A combined crossed beam and ab initio investigation on the reaction of carbon species with C4H6 isomers. I. The 1,3-butadiene molecule, H2CCHCHCH2(X1A')

Article abstract of DOI:10.1063/1.1290285

The reaction between ground state carbon atoms, C(³P_j), and 1,3-butadiene, H2CCHCHCH2, was studied at three averaged collision energies between 19.3 and. 38.8 kJmol^-1 using the crossed molecular beam technique. Our experimental data combined with electronic structure calculations show that the carbon atom adds barrierlessly to the ?-orbital of the butadiene molecule via a loose, reactantlike transition state located at the centrifugal barrier. This process forms vinylcyclopropylidene which rotates in a plane almost perpendicular to the total angular momentum vector J around its C-axis. The initial collision complex undergoes ring opening to a long-lived vinyl-substituted triplet allene molecule. This complex shows three reaction pathways. Two distinct H atom loss channels form 1- and 3-vinylpropargyl radicals, HCCCHC2H3(X²A ) and H2CCCC2H3(X²A ), through tight exit transition states located about 20 kJmol^-1 above the products; the branching ratio of 1- versus 3-vinylpropargyl radical is about 8:1. A minor channel of less than 10 percent is the formation of a vinyl, C2H3(X²A'), and propargyl radical C3H3(X²B₂). The unambiguous identification of two C5H5 chain isomers under single collision has important implications to combustion processes and interstellar chemistry. Here, in denser media such as fuel flames and in circumstellar shells of carbon stars, the linear structures can undergo a collision-induced ring closure followed by a hydrogen migration to cyclic C5H5 isomers such as the cyclopentadienyl radical-a postulated intermediate in the formation of polycyclic aromatic hydrocarbons (PAHs).

Full text of DOI:10.1063/1.1290285

A combined crossed beam and ab initio investigation on the reaction of carbon species
with C 4 H 6 isomers. I.The1,3-butadienemolecule, H 2 CCHCHCH 2 (X 1 A ′ )
I. Hahndorf, H. Y. Lee, A. M. Mebel, S. H. Lin, Y. T. Lee, and R. I. Kaiser
Citation: The Journal of Chemical Physics 113, 9622 (2000); doi: 10.1063/1.1290285
View online: http://dx.doi.org/10.1063/1.1290285
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/113/21?ver=pdfcov
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 113, NUMBER 21
1 DECEMBER 2000
A combined crossed beam and ab initio investigation on the reaction
of carbon species with C4H6 isomers. I. The 1,3-butadiene molecule,
H CCHCHCH „X1A …
Ј
2
2
I. Hahndorf, H. Y. Lee,a) A. M. Mebel, S. H. Lin,a) Y. T. Lee,a) and R. I. Kaiserb)
Institute of Atomic and Molecular Sciences, 1, Section 4, Roosevelt Road, 107 Taipei, Taiwan,
Republic of China
͑Received 24 March 2000; accepted 11 July 2000͒
The reaction between ground state carbon atoms, C͑3Pj), and 1,3-butadiene, H2CCHCHCH2 , was
studied at three averaged collision energies between 19.3 and 38.8 kJmolϪ1 using the crossed
molecular beam technique. Our experimental data combined with electronic structure calculations
show that the carbon atom adds barrierlessly to the ␲-orbital of the butadiene molecule via a loose,
reactantlike transition state located at the centrifugal barrier. This process forms
vinylcyclopropylidene which rotates in a plane almost perpendicular to the total angular momentum
vector J around its C-axis. The initial collision complex undergoes ring opening to a long-lived
vinyl-substituted triplet allene molecule. This complex shows three reaction pathways. Two distinct
H atom loss channels form 1- and 3-vinylpropargyl radicals, HCCCHC H (X2A ) and
Љ
2
3
H CCCC H (X2A ), through tight exit transition states located about 20 kJmolϪ1 above the
Љ
2
2
3
products; the branching ratio of 1- versus 3-vinylpropargyl radical is about 8:1. A minor channel of
less than 10% is the formation of a vinyl, C H (X2A ), and propargyl radical C H (X2B ). The
Ј
2
3
3
3
2
unambiguous identification of two C5H5 chain isomers under single collision has important
implications to combustion processes and interstellar chemistry. Here, in denser media such as fuel
flames and in circumstellar shells of carbon stars, the linear structures can undergo a
collision-induced ring closure followed by a hydrogen migration to cyclic C5H5 isomers such as the
cyclopentadienyl radical—a postulated intermediate in the formation of polycyclic aromatic
hydrocarbons ͑PAHs͒. © 2000 American Institute of Physics. ͓S0021-9606͑00͒00338-X͔
modeling studies of PAH formation in hydrocarbon flames3
the authors proposed that the origin of larger aromatics might
be resonance-stabilized cyclopentadienyl radicals. In particu-
lar, a mechanism is proposed combining two or three cyclo-
pentadienyl radicals, c-C5H5 , followed by rearrangements to
form naphthalene or phenanthrene molecules: both cyclopen-
tadienyl radicals recombine first and then undergo H atom
shifts and two H-atom ejections. Melius et al.4 supported this
mechanism for the self-combination of cyclopentadienyl
radicals by ab initio studies. The rate limiting step for this
reaction is a 33.5Ϯ21.0 kJmolϪ1 intrinsic barrier height at-
tributed to the ejection of the first H-atom from the bicyclo-
pentadiene adduct. The hydrogen shifts in the bicyclopenta-
dienyl adduct occur fairly rapidly. Based on these
considerations, the cyclopentadienyl radical combination
may contribute as a possible reaction path to the PAH for-
mation under the temperature conditions of circumstellar en-
velopes of hot carbon stars as well. In a recent investigation
of sooting combustion flames5 this c-C5H5 radical is as-
sumed to play a significant role in the reaction mechanism
and is therefore included in the modeling of the combustion
process. Despite this assumption the experimental confirma-
tion still remains. There is no evidence given which isomer
of the C5H5 radical mainly contributes to combustion pro-
cesses. Supported by ab initio calculations, Lin et al. sug-
gested a possible reaction path for the formation of c-C5H5
initiated by the phenyl radical which itself is formed via
activation of benzene by abstraction of a hydrogen atom:6
I. INTRODUCTION
The mechanisms to form polycyclic aromatic hydrocar-
bons ͑PAHs͒ and ultimately soot in oxygen-poor combustion
flames as well as outflow of carbon stars are of fundamental
importance to the combustion community as well as for as-
trophysics. The relevance is due to the potency of PAH iso-
mers inducing mutations and cancer together with the soot-
enhanced entry of PAHs in the human respiratory system.1 In
the interstellar medium, PAHs and their cations, anions, radi-
cals, alkyl and oxygen substituted PAHs are thought to com-
prise 10% to 20% of the interstellar carbon in molecular
form, and are suggested as a carrier of unidentified infrared
bands ͑UIRs͒. In addition, PAH species could be responsible
for some of the diffuse interstellar absorption bands ͑DIBs͒
covering the visible spectrum from 440 nm to the near
infrared.2
Due to the crucial importance of PAH-like species, ex-
perimentally and theoretically well-defined mechanisms to
synthesize PAHs and their precursors in various terrestrial
and extraterrestrial gaseous environments have been investi-
gated recently. As one result of experimental and kinetic
a͒
Also at Department of Chemistry, National Taiwan University, Taipei,
107, Taiwan, Republic of China.
b͒
Author to whom correspondence should be addressed. Also with Depart-
ment of Physics, National Taiwan University, Taipei, 107; and Department
of Physics, Technical University Chemnitz, 09107 Chemnitz, Germany.
