Exploring the Dynamics of Reaction C(3P) + C2H4 with Crossed

Jul 2, 2012 - ... bimolecular reaction dynamics using pulsed high-intensity vacuum-ultraviolet lasers for photoionization detection. Daniel R. Albert ...
1 downloads 0 Views 2MB Size
Download PDF
Article pubs.acs.org/JPCA

Exploring the Dynamics of Reaction C(3P) + C2H4 with Crossed Beam/ Photoionization Experiments and Quantum Chemical Calculations Chih-Hao Chin, Wei-Kan Chen, Wen-Jian Huang, Yi-Cheng Lin, and Shih-Huang Lee* National Synchrotron Radiation Research Center (NSRRC), 101 Hsin-Ann Road, Hsinchu Science Park, Hsinchu 30076, Taiwan ABSTRACT: We investigated the title reaction at collision energy 3.5 kcal mol−1 in a crossed molecular beam apparatus using undulator radiation as an ionization source. Time-of-flight (TOF) spectra of product C3H3 were measured in laboratory angles from 20° to 100° using two photoionization energies 9.5 and 11.6 eV. These two sets of experimental data exhibit almost the same TOF distributions and laboratory angular distributions. From the best simulation, seven anglespecific kinetic-energy distributions and a nearly isotropic angular distribution are derived for product channel C3H3 + H that has an average kinetic-energy release of 15.5 kcal mol−1, corresponding to an average internal energy of 33.3 kcal mol−1 in C3H3. Furthermore, TOF spectra of product C3H3 were measured at laboratory angle 52° with ionizing photon energies from 7 to 12 eV. The appearance of TOF spectra remains almost the same, indicating that a species exclusively contributes to product C3H3; the species is identified as H2CCCH (propargyl) based on the ionization energy of 8.6 ± 0.2 eV and the maximal kinetic-energy release of 49 kcal mol−1. Theoretical calculations indicate that the rapid inversion mechanism and rotation in intermediate H2CCCH2 can result in a forward−backward symmetric angular distribution for product C3H3 + H. The present work avoids the interference of reactions of C(1D) and C2 radicals with C2H4 and rules out the probability of production of other isomers like c-C3H3 and H3CCC proposed in the previous work at least at the investigated collision energy. H2CCCH + H with an isotropic angular distribution to fit the spectra. Kaiser and co-workers10 investigated reactions of C(3P) + C2H4 at Ec = 4.1 and 9.2 kcal mol−1 in a pulsed crossed molecular beam apparatus with a C-atom source by laser ablation of graphite. The authors stated that the carbon source contained exclusive 3P carbon atoms at a slow velocity segment,11 both 3P and 1D at a medium segment,12 and exclusive 1D at a fast segment13 based on some crossed beam experiments; the carbon-atom beam, however, was not characterized with a spectroscopic technique. Reaction product C3H3 was detected using time-of-flight (TOF) spectroscopy and electron-impact ionization. C3H3 had a forward-biased angular distribution at both collision energies, which was attributed to two microchannel reaction mechanisms with a strong and a weak correlation, respectively, between initial and final orbital angular momenta.10 The strong-correlation case resulted in a forward-preferred angular distribution, whereas the weak-correlation case resulted in an isotropic angular distribution. Later, Kaiser and co-workers investigated a reaction of C(1D) + C2H4 at Ec = 24.9 kcal mol−1 using the same experimental approach;14 the forward highly peaking angular distribution of C3H3 suggested that the reaction proceeded via stripping dynamics.

1. INTRODUCTION Carbon chemistry plays an important role in the formation of a variety of hydrocarbons in combustion1 and in carbon-rich interstellar and planetary environments.2 Although C3H3 is hitherto unobservable in the interstellar space,3 the reaction of carbon atoms with ethene (C2H4) is suggestive of a key mechanism for the formation of C3H3 as in a hydrocarbon flame.4 The recombination of two C3H3 radicals is postulated to form C6H6 isomers that are believed to be precursors for the synthesis of polycyclic aromatic hydrocarbons (PAHs) and soot.5 The rate coefficient of reaction C(3P) + C2H4 decreases monotonically with increasing temperature from 3.82 × 10−10 cm3 molecule−1 s−1 at 15 K to 3.1 × 10−10 cm3 molecule−1 s−1 at 295 K.6 The rate coefficient was determined also as 2.1 ± 0.4 × 10−10 cm3 molecule−1 s−1 at room temperature, and the absolute branching ratio of atomic hydrogen production was estimated to be 0.92 ± 0.04.7 Costes and co-workers8 measured an excitation function for the reaction C(3P) + C2H4 → C3H3 + H in the collision-energy (Ec) range of 0.12−6.0 kcal mol−1 by interrogating hydrogen atoms. The integral cross section decreases with the increase of collision energy, which coincides with the kinetic results6 and characteristic for a reaction process without any entrance barrier. Later, Costes and co-workers9 investigated the dynamics of the reaction C(3P) + C2H4 at Ec = 0.17 and 1.3 kcal mol−1 using H-atom Doppler spectroscopy; the authors employed a single reaction path leading to © 2012 American Chemical Society

