and ab initio study - KU Leuven

JOURNAL OF CHEMICAL PHYSICS

VOLUME 116, NUMBER 9

1 MARCH 2002

The reaction of C2 H with H2 : Absolute rate coefficient measurements and ab initio study Jozef Peetersa) and Benny Ceursters Department of Chemistry, University of Leuven, Celestijnenlaan 200 F, B-3001 Leuven, Belgium

Hue Minh Thi Nguyen Department of Chemistry, University of Leuven, Celestijnenlaan 200 F, B-3001 Leuven, Belgium and Faculty of Chemistry, University of Education, Hanoi, Vietnam

Minh Tho Nguyen Department of Chemistry, University of Leuven, Celestijnenlaan 200 F, B-3001 Leuven, Belgium

共Received 15 August 2001; accepted 28 November 2001兲 In this work, a pulsed laser photolysis/chemiluminescence 共PLP/CL兲 technique was used to measure absolute rate coefficients for the reaction of C2 H⫹H2 →products over the temperature range 295– 666 K. Ethynyl radicals were produced pulsewise by excimer laser photolysis of acetylene at 193 nm and real-time pseudo-first-order decays of C2 H were monitored by the CH(A 2 ⌬→X 2 ⌸) chemiluminescence resulting from their reaction with O2 . Over the experimental temperature range, the results indicate that the rate coefficient exhibits a non-Arrhenius behavior in line with theoretical predictions, k hydrogen(T)⫽3.92⫻10⫺19 T 2.57⫾0.30 exp关⫺(130⫾140) K/T 兴 cm3 molecule⫺1 s⫺1 . Experiments were supplemented by ab initio molecular orbital calculations up to the coupled-cluster theory including all single and double excitations plus perturbative corrections for the triples, UCCSD共T兲, with the 6-311⫹⫹G(d, p) basis set for geometry optimizations and the aug-cc-pVTZ for electronic energy single points, revealing that the direct hydrogen abstraction yielding HCwCH⫹H is the only product channel of any importance. There is also no important crossing between the doublet and quartet energy surfaces. Finally, geometry optimizations at the UCCSD共T兲/6-311⫹⫹G(2d f ,2p) level have shown that the transition structure for H-abstraction is linear; harmonic vibration frequencies at this level, and single-point UCCSD共T兲/aug-cc-pVTZ energies for these geometries result in an adiabatic barrier height for H-abstraction, including harmonic vibration zero point energies, of 12.8 kJ/mol, while the classical potential energy barrier is 9.2 kJ/mol. © 2002 American Institute of Physics. 关DOI: 10.1063/1.1436481兴

C2 H⫹H2 →C2 H2 ⫹H

I. INTRODUCTION

Ethynyl radicals, C2 H, are abundant in several environments, both natural and manmade. Their presence in interstellar space1,2 and in planetary atmospheres such as Titan’s3,4 has stimulated recent studies of their lowtemperature kinetics.5 On earth, C2 H plays a crucial role in hydrocarbon combustion processes in which it is involved in the formation of diacetylene (C4 H2 ) as well as the higher polyacetylenes (C2n H2 ), and probably of polycyclic aromatic hydrocarbons 共PAHs兲 and hence also soot.6 –15 Furthermore, ethynyl radicals react rapidly with NO yielding chiefly HCN⫹CO and CN⫹HCO, 13,16,17 and thus are expected to have an impact on NOx chemistry in fuel-rich hydrocarbon flames where C2 H is an important intermediate, including in high-temperature ‘‘NO-reburning.’’ 18 In this regard, detailed and quantitative kinetic/mechanistic information about important formation and destruction reactions of C2 H over a broad temperature range is of fundamental chemical importance. The reaction of C2 H with H2 ,

is of particular interest as a C2 H removal and C2 H2 regeneration process in flames as well as in planetary atmospheres and in the interstellar medium; the high relative abundance of H2 in interstellar clouds might compensate for the small rate coefficient of reaction 共1兲 at the low temperatures in such media. Moreover, the knowledge of the rate coefficient of this reaction and the temperature dependence thereof can provide needed kinetic information on the 共highly endothermic兲 reverse reaction, which may be an important C2 H-source in hot, fuel-rich hydrocarbon flames, but for which rate measurements are difficult to realize. The equilibrium constant K 1 can now be evaluated accurately, since the enthalpy of formation of C2 H as well as its vibration and rotation parameters are well established.19–22 Several rate measurements have been reported on the C2 H⫹H2 reaction;5,13,17,23–33 a brief overview was given earlier.13 The room temperature data 共293–300 K兲 reported over the past 15 years 共Refs. 13, 17, 26 –29兲 are in fair mutual accord, the average value of the rate coefficient being k 1 ⫽5.7⫻10⫺13 cm3 molecule⫺1 s⫺1 . However, only a few measurements over extended temperature ranges are available. Beside the indirect, relative data by Koshi et al. for the

