Absolute Rate Coefficient and Mechanism of Gas Phase Reaction of

Sep 28, 2012 - Pham-Cam Nam , P. Raghunath , Lam K. Huynh , Shucheng Xu , M. C. Lin. Combustion Science and Technology 2016 188 (7), 1095-1114 ...
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Absolute Rate Coefficient and Mechanism of Gas Phase Reaction of Ketenyl Radical and SO2 Lin Du*,† and Shaun A. Carl* Department of Chemistry, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium ABSTRACT: The kinetics of the gas phase reaction of the ketenyl radical with SO2 was investigated over the temperature range 296−568 K using a laserphotofragment/laser-induced fluorescence technique (LP/LIF). The reactor pressure was 10 Torr N2 or He. Pulsed photolysis of ketene (CH2CO) at 193 nm was used as the source of HCCO radicals. The rate coefficient for the title reaction was determined to be described by k(T) = (1.05 ± 0.33) × 10−12 exp[(690 ± 98)K/T] cm3 s−1 molecule−1 (2σ error). We applied the coupled cluster and density functional theory to explore the mechanism of the title reaction. The dominant reaction pathway begins with a barrierless association of the C of the CH group of HCCO and the O atom of SO2.

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with NO,18,24,27−29 NO2,17 O,30,31 O2,16,20,32 H,13,15 H2,17 and C2H2.32 There are also some other theoretical mechanism studies of HCCO reactions with other species including O2, NO, NO2, etc., see, for example, in refs 9 and 33−37. Sulfur dioxide (SO2) is not only an important molecule in the chemistry of the atmosphere and the combustion of petroleum products38 but also an astrophysically relevant molecule, which was observed in some interstellar regions.39−41 HCCO radical might be a significant one of the free radicals responsible for SO2 reaction chemistry in those environments. However, there is no previous report of the HCCO + SO2 reaction in the literature. Thermodynamically, there are five possible exothermal product channels for the reaction of HCCO radical with SO2.

INTRODUCTION The ketenyl radical (HCCO) is a key intermediate in a wide range of combustion reactions, especially in acetylene oxidation chemistry.1−5 HCCO is a significant one of the free radicals responsible for NOx (x = 1, 2) removal in the reburning processes, which are some of the most efficient and universal solutions to reduce the NOx emissions in industrial, stationary combustion sources.6−9 During hydrocarbon combustion, HCCO is formed primarily via the gas phase reaction of acetylene with atomic oxygen10,11 C2H 2 + O →HCCO + H → CH 2 + CO

HCCO radical has also been observed in several interstellar regions.12 Ketene has been known as the photochemical source of HCCO in both interstellar space and in laboratory work.12,13 In interstellar regions, HCCO may be generated by shortwavelength photolysis (λ < 210 nm) of ketene.14

HCCO + SO2 →CO + HSOCO (P1) → CO + CO + HSO (P2) → CO + CO2 + SH (P3)

CH 2CO + hυ → HCCO + H

→ cis‐HOCO + OCS (P4)

Several methods have been used to generate HCCO in laboratory experiments. The C2H2/O/H reaction system has been used to generate HCCO, but this method has limited use for time-resolved kinetic studies.10,15 More rapid generation of HCCO for time-resolved, kinetics studies has employed ketene photolysis13,16−18 and more recently, as suggested by Krisch et al.,19 photolysis of ethyl ethynyl ether (C2H5OCCH).5,20−25 As for the detection methods for HCCO, mass spectrometry, infrared spectroscopy, laser induced fluorescence (LIF) technique, and nascent photofragment laser-induced fluorescence (PF-LIF) technique have all been used for studying its spectroscopy and kinetics.26 Some experimental kinetic studies involving HCCO have been reported in the literature, such as the total reaction rate constant measurements for its reactions © 2012 American Chemical Society

→ trans‐HOCO + OCS (P5)

In this work, the HCCO + SO 2 reaction kinetics has been determined experimentally with our laser-photofragment/ laser-induced fluorescence technique (LP/LIF).16,18 By measuring the temperature dependence of the reaction rate constant, we obtained an Arrhenius form of the rate constant. The reaction mechanism and products have also been studied theoretically using quantum chemistry methods. Received: August 26, 2012 Revised: September 27, 2012 Published: September 28, 2012 10074

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Figure 1. Schematic diagram of the experimental apparatus.