Electronic mail: kaiser@po.iams.sinica.edu.tw
0021-9606/2000/113(21)/9622/15/$17.00
9622
© 2000 American Institute of Physics
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J. Chem. Phys., Vol. 113, No. 21, 1 December 2000
Reaction of carbon with C4H6 . I
9623
TABLE I. Experimental beam conditions and 1␴ errors averaged over the experimental time: peak velocity
,
vp
speed ratio S ͑Ref. 36͒, peak collision energy, Ecoll , center-of-mass angle, ␪C.M. , composition of the carbon
beam, and flux factor f ϭn(C) n(H CCCH )
in relative units, with the number density of the ith reactant
v
*
r
*
v
2
2
n and the relative velocity
.
vr
i
Ecoll ͑kJmolϪ1
)
␪
C1 :C2 :C3
fv
Beam
p (msϪ1
)
S
v
C.M.
C͑3Pj)
C͑3Pj)
C͑3Pj)
C4H6
1800Ϯ10
2260Ϯ20
3000Ϯ50
770Ϯ10
7.2Ϯ0.2
7.2Ϯ0.2
6.9Ϯ0.2
9.2Ϯ0.2
19.3Ϯ0.3
28.0Ϯ0.5
38.8Ϯ1.4
¯
62.5Ϯ0.4
56.9Ϯ0.3
49.0Ϯ0.4
¯
1:0.3:0.7
1:0.2:0.8
1:0.2:0.8
¯
1.0
1.3Ϯ0.2
1.6Ϯ0.3
¯
distribution in the laboratory frame ͑LAB͒ using a forward-
convolution routine.12 This approach initially assumes an an-
gular flux distribution T(␪) and the translational energy flux
distribution P(ET) in the center-of-mass system ͑C.M.͒.
Laboratory TOF spectra and the laboratory angular distribu-
tions were then calculated from these T(␪) and P(ET) aver-
aged over the apparatus and beam functions. Best TOF and
laboratory angular distributions were archived by refining
adjustable T(␪) and P(ET) parameters. The final outcome is
the generation of a product flux contour map which reports
C6H5ϩO2→C6H5OϩO,
C6H5O→c-C5H5ϩCO.
͑1͒
͑2͒
However, no reliable experimental information is avail-
able on the mechanism of c-C5H5 radical formation. There-
fore, we launched a systematic program to study alternative
reaction pathways and investigate the atom-neutral reaction
of C͑3Pj) with distinct C4H6 isomers. Here, we unravel the
chemical dynamics on the reaction of atomic carbon with
1,3-butadiene, H2CCHCHCH2 . Although atomic carbon is
only a minor species in oxidative flames, it is assumed to
contribute significantly to combustion chemistry.7 C4H6 iso-
mers have been observed in hydrocarbon flames, and about
90% of the C4H6 products are 1,3-butadiene.8 Various
crossed beam reactions of atomic carbon with unsaturated
hydrocarbon molecules demonstrated explicitly that these re-
actions are dominated by a carbon versus hydrogen exchange
to form highly unsaturated, hydrogen-deficient hydrocarbon
radicals. Therefore, our title reaction is strongly expected to
synthesize C5H5 isomers.
the differential cross section, I(␪,u)ϳP(u) T(␪), as the in-
*
tensity as a function of angle ␪ and product center-of-mass
velocity u. Hence this map serves as an image of the reaction
and contains all the information of the scattering process.
III. ELECTRONIC STRUCTURE AND RRKM
CALCULATIONS
The geometries of the reactants, products, various inter-
mediates, and transition states for the title reaction were op-
timized using the hybrid density functional B3LYP method,
i.e., Becke’s three-parameter nonlocal exchange functional13
with the nonlocal correlation functional of Lee, Yang, and
Parr,14 and the 6-311G(d,p) basis set.15 Vibrational frequen-
cies, calculated at the B3LYP/6-311G(d,p) level, were used
for characterization of stationary points and zero-point en-
ergy ͑ZPE͒ correction. All the stationary points were posi-
tively identified for minimum or transition state. In some
cases, geometries and frequencies were recalculated at the
MP2/6-311G(d,p) and CCSD͑T͒/6-311G(d,p) levels.16
In order to obtain more reliable energies, we used the
G2M͑RCC,MP2͒17 method, a modification of the Gaussian-2
͓G2͑MP2͔͒ approach.18 The total energy in G2M͑RCC,MP2͒
is calculated as follows:
II. EXPERIMENTAL SETUP
The experiments were performed under single-collision
conditions using a universal crossed molecular beams appa-
ratus described in Ref. 9 in detail. Briefly, a pulsed super-
sonic carbon beam was generated via laser ablation of graph-
ite at 266 nm.10 The 30 Hz, 30–40 mJ output of a Spectra
Physics GCR-270-30 Nd:YAG laser was focused onto a ro-
tating carbon rod, and the ablated species were seeded into a
pulse of neat helium gas at 4 atm backing pressure. A four-
slot chopper wheel mounted after the ablation zone selected
a 9.0 ␮s segment of the seeded carbon beam. Table I com-
piles the experimental beam conditions. The carbon beam
and a pulsed 1,3-butadiene beam hold at 820Ϯ5 torr backing
pressure passed through skimmers and crossed at 90° in the
interaction region of the scattering chamber. To elucidate the
position of the H atom loss, we performed experiments with
partially deuterated 1,1,4,4-tetradeuterium-1,3-butadiene,
D2CCHCHCD2 . Reactively scattered products were detected
in the plane defined by two beams using a rotable detector
consisting of a Brink-type electron-impact ionizer,11 quadru-
pole mass filter, and a Daly ion detector at laboratory angles
in 2.5° and 5.0° steps between 3.0° and 72.0° with respect to
the primary beam. The velocity distribution of the products
was recorded using the time-of-flight ͑TOF͒ technique, and
information on the chemical dynamics of the reaction was
gained by fitting the TOF spectra and the product angular
E G2M͑RCC,MP2͒]ϭE RCCSD͑T͒/6-311G d,p͒
͔
͓
͓
͑
ϩ⌬E ϩ3df2p͒ϩ⌬E HLC͒
͑
͑
ϩZPE͓B3LYP/6-311G d,p͒ ,
͑
͔
͑3͒
where
⌬E ϩ3df2p͒ϭE MP2/6-311ϩG 3df,2p͒
͔
͑
͓
͑
ϪE MP2/6-311G d,p͒
͔
͑4͒
͑5͒
͓
͑
and the empirical ‘‘higher level correction’’
⌬E HLC͒ϭϪ5.25n Ϫ0.19n ,
͑
␤
␣
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9624
J. Chem. Phys., Vol. 113, No. 21, 1 December 2000
Hahndorf et al.
