DFT study on the mechanism of the CF3O + NO reaction

Journal of Molecular Structure: THEOCHEM 948 (2010) 55–60

Contents lists available at ScienceDirect

Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem

DFT study on the mechanism of the CF3O + NO reaction Guohua Xu, Chengyin Shen, Haiyan Han, Jianquan Li, Hongmei Wang, Yannan Chu * Laboratory of Environmental Spectroscopy, Anhui Institute of Optics and Fine Mechanism, Chinese Academy of Sciences, P.O. Box 1125, Hefei, 230031 Anhui, PR China

a r t i c l e

i n f o

Article history: Received 4 December 2009 Received in revised form 16 February 2010 Accepted 16 February 2010 Available online 21 February 2010 Keywords: CF3O NO Potential energy surface Enthalpy of formation

a b s t r a c t The singlet potential energy surface of the CF3O + NO reaction has been studied at the B3LYP/6311+G(3df) level of theory. The relative energies were calculated by using the CCSD(T)/aug-cc-pVDZ and the G3B3 methods at the B3LYP/6-311 + G(3df) optimized geometries. The study shows that the reaction starts via an exothermic barrierless addition of NO to the CF3O radical to produce cis-CF3ONO, which will isomerize to trans-CF3ONO, followed by trans-CF3ONO dissociating to the products CF2O + FNO. transCF3ONO can also rearrange to trans-CF3OON and further isomerize to cis-CF3OON. Once cis-CF3OON is formed, it will finally dissociate to CF2O + FNO. This is another energetically facile reaction route to produce CF2O + FNO. The transition states involved in above reaction pathways all lie below the reactants in energy, thus the present calculations suggest the overall rate coefficient of the title reaction may exhibit a negative temperature dependence, in agreement with most experimental results. Additionally, the enthalpies of formation of CF3NO2, trans-CF3ONO and cis-CF3ONO were computed to be Df H298:15 ðCF3 NO2 Þ = 160.99 kcal/mol, Df H298:15 ðtrans  CF3 ONOÞ = 176.76 kcal/mol and Df H298:15 ðcis  CF3 ONOÞ = 173.24 kcal/mol, respectively. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction The CF3O radicals are key intermediates in the atmospheric degradation of hydrofluorocarbons [1–3], which have been increasingly used as replacements of chlorofluorocarbons. Various reactions referred to the CF3O radicals have attracted much attention due to their important roles in atmospheric chemistry [4–10]. Since CF3O can react with NO to yield the chemically stable CF2O and FNO [11–16], this reaction is a main sink of CF3O in stratosphere. There are a number of experimental studies to measure the rate coefficient and identify the products of this reaction in the past decades. Bevilacqua et al. [11] studied the reaction using a flow tube reactor coupled to a chemical ionization mass spectrometry (CIMS). The determined rate constant at 297 K is (2 ± 1)  1011 cm3 molecule1 s1 over a pressure range of 0.8– 2.0 Torr. A similar result of k(298 K) = (2.5 ± 0.4)  1011 cm3 molecule1 s1 was obtained by Zellner [17] using laser photolysis/laser induced fluorescence technique. However, subsequent several experiments reported larger reaction rates. For instance, Sehested and Nielsen [12] derived k(295 K) = (5.2 ± 2.7)  1011 cm3 molecule1 s1 for the title reaction by pulse radiolysis of CHF3/O2/NO mixtures. Bhatnagar and Carr [18] obtained k(293 K) = (4.72 ± 0.30)  1011 cm3 molecule1 s1 by means of flash photolysis with time-resolved mass spectrometry in the pressure range * Corresponding author. Tel./fax: +86 551 5591076. E-mail address: [email protected] (Y. Chu). 0166-1280/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2010.02.019