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EXPERIMENTAL SECTION The experimental apparatus for HCCO radical kinetics has been described in detail elsewhere.16 A schematic diagram of the apparatus is shown as Figure 1. The principal points and some modifications are given here. The reactor used for the kinetics study is a heatable stainlesssteel chamber with a volume of about 300 cm3. The chamber is internally coated with Teflon and a ceramic tube (99.7% Al2O3) with an internal oxidized SiC coating. The tube is surrounded by a Ni/Cr resistive wire, which allows the gas mixture to be heated to high temperature. The temperature of the gas in the probed reaction volume is periodically monitored using a moveable thermocouple. Spreads in the gas temperature range from ±1 at 296 K to ±12 at 568 K. The reaction chamber is connected to a throttled, rotary vacuum pump and a gas flow system allowing fresh, homogeneous gas mixtures of constant total pressure (typically 10.00 Torr) and known composition to continually pass. The gas mixture comprises the photolytic precursor of HCCO radical (diketene), the coreactant SO2, and N2 (or He) as bath gas. High-purity N2 (99.9995%, Messer) and SO2 from SO2 cylinder (99.98%, Messer) diluted in He (99.999%, Praxair) are admitted to the flow system via calibrated flow controllers (MKS Instruments Inc.). The total pressure of the reaction chamber is measured by a 0−10 Torr Barocel pressure sensor (Datametrics). At the two ends of the reaction chamber, quartz windows are sealed with O-rings. HCCO radicals are generated by laser photolysis of its precursor, ketene, which is produced upstream of the reaction chamber by pyrolysis of diketene vapor in He at about 800 K in a quartz tube. The diketene vapor is carried by a He flow passing through a bubbler with liquid-phase diketene (98%, Aldrich). The bubbler is held at a constant temperature of 292 K, a bit lower than room temperature of 296 K, by a water bath. A 195 K cooling trap situated immediately downstream of the pyrolysis tube is used to collect any undissociated diketene before the gas enters the reaction chamber. Under our experimental conditions, almost all diketene is converted to ketene. The ketene/He mixture flow is kept under the pressure of about 30 Torr by a needle valve before entering the reaction chamber. The typical concentration of ketene in the reactor is calculated to be about 2.3 × 1015 molecules cm−3.

on the basis of a molecular absorption cross-section of σ(ketene at 193 nm) = 8 × 10−19 cm2 and a quantum yield for dissociation to HCCO of 0.11.16 In the presence of excess [SO2] (126 < [SO2]/[HCCO] < 1034), [HCCO] observes pseudofirstorder kinetics with reaction half lifetimes ranging from about 26 to 442 μs. Under the typical conditions of experiments, with the total pressure of 10.00 Torr in the reactor, the two Renner− Teller states of HCCO are expected to be always equilibrated.16 The concentration of the coreactant [SO2] is accurately determined using the total reactor pressure and partial flow rates, measured using calibrated mass flow controllers. The total flow rate through the reactor is typically 93 sccm (cm3 min−1 at STP), which is sufficiently fast to replenish the active reaction volume in the 0.1 s period between laser pulses, but still slow enough to be effectively static over HCCO half lifetime. In kinetic studies, direct laser-induced fluorescence (LIF) from HCCO is unsuitable for use due to the low fluorescence quantum yield, especially at ambient and elevated temperatures, where broader rotational population distributions will lead to more diffuse LIF excitation spectra.26 The production and subsequent monitoring of HCCO requires three laser beams, which are all pulsed at a frequency of 10 Hz and have duration of about 10 ns. Two pulsed photolysis laser beams (193 and 266 nm) and a pulsed probe laser beam (ca. 430 nm) pass through the quartz windows along the central axis of the reactor. HCCO radicals are generated by photolysis of ketene with an ArF excimer laser (193 nm, Compex 102, Lambda Physik). Time-resolved measurements of the decreasing [HCCO] is achieved using the laser-photofragment/laser-induced fluorescence technique (LP/LIF) in which the first photolysis laser pulse (266 nm) photodissociates HCCO, yielding CH(X) + CO, and a second probe laser pulse (430 nm), delayed by only a few ns, excites the A ← X transition in the CH photofragment, thus inducing CH fluorescence. The intensity of the fluorescence is proportional to [HCCO], so the decay of [HCCO] can be measured. Practically, at right angle of the optical axis of the laser beams, there is a third glass window allowing the transmittance of the fluorescence from the center of the reaction chamber. The fluorescence emissions pass through the third window and are imaged onto a photomultiplier tube (PMT, R955, Hamamatsu) fitted with a band-pass filter (430 ± 10 nm, full width halfmaximum, Oriel 59295). The PMT photocurrent is converted to voltage and passed to a boxcar for integration (gate width = 300 ns, SR250, Stanford Research Systems). The result of this integration is collected as a single data point on a computer using an A/D converter (National Instruments). Exponential decay profiles of [HCCO] are slowly constructed over a few hundred seconds by incrementing the time delay between the excimer laser and the probe beams every three laser pulses. All the triggering and timing of the laser pulses, as well as the

