Formation of C9H2 and C10H2 from Reactions C3H + C6H2 and C4H

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Formation of CH and C H from Reactions CH + CH and CH + CH Yi-Lun Sun, Wen-Jian Huang, and Shih-Huang Lee

J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b08902 • Publication Date (Web): 12 Dec 2017 Downloaded from http://pubs.acs.org on December 13, 2017

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The Journal of Physical Chemistry

Submitted to J. Phys. Chem. A

Formation of C9H2 and C10H2 from Reactions C3H + C6H2 and C4H + C6H2

Yi-Lun Sun, Wen-Jian Huang, and Shih-Huang Lee*

National Synchrotron Radiation Research Center (NSRRC), 101 Hsin-Ann Road, Hsinchu Science Park, Hsinchu 30076, Taiwan

*Author to whom correspondence should be addressed. Fax: +886-3-578-3813.

Tel: +886-3-578-0281.

Electronic mail: [email protected]

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ABSTRACT The reactions of C3H and C4H radicals with C6H2 were investigated for the first time. Reactants C3H, C4H, and C6H2 were synthesized in two beams of C2H2 diluted with helium by pulsed high-voltage discharge.

We measured translational-energy distributions, angular

distributions, and photoionization-efficiency spectra of C9H2 and C10H2 produced from the title reactions in a crossed molecular-beam apparatus using synchrotron vacuum-ultraviolet photoionization.

The C3H (C4H) + C6H2 reaction releases 42% (33%) of available energy into the

translational degrees of freedom of product C9H2 (C10H2) + H and scatters products into a nearly isotropic angular distribution.

The photoionization-efficiency spectrum of C9H2 (C10H2) is in good

agreement with that of C9H2 (C10H2) produced from the C7H (C8H) + C2H2 reaction.

The

ionization threshold, after deconvolution, was determined as 8.0 ± 0.1 eV for C9H2 and 8.8 ± 0.1 eV for C10H2.

The combination of measurements of product translational-energy release and

photoionization-efficiency spectra indicates productions of 3HC9H/c-1HC3(C)C5H/c-1HC7(C)CH + H and 1HC10H + H in the two title reactions, which are supported also by quantum-chemical calculations.

Ratios branching to the three isomers of C9H2 remain unknown.

This work

demonstrates that long carbon-chain molecules (e.g., C9H2 and C10H2) can be synthesized from reactions of CmH (e.g., m = 3 and 4) radicals with polyynes (e.g., HC6H) and gives some valuable implications to planetary, interstellar, and combustion chemistry.

2


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1. INTRODUCTION Carbon chemistry plays an important role in planetary atmospheres, interstellar/circumstellar media, and combustion processes because carbon is the fourth most-abundant element in the universe.

C2H2 (ethyne or acetylene) is well known as an abundant species in carbon-rich

interstellar media and circumstellar environments1,2 and as a common intermediate in hydrocarbon combustion.3

Polyynes (sometimes called polyacetylenes, HC2n+2H) are hydrocarbon species with

alternating single and triple carbon-carbon bonds.

C2H2 and C4H2 (butadiyne or diacetylene) were

detected in the atmosphere of Titan that is the moon of Saturn.4

C2H2, C4H2, and C6H2 (hexatriyne

or triacetylene) were observed in the line of sight toward the circumstellar envelope of protoplanetary nebulae CRL 618.2

Besides, C2H2, C4H2, C6H2, C8H2 (octatetrayne or

tetraacetylene), and C10H2 (decapentayne or pentaacetylene) were detected in fuel-rich flames of allene (H2CCCH2), propyne (HCCCH3), and cyclopentene (c-C5H8) using the flame-sampling molecular-beam photoionization mass spectrometry.3

Polyynic carbon chains are proposed to be

building blocks of formation of polycyclic aromatic hydrocarbons (e.g. benzene, naphthalene, and anthracene) and fullerenes (e.g. C60 and C70) in interstellar space and combustion processes. CmH (m = 1 – 8) were observed in the line of sight toward Taurus Molecular Cloud (TMC-1)5,6,7,8,9,10 and the circumstellar envelope of carbon star IRC+10216.11

Besides, C2H, C3H,

C4H, and C5H were observed also toward the circumstellar envelope of CRL 618.12,13

CmH are

producible from CmH2 by photolysis 14,15,16,17 in a photon-rich environment or from chemical reactions like C + Cm-1H2 (and C2 + Cm-2H2) → CmH + H.18,19

Bimolecular reaction rates are slow

in a typical molecular cloud with a density of 103 – 105 cm-3, which enables the observation of highly-reactive CmH radicals survived in a molecular cloud.

In contrast, it is tough to detect CmH

radicals in a typical flame that has a gas density as high as 1018 – 1019 cm-3. polyynic C–H bond hinders pyrolysis of CmH2 to CmH + H in a flame.

Besides, the strong Nonetheless, CmH is

believed to be an important intermediate that reacts rapidly with unsaturated hydrocarbons in a combustion process.

For instance, the light of λ = 431.5 nm emitted from a hydrocarbon flame 3



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was assigned to the transition A2∆ → X2Π of CH radicals.20 Because of different reaction mechanisms, the reactions of CmH radicals with C2H2 can be classified

into

two

types

–

odd-carbon-numbered

radical

(C2n-1H)

reactions

and

even-carbon-numbered radical (C2nH) reactions. C2n-1H + C2H2 → C2n+1H2 + H

(1)

C2nH + C2H2 → C2n+2H2 + H

(2)

The rate coefficients of reactions of CH, C2H, and C4H with C2H2 were determined as (3.9–4.8)×10-10, (1.1–2.3)×10-10, and (1.5–3.9)×10-10 cm3 molecule-1 s-1 in temperature ranges of 23–295 K, 15–295 K, and 39–300 K, respectively.21,22,23

The so large rate coefficients at low

temperatures imply that there is no energy barrier higher than the reactant asymptote at the entrance channel.

In contrast to the kinetics studies by interrogating reactants, the dynamics of reactions

CH + C2D2, CD + C2H2, and C2D + C2H2 were investigated in a crossed-molecular-beam quadrupole-mass apparatus by measuring translational-energy distributions and angular distributions of products.24,25

The deuterium labeling enabled discrimination of elimination of

atomic hydrogen (H/D) and of molecular hydrogen (H2/HD/D2).

The reactions CH + C2H2 and

C2H + C2H2 were investigated also with quantum-chemical calculations.24,25

On the basis of the

established potential-energy surfaces, rate coefficients and product branching ratios were calculated with Rice-Ramsperger-Kassel-Marcus (RRKM) theory.

The hydrogen-loss channel was predicted

to be dominant by theory, which is in accord with the experimental result.

Recently, the dynamics

of reactions (1) and (2) with n = 1 – 4 were explored using a crossed-molecular-beam quadrupole-mass apparatus and synchrotron vacuum-ultraviolet (VUV) ionization. 26 , 27

The

translational-energy distributions and the angular distributions of hydrogen-loss exit channels were derived from time-of-flight (TOF) spectra of products C2n+1H2 and C2n+2H2 measured at various scattering angles.

