ4
Ϫ9.8
2
2
⌺
⌺
ϩ)ϩCH3(X A2)
ϩg )ϩCH4(X 1A1)
Љ
1
IV. RESULTS AND ANALYSIS
A. Reactive scattering signal
Reactive scattering signal was only observed at m/e
ϭ39, i.e., C3H3. TOF spectra of m/eϭ36–38 were recorded
at several laboratory angles, but depict identical patterns with
decreasing intensity. Therefore, the signal at m/eϭ36–38
originates in cracking of the C3H3 parent in the ionizer, and
channel 6–15 are not observed within detection limits ͑Table
II͒. In addition, no radiative association to C3H4 ͑m/eϭ40͒
or higher masses were detected. Endothermic channels
12–16 could not be opened at relative collision energies up
to 38.3 kJmolϪ1 employed in the present experiments.
The detection of reactive scattering products C2H2, C2H,
and C2 ͑channel 17–19͒ suffers from the inherent high back-
ground level at these masses arising from fragmentation of
C2H4 in the detector. Attempts were made to identify these
channels by replacing the continuous C2H4 source by a sec-
ond pulsed valve with 0.25 mm nozzle diameter operating at
30 Hz with 1 atm backing pressure and increasing the pump-
ing speed in the main chamber. Nevertheless, no reactive
scattering signal was observed at m/eϭ26, 25, 24, 16, or 15.
Upper limits of 60% ͑channel 17͒ and 25% ͑channel 18͒ and
3% ͑channel 19͒ relative to m/eϭ39 signal were derived.
maximum energy release of different C3H3 isomers confine
energetically accessible products to the propargyl,
cyclopropen-1-yl, or propyn-1-yl isomer. Cyclopropen-2-yl
can most likely be eliminated, since its observable range is
restricted between Ϸ42–470 at lower, and Ϸ15–450 at
higher collision energies. Reactive scattering signal, how-
ever, extends to at least 12.5–60.00 and 10–550, respectively.
Contributions from the velocity spread of the carbon beam
͑Table I͒ can hardly account for this discrepancy. The allenyl
isomer is energetically inaccessible at both collision energies
and is excluded from the discussion.
C. Center-of-mass translational energy distribution,
P(ET)
The translational energy distributions in the center-of-
mass-frame P(ET) are presented together with the center-of-
mass angular distributions T͑␪͒ in Figs. 7–8. Best fits of
TOF spectra and LAB distributions were achieved with
P(ET)s extending to Emaxϭ230 and 255 kJmolϪ1, respec-
tively. The fits are relatively insensitive to the q-parameter
͑Sec. II B͒: Adding or cutting the high energy tail by Ϯ20
kJmolϪ1 did not affect the calculated data due to the limited
signal to noise ratio and the unfavorable kinematic relation
as well as the uncertainty in the velocity spread of the carbon
beam. The magnitude of Emax can be used to identify the
nature of the product isomer if their energetics are well sepa-
rated. Table III compiles the maximal translational energy
release, i.e., the sum of the reaction exothermicity and rela-
tive collision energy, with the reasonable approximation of
cold ethylene molecules in the supersonic expansion. The
formation of the propargyl isomer is consistent with the ex-
B. Laboratory angular distribution (LAB) and TOF
spectra
The most probable Newton diagrams of the reaction
C͑3Pj͒ϩC2H4(X1Ag)→C3H3ϩH and the laboratory angular
distributions of the C3H3 product are displayed in Figs. 3 and
4 at collision energies of 17.1 and 38.3 kJmolϪ1, respec-
tively; TOF spectra are presented in Figs. 5 and 6. Both LAB
distributions are very broad, and products are spread at least
over a range of 500 in the scattering plane suggesting a large
average translational energy release. Comparison of this scat-
tering range with limiting circles which correspond to the
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Kaiser, Lee, and Suits: Reaction of carbon atoms with hydrocarbons. I.
8709
FIG. 4. Lower: Newton diagram for the reaction C͑3Pj͒ϩC2H4(X 1Ag) at a
collision energy of 38.3 kJ molϪ1. The circles stand for the maximum
center-of-mass recoil velocity of different C3H3 isomers; from outer to in-
ner: Propargyl, cyclopropen-1-yl, propyn-1-yl, and cyclopropen-2-yl. Up-
per: Laboratory angular distribution of product channel at m/eϭ39. Circles
and 1␴ error bars indicate experimental data, the solid lines the calculated
distributions for the upper and lower carbon beam velocity ͑Table I͒. C.M.
designates the center-of-mass angle. The solid lines point to distinct labora-
tory angles whose TOFs are shown in Fig. 6.
FIG. 3. Lower: Newton diagram for the reaction C͑3Pj͒ϩC2H4(X 1Ag) at a
collision energy of 17.1 kJ molϪ1. The circles stand for the maximum
center-of-mass recoil velocity of different C3H3-isomers; from outer to in-
ner: Propargyl, cyclopropen-1-yl, and propyn-1-yl. Upper: Laboratory angu-
lar distribution of product channel at m/eϭ39. Circles and 1␴ error bars
indicate experimental data, the solid lines the calculated distributions for the
upper and lower carbon beam velocity ͑Table I͒. C.M. designates the center-
of-mass angle. The solid lines point to distinct laboratory angles whose
TOFs are shown in Fig. 5.
2.0Ϯ0.1 as the collision energy rises. Since the total fraction
f of forward-scattered signal with respect to the carbon beam
slightly decreases from f ͑17.1 kJmolϪ1͒ϭ13Ϯ2% to f͑38.3
kJmolϪ1͒ϭ8Ϯ2% with increasing collision energy, the shape
of the T͑␪͒s does not propose the existence of a conventional
osculating C3H4 complex.40,41 The results rather suggest two
microchannels: A forward-scattered contribution with a
strong correlation of the initial and final orbital angular mo-
menta L and LЈ perpendicular to the initial and final relative
velocity vectors v and vЈ ͑microchannel 1͒ and an isotropic
channel, possibly symmetric around ␪ϭ␲/2 ͑microchannel
2͒, but governed by a weak L and LЈ coupling allowing any
of the four hydrogen atoms to depart, if the exit barriers are
close together. Two alternative scenarios might account for a
potential forward–backward symmetry of the center-of-mass
angular distribution of microchannel 2. First, the decompos-
ing C4H3 complex could hold a lifetime longer than its rota-
tional period.39–41 Second, a symmetric transition state might
result in a center-of-mass angular distribution symmetric
perimentally determined high energy cutoff. Even within the
error limits, the 100 kJmolϪ1 less stable cyclopropenyl radi-
cal can be clearly dismissed ͑Fig. 1͒.