Received: May 16, 2012 Revised: June 27, 2012 Published: July 2, 2012 7615

dx.doi.org/10.1021/jp304756t | J. Phys. Chem. A 2012, 116, 7615−7622

The Journal of Physical Chemistry A

Article

Casavecchia and co-workers8,15 investigated the reaction of C(3P) + C2H4 at Ec = 2.2, 4.1, and 7.4 kcal mol−1 using a crossed molecular beam apparatus similar to that of Kaiser et al. except employing continuous molecular beams and radiofrequency discharge for the production of carbon atoms from CO2. The authors introduced two additional product channels, c-C3H3 + H and H3CCC + H notably the former, to simulation of TOF spectra and laboratory angular distributions of product C3H3 because these angular and TOF distributions could not be fitted satisfactorily with a sole product channel H2CCCH + H; here, c-C3H3 includes cyclic isomers c-(CH)3 and cH2C(C)H. The best simulation gave a forward-biased angular distribution for channel H2CCCH + H and an isotropic angular distribution for channels c-C3H3 + H and H3CCC + H. It was concluded that, at Ec = 2.2 kcal mol−1, formation of less stable C3H3 isomers is minor (2%) and that this fraction was derived to increase with increasing Ec: from 0.02 ± 0.01 at Ec = 2.2 kcal mol−1 to 0.05 ± 0.02 at Ec = 4.1 kcal mol−1 and to 0.14 ± 0.04 at Ec = 7.4 kcal mol−1. This trend coincided with the integral cross-section measurements as a function of Ec of Costes and co-workers.8 Casavecchia and co-workers additionally employed the C(1D) + C2H4 reaction to fit the TOF spectra of C3H3 produced at a higher collision energy of 9.0 kcal mol−1;16 the authors suggested that this behavior might be due to an enhancement of the cross-section for the C(1D) reaction relative to the decreasing C(3P) one with increasing Ec. Mebel and co-workers17 calculated the triplet potentialenergy surface of the C(3P) + C2H4 reaction using the G2M method. The results indicated that, at the initial step, the C(3P) atom attacked the π-orbital of C2H4 to yield a triplet complex cyclopropylidene (c-H2C(C)CH2) without any entrance barrier. Subsequently, cyclopropylidene rearranged to allene (H2CCCH2) via ring-opening. At exit channels, allene either directly decomposed to H2CCCH + H or underwent hydrogen migration to form vinylmethylene (H2CCHCH) followed by decomposition to H2CCCH + H. The authors calculated product branching ratios using the Rice−Ramsperger−Kassel− Marcus (RRKM) theory for Ec ≤ 9.2 kcal mol−1. The results indicated that the H2CCCH + H channels occupied ca. 98− 99%, and the production of CH2 + C2H2 from vinylmethylene occupied ca. 1−2%. Other product channels, such as c-C3H3 + H and H3CCC + H, had negligibly small branching ratios. C2(X1∑+g /a3Πu) radicals existed more or less in carbon-atom sources produced by laser ablation of graphite and by discharge of CO2 in the previous experiments.8,10 The reaction C2 + C2H4 → C4H3 + H was investigated in crossed molecular beams by Kaiser et al.18 The dissociation of C4H3 to C3H3+, C3H2+, C3H+, and C3+ occurred following electron-impact ionization; the daughter ion C3H3+ from reaction C2 + C2H4 was faster than product C3H3 from reaction C + C2H4, but no clear feature is able to distinguish both components.19 The C2 reaction had a center-of-mass (CM) angle (ΘCM) smaller than that of the C reaction, which might mislead to a forward-biased angular distribution for product C3H3. Merits of selective photoionization have been demonstrated in our previous experiments on unimolecular photodissociation20,21 and bimolecular reactions;22,23 the major advantage is relatively small dissociative ionization compared with electronimpact ionization. To solve the problems of interference of reactions of C(1D) and C2(X1∑+g /a3Πu) radicals with C2H4, we investigated the C(3P) + C2H4 reaction in crossed beams using an exclusive 3P carbon-atom source and an energy-tunable photoionization source. No evidence was found for the

production of c-(CH) 3 /c-H 2 C(C)H/H 3 CCC + H but H2CCCH + H in the present work.