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Reaction of C2 H with H2

J. Chem. Phys., Vol. 116, No. 9, 1 March 2002

298 – 438 K range,27 absolute data were reported by Farhat et al. for T⫽466, 660, and 854 K,28 Peeters et al. for 295– 440 K,13 Opansky and Leone for 178 –359 K,29 and Kruse and Roth for 2900– 4000 K.33 As shown in Refs. 13 and 34 and in Fig. 3共b兲, the k 1 data in the regions of overlap 共300– 450 K兲 show a spread of a factor of almost 2, and none of the individual sets provides sufficiently detailed information on the T-dependence, in particular regarding the curvature共s兲 of the ln k1 versus 1/T plot. Thus, a primary objective of the present investigation was to determine the absolute rate coefficient of the title reaction over a wide temperature range 共300–700 K兲 using a single, proven method. To that end, we opted for the pulsed laser photolysis/chemiluminescence 共PLP/CL兲 technique, our version of which was validated earlier as a highly precise and accurate tool for gas-phase kinetics studies of C2 H(X 2 ⌺ ⫹ ) radical reactions, both with and without an appreciable energy barrier.13–15,35,36 In addition, the experimental study was complemented by ab initio calculations of the transition structures for the possible pathways of the title reaction in order to characterize the most favored transformations, emphasizing in particular the direct H-abstraction channel. Ab initio calculations on this channel have been carried out earlier by Harding et al.24 and by Kamiya,38 resulting in theoretical adiabatic barrier heights of respectively 16.7 kJ/mol at the POL-CI level, and 19.9 kJ/mol at the MP2/6-31G(d,p) level. Based on these, several theoretical kinetics treatments13,24,27,34,38 – 43 of reaction 共1兲 were performed, leading to the conclusion that a lower barrier of 8.4 –11.3 kJ/mol 共2.0–2.7 kcal/mol兲 is required to fit the experimental rate coefficient values. Among the recent theoretical studies,34,38 – 43 we have paid particular attention to that of Zhang et al.34 who investigated the direct hydrogen abstraction process at the ab initio quadratic configuration interaction level including all single and double substitutions, UQCISD/6-311⫹G(d, p), and obtained a barrier of 19 kJ/ mol 共4.55 kcal/mol兲. A G2 procedure on the UQCISDoptimized geometries led to a barrier of 10.5 kJ/mol 共2.52 kcal/mol兲. Based on the G2//UQCISD results, these authors calculated the rate coefficients of the forward and reverse reactions 共20–5000 K兲 using canonical variational transition state theory 共CVTST兲 with small-curvature tunneling 共SCT兲 corrections, obtaining a generally good agreement with the experimental k 1 values, except with those at 2900– 4000 K,33 which are a factor 3– 4 higher than the theoretical results. Zhang et al.34 found tunneling to be highly important at low temperatures—dominating the kinetics below 200 K—whereas the variational effect was found significant only above 800 K, remaining of moderate importance 共⬇⫺40%兲 even at 5000 K. Contrary to some previous theoretical predictions,13,38 – 43 the theoretical k ⫺1 values of Ref. 34 for the reverse reaction at flame temperatures are in rough agreement with the Baulch et al. recommendations.44,45 However, the ratio of the theoretical k 1 and k ⫺1 of Ref. 34 deviates from the known equilibrium constant13,46,47 by about an order of magnitude. More recently, Kurosaki et al.42 studied the kinetic isotope effects on rate constants using the QCISD共T兲/cc-pVTZ computations and found that the primary isotopic effects can

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mainly be attributed to tunneling whereas the secondary isotopic effects are not large in the C2 H⫹H2 reaction and its isotopic variants. In another approach, Szichman et al.43 treated the dynamics of the reaction and computed the total reactive probabilities, cross sections and thermal rate constants over the range of 200⬍T⬍400 K. A primary theoretical objective of the present study was 共i兲 to characterize the transition structure of the direct H-abstraction reaction at as high a level of theory as is currently feasible, specifically to optimize the geometries at the coupled-cluster theory CCSD共T兲 level of ab initio molecular orbital theory with a basis set of 6-311⫹⫹G(2d f ,2p) size, and to calculate single-point electronic energies using even larger and higherquality basis sets. Further aims were 共ii兲 to explore other reaction paths beside the direct H-abstraction as possible cause for the discrepancy between the CVTST-SCT predictions34 and the k 1 data33 at the highest temperatures 共see above兲; and 共iii兲 to re-examine the issue of the reverse rate coefficient k ⫺1 , with important implications for C2 H formation in hotter flames. The experimental measurements will first be presented and followed by theoretical results. II. EXPERIMENTAL SETUP