where n␣ and n␤ are the numbers of ␣ and ␤ valence
electrons, respectively. It has been shown that the
G2M͑RCC,MP2͒ method gives the averaged absolute devia-
tion of 4.8 kJmolϪ1 of calculated atomization energies from
experiment for 32 first-row G2 test compounds. The GAUSS-
21
IAN 94,19 MOLPRO 96,20 and ACES-II programs were em-
ployed for the potential energy surface computations. In this
article, we present only those results necessary to understand
our experimental data. All details are given in a forthcoming
publication.22
We used the Rice–Ramsperger–Kassel–Marrus
͑RRKM͒ theory23 for computations of rate constants of indi-
vidual reaction steps. Rate constant k(E) at a collision en-
#
*
ergy E for a unimolecular reaction A →A →P can be ex-
pressed as
␴ W# EϪE#͒
͑
k E͒ϭ
͑
•
,
͑6͒
h
␳ E͒
͑
where ␴ is a symmetry factor, W#(EϪE#) denotes the total
number of states for the transition state ͑activated complex͒
A# with a barrier E#, ␳(E) represents the density of states of
*
the energized reactant molecule A , and P is the product or
products. The saddle point method was applied to evaluate
␳(E) and W(E).23
FIG. 1. Lower: Newton diagram for the reaction C͑3Pj)
ϩH CCHCHCH (X1A ) at a collision energy of 19.3 kJmolϪ1. The circle
Ј
2
2
IV. RESULTS
stands for the maximum center-of-mass recoil velocity of the C5H5 isomer
assuming no energy channels into the internal degrees of freedom. Upper:
Laboratory angular distribution of product channel at m/eϭ63. Circles and
1␴ error bars indicate experimental data, the solid lines the calculated dis-
tribution. C.M. designates the center-of-mass angle. The solid lines originat-
ing in the Newton diagram point to distinct laboratory angles whose TOFs
are shown in Fig. 4.
A. Reactive scattering signal
We observed reactive scattering signals at mass-to-
charge ratios m/eϭ65 to 60, i.e., C5Hϩ5 ͑65͒ to the bare
carbon cluster Cϩ5 ͑60, Figs. 1–6͒. The relative intensity
ratios of m/e 65:64:63:62:61:60 are 0.26:0.32:1.0:
0.52:0.38:0.13 recorded at an electron energy of 200 eV;
errors are within 10%. All TOF spectra could be fit with
identical center-of-mass functions. Therefore, the signal at
lower m/e ratios originates in the cracking of the C5Hϩ5 par-
ent in the ionizer. Hence, we selected the most intense mass-
to-charge ratio and took our data at m/eϭ63. We like to
point out that no radiative association to C5H6 (m/eϭ66)
could be detected. In the case of partially deuterated 1,3-
butadiene, D2CCHCHCD2 , we recorded TOF spectra at the
center-of-mass angles, and took data at m/eϭ69 (C5D4Hϩ),
68 (C5Dϩ4 and/or C5D3H2ϩ), 67 (C5D3Hϩ), and 66 (C5D3ϩ
and/or C5D2Hϩ2 ).24 This indicates that at least the C versus H
exchange channel to form C5D4H exists. Since m/eϭ68 can
originate from fragmentation of m/eϭ69 in the detector or
from D atom loss, we cannot resolve at the present stage if a
D atom emission occurs. To tackle this question, we have to
fit the TOF spectra at m/eϭ69 and 68, cf. Sec. IV B.
complex͑es͒ holding a lifetime exceeding the͑ir͒ rotational
period͑s͒. In addition, all LAB distributions are very broad
and extend to about 45.0° in the scattering plane defined by
both beams. This data and the C5H5ϩH product mass ratio of
65 hint that the center-of-mass translational energy distribu-
tions P(ET)’s peak away from zero.
C. Center-of-mass translational energy distributions,
P„ET…
Figure 7 shows best fits of the translational energy dis-
tributions P(ET). Both the LAB distributions and TOF data
could be fitted with one P(ET) extending to a maximum
translational energy release Emax of 205, 230, and 250
kJmolϪ1, respectively. These high-energy cutoffs are accu-
rate within 10 kJmolϪ1. In the most favorable case the ener-
getics of the product isomers are well separated. Then Emax
,
i.e., the sum of the reaction exothermicity and relative colli-
sion energy, can be utilized to identify individual C5H5 iso-
mers. Correcting for the collision energy shows that our re-
action is exothermic by about 214Ϯ15 kJmolϪ1. In addition,
all P(ET)s peak away from zero and show distribution
maxima of 30–50 kJmolϪ1. In the case of partially deuter-
ated butadiene ͑Fig. 8͒, the TOF at m/eϭ69 could be fit with
kinematics of a H atom loss and a single P(ET) showing
identical pattern as the translational energy distribution of
1,3-butadiene. However, at m/eϭ68, two contributions of a
B. Laboratory angular distributions „LAB… and TOF
spectra
The most probable Newton diagrams of the title reaction
as well as the laboratory angular ͑LAB͒ distributions of the
C5H5 product are displayed in Figs. 1–3 collision energies of
19.3, 28.0, and 38.8 kJmolϪ1, respectively. At each collision
energy, the LAB distribution peaks close to the CM angles,
cf. Table I. This suggests that the reaction proceeds via in-
direct reactive scattering dynamics through long-lived C5H6
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J. Chem. Phys., Vol. 113, No. 21, 1 December 2000
Reaction of carbon with C4H6 . I
9625
FIG. 2. Lower: Newton diagram for the reaction C͑3Pj)
FIG. 3. Lower: Newton diagram for the reaction C͑3Pj)
ϩH CCHCHCH (X1A ) at a collision energy of 28.0 kJmolϪ1. The circle
ϩH CCHCHCH (X1A ) at a collision energy of 38.8 kJmolϪ1. The circle
Ј
2
2
Ј
2
2
stands for the maximum center-of-mass recoil velocity of the C5H5 isomer
assuming no energy channels into the internal degrees of freedom. Upper:
Laboratory angular distribution of product channel at m/eϭ63. Circles and
1␴ error bars indicate experimental data, the solid lines the calculated dis-
tribution. C.M. designates the center-of-mass angle. The solid lines originat-
ing in the Newton diagram point to distinct laboratory angles whose TOFs
are shown in Fig. 5.
stands for the maximum center-of-mass recoil velocity of the C5H5 isomer
assuming no energy channels into the internal degrees of freedom. Upper:
Laboratory angular distribution of product channel at m/eϭ63. Circles and
1␴ error bars indicate experimental data, the solid lines the calculated dis-
tribution. C.M. designates the center-of-mass angle. The solid lines originat-
ing in the Newton diagram point to distinct laboratory angles whose TOFs
are shown in Fig. 6.
D atom loss (C5D3Hϩ2 ) and fragmentation of the H atom loss
isomer to C5Dϩ4 are crucial to get a reasonable fit of the data.
These results show clearly the formation of at least two dis-
tinct C5H5 isomers.
plots I(␪,ET); since all translational energy distributions
look very similar, we show only data at the lowest collision
energy as a typical example. As we can expect from the
center-of-mass angular distribution, the best-fit data show a
forward-backward symmetric flux profile. Integrating the
I(␪,ET)s at each collision energy and correcting for the re-
actant flux as well as relative reactant velocity, we find an
integrated relative reactive scattering cross section ratio of
␴͑19.3 kJmolϪ1͒/␴͑28.0 kJmolϪ1͒/␴͑38.8 kJmolϪ1͒ϭ1.0:0.7
Ϯ0.2:0.5Ϯ0.1 within our error limits. Therefore, the cross
section slightly rises as the collision energy decreases. This
result together with recent kinetic data30 and our electronic
structure calculations, cf. Sec. V, suggest that the reaction
has no entrance barrier.