2. EXPERIMENTAL SECTION The experimental apparatus and procedure have been detailed elsewhere;22,23 thus, only a brief description is given here. The crossed molecular beam apparatus comprises a main (or reaction) chamber equipped with two source chambers and a detection chamber equipped with a quadrupole mass filter and a Daly detector. Source chamber #1 was equipped with an Even−Lavie valve and a discharge device24 to generate a pulsed carbon-atom beam from a mixture of 10% CO seeded in He with a stagnation pressure of 105 psi; C-atom pulses had a mean velocity of 1620 m s−1. Source chamber #2 was equipped with an Even−Lavie valve heated to 110 °C to generate a pulsed molecular beam of neat ethene (C2H4) with a backing pressure of 55 psi; C2H4 had a most probable velocity of 940 m s−1. The C-atom beam intercepted the C2H4 beam at 90° in the reaction chamber, giving a collision energy of 3.5 kcal mol−1. The source-chamber assembly was rotatable with respect to the detector for the purpose of detection at various laboratory angles Θ defined as the angle between the C-atom beam and the detector. Reaction products flying along a path of length 100.5 mm became ionized with synchrotron radiation from an undulator. Because only the radiation with fundamental frequency was desired in the present work, a windowless gas cell filled with 10 Torr noble gas was employed to absorb most of the photons with high harmonic frequencies. Downstream was an additional optical filter of MgF2 (2 mm thick) employed to effectively absorb remnant high-harmonic photons when the desired photon energy was below 10 eV. The filtered undulator radiation with a flux of ∼1 × 1016 photons s−1 and an energy resolution of ∼4% (at full width at half-maximum (fwhm)) was focused into a size of ∼1 mm2 in the ionization region. Ion optics extracted product cations into a quadrupole mass filter to select the desired product cations with a mass-to-charge ratio (m/z). A Daly detector counted the selected ions and a multichannel scaler sampled ion signals into 4000 bins of width 1 μs. Experimental components were synchronized with pulse generators operating at 200 Hz. After subtracting a flight interval of ions from the total flight duration, a TOF spectrum of a neutral product can be obtained. Two experimental modes were performed for measurements of photoionization spectra of reactants and products at a fixed laboratory angle and for the detection of TOF spectra of products at 16 laboratory angles. To characterize the carbonatom (ethene) beam, source chamber #1 was set at Θ = 0° (90°) and a small aperture was employed as an entrance into the ionization region to avoid signal saturation. For the measurement of photoionization spectra, the ionizing photon energy was scanned back to back on adjusting the gap of the undulator; a TOF spectrum was recorded at each photon energy. In the same manner, the photoionization spectrum of reaction product C3H3 was recorded at Θ = 52° with a large entrance aperture of diameter 5 mm. For the measurement of laboratory angular distribution of product C3H3, TOF spectra thereof were recorded back to back at sixteen laboratory angles from 20° to 100°. 3. RESULTS AND DISCUSSION We measured the photoionization spectrum of carbon reactants, as shown in Figure 1, to characterize if C(1D) 7616

dx.doi.org/10.1021/jp304756t | J. Phys. Chem. A 2012, 116, 7615−7622

The Journal of Physical Chemistry A

Article

Figure 1. Photoionization spectrum of atomic carbon reactants. The ionizing photon energy was scanned back to back with a step increment of ∼0.2 eV. No correction was made for a small variation of photon flux with photon energy. Arrows indicate the ionization thresholds for 3P and 1D carbon atoms.

Figure 2. Newton diagram and two-dimensional product velocity map for the reaction C(3P) + C2H4 → C3H3 + H. Dashed lines denote the detection axes at laboratory angles 20−100°.

atoms exist in the atomic carbon beam. Excited state 1D of carbon atoms lies 1.263 eV above the ground state 3P; thus, C(1D) is suggested to have an ionization threshold below that of C(3P). Figure 1 indicates that carbon atoms have an ionization threshold near 11.26 eV that is the ionization energy of C(3P);25 below this value, the ion signal is negligibly small, indicative of a little amount of carbon atoms on the state 1D. C(1D) atoms are suggested to be quenched mainly by CO molecules. Ion signals of C(1D) atoms, albeit small, became observable when a 3% (or more dilute) mixture of CO/He was employed as a discharge medium.26 The title reaction produced C3H3 + H, but only C3H3 was detected in the present work; H atoms were too elusive to detect. Although the channel CH2 + C2H2 was predicted to have a branching ratio of 1−2% with RRKM calculations,17 the detections at m/z = 14 and 26 suffer from interference of reaction O + C2H4 → CH2 + H2CO and dissociative ionization of reactant ethene, respectively. On the basis of previous ab initio calculations,17 four energetically accessible product channels for elimination of a hydrogen atom are listed as follows. C(3P) + C2H4 → H 2CCCH + H ΔH ° = −45.3 kcal mol−1

Figure 3. Photoionization spectrum (red) and TOF spectra of product C3H3 recorded at m/z = 39 and Θ = 52°. The photoionization spectrum was uncorrected for a small variation of photon flux with photon energy. Arrow indicates the literature-reported ionization energy 8.67 eV of propargyl (H2CCCH) radicals. Lower panels present four TOF spectra of C3H3 recorded at four photoionization energies (red solid line); the spectra are normalized to the same height. The lower right panel presents also a TOF spectrum of C3H3 recorded at 15 eV (black dashed line) for comparison. A photoionization spectrum (blue) of propargyl radicals produced from the pyrolysis of propargyl bromide at 1200 °C is shown in the top panel for comparison.