Besides identification of structural isomers, the most
probable translational energy gives the order-of-magnitude
of the barrier height in the exit channel. Both P(ET)s show
a broad plateau between 28–43 kJmolϪ1, nearly independent
of the collision energy. These data clearly indicate a signifi-
cant geometry as well as electron density change from the
C3H4 complex to the products resulting in a repulsive bond
rupture from a tight transition state. The existence of an exit
potential energy barrier is further indicated by the large frac-
tion of energy released into translational motion of the prod-
ucts, i.e., 31Ϯ3% and 42Ϯ3%, respectively.
D. Center-of-mass angular distribution, T(␪)
Both T͑␪͒s are weakly polarized and show an intensity
ratio of T͑␪͒ at ␪ϭ0° to 180° increasing from 1.7Ϯ0.1 to
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8710
Kaiser, Lee, and Suits: Reaction of carbon atoms with hydrocarbons. I.
FIG. 5. Time-of-flight data at m/eϭ39 for laboratory angle 27.5, 37.5, 45.0,
47.5, 52.5, and 60.0° at a collision energy of 17.1 kJ molϪ1. Open circles
represent experimental data, the solid line the fit. TOF spectra have been
normalized to the relative intensity at each angle.
FIG. 6. Time-of-flight data at m/eϭ39 for laboratory angle 15.0, 20.0, 25.0,
35.0, 45.0, and 55.0° at a collision energy of 38.3 kJ molϪ1. Open circles
represent experimental data, the solid line the fit. TOF spectra have been
normalized to the relative intensity at each angle.
around ␲/2 despite a complex lifetime shorter than its rota-
tional period since the hydrogen atom from either end can
depart with equal probability in ␪ and ␲-␪.
The weak polarization of microchannel 2 can be under-
stood in terms of total angular momentum conservation and
angular momentum disposal.40–41 The total angular momen-
tum J is given by
L
maxϭ␮ bmax
vr
,
͑12͒
where ␮ is the reduced mass and
the relative velocity of
vr
the reactants: Thus Lmax͑17.1 kJmolϪ1͒ϭ99ប and Lmax͑38.3
kJmolϪ1͒ϭ128ប. Since C2H4 is produced in a supersonic ex-
pansion and j peaks at only 3ប at a typical rotational tem-
perature of 30 K, j contributes less than 3% to the total
angular momentum, and J becomes the initial orbital angular
momentum L
JϭLϩjϩj ϭL ϩj ϩjЈ ,
͑10͒
Ј
Ј
n
n
with the rotational angular momenta of the reactants and
products j and jЈ, as well as jn and jЈn the initial and final
nuclear momenta. In terms of a classical treatment and bear-
LϷJϭL ϩj .
͑13͒
Ј
Ј
Further, an upper limit of LЈ can be estimated by assuming a
relative velocity of the recoiling products corresponding to
ing in mind that j ӶL, j Ӷj, jЈӶL , and jЈӶj , Eq. ͑10͒
Ј
Ј
n
n
n
n
the average translational energy release E , and choosing
͗
͘
reduces to Eq. ͑11͒
T
an acetylenic CϵC bond length of 1.08 Å as the exit impact
parameter to LЈ͑17.1 kJmolϪ1͒ϭ20ប and LЈ͑38.3
kJmolϪ1͒ϭ24ប. Since LЈϷ0.2 L, L and LЈ are not likely to
be strongly coupled on average, resulting in weakly polar-
ized T͑␪͒s. This prevents us from classifying the decompos-
ing complex as prolate- or oblate-like solely based on T͑␪͒:
In a prolate case, low MЈ values dominate, where MЈ de-
notes the projection of J on the decomposing complex’ prin-
cipal axis parallel to vЈ, and the complex decomposes in the
plane containing the relative velocity vector. An oblate de-
composition geometry directs large MЈ values, and a frag-
mentation parallel to J. Therefore, a sharply peaked T͑␪͒ is
JϭLϩjϭL ϩj .
͑11͒
Ј
Ј
A further simplification is introduced by comparing the
magnitude of L and j. Since bulk experiments indicate that
the reaction of C͑3Pj͒ with olefins and alkynes proceeds
within orbiting limits42 and our relative cross sections rise
with decreasing collision energy ͑Sec. IV E͒, the maximum
impact parameter bmax leading to a complex formation is
approximated in terms of the classical capture theory to
bmax͑17.1 kJmolϪ1͒ϭ3.7 Å and bmax͑38.3 kJmolϪ1͒ϭ3.2 Å
͑see Appendix A and Table IV͒. The maximum orbital an-
gular momentum Lmax relates to bmax via
J. Chem. Phys., Vol. 105, No. 19, 15 November 1996
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Kaiser, Lee, and Suits: Reaction of carbon atoms with hydrocarbons. I.
8711
FIG. 8. Lower: Center-of-mass angular flux distribution for the reaction
C͑3Pj͒ϩC2H4(X 1Ag) at a collision energy of 38.3 kJ molϪ1. Upper: Center-
of-mass translational energy flux distribution for the reaction
C͑3Pj͒ϩC2H4(X 1Ag) at a collision energy of 38.3 kJ molϪ1. Dashed and
solid lines limit the range of acceptable fits within 1␴ error bars.
FIG. 7. Lower: Center-of-mass angular flux distribution for the reaction
C͑3Pj͒ϩC2H4(X 1Ag) at a collision energy of 17.1 kJ molϪ1. Upper: Center-
of-mass translational energy flux distribution for the reaction
C͑3Pj͒ϩC2H4(X 1Ag) at a collision energy of 17.1 kJ molϪ1. Dashed and
solid lines limit the range of acceptable fits within 1␴ error bars.
tigated reaction rate constants at 293 K of C͑3Pj͒ atoms with
alkynes as well as alkenes, indicating the reactions proceed
fast ͑kϭ10Ϫ10Ϫ10Ϫ9 cm3 sϪ1͒ without entrance barrier
within orbiting limits, i.e., the C–C2H4 interaction is domi-
nated by a barrier-less, attractive long-range intermolecular
dispersion forces giving rise to a loose, reactant-like transi-
tion state located at the centrifugal barrier to the triplet C3H4
PES. Taking Lmax from Table IV, and Eq. ͑A6͒, we calculate
the lower limit of barrier locations to Rmax ͑17.1 kJmolϪ1͒ϭ3
Å and Rmax ͑38.3 kJmolϪ1͒ϭ2.6 Å.
expected only if L and LЈ strongly correlated, i.e., parallel or
antiparallel with jЈӶLЈ, or if MЈ is zero. This weak LϪLЈ
correlation is a direct result of large impact parameters con-
tributing to the complex formation and the inability of the
departing H atom to carry significant orbital angular momen-
tum supporting recent bulk experiments42 and our findings of
a long-range term dominated interaction potential.
