Reactions of OH with butene isomers: measurements of the overall rates and a theoretical study

Reactions of hydroxyl (OH) radicals with 1-butene (k(1)), trans-2-butene (k(2)), and cis-2-butene (k(3)) were studied behind reflected shock waves over the temperature range 880-1341 K and at pressures near 2.2 atm. OH radicals were produced by shock-heating tert-butyl hydroperoxide, (CH(3))(3)-CO-OH, and monitored by narrow-line width ring dye laser absorption of the well-characterized R(1)(5) line of the OH A-X (0, 0) band near 306.7 nm. OH time histories were modeled using a comprehensive C(5) oxidation mechanism, and rate constants for the reaction of OH with butene isomers were extracted by matching modeled and measured OH concentration time histories. We present the first high-temperature measurement of OH + cis-2-butene and extend the temperature range of the only previous high-temperature study for both 1-butene and trans-2-butene. With the potential energy surface calculated using CCSD(T)/6-311++G(d,p)//QCISD/6-31G(d), the rate constants and branching fractions for the H-abstraction channels of the reaction of OH with 1-butene were calculated in the temperature range 300-1500 K. Corrections for variational and tunneling effects as well as hindered-rotation treatments were included. The calculations are in good agreement with current and previous experimental data and with a recent theoretical study.     

A theoretical study of the H-abstraction reactions from HOI by moist air radiolytic products (H, OH, and O (3P)) and iodine atoms (2P(3/2))

The rate constants of the reactions of HOI molecules with H, OH, O ((3)P), and I ((2)P(3/2)) atoms have been estimated over the temperature range 300-2500 K using four different levels of theory. Geometry optimizations and vibrational frequency calculations are performed using MP2 methods combined with two basis sets (cc-pVTZ and 6-311G(d,p)). Single-point energy calculations are performed with the highly correlated ab initio coupled cluster method in the space of single, double, and triple (pertubatively) electron excitations CCSD(T) using the cc-pVTZ, cc-pVQZ, 6-311+G(3df,2p), and 6-311++G(3df,3pd) basis sets. Reaction enthalpies at 0 K were calculated at the CCSD(T)/cc-pVnZ//MP2/cc-pVTZ (n = T and Q), CCSD(T)/6-311+G(3df,2p)//MP2/6-311G(d,p), and CCSD(T)/6-311++G(3df,3pd)//MP2/6-311G(d,p) levels of theory and compared to the experimental values taken from the literature. Canonical transition-state theory with an Eckart tunneling correction is used to predict the rate constants as a function of temperature. The computational procedure has been used to predict rate constants for H-abstraction elementary reactions because there are actually no literature data to which the calculated rate constants can be directly compared. The final objective is to implement kinetics of gaseous reactions in the ASTEC (accident source term evaluation code) program to improve speciation of fission products, which can be transported along the reactor coolant system (RCS) of a pressurized water reactor (PWR) in the case of a severe accident.     

Dual-level direct dynamics studies for the reactions of OH radical with bromine-substituted ethanes

The dynamic properties of the multichannel hydrogen abstraction reactions of CH(3)CH(2)Br + OH --> products and CH(3)CHBr(2) + OH --> products are studied by dual-level direct dynamics method. For each reaction, three reaction channels, one for alpha-hydrogen abstraction and two for beta-hydrogen abstractions, have been identified. The minimum energy paths (MEPs) of both the reactions are calculated at the Becke's half-and-half (BH&H)-Lee-Yang-Parr (LYP)/6-311G(d, p) level and the energy profiles along the MEPs are further refined with interpolated single-point energies (ISPE) method at the G2M(RCC5)//BH&H-LYP level. There are complexes with energies less than those of the reactants or products located at the entrance or exit channels, which indicates that the reactions may proceed via an indirect mechanism. By canonical variational transition-state theory (CVT) the rate constants are calculated incorporating the small-curvature tunneling (SCT) correction in the temperature range of 220-2000 K. The agreement of the rate constants with available experimental values for two reactions is good in the measured temperature range. The calculated results show that alpha-hydrogen abstraction channel is the major reaction pathway in the lower temperature for two reactions, while the contribution of beta-hydrogen abstraction will increase with the increase in temperature.     