(1)

C(3P) + C2H4 → c ‐( CH)3 + H ΔH ° = −13.6 kcal mol−1

(2)

C(3P) + C2H4 → c ‐H 2C(C)CH + H ΔH ° = −5.0 kcal mol−1 3

C( P) + C2H4 → H3CCC + H

(3)

ΔH ° = −0.8 kcal mol−1 (4)

in which ΔH° denotes reaction enthalpy computed at 0 K. Available energy (Eava) of a reaction can be calculated based on Eava = Ec − ΔH°. Figure 2 exhibits a Newton diagram associated with a twodimensional velocity map for product C3H3. The reaction system had a center of mass (CM) traveling along a direction of Θ = 53.6°, hereafter referred to as ΘCM. We measured TOF spectra of C3H3 at m/z = 39 and Θ = 52° using ionizing photon energy from 7 to 12 eV with a step increment ∼0.2 eV. The upper and lower panels of Figure 3 present the photoionization spectrum and four corresponding TOF spectra of C3H3,

separately; an additional TOF spectrum of C3H3 recorded with photoionization energy 15 eV is presented in the lower right panel for comparison. The bandwidth (∼4% at fwhm) of the undulator radiation results in a red shift of the ionization threshold; similar behavior is observable in Figure 1. After deconvolution, the ionization energy of product C3H3 was determined to be 8.6 ± 0.2 eV in good agreement with the literature value 8.67 ± 0.02 eV of propargyl (2-propynyl, H2CCCH) radicals.27 H2CCCCH (1-buten-3-yn-2-yl) produced from the reaction C2 + C2H4 was observable at m/z = 51 but not shown here. H2CCCCH is calculated to have a 7617

dx.doi.org/10.1021/jp304756t | J. Phys. Chem. A 2012, 116, 7615−7622

The Journal of Physical Chemistry A

Article

Figure 4. Angle-specific TOF spectra of product C3H3 recorded at m/z = 39 with photoionization energies 9.5 and 11.6 eV, separately. Open circles denote the experimental data and solid curves denote the simulations using the center-of-mass kinetic energy and angular distributions shown in Figure 6. Each panel shows the corresponding laboratory angle Θ.

threshold of 14.36 eV for dissociative ionization to C3H3+ + C based on the enthalpy 5.69 eV of reaction H2CCCCH → H2CCCH + C28 and the ionization energy 8.67 ± 0.02 eV of H2CCCH.27 Thus, the dissociative ionization H2CCCCH → C3H3+ + C can be suppressed using single-photon ionization with energy below 12 eV. In contrast, dissociative ionization occurred with electron-impact ionization in the previous work.19 Ionization energies (IE) of isomers c-(CH)3 (cycloprop-2enyl) and H3CCC (1-propynyl) were calculated to be 6.10 and 13.1 eV, respectively;29 c-(CH)3 has an experimental IE value of 6.6 eV.30 Because the cation of c-H2C(C)CH (cycloprop-1enyl) was not located at the level of B3LYP/6-311G(d,p), here we calculated the vertical ionization energy 9.13 eV for this species using the method CCSD(T)/6-311+G(3df,2p)// B3LYP/6-311G(d,p) + ZPE[B3LYP/6-311G(d,p)]. Figure 3 indicates that no signal is observable below 8.3 eV. Since reactions 2, 3, and 4 have available energy, much less than that

of reaction 1 as well as c-(CH)3, c-H2C(C)CH, and H3CCC have ionization energies different from that of H2CCCH, the TOF distribution of C3H3 should vary with photoionization energy if c-(CH)3, c-H2C(C)CH, and H3CCC were produced. The TOF spectra of C3H3, as shown in the lower panels of Figure 3, are insensitive to photoionization energy even up to 15 eV, implying that yields of isomers c-(CH)3, c-H2C(C)CH, and H3CCC are negligibly small. Reaction 4 can be ruled out in the present work because there are transition structures lying 3.8−4.0 kcal mol−1 above reactant C(3P) + C2H4 en route to H3CCC + H.17 To confirm only single species H2CCCH was produced in the title reaction, we measured the photoionization spectrum of H2CCCH radicals produced from propargyl bromide (H2CCCHBr) by pyrolysis at 1200 °C; as shown in the top panel of Figure 3, the spectrum is in good agreement with that of C3H3 produced from the title reaction. Shown in Figure 4 are TOF spectra of C3H3 recorded at 16 laboratory angles from 20° to 100° using two photoionization 7618

