Mechanism and Kinetics for Ammonium Perchlorate Sublimation: A

Aug 23, 2008 - Electron Radiolysis of Ammonium Perchlorate: A Reflectron Time-of-Flight Mass ... Mechanism and Kinetics for Ammonium Dinitramide (ADN)...
0 downloads 0 Views 206KB Size
Download PDF
J. Phys. Chem. C 2008, 112, 14481–14485

14481

Mechanism and Kinetics for Ammonium Perchlorate Sublimation: A First-principles Study Rongshun Zhu and M. C. Lin* Department of Chemistry, Emory UniVersity, Atlanta, Georgia 30322, USA ReceiVed: April 14, 2008; ReVised Manuscript ReceiVed: June 27, 2008

We have studied for the first time the kinetics and mechanism for the sublimation/decomposition of NH4ClO4 by first-principles calculations, using a generalized gradient approximation with the plane-wave density functional theory. Supercells containing 4, 8, and 16 NH4ClO4 units were used; the predicted enthalpic change for solid NH4ClO4 to gaseous NH3 and HClO4 is 45.0 ( 1.5 kcal/mol. The calculated desorption activation energies for NH3, HClO4, and H3N · · · HOClO3 molecular complexes, individually, from the relaxed surface are 45.3, 43.5, and 28.1 kcal/mol, respectively. The rate constant for the dominant sublimation process desorbing H3N · · · HOClO3 as a pair can be presented by ksub.) 6.53 × 1012 exp (-28.8 kcal/mol/RT) s-1, which is in reasonable agreement with available experimental data. Expectably, the decomposition of H3N · · · HOClO3 (g) to NH3 (g) and HOClO3 (g) is considerably faster, about 1 × 107 times greater than that for the sublimation process in the same temperature range. The rate constant for the gas-phase dissociation step can be expressed by 1.20 × 1015 exp (-14.6 kcal/mol/RT) sec-1. This study further confirms that the activation energy for the sublimation of an ammonium salt is significantly lower than the enthalpic change and that the molecular complex of acid and base sublimes concurrently as a pair. 1. Introduction Ammonium perchlorate (AP), NH4ClO4, has been widely employed as an oxidizer in composite propellants for rocket propulsion because it is cheap and contains a large amount of oxygen that, in combustion, is entirely converted into stable gaseous reaction products.1-3 The crystal structure of AP depends on temperature; at temperatures below 513 K, it possesses an orthorhombic unit cell with the space group Pnma; the unit cell dimensions at 298 K are a ) 9.20, b ) 5.82, and c ) 7.45 Å; and at lower temperatures these values are slightly different, a ) 9.02, b ) 5.85, and c ) 7.39 Å at 78 K and a ) 8.94, b ) 5.89, and c ) 7.30 Å for 10 K.4 In this space group, it is composed of a network of ammonium cations (NH4+) and perchlorate anions (ClO4-).4 In the NH4+/ ClO4- network, the O-N distances and the H-O hydrogen-bond lengths are in the range of 2.9-3.25 and 1.891-2.077 Å, respectively. At temperatures above 513 K, it undergoes a crystal transformation from the orthorhombic to the cubic form.5 The initial decomposition step of AP was believed6-10 to be sublimation via a proton transfer mechanism to produce NH3 and HClO4. Experimental results8 show that the sublimation/decomposition activation energies for the orthorhombic and cubic forms are nearly equal (around 20∼30 kcal/mol), as obtained by using different forms of the compound, such as powder, pellets, and crystals. Davies et al.9 investigated the sublimation kinetics using both pressure-change measurements and thermogravimetric methods. They reported that the activation energy for the lowtemperature thermal decomposition is 26.6 ( 0.9 or 30.1 ( 2.0 kcal/mol using different methods; the activation energy for sublimation is 28.0 ( 0.4 kcal/mol from contracting volume rate constants; the kinetics was found to be independent of both particle size and ambient atmosphere. In 1967, Jacobs et al.10 studied the decomposition of AP using weight-loss and concluded that in the solid (crystal), proton transfer is the ratecontrolling step with an activation energy of ∼30.0 kcal/mol. * Corresponding author e-mail: [email protected]..

