Ab Initio Chemical Kinetics for the CH3 + O(3P) Reaction and Related

Article pubs.acs.org/JPCA

Ab Initio Chemical Kinetics for the CH3 + O(3P) Reaction and Related Isomerization−Decomposition of CH3O and CH2OH Radicals Z. F. Xu,*,† P. Raghunath,‡ and M. C. Lin*,†,‡ †

Department of Chemistry, Emory University, Atlanta, Georgia 30322, United States Center for Interdisciplinary Molecular Science, Department of Applied Chemistry, National Chiao Tung University, Hsinchu 300, Taiwan

‡

S Supporting Information *

ABSTRACT: The kinetics and mechanism of the CH3 + O reaction and related isomerization−decomposition of CH3O and CH2OH radicals have been studied by ab initio molecular orbital theory based on the CCSD(T)/ aug-cc-pVTZ//CCSD/aug-cc-pVTZ, CCSD/aug-cc-pVDZ, and G2M// B3LYP/6-311+G(3df,2p) levels of theory. The predicted potential energy surface of the CH3 + O reaction shows that the CHO + H2 products can be directly generated from CH3O by the TS3 → LM1 → TS7 → LM2 → TS4 path, in which both LM1 and LM2 are very loose and TS7 is roaming-like. The result for the CH2O + H reaction shows that there are three low-energy barrier processes including CH2O + H → CHO + H2 via H-abstraction and CH2O + H → CH2OH and CH2O + H → CH3O by addition reactions. The predicted enthalpies of formation of the CH2OH and CH3O radicals at 0 K are in good agreement with available experimental data. Furthermore, the rate constants for the forward and some key reverse reactions have been predicted at 200− 3000 K under various pressures. Based on the new reaction pathway for CH3 + O, the rate constants for the CH2O + H and CHO + H2 reactions were predicted with the microcanonical variational transition-state/Rice−Ramsperger−Kassel−Marcus (VTST/RRKM) theory. The predicted total and individual product branching ratios (i.e., CO versus CH2O) are in good agreement with experimental data. The rate constant for the hydrogen abstraction reaction of CH2O + H has been calculated by the canonical variational transition-state theory with quantum tunneling and small-curvature corrections to be k(CH2O + H → CHO + H2) = 2.28 × 10−19 T2.65 exp(−766.5/T) cm3 molecule−1 s−1 for the 200−3000 K temperature range. The rate constants for the addition giving CH3O and CH2OH and the decomposition of the two radicals have been calculated by the microcanonical RRKM theory with the time-dependent master equation solution of the multiple quantum well system in the 200−3000 K temperature range at 1 Torr to 100 atm. The predicted rate constants are in good agreement with most of the available data.

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reaction was done at room temperature by Morris and Niki,1 who reported 3.01 × 10−11 cm3 molecule−1 s−1. However, all subsequent authors2,5,6,8,9,13,16 obtained values at room temperature in the range of 1.10 × 10 −10 to 1.70 × 10 −10 cm3 molecule−1 s−1, which is about 4 times greater than the earliest value. Slagle et al.7 investigated this reaction at five sightly higher temperatures between 294 and 900 K and found the rate constant to be independent of temperature having an average value of 1.40 × 10−10 cm3 molecule−1 s−1. Fockenberg and Preses15 reported values in a similar temperature range of 354−925 K and determined a weak positive temperaturedependent rate constant expression (2.40 ± 0.30) × 10−10

INTRODUCTION The reaction of the methyl radical, CH3, with the oxygen atom, O(3P), has attracted a great deal of attention because it not only plays an important role in combustion chemistry but also has considerable theoretical implications for the dynamics of its apparently simple mechanism. The two radical reactants readily associate to form high vibrationally excited methoxy radical, CH3O*, which can further decompose exothermically into several reaction fragments via the following accessible reaction channels: CH3 + O → CH3O* → CH 2O + H

(1)

→ HCO + H 2

(2)

→ COH + H 2

(3)

→ CH + H 2O

(4)

Special Issue: 100 Years of Combustion Kinetics at Argonne: A Festschrift for Lawrence B. Harding, Joe V. Michael, and Albert F. Wagner

There are many experimental kinetic studies1−16 on the CH3 + O(3P) reaction with CH2O + H reported to be primary products. The earliest rate constant measurement for this © XXXX American Chemical Society

Received: January 19, 2015 Revised: March 3, 2015

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DOI: 10.1021/acs.jpca.5b00553 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A exp[−(202 ± 60)/T] cm3 molecule−1 s−1. At higher temperatures of 1550−1720 K by Biordi et al.,3 1700−2300 K by Bhaskaran et al.,4 and 1610−2000 K by Lim et al.,12 relatively close values were obtained with the former average rate constant being 1.74 × 10−10 cm3 molecule−1 s−1 and the latter two rate constants being about 1.40 × 10−10 cm3 molecule−1 s−1. These values are also identical to those in the moderate temperature range. More recently, CO was detected following the first report by Seakins and Leone10 in 1992. In this Fourier transform infrared (FTIR) step scan experiment, the branching ratio of CO detected by chemiluminescence was reported to be as high as 0.40 ± 0.10 at room temperature. Several years later, Min et al.11 further confirmed the existence of the CO product in this reaction, detected by laser-induced fluorescence. Fockenberg et al.13−15 reported that the branching ratios of CO were 0.17 ± 0.11 at 299 K, 0.18 ± 0.04 at 296 K, and 0.15 ± 0.06 in 354−925 K in 1999, 2000, and 2002, respectively, measured with a newly constructed apparatus, combining a tubular flow reactor and a time-of-flight mass spectrometer (TOFMS), using a hollow-cathode lamp for photoionization. The temperature-independent values are about a factor of 2 smaller than those reported by Seakins and Leone. The last kinetic measurement with laser flash photolysis and mass spectrometer by Hack et al.16 in 2005 gave the branching ratio of CO to be 0.45 ± 0.05 at room temperature, which is close to Seakins and Leone’s data.10 In spite of the inconsistency, these results do provide sufficient experimental evidence that CO is the direct product of the CH3 + O(3P) reaction. Recently, a few theoretical studies17−21 have attempted to explore the kinetics and mechanism of the CH3 + O(3P) reaction. An earlier rate constant calculation based on quantum Rice−Ramsperger−Kassel (QRRK) theory was done in 1987 by Dean and Westmoreland,17 who suggested an expression, 1.25 × 10 −10 (T/298)−0.03 exp[−150(kJ/mol)/RT] cm3 molecule−1 s−1, in the temperature range of 300−2500 K for CH2O formation. Their rate constants are in fact almost independent of temperature and were in the low limit of the above-mentioned experimental rate constants, about 1.20 × 10−10 cm3 molecule−1 s−1. In 2001, Marcy et al.18 presented the combined experimental and theoretical investigations of this reaction. They calculated the reaction pathways at the B3LYP/ 6-31G(d) and CCSD(T)/cc-pVDZ levels of theory and predicted the branching ratio of CO by the classical trajectory method to be 0.15 at room temperature. By scanning the potential energy surface, they could not find the dissociation transition state connecting the CH3O radical with the H2 + CO products. Accordingly, they concluded that no saddle point was involved in the direct elimination of H2 from methoxy. In 2002, Knyazev19 regarded this case as the issue of reaction path bifurcations; namely, this unknown reaction step might occur at a valley-ridge inflection point. He calculated the microscopic energy-dependent rate constants based on the Rice− Ramsperger−Kassel−Marcus (RRKM) theory. His values of the CO branching ratio lies between 4% and 7%, depending on the potential energy surfaces calculated by UHF, UMP2, QCISD, and B3LYP. In 2004, Yagi et al.20 investigated in detail the barrierless association process of CH3 + O(3P) → CH3O at the MRCI/6-311G(2df,2p) level of theory. Their rate constants for CH2O production calculated by multistate quantum reactive scattering method lie in the high limit field of the experimental values and show a slight positive dependence on temperature between 50 and 2000 K. In 2005, Harding et al.21 studied the reaction of CH3 + O(3P) with the MRCI/aug-cc-pVTZ level of