dx.doi.org/10.1021/jp304756t | J. Phys. Chem. A 2012, 116, 7615−7622

The Journal of Physical Chemistry A

Article

H2CCCH + H. The kinetic energy release, weakly correlated with scattering angles, has maximal probability near 10 kcal mol−1 and extends to the energetic limit of reaction 1. The P(θ) curve is nearly flat, indicative of a nearly isotropic angular distribution for product C3H3. The present angular distribution differs from the previous ones;8,10 the discrepancy is probably due to the interference of reactions of C(1D) and C2(X1∑+g / a3Πu) radicals with C2H4 and/or due to a large error bar in the previous experiments. Table 1 lists the available energies of

energies 9.5 and 11.6 eV. These two sets of experimental data are almost identical except in magnitude. The corresponding laboratory angular distributions of product C3H3 recorded with photoionization energies 9.5 and 11.6 eV are presented in Figure 5; maxima of both curves are normalized to 10 for

Table 1. Available Energies (Eava) of Four Product Channels and Calculated and Experimental Ionization Energies (IE) of Four Isomers of C3H3 product

Eava (kcal mol−1)

calcd IE (eV)

exptl IE (eV)

H2CCCH + H c-(CH)3 + H c-H2C(C)CH + H H3CCC + H

48.8 17.1 8.5 4.3

8.67a 6.10a 9.13d 13.1a

8.67b 6.60c N/A N/A

a Reference 29. bReference 27. cReference 30. dVertical IE calculated in this work.

Figure 5. Laboratory angular distribution of product C3H3 from the reaction C(3P) + C2H4. Red and blue circles represent integral ion signals of C3H3 recorded with photoionization energies 9.5 and 11.6 eV, respectively. Both distributions are normalized to the same height. ΘCM denotes the laboratory angle 53.6° of the center of mass of the reaction system C(3P) + C2H4.

reactions 1−4 and the ionization energies of four isomers of C3H3. We obtained average kinetic energy release ⟨Et⟩ = 15.5 kcal mol−1 and a fraction f t = 0.32 of available energy in translation for reaction 1 based on ⟨Et⟩ = ∫ ∫ EtP(Et;θ)dEtd(cos θ)/∫ ∫ P(Et;θ)dEtd(cos θ) and f t = ⟨Et⟩/Eava. Since atomic hydrogen fragment carries no internal energy, the distribution of internal energy (Eint) of product C3H3 is derivable based on P(Eint) = P(Eava − Et). Thus, H2CCCH has a most-probable internal energy of ∼39 kcal mol−1 and an average internal energy of 33.3 kcal mol−1. Figure 7 depicts the potential energy surface of the reaction C(3P) + C2H4 → H2CCCH + H calculated with the method of CCSD(T)/6-311+G(3df,2p)//B3LYP/6-311G(d,p) + ZPE[B3LYP/6-311G(d,p)]. Molecular structures were optimized with a density functional method B3LYP and a basis set 6311G(d,p). Total energies were calculated with a couple-cluster method CCSD(T) and a basis set 6-311+G(3df,2p) including the correction of zero-point energy (ZPE) calculated at the level of B3LYP/6-311G(d,p). At the entrance channel, the C(3P) atom adds to the CC π-bond of C2H4 to form a cyclic complex c-H2C(C)CH2 (i1) that readily opens the ring to form intermediate H2CCCH2 (i2). i2 rapidly inverses to its stereoisomer i3 via the CCC bending; the corresponding inversion barrier height is merely 4.9 kcal mol−1. H2CCCH2 has symmetry of C2v and thus has two types of hydrogen atoms with distinct chemical characteristics, hereafter referred to as a and b characters. As labeled on i2 and i3 structures in Figure 7, the two H atoms located on the opposite and same sides as the central carbon atom in H2CCCH2 have a and b characters, respectively. After inversion between i2 and i3, the two types of hydrogen atoms exchange their chemical characters; a → b and b → a. The rupture of bond C−Ha has a transition structure leading to product H2CCCH + H, whereas the rupture of bond C−Hb has no transition structure optimized. Furthermore, the b-type H atoms of i2 and i3 can migrate to the central carbon atom to form intermediate H2CCHCH (i4 and i5) that subsequently decomposes to H2CCCH + H. We calculated rate coefficients of individual reaction steps and relative branching ratios for the aforementioned microchannels leading to product H2CCCH + H by RRKM theory with Ec = 0 and 4 kcal mol−1; the results are summarized in Tables 2 and 3. The inversion

comparison. The laboratory angular distributions appear to be symmetric with respect to ΘCM. The agreements between two experimental data sets in TOF distributions and laboratory angular distributions also indicate that reaction 1 overwhelmingly prevails over other reaction pathways. We simulated the TOF spectra using forward convolution. From the best simulation shown in Figure 4, angle-specific kinetic energy distributions P(Et; θ) at seven θ values and the angular distribution P(θ) in the CM frame are derivable. Et is kinetic energy including momentum-matched products C3H3 and H. θ is defined as a scattering angle of product C3H3 with respect to the incidence direction of carbon reactants in the CM frame. The two sets of TOF spectra were simulated with the same P(Et; θ) and P(θ) distributions shown in Figure 6. In contrast to the experiment of Casavecchia and co-workers at Ec = 2.2 and 4.1 kcal mol−1,8 the present experimental data can be simulated satisfactorily with a sole product channel leading to