Direct dynamics study on mechanism and kinetics of the biradical self‐reaction of HOO

A theoretical study of the mechanism and the kinetics for the hydrogen abstraction reaction of the biradical hydroperoxy radical has been presented at the CCSD(T)/6‐311++G(3d,2p)//CCSD/6‐31+G(d,p) level of theory. Our theoretical calculations suppose a stepwise mechanism involving the formation of a postreactant complex in the triplet and singlet entrance channels. Four transition states of the six‐membered chain complexes (³TS1 and ¹TS1) and six‐membered ring complexes (³TS2 and ¹TS2) are located at the high dual level CCSD(T)/6‐311++G(3d,2p)//CCSD/6‐31+G(d,p) method. The rate constants of Path 1 ～ Path 4 at the CCSD(T)/6‐311++G(3d,2p)//CCSD/6‐31+G (d,p) level are calculated by means of the conventional transition state theory (TST) and canonical variational TST without and with small‐curvature tunneling (SCT) correction within the temperature range of 200–2,500 K. The calculated results show that the triplet channel is the dominating reaction channel and Path 2 is found to be the most favorable pathway. The rate constants of Path 2 are in good agreement with the experimental values at the experimentally measured temperatures. Moreover, the variational effect is not obvious in the low temperature range but is not neglectable in the high temperature range. The SCT plays an important role particularly in the low temperature range. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Mechanism of HCS + O2 reaction: hydrogen- or oxygen-transfer?

In spite of the potential importance of the HCS radical in both combustion and interstellar processes, its chemical reactivity has not been tackled previously. In the present paper, the oxidation reaction of the HCS radical is theoretically investigated for the first time at the CCSD(T)/6-311++G(3df,2p)//BH&HLYP/6-311++G(d,p)+ZPVE and Gaussian-3//B3LYP/6-31G(d) levels. It is shown that the most feasible pathway is the O2 addition to the HCS radical forming the intermediate SC(H)OO which can undergo a subsequent O-extrusion leading to SC(H)O + 3O. This features an indirect O-transfer mechanism with the overall barrier of 4.4 and 3.5 kcal mol(-1), respectively, at the two levels. However, formation of the H-transfer product CS + HO2 is kinetically much less feasible, i.e., the direct mechanism has barriers of 14.3 and 8.7 kcal mol(-1), whereas the indirect mechanism has barriers of 12.6 and 10.7 kcal mol(-1), respectively. This result is in sharp contrast to the analogous HCO + O2 reaction, where the direct (with a barrier of 2.98 kcal mol(-1)) and indirect (2.26 kcal mol(-1)) H-transfer processes are highly competitive over the indirect O-transfer process (the least endothermicity is 19.9 kcal mol(-1)). The possible explanations and implications of the present results are provided.     

C2H3与CH3F氢抽提反应机理与动力学性质

采用双水平直接动力学方法对C₂H₃与CH₃F氢抽提反应进行了研究. 在QCISD(T)/6-311++G(d, p)//B3LYP/6-311G(d, p)水平上, 计算的三个反应通道R1、R2和R3的能垒(ΔE^≠)分别为43.2、43.9和44.1 kJ·mol^-1, 反应热为-38.2 kJ·mol^-1. 此外, 利用传统过渡态理论(TST)、正则变分过渡态理论(CVT)和包含小曲率隧道效应(SCT)的CVT, 分别计算了200-3000 K温度范围内反应的速率常数k^TST、k^CVT和k^CVT/SCT. 结果表明: (1) 三个氢抽提反应通道的速率常数随温度的增加而增大, 其中变分效应的影响可以忽略, 隧道效应则在低温段影响显著; (2) R1反应是主反应通道, 但随着温度的升高, R2反应的竞争力增大, 而R3反应对总速率常数的影响很小.     

Theoretical study on the hydrogen abstraction reaction of CH3CH2F (HFC-161) with Cl atom

A direct dynamics method is employed to study the hydrogen abstraction reaction of CH₃CH₂F+Cl. Three distinct transition states are located, one for -H abstraction and two for β-H abstraction. The potential energy surface (PES) information is obtained at the QCISD(T)/6-311+G(3df,2p)//MP2/6-311G(d,p), CCSD(T)/6-311+G(3df,2p)//MP2/6-311G(d,p) and G2//MP2/6-311G(d,p) level. Based on the QCISD(T)/6-311+G(3df,2p)//MP2/6-311G(d,p) results, the rate constants of the three reaction channels are evaluated by using the canonical variational transition state theory (CVT) with small-curvature tunneling (SCT) contributions over the temperature range of 220–2800 K. The calculated results indicate that -H abstraction dominates the total reaction almost over the whole temperature range.     