2

CH 2CO + 193 nm →HCCO(X2A″ and/or à A′) Φ(R1a) = 0.11 + H(1S) → CH 2(a1̃ A1) + CO

Φ(R1b) = 0.19

→ CH 2(X3B1) + CO

Φ(R1c) = 0.63

1 +

→ C2O(b Σ ) + H 2

Φ(R1d) = 0.07

The fraction of ketene dissociated to HCCO along the central axis of the reactor is calculated to be about 7 × 10−4 10075

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boxcar gate, is controlled using a homemade pulse generator. The recordings of the [HCCO] decay profiles are accomplished by a LabView program. As for the laser settings, both of the two probe beams are derived from the same fundamental 1064 nm Nd:YAG pulse (SLIII-10, Continuum). The HCCO dissociation beam at 266 nm is simply the fourth harmonic of the fundamental output, generated using two KD*P doubling crystals placed in series. The CH LIF beam, which is tunable but fixed to a particular rovibronic transition for kinetic measurements, is generated using a KD*P mixing crystal by sum-frequency mixing of the fundamental laser output and a dye laser output (ND6000, Continuum) operating with LDS 750 dye (Exciton), which is pumped by the second harmonic of the same Nd:YAG fundamental pulse. It is well-known that photodissociation of HCCO at 266 nm leads mainly to CH(X). The possible concurrent production of electronically excited CH(4Σ+) is of no concern to the present measurements.26 In fact, the nascent CH photofragments resulting from HCCO exhibit a highly excited rotational population distribution (up to N″ = 28). In the experiments, the wavelength of the CH(A ← X) probe laser pulse is tuned to excite only a highly rotationally excited state (N″ = 13, Qbranch) at 430.35 nm. This line was preferred as it was slightly broader due to closely spaced Q1 and Q2 transitions at our resolution. However, the chemically generated CH possess a Boltzmann rotational distribution with a population maximum at N″ = 3 at 298 K and N″ = 5 at 800 K. Therefore, it is very easy to distinguish the highly rotational excited CH from any other chemically produced CH.

Figure 2. Relationship between excimer laser energy E193 and measured rate coefficients for HCCO + SO2 under room temperature (296 K).

Table 1. Experimental Absolute Rate Coefficient for Reaction HCCO + SO2 at Different Temperatures temperature (K)

bath gas

pressure (Torr)

E193 (mJ/pulse)

296 296 296 296 296 296 296 296 296 296 336 336 368 418 473 568 296 296

He He He N2 N2 N2 N2 N2 N2 N2 N2 N2 N2 N2 N2 N2 N2 N2

10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 6.00 30.00

16 12 6 18 14 12 10 8 8 8 8 8 8 8 8 8 8 8

HCCO + 266 nm → CH(X, ν″ = 0, N ″ ≤ 28) + CO

CH(X2Π, ν″ = 0, N ″ = 13) + hν(430.35 nm) → CH(A2Δ, ν″ = 0)

CH(A2Δ) → CH(X2Π) + hν(ca. 430 nm)

Probe laser absorption from thermally populated N″=13 level of CH(X) produced by chemical reaction is insignificant under our experimental conditions below a reactor temperature of 600 K. Nevertheless, effective discrimination of photofragment CH radicals requires that the time delay between the photodissociation and probe lasers be short enough that no significant rotational relaxation occurs. The short time delay between the two laser pulses, at the low experimental pressure of 10 Torr N2, ensures detection of CH with its nascent energy distribution approximately conserved. This helps to distinguish it from thermalized CH radicals produced by chemical processes in the system. Such a short time delay of several nanoseconds is achieved simply by the optical path difference between the two laser pulses.