The experimental setup used in the pulsed laser photolysis/chemiluminescence 共PLP/CL兲 experiments, which is part of a PLP/LIF configuration described in detail earlier,48,49 is similar to that used in our previous kinetic studies of the ethynyl radical,13–15,35,36 and only a brief overview is presented here. Ethynyl radicals were produced pulsewise by flowing a mixture of C2 H2 , O2 , H2 , and He 共as diluent gas兲 into a heated reaction cell and photolyzing the C2 H2 by a 193 nm pulsed ArF excimer laser 共30 mJ/pulse at 10 Hz, beam section of 8 mm⫻3 mm兲. In acetylene photolysis at 193 nm, the ethynyl radicals are formed in vibrationally excited levels of the X 2 ⌺ state as well as in the low-lying electronic A 2 ⌸ state.31,50 According to the A 2 ⌸ ⫹He→X 2 ⌺⫹He quenching constant of 4 ⫻10⫺12 cm3 molecule⫺1 s⫺1 measured by Shokoohi et al.,31 the lifetime of C2 H(A 2 ⌸) at the pressure of 10 Torr helium in the experiments is only 0.65 ␮s, such that after 3 ␮s the C2 H radicals are for ⭓99% in the X 2 ⌺ ground state. The quenching of A 2 ⌸ may result in vibrationally excited X 2 ⌺ radicals, but as verified earlier,35 at the total pressure of 10 Torr He and the oxygen number density 关 O2 兴 ⬇5 ⫻1015 molecules cm⫺3 of the experiments, the C2 H radicals are quasithermalized within the 3 ␮s period prior to the decay measurements. The real-time pseudo-first-order decay of 关 C2 H兴 was monitored by measuring the intensity I(CH* ) of the 430 nm CH(A 2 ⌬→X 2 ⌸) chemiluminescence36,37 resulting from the reaction of C2 H with O2 , present in a large and constant concentration,35 C2 H⫹O2 →products →CH共 A 2⌬兲⫹CO2, CH共 A ⌬ 兲 →CH共 X ⌸ 兲 ⫹h ␯ 共 ␭⫽430 nm兲 . 2

2

共2兲共3兲

At CH(A ⌬) quasisteady state as under the experimental conditions, I(CH* ) is directly proportional to the ethynyl concentration, 关 C2 H兴 . The CL perpendicular to the laser 2


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beam was collected via suitable optics and focused through an interference filter (␭⫽430⫾10 nm) onto a photomultiplier tube 共PMT兲, the output of which was fed to a boxcar integrator. The delay between firing the laser and opening the 1 ␮s wide boxcar gate was increased by 0.1 ␮s after each tenth laser pulse. The difference with the setup in our earlier measurements of k 1 共at 295– 440 K兲 is that the reaction cell in this work was equipped with an heated inner ceramic tube 共Al2 O3 99.7% with internal oxidized SiC coating兲 with a Ni/Cr resistive wire coil, ensuring a near-uniform temperature of the 共slowly兲 flowing gas mixture in the irradiated ‘‘reaction volume.’’ The excimer beam crosses the tube through two 15 mm diam openings. The temperature in the observed reaction volume (8 mm⫻3 mm⫻⬇10 mm) was measured by a movable calibrated chromel/alumel thermocouple. All gases were obtained commercially, and the purities were as follows: He 99.9996%, O2 99.995%, H2 99.9997% 共all AIR LIQUIDE兲 and C2 H2 99.5% 共HOEK LOOS兲. To remove the acetone, the acetylene was purified by passing it through a dry-ice/acetone trap. The flow rates of the admitted gases were regulated and measured each by calibrated mass flow controllers. The total gas flow rate was sufficient to refresh the gas in the observed volume between two successive laser shots 共0.1 s兲. The total pressure was measured using a Baratron absolute pressure transducer, calibrated against a Wallace and Tiernan gauge. Experiments were performed at concentrations 关 C2 H2 兴 ⬇5⫻1014, 关 O2 兴 ⬇5⫻1015 molecules cm⫺3 and 关 H2 兴 varied in the range 0 – 2⫻1017 molecules cm⫺3 , all three always in a very large excess over C2 H ( 关 C2 H兴 0 ⬇1012 molecules cm⫺3 ) such that contributions from secondary and/or radical–radical reactions are negligible. Transport of C2 H out of the observed volume by diffusion and convection, on a time scale of several ms, cannot compete with C2 H loss by chemical reaction on a time scale of several ␮s. Under the pseudo-first-order conditions of the experiments, 关 C2 H兴 decays by the reactions of ethynyl with C2 H2 , O2 , and H2 , 关 C2 H兴 t ⫽ 关 C2 H兴 0 exp共 ⫺k ⬘ t 兲

FIG. 1. Typical decay and semilog plot of the relative HCC concentration vs reaction time; T⫽529 K; p tot⫽10 Torr 共He bath gas兲; 关 C2 H2 兴 ⫽5.09 ⫻1014 molecules cm⫺3 ; 关 O2 兴 ⫽5.12⫻1015 molecules cm⫺3 ; 关 H2 兴 ⫽1.35 ⫻1016 molecules cm⫺3 . The straight line represents the weighted linear least-squares fit.

within ⬇1.5%, was found at all temperatures. Note that for all second-order rate coefficients k i an estimated probable systematic error of 10% has been included in the stated uncertainties; this systematic error is always much larger than the statistical ones. The k 1 measurements could be carried out only up to 700 K, corresponding to the branched-chain explosion limit at 10 Torr for the H2 /C2 H2 /O2 mixtures of interest. III. EXPERIMENTAL RESULTS

