Ab Initio Chemical Kinetic Study on the Reactions of ClO with C2H2

Dec 3, 2010 - The mechanisms for the reactions of ClO with C2H2 and C2H4 have been investigated at the CCSD(T)/CBS level of theory. The results show ...
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J. Phys. Chem. A 2010, 114, 13395–13401

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Ab Initio Chemical Kinetic Study on the Reactions of ClO with C2H2 and C2H4 R. S. Zhu and M. C. Lin* Department of Chemistry, Emory UniVersity, Atlanta, Georgia 30322, United States ReceiVed: August 11, 2010; ReVised Manuscript ReceiVed: October 23, 2010

The mechanisms for the reactions of ClO with C2H2 and C2H4 have been investigated at the CCSD(T)/CBS level of theory. The results show that in both systems, the interaction between the Cl atom of the ClO radical and the triple and double bonds of C2H2 and C2H4 forms prereaction van der Waals complexes with the O-Cl bond pointing perpendicularly toward the π-bonds, both with 2.1 kcal/mol binding energies. The mechanism is similar to those of the HO-C2H2/C2H4 systems. The rate constants for the low energy channels have been predicted by statistical theory. For the reaction of ClO and C2H2, the main channels are the production of CH2CO + Cl (k1a) and CHCO + HCl (k1b), with k1a ) 1.19 × 10-15T1.18 exp(-5814/T) and k1b ) 6.94 × 10-21 × T2.60 exp(-6587/T) cm3 molecule-1 s-1. For the ClO + C2H4 reaction, the main pathway leads to C2H4O + Cl (k2a) with the predicted rate constant k2a ) 2.13 × 10-17T1.52 exp(-3849/T) in the temperature range of 300-3000 K. These rate constants are pressure-independent below 100 atm. I. Introduction The composite mixture of ammonium perchlorate (AP) oxidizer and polymeric binder fuels, such as hydroxyl-terminated polybutadiene (HTPB) matrix, has been widely employed as rocket propellants. An overview of recent advances in AP/HTPB propellant prolysis and combustion from an experimental perspective is provided by Brill and Budenz.1 The mechanism for the decomposition and combustion of AP has been experimentally studied over the past few decades, as has been summarized in detail.2-4 HTPB is a long-chain, cross-linked, and high molecular-weight polymer. At temperature below 770 K, the main gaseous product of decomposition is butadiene,5 whereas a whole range of products arises as the temperature increases. At 1170 K, the main product is ethylene. Under the rocket-motor conditions, that is, above 2000 K, 20-100 atm, and with heating rates of 106 K/s, the thermal decomposition of HTPB was assumed to undergo as the following pathway:6

HTPB f C2H4 + light hydrocarbons species These authors assumed ethylene as the overall pyrolysis product of HTPB decomposition in their AP/HTPB combustion modeling. In the past several years, the sublimation/decomposition mechanism and kinetics of AP with and without water molecules present on the decomposing surface have been computationally studied in our group; meanwhile, over 85 gas-phase elementary reactions related to AP decomposition and the formation of its early products from NHx to ClOy (x ) 2, 3; y ) 0-4) have also been investigated in great detail in our laboratory,7-16 many of which are directly relevant to the chemistry of the Freon-polluted stratosphere. The key results have been reported in a review chapter on propellant chemistry.17 However, the kinetics and mechanisms of the pivotal reactions, such as ClO + C2H2 and C2H4, critical to the simulation of AP-HTPB combustion, have not been studied experimentally or theoretically. The major objective of this series of the work is to elucidate the mechanisms for the reactions of reactive ClOx * Corresponding author. E-mail: [email protected].