In 1999, Vyazovkin and Wight11 studied the decomposition of AP using thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) methods, and the activation energies for the isothermal and nonisothermal decompositions were reported to be 26.3 and 31.1 kcal/mol. Recently, we studied the kinetics for the sublimation/ decomposition reaction of NH4Cl solid by first-principles and statistical-theory calculations,12 and the results are in good agreement with existing experimental data. This study has convincingly illustrated that the generalized gradient approximation with the plane-wave density functional theory (DFT) can reliably account for the experimental molecular parameters and characteristics of ammonium salts under the periodic boundary condition. In the present work, a more complex system (AP) is investigated. 2. Computational Methods The calculation was carried out with the Vienna ab-initio simulation package (VASP)13-16 which evaluates the total energy of periodically repeating geometries on the basis of DFT with the pseudopotential approximation. For the periodic boundary condition, the valance electrons were expanded over a plane-wave basis set. The core electron calculations are applied with the cost-effective pseudopotentials implemented in VASP. The expansion includes all plane waves with their kinetic energies smaller than the chosen cutoff energy, that is, p2k2/2m < Ecut, where k is the wave vector, m is the electronic mass, and Ecut is the chosen cutoff energy. In this study, a cutoff energy of 400 eV was used. Generalized gradient approximation (GGA)17,18 with PW91 exchange-correlation functional was used for the present calculation. The Brillouin-zone (BZ) integration is sampled with 0.05 × 2 (1/Å) spacing in reciprocal space by the MonkhorstPack scheme.19 The Fermi-smearing with σ ) 0.1 eV was used. For comparison, different supercells were used in the calculation for elucidation of some characteristics of the system. Unless otherwise specified, the calculations are based on the orthor-

10.1021/jp803224x CCC: $40.75  2008 American Chemical Society Published on Web 08/23/2008

14482 J. Phys. Chem. C, Vol. 112, No. 37, 2008

Zhu and Lin

TABLE 1: Comparison of the Experimental and Calculated Structural Parameters for NH4ClO4 in a Crystal Environment, Calculated by VASPa parameters

calculated

lattice constant

a) , (8.93) , [8.72] b ) 5.94, (6.09), [5.98 ] c ) 7.21, (7.34), [7.21]

rN-H1 rN-H2 rN-H3

1.027 1.029 1.037 1.462 1.475 1.475 1.825 ∼ 2.045 2.862 ∼ 3.215

Cl-O1 Cl-O2 Cl-O3

rHsO rNsO

8.84c

d

exp.b e

a ) 8.94 b ) 5.89 c ) 7.30 1.028 1.031 1.058 1.440 1.446 1.449 1.891 ∼ 2.077 2.9 ∼ 3.25

a Distances are in Ångstrom, and angles are in degrees. For the calculated bond lengths list in this table, only those predicted by the model including 4 NH4ClO4 unit cells are included. b The values are at 10 K. (ref 4) c The values are calculated by 4 NH4ClO4 unit cells. d The values in the parentheses are calculated by 8 NH4ClO4 unit cells. e The values in the square brackets are calculated by 16 NH4ClO4 unit cells.