The values of the absolute bimolecular rate coefficients k 1 determined at temperatures between 295 and 700 K are listed in Table I, and an Arrhenius representation is displayed in Fig. 3共a兲. Contrary to other C2 H reactions for which k-measurements were made using both the previous 共300– 450 K兲 and the present, modified setups 共see, e.g., Refs. 15 and 35兲, the present k 1 results in the 295– 450 K range differ

with k ⬘ ⫽k 1 关 H2 兴 ⫹k acetylene关 C2 H2 兴 ⫹k oxygen关 O2 兴 . An example of an exponential C2 H decay is shown in Fig. 1. Bimolecular rate coefficients k 1 of the reaction with H2 were determined by measuring the first-order decay constant k ⬘ at varying 关 H2 兴 and at fixed 关 C2 H2 兴 as well as 关 O2 兴 . The slope of the linear plot of k ⬘ vs 关 H2 兴 yields k 1 , whereas the ordinate intercept is equal to the summed contributions of acetylene and oxygen to k ⬘ : k acetylene关 C2 H2 兴 ⫹k oxygen关 O2 兴 . A typical example of a plot of k ⬘ as a function of 关 H2 兴 at T ⫽380 K is shown in Fig. 2. The k 1 共380 K兲 value from the slope of this plot is (1.23⫾0.12)⫻10⫺12 cm3 molecule⫺1 s⫺1 ; the ordinate intercept with 1␴ random error of (2.13⫾0.01)⫻105 s⫺1 matches perfectly with the expected value of k acetylene关 C2 H2 兴 ⫹k oxygen关 O2 兴 ⫽(2.1⫾0.2) ⫻105 s⫺1 using our earlier results k acetylene(380 K)⫽1.3 ⫻10⫺10 and k oxygen(380 K)⫽2.9⫻10⫺11 cm3 mole⫺1 ⫺1 cule s 共cf. Refs. 13–15, 35兲. Such internal consistency,

FIG. 2. Pseudo-first-order decay constants k ⬘ plotted vs 关 H2 兴 at T ⫽380 K; p tot⫽10 Torr 共He bath gas兲; 关 C2 H2 兴 ⫽5.02⫻1014 molecules cm⫺3 ; 关 O2 兴 ⫽5.05⫻1015 molecules cm⫺3 . The solid line represents a weighted linear least-squares fit to the data points. The slope of the line yields k H2 (380 K)⫽(1.23⫾0.12)⫻10⫺12 cm3 molecule⫺1 s⫺1 .



J. Chem. Phys., Vol. 116, No. 9, 1 March 2002 TABLE I. Bimolecular rate coefficients k hydrogen for the C2 H⫹H2 reaction. The stated uncertainties include an estimated probable systematic error of 0.1⫻k hydrogen . T 共K兲

100/T 共K⫺1兲

k hydrogen 共cm3 molecule⫺1 s⫺1兲

295 335 380 424 479 529 601 666

3.39 2.99 2.63 2.36 2.09 1.89 1.66 1.50

(0.56⫾0.06)⫻10⫺12 (0.83⫾0.08)⫻10⫺12 (1.23⫾0.12)⫻10⫺12 (1.65⫾0.17)⫻10⫺12 (2.27⫾0.23)⫻10⫺12 (3.18⫾0.32)⫻10⫺12 (4.31⫾0.43)⫻10⫺12 (6.05⫾0.61)⫻10⫺12

slightly from the earlier values,13 by a maximum of ⫾20%; the reason for this could be the 共too兲 low maximum 关 H2 兴 of only 8⫻1016 molecules cm⫺3 in the earlier measurements, resulting in less precise slopes of the second-order plot. The repeatability and statistical error of the present k 1 determinations were typically 2%–3%. The stated total errors in Table I, amounting to about 10%, include estimated possible sys-

FIG. 3. 共a兲 Arrhenius plot of the k(C2 H⫹H2 ) rate coefficient data in the 295–700 K temperature range measured in this work. The solid line represents a three-parameter modified Arrhenius fit to the experimental data. Error bars include possible systematic errors. 共b兲 Arrhenius plot of available experimental k(C2 H⫹H2 ) data in the 180–5000 K range. The dashed line is the three-parameter modified Arrhenius fit to the data of this work, T ⫽295– 700 K, extrapolated to 2000 K.

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tematic errors that could result from inaccuracies in the absolute reactant concentrations and other experimental parameters. The Arrhenius plot features a strong nonlinear behavior showing an upward curvature. A nonlinear least-squares analysis leads to the following three-parameter modified Arrhenius expression for the range 295–700 K: k 1 共 T 兲 ⫽3.92⫻10⫺19T 2.57⫾0.30 ⫻exp关 ⫺ 共 130⫾140兲 K/T 兴 cm3 molecule⫺1 s⫺1 . value of (5.6⫾0.6)⫻10⫺13 cm3 Our k 1 (295 K) ⫺1 ⫺1 molecule s is nearly identical to the average of the experimental data reported over the last 15 years for 295–300 K: 5.7⫻10⫺13 cm3 molecule⫺1 s⫺1 . Also, as shown in Fig. 3共b兲, the 共extrapolated兲 modified Arrhenius fit to our data gives an almost optimum representation of all existing k 1 data, except for the data at T⬍220 K of Opansky and Leone29 and the results of Kruse and Roth33 at the extremities of their T-ranges. IV. QUANTUM CHEMICAL CALCULATIONS