D. Center-of-mass angular distributions, T„␪…, and
flux contour maps I„u,␪…
At all collision energies the T(␪)s are isotropic and sym-
metric around ␲/2. This implies that either the lifetime of the
decomposing C5H6 complex͑es͒ is͑are͒ longer than its rota-
tional period ␶ or that two hydrogen atoms of the interme-
r
diate can be interconverted through a rotational axis.25 In this
case, the light H atom could be emitted in ␪ and ␪Ϫ␲ to
result for the forward–backward symmetry of T(␪). We like
to point out that at the highest collision energy, a slightly
backward scattered T(␪) up to I(180°)/I(0°)ϭ1.05 can fit
the data as well. Due to the light H atom emission, these
isotropic angular distributions are the result of a poor cou-
pling between the initial and final angular momentum vec-
tors, L and LЈ, respectively, as already observed in crossed
beams reaction of atomic carbon with methylacetylene,26
allene,27 benzene,28 and propylene.29 Since angular momen-
tum has to be conserved, a large fraction of the initial orbital
angular momentum must therefore be routed into rotational
excitation of the C5H5 reaction products. Figure 9 shows
both two- and three-dimensional center-of-mass flux contour
V. DISCUSSION
A. The C5H6 potential energy surface
1. Addition to one CBC double bond
Our electronic structure calculation shows that 1,3-
butadiene can exist in a trans and cis form; the latter is en-
ergetically less favored by 12 kJmolϪ1; both isomers can be
inter-converted via a 23.5 kJmolϪ1 high barrier. The transi-
tion state of this process depicts a C–C bond distance in-
creasing slightly from 146 pm ͑trans͒ via 149 pm ͑transition
state͒ to 147 pm. Due to the enhanced repulsive interaction,
the cis isomer shows no symmetry at all whereas the trans
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9626
J. Chem. Phys., Vol. 113, No. 21, 1 December 2000
Hahndorf et al.
FIG. 4. Time-of-flight data at m/eϭ63 for indicated laboratory angles at a
collision energy of 19.3 kJmolϪ1. Open circles represent experimental data,
the solid line represents the fit.
FIG. 5. Time-of-flight data at m/eϭ63 for indicated laboratory angles at a
collision energy of 28.0 kJmolϪ1. Open circles represent experimental data,
the solid line represents the fit.
form belongs to the Cs point group. In this section, we dis-
cuss first the reaction of atomic carbon with the trans isomer.
Here, C͑3Pj) can add barrierlessly to the carbon–carbon
double bond forming a vinyl-substituted triplet cyclopropy-
lidene radical i1, Figs. 10 and 11. The latter is bound by 213
kJmolϪ1 with respect to the separated reactants and exists in
two nearly isoenergetic cis and trans forms ͑i1-cis and i1-
trans͒. We mention that the carbon additions to trans and cis
1,3-butadiens give i1-trans and i1-cis, respectively. The con-
formers of i1 are expected to readily rearrange to each other
by rotation around the single C–C bond with a low barrier.
i1 can undergo a ͓1,2͔ or ͓1,3͔ hydrogen shift via 200
kJmolϪ1 barriers ͑pathway 1 and 2͒ or a ring opening ͑path-
way 3͒. The first two pathways form the i3 ͑cis/trans͒ and the
i4 isomers ͑cis/trans͒, respectively. Compared to atomic car-
bon and 1,3-butadiene, i3 and i4 are 250 and 196 kJmolϪ1
more stable. No symmetry element exists; both isomers rep-
resent vinyl-substituted triplet cyclopropene molecules. A fi-
nal hydrogen loss can form the C5H5 isomers p3–p6 ͑from
i3͒ and p6–p11 ͑from i4͒. The optimized product geometries
are shown in Fig. 12. Among these isomers, p6 is the most
stable structure since the aromatic vinylcyclopropenyl radi-
cal is formed. The energy difference to the more stable vi-
nylpropargyl radicals of about 110 kJmolϪ1 corresponds very
well as found in the unsubstituted products propargyl and
cyclopropenyl ͑100Ϯ25 kJmolϪ1͒. Structures p3, p4, p7, and
p8 represent less stable, substituted cyclopropene molecules
formed via H atom loss from the vinyl group. The remaining
isomers p5, p10, and p11 can be visualized as derivatives of
cyclopropen-2-yl in which one H atom is replaced by a C2H3
group. Compared to the hydrogen migration pathways, the
ring opening of i1 ͑pathway 3͒ involves a much lower barrier
of only 51 kJmolϪ1. This process yields a vinyl substituted
triplet allene diradical i5 ͑trans͒ which is about 147 kJmolϪ1
more stable than i1.
The i5 intermediate can undergo a trans-cis isomeriza-
tion to i5 ͑cis͒ followed by a ͓1,2͔ hydrogen shift to give i8
which is almost isoenergetic to i5 ͑cis͒. The barrier for this
process is about 200 kJmolϪ1—identical to those H shifts in
i1. A subsequent ring closure via a 78 kJmolϪ1 barrier leads
to triplet cyclopentadiene i6—the global minimum of the
triplet C5H6 potential energy surface ͑PES͒. Another path-
way from i5 ͑cis͒ to i6 involves ring closure to i9 with a
barrier of 108.0 kJmolϪ1 followed by a ͓1,2͔ hydrogen shift
in the ring with a barrier of 216.0 kJmolϪ1. i6 can fragment
via C–H bond cleavages to form the cyclopentadienyl radi-
cal p16 which represents the global minimum of the C5H5
PES. Here, the theoretically derived exothermicity of 332
kJmolϪ1 is in excellent agreement with thermodynamical
data predicting 323 kJmolϪ1 31
.
Alternative H atom loss channels to p17 and p18 are less
favorable by about 140 kJmolϪ1. In these systems, the reso-
nance stabilization is less pronounced as compared to the
cyclopentadienyl radical p16. Besides the cis-trans isomer-
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J. Chem. Phys., Vol. 113, No. 21, 1 December 2000
Reaction of carbon with C4H6 . I
9627
FIG. 6. Time-of-flight data at m/eϭ63 for indicated laboratory angles at a
collision energy of 38.8 kJmolϪ1. Open circles represent experimental data,
the solid line represents the fit.
ization, i5-trans can decompose via C–H bond cleavage to
four distinct C5H5 isomers p12–p15. Here, tight exit transi-
tion states located about 20 kJmolϪ1 above the products lead
vinyl-substituted propargyl radicals, i.e., 1- and 3-vinylpro-
pargyl radicals, HCCCH–C2H3(p14), H2CCC–C2H3(p15).
FIG. 8. Time-of-flight data of m/eϭ69 ͑top͒ and 68 ͑bottom͒ at the center-
of-mass angle recorded at a collision energy of 38.8 kJmolϪ1. Experimental
data are indicated by open circles. At m/eϭ69, the solid line represents the
best fit of the H atom loss channel; at m/eϭ68 best fits are indicated by
dashed line ͑D atom loss͒, dashed-dotted line ͑H atom loss channel͒, and
solid line ͑sum of both contribution͒.