In addition, product isomers were identified with photoionization-efficiency

(PIE) spectroscopy and quantum-chemical calculations.

It was found that singlet c-1HC2n-1(C)CH

and/or triplet 3HC2n+1H were producible in reactions (1) whereas 1HC2n+2H (polyynes) were 4


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produced exclusively in reactions (2) as n = 1 – 4.

Furthermore, reaction (1) had a cross section

less than reaction (2) for each n value. In addition, reactions of CmH radicals with polyynes are proposed to be another source for formation of long carbon-chain molecules. categories – reactions (3) and (4).

This type of reactions can also be classified into two

To the best of our knowledge, study on kinetics of reactions of

CmH radicals with polyynes is still lacking in literatures.

The investigation on dynamics of

reaction C2D + C4H2 → DC6H + H in crossed molecular beams is the only work for this type of reactions.28,29

DC6H had a translational-energy distribution extending to the energetic limit and an

angular distribution enhanced at the forward direction.

In order to verify the proposal that CmH2

can be synthesized through reactions (3) and (4), more chemical reactions in eqs. (3) and (4) need be investigated.

In the present work, we explored the dynamics of reactions C3H + C6H2 and C4H

+ C6H2 by interrogating translational-energy distributions, angular distributions, and PIE spectra of products C9H2 and C10H2 and by calculating potential-energy surfaces of the two reactions with quantum-chemical methods. C2n-1H + C2x+2H2 → C2n+2x+1H2 + H

(3)

C2nH + C2x+2H2 → C2n+2x+2H2 + H

(4)

2. EXPERIMENTS The

reactions

of

rotating-source-assembly elsewhere.30,31,32

C3H

and

C4 H

radicals

crossed-molecular-beam

with

C6H2

apparatus

Thus, only a brief description is given here.

were

that

carried

had

been

out

in

a

described

One source chamber equipped

with an Even-Lavie valve and a discharge device33 served to generate a pulsed beam of C3H or C4H radicals (hereafter designated as primary beam) from a mixture of 1% C2H2 seeded in He with a stagnation pressure 105 psia.

The pulse of C3H (C4H) radicals had a most-probable speed 1890

(1875) m s-1 and a speed ratio greater than 7.

In the same manner, the other source chamber

equipped with an Even-Lavie valve and a discharge device served to generate a pulsed beam of 5



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C6H2 (hereafter designated as secondary beam) from a mixture of 5% C2H2 seeded in He with a stagnation pressure 105 psia.

The amount of C6H2 species produced from the 5% mixture is 3.8

times greater than that from the 1% mixture.

The pulse of C6H2 had a most-probable speed 1765 –

1770 m s-1 and a speed ratio better than 7.

The primary beam intercepted the secondary beam at

90° with a collision energy (Ec) of 19.7 kcal mol-1 for the C3H + C6H2 reaction and 23.4 kcal mol-1 for the C4H + C6H2 reaction.

Reaction products were scattered into the whole solid angles.

In

order to obtain angle-specific TOF spectra, however, only the products flying along a path of length 100.5 mm became ionized with tunable synchrotron VUV radiation.

The VUV radiation had a

photon flux ~ 8.4×1015 photons s-1 and an energy resolution (∆E/E) ~ 4.2% after suppression of high harmonics radiation with a noble gas filter of length ~ 30 cm.

Following photoionization, a

quadrupole-mass filter selected the desired product cations and then a Daly-type ion detector counted the ions. 1 µs.

Subsequently, a multichannel scaler sampled ion signals into 4000 bins of width

By subtracting the ion flight interval from the total flight duration, a neutral product TOF

spectrum was obtained.

In order to get the laboratory angular distribution, product TOF spectra

were measured at a variety of laboratory angles (Θ) by scanning the angle back to back.

Θ was

defined as an angle between the detection axis and the primary beam and was tunable from -18° to 108° by rotating the source-chamber assembly.

As for the measurement of a PIE spectrum, TOF

spectra were recorded at a fixed laboratory angle by scanning the ionizing photon energy back to back.

All the TOF spectra recorded at the same experimental condition were summed together in

order to yield a good signal-to-noise ratio and to avoid a long-term drift.

Components of the

experimental apparatus were synchronized with two pulse generators operating at 200 Hz.

For the

purpose of characterizing the primary (secondary) beam, reactants’ PIE spectra were measured at Θ = 0° (90°).

3. COMPUTATIONS 6


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Quantum-chemical calculations were performed with programs Gaussian-03/09 in a computer equipped with a six-core processor and 64 GB of memory.

The geometric structure and the

zero-point energy (ZPE) of a molecular species were calculated with a density-functional method B3LYP and a basis set aug-cc-pVDZ.

Either a stationary structure or a transition structure was

judged by its imaginary vibrational frequency number; 0 is referred to the former and 1 to the latter. The connection of a transition structure with its reactant and product was confirmed with the calculation of intrinsic reaction coordinate (IRC) at the level of B3LYP/aug-cc-pVDZ.

In the case

of no transition structure found on a reaction path, the potential-energy surface was scanned at the B3LYP/aug-cc-pVDZ level to confirm the absence of a transition state.

One or two bond angles

can be fixed, if necessary, in the SCAN calculation in order to constrain the molecular structure in the expected range.

Total energy of the optimized molecular species was calculated with a

couple-cluster method CCSD(T) and a basis set aug-cc-pVTZ.

The potential energy of a loose

transition state corrected with ZPE might become below its neighboring intermediates using this widely-employed computational approach that had a computational uncertainty of 2 – 3 kcal mol-1. Besides, the geometric structure and the total energy of a molecular cation were calculated also with the computational method mentioned above.

Therefore, the adiabatic ionization energy of a

molecular species can be calculated by the cationic-neutral energy difference corrected with ZPEs.

4. RESULTS AND DISCUSSION 4.1. Characterization of molecular beams.

The mass distribution of molecular species

synthesized in the primary beam of 1% C2H2/He by discharge has been reported as a supporting material in the previous work.26

Due to its importance in the present work, that mass spectrum is

adapted to present in the upper panel of Fig. 1.

Species C3H or C4H in the primary beam serves

as one of reactants in the crossed-beam experiments.

Reactant C3H includes linear (hereafter

referred to as l) and cyclic (hereafter referred to as c) isomers because l-C3H is mere 1.4 kcal mol-1 less stable than c-C3H (i.e., c-HC(C)C).27 Reactant C4H is identified as butadiynyl because its 7



PIE spectrum resembles that of l-C4H produced from reaction C2 + HCCH → l-C4H + H.26

For a

clear comparison, the lower panel of Fig. 1 presents the mass distribution of carbonaceous species synthesized in the secondary beam of 5% C2H2/He by discharge.