hombic crystal structure. For the bulk calculation, 4, 8, and 16NH4ClO4 supercells with 4 × 6 × 5, 1 × 3 × 2, and 1 × 3 × 1 Monkhorst-Pack k-points, respectively, were employed. To minimize the interaction between the distinct slab surfaces in this infinitely periodic model system, a vacuum region of 30 Å was used to separate the top and bottom surfaces of the slabs; 1 × 6 × 5 Monkhorst-Pack k-points were used in the surface calculation. 3. Results and Discussion 3.1. Lattice Constant and Geometric Parameters. To select a computationally practical and reasonable model, supercells including 4, 8, and 16 NH4ClO4 units were employed for the bulk calculations, which were performed without any symmetry constrains and with all atomic positions of the molecules relaxed. The calculated lattice constants are a ) 8.84, 8.93, and 8.72 Å; b ) 5.94, 6.09, and 5.98 Å; and c ) 7.21, 7.34, and 7.21 Å for the above three cases, respectively, which are close to the experimental values4 a ) 8.94, b ) 5.89, and c ) 7.30 Å at 10 K (see Table 1.) Because the NH4ClO4 structural parameters with 4, 8, and 16 unit cells are similar, only those including 4 NH4ClO4 unit cells are collected in Table 1. For the calculations of the surface reconstruction energies and the sublimation process from the surface, the model including four NH4ClO4 was used. The vibrational frequencies of NH4ClO4 in the crystal environment are summarized in Table 2 and are compared with the available experimental values.20 The frequency scaling factor using PW91 in a plane wave basis was not available, if one uses the B3PW91 values as references, at the B3PW91/ 6-31+G(d, p), B3PW91/6-311G (d), and B3PW91/6-311+ G(3df,2p) levels, the recommended scaling factors21,22 are 0.9601, 0.9627, and 0.9573, respectively. Therefore, the frequencies displayed in Table 2 were scaled by a factor of 0.96. One can see that both the predicted bond lengths (see Table 1) and vibrational frequencies (see Table 2) are in good agreement with available experimental values. 4,20 3.2. Sublimation Enthalpy Change. The sublimation energy of the NH4ClO4 crystal was calculated as the energy difference between a single fully optimized NH4ClO4 molecule in the crystal and that of the gas-phase products, NH3 and HClO4; that is,

∆Hsub)E[NH3(g) + HClO4(g)]-[E(supercell)] ⁄ X where X is the number of NH4ClO4 units in the supercell. The values obtained by one-step calculations are 44.5, 44.9, and 44.1 kcal/mol, respectively, with the models including 4, 8, 16 NH4ClO4 unit cells. The enthalpy change for the above process can also be determined by combining the computed heat of reaction based on the following reaction scheme:

NH4C1O4(s) f NH4+ + C1O4-

(1)

NH4+ f NH3+H+

(2)

C1O4-+H+ f HOC1O3

(3)

For reaction 1, the heat of reaction was experimentally determined to be 140 kcal/mol.23 For reactions 2 and 3, the heats of reaction calculated at the CCSD(T)/6-311+G(3df, 2p)// B3LYP/6-311+G(3df,2p) and B3LYP/6-311+G(3df,2p) levels are 211.7, 211.0 and -306.9, -306.8 kcal/mol. By adding the heats of reaction of 1-3, we get the enthalpy change for the reaction NH4ClO4(s) f NH3 (g) + HOClO3 (g), which is 44.9 and 44.1 kcal/mol at the CCSD(T)/6-311+G(3df, 2p)// B3LYP/6-311+G(3df,2p) and B3LYP/6-311+G(3df,2p) levels, respectively, which are in excellent agreement with the values mentioned above and with the value of 45.0 kcal/mol predicted by Politzer and Lane. 2 The calculated data lie between the experimental values 30.6 kcal/mol,24 obtained by the differential scanning calorimetry (DSC) method, and 58 ( 2 kcal/mol,25 obtained by the transpiration method. 3.3. Sublimation Energies of NH3, HClO4, and H3N · · · HOClO3 from the Relaxed Top Layer. The sublimation energy Esub for NH3, HClO4, and one of the NH4+ClO4molecules desorbing from the relaxed surface is defined as:

Esub)[Eslab(hole) + Emolec(g)]-Eslab The “relaxed surface” here is the surface created by cleaving from the bulk material that naturally relaxes its atoms to reach TABLE 2: Comparison of the Experimental and Calculated Vibrational Frequenciesa for NH4ClO4 in a Crystal Environment

a

b

calculated (cm-1)

exp. (cm-1)b

3309 3282 3232 3113 1626 1589 1402 1380 1347 1003 975 970 854 579 557 548 435 412 339 288 230 224 215 210

3304 3285 3252 3198 1417 1065 950 935 638 630 624 464 443

Scaled by 0.9621,22 using VASP (PW91 in a plane wave basis). Experimental values in the temperature range 17∼300 K [ref 20].