The reaction exothermicities of these processes are calcu-
lated to be 210 and 192 kJmolϪ1, respectively. The stability
sequence can be rationalized in terms of an enhanced delo-
calization of the unpaired electron in p14 ͑increased delocal-
ization incorporating the C2H3 group͒ compared to p15. The
energetics to form substituted allene radicals p12 and p13
are less favorable and are only exothermic by 125 and 94
kJmolϪ1. We like to point out that we were unable to find an
exit transition state from i5 to p12ϩH. Both at the
**
B3LYP/6-31G
**
levels of theory the
and MP2/6-311G
transition state optimization converged to the separated prod-
ucts indicating that the exit barrier does not exist. i5-trans
can also dissociate to the vinyl and propargyl radicals by
splitting the C–C bond with a barrier of 219.6 kJmolϪ1. The
exit barrier in this case is 25.5 kJmolϪ1 and the total reaction
exothermicity is 165.7 kJmolϪ1, i.e., lower than those for
p14 and p15 but significantly higher than for p12 and p13.
FIG. 7. Center-of-mass translational energy flux distributions for the reac-
tion C͑3P )ϩH CCHCHCH (X1A ) at collision energies of 19.3 ͑solid
Ј
j
2
2
line͒, 28.0 ͑dashed-dotted line͒, and 38.3 kJmolϪ1 ͑dashed line͒.
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9628
J. Chem. Phys., Vol. 113, No. 21, 1 December 2000
Hahndorf et al.
FIG. 9. Contour flux map for the reac-
tion C͑3P )ϩH CCHCHCH (X1A ) at
Ј
j
2
2
a collision energy of 19.3 kJmolϪ1. ͑a͒
Three-dimensional map, ͑b͒ two-
dimensional projection. Units are
given in msϪ1
.
2. Addition to two CBC double bonds
i1 or i5, indicating that the insertion pathway does not con-
tain a first-order saddle point. Our finding strongly correlates
with previous crossed beam experiments of C͑3Pj) with un-
saturated hydrocarbons acetylene,32 ethylene,33 methylacety-
lene,26 allene,27 propylene,29 benzene,28 and the propargyl
radical.34 Here, only an addition to the ␲-electronic system
was observed, but no symmetry forbidden insertion into
C–H or C–C bonds.
If the 1,3-butadiene molecule reacts in its cis form with
atomic carbon, C͑3Pj) could attack both terminal carbon at-
oms simultaneously without entrance barrier under C2v or Cs
symmetry forming a pentacyclic triplet intermediate i2. The
latter is stabilized by 341 kJmolϪ1 with respect to atomic
carbon plus trans 1,3-butadiene and can either undergo H
atom migration via a 184 kJmolϪ1 barrier to i6 or fragments
through a barrier located 10 kJmolϪ1 above the products to
C5H5 isomer p17. The fate of i6 was already outlined in the
previous section.
B. Identification of reaction product„s…
The translational energy distributions show that the re-
action to the C5H5 isomer͑s͒ is exothermic by 215Ϯ15
kJmolϪ1. If we compare this data with our electronic struc-
ture calculations, it is evident that the C5H5 isomers p16,
p17, p18 ͑from intermediate i6͒ or p14 and p15 ͑from inter-
mediate i5-trans͒ contribute to the reactive scattering signal
within the error limits. Since trans 1,3-butadiene is more than
99.4% in our secondary beam, the contribution of the cis
isomer is marginally. An alternative pathway—a collision-
induced trans-cis isomerization of 1,3-butadiene—is ener-
getically feasible since even our lowest collision energy of
19.3 kJmolϪ1 can pass the isomerization barrier of 24
kJmolϪ1. The reader has to keep in mind, however, that our
experiments are performed under single-collision conditions;
3. Insertion into C–H and C–C bonds
Despite a careful search, no transition states of a C͑3Pj)
insertion into C–H and C–C bonds could be found. We
started the saddle point optimization from the geometries
with a CCH three-membered ring suggesting that a C–H
bond in 1,3-butadiene is broken and two new bonds, C–C
and C–H, with the attacking carbon atom are formed during
the insertion process. This process would lead directly to a
HCCHCHCHCH2 intermediate, a trans conformer of i8.
However, the energies of the initial structures are very high.
Upon the transition state search, the C–H bond in 1,3 buta-
diene is restored, and the system descends to the vicinity of
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J. Chem. Phys., Vol. 113, No. 21, 1 December 2000
Reaction of carbon with C4H6 . I
9629
FIG. 10. Schematic representation of the lowest energy pathways on the triplet C5H6 PES.
this means that upon cis-trans isomerization, no third body
reaction partner to form i2 is present, and hence this complex
cannot be formed. p17 and p18 do not play a role in our
experiments. Reaction to both isomers must proceed via i6
though H atom emission. If i6 existed however, a C–H bond
rupture is expected to proceed via the lowest energy pathway
to cyclopentadienyl, p16. This conclusion gains strong sup-
port from our RRKM calculations: the ratios of the rate con-
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9630
J. Chem. Phys., Vol. 113, No. 21, 1 December 2000
Hahndorf et al.
FIG. 10. ͑Continued.͒
FIG. 11. Structures of potentially involved triplet C5H6 collision complexes. Bond lengths are given in Angstrom, bond angles in degrees.
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J. Chem. Phys., Vol. 113, No. 21, 1 December 2000
Reaction of carbon with C4H6 . I
9631
FIG. 12. Structures of doublet C5H6 isomers. Bond lengths are
given in Angstrom, bond angles in degrees.
have been formed. This will be subject to RRKM studies, cf.
Sec. V D. Based on these considerations, p14 and p15 are the
only possible major reaction products which do confirm with
the experimentally determined energetics of the reaction.
But is it feasible that less stable C5H5 isomers are
formed as well to a minor amount? In principle, these iso-
mers might be synthesized via C–H bond ruptures of reac-
tive intermediates i3, i4, and i5. All three complexes, how-
ever, can only be formed through i1. The fate of the latter is
governed by ring opening to i5. Compared to a 200 kJmolϪ1
stants show k(p16):k(p18):k(p17)ϭ1:0.005:0.019 (19.3
kJmolϪ1),
k(p16):k(p18):k(p17)ϭ1:0.007:0.022 (28.0
kJmolϪ1͒, and k(p16):k(p18):k(p17)ϭ1:0.008:0.027 (38.8
kJmolϪ1͒. Therefore, p16 would be the dominate reaction
product, and the reaction should be exothermic by 332
kJmolϪ1. This is not supported by our experiments which
suggest an exothermicity of 215Ϯ15 kJmolϪ1. We like to
stress, however, that a long energy tail of our P(ET)’s with
P(E)ϭ0.01–0.03 extending to 350 kJmolϪ1 has no signifi-
cant influence on our fit. Hence minor amounts of p16 might
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9632
J. Chem. Phys., Vol. 113, No. 21, 1 December 2000
Hahndorf et al.
FIG. 13. Decomposition of the partially deuterated
complex i5-trans to p14 and p15.