After having redetermined the rate constants of the C2 H⫹H2 reaction for a large range of temperatures, we now attempt to address some of the many unresolved questions, using high level ab initio quantum chemical calculations. The first question addressed here concerns the linearity of the transition state structure for hydrogen abstraction whereas the second is about the identity of the other possible product channels. We aim to find out whether the hydrogen abstraction constitutes the sole route for the disappearance of ethynyl radicals or other low-lying reaction paths could somehow intervene in the process, in particular at very high temperatures 共2900– 4000 K兲, at which the theoretical CVTST-SCT predictions of Zhang et al.34 for the H-abstraction rate coefficient appear to be a factor 3– 4 below the experimental rate coefficient values.33 As a matter of fact, while the (C2 H3 ) species were studied in several earlier theoretical studies,51 only different separate portions of the energy surface were investigated; there is no study to date considering the whole (C2 H3 ) energy surface. This system contains two main isomers of fundamental importance including the vinyl radical (H2 CvCH) and methylcarbyne (H3 C–C) and a number of fragments. Due to the fact that while methylcarbyne is only a marginally transient species in its doublet electronic ground state (X 2 A ⬙ ) readily rearranging to the lower-lying vinyl isomer, it is quite stable in the lowest-lying quartet state (a 4 A 2 ). 52–54 Therefore a certain crossing between both states might be possible. For this purpose, it is our intention here to explore the interesting (C2 H3 ) potential energy surfaces in both lowest-lying doublet and quartet states. Thus our search was not only for the part of the energy surface comprising the hydrogen abstraction but also for other channels and the connections between the intermediates irrespective of their relevance to the main product formation of the C2 H⫹H2 reaction. All calculations were performed using the GAUSSIAN 94 suite of programs.55 Geometry optimizations were initially conducted using molecular orbital theory at the Hartree–


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Fock 共HF兲 and density functional theory 共DFT兲 with the popular hybrid functional B3LYP, in conjunction with the 6-311⫹⫹G(d,p) basis set. Harmonic vibrational wave numbers were calculated at both HF and B3LYP level in order to characterize the stationary points as equilibrium and transition structures. In all cases, both methods gave the same identity for each of the structures considered. The zeropoint energies 共ZPE’s兲 were derived from B3LYP frequencies scaled down by a uniform factor of 0.97. In order to improve further the geometrical parameters, they were reoptimized at the coupled-cluster theory level with all single and double excitations plus perturbative corrections for triple substitutions 共CCSD共T兲兲 with the same basis set. The unrestricted formalism 共UHF, UB3LYP, and UCCSD兲 was used for open-shell states. In 共U兲CCSD共T兲 calculations, the core orbitals were kept frozen. Due to the presence of multiple bond systems, the UHF reference wave functions for doublet and quartet states are normally expected to be spincontaminated but fortunately, the contaminations by higher spin states encountered in the present system are rather small. Improved relative energies between stationary points were finally derived using single-point electronic energies computed at the CCSD共T兲 level with the extended correlation-consistent aug-cc-pVTZ basis set at CCSD共T兲/6-311⫹⫹G(d, p) optimized geometries. In general, the ordering of relative energies obtained by both B3LYP and CCSD共T兲 methods is similar; there are, as expected, some differences in the absolute relative energies here and there. To simplify the presentation of data we report here only the selected coupled-cluster geometries and the best relative energies. Thus, unless otherwise stated, the energetic values quoted hereafter refer to the ones obtained from UCCSD共T兲/aug-cc-pVTZ//UCCSD共T兲/6-311 ⫹⫹G(d,p)⫹ZPE computations. Throughout this section, bond lengths are given in angstrom, bond angles in degree, and relative energies in kJ/mol. A. The doublet „C2 H3 … potential energy surface

While Fig. 4 displays the selected UCCSD共T兲/6-311 ⫹⫹G(d,p) geometrical parameters of the relevant stationary points, Fig. 5 illustrates the schematic potential energy profiles showing the different pathways on the doublet (C2 H3 ) energy surface. Parameters of the fragments (C2 H,C2 H2 ,H2 ) are omitted for the sake of clarity. The minimum energy structures shown in Fig. 5 include the reactants C2 H(X 2 ⌺)⫹H2 1, C2 H(A 2 ⌸)⫹H2 1쐓 , methylcarbyne 共ethylidyne兲 2, vinyl radical 3, the fragments HCwCH⫹H 4, H2 CvC⫹H 5, and H3 C⫹C( 3 P) 6q. As for a convention, a ts XÕY stands for a transition structure connecting two equilibrium structures X and Y. As mentioned above, the vinyl radical and its isomers has been the subject of a large number of theoretical studies, we would refer to the compilation Quantum Chemistry Library Data Base 共QCLDB兲共Ref. 51兲 for a complete list of available papers. The geometrical parameters of these isomeric species have abundantly been examined and thus warrant no further comments.57– 62 In many aspects, the (C2 H3 ) energy surface is similar to that of the isoelectronic (CNH2 ) 共Ref. 56兲 species but be-

FIG. 4. Selected UCCSD共T兲/6-311⫹⫹G(d,p)-optimized geometrical parameters of the stationary points considered on the lowest-lying doublet potential energy surface. Bond lengths are given in angstroms and bond angles in degrees.

comes much simpler than the latter thanks to the symmetry of two carbon atoms. In agreement with earlier studies,57– 61 the vinyl radical 3 is calculated to be by far the most stable isomer lying 267 and 147 kJ/mol below the fragments C2 H(X 2 ⌺)⫹H2 1 and HCCH⫹H 4, respectively. We note that the latter value differs somewhat from the bond energy of D o (C2 H2 – H)⫽138 kJ/mol recently derived from a spectroscopic study using the Rydberg-atom time-of-flight technique63 but deviates significantly from the earlier theoretical values of 168 kJ/mol 共Ref. 61兲 and 170 kJ/mol 共Ref.