Species C6H2, second most

abundant in the secondary beam, serves as the other reactant in the crossed-beam experiments. Reactant C6H2 is identified as hexatriyne because its PIE spectrum resembles that of HC6H produced from reaction C4H + HCCH → HC6H + H.32

There is no evidence for the presence of

cumulene carbene H2C6 that lies above HC6H by 48.5 kcal mol-1.

Since the electric discharge

current and duration are kept at mere 20 mA and 10 µs in both molecular beams, reactants C3H, C4H, and C6H2 are all cooled down to their ground states by supersonic expansion at a stagnation pressure of 105 psia. Furthermore, the flight interval (~ 50 µs) of reactants from their pulsed valve to the reaction center also facilitates relaxation of excited-state species by radiative emission. Provided that excited-state species have ionization energy below their ground-state ionization energy, we do not observe any clues to the existence of excited-state reactants from their PIE spectra.

120 C3

100

1% C2H2/He

C4H2

80 60

Ion signals (arb. units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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40 20

C6H2 C5

C

C8H2

0 C4H2

100

5% C2H2/He

80 60 C6H2 40 C3H2 20 C8H2 0 10

20

30

40

50

60

70

80

90

100 110

Mass / u

8


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Figure 1. Mass spectrum of molecular species synthesized in a mixture of 1% C2H2/He (upper) and of 5% C2H2/He (lower) initiated by discharge. eV.

The ionizing photon energy is 12.5

The detection of ions at m/z = 24 – 28 u are omitted due to a severe interference

from precursor C2H2. The largest ion signal of each mass spectrum is normalized to 100.

The upper spectrum is adapted from Ref. 26.

4.2. Why the title reactions dominate in experiments?

The ion signals observed at

mass-to-charge ratios (m/z) 110 u and 122 u are assigned to C9H2 and C10H2 produced mainly from the reactions C3H + C6H2 and C4H + C6H2, respectively, based on the following reasons.

First, the

reactions C3Hx + C6Hy (C4Hx + C6Hy) are responsible mainly for production of C9H2 (C10H2) because they have CM angles ranging from 59.3° to 63.1° (52.6° to 56.2°) for any combination of x ≤ 4 and y ≤ 4.

As illustrated in Fig. 1, yields of hydrocarbon species that contain more than four

hydrogen atoms are negligible.

The detected product C9H2 (C10H2) has an angular distribution

(vide infra) spanning from 55° to 68° (48° to 62°) with a maximal probability at 62° (55°) that is close to those CM angles mentioned above.

In contrast, other crossed-beam reactions will have

CM angles away from the angular range of products detected.

For example, the CM angles of

reactions C4Hx + C5Hy and C2Hx + C7Hy (C5Hx + C5Hy and C3Hx + C7Hy) are calculated to be 47.1° – 51.2° and 70.4° – 73.7° (41.5° – 45.2° and 63.2° – 66.6°), respectively, for any combination of x ≤ 4 and y ≤ 4.

Second, there is no reaction product observed convincingly in the mass range

123 u (C10H3) – 150 u (C12H6) with ionizing photons at 11.6 eV.

Accordingly, the dissociations of

CxHy (10 ≤ x ≤ 12) to C9H2+ and CxHy (11 ≤ x ≤ 12) to C10H2+ following photoionization at 11.6 eV might not take place. Besides, the yields of larger CxHy species with x ≥ 13 should be negligibly small due to low concentrations of their corresponding reactants, though Cx≥13Hy is beyond the detection limit of the quadrupole mass filter employed.

Third, any bimolecular association that

leads to adduct C9H2 or C10H2 was not observed in the present single-collision experiments. 9


A


Page 10 of 33

bimolecular association (e.g., C3Hx + C6H2-x → C9H2 and C4Hx + C6H2-x → C10H2) will form adduct (e.g., C9H2 and C10H2) of which the angular distribution is defined by the angular divergences of both molecular beams.

The angular distribution width of adduct is predicted to be ~ 2° that is

much less than the experimental value.

Fourth, the ion signal at m/z = 109 u (C9H) is ~ 0.3 times

that of m/z = 110 u and the ion signal at m/z = 121 u (C10H) is also ~ 0.3 times that of m/z = 122 u as well.

On the basis of natural isotopic ratio, the contribution of

13 12

C C9H to 122 u are mere ~ 3% (≈ 0.3×0.011×9 or 0.3×0.011×10).

13 12

C C8H to 110 u and of

Moreover, this value might

be overestimated because dissociative ionization of C9H2 to C9H+ + H and C10H2 to C10H+ + H are ignored here.

Fifth, the ion-signal ratios are 118:100:54:5:1 for the species at m/z = 36 – 40 u and

38:100:178:8:1 for the species at m/z = 48 – 52 u in the primary beam.

On the other hand, the

ion-signal ratios are 1:7:100:10:6 for the species at m/z = 72 – 76 u in the secondary beam. the natural isotopic ratio

13

Taking

C/12C = 0.011 into account, the yield ratios are corrected as

123:100:53:3:1 for C3:C3H:C3H2:C3H3:C3H4, 39:100:177:1:1 for C4:C4H:C4H2:C4H3:C4H4, and 1:7:100:4:5 for C6:C6H:C6H2:C6H3:C6H4.

According to that, the multiplication of concentrations

[C3]×[C6H3], [C3H2]×[C6H], and [C3H3]×[C6] are 0.05, 0.04, and ~ 0 times the value of [C3H]×[C6H2] as well as [C4]×[C6H3], [C4H2]×[C6H], and [C4H3]×[C6] are 0.02, 0.12, and ~ 0 times [C4H]×[C6H2].

Therefore, the reaction C3 + C6H3 / C3H2 + C6H → C9H2 + H possibly has a

fraction of 5% / 4% contributing to C9H2 and the reaction C4 + C6H3 / C4H2 + C6H → C10H2 + H possibly has a fraction of 2% / 12% contributing to C10H2 provided that they have the same reactive cross sections as the title reactions.

On the basis of capture theory and quantum-chemical

calculations, the two title reactions have rate coefficients close to the collision limit 10-10 cm3 molecule-1 s-1 (vide infra).

Sixth, a collision system that contains more than three hydrogen atoms

is negligibly minor for production of C9H2 or C10H2 due to a rather small value on multiplication of corresponding reactant concentrations.

Furthermore, reactions C3H2 + HC6H and HC4H + HC6H

are predicted to incur large entrance barriers based on previous calculations on l-C3H2/c-C3H2 + 10


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HC2H reactions27 and to favorably produce C9H3 + H and C10H3 + H at exit channels.

However,

there is no compelling signal observed at m/z = 111 u (C9H3) and 123 u (C10H3).

4.3. Product TOF, translational-energy, and angular distributions.

Since the two title

reactions have a dominant contribution (~ 90%) to products C9H2 and C10H2, other minor reactions are ignored in analysis yet to be discussed in a latter section.