C. The actual reaction pathway on the C5H6 potential
energy surface
barrier which must be passed to i3 and i4, the barrier to i5 is
only 50 kJmolϪ1 and hence this pathway is the energetically
most favorable one. Our RRKM investigation verifies this
result as well, and the rate constants calculate to k(i3):
But what are the underlying dynamics to form the C5H5
isomers p14 and p15? Based on our data, the chemical reac-
tion dynamics are indirect and proceed via complex forma-
tion. In our molecular beam, more than 99.4% of the 1,3-
butadiene exists in the energetically more stable trans form.
Here, the singly occupied px and py orbitals of C͑3Pj) can
interact without entrance barrier perpendicular to the butadi-
ene plane with the ␲ orbital at the carbon–carbon double
k(i4):k(i5)ϭ7ϫ10Ϫ8:1ϫ10Ϫ5:1(19.3 kJmolϪ1),
k(i4):k(i5)ϭ2ϫ10Ϫ7:4ϫ10Ϫ5:1(28.0 kJmolϪ1),
k(i3):
and
k(i3):k(i4):k(i5)ϭ5ϫ10Ϫ7:2ϫ10Ϫ4:1(38.8 kJmolϪ1).
Therefore, i1 reacts predominantly to i5, and p3–p11 play no
role in our reaction. i5 decomposes via C–H rupture or un-
dergoes ring closure, H shifts, and H atom emission. The
latter process gives p16, which has not been observed as a
major product in our crossed beam experiments. Based on
these results, only p12 and p13 might resemble additional
candidates. But since the exit barriers to form these isomers
are about 105 kJmolϪ1 higher compared to those involved in
a H atom emission to p14 and p15, both p12 and p13 are
negligible.
3
bond under C1 symmetry on the A surface to form i1-trans,
cf. Fig. 13. This approach supports a maximum orbital over-
lap to form two C–C–␴ bonds in triplet vinyl cyclopropy-
lidene. Since the butadiene molecules are prepared in a su-
personic expansion, their rotational angular momentum is
negligible, and the total angular momentum J is the initial
orbital angular momentum L. Since LϷJ, i1 rotates in a
plane almost perpendicular to L around the C axis of the
C5H6 isomer i1. A consecutive ring opening via a 50
kJmolϪ1 barrier conserves the rotational axis of the highly
prolate triplet vinylallene complex i5-trans which has an
asymmetry parameter ␬ϭϪ0.994. The deep potential energy
well of 360 kJmolϪ1 of i5 explains the forward–backward
symmetric center-of-mass angular distributions as found ex-
perimentally, and hence the decomposing i5 complex has a
lifetime longer than its rotation period around the C axis. An
alternative explanation of a decomposing complex in which
two hydrogen atoms can be interconverted through a rotation
axis can be dismissed, since i5 belongs to the C1 point
group. We like to stress that the reaction dynamics discussed
so far are in line with large impact parameters leading to i5
within orbiting limits. The contribution of large impact pa-
rameters which dominate the reaction was already mentioned
in Sec. IV D. Our data suggest that the relative cross section
rises as the collision energy decreases. Final C–H bond rup-
tures in i5 yield the experimentally observed vinylpropargyl
Our isotopic studies with partially deuterated 1,3-
butadiene help to unravel the final question if p14 or p15, or
even both radicals are formed, cf. Fig. 13. Once i5-trans
(mϭ70) has been formed, only a H atom loss (m/eϭ69) at
the C3 atom goes hand in hand with the formation of p14; an
alternative H loss at C4 would yield p13, which was elimi-
nated earlier as a possible reaction product. In strong anal-
ogy, solely a D fragmentation of the C1–D bond is con-
firmed with the experimentally determined reaction energy
of 215Ϯ15 kJmolϪ1; and a C5–D loss would have formed
unobserved p12. In conclusion, these isotopic studies com-
bined with the energetics of the reaction confirm the forma-
tion of p14 and p15. This experimental result is well sup-
ported by RRKM studies as well, and the ratios of
the
rate
constants
are
k(p13):k(p14):k(p15)ϭ8
ϫ10Ϫ6:0.12:1(19.3 kJmolϪ1), k(p13):k(p14):k(p15)ϭ1
ϫ10Ϫ5:0.13:1(28.0 kJmolϪ1), and k(p13):k(p14):k(p15)
ϭ1ϫ10Ϫ5:0.13:1(38.8 kJmolϪ1). Therefore, p14 and p15
are clearly identified as the reaction products. Obviously,
p13 does not play any role in the reactions.
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J. Chem. Phys., Vol. 113, No. 21, 1 December 2000
Reaction of carbon with C4H6 . I
9633
radicals p14 and p15 rotating around their C axis. The iso-
topic studies show clearly that only those H atoms adjacent
to the carbon atom close to the activated bonds formally
inserted in the former carbon-carbon double bond are lost.
No C4–H or C5–H bond is broken. Further, both exit tran-
sition states to vinylpropargyl are tight and located about 20
kJmolϪ1 above the products; this gains support from our ab
initio calculations showing imaginary frequencies of 588i
and 561i cmϪ1, respectively. The characteristics of both
transition states are consistent with the reversed reaction of a
H atom addition to an unsaturated olefinic or acetylenic sys-
tem which has similar orders of magnitude of the entrance
barriers as observed in our experiments. In addition, the in-
direct scattering dynamics of the title reaction are supported
by a small fraction of 30%–35% of total available energy
channeling into translation as already observed in a similar
complex forming reaction of atomic carbon with unsaturated
hydrocarbons as studied in our group.
These considerations show clearly that the reaction of
atomic carbon with trans 1,3-butadiene is not thermodynami-
cally controlled since the most stable cyclopentadienyl radi-
cal p16 is not a major product. The formation of 1- and
3-vinylpropargyl is a direct consequence of the involved PES
and the transition state choking the H atom migration from
i5-cis to i8. A similar case in which the reaction was not
controlled thermodynamically was found in the C͑3Pj)/C6H6
system in which the thermodynamically less stable 1,2-
didehydrocycloheptatrienyl isomer was formed.
FIG. 14. Diagram showing the reaction pathways included in our RRKM
calculations.
tion functions at high temperatures or with large available
energies such frequencies should be treated as free or hin-
dered internal rotors rather than as harmonic oscillator. At
this stage we estimate possible variations of rate constant k4
by replacing the lowest vibrational frequency in the transi-
tion states by the value of 100 cmϪ1. Than, we obtain k4Ј
which is 4.4 times lower than k4 and 2.6–3.9 times lower
than k5 ͑see Table II͒ for the formation of p14, in line with
more favorable energy barrier for the latter. Using kЈ4 instead
k4 lowers the contribution of C2H3ϩC3H3 to 3%–4%. We
can conclude here that the C2H3ϩC3H3 channel can play a
minor but not insignificant role in the reaction.
We have also calculated the product branching ratios for
the case when the cyclic intermediate i2 is formed in the
reaction of the carbon atom with cis 1,3-butadiene, cf. Fig.
10. Although this consideration is not directly related to our
present experiment, i2 can be formed in high-temperature
combustion flames since 1,3-butadiene is present in its cis
form as well. We solved the rate equations for the reaction
scheme shown in Fig. 14͑b͒ based on the steady-state ap-
proximation. The results show that i2 would produce 95.6%
of p17, only 4.4% of p16, and a negligible amount of p18.