(x ) 1-4) radicals with key fragments of HTPB and to provide reliable estimates of their rate constants for kinetic simulation of the AP-HTPB combustion reaction. The data obtained for the title reactions are expected to be relevant to the stratospheric ClO chemistry also. II. Computational Methods The geometric parameters of the reactants, products, intermediates, and transition states on the potential energy surfaces of the system studied in this work were optimized at the UB3LYP level of theory18,19 (i.e., Becke’s three-parameter nonlocal exchange functional with the nonlocal correlation functional of Lee, Yang, and Parr20) using 6-311+G(3df, 2p) basis set. All the stationary points have been identified for local minima and transition states by vibrational analysis. Intrinsic reaction coordinate analyses21 have been performed to confirm the connection between transition states and designated reactants, products, or intermediates. Higher level single-point energy calculations of the stationary points were refined at the CCSD(T)/CBS level, based on the optimized geometries at the B3LYP/6-311+G(3df, 2p) level. The CCSD(T)/CBS energies were evaluated at these geometries as follows. The total energies E(X) computed with the aug-cc-PVXZ basis sets (X ) 2, 3, 4) were extrapolated to the CBS limits ECBS employing a mixed Gaussian/exponential form:22

E(X) ) ECBS + b exp[-(X - 1)] + c exp[-(X - 1)2] (1) where X is the cardinal number associated with each basis set, X ) 2 (DZ), 3 (TZ), 4 (QZ), and ECBS, b, and c are parameters to be fitted. All calculations have been carried out using the Gaussian 03 program package.23 The extrapolation eq 1 was chosen because it is highly efficient when the double through quadruple-ζ correlation-consistent basis sets are used.24 The energies cited in the following sections are based on the CCSD(T)/CBS level. Rate constants for the major product channels have been predicted by the Rice-Ramsperger-Kassel-Marcus (RRKM) theory implemented in the Variflex code.25

10.1021/jp107596y  2010 American Chemical Society Published on Web 12/03/2010

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For those paths involving hydrogen atom transfer, tunneling effects were taken into account in the rate constant calculation. The rate constant is computed and further corrected by the Eckart transmission probability,26 P(E), as follows:

P(E) )

cosh[2π(a + b)] - cosh[2π(a - b)] cosh[2π(a + b)] + cosh[2πc] 25

implemented in the Variflex program. In the above equation, a ) (2µl2E/h2)1/2, b ) {2µl2[E - (E1 - E-1)]/h2}1/2, and c ) [(4E1E-1/hν2) - (1/4)]1/2. Here, E1 and E-1 represent forward and reverse barrier heights, respectively, ν is the imaginary frequency of the transition state, µ is the reduced mass, h is Planck’s constant, and l is the tunneling width, which is expressed by

l)

√2E1E-1 /µ ν(√E1 + √E-1)

Microcanonical RRKM calculations for the ClO + C2H2 (C2H4) reactions were performed by solving the master equation27 involving multistep vibrational energy transfer for the excited intermediates (ClOCHCHq or ClOCH2CH2q) for the dissociation processes. For the one-well system assumed in the present calculations, the master equation takes the form: m dFi(t) PijFj(t) - ωFi(t) - (ki1 + ki2)Fi(t) ) φi + ω dt j)1

∑

where φi represents the rate of ClO + C2H2 (C2H4) association reaction, m is the number of grains, which is chosen such that the population of the mth grain contributes negligibly to the bimolecular rate coefficient, ω is the collision frequency (which is a function of temperature and pressure), ki1(E) and ki2(E) are the microcanonical rate coefficients for the decomposition and redissociation, and Pij is the probability of energy transfer from grain j to grain i upon collision. A simple exponential-down model27,28 was employed for Pij:

Pij ) Aj exp[-R(Ej - Ei)]; j g i where R is a parameter governing the efficiency of energy transfer; R-1 corresponds to the average energy removed per collision for down collisions, 〈∆E〉down. Aj’s are normalization constants satisfying the condition:

∑ Pij ) 1 i

The energy-transfer process was computed on the basis of the exponential down model with the 〈∆E〉down value (the mean energy transferred per collision) of 400 cm-1 (in Ar). The L-J parameters, σ ) 3.47 Å, ε/κ ) 114 K for Ar, are taken from ref 29, and the L-J parameters of ethylene oxide (C2H4O),29 σ ) 4.08 Å, ε/κ ) 421 K, are approximately used for the adducts ClO-C2H4/C2H2. In the calculation for the electronic partition function of the ClO radical, the multiplicity of the states 2Π3/2

Zhu and Lin and 2Π1/2 and the energy gap of 318 cm-1 between the two states have been taken into consideration. III. Results and Discussion 3.1. ClO + C2H2 Reaction. On the basis of the predicted PES, possible channels for the ClO + C2H2 reaction are:

ClO + C2H2 f Vdw-OCl-C2H2 f ClOCHCH f CH2CO + Cl

(1a)

f CHCO + HCl

(1b)

ClO + C2H2 f HOCl + C2H

(1c)

The structures of the key stationary points and the PES diagram are displayed in Figures 1 and 2, respectively. The vibrational frequencies and rotational constants are summarized in the Supporting Information, SI-I (A). Association/Dissociation Processes. The interaction between the electron-deficient Cl atom of the ClO radical and the electron cloud of the triplet CtC bond in the HCtCH molecule forms a prereaction van der Waals complex (Vdw-OCl---C2H2) in which the ClO is perpendicular to the CtC bond with the Cl atom pointing toward the triplet bond. A similar phenomenon was found in the reactions of HO with C2H230 and C2H4.31 The complex is illustrated in Figure 1; the OCl · · · C bond length is 3.294 Å at the B3LYP/6-311+G(3df,2p) level, which can be compared to the values of 3.23-3.29 Å for the intermolecular distance of OH-C2H2 complex30 predicted at the RCCSD(T) level of theory. The stabilization energy of this OCl---C2H2 complex, 2.1 kcal/mol, is close to the experimentally determined upper limit value (2.7 kcal/mol)30 for OH---C2H2 complex, and the value for OH-C2H4, 1.8 ( 0.1 kcal/mol,31 predicted at different levels of theory. TS1 connects with Vdw-OCl---C2H2 and ClOCHCH adduct. The structure of this addition transition state TS1 differs from the reactant complex mainly in the orientation of the ClO radical with respect to the acetylene molecule. As mentioned above, in the complex, ClO lies perpendicular to the π bond of acetylene, while in TS1, the O atom in the ClO group is rotated toward one of the carbon atoms to form a new C-O bond. TS1 lies 11.7 kcal/mol above the reactants at the CCSD(T)/CBS//B3LYP/6-311+G(3df, 2p) level. Basis set superposition error (BSSE) corrections are not included in the energies of the complex and TS1 because of the large basis set (aug-cc-PVQZ) used in the single point energy calculations; the BSSE correction is expected to be negligible. For channel 1a, the ClOCHCH isomerizes to Cl-CH2CO via TS2 involving concerted Cl and H atoms migration with 1.1 kcal/mol barrier above the reactants. Cl-CH2CO lies 75.1 kcal/ mol below the reactants, and it can readily dissociate to give CH2CO + Cl with 62.6 kcal/mol exthothermicity. Meanwhile, the elimination of an HCl molecule from ClOCHCH can take place via TS3 with a 20.5 kcal/mol barrier to produce CHCO + HCl with 61.4 kcal/mol exthothermicity. Because the forward barrier for the dissociation of ClCH2CO is 63.7 kcal/mol lower than that of the backward process, that is, Cl-CH2CO can readily decompose to the products of CH2CO + Cl, the deactivation of Cl-CH2CO can be ignored. The rate constants with Eckart tunneling corrections26 for the lower energy channels 1a and 1b can be represented by the following expressions in units of cm3 molecule-1 s-1 in the temperature range of 300-3000 K:

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Figure 1. The optimized geometries of the intermediates, transition states computed at the B3LYP/6-311+G(3df, 2p) level for the ClO-C2H2 system. The bond lengths are given in angstroms, angles in degrees.