Figure 2 presents two Newton

diagrams superimposed with corresponding velocity-distribution maps of hydrocarbon products for the reactions C3H + C6H2 → C9H2 + H at Ec = 19.7 kcal mol-1 and C4H + C6H2 → C10H2 + H at Ec = 23.4 kcal mol-1.

VC3H, VC4H, and VC6H2 represent reactant velocities.

A horizontal line in each

Newton diagram denotes relative velocity Vrel between two colliding reactants and is the symmetric axis of reaction products.

Θ = 0° (90°) is defined as the direction of primary (secondary) beam.

VCM represents velocity of the center of mass (CM) of two colliding reactants with an angle of ΘCM relative to VC3H or VC4H.

Figure 3 presents twelve angle-specific TOF spectra and simulations of

products C9H2 (m/z = 110 u) and C10H2 (m/z = 122 u) recorded with photon energy 11.6 eV. Figure 4 exhibits the corresponding laboratory angular distributions P(Θ), i.e., the plot of integral ion signals versus laboratory angles, and simulations for the two products; here, product ion signals in the range 50 – 100 µs were integrated.

A small amount of C9H2 and C10H2 molecules scattered

non-reactively from both molecular beams were observed at m/z = 110 u and 122 u, separately. Nonetheless, the background from the primary (secondary) beam can be obtained alone by switching off discharge of the secondary (primary) beam.

Both backgrounds have been subtracted

in Figs. 3 and 4.

11



66° 58°

Vrel = 2586 m s

90°

VCM

-1

0° -1

ΘCM = 61.8°

=

H2

V C6

65 17

=

m

90 18

s

m

H

s

-1

V C3

C3H + C6H2 → C9H2 + H 62°55°48°

Vrel = 2578 m s

90°

VCM Θ = 55.0° CM

V C6 =

2 H

70 17

=

m

V

s

-1

C

-1

0° -1

75 18

m

s

4H

C4H + C6H2 → C10H2 + H

Figure 2. Newton diagrams superimposed with velocity distribution maps of corresponding hydrocarbon products for the reactions C3H + C6H2 → C9H2 + H (upper) and C4H + C6H2 → C10H2 + H (lower).

In each product velocity distribution map, colors red,

green, and blue denote high, middle, and low signal levels, respectively. represent the detection axes at several laboratory angles.

C3H + C6H2 → C9H2 + H 200 56°

57°

58°

59°

61°

62°

63°

65°

66°

67°

150 100 50 Relative ion signals (arb. units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 33

0 200 60° 150 100 50 0 200 64° 150 100 50 0 0

50

100

0

50

100

0

50

100

0

50

100

150

Flight time / µs

12


Dash lines

Page 13 of 33

C4H + C6H2 → C10H2 + H 200 49°

50°

51°

52°

54°

55°

56°

58°

59°

60°

150 100 50 Relative ion signals (arb. units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0 200 53° 150 100 50 0 200 57° 150 100 50 0 0

50

100

0

50

100

0

50

100

0

50

100

150

Flight time / µs

Figure 3. Angle-specific TOF spectra of products C9H2 (upper) and C10H2 (lower) recorded at m/z = 110 u and 122 u, separately, with photoionization energy 11.6 eV. denote the experimental data and solid lines the simulations.

Open circles

Each panel shows the

corresponding laboratory angle.

Figure 5 presents CM product translational-energy distributions P(Et) and a CM angular distribution P(θ) employed to simulate all angle-specific TOF spectra and laboratory angular distributions by forward convolution.

Here, Et includes translational energies of two

momentum-matched products C9H2 + H or C10H2 + H.

Because C9H2 or C10H2 carries a rather

small fraction of translational-energy release by scattering off a hydrogen atom, P(Et) cannot be determined accurately from a TOF distribution of C9H2 or C10H2.

In contrast, the laboratory

angular distribution appears to be more sensitive than the TOF distribution on determination of P(Et).

In order to know the uncertainty, we employ three P(Et) distributions (dotted, solid, and

dash lines presented in Fig. 5) to simulate product’s laboratory angular distribution for each reaction; the corresponding results are presented with dotted, solid, and dash lines in Fig. 4.

From

the fittings, we choose the solid line as the most probable P(Et) that has translational energy stretch to the energetic limit of reaction l-2C3H + 1HC6H → 3HC9H + H and of reaction l-2C4H + 1HC6H → 1HC10H + H; the superscripts 1, 2, and 3 denote singlet, doublet, and triplet spin multiplicities, respectively.

Besides, the area between dotted and dash lines can be viewed as the acceptable 13



uncertainty of P(Et).

The average translational-energy release is 9.3 (17.0) kcal mol-1

corresponding to a fraction of 0.42 (0.33) in product translational degrees of freedom for the reaction l-C3H + HC6H → 3HC9H + H (l-C4H + HC6H → 1HC10H + H).

Since atomic hydrogen

has no internal energy, the internal-energy distribution of its counter-product C9H2 or C10H2 is derivable straightforward from product translational-energy distribution.

A flat (i.e., isotropic)

angular distribution is favorably employed for P(θ) based on the kinematic model (vide infra). = 0° (180°) is defined as the incidence direction of C3H or C4H (C6H2) in the CM frame.

θ

The

solid-line P(Et) and P(θ) were also employed to construct the velocity-distribution maps presented

10 8 6 4

+

C9H2 ion signal (arb. units)

in Fig. 2 and to simulate the TOF spectra presented in Fig. 3.

2 0 55

60

65

70

Laboratory angle (Θ) / °

10 8 6 4

+


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 33

2 0 50

55

60

Laboratory angle (Θ) / °

Figure 4. Laboratory angular distributions of products C9H2 (upper) and C10H2 (lower) recorded at m/z = 110 u and 122 u, respectively, with photoionization energy 11.6 eV. denote the experimental data.

Open circles

Dotted, solid, and dash curves are simulations with the 14


Page 15 of 33

corresponding P(Et)s exhibited in Fig. 5.

The three curves are normalized to the same

area.

l-C4H + HC6H → HC10H + H

10

P(Et)

8 6 4 2 0 0

10

20

30

40

50

60

-1

Et / kcal mol 2

P(θ)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

0 0

45

90

135

180

C.M. angle (θ) / °

Figure 5. Upper: CM product translational-energy distributions of the reactions C3H + C6H2 → C9H2 + H (red lines) and C4H + C6H2 → C10H2 + H (blue lines).

Dotted, solid, and

dash curves, normalized to the same height, are three P(Et)s employed to simulate product’s laboratory angular distribution exhibited in Fig. 4.

Left three arrows indicate

the calculated energetic limits for the l-C3H + HC6H reaction leading to c-1HC3(C)C5H, c-1HC7(C)CH, and

3

HC9H with an H atom.

Lower: an isotropic CM angular

distribution employed for simulations of the two title reactions.