E. Flux contour map and total relative cross section
Simple capture calculations yield a cross section propor-
tional to Ecoll
The center-of-mass flux contour maps I(␪,ET)
ϳT(␪)ϫP(ET) for both collision energies are shown
in Figs. 9–10. As expected from discussed T͑␪͒s, the product
flux peaks in forward direction with respect to the carbon
beam on the relative velocity vector. Integrating this flux
distribution over ␪, ␸, ET , and correcting for the reactant
flux as well as relative reactant velocity, we find a total,
relative cross section ratio of ␴ ͑17.1 kJmolϪ1͒/␴͑38.3
kJmolϪ1͒ϭ3.5Ϯ1.1. This ratio is most sensitive to the
fragmentation applied for C3, especially in the Ne seeded
experiments where larger carbon clusters contribute ϳ80%
to the carbon number density ͑Table I͒. Lowering the frag-
mentation pattern of C3 by 30% reduces ␴͑17.1
kJmolϪ1͒/␴͑38.3 kJmolϪ1͒ to 2.6Ϯ0.9. Nevertheless, the
drop in the cross section with increasing collision energy is
consistent with recent bulk experiments.42 Clary et al. inves-
Ϫ1/3
and ͓␴ ͑17.1 kJmolϪ1͒/␴͑38.3
kJmolϪ1͔͒captureϭ1.3Ϯ0.1. This treatment assumes the reac-
tion proceeds with unit efficiency after barrier-crossing and
under absence of steric effects. However, at higher relative
collision energies the orbiting radii become comparable or
smaller than the van der Waals radii. Since the capture as-
sumption is based solely on a long-range C6 attraction, this
approximation breaks down, and the structure of the mol-
ecule becomes important. Alternatively, the presence of a
second reaction channel might contribute to this deviation.
Equation ͑14͒ outlines this alternative for j exit channels
with cross sections ␴ at two collision energies E1 and E2:
i
j
͚
͚
␴ E ͒
͑
i 1
␴ E ͒
͑
1
iϭ1
ϭ
.
͑14͒
ͫ
ͬ
ͫ
ͬ
j
␴ E ͒
͑
␴ E ͒
͑
2
i
2
iϭ1
capture
experiment
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8712
Kaiser, Lee, and Suits: Reaction of carbon atoms with hydrocarbons. I.
TABLE III. Comparison of the maximal available translational energy release, Etot͑theor͒ , of the reaction
C͑3Pj͒ϩC2H4(X 1Ag)→C3H3ϩH͑2S1/2͒ for different C3H3 isomers with experimental data, Etot͑exp͒
Etot͑theor͒ , kJ molϪ1
.
Etot͑exp͒
,
Ecoll , kJ molϪ1 Propargyl Cyclopropen-1-yl
Propyn-1-yl
Cyclopropen-2-yl Allenyl kJ molϪ1
17.1
38.3
232Ϯ9
253Ϯ10
132Ϯ34
153Ϯ35
85Ϯ9
106Ϯ10
1Ϯ9
20Ϯ10
•••
•••
230Ϯ30
255Ϯ25
The framework of the capture theory cannot supply informa-
tion on how many exit channels are involved and yields only
a total cross section, here ␴͑E1͒ and ␴͑E2͒. Assuming a con-
stant opacity function and an ideal, long range-term domi-
nated potential, both sides in Eq. ͑14͒ are identical only if we
find all ␴i(E1) and ␴i(E2) or if only one channel is involved
͑jϭ1͒. Therefore, our data might suggest the existence of at
least a second channel leading to products with m/e ratios
different from 39. Its relative cross section must increase
with rising collision energy to reduce the right hand side of
Eq. ͑14͒.
microchannel 1 corresponds to rotations of the propargyl
radical around its C2 axis. Finally, the highest energetically
accessible K states, Kmax , are computed assuming no vibra-
tional excitation of the C3H3. This gives us the upper limit of
the average product rotational excitation and an order of
magnitude of the lowest tilt angle ␣min of the propargyl C2
axis with respect to jЈ in terms of the classical vector model
to
␣
ϭarcos K /j ͒.
͑16͒
͑
Ј
min
max
As evident from Table V, the low K approximation
yields an increasing channeling of total energy into rotational
degrees of freedom as the collision energy rises. The reduced
fraction of vibrational energy from 59% to 43% indicating an
incomplete energy randomization before the C4H3 complex
decomposes, cf. Sec. V E. In case of zero vibrational excita-
tion of the propargyl radical and upper K limit, the C2 prin-
cipal axis tilts about 68° on average with respect to j and
clearly indicates a dominant end-over-end-rotation of the
C3H3 radical. Even the assumption that microchannel 1 con-
tributes solely to rotations around the propargyl figure axis is
consistent with the energy conservation ͑Table V͒ as well as
with a decreasing fraction of vibrational energy, in this case
from 24% to 8%, as the relative collision energy rises.
F. Energy partition of total available energy
The total available energy, Etot , channels into product
translation, Etr , rotation, Erot , and vibration, Evib . Etr can be
obtained from the P(E )s and, hence, equals E , cf. Sec.
͗
͘
T
T
IV C. Since the reaction products in the crossed beam experi-
ment were identified as atomic hydrogen and the propargyl
radical, the rotational energy is confined to the C3H3 isomer.
The rotational constants Aϭ9.6081 cmϪ1, Bϭ0.317 57
cmϪ1, and Cϭ0.307 65 cmϪ1 classify this radical as a highly
prolate asymmetric top with asymmetry parameter
␬ϭϪ0.9978.43 Its energy levels follow therefore in good ap-
proximation those of a symmetric top
Eϭhc BJ Jϩ1͒ϩ AϪB͒K2
.
͔
͑15͒
͓
͑
͑
J denotes the rotational quantum number of 79 ͑Ecollϭ17.1
kJmolϪ1͒ and ϳ104 ͑Ecollϭ38.3 kJmolϪ1͒ since the total an-
gular momentum is conserved. K indicates the component of
the rotational angular momentum about the principal axis,
with Kϭ0 for no rotation about the figure axis, but perpen-
dicular to it, and KϷJ for a fast rotation about the principal
axis, with a slow end-over-end one.
Since no explicit information on the K-distribution is
available, an exact solution of this problem is unrealizable.
Here, we calculate first the rotational energy for Kϭ0, and,
therefore the maximal vibrational energy release Evib in the
propargyl product. This approach is referred to as ‘‘low K
approximation.’’ Second, we assume the forward-peaking
V. DISCUSSION
The crossed beam method allows insight into the dynam-
ics of the reaction and reveals unprecedented information on
the reaction intermediate. In the following discussion, we
outline all theoretically feasible reaction pathways on the
C3H4 PES43–58 to the propargyl radical without imposing any
dynamic or energetic constraints ͑Sec. V B͒. Thereafter, the
observed dynamics and energetics are compared to what is
expected based on these ad-hoc pathways. Channels not
compatible with the experimental results are eliminated. This
approach ultimately identifies the remaining channel as the
only possible one.