k1a ) 1.19 × 10-15T1.18 exp(-5814/T) k1b ) 6.94 × 10-21T2.60 exp(-6587/T) These rate constants are also graphically presented in Figure 3. Caculated results show that CH2CO + Cl is dominant in the whole temperature range. Below 1200 K, the ratio of this channel is more than 90%; over 1200 K, the ratio of formation CHCO + HCl increases with temperature; at 3000 K, it can reach as much as 27%. These rate constants are predicted to be pressure-independent below 100 atm. Direct Abstraction Process. For channel 1c, the ClO radical directly abstracts one of the H atoms in C2H2 via TS4 with a significantly high barrier (39.0 kcal/mol) to form CH2 + HOCl; as a result, this channel is not expected to play an important role in the combustion of the AP-HTPB system. It needs to be mentioned that the lower energy products ClCCH + OH cannot be directly formed from the reactants or the intermediates; however, they can be formed via the secondary reaction HOCl + C2H with a 4.3 kcal/mol barrier (TS5). Because the products HOCl + C2H already lie 36.7 kcal/ mol above ClO + C2H2, therefore, the formation of ClCCH + OH is unfavorable and not important in the reaction ClO + C2H2. 3.2. ClO + C2H4 Reaction. The optimized structures of the complexes and transition states and the corresponding PES of the system are presented in Figures 4 and 5, respectively. The

PES can be shown in Scheme 1, and the related low-lying energy channels are considered in our kinetic analysis. Similar to the ClO + C2H2 system, the reactant complex is predicted to have a T-shaped structure with the Cl atom of ClO pointing toward to the π bond of ethylene. In this OCl-C2H4 complex, the Cl-C bond length, 3.332 Å, is slightly longer than that of 3.294 Å in the OCl-C2H2 complex. The OCl-ethylene complex was computed to have a well depth of 2.1 kcal/mol, which is the same as that of OCl-C2H2. Similarly, by the rotation of the ClO in the complex, OCl-C2H4, can transform it to a more stable intermediate ClOCH2CH2 via TS1. ClOCH2CH2 has 11.0 kcal/mol stabilization energy, and TS1 lies 7.9 kcal/mol above the reactants. The Cl atom can be eliminated from ClOCH2CH2 to produce C2H4O + Cl with 21.0 kcal/mol exthothermicity via TS2 lying above the reactants by 3.3 kcal/mol. When the Cl atom in ClOCH2CH2 migrates to the second carbon via a four-member ring TS3 lying above the reactants by 7.4 kcal/mol, it forms a more stable intermediate ClCH2CH2O with 46.6 kcal/mol stabilization energy. Breaking the C-C bond in ClCH2CH2O via TS4 forms the final products, CH2O + CH2Cl. TS4 lies below the reactants by 29.7 kcal/ mol, and the formation of the final products has 37.9 kcal/ mol exthothermicity. Eliminating one of the H atoms from ClCH2CH2O to form ClCH2CHO + H via TS5 has to overcome a 19.5 kcal/mol barrier, with 31.1 kcal/mol exothermicity. Meanwhile, ClCH2CH2O can isomerize to ClCHCH2OH via a four-member ring TS6 with a 29.7 kcal/mol barrier. ClCHCH2OH has a stability similar to that of CH3CHOCl, lying

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Figure 2. Schematic energy diagram (in kcal/mol) of the ClO C2H2 system computed at the CCSD(T)/CBS//B3LYP/6-311+G(3df, 2p) level.

Figure 3. Predicted rate constants for the formation of CH2CO + Cl (solid line) and CHCO + HCl (dotted line) from the reaction of ClO + C2H2 in 760 Torr Ar.