1011 k (cm3 s−1 molecule−1) 1.88 1.57 1.09 2.31 1.63 1.29 1.00 1.09 1.14 1.09 0.83 0.72 0.68 0.73 0.44 0.33 0.89 1.14

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.10 0.09 0.16 0.08 0.13 0.05 0.09 0.06 0.10 0.14 0.11 0.10 0.14 0.13 0.08 0.11 0.15 0.10

(ZPE) corrections are obtained at the same level of theory with a scaling factor of 0.97. In order to confirm that the transition states connect designated isomers or products, intrinsic reaction coordinate (IRC) calculation is employed at the B3LYP/631G(d) level. The single-point electronic energy of each optimized geometry was recalculated using the coupled-cluster CCSD(T) method (coupled-cluster approach with single and double substitutions including a perturbative estimate of connected triple substitutions) with the basis set 6-311++G(d,p) based on the B3LYP/6-311++G(d,p) optimized geometries. Unless otherwise specified, the CCSD(T) single-point energies with inclusion of B3LYP zero-point energy (ZPE) corrections (simplified as CCSD(T)//B3LYP) are used in the following discussions.

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CALCULATIONS All calculations are carried out with Gaussian03 program packages.42 The geometries of all the reactants, products, intermediates, and transition states are optimized by using the hybrid density functional B3LYP method with the 6-311++G(d,p) basis set, which includes diffuse functions. The stationary nature of structures is confirmed by harmonic vibrational frequency calculations, i.e., equilibrium species possess all real frequencies, whereas transition states possess one and only one imaginary frequency. The zero-point energy

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RESULTS AND DISCUSSION Experimental Results. In the presence of an excess concentration of SO2, the time profile of [HCCO] should take the following simple exponential form: 10076

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Figure 3. (a) Experimental time profile of [HCCO] (fitted to a single-exponential function) following the dissociation of CH2CO (time = 0) in the presence of a SO2 concentration of 6.33 × 1014 molecules cm−3 under a reactor pressure of 30 Torr at 296 K. (b) Same profile displayed with a logarithmic y axis.

Figure 5. Experimental rate coefficients for HCCO + SO2 as a function of temperature plotted in Arrhenius form. The results are fitted by a weighted least-squares analysis to a simple Arrhenius expression, yielding k(T) = (1.05 ± 0.33) × 10−12 exp[(690 ± 98)K/T] cm3 s−1 molecule−1 (2σ error).

Figure 4. Variation of pseudofirst-order [HCCO] decay constants with [SO2] at 296 and 336 K fitted to the type y = a + bx by a leastsquares analysis.

[HCCO]t = [HCCO]0 exp( −(k′ + Σki[X i])t )

(1)

SO2 + 193 nm → O(3P) + SO

where k′ = k[SO2] and Σki[Xi] represents removal of HCCO by secondary reactions involving species Xi, having a rate constant ki (which is mainly due to the reaction of HCCO with H atoms). Diffusion out of the observation region under our experimental conditions is negligibly slow compared to reactive removal. Unlike the HCCO reactions with other species, such as NO2 and NO, in this HCCO + SO2 system, a small fraction of SO2 can be photodissociated by 193 nm excimer laser. The large absorption cross-section of SO2 at 193 nm of 6 × 10−18 cm2 requires that relatively low excimer laser energy be used to avoid [SO2]-dependent secondary chemistry arising from significant and variable concentration of O atoms.43 In order to establish the extent of secondary chemistry, the rate constant at 296 K was determined at seven different laser intensities, but otherwise under identical experimental conditions (either N2 or He are used as bath gas).

The effect of the laser pulse energy on the apparent bimolecular rate constant of HCCO + SO2 at 296 K is shown in Figure 2. These results clearly show the effect of the laser intensity and demonstrate that the effect becomes negligible when the laser pulse energy is below about 10 mJ/pulse. Therefore, the subsequent determinations of the rate constant are employing laser pulse energy of 8 mJ/pulse. Since the floor energy of the excimer laser was higher than 8 mJ/pulse, the laser beam was attenuated by passing it through a dilute nitric acid solution in a 1 cm long quartz curvet. Such method has been used previously for studying the reaction of C2H + SO2.43 Most of the kinetic measurements were carried out at a total reactor pressure of 10.00 Torr, and the experimental condition and results are summarized in Table 1. Under typical experimental conditions, the concentration of CH2CO in the reactor was about 2.3 × 1015 molecules cm−3, and the calculated initial 10077

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Figure 6. Optimized geometries of all species for the HCCO + SO2 reaction at the B3LYP/6-311++G(d,p) level. Bond lengths are in angstroms and angles in degrees. 10078