theory and the rate constants calculated by variable reaction coordinate (VRC) transition-state theory with classical trajectory simulations. The high-pressure recombination rate constants are expressed as 9.20 × 10−11 T0.050 exp[68/T] cm3 molecule−1 s−1 at 200−2500 K with a small negative temperature dependence located in the midst of the experimental data. However, all these theoretical works have not reasonably clarified the mechanism for CH3O radical evolution into the H2 + CO + H products. Significantly, the reverse reaction kinetics of CH2O + H, the primary product of the CH3 + O(3P) reaction, in the gas phase is of special importance to the understanding of the radical chemistry involving these two radicals. The reactions of H with CH2O can produce both CH3O and CH2OH radicals by association reactions under high-pressure and low-temperature conditions, and the corresponding reactions along with Habstraction may take place as follows: CH 2O + H → CHO + H 2

(5)

CH 2O + H + M → CH 2OH* + M → CH 2OH + M (6)

CH 2O + H + M → CH3O* + M → CH3O + M

(7)

In the above reaction scheme, “*” denotes an internally activated intermediate and M stands for a third body or quencher. The addition reactions produce highly vibrationally excited CH2OH and CH3O radicals, which can also undergo either unimolecular isomerization, fragmentation or collisional stabilization. These complicated radical reaction processes have attracted a great deal of attention from experimentalists and theoreticians in the atmospheric chemistry and combustion chemistry communities in the past decades. For the CH2O + H reaction, direct H atom abstraction producing CHO + H2, several kinetic experiments have been carried out in different temperature ranges in the past decade.22−38 In 1999, Baulch et al.33 recommended the rate constant expression for the temperature range 300−1700 K, k = 2.1 × 10−16 T1.62 exp[−1090/T] cm3 molecule−1 s−1, derived by Choudhury and Lin31 from a nonlinear least-squares analysis of their high-temperature shock tube data with the low-temperature data of Baldwin and Cowe,22 Westenberg and deHaas,25 Ridley et al.,24 and Klemm.28 Dóbé et al.34 reported a rate constant at 298 K, (3.98 ± 0.83) × 10−14 cm3 molecule−1 s−1, measured by the discharge flow technique. In 2000, Oehlers et al.35 studied the kinetics of this reaction in the temperature range 296−603 K in an isothermal discharge flow reactor, and their rate constant was represented by the expression k = (1.45 ± 0.3) × 10−11 exp[−(11740 ± 84)/T] cm3 molecule−1 s−1. In 2002, Friedrichs et al.36 reported the rate constant for the same reaction, k = 1.1 × 10−9 exp[−4880/T] cm3 molecule−1 s−1. It was measured behind shock waves by means of the visible− ultraviolet (vis−UV) detection of formaldehyde in the temperature range 1510−1960 K. These recent three experimental results are very close to the values recommended by Baulch et al.33 for the low- and high-temperature ranges. Most recently, Wang et al.37 reinvestigated the same reaction by using the direct shock tube measurement and transition-state theory (TST) calculation. They reported a rate constant over the 1304−2006 K temperature range at 1 atm pressure, which was expressed by k = 1.97 × 1011(T/K)1.06 exp[−3818 K/T] cm3 mol−1 s−1, with uncertainty limits approximately +18%/− 26%. The results of their TST and our calculations (to be B


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Table 1. Comparison of Our Predicted Heats of Formationa with the Literature Data for CH2OH and CH3O at 0 K (in kcal/mol)

presented in a later section) also agree well with the experimental results. The two association reactions producing CH2OH (reaction 6) and CH3O (reaction 7) radicals have not been studied well. Only the formation of CH2OH result was reported by Tsuboi et al.38 in 1981 with the rate constant k = 2.09 × 10−14 exp[−601/T] cm3 molecule−1 s−1 at 1500−1900 K and 7 atm Ar pressure in the thermal decomposition of CH3OH carried out behind incident and reflected shock waves. However, there are more experimetnal and theoretical data available for the reverse of the unimolecular decomposition of the CH2OH and CH3O reactions (reactions 6 and 7, respectively) producing CH2O + H as will be discussed later.39−49 In light of the above experimental and theoretical results as well as the critical importance of the various related processes, we have attempted to elucidate the potential energy surface (PES) of the C1H3O1 system and its primary reverse product reactions of CH2O and H. The temperature and pressure dependences of the rate constants for these processes and, in particular, the product branching in the CH3 + O reaction (i.e., CH2O versus CO formation) have been derived using TST− variational RRKM theory by solving the master equation for the processes occurring by CH3O and/or CH2OH intermediates.

reaction

ΔfH°0(CH2OH)

G2M//B3LYP/6-311+G(3df,2p) −26.5 1.0 CH2O + H → CH2OH CH2O + H → CH3O −18.4 OH + CH3OH → H2O+CH3O −13.5 CH3 + CH3OH → CH4 + −8.2 −1.8 CH2OH CCSD(T)/aug-cc-pVTZ//CCSD/aug-cc-pVTZ −27.9 −1.4 CH2O + H → CH2OH CH2O + H → CH3O −19.5 OH + CH3OH → H2O + −12.9 CH3O −7.6 −1.2 CH3 + CH3OH → CH4 + CH2OH Literature Data Holmes et al. (1984)b −5.7 Lias et al. (1988)c Osborn et al. (1995)d Handbook Chem. and Phys. (1998)e Zhu et al. (2001)f Janoschek et al. (2002)g Rauk et al. (2003)h Rusic et al. (2005)i −2.5 Marenich et al. (2006)j Dyke et al. (1984)k −4.1 Seetula et al. (1992)l −0.4 Bauschlicher (1994)m −2.0 Dóbé et al. (1996)n −2.3 Johnson et al. (1996)o −2.7 Litorja et al. (1998)p −2.6 Marenich et al. (2003)q −2.5 CH2O + H→ CH2OH (Dames −28.7 r et al.) −19.3 CH2O + H→ CH3O (Dames et al.)r

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COMPUTATIONAL METHODS The geometries of the reactants, products, intermediates, and transition states involved in the ground state PES of the C1H3O1 system are optimized by the B3LYP hybrid density functional with the 6-311+G(3df,2p) basis set and the singleand double-substituted coupled cluster (CCSD) with the Dunning’s correlation consistent basis sets (aug-cc-pVDZ and aug-cc-pVTZ).50 All the stationary points have been identified for local minima and transition states by vibrational analysis. Unscaled vibrational frequencies were employed for the calculation of zero-point energy (ZPE) corrections and rate constant calculations. For a more accurate evaluation of the energetic parameters, higher-level single-point energy calculations of the stationary points were carried out by the CCSD(T) method with the aug-cc-pVTZ basis set and compared with the results by the modified Gaussian-2 (G2M) theory.51 On the basis of the optimized geometries at the B3LYP/6-311+G(3df,2p) level of theory, the G2M method calculates the base energy at the PMP4/6-311G(d,p) level of theory and improves it with the expanded basis set and coupled cluster corrections as well as a “higher level correction (HLC)”. All electronic structure calculations were performed with Gaussian 03 program.52 Methods and procedures for prediction of rate coefficients and branching ratios of the association and dissociation reaction channels are explained in Rate Constant Calculations.