Ammonium Perchlorate Sublimation

J. Phys. Chem. C, Vol. 112, No. 37, 2008 14483

Figure 2. Relative energy for one of NH4ClO4 molecules desorbing from the relaxed crystal surface, where R represents the distance between Cl1 and Cl2, as in the configuration indicated in Figure 1; the solid square symbol is the calculated value. Figure 1. Optimized configuration for the relaxed crystal surface model.

their minimum energy positions within the 30 Å vacuum space. Eslab (hole) is the energy of the slab after eliminating an individual molecule (NH3, HOClO3, or H3N · · · HOClO3); Emolec (g) is the energy of the isolated NH3, HOClO3, and H3N · · · HOClO3 in the gas-phase; Eslab is the total energy of the slab with the 30 Å vacuum space. Emolec (g) was calculated in a 20 × 20 × 20 Å3 cubic box. Esub was predicted to be 45.3, 43.5, or 28.1 kcal/mol for NH3, HOClO3, or H3N · · · HOClO3, respectively. Apparently, the sublimation of NH3 and HOClO3, individually from the relaxed first surface layer, cannot compete with that of H3N · · · HOClO3 as a pair. These data clearly indicate that the molecular complex of NH3 and HOClO3 sublimes more favorably as a pair instead of the separated NH3 and HOClO3 molecules, as is commonly assumed for the sublimation of ammonium salts. A similar conclusion has been reached for the sublimation of NH4Cl,12 in which the H3N · · · HCl molecule pair preferentially desorbs from the relaxed surface. To investigate the sublimation process of H3N · · · HOClO3 as a pair, one of the top layer NH4ClO4 molecules was pulled off along the x-axis from the relaxed surface (see Figure 1). The distance between the Cl atom (Cl1) of the leaving NH4ClO4 and another Cl atom (Cl2) in the second layer of NH4ClO4 is defined as R. The sublimation/dissociation minimum energy path (MEP) (solid square symbol) as a function of the separation (R) is plotted in Figure 2. The structure of each point along the curve was fully optimized without any constraint. No distinct intrinsic transition state was found in the calculation. The result indicates that the proton gradually transfers from the NH4+ moiety to the ClO4- moiety as R increases during the sublimation process. On the asymptote side, the H3N · · · HOClO3 pair at R ) 20.0 Å, the N-H and H-O bond lengths and the O-H-N bond angle are 1.078 and 1.648 Å and 168.6°, respectively. In the gas-phase H3N · · · HOClO3 calculated in a 20 × 20 × 20 Å3 cubic box, the N-H and H-O bond lengths and the O-H-N bond angle are 1.354 and 1.160 Å and 176.0°, respectively. The sublimation/dissociation energy at the asymptote with R ) 20.0 Å is 19.1 kcal/mol, which is 9.0 kcal/mol lower than the value (28.1 kcal/mol) at R ) ∞. Similar to the sublimation process of the NH4Cl system,12 the H3N · · · HOClO3 pair in the slab at R ) 20.0 Å does not reach the real gas-phase (R ) ∞ for three dimensions) due to the slab spatial constraint,