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concentration of HCCO after dissociation of CH2CO is 1.6 × 1012 molecules cm−3. The concentration of SO2 covered the range from 2.03 × 1014 to 1.66 × 1015 molecules cm−3. Practically, the net time profile signal is constructed by subtraction of a raw time profile taken with the absence of the dye laser output (ca. 430 nm) from one taken under normal conditions with the presence of the dye laser. This procedure, which is routinely used, effectively distinguishes the intensity observed from the laser-induced fluorescence from other source of light, such as 2-photogenerated CH(A), scattered laser light and window fluorescence.16−18 As for the bath gas in the reactor, both He and N2 were used. Although N2 is a much more efficient quencher of fluorescence than He, there is no significant difference for the results of our measurements between He and N2 as bath gas under low laser energy determinations and room temperature. Finally, N2 was used as bath gas for the majority of measurements. Figure 3 shows an example time profile of [HCCO] obtained from nascent photofragment LIF of CH at 430 ± 10 nm following its initial excitation at 430.35 nm (from N″ = 13) in the presence of excess [SO2] at 296 K. All decays measured in the presence of SO2 exhibit the expected exponential behavior described by eq 1 over the whole signal range. Typically, the decay profiles were exponential over about 2 orders of magnitude, as indicated by the weighted least-squares fit. The resulting pseudofirst-order rate constants, as derived from fitting single-exponential function to the [HCCO] decay profile, are plotted in Figure 4 as a function of [SO2] for representative experimental temperatures of 296 and 336 K. A weighted, least-squares linear fit to the data gives the secondorder rate coefficient k. All experimental derivatives of k obtained over the range T = 296−568 K are listed in Table 1. The average of six room temperature determinations gives k(296 K) = (1.07 ± 0.12) × 10−11 cm3 s−1 molecule−1. For the low laser energy (8 mJ/pulse) used in the present measurements, the average initial concentration of the O atoms was calculated to be about 3.7 × 1013 molecules cm−3, based on the absorption cross-section for SO2 of 6 × 10−18 cm2 at 193 nm with a quantum yield for O production of near unity and an average concentration of [SO2] at room temperature of 8 × 1014 molecules cm−3.43 The rate constant for the HCCO + O reaction at 298 K is 1.99 × 10−12 cm3 s−1 molecule−1 and that of HCCO + SO2 as derived from the present study is (1.07 ± 0.12) × 10−11 cm3 s−1 molecule−1, thus the HCCO + O reaction could contribute a maximum of 1% to the observed removal rate of HCCO radicals at 296 K, which can be neglected. The temperature dependence of kHCCO+SO2 is shown in Figure 5. The present results clearly show a decrease in rate coefficient with increasing temperature and with no curvature detectable over the experimental temperature range. It follows a simple Arrhenius form after a weighted least-squares fit to the data, described by k(T) = (1.05 ± 0.33) × 10−12 exp[(690 ± 98)K/T] cm3 s−1 molecule−1 (2σ error). The negative temperature dependence observed for this reaction suggests that the reaction takes place through the formation of a combination intermediate. Furthermore, the rate coefficient for HCCO + SO2 was measured at different pressures at room temperature. As seen from the results (Table 1), there is no significant difference on the obtained rate coefficients within the pressure range between 6 and 30 Torr. Computational Results. Quantum chemical methods are used to explore the possible reaction paths for reaction HCCO + SO2. Ten intermediate isomers and 14 transition states are obtained at the B3LYP/6-311++G(d,p) level. The optimized

Table 2. Total Energies (hartree), Zero-Point Energies (ZPE, hartree), and Relative Energies (kcal/mol) for the Reactants, Products, Intermediates, and Transition States geometry optimization

single-point energy

species

B3LYP/6-311+ +G(d,p)

ZPEa

CCSD(T)/6311++G(d,p)

Erelb

R (HCCO + SO2) P1 (CO + HSOCO) P2 (CO + CO + HSO) P3 (CO + CO2 + SH) P4 (cis-HOCO + OCS) P5 (trans-HOCO + OCS) IM1 IM2 IM3 IM4 IM5 IM6 IM7 IM8 IM9 IM10 TS1 TS2 TS3 TS4 TS5 TS6 TS7 TS8 TS9 TS10 TS11 TS12 CO + TS13 CO + TS14