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5, a hydrogen addition invariably leads to the formation of vinyl radical 3 via different indirect routes. Overall, the most interesting and relevant result emerging from Fig. 5 is a demonstration that when starting from the thermal reactants C2 H⫹H2 , the hydrogen abstraction process via ts 1Õ4 with its barrier of only ⬇10 kJ/mol is, beyond any doubt, the sole product channel of any importance. According to IRC analyses, the low-lying electronically excited state C2 H(A 2 ⌸)⫹H2 1쐓 correlate likewise with the C2 H2 ⫹H products, but via a barrierless path, and these reactants 1쐓 also correlate with methylcarbyne 2, via ts 1쐓 /2. The C2 H(A 2 ⌸)⫹H2 insertion reaction via ts 1쐓 /2 giving 共first兲 the methylcarbyne 2 is not at all competitive, even at the highest flame temperatures. The difference in energy between ts 1쐓 /2 and ts 1Õ4 for the C2 H(X 2 ⌺)⫹H2 hydrogen-abstraction reaction amounts to 94 kJ/mol, and ts 1쐓 /2 is a highly rigid structure, while ts 1Õ4 is an early and very loose one. As a result, for thermal reactants, even at a temperature of 5000 K, the rate of a C2 H(A 2 ⌸)⫹H2 reaction channel via ts 1쐓 /2 can only be a few percent of the rate of the direct C2 H(X 2 ⌺)⫹H2 hydrogen-abstraction via ts 1Õ4. B. The quartet „C2 H3 … potential energy surface

FIG. 5. Schematic energy profiles illustrating the different pathways on the lowest-lying doublet (C2 H3 ) energy surface starting from C2 H⫹H2 . Relative energies, given in kJ/mol, are obtained from UCCSD共T兲/aug-cc-pVTZ//UCCSD共T兲/6-311⫹⫹G(d,p)⫹ZPE computations.

59兲共see also Ref. 64兲. A detailed analysis of this discrepancy obviously goes beyond the purpose of the present work but this certainly merits an appropriate study.65 The methylcarbyne 2 is calculated to be less stable than the vinyl radical by 203 kJ/mol which compares well with an earlier estimate of 204 kJ/mol derived from CISDQ/TZ ⫹2P computations.53 This carbyne is relatively stable with respect to the loss of atomic and molecular hydrogen, but is confirmed to isomerize readily to vinyl radical through an energy barrier of only 35 kJ/mol 共a value of 37 kJ/mol being reported in Ref. 53兲. For the sake of completeness, Fig. 5 also includes the transition structure connecting acetylene and vinylidene without involvement of a H atom, denoted as ts-acet-singlet. The relative energy between the two C2 H2 isomers and the energy barrier compare well with previous results.65 It is important to note that at the UCCSD共T兲/6-311 ⫹⫹G(d,p) level, the ts 1Õ4 for H-abstraction from H2 by C2 H(X 2 ⌺) is not linear but the Ha – Hb and – Cc – Cd – He moieties form a Hb Cc Cd bond angle of 165°. A previous study using the UQCISD/6-311⫹G(d, p) method obtained a value of 168° for this parameter.34 Proceeding in the opposite direction the hydrogen addition to acetylene giving vinyl radical via ts 3Õ4 is the preferential process over the hydrogen abstraction through ts 1Õ4. Starting from vinylidene⫹H

Figure 6 displays the selected UCCSD共T兲/6-311 ⫹⫹G(d,p) geometrical parameters of the structures considered on the lowest-lying quartet electronic state and Fig. 7 the schematic potential energy surface. The structures essentially include those seen on the doublet surface but involving instead the triplet C2 H2 and quartet C2 H2 . In addition to the corresponding number given on the doublet surface, the letter q stands for quartet. Again, for the sake of completeness, the ts-acet-triplet shown in Fig. 7 designates the ts connecting both triplet C2 H2 isomers 共acetylene and vinylidene, without involvement of a H atom兲. While methylcarbyne 2q ( 2 A 2 ) restores now the C 3 v symmetry group that it lost in the doublet state due to a Jahn-Teller effect, the vinyl radical is losing the planarity of all atoms but still keeps a C s symmetry ( 4 A ⬙ ). The most important result is perhaps the fact that as in the case of the (CNH2 ) system,56 both doublet and quartet surfaces are well separated from each other, at least for the portions involving the hydrogen abstraction. The doublet ts 1Õ4 lies in fact about 30 kJ/mol below the quartet vinyl radical 3q which remains energetically the most stable isomer in this electronic state. However, the energy separation between both vinyl radical 3q and methylcarbene 2q is now reduced to only 21 kJ/mol as compared with that of 203 kJ/mol in the doublet surface. The former is larger than the gap of 11 kJ/ mol reported in Ref. 52. Both isomers 2q and 3q are also separated by large energy barriers for isomerisation and fragmentations. Starting from the reactants 1q, a ts for direct hydrogen abstraction was not found. Instead, a barrier-free insertion giving methylcarbyne 2q and an insertion associated with a barrier of 17 kJ/mol through the ts 1Õ3q giving vinyl radical 3q have been detected. Loss of a hydrogen atom from both 2q and 3q isomers invariably yields triplet vinylidene 5q