54.3 kcal/mol below the reactants, and can further dissociate to the final products ClCHCH2 + OH with an overall 24.8 kcal/ mol exothermicity. For the other isomer, ClOCH2CH2, it isomerizes to CH3CHOCl via TS7; CH3CHOCl can further dissociate to produce Cl + CH3CHO. TS7 lies above the reactants by 16.4 kcal/mol. The H-elimination from ClOCH2CH2 can also occur, but it needs to overcome a high barrier of 25.5 kcal/mol at TS8; the products H + CH2CHOCl also have a rather high energy as compared to ClCH2CHO + H; thus, this process is expected to be unimportant. In principle, ClO can also directly abstract one of the H atoms in CH2CH2 via TS9 to form a postreaction complex CH2CH---HOCl, which can readily dissociate to CH2CH + HOCl. The CH2CH---HOCl complex, TS9, and CH2CH + HOCl lie above the reactants by 12.6, 17.9, and 15.5 kcal/mol, respectively. It is worth pointing out that the barrier for ClO addition to C2H4, 7.9 kcal/mol above the reactants ClO + C2H4, is much greater than that of OH + C2H4, -0.8 kcal/mol,31 which can be ascribed to the loose structure of the addition TS in the HO-C2H4 system. For example, at the B3LYP/6-311+G(3df,

2p) level, the O-C bond in the addition transition state of ClO-C2H4 system is 1.974 Å; however, in the HO-C2H4 system, it is 3.105 Å. The above addition barriers imply that the significant barrier would make ClO radical association with unsaturated hydrocarbons in the troposphere slow and unimportant. 3.3. Heats of Reaction for Different Channels. To confirm the reliability of the methods employed, we compared the heats of reaction for these two reactions with available experimental values in Table 1. The heats of reaction predicted at the CCSD(T)/CBS level for the production of CH2CO + Cl and HOCl + C2H from C2H2 + ClO, -62.6 and 36.7 kcal/mol, respectively, are in good agreement with the experimental values, -61.4 ( 0.5 and 38.3 ( 1.5 kcal/mol. For the reaction ClO + C2H4, the calculated heats of reaction for C2H4O + Cl, ClCH2 + CH2O, and CH3CHO + Cl, -21.0, -37.9, and -48.5 kcal/mol, are in excellent agreement with the experimental values, -19.8 ( 0.3, -37.1 ( 1.7, and -48.5 ( 0.5 kcal/mol. Experimental heats of reaction are calculated on the basis of the experimental heats of formation (at 0 K) of ClO (24.2 ( 0.02 kcal/mol),32 C2H2 (54.7 ( 0.2 kcal/mol),33 C2H4 (14.6 ( 0.07),33 CH2O (-26.8 ( 1.5),32 Cl (28.6 ( 0.01 kcal/mol),32 CH3CHO (-38.3 ( 0.4),33 C2H4O (-9.6 ( 0.2),33 HOCl (-17.1 ( 0.5),32 ClCH2 (28.5 ( 0.1),33 C2H (134.3 ( 0.7),34 and CH2CO (-11.10 ( 0.2).35 The temperature-dependent rate constants at 1 atm Ar for the low energy channels given in units of cm3 molecule-1 s-1 have been predicted for the formation of C2H4O (k2a) and CH2O (k2b) in the temperature range 300-3000 K. They can be presented by:

k2a ) 2.13 × 10-17T1. 52 exp(-3849/T) k2b ) 2.72 × 10-21T2. 35 exp(-4248/T) The results are also shown in Figure 6. Similar to the above ClO-C2H2 system, Cl elimination channel is dominant. In the

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Figure 4. The optimized geometries of the intermediates and transition states computed at the B3LYP/6-311+G(3df, 2p) level for the ClO-C2H4 system. The bond lengths are given in angstroms, angles in degrees.

temperature range of 300-3000 K, the ratio for formation of C2H4O + Cl is over 90%.

In the calculation, the effects of the prereaction and postreaction complexes on final product formation in both systems

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Figure 5. Schematic energy diagram (in kcal/mol) of the ClO-C2H4 system computed at the CCSD(T)/CBS//B3LYP/6-311+G(3df, 2p) level.