Gaseous reaction mechanism of C2F radical with water

The kinetic properties of the carbon-fluorine radicals are little understood except those of CFn (n =1-3). In this article, a detailed mechanistic study was reported on the gas-phase reaction between the simplest pi-bonded C2F radical and water as the first attempt to understand the chemical reactivity of the C2F radical. Various reaction channels are considered. The most kinetically competitive channel is the quasi-direct hydrogen-abstraction route forming P5 HCCF + OH. At the CCSD(T)/6-311+G(2d,2p)//B3LYP/6-311G(d,p)+ZPVE, CCSD(T)/6-311+G(3df,2p)//QCISD/6-311G(d,p)+ZPVE and Gaussian-3//B3LYP/6-31G(d) levels, the overall H-abstraction barriers (4.5, 4.7, and 4.2 kcal/mol) for the C2F + H2O reaction are comparable to the corresponding values (5.5, 3.7, and 5.7 kcal/mol) for the analogous C2H + H2O reaction. This suggests that C2F is a reactive radical like the extensively studied C2H, in contrast to the situation of the CF and CF2 radicals that have much lower reactivity than the corresponding hydrocarbon species. Thus, the C2F radical is expected to play an important role in the combustion processes of the carbon-fluorine chemistry. Furthermore, addition of a second H2O can catalyze the reaction with the H-abstraction barrier significantly reduced to a marginally zero value (0.5 kcal/mol). This is also indicative of the potential relevance of the title reactions in the low-temperature atmospheric chemistry.     

Theoretical study and rate constant computation on the reaction HFCO + OH --> CFO + H2O

The potential energy surface, including the geometries and frequencies of the stationary points, of the reaction HFCO + OH is calculated using the MP2 method with 6-31+G(d,p) basis set, which shows that the direct hydrogen abstraction route is the most dominating channel with respect to addition and substitution channels. For the hydrogen abstraction reaction, the single-point energies are refined at the QCISD(T) method with 6-311++G(2df,2pd) basis set. The calculated standard reaction enthalpy and barrier height are -17.1 and 4.9 kcal mol(-1), respectively, at the QCISD(T)/6-311++G(2df,2pd)//MP2/6-31+G(d,p) level of theory. The reaction rate constants within 250-2500 K are calculated by the improved canonical variational transition state theory (ICVT) with small-curvature tunneling (SCT) correction at the QCISD(T)/6-311++G(2df,2pd)//MP2/6-31+G(d,p) level of theory. The fitted three-parameter formula is k = 2.875 x 10(-13) (T/1000)1.85 exp(-325.0/T) cm(3) molecule(-1) s(-1). The results indicate that the calculated ICVT/SCT rate constant is in agreement with the experimental data, and the tunneling effect in the lower temperature range plays an important role in computing the reaction rate constants.     

Theoretical studies of the reactions of CF3CHCLOCHF2/CF3CHFOCHF2 with OH radical and Cl atom and their product radicals with OH

The mechanisms and dynamics studies of the OH radical and Cl atom with CF(3)CHClOCHF(2) and CF(3)CHFOCHF(2) have been carried out theoretically. The geometries and frequencies of all the stationary points are optimized at the B3LYP/6-311G(d,p) level, and the energy profiles are further refined by interpolated single-point energies (ISPE) method at the G3(MP2) level of theory. For each reaction, two H-abstraction channels are found and four products (CF(3)CHFOCF(2), CF(3)CFOCHF(2), and CF(3)CHClOCF(2), CF(3)CClOCHF(2)) are produced during the above processes. The rate constants for the CF(3)CHClOCHF(2)/CF(3)CHFOCHF(2) + OH/Cl reactions are calculated by canonical variational transition-state theory (CVT) within 200-2000 K, and the small-curvature tunneling is included. The total rate constants calculated from the sum of the individual rate constants and the branching ratios are in good agreement with the experimental data. The Arrhenius expressions for the reactions are obtained. Our calculation shows that the substitution of Cl by F decreases the reactivity of CF(3)CHClOCHF(2) toward OH and Cl. In addition, the mechanisms of subsequent reactions of product radicals and OH radical are further investigated at the G3(MP2)//B3LYP/6-311G(d,p) level, and the main products are predicted in the this article.     