4.4. Product photoionization efficiency spectra.

Figure 6 exhibits the PIE spectra of

products C9H2 and C10H2 recorded at Θ = 62° and 55°, respectively. 15


The literature-reported PIE


spectra 3

of

C9H2

and

C10H2

produced

from

reactions

C7H

HC9H/c-1HC7(C)CH/c-1HC3(C)C5H + H and C8H + C2H2 → 1HC10H + H

therein for comparison.

26,27

+

C2H2

→

are also presented

The high similarity on product PIE spectra implies that the C3H (C4H) +

C6H2 reaction produces C9H2 (C10H2) with an isomeric ratio similar to that of the C7H (C8H) + C2H2 reaction.

Alternatively, the most-stable isomer 3HC9H (1HC10H) is overwhelmingly dominant in

the C7H + C2H2 and C3H + C6H2 (C8H + C2H2 and C4H + C6H2) reactions.

1

HC10H is doubtlessly

exclusive because its isomers are energetically inaccessible in the present work (vide infra).

After

deconvolution with the photon-energy bandwidth, the ionization threshold of C9H2 was determined as 8.0 ± 0.1 and C10H2 8.8 ± 0.1 eV; the latter one is in good agreement with the literature-reported ionization energy 8.75 ± 0.05 eV of 1HC10H.34

Besides, the adiabatic ionization energy was

calculated as 7.69 eV for 3HC9H, 8.51 eV for c-1HC3(C)C5H, 8.49 eV for c-1HC7(C)CH, and 8.88 eV for 1HC10H.

Because c-1HC7(C)CH and c-1HC3(C)C5H lie above 3HC9H by mere 2.0 kcal

mol-1 and 3.4 kcal mol-1, respectively, we cannot distinguish these three isomers that are energetically accessible in the present work.

We refrain from simulating the PIE spectra because

the broad vibrational-state distribution will result in a much-time-consuming calculation on all Franck-Condon factors.

Moreover, we neither know the population of products on each

vibrational state.

10

C3H+C6H2→C9H2+H

3

2

1

l- HC9H

4

1

6

c- HC7(C)CH

c- HC3(C)C5H

C7H+C2H2→C9H2+H

8

+


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 33

0 7

8

9

10

11

12

Photon energy / eV

16


10

C4H+C6H2→C10H2+H C8H+C2H2→C10H2+H

8

l-HC10H

6 4

+

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



Page 17 of 33

2 0 8

9

10

11

12

Photon energy / eV

Figure 6. PIE spectra of products C9H2 (upper) and C10H2 (lower).

Circles are recorded from

reactions of C3H and C4H with C6H2 and squares are adapted from previous works (Refs. 26 and 27) on reactions of C7H and C8H with C2H2. versus photon energy is not corrected.

A small variation of photon flux

Baselines are shifted to zero.

the calculated ionization energies of C9H2 and C10H2.

17


Arrows indicate


Page 18 of 33

Figure 7. Potential-energy surfaces of the reactions l-C3H/c-C3H + HC6H → C9H2 + H. Stationary and transition structures are presented but H-atom products are omitted. Relative potential energy is given in kcal mol-1.

Dash line represents collision energy

19.7 kcal mol-1 for the l-C3H + HC6H reaction.

The dash line should be shifted down

by 1.4 kcal mol-1 for the c-C3H + HC6H reaction.

4.5. Potential energy surfaces of reactions. reactions l-C3H/c-C3H + HC6H.

Figure 7 presents the potential-energy surface of

HC6H has three (i.e., one middle and two terminal) C≡C bonds.

Because a carbon atom has four valence electrons, the terminal carbon atom of l-C3H can offer two unpaired electrons to interact with one of the three triplet bonds of HC6H.

l-C3H can add to a

terminal C≡C bond of HC6H to form a cyclic complex c-HC3(CH)C5H (I3) without an energy barrier or add to the middle C≡C bond to form another cyclic complex c-HC3(C3H)C3H (I2) with a barrier TS1 of height 6.4 kcal mol-1.

I3 can decompose directly to C5H + HC4H and to

c-1HC3(C)C5H + H or rearrange to HC2CHC6H (I10) that in turn decomposes to 3HC9H + H with a small exit barrier TS14.

3

HC9H is 11.5 kcal mol-1 more stable than 1HC9H.

Because the

isomerization barriers TS10 and TS11 on the routes from I3 to I10 lie 11.6 – 14.3 kcal mol-1 below the product c-1HC3(C)C5H + H, the isomerization process followed by decomposition to 3HC9H + H is also favorable.

I3 can also rearrange to c-HC(C)CCHC5H (I7) through TS6, I5, and TS7

followed by decomposition to c-HC(C)C7H + H with a barrier TS12.

This pathway is probably

less favorable due to a large exit barrier TS12 that is 8.9 kcal mol-1 higher than TS14.

I2 needs a

large enthalpy to decompose to c-HC3(C3)C3H + H and incurs a high energy barrier TS5 to isomerize to HC5(C2H)C2H (I4) that also needs a large enthalpy to decompose to HC5(C2)C2H + H and C5(C2H)C2H + H; these three products are near the energetic limit 19.7 kcal mol-1 and thus are negligible in the present work.

The head-on collision leads to a van-der-Waals (vdW) complex

HC3–HC6H (I1) that readily rearranges to an intermediate HC3CHC5H (I6) through a loose transition structure TS2.

I6 can decompose directly to c-1HC3(C)C5H + H or rearrange to I3 or I10 18


Page 19 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


followed by the aforementioned decomposition processes. + 3HC5H are energetically inaccessible in the present work.

The asymptotes C2H + 3HC7H and C4H Since c-C3H is present in the primary

beam, its reaction with C6H2 needs also be taken into account.

The c-C3H + C6H2 reaction incurs

an entrance barrier TS4 of height 9.0 kcal mol-1 for formation of I7 that either decomposes directly to c-HC(C)C7H + H or rearranges to I3 followed by the aforementioned decomposition process. The latter process is more favorable than the former one because isomerization barriers TS6 and TS7 are 18.8 – 20.0 kcal mol-1 below the dissociation barrier TS12.

Owing to the existence of TS4,

the c-C3H + C6H2 reaction might have a cross section less than that of the l-C3H + C6H2 reaction. Overall, the l-C3H + C6H2 reaction is more significant than the c-C3H + C6H2 reaction and the products 3HC9H, c-1HC7(C)CH, and c-1HC3(C)C5H are energetically accessible in hydrogen-loss channels.

The difference in enthalpies of formation of these three lower-lying isomers of C9H2 is

within 3.4 kcal mol-1. Note that TS9 (TS13) lies above I8 (I9) at the level of B3LYP/aug-cc-pVDZ but becomes below I8 (I9) at the level of CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVDZ + ZPE(B3LYP/aug-cc-pVDZ).

19



Page 20 of 33

Figure 8. Potential-energy surface of the reaction l-C4H + HC6H → C10H2 + H. Stationary and transition structures are presented but H-atom products are omitted. energy is given in kcal mol-1.