Figure 6. Angle-specific distributions of kinetic energy (red) and angular distribution (blue) of product channel C3H3 + H. 7619

dx.doi.org/10.1021/jp304756t | J. Phys. Chem. A 2012, 116, 7615−7622

The Journal of Physical Chemistry A

Article

Figure 7. Potential-energy surface for the reaction C(3P) + C2H4 → H2CCCH + H calculated with the method of CCSD(T)/6-311+G(3df,2p)// B3LYP/6-311G(d,p) + ZPE[B3LYP/6-311G(d,p)]. Stationary and transition structures are exhibited therein. Letters a and b are employed to distinguish two types of hydrogen atoms in i2 and i3.

rotation of an intermediate prior to decomposition can smear out the original orientation in the space. In fact, the rotational effect just guarantees forward−backward (fw−bw) symmetry in product angular distributions. Lifetime, however, is not a sole factor able to result in a fw−bw symmetric angular distribution especially in hydrogen elimination of a reaction system involving some hydrogen atoms chemically equivalent. The equilibrium structure of triplet allene (H2CCCH2) was calculated to have moments of inertia IA = 5.3910 μÅ2, IB = 51.8501 μÅ2, and IC = 57.2411 μÅ2 (IA = 5.0687 μÅ2, IB = 53.0934 μÅ2, and IC = 58.1622 μÅ2 in the present work),10 indicative of a near prolate. H2CCCH2 has principal axis a close to the CCC skeleton, axis b is the C2 axis, and axis c is perpendicular to the molecular plane. Rotational periods were calculated to be 0.05, 0.52, and 0.57 ps for a maximal orbital angular momentum Lmax = 99ℏ along principal axes a, b, and c, respectively; this Lmax value was calculated with a maximal impact parameter bmax = 3.7 Å estimated in terms of the classical capture theory for Ec = 4.1 kcal mol−1.10 The previous RRKM calculations17 at Ec = 4.1 kcal mol−1 indicated that H2CCCH2 had a decay rate of ∼1.2 × 1012 s−1 corresponding to a lifetime of 0.83 ps longer than the aforementioned rotational periods for the limiting case, consistent with the present RRKM calculations at Ec = 4.0 kcal mol−1. Nonetheless, the rotational effect on product angular distribution becomes less significant for collision events with smaller L values and with Ka ≪ L. The a-type rotation (Ka ≈ L) has reaction probability less than that of the c-type rotation (Ka ≪ L) due to a large rotational energy in the former case; bulk experiments support this suggestion of dominating c-type rotation.10 In analogous reactions of carbon atoms with vinyl halide, the product angular distribution behaves nearly isotropic in the Helimination process but fw−bw asymmetric in the halogenelimination process.31 Therefore, the rotation of H2CCCH2

process between i2 and i3 was not considered and the ruptures of two types of C−H bonds were not distinguished, either, in the previous calculations.17 Table 2. Microcanonical Rate Coefficients (s−1) for the Reaction C(3P) + C2H4 → H2CCCH + H at Collision Energies Ec = 0 and 4 kcal mol−1 path i1 i2 i2 i3 i2 i4 i3 i5 i2 i3 i4 i5 i2 i3

→ → → → → → → → → → → → → →

i2, k1 i1, k−1 i3, k2 i2, k−2 i4, k3 i2, k−3 i5, k4 i3, k−4 H2CCCH H2CCCH H2CCCH H2CCCH H2CCCH H2CCCH

degeneracy

+ + + + + +

H, H, H, H, H, H,

k5 k6 k7 k8 kv1 kv2

1 1 1 1 2 1 2 1 2 2 1 1 2 2

Ec = 0 1.63 3.42 5.06 5.06 3.30 2.40 3.30 2.40 5.29 5.29 7.68 7.68 3.31 3.31

× × × × × × × × × × × × × ×

Ec = 4

1013 1010 1012 1012 1010 1010 1010 1010 1011 1011 1011 1011 1011 1011

1.97 4.94 5.20 5.20 5.40 3.92 5.40 3.92 7.76 7.76 1.14 1.14 4.56 4.56

× × × × × × × × × × × × × ×

1013 1010 1012 1012 1010 1010 1010 1010 1011 1011 1012 1012 1011 1011

Table 3. Relative Branching Ratios Calculated for the Pathways via Intermediates i2−i5 in the Reaction C(3P) + C2H4 → H2CCCH + H at Collision Energies Ec = 0 and 4 kcal mol−1 Ec