ΔfH°0(CH3O)

± 0.2 8.1 ± 0.2 7.0 ± 0.3 ± 0.4 ± 0.2 7.0 ± 0.2 7.6 ± 0.3 ± 0.4 ± 2.0

± 0.2

5.6 5.6 6.8 5.9

± ± ± ±

2.0 0.7 0.4 0.9

5.4 ± 0.5 6.4 6.9 6.8 ± 0.5 7.5 ± 0.2

± 3.0 ± 0.4 ± ± ± ±

0.3 0.3 0.2 0.2

Calculated by the experimental heats of formation:49 ΔfH°0(CH2O) = −25.1 ± 0.2 kcal/mol, ΔfH°0(H) = 51.6 kcal/mol, ΔfH°0(CH4) = −15.9 ± 0.1 kcal/mol, ΔfH°0(CH3OH) = −45.4 ± 0.2 kcal/mol, ΔfH°0(H2O) = −57.1 kcal/mol, ΔfH°0(OH) = −8.8 ± 0.1 kcal/mol, ΔfH°0(CH3) = −35.9 ± 0.1 kcal/mol. bRef 53. cRef 54. dRef 55. eRef 56. fRef 57. gRef 58. hRef 59. iRef 60. jRef 61. kRef 62. lRef 63. mRef 64. nRef 65. oRef 66. pRef 67. qRef 68. rRef 49. a

available literature values,53−68 including experimental and theoretical estimates. It is apparent that the literature data of ΔfH°0(CH3O) vary from 5.4 ± 0.5 to 7.5 ± 0.2 kcal/mol and the high -level theoretical evaluations53−61 in recent years give bigger values than the values reported in earlier years53,54,56,57 except the value of Osborn et al. 55 Our calculated ΔfH°0(CH3O) values are 7.0−8.1 kcal/mol and 7.0−7.6 kcal/ mol at the G2M//B3LYP/6-311+G(3df,2p) level and at the CCSD(T)/aug-cc-pVTZ// CCSD/aug-cc-pVTZ level, respectively, which cluster around the higher values of Osborn et al.,55 Rauk et al.,59 and Marenich et al.61 For the heat of formation of CH2OH, the reported data53,58−68 of ΔfH°0(CH2OH) vary sparsely from −0.4 ± 0.4 to −5.7 ± 2.0 kcal/mol. However, its values evaluated after 199660,65−68 fall in a narrow range of −2.3 ± 0.3 kcal/mol and −2.7 ± 0.3 kcal/mol. Our calcualted heats of formation of CH2OH, −1.0 to −1.8 kcal/mol by G2M//B3LYP/6-311+G(3df,2p) and −1.2 to −1.4 kcal/mol

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RESULTS AND DISCUSSION Heats of Formation of CH3O and CH2OH. To assess the quality of theoretical predictions, we have derived the heats of formation for CH3O and CH2OH through reactions 6 and 7 as well as the following isodesmic reactions: OH + CH3OH → H 2O + CH3O (8) CH3 + CH3OH → CH4 + CH 2OH

ΔrH°0

(9)

Table 1 lists the calculated heats of formation at the G2M// B3LYP/6-311+G(3df,2p) and CCSD(T)/aug-cc-pVTZ// CCSD/aug-cc-pVTZ levels of theory to compare with the C


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The Journal of Physical Chemistry A by CCSD(T)/aug-cc-pVTZ//CCSD/aug-cc-pVTZ, are comparable to the recent literature data.53,60−68 In addition, the heats of formation predicted at the G2M//B3LYP/6-311+G(3df,2p) level for both CH3O and CH2OH radicals are in good agreement with those obtained by CCSD(T)/aug-cc-pVTZ// CCSD/aug-cc-pVTZ. Thus, these two methods should be reliable for prediction of the PES of the C1H3O1 system. Reaction Mechanism of the CH3 + O(3P) Reaction. Figure 1 shows the full PES of the CH3−O(3P) system. The

Table 2. Rotational Moments of Inertia and Harmonic Frequencies Calculated at the CCSD/aug-cc-pVTZ Level of Theory species

Ia, Ib, Ic (amu)

CH2O CH2OH

6.3, 46.3, 52.6 9.3, 60.2, 68.9

CH3O

11.4, 65.1, 65.5

CHO H2 LM3a TS1

2.4, 40.2, 42.7 1.0, 1.0 10.5, 111.2, 113.4 11.5, 60.6, 61.7

TS2

10.3, 61.9, 64.2

TS3

16.5, 58.0, 62.0

TS4

16.6, 61.5, 78.1

TS5a

9.5, 91.0, 94.4

TS6a

13.2, 62.5, 70.8

frequencies (cm−1) 1226, 1323, 1557, 1825, 2949, 3078 605, 809, 1142, 1228, 1404, 1522, 3159, 3333, 3890 1054, 1168, 1174, 1425, 1443, 1549, 2954, 3082, 3124 1151, 1949, 2801 4400 258, 286, 612, 616, 1057, 1660, 2889, 3801, 3888 i1250, 595, 641, 1148, 1300, 1495, 1641, 3011, 3155 i2005, 927, 1071, 1186, 1230, 1522, 2486, 3081, 3249 i605, 477, 855, 1212, 1308, 1530, 1706, 2958, 3084 i1639, 349, 846, 1183, 1215, 1338, 1410, 1889, 2951 i1621, 444, 534, 850, 1091, 1343, 2248, 3101, 3789 i1214, 281, 707, 954, 1102, 1202, 1329, 2612, 3818

a

Rotational moments of inertia and harmonic frequencies calculated at the CCSD/aug-cc-pVDZ level.

Figure 1. Schematic energy diagram of the CH3 + O (3P) predicted on the ground electronic doublet state potential energy surface at the CCSD(T)/aug-cc-pVTZ//CCSD/aug-cc-pVTZ level of theory.

eliminated from LM1 to the CH2O + H products. In fact, the energy of LM1 is only 0.2 kcal/mol lower than that of the products at the CCSD(T)/aug-cc-pVTZ//CCSD/aug-ccpVTZ level. In addition, the loose hydrogen-bonding complex LM1 can isomerize to another loose hydrogen-bonding complex LM2 almost freely with the ∠HCH bond angle (θ) changing via the transition state TS7, at which the C−H bond slightly elongates to 3.555 Å and the H−H bond slightly shortens to 2.933 Å. We can see that at LM2 three atoms C− H−H lie almost in line and the H−H bond shortens to 2.896 Å. From LM1 to TS7 to LM2, the bond angle θ changes from 74.3 to 47.9 to 3.0 degrees. Figure 3 displays the changes in the energy and the imaginary vibrational frequency with respect to the angle θ. Apparently, the loose hydrogen-bonding complex LM2 can easily decompose to CH2O + H as LM1 does. Also, LM2 can easily decompose to CHO + H2 by the hydrogen abstraction transition state TS4 with a potential barrier of only 6.3 kcal/mol, as shown in Figure 1. Because CHO + H2 and CO + H + H2 lie below CH3 + O by 80.7 and 66.8 kcal/mol, respectively, and the barrier of CHO → CO + H is only 17.7 kcal/mol, the highly vibrationally excited HCO radical is unstable and can rapidly fragment into CO and H completely. Therefore, the predicted final product should be CO + H instead of HCO, which is consistent with the experimental observations mentioned in the above paragraph. Accordingly, the critical reaction step LM1 → TS7 → LM2 connects the CH3O radical with the products CHO + H2, satisfactorily rationalizing the formation of the CHO + H2 and its final products CO + H + H2 as observed by Leone and coworkers10,18 and other experimental groups.13−16 Reaction Mechanism of the CH2O + H Reaction. The geometric parameters of the stationary points, shown in Figure 2, were computed at the B3LYP/6-311+G(3df,2p), CCSD/ aug-cc-pVDZ, and CCSD/aug-cc-pVTZ levels of theory. The potential energy diagram obtained at the CCSD(T)/aug-ccpVTZ//CCSD/aug-cc-pVTZ level is presented in Figure 4,