−700.6390673 −700.6837850 −700.7020719 −700.7689773 −700.7590140 −700.7622223 −700.6741033 −700.6833572 −700.7042842 −700.7029017 −700.6939582 −700.6645918 −700.6595159 −700.6608461 −700.7625080 −700.7609863 −700.6710813 −700.6777855 −700.7025848 −700.6775389 −700.6774323 −700.6412986 −700.6278140 −700.6268769 −700.6078969 −700.7427375 −700.7464874 −700.7406804 −700.6693888 −700.6721745

0.024616 0.023505 0.019622 0.022114 0.028746 0.029165 0.029490 0.030817 0.030977 0.030901 0.027952 0.030455 0.029808 0.031081 0.032893 0.032772 0.029549 0.029800 0.030690 0.025541 0.025063 0.026884 0.027967 0.028747 0.025505 0.030913 0.030585 0.029727 0.021628 0.021499

−699.3981763 −699.4606884 −699.4850415 −699.5466887 −699.5237502 −699.5271905 −699.4285911 −699.4406103 −699.4725545 −699.4710412 −699.4591407 −699.4208598 −699.4214283 −699.4185052 −699.5315787 −699.5299353 −699.4219894 −699.4328368 −699.4705328 −699.4384078 −699.4480751 −699.3969038 −699.3828433 −699.3879464 −699.3689166 −699.5122106 −699.5071210 −699.5038153 −699.4406576 −699.4458744

0.00 −39.92 −57.64 −94.76 −76.21 −78.10 −16.03 −22.74 −42.68 −41.78 −36.16 −10.57 −11.33 −8.70 −78.52 −77.56 −11.85 −18.50 −41.59 −24.66 −31.03 2.22 11.73 9.01 18.92 −67.61 −64.62 −63.08 −28.53 −31.89

a

ZPE is based on the B3LYP/6-311++G(d,p) vibrational frequencies and scaled by a factor of 0.97. bErel is the energy relative to reactants and corrected for ZPE.

structures of stationary points are depicted in Figure 6. Table 2 displays the relative energies including ZPE corrections of reactants, products, intermediates, and transition states at CCSD(T)/ 6-311++G(d,p) level. To simplify the discussion, the energy of reactants R is set to zero for reference. The reaction pathways of the potential energy surface for HCCO + SO2 reaction are depicted in Figure 7 to clarify the reaction mechanism. HCCO radical has Cs symmetry and 2A″ electronic state. The calculated CC bond length (1.286 Å) lies between the typical CC double bond and triple bond, and the CO bond is close to the typical CO double bond length. HCCO has the resonant structure H−CCO ↔ H−C≡C−O, while the former one has more weight as shown by B3LYP/6-311++G(d,p) spin densities: 0.730706 e on the C atom of CH group and 0.300365 e on the O atom. Therefore, it is most possible that the initial association with SO2 mainly focuses on the C atom of CH. On the potential energy surface, two possible attack pathways are considered for the C of CH group at the SO2 molecule, S attack and O attack. The O attack can lead to a low-lying adduct OCCHOSO (IM1). We attempted to locate the transition state from R to IM1 at the B3LYP/6-311++G(d,p) level, but with no success. This barrierless association is expected to be fast and to 10079

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Figure 7. Profile of potential energy surface for the HCCO + SO2 reaction. Relative energies are calculated at the CCSD(T)/6-311++G(d,p)// B3LYP/6-311++G(d,p) level.

deeply with an internal energy of −78.52 kcal/mol relative to the initial reactants. If IM9 is produced as an intermediate in this reaction, it might not be able to have reverse reactions toward the reactants side. IM9 could proceed by further rearrangement to IM10 via TS10 or simply undergo C−C bond dissociation to form P5 (trans-HOCO + OCS) via TS11. The intermediate IM10 has also very high internal energy of 77.56 kcal/mol; if formed, it will rapidly dissociate to final products P4 (cis-HOCO + OCS) via TS12 with a barrier height of 14.48 kcal/mol. It is clear that the two latter pathways cannot compete with the former ones via IM1, in such a way that they are not expected to play any important role in forming final products. In a summary, a combination of the C atom of HCCO with the O atom in SO2 entirely leads to the products of P2 and P3, whereas combination with S atom in SO2 via the adduct IM6 produces almost exclusively P4 and P5. The observed negative temperature dependence for the HCCO + SO2 reaction is consistent with the potential energy surface calculation. A combination of a barrierless association followed by rearrangement leading to products, over a submerged barrier can lead to negative temperature dependence in two ways. The first is due to the possibility of redissociation from initially formed adduct (IM1) owing to the increasing availability of states of the loose association transition state (see below) compared to the tighter rearrangement transition state (TS1); the second is associated with conservation of angular momentum quantum number J of the interacting system. Since the effective radius of the interacting system is reduced as HCCO and SO2 approach each other, J conservation dictates that more energy becomes associated with rotational motion and less, therefore, as redistributable energy of the system. This has the effect of producing an actual transition state on an otherwise monotonically decreasing potential energy surface. The position of this transition state moves to smaller internuclear distances with increasing collision energy. Since, for the case of HCCO + SO2, the first submerged barrier (TS1) along the dominant reaction path lies more than 15 kcal mol−1 below the reactants, redissociation of the initial adduct has a very low probability even at high combustion temperatures. Thus, the negative temperature dependence is associated with