i2a

i2b

i3a

i3b

i4

i5

0 4

0.320 0.335

0.201 0.197

0.272 0.269

0.171 0.158

0.019 0.023

0.017 0.018

A nearly isotropic angular distribution is typically attributed to a long-lived intermediate in a reaction system because 7620

dx.doi.org/10.1021/jp304756t | J. Phys. Chem. A 2012, 116, 7615−7622

The Journal of Physical Chemistry A

Article

also result in a forward−backward symmetric angular distribution for product C3H3. In another words, the four hydrogen atoms can be viewed as chemically identical due to the inversion mechanism and thus scattered widely and equivalently into the forward and backward hemispheres.

prior to decomposition is not a mandatory factor for the fw− bw symmetric angular distribution of product C3H3. Because hydrogen atoms are much less massive than carbon atoms, the CCC plane is presumably fixed during rearrangement among intermediates i1−i5. The central carbon atom of i2 can be viewed as the incident carbon reactant traveling from top to bottom based on the i2 structure shown in Figure 7. The two hydrogen atoms located upward (downward) in i2 and i3 are viewed to be scattered preferentially into the fw (bw) hemisphere relative to the incident direction of ethene. However, coproduct C3H3 is recoiled opposite to the leaving H atom and scattered preferentially into the fw (bw) hemisphere relative to the incident direction of carbon reactant. For i2 (i3), Ha atoms are scattered into the bw (fw) hemisphere but the Hb atoms into the fw (bw) hemisphere. Analogously, the leaving H atom of i4 (i5) is scattered into the fw (bw) hemisphere. The same argument is applicable to their coproducts C3H3. Thus, the fw/bw ratio of C3H3 is predicted to be 0.97 at Ec = 0 kcal mol−1 and 0.96 at Ec = 4 kcal mol−1 based on the equation fw/bw = (i2b + i3a + i4)/(i2a + i3b + i5); here, i2a−i5 denote relative branching ratios, summarized in Table 3, for the pathways leading to product H2CCCH + H via intermediates i2−i5. The theoretical value is close to the experimental value 0.99 calculated based on the equation fw/ π bw = ∫ π/2 0 P(θ)d(cos θ)/∫ π/2P(θ)d(cos θ). Therefore, in addition to rotation the rapid inversion process (k2 = k−2 = 5.2 × 1012 s−1) plays an important role in the fw−bw symmetric product angular distribution in the title reaction. The final (product) orbital angular momentum L′ is suggested to be much less than L based on the heavy−heavy−light model. The weak L−L′ correlation results in the less anisotropic product angular distribution. The reaction of singlet methylene (CH2) with ethyne (C2H2) can form cyclopropene, propyne, and/or allene on the singlet potential energy surface of C3H4 that leads to product C3H3 + H with an isotropic angular distribution and a kinetic energy release biased to low energy;32 ⟨Et⟩ ≈ 5.4 kcal mol−1 and f t ≈ 0.26. There is, however, no direct evidence for the intersystem crossing in the C3H4 reaction systems of C(3P) + C2H4 and CH2(1A1) + C2H2, although both reactions have similar angular distributions and translational fractions f t.

■

AUTHOR INFORMATION

Corresponding Author

*Tel: +886-3-578-0281. Fax: +886-3-578-3813. E-mail: shlee@ nsrrc.org.tw. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank National Synchrotron Radiation Research Center, Academia Sinica, and the National Science Council of Taiwan (Grants NSC100-2113-M-213-001-MY3 and NSC100-2811-M213-004) for supports.