SCHEME 1

TABLE 1: Comparison of Calculated Heats of Reaction for ClO + C2H2/C2H4 with Available Experimental Dataa method

CCSD(T)/ CCSD(T)/ CCSD(T)/ exp. Aug-cc-PVTZ Aug-cc-PVQZ CBS (0 K)32-35

ClO + C2H2 CH2CO + Cl HOCl + C2H ClO + C2H4 C2H4O + Cl ClCH2 + CH2O CH3CHO + Cl

0.0 -64.3 36.5 0.0 -23.0 -37.7 -50.5

0.0 -63.2 36.7 0.0 -21.7 -37.8 -49.2

0.0 -62.6 36.7 0.0 -21.0 -37.9 -48.5

-61.4 ( 0.5 38.3 ( 1.5 -19.8 ( 0.3 -37.1 ( 1.7 -48.5 ( 0.5

a The exothermicity for the formation of ClO + C2H2 and ClO + C2H4 was calculated on the basis of the experimental heats of formation (at 0 K) (refs 32-35) as described in the text.

have been reasonably ignored due to their shallow wells and the high energies of the entrance and exit transition states. Similar to the ClO-C2H2 reaction, the rate constants are also predicted to be pressure-independent below 100 atm. IV. Conclusions The mechanisms for the reactions of ClO with C2H2 and C2H4 have been elucidated at the CCSD(T)/CBS level of theory. For the ClO + C2H2 system, the predicted result shows that the formation of CH2CO + Cl is dominant in the whole temperature range below 1200 K; the yield of this product channel accounts for more than 90%; over 1200 K, the formation of CHCO + HCl increases with temperature, and, at 3000 K, it reaches as much as 27%. For the ClO + C2H4 system, Cl elimination

Figure 6. Predicted rate constants for the formation of C2H4O + Cl (dotted) and ClCH2 + CH2O (solid) from the reaction of ClO + C2H4 in 760 Torr Ar.

channel is dominant in the whole temperature range 300-3000 K; the branching ratio for formation of C2H4O + Cl is predicted to be >90%. Our predicted rate constants for formation of various products may be employed for a more realistic kinetic modeling of the AP-HTPB combustion. Acknowledgment. This work is sponsored by the Office of Naval Research under contract no. N00014-08-1-0106. M.C.L. acknowledges Taiwan’s National Science Council for the distinguished visiting professorship and the TSMC Distinguished

Reactions of ClO with C2H2 and C2H4 Professorship from Taiwan Semiconductor Manufacturing Co. at the National Chiao Tung University in Hsinchu, Taiwan. Supporting Information Available: Vibrational frequencies and rotational constants for the intermediates and transition states of the ClO + C2H2 reaction (A) and ClO + C2H4 reaction (B), computed at the B3LYP/6-311+G(3df, 2p) level of theory. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Brill, T. B.; Budenz, B. T. In Progress in Astronautics and Aeronautics; Yang, V., Brill, T. B., Ren, W.-Z., Eds.; American Institute of Aeronautics and Astronautics: 2000; Chapter 2. (2) Jacobs, P. W. M.; Whitehead, H. M. Chem. ReV. 1969, 6, 551. (3) Tanaka, M.; Beckstead, M. W. Kagaku, Gakkaishi 1997, 58, 245. (4) Ermolin, N. E.; Korobeinichev, O. P.; Tereshchenko, O. P.; Fomin, V. M. Combust., Explos. Shock WaVes 1982, 18, 46. (5) Radhakrishnan, T. S.; Rama, R. M. J. Polym. Sci. 1981, 19, 3197. (6) Cai, W. D.; Thakre, P.; Vigor, Y. Combust. Sci. Technol. 2008, 180, 2143. (7) Zhu, R. S.; Lin, M. C. J. Phys. Chem. A 2007, 111, 3977. (8) Zhu, R. S.; Lin, M. C. ChemPhysChem 2005, 6, 1514. (9) Zhu, R. S.; Lin, M. C. ChemPhysChem 2004, 5, 1864. (10) Zhu, R. S.; Lin, M. C. J. Chem. Phys. 2003, 119, 2075. (11) Zhu, R. S.; Lin, M. C. J. Chem. Phys. 2003, 118, 409. (12) Zhu, R. S.; Lin, M. C. J. Chem. Phys. 2003, 118, 8645. (13) Zhu, R. S.; Lin, M. C. J. Phys. Chem. A 2003, 107, 3836. (14) Xu, Z. F.; Lin, M. C. J. Phys. Chem. A 2007, 111, 584. (15) Zhu, R. S.; Lin, M. C. Int. J. Chem. Kinet. 2010, 42, 253. (16) Xu, Z. F.; Lin, M. C. J. Phys. Chem. A 2010, 114, 833. (17) Zhu, R. S.; Lin, M. C. In Energetic Materials, Part 2, Detonation and Combustion; Politzer, P., Murray, J. S., Eds.; Elsevier Science Pub.: New York, 2003; Chapter 11, pp 373-443. (18) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (19) Becke, A. D. J. Chem. Phys. 1992, 96, 2155; 1992, 97, 9173.