Allylic hydrogen abstraction II. H-abstraction from 1,4 type polyalkenes as a model for free radical trapping by polyunsaturated fatty acids (PUFAs)

Unsaturated radicals, containing different number of delocalized electrons, are formed via H-atom abstractions with CH(3), iso-C(3)H(7), OOH and OH radicals from (Z,Z) and (E,E)-hepta-2,5-dienes. These reactions and the relative stability of the different allyl-type radicals formed, were studied within the BH&HLYP method, using a 6-311+G(3df,2p) basis set, as well as within the G3MP2 level of theory on BH&HLYP/6-31G(d) geometries. The biallyl type radicals (involving 5 electrons delocalized on 5 carbon atoms) are more stable, by about 47.6 +/- 0.4 kJ mol(-1), than monoallyl type radicals (which involve 3 electrons delocalized on 3 carbon atoms). Three types of the H-atom abstractions were distinguished: direct H-abstraction with CH(3), indirect abstraction with a higher barrier height with iso-C(3)H(7), OOH and a non-direct quasi-barrierless H-abstraction with OH radicals. These observations were also confirmed by the activation entropy versus activation enthalpy as well as the Evans-Polányi's plots. The OOH-hepta-2,5-diene complexes are found to be extremely stable (from -19.6 to 22.3 kJ mol(-1)). The room temperature rate constants were calculated with transition state theory. Formations of monoallyl and biallyl radicals through H-abstraction with OH are fast; the calculated rate constants range from 5.84 x 10(-11) to 1.92 x 10(-9) cm(3) molecule(-1) s(-1) at room temperature. These reactions may play a key role in the "very low temperature combustion" like biological oxidations.     

Computational study of static first hyperpolarizability of donor-acceptor substituted (E)-benzaldehyde phenylhydrazone

Various hybrid functionals (B3LYP, B97-2, PBE0, BMK, BH&HLYP, CAM-B3LYP, and LC-ωPBE) implemented in density functional theory were applied to give estimate of static first hyperpolarizabilty (β(0)) of (E)-benzaldehyde phenylhydrazone designated as (E)-BPH. Against those of MP2 computations as a function of the underlying density functional, good agreement was obtained with the BH&HLYP and CAM-B3LYP functionals. The LC-ωPBE functional and the B3LYP, PBE0, B97-2, and BMK functionals underestimated and overestimated β(0), respectively. The basis set effect on the calculated β(0) was also investigated. It turned out that the 6-311+G(2d,p) basis set provided excellent converged value of β(0). On the basis of the calculated results, we investigated the substituent effect on β(0) of donor-acceptor (D-A) substituted (E)-BPH systematically by using the BH&HLYP and CAM-B3LYP computations with the 6-311+G(2d,p) basis set. We proposed a Zwitterion structure to explain the calculated trend in the substituent effect and the enhanced hyperpolarizability of type II compounds (A-(E)-BPH-D) than type I compounds (D-(E)-BPH-A). Natural bonding orbital analysis carried out at BH&HLYP/6-311+G(2d,p)//B3LYP/6-31G(2df,p) level of theory substantiated the claim.     

Kinetic mechanism of the hydrogen abstraction reactions of the chlorine atoms with CH3CF2Cl and CH3CFCl2: a dual level direct dynamics study

The mechanisms of the reactions: CH(3)CFCl(2) + Cl (R1) and CH(3)CF(2)Cl + Cl (R2) are studied over a wide temperature range (200-3000 K) using the dual-level direct dynamics method. The minimum energy path calculation is carried out at the MP2/6-311G(d,p) and B3LYP/6-311G(d,p) levels, and energetic information is further refined by the G3(MP2) theory. The H-abstraction from the out-of-plane for (R1) is the major reaction channel, while the in-plane H-abstraction is the predominant route of (R2). The canonical variational transition-state theory (CVT) with the small-curvature tunneling (SCT) correction method is used to calculate the rate constants. Using group-balanced isodesmic reactions and hydrogenation reactions as working chemical reactions, the standard enthalpies of formation for CH(3)CFCl(2), CH(3)CF(2)Cl, CH(2)CFCl(2), and CH(2)CF(2)Cl are evaluated at the CCSD(T)/6-311 + G(3df,2p)//MP2/6-311G(d,p) level of theory. The results indicate that the substitution of fluorine atom for the chlorine atom leads to a decrease in the C-H bond reactivity with a small increase in reaction enthalpies. Also, for all reaction pathways the variational effect is small and the SCT effect is only important in the lower temperature range on the rate constants.     