initial step from CH3 + O(3P) is the formation of CH3O, which is a highly exothermic barrierless association process. The minimum energy path, depicted by changing the O−CH3 distance at the CCSD/aug-cc-pVTZ level of theory, is comparable with the results calculated by B3LYP/6-311+G(3df,2p), CASSCF(9,9)/aug-cc-pVDZ, and CASPT2(9,9)/augcc-pVDZ levels, and their minimum energy paths (MEPs) curves are shown in Supporting Information (Figure S1). It implies that the single reference methods can reasonably describe the barrierless association process CH3 + O(3P) → CH3O for kinetical predicton, as will be illustrated later. The association reaction producing CH3O is predicted to be exothermic by 89.6 and 83.8 kcal/mol at the G2M//B3LYP/ 6-311+G(3df,2p) and CCSD(T)/aug-cc-pVTZ//CCSD/augcc-pVTZ levels, respectively; the former agrees better with the experimental heat of reaction of 88.1 ± 0.5 kcal/mol at 0 K.60 Furthermore, Figure 1 illustrates that there are two isomerization channels from CH3O to CH2OH and LM1 complex via transition states TS2 and TS3, respectively. The predicted vibrational frequencies and moments of inertia for most of these species are summarized in Table 2 to be applied for kinetic calculations in the next section. The optimized geometries of reactants, intermediates, transition states, and products are shown in Figure 2. In the first channel, TS2 is of a triangular structure with the hydrogen atom migrating from C to O. The newly formed CH2OH radical can further decompose to CH2O + H, COH + H2, and CH + H2O via transition states TS1, TS5, and TS6, respectively. However, the latter two should not be significant decomposition channels because their barriers are much higher than that of TS1 by as much as 44 kcal/mol. In the second channel, TS3 corresponds to the C−H bond-stretching motion to form the complex LM1, which has loose hydrogen bonds C−H of 3.325 Å and H−H of 3.210 Å. Thus, the hydrogen atom is expected to be easily D


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Figure 2. Geometries of the reactants, intermediates, and transition states (length in angstroms and angle in degrees) optimized at the B3LYP/6311+G(3df,2p) (top line), CCSD/aug-cc-pVDZ (middle line), and CCSD/aug-cc-pVTZ (bottom line) levels of theory.

relative to the energy of CH2O + H. Also, for the sake of comparison, the G2M energies of all stationary points are placed in Figure 4 in parentheses. The deviation between the values predicted by both methods for the worst cases is ∼10%. Unless otherwise stated, all energies cited in our discussion below will be based on the values obtained by the CCSD(T)/ aug-cc-pVTZ//CCSD/aug-cc-pVTZ method. Abstraction Reaction CH2O + H → CHO + H2. As shown in Figure 4, this reaction was predicted to take place via the transition state TS4, whose geometric parameters optimized at the three levels of theory are shown in Figure 2. It can be seen that the C−H breaking bond is slightly shorter and the H−H forming bond is slightly longer at the CCSD/aug-cc-pVTZ level than at the CCSD/aug-cc-pVDZ and B3LYP/6-311+G(3df,2p) levels. The barriers of the forward and reverse hydrogen atom abstraction reactions are predicted to be 6.1 and 22.5 kcal/mol, respectively, which are almost the same as those calculated at the G2M//B3LYP/6-311+G(3df,2p) level. In 2000, Oehlers et al.35 gave the forward reaction activation energy of 4.4 ± 0.4 kcal/mol by analyzing their kinetic results in the temperature range of 296−780 K. Two years later, another

Figure 3. Minimum energy path and lowest frequency along the angle θ in the LM1 → TS7 → LM2 process with the geometries of LM1, TS7, and LM2 (length in angstroms). E


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a 38.0 kcal/mol barrier. The second association channel forms CH3O via TS3 with a smaller barrier of 5.7 kcal/mol. Among these three transition states, TS1 and TS3 represent the processes involving the O and C atoms of CH2O as the reaction centers and TS2 is a triangle transition state for the isomerization involving the breaking of the O−H bond and forming of the C−H bond concurrently. There are no essential differences for the geometric parameters of the transition states predicted by the three optimization methods. The energies of TS1 and TS3 at the CCSD(T)/aug-cc-pVTZ//CCSD/aug-ccpVTZ level are slightly greater than those at the G2M// B3LYP/6-311+G(3df,2p) level by only 0.4 and 0.7 kcal/mol; however, the energy of TS2 at the CCSD(T) level is 2.1 kcal/ mol lower than that by the G2M method, although the barrier for the isomerization process predicted by both methods are very close (38.0 versus 38.7 kcal/mol). As shown in Figure 4, at the CCSD(T)/aug-cc-pVTZ//CCSD/aug-cc-pVTZ level, the association barriers from CH2O + H to CH3O and CH2OH are 5.7 and 11.6 kcal/mol, respectively, implying that the former addition process is favored. For the CH3O barrier, there have been six literature values as listed44,46,49,59,70,71 in Table 3, ranging from 4.4 to 8.0 kcal/mol. Our calculated value (5.7 kcal/mol) lies in the midrange and is almost equal to the theoretical results of Walch70 and Dames and Golden.49 The isomerization barrier for CH2OH → CH3O predicted by the two methods (38.0 and 38.7 kcal/mol) and those for the reverse reaction (29.6 and 30.6 kcal/mol) are also close to that obtained by Walch,70 who reported 30.1 kcal/mol at the CCI// CASSCF level of theory, and to the values reported by Burgers et al.,72 29.7 kcal/mol, and by Dames and Golden,49 29.5 kcal/ mol, computed at the CBS-QB3 and RCCSD(T)/CBS levels of theory, respectively. Reaction Mechanism of the CH2OH Decomposition. In addition to the isomerization process from CH2OH to CH3O, there are three other channels involved in the unimolecular decomposition reactions of CH2OH as shown in Figure 4. The first one is the fragmentation of CH2OH via TS1 to CH2O + H. The decomposition barrier was predicted to be 39.5 kcal/mol at the CCSD(T)/aug-cc-pVTZ//CCSD/aug-cc-pVTZ level, which is 1.8 kcal/mol greater than that by the G2M//B3LYP/ 6-311+G(3df,2p) method. Recently, Dames and Golden49 computed the barrier of 40.0 kcal/mol at the RCCSD(T)/CBS level. In 2006, Wei et al.73 published their spectroscopic experimental result for CH2OH → CH2O + H. The decomposition barrier they obtained is 43.5 kcal/mol, which is greater than our CCSD(T) value by 4.0 kcal/mol, although their heat of reaction, 27.5 kcal/mol, is almost the same as ours predicted at the CCSD(T) level. It should be mentioned that earlier kinetic measurements41 gave much smaller barriers, below 30 kcal/mol, for the decomposition process attributable in part to the pressure effect. The second decomposition channel is to form CH and H2O via a transition state TS5 and a complex LM with a high potential barrier of 83.4 kcal/mol. The LM complex was predicted to lie below both TS5 and CH + H2O by 8.0 kcal/mol. In 1996, Wang et al.74 reported that, at the MP2 level of theory, TS5 is 82.7 and 8.1 kcal/mol higher than CH2OH and LM, respectively, which is consistent with our result. The third channel is the decomposition from CH2OH to COH + H2 via TS6. This reaction process needs to overcome a barrier of 56.9 kcal/mol, which is the highest potential barrier among these three decomposition channels of CH2OH. When compared to the first channel, the latter are far less competitive.