Relative potential

Dash line represents collision energy 23.4 kcal mol-1.

Figure 8 presents the potential-energy surface of reaction l-C4H + HC6H.

HC6H has three

types of carbon atoms referred to as α, β, and γ from terminal to middle carbon atoms.

The

terminal carbon atom of l-C4H has an unpaired electron so that l-C4H can add to the α-, β-, and γ-carbon atom of HC6H to form complexes HC4CHC5H (I2), HC5(CH)C4H (I4), and HC5(C2H)C3H (I5), respectively, without any energy barriers.

I4 can rearrange to I2 through two transition

structures TS4 and TS2 separated by a cyclic intermediate c-HC4(CH)C5H (I3) or through a higher transition state TS3.

Besides, the head-on collision leads to a vdW complex HC4–HC6H (I1) that

readily rearranges to I2 through a loose transition structure TS1. 1

HC10H + H with a small exit barrier TS5.

Subsequently, I2 decomposes to

I5 needs overcome a large barrier TS6 to reach I4 or

passes through a lower barrier TS7 to reach a cyclic intermediate c-HC4(C3H)C3H (I6). 20


I5 can

Page 21 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


decompose directly to C2H + HC8H without an exit barrier, which is a thermodynamically preferred exit channel of I5.

In contrast, I5 and I6 need enthalpies, that are larger than the collision energy

23.4 kcal mol-1, to reach HC5(C2H)C3 + H and c-HC3(C4)C3H + H.

Besides, production of

c-HC5(C2)C3H + H, 3C5(C2H)C3H + H, C3H + 3HC7H, and C5H + 3HC5H need enthalpies much larger than the collision energy and thus can be ruled out.

Overall, 1HC10H is the exclusive

product in the C4H + C6H2 collision followed by hydrogen elimination.

4.6. Relative reaction cross sections.

The relative cross sections of reactions C3H + C6H2 →

C9H2 + H versus C4H + C6H2 → C10H2 + H can be evaluated from reactant and product ion signals. Reactants C3H and C4H (C6H2) were detected at Θ = 0° (90°) with ionizing photons at 12.5 eV.

As

presented in Figs. 3 and 4, products C9H2 and C10H2 were ionized with photons at 11.6 eV. Products’ TOF distributions and angular distributions are taken into account for counting total product ion signals.

Normalized to the same reactant ion signals, the reaction C3H + C6H2 →

C9H2 + H at Ec = 19.7 kcal mol-1 is about half the cross section of the reaction C4H + C6H2 → C10H2 + H at Ec = 23.4 kcal mol-1.

This behavior is attributed mainly to the following reasons.

The

C3H/H exchange reaction is nearly isoergic so that a portion of collision events go back to reactants. The barrier TS1 of height 6.4 kcal mol-1 hinders the addition of l-C3H to the middle C≡C bond of C6H2 to some extent.

Since c-C3H is less reactive than l-C3H based on the established

potential-energy surface, the abundance of c-C3H in the primary beam27 diminishes the average reactivity of total C3H reactants.

4.7. Angular momentum disposal based on the kinematic model.

There is a dispersion

potential Vdisp = –C6/R6 between C3H or C4H and C6H2 at a long distance R.

C6 is the

Lennard-Jones coefficient expressible in terms of polarizabilities and ionization energies of two colliding reactants.31,35

The classical capture theory 36 predicts that the C3H (C4H) + C6H2 21



Page 22 of 33

reaction under the present experimental condition has a maximal impact parameter bmax of 3.98 (4.21) Å and a maximal orbital angular momentum ℓmax of 399 (503) ħ based on ℓ = µ×b×Vrel. is the reduced mass of two colliding reactants.

µ

Parameter b has a random distribution in

crossed-beam experiments but has a maximal value bmax determined by reactant collision energy and centrifugal barrier.

Collision events with impact parameters larger than bmax are non-reactive.

The isotropic polarizabilities 5.45, 8.59, and 13.26 Å3 and the ionization energies 9.01, 10.07, and 9.47 eV are employed for l-C3H, l-C4H, and HC6H, respectively.

Rate coefficients are predicted

to be (4.1–7.3)×10-10 cm3 molecule-1 s-1 for the C3H + C6H2 reaction and (4.5–7.9)×10-10 cm3 molecule-1 s-1 for the C4H + C6H2 reaction in a temperature range 10–300 K.

Because of

ignorance of short-range interactions, the capture theory typically overestimates rate coefficients of bimolecular reactions particularly at high temperatures. Here, we evaluate rotational periods (Trot) of one or two complexes or intermediates dominant in each title reaction at the limiting case of ℓ = ℓmax.

If a reaction has a uniform opacity function,

i.e., constant P(b) at b ≤ bmax, its partial cross section will be proportional to b, i.e. to ℓ.

For the

C3H + C6H2 reaction, rotational periods of complex I3 (I10) that has ℓmax along its principal axes a, b, and c are calculated to be 0.2, 2.1, and 2.3 ps (0.1, 2.8, and 2.9 ps).

As for the C4H + C6H2

reaction, rotational periods of complex I2 that has ℓmax along its principal axes a, b, and c are calculated as 0.2, 2.8, and 3.0 ps.

Rotational periods of these complexes that have different ℓ

values can be readily calculated based on the relation of Trot ∝ ℓ-1.

On the basis of RRKM theory,

a reaction complex with a larger ℓ value (i.e., smaller vibrational energy) probably has a lifetime longer than that with a smaller ℓ value (i.e., larger vibrational energy) as total energy is conserved. Overall, a collision event of larger ℓ probably has a greater reactive cross section, a shorter rotational period, and a longer lifetime than that of a smaller ℓ event.

However, a

quantum-mechanics or quasi-classical-trajectory calculation is needed in order to understand the details of reaction dynamics. In a triatomic reaction A + BC (j) → AB (j’) + C, angular momenta obey J = ℓ + j = ℓ’+ j’. 22


Page 23 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The total angular momentum J is composed of reactant’s rotational angular momentum j and orbital angular momentum ℓ or is disposed into product’s rotational angular momentum j’ and orbital angular momentum ℓ’.

In a crossed molecular-beam experiment, j is near zero due to

supersonic expansion so that the angular-momentum equation can be approximated as J = ℓ = ℓ’+ j’.

The kinematic model36,37 indicates that J is disposed to ℓ’and j’ in accordance with j’ = ℓ –

(ℓ–d)cos2β and ℓ’ = (ℓ–d)cos2β; d is a dynamics-related angular momentum and cos2β is a mass factor expressible as MAMC/(MAB+MBC).

On the assumption of a triatomic reaction system, the

mass factor is as small as 0.0045 for the reaction C3H + C6H2 → C9H2 + H and 0.0054 for the reaction C4H + C6H2 → C10H2 + H.