TABLE IV. Maximum impact parameter bmax , maximum initial orbital angular momentum, Lmax , and capture
cross sections ␴ at two relative collision energies Ecoll employed in the present experiments. Cross sections ␴
are calculated for no ͓P(b)ϭ1͔, one ͓P(b)ϭ2/3͔, and two ͓P(b)ϭ1/3͔ repulsing surfaces of the split triplet
manifold.
Ecoll , kJ molϪ1
bmax , Å
Lmax , ប
␴, Å2 ͓P(b)ϭ1͔
␴, Å2 ͓P(b)ϭ2/3͔
␴, Å2 ͓P(b)ϭ1/3͔
17.1
38.3
3.7
3.2
99
128
42
32
28
21
14
11
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Kaiser, Lee, and Suits: Reaction of carbon atoms with hydrocarbons. I.
8713
FIG. 9. Contour flux map distribution for the reaction C͑3Pj͒ϩC2H4(X 1Ag)
at a collision energy of 17.1 kJ molϪ1
FIG. 10. Contour flux map distribution for the reaction
C͑3Pj͒ϩC2H4(X 1Ag) at a collision energy of 38.3 kJ molϪ1
.
.
A. C3H4 ab initio potential energy surface
participation of a cyclopropene complex can be ruled out as
well. A potential barrier connecting cyclopropylidene with
cyclopropene is located at least 120 kJmolϪ1 above the tran-
sition state to allene. If a triplet cyclopropylidene complex is
initially formed, the reaction proceeds via the lowest energy
pathway, in our case to allene. In this framework, the large
potential energy difference of both transition states and the
participation of only one isomer at m/eϭ39 is consistent
with the TOFs and both LAB distributions, cf. Secs. IV A–
IV D. The four remaining pathways differ by the migration
of a H atom before the final bond rupture, but cannot be
reduced further by investigating solely the C3H4 PES. How-
ever, hydrogen rearrangement prior to decomposition might
be involved to certain extend.
We investigate two mechanisms, the addition of C͑3Pj͒
to the ethylenic ␲-bond vs insertion into the olefinic C–H
bond, as well as the fate of the initially formed triplet C3H4
intermediates. Addition of C͑3Pj͒ to the ethylene ␲-bond
yields cyclopropylidene, Fig. 11, followed by ring opening to
allene, or 1,2-hydrogen migration to cyclopropene. A 1,3-
diradical tricarbon chain holds no local minimum on the trip-
let C3H4 PES. Triplet-allene fragments via C–H bond cleav-
age to the propargyl radical or undergoes 1,2-H-migration to
triplet trans/cis vinylmethylene or 1,3-H-migration to triplet
methylacetylene, which subsequently yields propargyl or
propyn-1-y1 via C–H bond rupture. Triplet cyclopropene ei-
ther decomposes to cyclopropen-1-yl/cyclopropen-2-yl radi-
cals, or ring opens to vinylmethylene. This might fragment to
the propargyl radical. C–H bond rupture in cycloprop-
ylidene may yield cyclopropen-2-yl. Finally, insertion of
C͑3Pj͒ into the olefinic C–H bond leads to vinylmethylene.
The rigorous identification of the propargyl radical alone
eliminates all exit channels to competing C3H3 isomers. The
B. Rotation axis of decomposing C3H4 complexes
The rotational motions of the prevailing C3H4 complexes
are very interesting and help to explain the shapes of both
T͑␪͒s, if the distributions for distinct rotations are compared
to what is found experimentally. We point out that the initial
trajectory of the carbon atom prior to capture is unimportant
in the frame of the capture theory, since the potential energy
is assumed to depend only on the C6 parameter. But sterical
effects and attractive chemical forces come into play if the
capture radius is in the order of the bond lengths, so that
certain approach geometries and rotations might be favored.
Based on this, we identify allowed rotations in each C3H4
intermediate, elucidate trajectories under highest possible
symmetry of C͑3Pj͒ toward C2H4 which excite these rota-
tions, and discuss the range of contributing impact param-
eters. Finally, we demonstrate that the title reaction proceeds
via addition to the ethylene ␲-bond yielding cyclopropy-
lidene, followed by ring opening to allene and decomposition
to propargyl and atomic hydrogen.
TABLE V. Minimum rotational energy Erot of the propargyl radical for
Kϭ0, remaining vibrational energy Evib , the highest energetically acces-
sible K-states for Evibϭ0, and the minimum tilt angle ␣min of the propargyl
principal axis with respect to j . The partitions of the total available energy
Ј
in percent for Kϭ0 are included in parentheses.
E
collϭ17.1
Ecollϭ38.3
kJ molϪ1
kJ molϪ1
Etot , kJ molϪ1
232
71͑31͒
23͑10͒
253
105͑41͒
39͑15͒
Etr , kJ molϪ1
Erot ͑Kϭ0, microchannel 2͒,
kJ molϪ1
Erot ͑Kϭ0, microchannel 2;
KϭJ, microchannel 1͒, kJ molϪ1
Evib ͑Kϭ0, microchannel 2͒,
kJ molϪ1
Evib ͑Kϭ0, microchannel 2;
KϭJ, microchannel 1͒, kJ molϪ1
Kmax
105͑45͒
138͑59͒
55͑24͒
127͑50͒
109͑43͒
20 ͑8͒
1. Triplet allene complex
Maintaining the C–C–C plane as a plane of symmetry,
the carbon atom might add to the C2H4 molecular plane con-
serving Cs symmetry ͑Fig. 12͒. This pathway does not force
36
63
32
72
␣
min
J. Chem. Phys., Vol. 105, No. 19, 15 November 1996
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8714
Kaiser, Lee, and Suits: Reaction of carbon atoms with hydrocarbons. I.
TABLE VI. Principal moments of inertia Ii , in amu Å2, rotational constants in MHz, and asymmetry parameters ␬ of triplet C3H4 complexes ͑TS: transition
state͒ calculated from geometries in Refs. 43–55.