Figure 4. Schematic energy diagram of the CH2O + H reaction predicted on the ground electronic doublet state potential energy surface at the CCSD(T)/aug-cc-pVTZ//CCSD/aug-cc-pVTZ level of theory. The numbers in parentheses are at the G2M//B3LYP/6311+G(3df,2p) level of theory.

direct measurement of the reaction by Friedrichs et al.36 determined the activation energy to be 9.7 kcal/mol for the temperatures from 1510 to 1960 K. Recently, Wang et al.37 have located a transition state for the H-abstraction process at the CCSD(T)-F12/VTZ-F12 level to be 6.4 kcal/mol, which is close to our values of 6.1 kcal/mol. The energy of CHO + H2 relative to that of CH2O + H was predicted to be −16.4 and −16.1 kcal/mol at the CCSD(T) and G2M levels, respectively, which agree quantitatively with the heat of reaction, −16.5 ± 0.2 kcal/mol, calcualted by the heats of formation of the related species (ΔfH°0(CHO) = 10.0 kcal/mol69 and others in Table 3). Addition Reactions CH2O + H → CH2OH and CH3O. The formation of CH2OH occurs via transition state TS1 with a 11.6 kcal/mol barrier, which is very close to that predicted by the G2M method, 11.2 kcal/mol (see Figure 4). CH2OH may isomerize to form CH3O through the transition state TS2 with Table 3. Experimental Activation Energies and Calculated Reaction Barriers of CH2O + H → CH3O in kcal/mol (ΔEa, Association; ΔEd, Decomposition) ΔEa Batta (1979) (400−476 K) Greenhill et al. (1986)b (RRKM) Zaslonko et al. (1988)c (900−1600 K) Page et al. (1989)d (MRCI) Choudhury et al. (1990)e (550−1660 K) Walch (1993)f (CCI) Dertinger et al. (1995)g Yamaguchi et al. (1999)h (CCSD(T)) Oguchi et al. (2000)i (610−740 K) Hippler et al. (2001)j (expt. 680−810 K) (QCISD(T)) Rauk et al. (2003)k (CBS) Dames et al. (2013)l this work (G2M) this work (CCSD(T))

8.0 5.6 7.6 4.4

4.5 5.4 5.0 5.7

ΔEd 27.5 24.0 22.1 25.6 33.3 23.4 24.3 25.7 24.3 26.2 24.7 24.2 24.7 23.4 25.2

a

Ref 42. bRef 48. cRef 43. dRef 44. eRef 45. fRef 70. gRef 76. hRef 71. Ref 46. jRef 47. kRef 59. lRef 49.

i

F


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The Journal of Physical Chemistry A Reaction Mechanism of the CH3O Decomposition. For CH3O, two decomposition channels are considered in this work: the formation of O + CH3 by O−C bond breaking and the formation of CH2O + H by C−H bond breaking. The former process has no intrinsic transition state available with a high endothermicity of 83.8 kcal/mol at the CCSD(T)/aug-ccpVTZ//CCSD/aug-cc-pVTZ level of theory, which is 6.9 kcal/ mol less than that predicted by G2M//B3LYP/6-311+G(3df,2p). Although the predicted value by the former method is less than the experimental value of 88.7 kcal/mol reported by Berkowitz et al.75 in 1994 and the theoretical value of 85.0 kcal/ mol calculated at CCSD(T)/aug-cc-pVTZ//CCSD(T)/ccpVDZ level by Marcy et al.18 in 2001, it is in excellent agreement with the recent theoretical value of 83.7 kcal/mol predicted at MR-SDCI/6-311G(2df,2pd) level by Yagi et al.20 The second decomposition channel, CH3O → CH2O + H, has the predicted barriers of 25.2 and 23.4 kcal/mol at the CCSD(T)/aug-cc-pVTZ//CCSD(T)/cc-pVDZ and G2M// B3LYP/6-311+G(3df,2p) levels, respectively. Experimental and theoretical barriers for this process, shown in Table 3, vary from 22.1 to 33.3 kcal/mol. Apparently, aside from the earlier activation energy data reported by Batt42 (27.5 kcal/ mol) and Choudhury et al.45 (33.3 kcal/mol) and that by Zaslonko et al.43 (22.1 kcal/mol) most values lie in the range of 24.0−26.2 kcal/mol.44,46−49,59,71,76 Our predicted barrier at the CCSD(T) level falls in this narrow range and agrees excellently with the recent theoretical and experimental results reported by Page,44 Yamaguchi,71 and Hippler47 and co-workers. In addition to TS1-TS3 for the fragmentation of CH3O and CH2OH discussed above, we have attempted to search for the transition states of the two H2-elimination pathways: CH2OH → CHO + H2 and CH3O → CHO + H2. Although they have not been found with the automatic search technique provided by the Gaussain code, the transition states were located manually along both MEPs. At the G2M//B3LYP/6-311+G(3df,2p) level of theory, the energies of the transition structures for the decomposition reactions occurring by 4- and 3-centered H2-molecular elimination producing CHO + H2 are 73.2 and 43.1 kcal/mol and the imaginary frequencies are i2040 cm−1 for the former and i1626 cm−1 for the latter, respectively. The high potential barriers of the two reactions make them kinetically uncompetitive in the thermally activated decomposition or the reverse H + CH2O addition reactions. The implication for the existence of these transition states, contrary to the conclusion reached earlier by Marcy et al.,18 to the subsequent CO formation from CHO should be negligible. To determine the reliability of CCSD(T) energies, the single-determinant nature of wave functions of the above key transition states, CH3O and CH2OH, has been confirmed by T1 diagnostics77 at the CCSD(T)/aug-cc-pVTZ level of theory. The T1 parameters of the transition states TS1, TS2, TS3, and TS4 are predicted to be 0.040, 0.020, 0.038, and 0.025, respectively, and those of CH3O and CH2OH to be 0.018 and 0.016, respectively. These small values indicate that the singlereference treatment of the present doublet system on the ground potential energy surface at the CCSD(T) level of theory is adequate.