ℓ’ is mere 2 – 3 ħ as the angular momentum ℓ–d equals ℓmax.

Product’s angular distribution is nearly isotropic as ℓ’ approaches zero. Besides, product’s recoil direction with respect to J also determines product’s angular distribution as ℓ’ is not zero.

Based

on the transition structures TS14 in the C3H + C6H2 reaction and TS5 in the C4H + C6H2 reaction, the leaving hydrogen atom is recoiled to a direction nearly parallel with the principal axis b, i.e., nearly perpendicular to principal axes a and c.

Therefore, the b-type rotation with Jb ≈ J will

scatter products preferentially into the sideway direction and the a-type (Ja ≈ J) and c-type (Jc ≈ J) rotations will scatter products preferentially into the forward and backward directions if the reaction complex has a lifetime longer than its rotational period.

In other words, the projections

of J on three principal axes determine product’s angular distribution.

Type-a rotation has a much

smaller moment of inertia and thus needs much more rotational energy than that of b-/c-type rotation particularly as the reaction approaches the exit transition state where the structure is nearly prolate.

Therefore, a-type rotation is much less favorable than b- and c-type rotations in the two

title reactions.

Since type-b and type-c rotations are nearly degenerate, product’s angular

distribution will be nearly isotropic if the conversion between Jb and Jc is free before decomposition.

23



Page 24 of 33

4.8. Other possible reactions producing C9H2 and C10H2. As mentioned earlier, the reactions C3 + C6H3 and C3H2 + C6H are predicted to have ~ 5% and ~ 4% contributions to product C9H2 + H as well as the reactions C4 + C6H3 and C4H2 + C6H are predicted to have ~ 2% and ~ 12% contributions to product C10H2 + H based on reactant concentrations.

Below, we address

some possible mechanisms for these minor reactions and the competition between hydrogen abstraction and hydrogen elimination in product channels. C6H3 has three lower-lying isomers – a linear isomer H2C6H and two six-membered carbon-ring isomers – with energy differences within 2.1 kcal mol-1.29 molecule, is the most stable isomer of C6H6.

Benzene, an aromatic

However, benzene is a minor species of C6H6

isomers synthesized in the secondary beam by a comparison of PIE spectra between C6H6 and benzene.

It is rationalized by the rapid supersonic expansion following electric discharge.

Analogously, the yield of six-member-ring isomers of C6H3 is predicted to be negligibly small. Since HC6H and H atoms are quite rich in the secondary beam, the HC6H + H association that has a barrier of height mere 2.0 kcal mol-1 stabilized by expansion.

29

is suggested to be responsible for synthesis of H2C6H

The reaction l-1C3 + 2H2C6H → 2C9H3 → 3HC9H + H (∆H = -32.9 kcal

mol-1) needs multiple hydrogen migrations following addition of C3 to 2H2C6H or needs insertion of C3 into the carbon skeleton of H2C6H before leading to 3HC9H + H.

As illustrated in Fig. 7,

several C9H3 intermediates are predicted to decompose to C3H + C6H2 in addition to C9H2 + H based on energetics.

The reaction l-1C3 + 2H2C6H → 1H2C9 + H (∆H = -11.5 kcal mol-1) is a direct

addition-decomposition process by C3/H exchange but the product is 1H2C9 rather than 3HC9H. The reaction l-1C3 + 2H2C6H → l-2C3H + HC6H (∆H = -30.7 kcal mol-1) via a direct hydrogen abstraction may compete severely with the aforementioned mechanisms leading to C9H2 + H. Triplet state l-3C3 lying above l-1C3 by 48.7 kcal mol-1 is mere 3% of the yield of l-1C3 in the primary beam38 so that the l-3C3 + 2H2C6H reaction is negligible here. C4 has two lower-lying isomers, rhombic (r-) 1C4 and linear (l-) 3C4, in energetics.

Because

l-3C4 lies mere 0.9 kcal mol-1 above r-1C4, both C4 isomers are possibly synthesized simultaneously 24


Page 25 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


in the primary beam. The reaction l-3C4 (r-1C4) + 2H2C6H → 2C10H3 → 1HC10H + H has an enthalpy of -96.0 (-95.1) kcal mol-1 but needs multiple hydrogen transfers following addition of C4 to H2C6H or needs insertion of C4 into the carbon skeleton of H2C6H for production of 1HC10H + H. Moreover, the complex of reaction r-1C4 + 2H2C6H requires an additional step of C4 ring disclosure before leading to 1HC10H + H.

As illustrated in Fig. 8, several C10H3 intermediates are predicted

to decompose to C2H + C8H2, C4H + C6H2, or products other than C10H2 + H due to their abundant internal energy (e.g., ~ 154 kcal mol-1 in I2 including Ec).

The reaction l-3C4 + 2H2C6H → 1H2C10

+ H is a direct addition-decomposition process (i.e., C4/H exchange) with an enthalpy of -40.0 kcal mol-1 but the corresponding product is 1H2C10 rather than 1HC10H. 2

The reactions l-3C4 / r-1C4 +

H2C6H → l-2C4H / c-2C4H + 1HC6H (∆H = -67.2 / -28.7 kcal mol-1) undergo a mechanism of direct

hydrogen abstraction and may compete violently with those aforementioned mechanisms leading to C10H2 + H. C3H2 has two lower-lying isomers c-1HC(C)CH (or designated as c-1C3H2) and 3HC3H in energetics.

It is known that the CH + C2H2 reaction can produce c-1C3H2 and 3HC3H with ejection

of a hydrogen atom.24,27 the primary beam.

Thus, that reaction is suggested to be responsible for synthesis of C3H2 in

Because c-1C3H2 is 11.4 kcal mol-1 more stable than 3HC3H, c-1C3H2 is

expected to be more abundant than 3HC3H after supersonic expansion.

The reaction c-1C3H2

(3HC3H) + 2C6H → c-2HC7(CH)CH (2HC3HC6H) → c-1HC7(C)CH (3HC9H) + H undergoes a direct addition-decomposition process with an enthalpy of -28.6 (-42.0) kcal mol-1 that is 29.8 (39.8) kcal mol-1 more exothermic than the title reaction c-C3H (l-C3H) + HC6H → c-1HC7(C)CH (3HC9H) + H. Compared with those minor reactions mentioned above, the C4H2 + C6H reaction is more significant due to higher reactant abundance. 1

Fortunately, the reaction 1HC4H + 2C6H → 2HC4HC6H →

HC10H + H (∆H = -28.6 kcal mol-1) undergoes an addition-decomposition mechanism similar to

that of the title reaction 2C4H + 1HC6H → 2HC4HC6H → 1HC10H + H (∆H = -28.8 kcal mol-1). Moreover, they have almost the same reaction enthalpy, reactant collision energy, and CM angles. 25



Page 26 of 33

Therefore, the influence of reaction 1HC4H + 2C6H on the study of reaction 2C4H + 1HC6H should not be prominent due to the resemblance in energetics and in reaction mechanisms.