Complex
IA
IB
IC
A
B
C
␬
trans-vinylcarbene
cis-vinylcarbene
allene
allene ͑TS͒
methylacetylene
8.8629
7.3813
5.3910
3.3489
4.7216
44.6369
47.2273
51.8501
58.3671
45.5987
53.4998
54.6086
57.2411
61.7160
50.3203
57022
68468
93746
150911
107037
11322
10701
9747
8658
11083
9446
9254
8829
8188
10043
Ϫ0.92
Ϫ0.95
Ϫ0.98
Ϫ0.99
Ϫ0.98
perpendicular approaches towards the CϭC bond, but per-
mits rather in-plane trajectories skewed with respect to the
perpendicular vector. Since Lӷj, the three heavy atoms ro-
tate in a plane roughly perpendicular to L around the C-axis
of the prolate cyclopropylidene adduct. The successive ring
opening to triplet allene conserves Cs symmetry and con-
verts the previously out-of-plane H-atoms into the symmetry
plane. This scenario opens larger impact parameters than
typical C2H4 bond dimensions of r͑CϭC͒ϭ1.325 Å, and
r͑C–H͒ϭ1.076 Å compared to the large b-dominated opac-
ity function with bmaxϭ3.7 and 3.2 Å ͑Secs. IV D and IV E͒.
In addition, the nearly in-plane rotation about the C-axis
gives rise to extremely low K values and, therefore, a negli-
gible J component about the C2 figure axis of the triplet
allene. This rotation axis could be associated with preferen-
tially low K states populated in the propargyl product. There-
fore, our results suggest that C-like rotations of the triplet
allene complex contribute predominantly to the isotropic mi-
crochannel 2, and that any of the four hydrogen atoms H1–
H4 departs with almost equal probability to yield a weak
L-LЈ correlation. Alternatively, a long-lived complex behav-
ior was suggested in Sec. IV D, but can likely be dismissed:
The rising collision energy should reduce the lifetime of the
triplet allene complex and would have resulted in a more
forward scattered fraction which was not verified in our ex-
periments.
the triplet allene complex. The rotational period depends
strongly on the rotational axis A vs C and varies between
0.04 and 0.57 ps. Reactions with collision times Ͻ0.1 ps
follow direct reactive scattering dynamics with almost zero
intensity at ␪ϭ180°.61 Based on this and a strong L-LЈ cor-
relation, only A-like rotations and H2-C3/H3-C1 bond rup-
tures should contribute to the forward-peaked microchannel
1. This conclusion is consistent with the partition of energy
into the rotational degrees of freedom and the total conser-
vation of energy ͑Table V͒, calculated for a dominant end-
over-end rotation of propargyl ͑microchannel 2͒ and contri-
butions of 8%–14% A-like rotations ͑microchannel 1͒.
However, a rapid inversion of triplet allene via a planar, D2h
transition state ͑Fig. 13͒ could induce a symmetric exit tran-
sition state as well as T͑␪͒ and could contradict our findings.
Although the inversion barrier height ranges about 25
kJmolϪ1, well below the total available energy, the transition
state would rotate fast about its principal axis with KϷJ.
This increases the inversion barrier to at least 420 kJmolϪ1 at
E
collϭ17.1 kJmolϪ1 and 650 kJmolϪ1 at Ecollϭ38.3 kJmolϪ1
,
well above the total available energy. Bulk experiments sup-
port our conclusion of dominating C-rotations. The typical
time between two collisions of the initially formed C3H4
complex in 11C tracer studies and a second bath molecule are
on the order of 1 ps at 100 Torr neat ethylene. A lifetime at
least one order of magnitude less cannot account for detected
C5 compounds.
Finally, we discuss the potential contribution of B-type
rotations of the triplet allene complex ͑Fig. 13͒. B-transitions
can be excited by C-atom trajectories following C1 symme-
try and give rise to a symmetric exit transition state, since
H2 and H3 as well as H4 and H1 can depart from either
end, cf. Sec. IV D. Therefore, the strongly forward scattered
microchannel 2 can be dismissed. Based only on the experi-
mentally found T͑␪͒, a symmetric transition state might ex-
plain microchannel 2. Compared to reactions conserving Cs
symmetry, however, encounters without any symmetry ele-
ment show a reduced overlap of the p-type orbitals of the
C-atom with the ␲-molecular orbital of the ethylene mol-
ecule, and should be energetically less favorable.
In addition, a parallel approach of C͑3Pj͒ with respect to
the ethylene plane under Cs symmetry induces rotations
around the cyclopropylidene A-axis, Figs. 12 and 13. Ring
opening yields triplet allene. The rotation period ␶ of the
rot
complex around its A-axis helps us to elucidate the effect of
these trajectories on the T͑␪͒s. Investigating a rotation
around the i-axis, ␶ is calculated via Eq. ͑17͒
rot
␶rotϭ2␲Ii /Lmax
͑17͒
with the moment of inertia Ii in respect to the i-axis and the
maximum angular momentum Lmax . Table 7 compiles the
calculated rotational periods around the A, B, and C-axis of
TABLE VII. Rotational periods ␶ of triplet allene calculated for rotations
rot
about the A, B, and C axis at collision energy Ecoll . Lmax denotes the
maximum impact parameter.
2. Triplet cis/trans vinylcarbene complex
A pathway to triplet cis/trans vinylcarbene follows ei-
ther 1,2-H-migration in triplet allene or a direct insertion of
C͑3Pj͒ into a C–H bond of ethylene. Figure 13 displays the
principal rotational axis with the embodied carbon atom des-
ignated as C2 and C3, respectively. As evident, only a
Ecoll
,
kJ molϪ1
I
Lmax , ប
␶
rot(A), ps
␶
rot(B), ps
␶
rot(C), ps
16.1
38.3
1.7
2.0
99
128
0.05
0.04
0.52
0.40
0.57
0.44
J. Chem. Phys., Vol. 105, No. 19, 15 November 1996
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Kaiser, Lee, and Suits: Reaction of carbon atoms with hydrocarbons. I.
8715
FIG. 11. Schematic representation of the lowest energy pathways on the triplet C3H4 PES and structure of potentially involved collision complexes. Enthalpies
of formation, electronic states, and were taken from Refs. 43–58: Cyclopropylidene ͑1͒: 501 kJ molϪ1 3B1 , C2v; allene ͑2/2 ͒: 405 kJ molϪ1 3A2 , C2v
cyclopropene ͑3͒: ϳ720 kJ molϪ1; propargyl ͑4͒: 557 kJ molϪ1, 2B2 , C2v; cis vinylcarbene ͑5͒: 408 kJ molϪ1, 3A , C ; trans vinylcarbene ͑6͒: 409 kJ molϪ1
,
,
;
Ј
,
Љ
s
3A , C ; methylacetylene ͑7͒: ϳ630 kJ molϪ1; propyn-1-yl ͑8͒: 704 kJ molϪ1, 2E, D3h; cyclopropen-1-yl ͑9͒: 657 kJ molϪ1, 2E , D3h; cyclopropen-2-yl ͑10͒:
Љ
Љ
s
2
790 kJ molϪ1, A , C •••?: No information available.