Dual-level direct dynamics studies on the reaction Cl + CHBr(2)Cl

Theoretical investigations are carried out on the multichannel reaction CHBr(2)Cl + Cl by means of direct dynamics methods. The minimum energy path (MEP) is obtained at the BH&H-LYP/6-311G(d,p) level, and energetic information is further refined at the CCSD(T)/6-311+G(2df,2p) (single-point) level. The rate constants for three reaction channels, H-abstraction, Br-abstraction, and Cl-abstraction, are calculated by using the improved canonical variational transition state theory (ICVT) incorporating with the small-curvature tunneling (SCT) correction. The theoretical overall rate constants are in good agreement with the available experimental data and are found to be k=2.58 x 10(-15) T(1.18) exp(-861.17/T) cm(3)molecule(-1)s(-1) over the temperature range 200--2400 K. For the title reaction, H-abstraction reaction channel is the major channel at the lower temperatures, while as the temperature increases, the contribution of Br-abstraction reaction channel should be taken into account. At 2180 K, the rate constants of these two pathways are equal. Cl-abstraction reaction channel is minor channel over the whole temperature region.     

A theoretical study on the mechanism and thermodynamics of ozone-water gas phase reaction

Ozone water reaction including a complex was studied at the MP2/6-311++G(d,p) and CCSD/6-311++G(2df,2p)//MP2/6-311++G(d,p) levels of theory. The interaction between water oxygen and central oxygen of ozone produces stable H₂O-O₃ complex with no barrier. With decomposition of this complex through H-abstraction by O₃ and O-abstraction by H₂O, three possible product channels were found. Intrinsic reaction coordinate, topological analyses of atom in molecule, and vibrational frequency calculation have been used to confirm the preferred mechanism. Thermodynamic data at T = 298.15 K and atmospheric pressure have been calculated. The results show that the production of hydrogen peroxide is the main reaction channel with ΔG = ?21.112 kJ mol^-1.     

H2FCS单分子分解反应的直接动力学研究

采用量子化学QCISD(T)/6-311++G(d,p)//B3LYP/6-311+G(d,p)方法研究了H2FCS单分子分解反应的微观动力学性质, 构建了反应势能剖面. 利用经典过渡态理论(TST)与变分过渡态理论(CVT)并结合小曲率隧道效应模型(SCT), 分别计算了在200～3000 K温度范围内的速率常数kTST、kCVT和kCVT/SCT. 计算结果表明, H2FCS可经过不同的反应通道生成10种小分子产物, 脱H反应和HF消去反应为标题反应的主反应通道, 其中HF消去反应产物HCS可由两条反应通道生成. 在200~3000 K温度区间内得到三条反应通道的表观反应速率常数三参数表达式分别为 , 和 . 速率常数计算结果显示, 量子力学隧道效应在低温区间对反应速率常数的影响显著, 而变分效应在计算温度范围内可以忽略.     

Theoretical study on the reaction of tropospheric interest: hydroxyacetone + OH. Mechanism and kinetics

A theoretical study of the mechanism and kinetics of the OH hydrogen abstraction from hydroxyacetone is presented. Optimum geometries and frequencies have been computed at the BH and HLYP/6-311++G(d,p) level of theory for all stationary points. Energy values have been improved by single-point calculations at the above geometries using CCSD(T)/ 6-311++G(d,p). The rate coefficients are calculated for the temperature range 280-500 K by using conventional transition state theory (TST), including tunneling corrections. Our analysis supports a stepwise mechanism involving the formation of a reactant complex in the entrance channel and a product complex in the exit channel, for all the modeled paths. Four experimental values of the rate constant at 298 K have been previously reported: three of them in great agreement (approximately 3 x 10(-12) cm(3) molecule(-1) s(-1)), and one of them twice larger. The calculations in the present work support the smaller value. A curved Arrhenius plot was found in the studied temperature range; thus the expression that best describes the obtained data is k(280-500)(overall) = 5.29 x 10(-23)T(3.4)e(1623/T) cm(3) molecule(-1) s(-1). The activation energy was found to vary with temperature from -1.33 to +0.15 kcal/mol.     