which results in the 9 kcal/mol difference as mentioned above. This can be confirmed by recalculating the gas-phase H3N · · · HOClO3 energy in a smaller 38.84 × 7.21 × 5.94 box, in which the sublimation process was investigated. The three dimensions are kept constant during the optimization process. On the basis of the energy of H3N · · · HOClO3 in this box, the sublimation energy is 24.4 kcal/mol. If all of the x, y, and z dimensions are allowed to relax, then the value is decreased to 19.6 kcal/mol, which is close to 19.1 kcal/mol at R ) 20.0 Å, as mentioned above. Apparently, due to the interaction between the distinct slab along the y and z directions, the geometry of H3N · · · HOClO3 in the slab with the computationally affordable 30 Å vacuum space does not really reach that predicted in the gas-phase. This calculation can quantitatively explain why the sublimation energies of this system given in Figure 2, as well as that in the NH4Cl system (Figure 3 in ref 10) at the asymptotes, are lower than those at R ) ∞. 3.4. Proposed Sublimation/Dissociation Mechanism. On the basis of the results presented above, we suggest that the sublimation/dissociation reaction is a multistage process, taking place as shown below, where (c) refers to NH4+ClO4- in the

crystal environment (bulk); (s) refers to the relaxed surface, and (g) refers to the gas phase. The energy diagram for this process is plotted in Figure 3. Similar to the NH4Cl system,12 the result of our calculations indicates that three steps are involved in the sublimation process (see Figure 3). Most interestingly, there is a distinct difference between the two systems in the first step, namely, the NH4+ClO4- molecules relax from their crystal structure on the surface with only 0.1 kcal/mol relaxation energy, which is much lower than the value 18.7 ( 1.0 kcal/mol predicted for the NH4Cl system; the result may be attributed to the loose lattice structure of AP. In the second step, one of the NH4+ClO4- molecules on the surface undergoes proton transfer to form a H3N · · · HOClO3 (g) complex and desorbs with a 28.1 kcal/mol barrier. This value can be compared with the experimental results 20∼30,8 30.1 ( 2.0,9 28.0 ( 0.4,9 and

14484 J. Phys. Chem. C, Vol. 112, No. 37, 2008

Zhu and Lin

Figure 3. Schematic energy diagram (in units of kcal/mol) for the sublimation/dissociation processes of NH4ClO4. Where NH4ClO4 (c) refers to NH4ClO4 in the crystal environment; NH4ClO4 (s) represents NH4ClO4 on the relaxation surface; and NH3 (g), HOClO3 (g), and H3N••HOClO3 (g) represent those products in gas-phase.

26.3∼31.111

kcal/mol. In the last step, the molecular complex H3N · · · HOClO3 (g) dissociates in the gas-phase to NH3(g) and HOClO3(g) with a relatively smaller energy of 18.5 kcal/mol. The enthalpy change via these three steps, 46.7 kcal/mol, is close to the predicted one-step values (44.1∼44.9 kcal/mol) as discussed in the previous section. 3.5. Rate Constant Calculation. The rate constants were calculated in this work on the basis of the classical transition state theory.26

ks )

kBT Q* exp(-E0 ⁄ kBT) h Q

(4)

Here, kB is the Boltzmann constant, T is the temperature, h is the Planck’s constant, E0 is the energy of activation per molecule at 0 K, and Q* and Q are the molecular partition function for the transition state and the reactant, respectively. As one can see, the first relaxation step needs only 0.1 kcal/ mol energy; therefore, only the rate constants for the ratecontrolling second step and the last step for the gas-phase H3N · · · HOClO3 decomposition will be discussed in the following paragraphs. The sublimation process, (NH4ClO4)X f (NH4ClO4)X* f (NH4ClO4)X-1 + H3N · · · HOClO3 (g), is a barrierless dissociation reaction as calculated above for X ) 4. The potential energy along the MEP is shown in Figure 2. The necessary information (the structures, frequencies, etc.) to calculate molecular partition functions for the reactant and transition state is provided by VASP calculations. For the barrierless (not well-defined) transition states, the parameters were canonically evaluated for each temperature and critical separation, r*(T), based on the maximum Gibbs free energy criterion as described in refs 27 and 28. The result shows that in the temperature range 450-600 K, in which most of the experimental temperatures lie, the transition state locates at nearly the same point at R ) 12.4 Å. In the sublimation process, only the structures and frequencies of the subliming NH4/ClO4 pair have significant changes along the reaction coordinate; other parts of the relaxed surface have minor changes. Therefore, only the frequencies of the subliming NH4/ClO4 pair in the relaxed surface (reactant) and in the transition point are included in the rate constant calculation; the frequencies of vibrations of other atoms of the reactant and of the transition state are effectively canceled in the partition function ratio Q*/Q in the abovementioned eq 1. The Cartesian coordinates and the key vibrational frequencies of the relaxed surface and the transition state are displayed in the Supporting Information, SM-I and SMII, respectively. The rate constant was calculated by the ChemRate code29 with D0 ) 28.1 kcal/mol at R ) ∞. The predicted values (see