component rates were evaluated at the E/J-resolved level, and the pressure dependence was treated by one-dimensional master equation calculations using the Boltzmann probability of the intermediate (CH3O*) for the J-distribution. Statisticaltheory rate constant calculation for the direct hydrogen abstraction reaction CH2O + H → CHO + H2 was performed by the Polyrate program79 using the canonical variational transition-state theory (CVT). The CVT rate constant includes multidimensional tunneling (MT) along the reaction coordinate.80 For the hydrogen addition reactions related to the association, isomerization and decomposition processes, the chemically activated time-dependent master equation (ME)81 was used to predict the rate constants and product distributions with the ChemRate program.82 Rate Constant for CH3 + O. According to the predicted reaction pathway, the microcanonical variational TST/RRKM theory with master equation analysis was employed to calculate the individual product branching ratios and rate constants in the temperature range of 200−2600 K by the Varif lex program.78 For the barrierless association process CH3 + O(3P) → CH3O, the potential along the reaction coordinate was approximated by the fitted Morse function and the potential for the transitional degrees of freedom orthogonal to reaction coordinate was described in terms of internal angles with a sum of products of sinusoidal functions.83 The computed potential energies could be fitted to the Morse function with the parameters of β = 2.09, 2.44, and 2.97 Å−1 calculated at the B3LYP, CASPT2, and CCSD levels of theory, respectively, and their fitted curves are shown in Figure S1 in Supporting Information. Also, in the present calculation the rotational symmetric numbers of both CH3 and CH3O are taken to be 6 and 3, respectively; the electronic state degeneracies of the three spin−orbit splitting electronic state for the ground state O(3P) are taken to be 5, 3, and 1, corresponding to the energy levels 0, 158, and 226 cm−1, respectively. Based on the Morse functions at the B3LYP, CASPT2, and CCSD levels, the predicted rate constants are shown in Figure 5. It should be first mentioned that our calculation result shows that this reaction is effectively independent of pressure in a wide pressure range and has a very weak temperature effect from 200 to 2600 K because of the small molecular size of this

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Figure 5. Predicted total rate constant for the CH3 + O reaction in the temperature range from 200 to 2600 K compared with experimental values. a, Washida (1973);2 b, Washida (1980);5 c, Biordi (1973);3 d, Bhaskaran (1980);4 e, Plumb (1982);6 f, Slagle (1987);7 g, Zellner (1988);8 h, Oser (1991);9 i, Lim (1993);12 j, Fockenberg (1999);13 k, Fockenberg (2002);15 l, Hack (2005);16 m, Dean (1987);17 n, Yagi (2004);20 o, Harding (2005).21

RATE CONSTANT CALCULATIONS Rate constant and individual product branching ratio calculations for the bimolecular CH3 + O reaction were carried out with the Varif lex program78 based on the microcanonical RRKM theory and variational transition-state theory. The G


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of temperature as the experimental result by Fockenberg et al.15 However, our predicted branching ratios of HCO + H2 are over 2 times higher than these authors’ data,13−15 which are 0.17 ± 0.11, 0.18 ± 0.04, and 0.15 ± 0.06 at 299 K, 296 K, and 354− 925 K, respectively. However, our predicted branching ratios of HCO + H2 at 298 K are in good agreement with Seakins and Leone’s value,10 0.40 ± 0.10, and within the error range of 0.45 ± 0.05 reported by Hack et al.16 This effectively substantiates the reaction path predicted in the present work, and the evaluated rate constants are believed to be reliable. Rate Constant for H-Abstraction of CH2O + H. The rate constants for the hydrogen abstraction channel over a wide range of temperatures have been calculated by conventional transition-state theory and canonical variational transition-state theory with small-curvature tunneling corrections. The minimum energy path (VMEP) and the ground-state vibrationally adiabatic potential (VGa ) are calculated at the CCSD(T)/ aug-cc-pVTZ level, as displayed in Figure 7, so as to evaluate

reaction system and the highly excited intermediate complexes. This is basically consistent with the experimental observations. From Figure 5, we can see that the values of the predicted rate constants depend noticeably on the different Morse functions calculated at the B3LYP, CASPT2, and CCSD levels, although the deviation lies within ±15% over the entire temperature range studied. The predicted rate constants with the CASPT2 and CCSD Morse functions are somewhat smaller than that with the B3LYP Morse function by around 10% and 20%, respectively. The predicted values with the three methods lie well within the experimental scatter, which covers the (1−2) × 10−10 cm3 molecule−1 s−1 range. Interestingly, of the three predicted rate constant curves, the one with the B3LYP Morse function lies in the middle of the scatter with the value (1.45 ± 0.05) × 10−10 cm3 molecule−1 s−1. In addition, one can see from Figure 5 that the predicted rate constant by Dean and Westmoreland17 by QRRK is in reasonable agreement with our values obtained by the CASPT2 and CCSD Morse functions at temperatures between 300 and 2000 K, but the theoretical rate constant curve of Yagi et al.20 is higher, with a positive temperature dependence, than the one with the B3LYP Morse function over the temperature range studied. When compared with the recent theoretical rate constants predicted by Harding et al.21 with a small negative dependence, their curve crosses with the ones predicted with the B3LYP Morse function near 500 K. When compared with the available experimental data, the best predicted rate constants are those by the B3LYP Morse function, varying between 1.40 × 10−10 and 1.48 × 10−10 cm3 molecule−1 s−1 in the temperature range of 200−2600 K, and can be expressed in units of cubic centimeters per molecule per second as follows: k = 1.79 × 10−10T −0.027 exp( −1.2/T ) −11 0.187

= 4.97 × 10

T

(200−1000 K) Figure 7. Minimum energy path (VMEP) and the ground-state vibrationally adiabatic potential (VGa ) evaluated at the CCSD(T)/ aug-cc-pVTZ level for the direct hydrogen abstraction channel CH2O + H → CHO + H2.

exp( −207.0/T ) (1000−2600 K)

Figure 6 presents the comparison of our predicted branching ratios of the individual products with the experimental values. The predicted branching ratios of CH2O + H and HCO + H2 are 0.60 and 0.40, respectively, based on the rate constants calculated by the B3LYP Morse function. They are independent

variational point and tunneling effect. The predicted individual rate constants are shown in Figure 8. The rate constants exhibit a positive temperature dependence because of the distinct

Figure 8. Rate constants, k(CH2O+H), of CH2O + H → CHO + H2 compared with experimental values. a, ref 23; b,ref 24; c, ref 25; d, ref 26; e, ref 27; f, ref 28; g, ref 29; h,ref 30; i, ref 31; j, ref 32; k, ref 33; l, ref 34; m, ref 35; n, ref 36; o, ref 37 (theory); p, ref 37 (exptl).

Figure 6. Comparison of our predicted branching ratios for CH3 + O reaction of individual products as functions of temperature relative to the total rate constant with experimental values. a, ref 10; b, ref 13; c, ref 14; d, ref 15; e, ref 16. H


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used for the energy integration in the master equation computation to ensure the convergence at high temperature. The rate constants producing CH2OH and CH3O from the CH2O + H association reactions at Ar pressure (denoted as ka(CH2OH) and ka(CH3O)) are displayed in Figures 9A and

barrier of 6.1 kcal/mol. The effect of variational corrections for these reactions is very small and the effects of tunneling and small curvature corrections are very large at low temperatures, as shown in Figure 8. Above 1000 K, three rate constants calculated by CVT (or TST), CVT/ZCT, and CVT/SCT merge gradually. The CVT/SCT result at 400 K is higher than the CVT and CVT/ZCT values by 6.0 and 2.4 times, respectively, suggesting the importance of the small-curvature corrections. Figure 8 compares our predicted rate constants with the earlier literature data, including the experimental and theoretical results. The rate constant curve predicted by CVT/SCT is in good agreement with most of the experimental data. In the high-temperature range, the theoretical values have a larger deviation from the results reported by Cribb et al.32 and Oehlers et al.,35 but are in excellent agreement with the shock tube result of Friedrichs et al.36 and the more recent experimental rate constant obtained by Wang et al.37 at 1304−2006 K and 1 atm pressure, given by 3.27 × 10−13 T1.06 exp(−3818/T) +18/−26% cm3 molecule−1 s−1. For practical applications, the predicted rate constants for this H-abstraction channel have been fitted by least-squares analysis and are given below in units of cubic centimeters per molecule per second for the temperature range of 200−3000 K: k(CH 2O + H → CHO + H 2) = 2.28 × 10−19T 2.65 exp(−766.5/T )