■

REFERENCES

(1) Kern, R. D.; Xie, K.; Chen, H. Combust. Sci. Technol. 1992, 85, 77. (2) Herbst, E. Annu. Rev. Phys. Chem. 1995, 46, 27. (3) List of Molecules in Intersteller Space. http://en.wikipedia.org/ wiki/List_of_molecules_in_interstellar_space. (4) Herbst, E.; Leung, C. M. Astrophys. J., Suppl. Ser. 1989, 69, 271. (5) Miller, J. A.; Melius, C. F. Combust. Flame 1992, 91, 21. (6) Chastaing, D.; James, P. L.; Sims, I. R.; Smith, I. W. M. Phys. Chem. Chem. Phys. 1999, 1, 2247. (7) Bergeat, A.; Loison, J.-C. Phys. Chem. Chem. Phys. 2001, 3, 2038. (8) Geppert, W. D.; Naulin, C.; Costes, M.; Capozza, G.; Cartechini, L.; Casavecchia, P.; Volpi, G. G. J. Chem. Phys. 2003, 119, 10607. (9) Naulin, C.; Daugey, N.; Hickson, K. M.; Costes, M. J. Phys. Chem. A 2009, 113, 14447. (10) Kaiser, R. I.; Lee, Y. T.; Suits, A. G. J. Chem. Phys. 1996, 105, 8705. (11) Kaiser, R. I.; Suits, A. G. Rev. Sci. Instrum. 1995, 66, 5405. (12) Kaiser, R. I.; Stranges, D.; Bevsek, H. M.; Lee, Y. T.; Suits, A. G. J. Chem. Phys. 1997, 106, 4945. (13) Kaiser, R. I.; Mebel, A. M.; Lee, Y. T. J. Chem. Phys. 2001, 114, 231. (14) Kaiser, R. I.; Nguyen, T. L.; Mebel, A. M.; Lee, Y. T. J. Chem. Phys. 2002, 116, 1318. (15) Casavecchia, P.; Balucani, N.; Cartechini, L.; Capozza, G.; Bergeat, A.; Volpi, G. G. Faraday Discuss. 2001, 119, 27. (16) Casavecchia, P. Faraday Discuss. 2001, 119, 128. (17) Le, T. N.; Lee, H.-Y.; Mebel, A. M.; Kaiser, R. I. J. Phys. Chem. A 2001, 105, 1847. (18) Gu, X.; Guo, Y.; Zhang, F.; Mebel, A. M.; Kaiser, R. I. Chem. Phys. 2007, 335, 95. (19) Guo, Y.; Gu, X.; Kaiser, R. I. Int. J. Mass Spectrom. 2006, 249− 250, 420. (20) Lee, S.-H.; Lin, J. J.; Lee, Y. T. J. Electron Spectrosc. Relat. Phenom. 2005, 144−147, 135. (21) Lee, S.-H.; Ong, C.-S.; Lee, Y. T. J. Chem. Phys. 2006, 124, 074306. (22) Lee, S.-H.; Chen, W.-K.; Huang, W.-J. J. Chem. Phys. 2009, 130, 054301. (23) Lee, S.-H.; Chin, C.-H.; Chen, W.-K.; Huang, W.-J.; Hsieh, C.C. Phys. Chem. Chem. Phys. 2011, 13, 8515. (24) Lu, I-C.; Huang, W.-J.; Chaudhuri, C.; Chen, W.-K.; Lee, S.-H. Rev. Sci. Instrum. 2007, 78, 083103. (25) Kelly, R. L. J. Phys. Chem. Ref. Data 1987, 16. (26) Lu, I-C.; Chen, W.-K.; Huang, W.-J.; Lee, S.-H. J. Chem. Phys. 2008, 129, 164304. (27) Minsek, D. W.; Chen, P. J. Phys. Chem. 1990, 94, 8399. (28) Le, T. N.; Mebel, A. M.; Kaiser, R. I. J. Comput. Chem. 2001, 22, 1522.

4. CONCLUSIONS We explored the dynamics of reaction of 3P carbon atoms with ethene at collision energy Ec = 3.5 kcal mol−1 by interrogating product channel C3H3 + H. Little concentration of C(1D) atoms was found in the carbon-atom beam. We measured timeof-flight spectra of product C3H3 at 16 laboratory angles covering the whole ion signals, from which angle-specific kinetic energy distributions and the angular distribution of C3H3 were derived. Furthermore, we measured the photoionization spectrum of product C3H3 to identify the species as propargyl (H2CCCH) radicals; no other isomers, such as c(CH)3, c-H2C(C)CH, and H3CCC previously proposed, were observable at Ec = 3.5 kcal mol−1. The present work has better temporal resolution, better signal-to-noise ratios, less interference from reactions of C(1D) atoms, and C2 radicals with ethene than in the previous work. Theoretical calculations indicate that atomic C(3P) adds to the CC π-bond of ethene to form a cyclic complex c-H2C(C)CH2 that rapidly opens the ring to form intermediate H2CCCH2 followed by decomposition to H2CCCH + H. In addition to rotation of intermediates, the rapid inversion process of H2CCCH2 can 7621

dx.doi.org/10.1021/jp304756t | J. Phys. Chem. A 2012, 116, 7615−7622

The Journal of Physical Chemistry A

Article

(29) Nguyen, T. L.; Mebel, A. M.; Kaiser, R. I. J. Phys. Chem. A 2001, 105, 3284. (30) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J. Phys. Chem. Ref. Data 1988, 17 (Suppl. 1), 1. (31) Lee, S.-H.; Chin, C.-H.; Huang, W.-J.; Lin, Y.-C. Unpublished results. (32) Davis, H. F.; Shu, J.; Peterka, D. S.; Ahmed, M. J. Chem. Phys. 2004, 121, 6254.

7622

dx.doi.org/10.1021/jp304756t | J. Phys. Chem. A 2012, 116, 7615−7622