Again, the most thermodynamically stable p16 is not the
major product because the barrier for H elimination in i2 is
11.7 kJmolϪ1 lower than the barrier for ͓1,2͔ hydrogen mi-
gration leading to i6, which eventually dissociates to p16.
D. RRKM Calculations
Our experimental data alone cannot identify the contri-
bution of the cyclopropenyl radical, p16. Further, we inves-
tigate the experimentally not observed C2H3 elimination
from i5. To solve this problem, we employ RRKM calcula-
tions. The rate equations for the title reaction were derived
according to Fig. 14 and solved with the rate constants com-
puted by the RRKM theory. We employed the steady-state
approximation to obtain the branching ratios. Table II shows
the calculated rate constants for each elementary step in Fig.
14 and the branching ratios at various collision energies.
These computations show that p15 is the major reaction
product which contributes at least 76.5% at 19.3 kJmolϪ1
and at least 73% at 38.8 kJmolϪ1. The contribution of p14 is
in the range of 9%–11% and that of p16 is less than 1%.
Other isomers of C5H5 do not play any role in the reaction.
It is interesting to address the possibility of the forma-
tion of C2H3ϩC3H3 in the reaction via intermediate i5-trans.
Initial calculations showed that the rate constant k4 for the
formation of C2H3ϩC3H3 is somewhat higher than k5 for
p14ϩH despite the fact that the energetics for the latter is
more favorable than for the former. This result is attributed
**
to the fact that at the B3LYP/6-31G level the transition
state for the C–C bond splitting in i5-trans has one very low
vibrational frequency of 21 cmϪ1. This leads to very high
total number of states for this transition state, which results
in the high values for k4 . The contribution of C2H3ϩC3H3 is
in this case 13.4%–16.6%. However, low vibrational fre-
quencies are usually very sensitive to the theoretical approxi-
mation used in calculations. Also, in computations of parti-
3
E. Comparison with the reactions of C„ Pj… with C2H4
and C3H6
The chemical dynamics and involved potential energy
surfaces of reactions of atomic carbon with olefinic mol-
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9634
J. Chem. Phys., Vol. 113, No. 21, 1 December 2000
Hahndorf et al.
TABLE II. RRKM rate constants in units of sϪ1 as depicted in Figs. 10 and 14, and calculated branching ratios
of various reaction products.
Collision energy
͑kJmolϪ1
͒
0
19.3
28.0
38.8
k1
k2
k3
k4
k4Јa
k5
k6
k8
k9
kϪ9
k10
kϪ10
k11
kϪ11
k12
k13
k14
k19
kϪ19
k20
k21
kϪ21
k22
kϪ22
1.87ϫ103
1.15ϫ105
5.60ϫ1011
3.36ϫ109
(7.62ϫ108)
2.97ϫ109
1.02ϫ105
2.61ϫ1010
8.14ϫ1011
1.31ϫ1012
3.40ϫ108
7.01ϫ108
3.66ϫ1010
3.16ϫ109
7.95ϫ107
2.26ϫ107
6.33ϫ109
2.97ϫ109
2.04ϫ106
6.41ϫ1010
1.78ϫ1010
1.13ϫ1011
1.39ϫ108
1.96ϫ106
4.97ϫ104
8.98ϫ106
7.25ϫ1011
7.88ϫ109
(1.78ϫ109)
5.52ϫ109
3.56ϫ105
4.50ϫ1010
8.77ϫ1011
1.38ϫ1012
7.04ϫ108
1.45ϫ109
4.38ϫ1010
4.31ϫ109
1.54ϫ108
4.55ϫ107
8.28ϫ109
5.13ϫ109
3.97ϫ106
1.09ϫ1011
2.35ϫ1010
1.60ϫ1011
2.65ϫ108
3.92ϫ106
1.45ϫ105
3.48ϫ107
8.06ϫ1011
1.12ϫ1010
(2.52ϫ109)
7.14ϫ109
5.89ϫ105
5.65ϫ1010
9.05ϫ1011
1.41ϫ1012
9.50ϫ108
1.95ϫ109
4.72ϫ1010
4.92ϫ109
2.04ϫ108
6.10ϫ107
9.28ϫ109
6.45ϫ109
5.24ϫ106
1.37ϫ1011
2.64ϫ1010
1.86ϫ1011
3.46ϫ108
5.24ϫ106
4.52ϫ105
1.42ϫ108
9.11ϫ1011
1.68ϫ1010
(3.78ϫ109)
9.66ϫ109
1.05ϫ106
7.38ϫ1010
9.40ϫ1011
1.45ϫ1012
1.35ϫ109
2.76ϫ109
5.17ϫ1010
5.76ϫ109
2.83ϫ108
8.62ϫ107
1.06ϫ1010
8.43ϫ109
7.28ϫ106
1.78ϫ1011
3.24ϫ1010
2.21ϫ1011
4.74ϫ108
7.37ϫ106
k(p16)b
k(p17)b
k(p18)b
2.14ϫ108
2.69ϫ106
7.65ϫ105
4.38ϫ108
8.17ϫ106
2.41ϫ106
5.86ϫ108
1.29ϫ107
3.85ϫ106
8.23ϫ108
2.19ϫ107
6.68ϫ106
c
k(p16)
k(p17)
k(p18)
2.92ϫ109
6.41ϫ1010
1.04ϫ107
5.01ϫ109
1.10ϫ1011
2.75ϫ107
6.26ϫ109
1.37ϫ1011
4.12ϫ107
8.14ϫ109
1.78ϫ1011
6.60ϫ107
Ј
Ј
Ј
c
c
Branching ratiosd ͑%͒
p13
C2H3ϩC3H3
p14
3.11(3.38)ϫ10Ϫ4
10.3͑2.5͒
9.1͑9.9͒
6.05(6.75)ϫ10Ϫ4
13.4͑3.4͒
9.4͑10.5͒
7.81(8.83)ϫ10Ϫ4
14.8͑3.8͒
9.5͑10.7͒
0.001͑0.001͒
16.6͑4.3͒
9.6͑11.0͒
p15
p16
79.9͑86.8͒
0.7͑0.7͒
76.5͑85.3͒
0.7͑0.8͒
74.9͑84.6͒
0.8͑0.9͒
73.0͑83.4͒
0.8͑0.9͒
p17
p18
0.008͑0.009͒
0.002͑0.003͒
0.014͑0.015͒
0.004͑0.005͒
0.017͑0.019͒
0.005͑0.006͒
0.022͑0.025͒
0.007͑0.008͒
Branching ratiose ͑%͒
p16
p17
p18
4.4
95.6
0.016
4.4
95.6
0.024
4.4
95.6
0.029
4.4
95.6
0.035
Ј
Ј
Ј
aRate constant k4 computed with the change of the lowest real vibrational frequency in transition state t27 from
Ϫ1
21 cmϪ1 ͑B3LYP/6-311G ͒ to 100 cm
.