Rate Constants for CH2O + H Addition Reactions. The addition of the H atom to CH2O can be described by the coupled scheme:

where k is rate constant, α branching ratio, and M the inert gas molecule. The formation of CH2OH is influenced by not only k1 but also k2 because of the isomerization between CH2OH and CH3O, similarly for the formation of CH3O. It should be mentioned that in the scheme, the contribution of LM1 and LM2 intermediates via TS4 cannot compete with the loose variational TS from LM1 directly to CH2O + H; namely, the decomposition of CH3O is mainly controlled by TS3. The same was found to be the case for the reverse unimolecular decomposition of both radicals. To treat this mutually coupled mechanism kinetically, the time-dependent master equation (ME) solution of the present multiple quantum well system was made by employing the ChemRate program,82 as presented in the above rate constant calculation section, in the temperature range of 200−3000 K at 1 Torr to 100 atm. Lennard-Jones (L-J) parameters were taken from the literature84 for He, N2, and Ar bath gases (σHe = 2.556 Å, εHe/kB = 10.2 K; σN2 = 3.798 Å, εN2/kB = 71.4 K; σAr = 3.542 Å, εAr/kB = 93.3 K) and CH2OH and CH3O radicals (σ = 3.626 Å, ε/kB = 481.8 K) to estimate the frequency of collisions. The energy increment was fixed at 10 cm−1 in all sum-of-state and density-of-state calculations that were performed using the modified Beyer−Swinehart algorithm.85 The energy transfer parameters (α) are taken to be 120, 250, and 400 cm−1 for He, N2, and Ar bath gases, respectively, according to the “exponential down” model. The energy bin size, ΔE = 100 cm−1, and a maximum energy limit, Emax = 168.3 kcal/mol, were

Figure 9. (A) Rate constants, ka(CH2OH), forming CH2OH from the CH2O + H → CH2OH association reaction at Ar bath gas. (B) The branching ratios of k1α1/ka(CH2OH) and (k2α−i − k1αi)α1/ ka(CH2OH) at 1 atm pressure. a, ref 38, at 7 atm Ar pressure and 1500−1900 K.

10, respectively. Apparently, both ka(CH2OH) and ka(CH3O) exhibit positive temperature dependencies below about 1000 K with negative temperature dependencies over about 1000 K attributable to the fact that the deactivation of both activated CH2OH and CH3O are not able to compete with their dissociation processes at high temperatures. On the effect of pressure, ka(CH3O) appears to be increasing with pressure, while ka(CH2OH) appears to be increasing with pressure below about 1 atm but decreasing with pressure above about 1 atm at low temperatures. This abnormal pressure effect on k a (CH 2 OH) is caused by the isomerization between CH2OH* and CH3O*. As seen in Figure 4, the potential barrier of CH2O + H → CH2OH is 5.9 kcal/mol higher than that of CH2O + H → CH3O. The former rate flux is much less than the latter by over 1 order of magnitude at low temperatures. Accordingly, ka(CH2OH) is the sum of two contributions from the direct association and the indirect isomerization at low temperatures: I


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The Journal of Physical Chemistry A ka100atm (CH3O) = 7.12 × 10−14T 0.45 exp( −1587.1/T ) 21 −10.15

= 3.80 × 10 T

(200−800K)

exp( −9000.0/T ) (800−3000K)

Rate Constant for Decompositions of CH2OH and CH3O. Figures 11 and 12 compare our predicted rate constants

Figure 10. Rate constants, ka(CH3O), forming CH3O from the CH2O + H → CH3O association reaction at different Ar bath gas pressures.

ka(CH 2OH) = k1α1 + (k 2α −i − k1αi)α1

Figure 9B shows the ratios of these two contributions to ka(CH2OH) at 1 atm pressure, which indicates that the second term, (k2α−i − k1αi)α1, is dominant at lower temperatures, whereas the first term, k1α1, is dominant at higher temperatures. In addition, the deactivation of the CH3O* is sensitive to pressure and influences the isomerization from CH3O* to CH2OH*. Also, at low pressures, ka(CH2OH) tends to increase because of the increasing CH3O isomerization to CH2OH. However, at high pressures, it tends to decrease because of the deactivation of CH3O*. The quantum tunneling effect was examined at 1 atm pressure as shown in Figures 9A and 10. The dashed line denotes the rate constants without Eckart tunneling corrections. It can be seen that the tunneling effect plays a role only in the low-temperature range at less than 300 K. At 200 K, the rate constant with Eckart tunneling corrections is about 3−5 times greater than that without the tunneling corrections. In Figure 9A, one available experimental value estimated at 7 atm in the 1500−1900 K range by Tsuboi et al.38 was compared with our predicted results. The experimental data agree reasonably well with the predicted theoretical curve at 7 atm pressure. For practical applications, the predicted rate constants at 1 and 100 atm at 200−3000 K were fitted with the following expressions in units of cubic centimeters per molecule per second:

Figure 11. Rate constants, kd(CH2OH), for the CH2OH decomposition to produce CH2O + H at different Ar bath gas pressures. Experimental data: a, ref 32, at 6−19 Torr Ar pressures and 1900− 2700 K; b, ref 40, at 1 atm N2 pressures and 900−2500 K; c, ref 41, at 300−400 Torr Ar pressures and 1370−1840 K; d, ref 39, at 160−465 Torr Ar pressures and 1450−2180 K.

ka1atm (CH 2OH)

Figure 12. Rate constants, kd(CH3O), for the CH3O decomposition to produce CH2O + H at different Ar bath gas pressures. Experimental data: a, ref 43, at 100−342 Torr Ar pressures and 900−1600 K; b, ref 42, at 1 atm N2 pressure and 393−433 K; c, ref 44, at 710 Torr Ar pressure and 550−1620 K; d, ref 45, at 710 Torr Ar pressure and 550− 1660 K.