4.9. Implications on planetary atmospheres, interstellar space, and combustion.

There is

a fractional abundance of 5.5×10-6 for C2H2 and 2.0×10-9 for C4H2 in Titan’s atmosphere that contains ~ 98% N2, 1.8% CH4, and 0.11% H2.39 reaction of C2H with C2H2.

Formation of C4H2 is attributed mainly to the

In contrast, radicals CmH (m ≥ 1) have yet been detected in Titan’s

atmosphere owing to their high reactivity and the dense atmosphere with a surface pressure of 1.5 bar.

Nonetheless, It is believed that C2H and C4H are producible from C2H2 and C4H2 by solar

UV-light photolysis,14,15,16,17 which might drive formation of larger polyynes on Titan.

The mole

fractions of C6H2 and C8H2 were derived to be 8.0×10-7 and 2.0×10-7, respectively, by ion chemistry fitting to the ion mass spectrum measured in Titan’s atmosphere.40

The reactions C2H

+ C4H2 and C4H + C2H2 were considered as the sources of C6H2 as well as the reactions C2H + C6H2, C4H + C4H2, and C6H + C2H2 were considered as the sources of C8H2 in modeling the chemistry of Titan’s atmosphere.41

Analogously, the C4H + C6H2 reaction is suggested to be a

source for formation of C10H2 albeit not detected yet on Titan. The column density was determined as 2.0×1015 cm-2 for C2H, 1.2×1015 cm-2 for C4H, 2×1017 cm-2 for C2H2, 1.2×1017 cm-2 for C4H2, and 6×1016 cm-2 for C6H2 in the line of sight toward CRL 618 that has a thick molecular envelope surrounding a B0 star.42

Besides, C3H and C4H were

found to have mole fractions 0.08 and 0.04 times that of C2H in CRL 618.43

The strong UV light

(~ 3×106 photons s-1) coming from the hot central star results in high abundances of polyynes and polyynic radicals in the molecular envelope.

The existences of C3H, C4H, and C6H2 suggest that

the reactions C3H + C6H2 and C4H + C6H2 take place in the circumstellar envelope of CRL 618. Polyynes have yet been found in molecular cloud TMC-1 and in the circumstellar envelope of IRC+10216.

Nevertheless, the existences of C2nH (n = 1 – 4) and C2H2 in IRC+10216 give an 26


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important implication for formation of C2n+2H2 in IRC+10216 via barrier-less reactions (2). Similar to the relation between reactions (1) and (2),26,27 reactions (4) are typically exothermic but reactions (3) are nearly isoergic for n ≥ 2.

Accordingly, reactions (4) are suggested to be more

significant than reactions (3) at low temperatures. CmH are highly reactive radicals and thus unable to accumulate their concentrations up to a high level in flames.

Nonetheless, the findings of C2H2, C4H2, C6H2, C8H2, and C10H2 in fuel-rich

flames of allene, propyne, and cyclopentene3 strongly imply occurrence of reactions (2) and (4) in those flames. C2n+1H2 are open-shell species and able to react with other species, that accounts for their low concentrations in combustion.

Furthermore, species CmH and CmH2 (m ≤ 8) can be

synthesized in pulsed beams of 1% and 5% C2H2/He by discharge.

As illustrated in Fig. 1, the

yield ratio of CmH2 to CmH increases as C2H2 concentration increases from 1% to 5%.

Moreover,

the amount of C6H2 in the 5% mixture is 3.8 times more than that in the 1% mixture.

This

behavior indicates that reactions (1) – (4) take place vigorously even in a diluted C2H2 mixture initiated by discharge.

5. CONCLUSIONS It is challenging to synthesize reactants C3H, C4H, and C6H2 at a high level of concentration but suppress other species to a low level of concentration for crossed-beam experiments.

In the

current work, we employ a pulsed-discharge molecular-beam technique and a mixture of 1% or 5% C2H2/He as a precursor to make the experiments successful. We investigated the dynamics of reactions of C3H and C4H radicals with C6H2 in crossed molecular beams using synchrotron VUV photoionization.

Products C9H2 and C10H2 were interrogated by measuring their TOF spectra,

angular distributions, and PIE spectra.

The combination of product translational-energy

distributions and PIE spectra accounts for production of 3HC9H/c-1HC3(C)C5H/c-1HC7(C)CH in the C3H + C6H2 reaction and 1HC10H in the C4H + C6H2 reaction.

Due to similarity in enthalpy of

the three isomers of C9H2, their branching ratios remain ambiguous. 27


The C3H + C6H2 reaction is


Page 28 of 33

half the cross section of the C4H + C6H2 reaction in the current experimental condition. Analogous to a heavy-heavy-light reaction, the kinematic model can qualitatively interpret the less anisotropic angular distribution of products.

The quantum-chemical calculations indicate that

l-C3H adds to a terminal C≡C bond of HC6H to form complex c-HC3(CH)C5H that either decomposes to c-HC3(C)C5H + H or rearranges to HC3CHC5H followed by decomposition to 3

HC9H + H.

The addition of l-C3H to the middle C≡C bond of HC6H forms complex

HC3(C3H)C3H that undergoes hydrogen ejection with a large enthalpy.

In contrast, l-C4H adds to

the α carbon of HC6H to form complex HC4CHC5H that directly decomposes to HC10H + H. l-C4H can also add to the β carbon of HC6H to form complex HC4(CH)C5H that rearranges to HC4CHC5H followed by decomposition to HC10H + H.

The addition of l-C4H to the γ carbon of

HC6H forms complex HC4(HC2)C4H that favors dissociation to C2H + HC8H thermodynamically. Besides, some minor reactions that possibly produce C9H2 and C10H2 are stated.

This work

demonstrates that C3H and C4H can react with hexatriyne to produce larger carbon-chain molecules and gives valuable implications to atmospheric, astronomical, and combustion chemistry.

In

conjunction with previous works on the CmH (m = 1 – 8) + C2H2 reactions, this type of reactions can be extended to CmH + C2x+2H2 → Cm+2x+2H2 + H.

ACKNOWLEDGEMENTS The National Synchrotron Radiation Research Center (NSRRC) and the Ministry of Science and Technology (MOST) of Taiwan (Grant Nos. MOST 103-2113-M-213-003-MY3 & MOST 106-2113-M-213-004) supported this work.

Y.L.S. gratefully thanks the financial support (Grant

Nos. MOST 106-2811-M-213-002 & MOST 106-2811-M-213-007) for his postdoctoral fellowship.

28


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Table of Contents Graphic:

C9H2 / C10H2

C3H C4H C6H2 C3H / C4H + C6H2 → C9H2 / C10H2 + H

A schematic representation of the velocity-distribution contour of C9H2 (C10H2) produced from the reaction of C3H (C4H) with C6H2.

33


Formation of C9H2 and C10H2 from Reactions C3H + C6H2 and C4H

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