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FIG. 7. Schematic energy profiles illustrating the different pathways on the lowest-lying quartet (C2 H3 ) energy surface starting from C2 H⫹H2 . Relative energies obtained from UCCSD共T兲/aug-cc-pVTZ//UCCSD共T兲/6-311 ⫹⫹G(d,p)⫹ZPE computations are given in kJ/mol with respect to C2 H ⫹H2 1. FIG. 6. Selected UCCSD共T兲/6-311⫹⫹G(d,p)-optimized geometrical parameters of the stationary points considered on the lowest-lying quartet potential energy surface. Bond lengths are given in angstroms and bond angles in degrees.

rather than triplet acetylene 4q. In a sense, the H-loss is a regio-specific fragmentation process. It is thus remarkable that the starting system including triplet acetylene plus H atom 4q does not lead to any product on the quartet surface, unless the acetylene undergoes a preliminary rearrangement to its vinylidene isomer. As a matter of fact, the triplet vinylidene plus H atom supermolecule 5q is characterized by two different hydrogen additions producing either methylcarbyne 2q or vinyl radical 3q. Formation of the former is favored over the latter. In any case, it thus appears that the triplet vinylidene plays a crucial role in the reactions of (C2 H3 ) species in their lowest-lying but excited quartet state. Note that a reaction of triplet C2 H2 with H will also occur on the doublet surface, resulting in doublet 共ground state兲 C2 H3 , which is likely to be a barrierless process, and very fast at high enough pressures, thus outrunning any other reaction of triplet C2 H2 with H. In summary, it seems reasonable to conclude that the quartet (C2 H3 ) species are not involved in the transformation of their doublet counterparts, and if generated in the quartet state, the system considered could be expected to undergo a totally different reactivity.

C. Linearity of the transition structure for hydrogen abstraction C2 H¿H2 : Geometries, vibration frequencies, and relative energies at higher levels of theory

As stated above, the ts 1Õ4 was calculated to be slightly bent at the level of theory employed above 共Fig. 4兲. Nevertheless, earlier or even more recent theoretical studies24,41,42 often assumed a collinearity of this structure. Even though the barrier to linearity from such structure is rather small, a bent shape of this ts may induce some deviations in the calculated partition functions and thereby in the rate coefficients. In an attempt to investigate further this important point, we have reoptimized the geometry of the ts 1Õ4 with the UCCSD共T兲 method making use of the larger 6-311 ⫹⫹G(2d f ,2p) basis set. It turns out that at this high level the ts 1Õ4 becomes essentially linear 共cf. Fig. 8兲. We have also computed the harmonic vibration frequencies of the H-abstraction transition structure ts 1Õ4 and of the reactants C2 H and H2 at this same UCCSD共T兲/6-311⫹⫹G(2d f ,2p) level. The harmonic vibration frequencies for C2 H thus obtained 关3455, 2053, and 378共2⫻兲 cm⫺1, unscaled兴 are close to the experimental values, 关3289, 1840, and 372共2⫻兲 cm⫺1兴,66 which however are observed fundamental frequencies, rather than harmonic values. Even the unusually low CCH bending frequency of 372 cm⫺1, for which Zhang et al.34 obtained a UQCISD/6-311⫹G(d,p) result of 469 cm⫺1, is reproduced quite well at the high level employed by us. We can therefore expect that the frequencies of ts 1Õ4, 关i555, 3545, 3452, 2048, 545, 532, 499共2⫻兲, and 83共2⫻兲




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best estimate in the harmonic oscillator approximation. In addition, we have also been able to locate two weak complexes arising from interactions of ethynyl radical with molecular hydrogen; their geometries are also displayed in Fig. 8 as denoted by Complex1 and Complex2. Again, although both complexes are quite weak lying only about 1 kJ/mol below the reactant limit, their possible role in the abstraction kinetics at the very low temperatures of the interstellar medium deserves to be clarified in future studies. V. DISCUSSION AND CONCLUSIONS

FIG. 8. Selected UCCSD共T兲/6-311⫹⫹G(2d f ,2p)-optimized geometrical parameters of the ts 1Õ4 and two complexes of C2 H⫹H2 . Bond lengths are given in angstroms and bond angles in degrees.