**
bRate constants for the formation of the p16, p17, and p18 products from intermediate i5-trans calculated by
solving the kinetic rate equations ͓see Fig. 14͑a͔͒ based on the steady-state approximation.
cRate constants for the formations of the p16, p17, and p18 products from intermediate i2 in the reaction of
C͑3Pj) with cis-1,3-butadiene calculated by solving the kinetic rate equations ͓see Fig. 14͑b͔͒ based on the
steady-state approximation.
dCalculated branching ratios of various products for the reaction proceeding via intermediate i5-trans. In
parentheses: the values computed using kЈ4 instead of k4 .
eCalculated branching ratios of various products for the reaction proceeding via intermediate i2.
ecules such as ethylene and propylene depict common fea-
tures. The reactions are governed by indirect scattering dy-
namics and about 30%–35% of the total available energy
channels into the translational degrees of freedom. The car-
bon attack proceeds via complex formation through a barri-
erless addition of C͑3Pj) to the ␲ electron density. This path-
way yields ͑substituted͒ cyclopropylidene intermediates
which are stabilized by 210–270 kJmolϪ1 with respect to the
reactants. All complexes rotate around their C axes and un-
dergo ring opening through barriers between 40 and 60
kJmolϪ1 to form ͑substituted͒ triplet allene intermediates.
The latter reside in potential energy wells 360–400 kJmolϪ1
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J. Chem. Phys., Vol. 113, No. 21, 1 December 2000
Reaction of carbon with C4H6 . I
9635
deep compared to atomic carbon and the olefine. The fate of
the triplet allene complexes is governed by H loss channels
to ͑substituted͒ propargyl radicals via tight exit transition
states located about 10–25 kJmolϪ1 above the products.
Most of the initial angular momentum channels into rota-
tional excitation of the products predominantly excited to
C-like rotations. The presence of an exit barrier is docu-
mented in the center-of-mass translation energy distributions
as well as all P(ET)’s peak around 20–50 kJmolϪ1. The
exothermicities to the C3H2R (RϩCH3 or C2H3) are very
similar and range between 200 and 220 kJmolϪ1. This dem-
onstrates that the substitution of a hydrogen atom in ethylene
by a side group has little effect on the energetics of the
reaction.
Besides these similarities, there is one striking difference
in the reaction of atomic carbon with propylene and 1,3 buta-
diene. Here, the CH3 group is conserved in the reaction and
acts as a spectator. Although no H atom loss occurs from the
C2H3 group, the increased stabilization of p14 versus p15
demonstrates an enhanced delocalization of the unpaired
electron. In addition, if the cis 1,3-butadiene reacts, the side
group can be actively involved in the chemistry, since atomic
carbon can add to both terminal carbon atoms. Therefore, we
cannot regard C2H3 as a spectator side group in this case.
cal details leading to large organic molecules are only dimly
understood and possibly initiated by a recombination of two
pentadienyl radicals, cf. Sec. I. Our proposed mechanism
suggests the growth by addition of carbon atoms to unsatur-
ated molecules such as 1,3-butadiene and is supported by
recent investigations. Although our crossed beam experi-
ments did not give any proof of a cyclic C5H5 isomer, the
situation in circumstellar envelopes close to the central car-
bon star is different from the single collision conditions.
Compared to our experiments, the molecular number density
is higher, and the C5H5 chain can isomerize upon a succes-
sive collision to cyclic C5H5 isomers. In strong analogy to
combustion processes, a collision-induced trans-cis isomer-
ization of 1,3-butadiene can precede the reaction with atomic
carbon, and the pentadienyl radical can be formed via i2 and
i6.
VIII. CONCLUSIONS
The reaction between ground state carbon atoms, C͑3Pj),
and 1,3-butadiene, H2CCHCHCH2 , was studied at averaged
collision energies of 19.3, 28.0, and 38.8 kJmolϪ1 using the
crossed molecular beam technique. The carbon atom attacks
the ␲-orbital of the butadiene molecule without a barrier via
a loose, reactantlike transition state located at the centrifugal
barrier to form a cyclopropylidene derivative. The triplet
radical rotates in a plane which is almost perpendicular to the
total angular momentum vector J around its C-axis undergo-
ing ring opening to a vinyl substituted triplet allene mol-
ecule. This complex fragments via two micro-channels
through H atom emission to form 1- and 3-vinylpropargyl
radicals, HCCCH–C H (X2A ), and H CCC–C H (X2A ),
VI. COMBUSTION CHEMISTRY APPLICATIONS
Our crossed beam studies showed explicitly that the title
reaction leads to 1- and 3-vinylpropargyl radicals,
HCCCH–C H (X2A ), and H CCC–C H (X2A ). This re-
Љ
Љ
2
3
2
2
3
action proceeds via an initial addition of C͑3Pj) to trans-1,3-
butadiene to form a three-membered ring intermediate i1 fol-
lowed by ring opening to a substituted triplet allene species
i5 and H atom emission to the products. Although these ex-
periments did not show any evidence of the cyclopentadienyl
radical which is thought to be a potential precursor to PAH
molecules, the explicit identification of chain C5H5 radicals
holds far-reaching consequences for combustion processes.
Here, Burcat and Dvinyaninov investigated the decomposi-
tion pattern of the cyclopentadienyl radical and found
HCCCHC2H3 as the main decomposition product.35 Based
on this finding it can be strongly assumed that in combustion
flames HCCCHC2H3 can undergo ring closure followed by
H atom migration to form the cyclopentadienyl radical once
the entrance barrier can be passed via a third body reaction.
Likewise, in denser reaction environments such as flames, a
collision induced trans-cis isomerization of 1,3-butadiene
prior to a C͑3Pj) addition can form the cyclopentadienyl radi-
cal via i2 and i6.
Љ
Љ
2
3
2
2
3
through tight exit transition states. The unambiguous identi-
fication of two chain isomers of C5H5 under a single colli-
sion represents a further example of a carbon-hydrogen ex-
change in reactions of ground state carbon atoms with
unsaturated hydrocarbons. In denser media such as combus-
tion flames and close to the central star of circumstellar en-
velopes, the linear isomer can show a ring closure to form
cyclic C5H5 isomers such as the cyclopentadienyl radical—a
postulated intermediate in the formation of PAHs—via
HCCCHC2H3 . Finally, a collision-induced trans-cis isomer-
ization of 1,3-butadiene prior to a C͑3Pj) addition can form
the pentadienyl radical via cyclic reaction intermediates. The
role of cyclic C5H5 isomers in these environments will be
investigated in future RRKM calculations.
ACKNOWLEDGMENTS
R.I.K. is indebted the Deutsche Forschungsgemeinschaft
for a Habilitation fellowship ͑IIC1-Ka1081/3-1͒. This work
was supported by Academia Sinica, Taiwan, the National
Science Council of R.O.C., and by the Petroleum Research
Fund of R.O.C. We are thankful to Dr. A. H. H. Chang for
her assistance with RRKM calculations. This work was per-
formed within the international astrophysics network.
VII. ASTROPHYSICAL IMPLICATIONS
Besides its potential importance in combustion chemis-
try, investigating the formation of C5H5 isomers is expected
to contribute to the modeling of formation of complex mol-
ecules in the interstellar space. Here, the PAH synthesis in
circumstellar envelopes is of crucial importance since these
molecules are considered as the condensation nuclei to form
larger carbon-rich grain materials which are considered to be
formed in carbon-rich circumstellar shells. Here, the chemi-
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