2–30 Torr. Bourbon et al. [19] also measured the rate constant at room temperature for the reaction to be (4.7 ± 0.9)  1011 cm3 molecule1 s1 using flow tube/laser induced fluorescence technique. Besides measuring rate constant at single temperature as mentioned above, some studies investigated the title reaction over a much wider temperature range. Turnipseed et al. [6] derived k(T) = (3.34 ± 0.68)  1011exp[(160 ± 45)/T] cm3 molecule1 s1 in the range of 233–360 K, and they found that the rate constant has a negative temperature dependence. Dibble [16] and Jensen [20] gave the rate constant k(T) = (4.4 ± 1.5)  1011 exp[(100 ± 88)/T] cm3 molecule1 s1 over the range 213–353 K and k(T) = (4.1 ± 0.6)  1011exp[(60 ± 100)/T] cm3 molecule1 s1 in the range 231–391 K, respectively. They also suggested that the rate constant has a weak negative dependence on temperature. In the latest experiment by laser photolysis/laser induced fluorescence technique [14], Fockenberg and co-workers reported a temperature independent rate constant of (4.5 ± 1.2)  1011 cm3 molecule1 s1 over 222–302 K. As to the products of the title reaction, the FNO molecule was identified by Bevilacqua et al. [11], Sehested and Nielsen [12], and Li and Francisco [13], while CF2O was detected in Fockenberg’s experiment [14] using FTIR spectroscopy. Both FNO and CF2O were observed in Chen’s long path FTIR spectroscopic study [15] and Dibble’s laser flash photolysis/transient diode laser absorption study [16]. The FTIR spectroscopic measurements [14,15] were performed around 760 Torr, at such a high pressure the combination of CF3O with NO may form the intermediate CF3ONO,

56

G. Xu et al. / Journal of Molecular Structure: THEOCHEM 948 (2010) 55–60

however, no infrared bands of CF3ONO were observed probably due to the limited detection sensitivity. Theoretically, in the study by Fockenberg et al. [14], the addition–elimination path, CF3O + NO ? CF3ONO ? CF2O + FNO, was investigated at the B3LYP/cc-pVDZ level of theory in order to explain the experimentally observed pressure independent rate constant. However, the detailed mechanism of the CF3O + NO reaction has not been well established. In the present study, we carry out a more extensive investigation on the CF3O + NO reaction using density functional theory. It is the main aim of this work to identify whether other possible reaction channels exist. We hope that our high-level theoretical study will be beneficial for future experimental investigations. 2. Computational methods The geometries of all reactants, products, intermediates and transition states have been optimized using Beck’s three-parameter exchange functional with Lee, Yang and Parr’s correlation functional B3LYP method in conjunction with 6-311 + G(3df) basis set. Vibrational frequencies were obtained at the same level to determine the nature of different stationary points and the zero-pointenergy. The number of imaginary frequencies for intermediates and transition states is 0 and 1, respectively. The intrinsic reaction coordinate (IRC) calculation has been performed to check whether the transition states connect with the proper reactants and products. To obtain more accurate relative energies, the CCSD(T)/augcc-pVDZ and G3B3 [21] methods were employed to compute single-point electronic energies based on the B3LYP/6-311 + G(3df) optimized geometries. In this paper, unless otherwise specified, the energies calculated at the G3B3//B3LYP/6-311 + G(3df) level are presented in the discussion described below. All molecular orbital calculations were completed using the Gaussian03 package [22]. 3. Results and discussion The optimized geometries of the reactants, products, intermediates and transition states are shown in Figs. 1 and 2. The overall energy profile is depicted in Fig. 3. The relative energies for all species involved in this study are listed in Table 1. The vibrational frequencies are contained in the supplementary data. On the basis of the predicted potential energy surface, the reaction of CF3O with NO is expected to take place primarily by the association/isomerization–decomposition mechanism. 3.1. Reaction mechanisms 3.1.1. Formation of initial intermediates The addition of the N atom in NO radical to the O atom in CF3O results in the formation of the adduct cis-CF3ONO (IM1). IM1 formation is an energetically favorable process without energy barrier, confirmed by the relaxed scan calculation of the 5O–6N bond. IM1 lies 43.50 kcal/mol below the reactant. It can convert to trans-CF3ONO (IM2) via TS1 by rotation of the 6N–7O moiety around the 5O–6N bond. TS1 is located at 3.66 kcal/mol higher than IM1, while IM2 is more stable than IM1 by 3.33 kcal/mol. The geometrical parameters of IM1 and IM2 at the B3LYP/6311 + G(3df) level is close to that reported previously at the MP2(FU)/6-31G(d) level [23], Fig. 1 shows that the bond lengths of IM1 and IM2 at the B3LYP/6-311 + G(3df) level are a little shorter than that obtained at the MP2(FU)/6-31G(d) level. Since IM1 and IM2 are energy-rich intermediates, they could undergo further decomposition or intramolecular rearrangement, leading to the finial products.