cm⫺1兴, in particular the crucial degenerate bending frequencies, are also approximated well. Combined with our result, at the same level, of 4412 cm⫺1 for H2 , we find a difference between the UCCSD共T兲/6-311⫹⫹G(2d f ,2p) harmonic vibration ZPE of ts 1Õ4 and that of the reactants 1 of ⌬ZPE ⫽3.65 kJ/mol, whereas the UQCISD/6-311⫹G(d, p) ⌬ZPE of Zhang et al.34 is 1.13 kJ/mol, likewise in the harmonic oscillator approximation for all internal modes. Moreover, we have performed single-point UCCSD共T兲 energy computations on the above UCCSD共T兲/6-311 ⫹⫹G(2d f ,2p) geometries of ts 1Õ4 and the reactants employing the larger 6-311⫹⫹G(3dp,2p) basis and also the higher-quality aug-cc-pVTZ basis set. Thus, including the harmonic ⌬ZPE of 3.65 kJ/mol, adiabatic barrier height values are obtained of E o ⫽10.82⫹3.65⫽14.5, and 9.16⫹3.65 ⫽12.8 kJ/mol, respectively, with the latter undoubtedly the

In the present study, the absolute rate coefficients of the gas phase reaction of the ethynyl radical with molecular hydrogen (HCwC⫹H2 ) were measured at higher temperatures. In the 295– 666 K experimental temperature range, the results indicate that the rate coefficient exhibits a marked non-Arrhenius behavior, k hydrogen(T)⫽3.92 ⫻10⫺19T 2.57⫾0.30 exp 关⫺(130 ⫾ 140) K / T 兴 cm3 molecule⫺1 s⫺1 , in near-quantitative accord with theoretical predictions.13,24,29,34 Ab initio MO calculations up to the UCCSD共 T 兲/aug-cc-pVTZ // UCCSD 共 T 兲/ 6-311⫹⫹G (d,p) level on both lowest-lying doublet and quartet energy surfaces revealed that among the possible mechanisms of H-abstraction, insertion and addition reactions, the direct H-abstraction yielding HCwCH⫹H is associated with the lowest barrier height. The other possible product channels do not participate significantly, not even at 5000 K. Our calculations also revealed the existence of two weak complexes at the entrance channel; further studies clarifying their possible implication in the kinetics of the HCwC⫹H2 reaction at very low temperatures is desirable. Also, the doublet and quartet energy surfaces are well separated from each other. Quartet C2 H lies too high above the doublet ground state to be thermally populated to any significant extent in flame conditions, even at 5000 K. UCCSD共T兲 geometry optimizations and associated harmonic vibration frequency calculations using the 6-311 ⫹⫹G(2d f ,2p) basis function reveal the collinearity of the ts 1Õ4 for H-abstraction 共on the doublet surface兲 and result in a harmonic-oscillator zero point energy difference between ts 1Õ4 and the reactants of ⌬ZPE⫽3.65 kJ/mol, i.e., 2.5 kJ/mol higher than obtained in a recent 共lower-level兲 UQCISD/6-311⫹G(d,p) study.34 On the other hand, our best-level UCCSD共T兲/aug-cc-pVTZ//UCCSD共T兲/6-311 ⫹⫹G(2d f ,2p) classical potential energy barrier 共i.e., without ⌬ZPE兲, of 9.2 kJ/mol, is in excellent agreement with the G2//UQCISD/6-311⫹G(d,p) result of 9.4 kJ/mol reported in the above-mentioned study.34 Given the high level of theory and the high-quality basis set of our calculation, our classical barrier value is expected to be nearly converged, within 1–2 kJ/mol. Yet, due to the higher harmonic oscillator ⌬ZPE of the present work, using harmonic vibration frequencies obtained at a higher level of theory, our best estimate for the adiabatic barrier, E o ⫽12.8 kJ/mol, is significantly higher than the G2//UQCISD/6-311⫹G(d,p) result of E o ⫽10.5 kJ/mol of Zhang et al.34 It must be noted that an increase in the adiabatic barrier value by 2.3 kJ/mol at a fixed frequency factor in a transition state theory calculation, will entail a decrease of the 300 K rate coefficient by a factor


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of 2.5. It thus appears that the fair agreement of the CVTST/ SCT predictions of Zhang et al.34 for the k(C2 H⫹H2 ) rate coefficient with the experimental data in the range 180–500 K (k th /k exp⫽0.67– 1.25) may be fortuitous and involve a cancellation of errors, the less satisfactory agreement for the 2900– 4000 K range (k th /k exp⫽0.25– 0.35) 共Refs. 33, 34兲 already suggesting a serious deficiency in the theoretical frequency factor. The very low values of some of the bending frequencies of the transition state—especially considering the involvement of H atoms, suggests that the usual approximations of separable harmonic motions will not work well in transition state calculations. In a future paper we intend to show, quantitatively, that 共variational兲 transition state theory predictions can only be reconciled with the experimental data for the entire temperature range of 180–5000 K by incorporating important, multiple effects of strong anharmonicity for several internal modes of the H-abstraction transition state, lowering its zero-point energy and hence the adiabatic barrier, and effecting both the absolute magnitude and temperaturedependence of the partition function ratio. In that theoretical paper we also intend to address the rate coefficient of the reverse reaction.

SUPPORTING INFORMATION

Upon request, the authors can provide absolute, relative and zero-point enegies of the stationary points on the doublet and quartet (C3 H2 ) surfaces at the various levels of theory stated in the paper.

ACKNOWLEDGMENTS

The authors wish to thank the Fund for Scientific Research 共FWO-Vlaanderen兲 and the KU-Leuven Research Council 共GOA and OT programs兲 for continuing support. 1

Peeters et al.


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