= 7.00 × 10−10T −1.40 exp( −2612.5/T ) (200−1000 K) = 3.41 × 107T −6.23 exp( −7720.3/T )

(1000−3000 K)

ka100atm (CH 2OH) = 7.43 × 10−21T 2.84 exp( −3003.7/T ) 15 −8.04

= 6.09 × 10 T

for the decomposition reactions of CH2OH and CH3O, respectively, with the published kinetic data,32,39−49 using the ChemRate code82 coupling all accessible low-energy paths. Similar to the formation of CH2OH from CH2O + H, CH2OH can decompose via the direct O−H bond fragmentation or via isomerization to CH3O followed by C−H bond breaking. The result of the calculation reveals that at low pressures, the latter reaction path contribution to the decomposition rate constant of CH2OH is greater than the former, particularly at low

(200−1000 K)

exp( −10826.2/T ) (1000−3000 K)

ka1atm (CH3O) = 2.32 × 10−10T −1.22 exp( −1813.2/T ) (200−800 K) = 3.10 × 108T −6.79 exp( −5573.9/T )

(800−3000 K) J


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The Journal of Physical Chemistry A temperatures. From these figures we can see that the decomposition rate constants appear to have a strong positive temperature dependence and a weak negative pressure dependence because of the high decomposition potential barriers. Eckart tunneling corrections result in a 4-fold increase at 400 K for the rate constant of CH3O decomposition, but its effect is negligible on both the CH 3 O and CH 2 OH decomposition at T > 500 K. Compared to the literature data at different pressures in Figure 11, our predicted rate constants for the CH2OH decomposition are basically consistent with the data reported by Bowman,39 Tsang,40 and Hidaka et al.41 and somewhat greater than that of Cribb et al.32 For the CH3O decomposition reaction, our predicted rate constants are in good agreement with those reported by Batt42 and are close to the data reported by Page et al.44 and Choudhury et al.45 However, the experimental data of Zaslonko et al.43 are much greater than the predicted values. Figure 13 shows the predicted rate constants of the CH2OH and CH3O decomposition reactions in He, N2, and Ar bath

Figure 14. High-pressure rate constants, k d ∞(CH2 OH) and kd∞(CH3O), for the decomposition reactions of CH2OH and CH3O. Experimental data: a, ref 47, at 300−850 K; b, ref 48, at 1000 K; c, ref 48, at 1000 K; d, ref 49, CH2OH decomposition at N2 pressure and 1000−1800 K; e, ref 49, CH3O decomposition at He pressure and 600−1200 K.

The theoretical rate constants for the decomposition of CH2OH and CH3O at 1 and 100 atm Ar pressures given in the unit of reciprocal seconds could be represented by kd1atm(CH 2OH) = 4.52 × 1034T −7.11 exp( −22176.3/T )

(500−3000 K)

kd100atm(CH 2OH) = 3.39 × 1032T −5.88 exp( −23371.8/T )

(500−3000 K)

kd1atm(CH3O) = 3.17 × 1024T −4.25 exp( −13104.9/T )

(300−3000 K)

kd100atm(CH3O)

Figure 13. Low-pressure rate constants, kd0(CH2OH) and kd0(CH3O), for the decomposition reactions of CH2OH and CH3O. Experimental data: a, ref 47, at N2 pressure and 678−808 K; b, ref 47, at He pressure and 678−808 K; c, ref 46, at N2 pressure and 610−740 K.; d, ref 46, at He pressure and 610−740 K; e, ref 48, at Ar pressure and 600−1000 K; f, ref 48, at Ar pressure and 600−1000 K.

These results, which correlate well with the majority of available experimental data, may be reasonably employed for combustion simulation applications.

gases at low pressures. For CH2OH, Greenhill et al.48 estimated a somewhat greater value at 600 K, but a good agreement with ours exists at 1000 K. For CH3O, our predicted results are slightly smaller than the data reported by Oguchi et al.,46 Hippler et al.,47 and Greenhill et al.48 The high-pressure rate constants for the CH2OH and CH3O decomposition reactions are presented in Figure 14. The predicted rate constants for CH3O decomposition are in good agreement with the experimental results by Hippler et al.47 and Greenhill et al.48 However, for CH2OH decomposition, the rate constant at 1000 K reported by Greenhill et al.48 is greater than our predicted value by 2 orders of magnitude. Very recently, Dames and Golden49 have studied the effects of pressure and temperature on the unimolecular decomposition of CH3O and CH2OH in great detail using the RRKM theory. Their high-pressure limit values compare closely with our predicted results, as shown in Figure 14.

CONCLUSIONS The ground electronic doublet state potential energy surface of the C1H3O1 system was optimized at the CCSD/aug-cc-pVTZ, CCSD/aug-cc-pVDZ, and B3LYP/6-311+G(3df,2p) levels of theory and refined by single-point energy calculations by the CCSD(T)/aug-cc-pVTZ//CCSD/aug-cc-pVTZ and G2M// B3LYP/6-311+G(3df,2p) methods, with the variational potential energy function for the CH3−O association process characterized by B3LYP, CASSCF, and CAPT2. The predicted CH3 + O reaction PES shows that the CH2O + H and CHO + H2 product channels are directly accessible. CH2O + H can be produced by both CH3O → TS2 → CH2OH → TS1 → CH2O + H and CH3O → TS3 → LM1 → CH2O + H, whereas CHO + H2 can be formed by CH3O → TS3 → LM1 → TS7 → LM2 → TS4 → HCO + H2 with well-defined transition states, contrary to the conclusion reached by Marcy et al.18 based on their classical trajectory calculation. TS7 is very loose and roaming-like. The rate constants for these low-energy product channels (CH2O + H and CHO + H2) were computed with the

= 8.50 × 1028T −5.09exp( −14384.5/T )

(300−3000 K)

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K



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microcanonical VTST/RRKM theory in the temperature range from 200 to 2600 K. The predicted rate constants are independent of pressure and weakly dependent on temperature and are in good agreement with the experimental data. The total rate constant is k = 1.40 × 10−10 to 1.48 × 10−10 cm3 molecule−1 s−1 in the temperature range of 200−2600 K and the predicted branching ratios of CH2O + H and HCO + H2 are 0.60 and 0.40, respectively; all are consistent with experimental measurements. The rate constants for the three low-barrier processes including CH2O + H → CHO + H2, CH2O + H → CH2OH, and CH2O + H → CH3O, have been computed with appropriate statistical theories using the energies predicted at the CCSD(T)/aug-cc-pVTZ level. The majority of existing kinetic data for all three reaction channels can be well accounted for by the predicted results for the abstraction and the decomposition of the CH2OH and CH3O radicals. The hydrogen abstraction reaction was calculated by the canonical variational transition-state theory with quantum tunneling and small-curvature corrections, k(CH2O + H → CHO + H2) = 2.28 × 10−19 T2.65 exp(−766.5/T) cm3 molecule−1 s−1 for the temperature range of 200−3000 K. The rate constants for the association and decomposition reactions involving CH3O and CH2OH were calculated by the microcanonical RRKM theory with the time-dependent master equation solution of the present multiple quantum well system in the temperature range of 200−3000 K at 1 Torr to 100 atm. These rate constants exhibit strong temperature and pressure dependencies as expected. The predicted P, T-dependent rate constants are in good agreement with most of the earlier experimental and theoretical data.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Minimum energy paths (MEPs) for decomposition of CH3O → CH3 + O calculated at the B3LYP/6-311+G(3df,2p), CASPT2(9,9)/aug-cc-pvdz, and UCCSD/aug-cc-pvdz levels (Figure S1). This material is available free of charge via the Internet at http://pubs.acs.org.

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Article

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (M.C.L). *E-mail: [email protected] (Z.F.X.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The preliminary result of this work on the CH3 + O reaction, first presented in the Fall Technical Meeting of the Eastern Sates Section of the Combustion Institute on October 21−24, 2007, at the University of Virginia, Charlottesville, Va., was supported by the Basic Energy Sciences, Department of Energy, under Contract DE-FG02-97-ER14784. M.C.L. and P.R. appreciate the partial support of this work by the Ministry of Education, Taiwan (“Aim for the Top University Plan” of National Chiao Tung University). M.C.L. also acknowledges the support from Taiwan’s Ministry of Science and Technology for a Distinguished Visiting Professorship at the Center for Interdisciplinary Molecular Science, Chiao Tung University, Hsinchu, Taiwan. L


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Ab Initio Chemical Kinetics for the CH3 + O(3P) Reaction and Related

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