Theoretical studies on dynamics and thermochemistry of the reactions CF(3)CHCl(2)+Cl-->CF(3)CCl(2)+HCl and CF(3)CHFCl+Cl-->CF(3)CFCl+HCl

A dual-level direct dynamics study has been carried out for the two hydrogen abstraction reactions CF(3)CHCl(2)+Cl and CF(3)CHFCl+Cl. The geometries and frequencies of the stationary points are optimized at the BHLYP/6-311G(d,p), B3LYP/6-311G(d,p), and MP2/6-31G(d) levels, respectively, with single-point calculations for energy at the BHLYP/6-311++G(3df,2p), G3(MP2), and QCISD(T)/6-311G(d,p) levels. The enthalpies of formation for the species CF(3)CHCl(2), CF(3)CHFCl, CF(3)CCl(2), and CF(3)CFCl are evaluated at higher levels. With the information of the potential energy surface at BHLYP/6-311++G(3df,2p)//6-311G(d,p) level, we employ canonical variational transition-state theory with small-curvature tunneling correction to calculate the rate constants. The agreement between theoretical and experimental rate constants is good in the measured temperature range 276-382 K. The effect of fluorine substitution on reactivity of the C-H bond is discussed.     

Reaction of CH3 with NO2

The elementary reaction of the CH3 radical with NO2 was investigated by time-resolved FTIR spectroscopy and quantum chemical calculations. The CH3 radical was produced by laser photolysis of CH3Br or CH3I at 248 nm. Vibrationally excited products OH, HNO and CO2 were observed by the time-resolved spectroscopy for the first time. The formation of another product NO was also verified. According to these observations, the product channels leading to CH3O+NO, CH2NO+OH and HNO+H2CO were identified. The channel of CH3O+NO was the major one. The reaction mechanisms of the above channels were studied by quantum chemical calculations at CCSD(T)/6-311++G(df,p)//MP2/6-311G(d,p) level. The calculated results fit with the experimental observations well.     

Rate coefficients of the CF3CHFCF3 + H → CF3CFCF3 + H2 reaction at different temperatures calculated by transition state theory with ab initio and DFT reaction paths

The minimum energy path (MEP) of the reaction, CF₃CHFCF₃ + H → transition state (TS) → CF₃CFCF₃ + H₂, has been computed at different ab initio levels and with density functional theory (DFT) using different functionals. The computed B3LYP/6‐31++G**, BH&HLYP/cc‐pVDZ, BMK/6‐31++G**, M05/6‐31+G**, M05‐2X/6‐31+G**, UMP2/6‐31++G**, PUMP2/6‐31++G**//UMP2/6‐31++G**, RCCSD(T)/aug‐cc‐pVDZ//UMP2/6‐31++G**, RCCSD(T)/aug‐cc‐pVTZ(spd,sp)//UMP2//6‐31++G**, RCCSD(T)/CBS//M05/6‐31+G**, and RCCSD(T)/CBS//UMP2/6‐31++G** MEPs, and associated gradients and Hessians, were used in reaction rate coefficient calculations based on the transition state theory (TST). Reaction rate coefficients were computed between 300 and 1500 K at various levels of TST, which include conventional TST, canonical variational TST (CVT) and improved CVT (ICVT), and with different tunneling corrections, namely, Wigner, zero‐curvature, and small‐curvature (SCT). The computed rate coefficients obtained at different ab initio, DFT and TST levels are compared with experimental values available in the 1000–1200 K temperature range. Based on the rate coefficients computed at the ICVT/SCT level, the highest TST level used in this study, the BH&HLYP functional performs best among all the functionals used, while the RCCSD(T)/CBS//MP2/6‐31++G** level is the best among all the ab initio levels used. Comparing computed reaction rate coefficients obtained at different levels of theory shows that, the computed barrier height has the strongest effect on the computed reaction rate coefficients as expected. Variational effects on the computed rate coefficients are found to be negligibly small. Although tunneling effects are relatively small at high temperatures (～1500 K), SCT corrections are significant at low temperatures (～300 K), and both barrier heights and the magnitudes of the imaginary frequencies affect SCT corrections. © 2012 Wiley Periodicals, Inc.