Figure 4. Predicted AP sublimation/dissociation rate constant. The solid line is the calculated values with a barrier of 28.1 kcal/mol; symbols are the experimental values taken from ref 9.

Figure 4) lie within the scattered experimental data obtained under different conditions.7 The calculated result can be represented as: kdec.) 6.53 × 1012 exp (-28.8 kcal/mol/RT) s-1. After sublimation, the H3N · · · HOClO3 complex readily fragments to HOClO3(g) and NH3 (g). The dissociation rate constant for H3N · · · HOClO3 (g) f HOClO3(g) + NH3 (g) was calculated using the variational RRKM theory.30-35 The molecular parameters employed in the calculation are listed in Supporting Information SM-III; Supporting Information SMIV displays the variational dissociation curve of H3N · · · HOClO3 (g) f HOClO3(g) + NH3 (g) at the UB3LYP/6-311+G(3df, 2p) level and the fitted values using the Morse potential. As expected, this process is considerably faster, about 1 × 107 times greater than that of step 2 in the same temperature range. The rate constant for this dissociation step can be expressed by 1.20 × 1015 exp (-14.6 kcal/mol/RT) sec-1. 4. Concluding Remarks In this paper we have performed first-principles calculations using the plane-wave DFT for elucidation of the sublimation/ dissociation mechanism of NH4ClO4. The result of our calculations indicates that three distinct steps are involved in the sublimation process. In the first step, NH4+ClO4- molecules relax from their crystal structure on the surface with a small (0.1 kcal/mol) relaxation energy; in the second step, one of the surface NH4+ClO4- molecules undergoes proton transfer and desorbs as the molecular complex H3N · · · HOClO3 with a 28.1 kcal/mol barrier without an intrinsic transition state; in the last step, the molecular complex H3N · · · HOClO3 rapidly dissociates to NH3(g) and HOClO3(g) with 18.5 kcal/mol energy, also without a distinct barrier. The rate constants for the last two steps were calculated. As expected, the last step (3) is much faster than the rate-controlling sublimation step (2). The predicted overall sublimation activation energy and the rate constant are in good agreement with most of the available experimental data. Acknowledgment. This work was supported by the Office of Naval Research under grant No. N00014-02-1-0133. M.C.L. gratefully acknowledges the supports from Taiwan’s MOE ATU program, as well as the National Science Council and the Taiwan Semiconductor Manufacturing Co. for the NSC-distinguished visiting professorship and the TSMC distinguished professorship, respectively, at the Center for Interdisciplinary Molecular