Ј
s
H2/C2 bond rupture in vinylcarbene yields the propargyl
radical. Since any of the four hydrogen atoms is required to
depart equally likely under weak L and LЈ coupling to ac-
count for the isotropy of microchannel 2 ͑Sec. IV C͒, a con-
tribution of a cis/trans vinylcarbene intermediate to micro-
channel 2 can be likely ruled out. Further, only A-like
rotations could give rise to microchannel one. The vinylcar-
bene complex rotating around the B/C axis must hold life-
times of at least 0.4–0.3 ps to induce any forward-scattering,
but the strongly forward-scattered T͑␪͒ at higher collision
energy requires collision times Ͻ0.1 ps to account for a
strong L-LЈ correlation.61 These rotations around the A-axis
are induced, if C͑3Pj͒ inserts via a perpendicular pathway
into the C–H bond of the ethylene molecule. This trajectory,
however, seems unlikely, since only a narrow range of im-
pact parameters between 0.66 and 1.2 Å contributes to reac-
tive scattering signal. The overwhelming contribution of
large impact parameters up to 3.7 Å was already validated.
Likewise, this insertion resembles a symmetry forbidden re-
action, and an entrance barrier larger than our maximum col-
lision energy of 38.3 kJmolϪ1 is expected. Our interpretation
correlates with 11C-tracer experiments: thermal 11C͑3Pj͒ and
even 11C͑1D2͒ add to the ␲-bond, but only suprathermal
C-atoms in both spin states insert into the C–H bond. The
only remaining pathway to A-like rotations in vinylcarbene
involves a ͓3,2͔-H-shift in triplet allene, rotating around its
A-axis. Since the forward-peaking demands collision times
FIG. 12. Approach geometries of the carbon atom toward the ethylene mol-
ecule conserving Cs symmetry and induced rotations. Upper: Perpendicular
approach; lower: Parallel approach.
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8716
Kaiser, Lee, and Suits: Reaction of carbon atoms with hydrocarbons. I.
FIG. 13. Rotation axis of triplet C3H4 isomers calculated with moments of inertia of Table VI; the C axis is perpendicular to the paper plane. Hydrogen atoms
are hatched. The designation is taken from Fig. 11. Top left: allene; top right: TS of allene inversion; bottom left: cis vinylcarbene; bottom right: trans
vinylcarbene.
try reduces to AЈ. The total electronic wave function is
gained via the direct product of the reactant’s wave function
Ͻ0.1 ps, a hydrogen migration can most likely be excluded.
Even a fast ͓1,2͔-H-rearrangement from vinylidene to acety-
lene takes more than 0.2 ps.62
A ϩA ϩA ͒ϫA ϭ2A ϩA .
͑18͒
͑
Љ
Љ
Ј
Ј
Љ
Ј
The B2 ground state of the propargyl radical reduces to AЉ in
Cs symmetry ͑C-like rotations of the triplet allene complex͒
and the S state of hydrogen atom to AЈ
3. Triplet methylacetylene complex
The triplet allene-methylacetylene rearrangement in-
volves a symmetry-allowed ͓1,3͔-H-shift60 similar to Sec.
V B. The height of this barrier, however, ranges well above
any conceivable one arising from ͓1,2͔-H-migration. Consid-
ering that the lower energy pathway is closed, ͓1,3͔-H-
migration cannot take place either.
A ϫA ϭA .
͑19͒
Љ
Ј
Љ
The ground state electronic wave functions of all triplet com-
plexes and transition states involved in the elucidated reac-
tion pathway, i.e., cyclopropylidene and allene, belonging to
the AЉ representation. Therefore, reactants, collision com-
plexes, and products correlate on the AЉ surface, and the title
reaction can proceed on the AЉ ground state surface under Cs
symmetry via excitation of C-like rotations. If the carbon
atom approaches slightly off-axis, the Cs symmetry reduces
to C1 and the electronic wave function to A. Likewise,
A-rotations of the decomposing triplet allene complex do not
conserve the symmetry plane in the final carbon-hydrogen
bond rupture, and the symmetry of the electronic wave func-
C. Surface splitting
The symmetry of the total wave function has to be con-
served during the title reaction and is assumed to be sepa-
rable into an electronic and spin part. Since we are dealing
with light carbon atoms and the spin–orbit coupling constant
increases with the fourth power of the nuclear charge, this
simplification is justified. Interacting under highest possible
Cs symmetry, the P-term of the carbon atom splits into the
irreducible representations AЉϩAЉϩAЈ. The C2H4 symme-
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Kaiser, Lee, and Suits: Reaction of carbon atoms with hydrocarbons. I.
8717
triplet allene complex prior to decomposition. Hence, the
lifetime of the triplet C3H4 complex is too short.
E. Possible contributions from the singlet C3H4
surface
The experimental results strongly indicate that the title
reaction proceeds on the ground-state triplet surface. How-
ever, we will also investigate the singlet PES for complete-
ness. Here, intersystem crossing ͑ISC͒ might occur if the
spin–orbit coupling operator acts as a perturbation capable
of mixing the triplet wave function ͑3B2 in cyclopropylidene,
3A2 in allene͒ with the final singlet wave function ͑1A1 in
cyclopropylidene and allene; reduced via C2v symmetry͒.
Since the operators transform as rotations, they span the ir-
reducible representations A2, B1, and B2. Hence, the a3B2
state of cyclopropylidene is mixed via a B2 spin–orbit op-
erator with X1A1 and the allene a3A2 state via a A2 operator
to its electronic ground state. This direct product approach
however, yields no information on the magnitude of the
spin–orbit interaction. Since no heavy atom is present in our
complexes and the spin–orbit coupling constant rises with
the fourth power of the atomic number, the ISC crossing is
too slow compared to the lifetime ␶ of the C3H4 complex.
This conclusion is consistent when comparing the rotational
period of the triplet allene complex with typical ISC times-
cales: Even the largest known ISC rate constants between
1010Ϫ1011 sϪ1 for polycyclic aromats containing heavy at-
oms, e.g., bromonaphthalene, are at least one order of mag-
nitude too low.65
FIG. 14. Equilibrium geometries of triplet allene and the propargyl radical
Refs. 36–37.
3
tion is reduced to A. Finally, we point out that the opacity
function P(b) might be different for the 3A ͑microchannel 1͒
and 3AЉ surface ͑microchannel 2͒. This could account for the
deviation of the relative energy dependent cross sections
from the simple capture picture as well.
An alternative ISC mechanism follows a rotation of two
perpendicular ␲-electron systems each filled with one
electron.66–67 In the case of triplet cyclopropylidene as well
as allene, the first electron occupies a ␲-type orbital, the
second one a nonbonding orbital with ␴-symmetry. There-
fore, this pathway cannot contribute to ISC in the title reac-
tion. Summarized, our findings indicate ISC should not play
an important role and strongly correlate with 11C͑3Pj/1D2͒
tracer experiments in C2H4 systems: allene molecules are
solely the reaction product of C͑1D2͒ with a single ethylene
molecule. C͑3Pj͒ yields triplet C3H4 which fragments or re-
acts with a second C2H4 molecule.