play a significant role in the reaction kinetics. The second possible pathway, S attack, can lead to the formation of an adduct OCCHSO2 (IM6) with a shallow transition state TS6 (2.22 kcal/mol). With the large exothermicity released from the reactant R, the initially formed isomer IM1 can take an isomerization pathway followed by final decomposition. The initial adduct OCCHOSO (IM1) (Cs, 1A′) is a stable and chainlike isomer, with −16.03 kcal/mol energy relative to the reactants. As shown in Figure 7, the ring closure of isomer IM1 may proceed to a planar five-membered ring intermediate IM2 (Cs, 1A′) via transition state TS1 (Cs, 1A′) with a barrier of 4.18 kcal/mol. TS1 has also a CCOSO five-membered ring structure in which the length of the forming C−O bond is 1.971 Å (Figure 6). Subsequently, a ring-open process occurs at the S−O bond of the HCOS side of IM2 via a transition state of TS2. The S−O bond length changes from 1.743 Å in IM2 to 1.934 Å in TS2, and this bond finally disconnects when forming IM3. After the C−C bond rotation with TS3 as the transition state, IM4 then undergoes a 1,4-hydrogen migration from the C atom to the S atom via the transition state of TS4 with a barrier height of 17.12 kcal/mol. IM5 can easily lead to product P1(CO + HSOCO) via a C−C bond dissociation process along with the formation of HSOCO. Only a 5.13 kcal/mol barrier must be overcome for the process IM5 → P1. The corresponding transition state TS5 is characterized by an elongated C−C bond length of 2.114 Å. The intermediate product HSOCO will decompose rapidly into CO2 + SH via TS13 with a barrier of 11.39 kcal/mol. Alternatively, it can also undergo C−O bond decomposition and finally form CO + HSO with a lower barrier (8.03 kcal/mol). As for S attack pathway, after the adduct OCCHSO2 (IM6) is formed, it faces a barrier height of 22.30 kcal/mol. The corresponding transition state TS7 has a ring closure structure in which the C−O bond length is 1.951 Å. Subsequently, IM7 undergoes a rearrangement of the CSO group to form IM8. The isomer IM8, with energy 8.70 kcal/mol below the initial reactants, once formed, undergoes a 1,3-hydrogen migration to IM9 via TS9. This step is characterized by a barrier height of 27.62 kcal/mol. The isomer IM9 has a Cs symmetry and lies 10080

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Article

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the latter effect and must be treated by variation transition state theory, which is beyond the scope of the current investigation. Since this reaction is barrierless, it may play an important role in the neutral chemistry of certain cold interstellar environments as well as in hydrocarbon combustion processes supporting sulfur chemistry.

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CONCLUSIONS This study give the first determination of the rate coefficient and possible product channels of the HCCO + SO2 reaction. Over the temperature range 296−568 K, the rate constant can be described by the simple Arrhenius expression k(T) = (1.05 ± 0.33) × 10−12 exp[(690 ± 98)K/T] cm3 s−1 molecule−1 (2σ error). The rate constant decreases with increasing temperature, which agrees with the theoretical calculated potential energy surface. According to the calculations, the possible products for the HCCO + SO2 reaction are CO, CO2, SH, and HSO.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (L.D.); [email protected] (S.A.C.). Present Address †

Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the GOA program (GOA/2008/05) and KULeuven Research Council for financial support. REFERENCES

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dx.doi.org/10.1021/jp308457m | J. Phys. Chem. A 2012, 116, 10074−10081