3.1.2. Decomposition of IM1 (cis-CF3ONO) As shown in Fig. 3, IM1 can form a van der Waals complex IM4 via a five-member-ring transition state TS2 by the migration of the 2F atom to the terminal 7O atom and the simultaneous break of 5O–6N bond. The activation energy barrier is estimated to be 36.65 kcal/mol. IM4 can further decompose to CF2O + FON. Both standard and counterpoise-corrected (CP) [24,25] optimization were performed on IM4. The 1C–2F and 5O–6N distances optimized by the CP-corrected method are obviously longer as shown in Fig. 1. IM4 is more stable than the reactants by 9.01 kcal/mol based on the structure from CP-corrected method and 7.78 kcal/ mol lower than the final products CF2O + FON. The products CF2O + FON is calculated to be 1.23 kcal/mol exothermic relative to the reactants at the G3B3//B3LYP/6-311 + G(3df) level, while 0.65 kcal/mol endothermic at the CCSD(T)/aug-cc-pVDZ//B3LYP/ 6-311 + G(3df) level, thus this reaction channel could be considered to be nearly thermoneutral.

3.1.3. Isomerization and decomposition of IM2 (trans-CF3ONO) The activated trans-CF3ONO will dissociate through the fourcenter transition state TS4 to CF2O + FNO. The calculated imaginary harmonic frequency of 415.5i cm1 indicates that it is a first-order saddle point. TS4 has an activation energy barrier of 25.70 kcal/mol and is calculated to be 21.13 kcal/mol lower in energy than the reactants. In TS4, the 1C–2F and 5O–6N bonds are stretched by 0.269 and 0.536 Å to 1.612 and 2.127 Å, respectively, while the 2F–6N distance is shortened to 1.945 Å. For the second pathway, IM2 first isomerizes to IM5 (transCF3OON) via transition state TS5, which results from the substantial elongation of the 5O–6N bond by 0.832 Å and the simultaneous approach of the 7O atom to the 5O atom. This leads to a triangular geometry with the forming 5O–7O bond to be 2.196 Å. The G3B3// B3LYP/6-311 + G(3df) calculation locates TS5 at 36.19 kcal/mol higher than IM2, while lower than the reactants CF3O + NO by 10.64 kcal/mol. IM5 can isomerize through the transition state TS7 to cis-CF3OON (IM6) via a low energy barrier of 0.69 kcal/ mol. The further decomposition of IM6 via TS8 with an energy barrier of 2.66 kcal/mol leads to the final products CF2O + FNO. In TS8, the 1C–2F and 5O–7O bonds are elongated to 1.564 and 2.199 Å, respectively, while the 2F–6N bond is shortened to 2.132 Å. The dissociation of cis-CF3OON is 22.0 kcal/mol exothermic. Considering the possible diradical character of TS5 and IM5, the stability of spin-restricted wave functions of TS5 and IM5 at the B3LYP/6311 + G(3df) level of theory was checked. Both spin-restricted wave functions show RHF-to-UHF instability, which indicates TS5 and IM5 are singlet diradicals instead of closed shell singlet. It should be stressed that the present singlet-reference method is not sufficient in treating diradicals due to their multireference character. The multiconfigurational models such as complete active space perturbation theory or multireference configuration interaction method are required to give proper description of singlet diradicals. However, this goes beyond the scope of the present work and is worthy of further study. As far as we know, the intermediate CF3OON has not been reported previously in the literature. However, the analogue of CF3OON, i.e. HOON has ever been studied theoretically [26,27]. Miller and co-workers [27] studied the direct OH-stretch overtone induced behavior of HONO molecule by classical trajectory simulation. They found that both trans- and cis-HONO can convert to the weakly bound species HOON by high overtone excitation of HONO. The formation of HOON from trans-HONO is analogous with the isomerization between trans-CF3ONO and trans-CF3OON in present system. The energy difference [27] between trans-HOON and transHONO was predicted to be 46.12 kcal/mol at the MP2/DZP level and 44.28 kcal/mol at the PM3 level, respectively, which is compa-