Ammonium Perchlorate Sublimation Science, National Chiao Tung University, Hsinchu, Taiwan. We are very much indebted to Taiwan’s National Center for Highperformance Computing for the extensive CPU time needed in this work. Supporting Information Available: Additional information mentioned within the text is provided. 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. Solid Propellant Chemistry, Combination, and Motor Interio Ballistics, Progress in Astronautics and Aeronautics Series; Yang, V., Brill, T. B., Ren, W.-Z., Eds.; AIAA, 2000; Vol. 185, ch. 2. (2) Politzer, P.; Lane, P. J. Mol. Strut. 1998, 454, 229. (3) Jacobs, P. W. M.; Whitehead, H. M. Chem. ReV. 1969, 69, 551. (4) Choi, C. S.; Prask, H. J. J. Chem. Phys. 1974, 61, 3523. (5) (a) Vorlander, D.;. Kaascht, E. Ber. Dtsch. Chem. Ges. 1923, 56B, 1157; (b) Chem. Abs. 1923, 17, 2682. (6) Jacobs, P. W. M.; Russell-Jones, A. J. Phys. Chem. 1968, 72, 202. (7) Davies, J.; Jacobs, P. W. M.; Russel-Jones, A. Trans. Faraday Soc. 1967, 63, 1737. (8) Galwey, A. K.; Jacobs, P. W. M. Proc. R. Soc. (London) 1960, A254, 455. (9) Heath, G. A.; Majer, J. R. Trans. Faraday Soc. 1964, 60, 1783. (10) Jacobs, P. W. M.; Russell-Jones, A. AIAA J. 1967, 5, 829. (11) Vyazovkin, S.; Wight, C. A. Chem. Mater. 1999, 11, 3386. (12) Zhu, R. S.; Wang, J. H.; Lin, M. C. J. Phys. Chem. C 2007, 111, 13831. (13) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 47, 558. (14) Kresse, G.; Hafner, J. Phys. ReV. B 1994, 49, 1425. (15) Kresse, G.; Furthmuller, J. Comput. Mater. Sci. 1996, 6, 15.

J. Phys. Chem. C, Vol. 112, No. 37, 2008 14485 (16) Kresse, G.; Furthmuller, J. Phys. ReV. B 1996, 54, 11169. (17) Perdew, J. P.; Yang, Y. Phys. ReV. B. 1992, 45, 244. (18) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (19) Monkhorst, H.; Pack, J. Phys. ReV. B. 1976, 13, 5188. (20) Van Rensburg, D, J. J.; Schutte, C. J. H. J. Mol. Struct. 1972, 11, 229. (21) Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502. (22) Computational Chemistry Comparison and Benchmark Data Base (CCCBDB), release 12; NIST Standard reference Database 101: 2005. (23) Lide, D. R. Ed., Handbook of Chemistry and Physics, 71st ed.; CRC Press, Boca Raton, FL, 1990. (24) Waesche, R.; Woodward, H.; Wenograd, J. West. States Sect., Combust. [Pap.] 1967, (WSS//CI-67-8), p 29. (25) Inami, S. H.; Rosser, W. A.; Wise, H. J. Phys. Chem. 1963, 67, 1077. (26) Laidler, K. J., Theories of Chemical Reaction Rates, McGraw-Hill, London, 1969, Ch. 3. (27) Hsu, C. -C.; Mebel, A. M.; Lin, M. C. J. Chem. Phys. 1996, 105, 2346. (28) Chakraborty, D.; Hsu, C.-C.; Lin, M. C. J. Chem. Phys. 1998, 109, 8889. (29) Mokrushin, V. B.;. Tsang, W.;. Zachariah, M. R.;. Knyazev, V. D.; ChemRate, Ver. 1.19; National Institute of Standards and Technology: Gaithersburg, MD, 2002; p 20899. (30) Hase, W. L. J. Chem. Phys. 1972, 57, 730. (31) Hase, W. L. Acc. Chem. Rec. 1983, 16, 258. (32) Klippenstein, S. J.;. Wagner, A. F.;. Dunbar, R. C.;. Wardlaw, D. M.;. Robertson, S. H. VARIFLEX, VER. 1.00; 1999. (33) Wardlaw, D. M.; Marcus, R. A. Chem. Phys. Lett. 1984, 110, 230. (34) Wardlaw, D. M.; Marcus, R. A. J. Chem. Phys. 1986, 90, 5383. (35) Holbrook, K. A.; Pilling, K. J.; Robertson, S. H.; Unimolecular Reactions; Wiley: Chichester, U.K., 1996.

JP803224X