J. Phys. Chem. A, Vol. 114, No. 51, 2010 13401 (20) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. 1988, B37, 785. (21) Gonzalez, C.; Schlegel, H. B. J. Phys. Chem. 1989, 90, 2154. (22) Peterson, K. A.; Woon, D. E.; Dunning, T. D., Jr. J. Chem. Phys. 1994, 100, 7410. (23) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, T.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzales, C.; Martin, R. L.; Fox, D. J.; DeFrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92/DFT, revision B; Gaussian, Inc.: Pittsburgh, PA, 2003. (24) Feller, D.; Peterson, K. A.; de Jong, W. A.; Dixon, D. A. J. Chem. Phys. 2003, 118, 3510. (25) Klippenstein, S. J.; Wagner, A. F.; Dunbar, R. C.; Wardlaw, D. M.; Robertson, S. H. Varifliex: Version 1.00, 1999. (26) (a) Eckart, C. Phys. ReV. 1930, 35, 1303. (b) Bell, R. P. The Tunnelling Effect in Chemistry; Chapman and Hall: New York, 1980. (c) Hase, W. L. Baer Unimolecular Reaction Dynamics (International Series of Monographs on Chemistry); Oxford University Press: New York, 1996. (27) Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recombination Reactions; Blackwell Scientific: Carlton, Australia, 1990. (28) Troe, J. J. Chem. Phys. 1977, 66, 6745. (29) Hippler, H.; Troe, J.; Wendelken, H. J. J. Chem. Phys. 1983, 76, 6709. (30) Davey, J. B.; Greenslade, M. E.; Marshall, M. D.; Lester, M. I.; Wheeler, M. D. J. Chem. Phys. 2004, 121, 3009. (31) Zhu, R. S.; Park, J.; Lin, M. C. Chem. Phys. Lett. 2005, 408, 25. (32) Chase, M. W., Jr. NIST-JANAF Thermochemical Tables, 4th ed.; Woodbury: New York, 1998. (33) Afeefy, M. C.; Liebman, M. C.; Stein, S. E. In Neutral Thermochemical Data: NIST Chemistry WebBook, NIST Standard Reference Database Number 69; Mallard, W. G., Linstrom, P. J., Eds.; National Institute of Standards and Technology: Gaithersburg, MD, 1998; p 20899. (34) Ervin, K. M.; Gronert, S.; Barlow, S. E.; Gilles, M. K.; Harrison, A. G.; Bierbaum, V. M.; DePuy, C. H.; Lineberger, W. C.; Ellison, G. B. J. Am. Chem. Soc. 1990, 112, 5750. (35) Ruscic, B.; Litorja, M.; Asher, R. L. J. Phys. Chem. A 1999, 103, 8625.

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