D. Exit transition state
The collision energy dependent P(ET) shape and their
average translational energy releases, E reveal the chemi-
͗
͘
T
cal dynamics between the moment of the triplet allene com-
plex formation and the final separation into products. As
shown in Sec. IV C, both P(ET)s peak at 28–43 kJmolϪ1
and indicate that the C–H bond rupture in triplet allene does
not resemble a system with a loose transition state. This find-
ing and the lack of intensity in both P(ET)s below 3 and 12
kJmolϪ1 suggest instead a tight transition state, and should
go hand in hand with a significant geometry change from the
triplet allene complex to the propargyl radical. As evident
from Fig. 14, this requirement is fulfilled. Predominantly, the
C2-C3-bond length in the propargyl radical is reduced by
0.141 Å, corresponding to a bond order increase from 1.5 to
3, and the C1-C2-C3 bond angle widens by 52.7°. The
order of magnitude of the exit barrier is consistent when
compared to the 7–10 kJmolϪ1 peaking P(ET) of the reac-
tion C͑3Pj͒ϩC2H2 (X1⌺gϩ)→1ϪC3HϩH:63 The carbon
chain is almost linear in the triplet propargylene complex,
HCCCH, as well as in the 1-C3H product, and the internu-
clear distances differ by less than 0.05 Å. But even the tight
transition state theory of Marcus predicts an increasing frac-
tion of total available energy channeling into vibration as the
collision energy rises, if the energy is completely
randomized.64 Therefore, our decrease of fractional vibra-
tional energy deposition as the collision energy rises ͑Sec.
VI F͒ suggests an incomplete energy randomization in the
F. Comparison with the reaction O(3Pj)؉C2H4
The dynamics of the reaction O͑3Pj͒ with C2H4 were
recently studied in our lab28 and two major channels were
detected. The oxygen–hydrogen exchange channel yields
3
HϩC2H3O on the AЉ surface via a short lived triplet 1,3
CH2CH2O diradical undergoing C–H bond rupture. Alterna-
tively, the C2H4O complex undergoes ISC, followed by 1,2-
hydrogen migration to acetaldyhyde and C–C bond rupture
to CH3 and HCO. The different dynamical behavior as com-
pared to C͑3Pj͒ϩC2H4 is solely the effect of a stable triplet-
1,3-diradical on the C2H4O PES and a successive ISC via
rotation of both perpendicular ␲-electron systems to a deep
potential well. These dynamics increase the lifetime of the
complex and open up the channel of H-migration to acetal-
dehyde. A triplet, 1,3 CH2CH2C diradical, however, holds no
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8718
Kaiser, Lee, and Suits: Reaction of carbon atoms with hydrocarbons. I.
C2H4ϩCϩ→cϪC3Hϩ3 ϩH,
→cϪC3Hϩ2 ϩH2,
͑21͒
͑22͒
͑23͒
local minimum on the C3H4 PES and collapses to cyclopro-
pylidene. ISC, successive ring opening to allene, and 1,2-H-
migration to singlet methylacetylene are closed, and no
CH3-loss can occur.
→lϪC3Hϩ2 ϩH2,
hold higher rate constants with k͑CϩϩC2H4; 293
K͒ϭ͑1.2Ϯ0.1͒ϫ10Ϫ9 cm3 sϪ1 as compared to the atom neu-
G. Undetected channels
tral reaction k͑CϩC2H4; 293 K͒ϭ͑2.0Ϯ0.1͒ϫ10Ϫ10 cm3 sϪ1
,
The dynamics of the title reaction account for the unob-
served exothermic exit channels ͑Table II͒. First, all singlet
channels 6, 8, and 9 to C3H2-isomers as well as to CH4, # 19,
are closed, since the reaction proceeds via spin conservation
on the triplet surface. Reactions ͑10͒ and ͑11͒ to triplet cy-
clopropenylidene and vinylidenecarbene must proceed via
cyclopropylidene and allene, respectively. Channel 10 is a
symmetry-forbidden, 4 center-4 electron elimination ͑retro-
addition of H2 to the CϭC in triplet cyclopropenylidene͒,
whereas # 11 involves a symmetry forbidden, 3 center-4
electron elimination ͑retro cheletop reaction of H2 with vi-
nylidenecarbene͒. Both pathways are expected to involve a
symmetry imposed barrier: lower barrier limits of 82
kJmolϪ1 ͑# 10͒ and 103 kJmolϪ1 ͑# 11͒ are reasonable for
this class of symmetry forbidden reactions.68 Reaction to
triplet propargylene ͑# 7͒ must pass triplet allene, but geo-
metrical constraints hinder this pathway. Further, elimination
of a CH3 group ͑# 18͒ remains unobserved, and the 1,3-H-
migration to triplet methylacetylene is likely prevented in the
triplet allene complex.
Channel 17 remains the only additional pathway. How-
ever, a direct fragmentation of cyclopropylidene or allene to
C2H2 is not feasible. The elimination must proceed via a
cyclopropylidene ring cleavage ͓retrocycloaddition of
CH2(X3B2) to H2CC, vinylcarbene (X1A1)͔ or a C1-C2
bond cleavage in allene to CH2(X3B2)ϩH2CC (X1A1).
Since vinylcarbene ranges ϳ180 kJmolϪ1 higher in energy
than acetylene and the 1,2-H-migration to C2H2 involves a
barrier of about 11 kJmolϪ1, the transition state is placed
about 30 kJmolϪ1 above the reactants. Hence, channel 18
could only be opened at the higher collision energy of 38.3
kJmolϪ1 and might explain the deviation of the experimen-
tally determined cross-section ratio from the theoretical one,
cf. Sec. IV E as well as the diminishing acetylene yield in
11C tracer experiments with increasing thermalization.
but modeling of high and low ionization phases in dark in-
terstellar clouds yielded neutral carbon fractional abundances
of about 10Ϫ5 and 10Ϫ7 vs Cϩ data of ϳ3ϫ10Ϫ8 and
3ϫ10Ϫ9, respectively.69 White and Sandell70 confirmed these
calculations and observed neutral carbon fractional abun-
dances between 3.0ϫ10Ϫ5 and 5.0ϫ10Ϫ7 toward OMC-1.
These data clearly undermine the order-of-magnitude advan-
tage for the rate of ion-molecule reactions as compared to
atom-molecule reactions. Most important, however, synthe-
sis of carbon-hydride radicals via atom-neutral reaction pro-
ceeds in one step, eliminating the need for successive binary
encounters. Lowest applied translational energies of ϳ17.1
kJmolϪ1 in our experiments are equivalent to about 1500 K
and are easily accessible in the outflow of carbon stars with
temperatures up to 4000 K. In addition, a verified rising re-
active cross sections with decreasing collision energy identi-
fies this reaction class as a potentially important means to
form complex hydrocarbons even for dark and diffuse inter-
stellar clouds, but extrapolation to typical temperatures of
10–100 K depends on the absence of small entrance barriers.
Our findings, however, strongly encourage astronomical
search for the hitherto unobserved propargyl isomer and hy-
drocarbon radicals as potential C–H exchange channels of
atom-neutral reactions, e.g.,
3
C P ͒ϩHCCCH →C H ϩH.
͑24͒
͑
j
3
4
3
In particular, methylacetylene has been widely observed to-
ward the Orion ridge and TMC-1. These clouds serve as
ideal targets to identify potential C4H3-isomers, perhaps
among unidentified microwave transitions in the spectrum
toward OMC-1.
VII. CONCLUSIONS
The reaction between ground state carbon atoms, C͑3Pj͒,
and ethylene, C2H4(X1Ag), was studied at average collision
energies of 17.1 and 38.3 kJmolϪ1 using the crossed molecu-
lar beam technique. Our results suggest two microchannels,
both initiated via an attack of the carbon atom to the
␲-orbital of the C2H4 molecule via a loose, reactant like
transition state located at the centrifugal barrier. One micro-
channel follows the highest symmetric C-atom approach via
Cs symmetry on the ground state 3AЉ surface and contributes
to an isotropic center-of-mass angular distribution. Initially,
the cyclopropylidene complex rotates in a plane roughly per-
pendicular to J around its C-axis and undergoes ring opening
to allene prior to decomposition to the propargyl radical in
its X2B2 state. A second microchannel contributes ϳ10% of
the scattering signal. Here, the A-like rotations of the cyclo-
propylidene adduct, ring opening to triplet allene, and a
VI. IMPLICATIONS TO INTERSTELLAR CHEMISTRY
AND COMBUSTION PROCESSES
The explicit identification of the C3H3 propargyl isomer
in the crossed beam reaction C͑3Pj͒ with C2H4 portrays a
further example of the dominant carbon–hydrogen exchange
channel in the reaction of neutral carbon atoms with unsat-
urated hydrocarbons.63 This pathway was elucidated recently
based on molecular beams studies of reaction ͑20͒
ϩ
g
3
1
C P ͒ϩC H X ⌺ ͒→C HϩH,
͑20͒
͑
͑
2
j
2
3
and presents an alternative, one-step approach to build up
carbon bearing molecules in interstellar environments and
hydrocarbon flames. Competing ion-molecule reactions ͑21–
23͒, for example,
J. Chem. Phys., Vol. 105, No. 19, 15 November 1996
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Kaiser, Lee, and Suits: Reaction of carbon atoms with hydrocarbons. I.
8719
strong L-LЈ correlation give rise to a forward-peaking T͑␪͒.
Both exit transition states are found to be tight and located at
least 30–40 kJmolϪ1 above the products.
Consequently, the remaining kinetic energy at RрRmax has
to fulfill the condition for reaction
1
2
ETb2 C6
This mechanism is consistent with 11C͑3Pj͒-tracer stud-
ies under bulk conditions. The postulated triplet cyclopropy-
lidene complex was trapped as a spirane, and an assumed
C3H3 intermediate yielded 1-propyneyl-5 and 1,2-
pentadienyl-5 products. The acetylene production can be ex-
plained by assuming a second, but in our experiments unde-
tected channel of the allene complex decomposing to
vinylidene and triplet carbene.
2
˙
␮R ϭ E Ϫ
ϩ
у0,
͑A7͒
ͫ
ͬ
T
R2
R6
RϭR
max
yielding the maximum impact parameter bmax
L2max
1/2
bmax
ϭ
.
͑A8͒
ͫ
ͬ
2␮E
This treatment assumes the reaction proceeds with unit effi-
ciency after barrier-crossing and under absence of sterical
effects. The Lennard-Jones coefficient C6 is approximated
according to Hirschfelder et al.71 to
The explicit identification of C3H3 under single collision
represents a second example of a carbon–hydrogen exchange
in reactions of ground-state carbon with unsaturated hydro-
carbons. This versatile concept represents an alternative
pathway to build up unsaturated hydrocarbons chains in
combustion processes and in the interstellar medium.
Note added in proof. The assignment of the symmetry of
the electronic wave function for C2v molecules follows the
convention that the molecular plane is defined as the mirror
plane, e.g., C3H3͑X2B2͒ instead of C3H3͑X2B1͒.
3
2
ECEC2H4
C6ϭ
␣ ␣
,
C2H4
͑A9͒
ͩ
ͪ
C
ECϩEC2H4
with the ionization potentials Ei for iϭC͑3Pj͒, and
1
C2H4(X Ag), and the polarizabilities ␣i . Using
␣
C(3pj)ϭ1.76ϫ10Ϫ30
m3,
␣
C2H4ϭ4.25ϫ10Ϫ30
m3,
E
C(3Pj)ϭ11.76, EC2H4ϭ10.5 eV, the maximum impact pa-
rameter bmax calculates to bmax ͑17.1 kJmolϪ1͒ϭ3.7 Å and
bmax ͑38.3 kJmolϪ1͒ϭ3.2 Å ͑Table II͒.
ACKNOWLEDGMENTS
1 E. Herbst, H. H. Lee, D. A. Howe, and T. J. Millar, Mon. Not. Royal
Astronomical Society 268, 335 ͑1994͒.
R.I.K. is indebted the Deutsche Forschungsgemeinschaft
for a post-doctoral fellowship. This work was supported by
the Director, Office of Energy Research, Office of Basic En-
ergy Sciences, Chemical Sciences Division of the U.S. De-
partment of Energy under Contract No. DE-AC03-
76SF00098.
2 Symposium on Titan ͑ESA-SP 338, ESTEC, Noordwijk, 1992͒.
3 R. D. Kern, K. Xie, and H. Chen, Combust. Sci. and Tech. 85, 77 ͑1992͒.
4 G. J. Collin, H. Deslauriers, G. R. De Mare, and R. A. Poirier, J. Phys.
Chem. 94, 134 ͑1990͒.
5 P. R. Westmoreland, A. M. Dean, J. B. Howard, and J. P. Longwell, J.
Phys. Chem. 93, 8171 ͑1989͒, and references therein.
6 G. Rotzell, Int. J. Chem. Kinetics 17, 637 ͑1985͒.
7 R. D. Smith, Combust. Flame 35, 179 ͑1979͒.
8 I. R. Slagle and D. Gutman, Proc. 23rd Symp. Int. Combust. Chemistry,
875 ͑1988͒.
APPENDIX
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