G. Xu et al. / Journal of Molecular Structure: THEOCHEM 948 (2010) 55–60

57

Fig. 1. Optimized geometries of the reactants, intermediates and products in the CF3O + NO reaction obtained at the B3LYP/6-311 + G(3df) level. Bond lengths are in angstrom and bond angles are in degree. Numbers in parenthesis are available experimental values (Ref. [31] for NO, CF2O, FNO, FO and CF2, Ref. [28] for CF3NO2(IM3)). For IM1 and IM2, numbers in square brackets are optimized structure parameters at the MP2(FU)/6-31G(d) level in Ref. [23]. For IM4, numbers in italics are optimized structure parameters by standard optimization method, while numbers in roman are optimized structure parameters by counterpoise-corrected method.

Fig. 2. Optimized geometries of the transition states in the CF3O + NO reaction obtained at the B3LYP/6-311 + G(3df) level. Bond lengths are in angstrom and bond angles are in degree.

58

G. Xu et al. / Journal of Molecular Structure: THEOCHEM 948 (2010) 55–60

Fig. 3. Singlet potential energy profile of the CF3O + NO reaction. Numbers in roman indicate relative energies (in kcal/mol) of various species at the G3B3//B3LYP/6311 + G(3df) level, and numbers in parenthesis are relative energies (in kcal/mol) at the CCSD(T)/aug-cc-pVDZ//B3LYP/6-311 + G(3df) level.

Table 1 Calculated relative energies (kcal/mol) for various species in the CF3O + NO reaction. Species

CF3O + NO IM1 IM2 IM3 IM4 IM5 IM6 IM7 TS1 TS2 TS3 TS4 TS5 TS6 TS7 TS8 TS9 TS10 CF2O + FNO CF2O + FON CF3 + NO2 CF2O + F + NO FONO + CF2 F2CNO(2A0 )+FO a b c

B3LYP/6-311 + G(3df)

CCSD(T)/aug-cc-pvdz//B3LYP/6-311 + G(3df)

G3B3//B3LYP/6-311 + G(3df)

Dr H298:15

ZPEa

Energies

Energies

ZPEb

Energies

Experimentc

0K

298.15 K

0K

298.15 K

0K

298.15 K

12.29 14.69 14.72 16.15 13.60 14.09 14.08 14.32 14.31 13.48 13.27 13.82 13.55 14.06 13.90 13.41 13.90 12.50 12.98 12.78 12.61 11.22 10.39 12.03

0.0 38.28 41.80 26.65 6.85 13.09 13.46 81.89 34.88 6.71 96.80 20.95 9.67 31.47 12.24 12.04 90.62 103.67 37.07 1.41 19.52 23.70 91.47 98.69

0.0 38.35 41.82 27.05 5.81 12.72 13.20 81.93 35.26 6.37 96.40 21.04 9.56 31.20 12.40 11.94 92.01 103.93 37.17 1.37 19.38 23.99 91.83 98.82

0.0 40.05 43.09 25.21 8.07 13.84 15.40 89.48 37.05 7.26 94.69 20.64 11.32 35.63 13.64 13.77 97.27 106.53 33.85 0.65 28.62 21.59 93.24 110.11

0.0 40.11 43.12 25.61 7.03 13.48 15.14 89.52 37.43 6.92 94.29 20.73 11.21 35.37 13.80 13.68 97.04 106.80 33.95 0.69 28.48 21.88 93.59 110.24

12.19 14.57 14.60 16.02 13.49 13.98 13.97 14.20 14.19 13.37 13.17 13.71 13.44 13.95 13.79 13.30 13.79 12.39 12.87 12.67 12.51 11.13 10.31 11.94

0.0 43.50 46.83 30.50 9.01 15.47 15.78 84.91 39.84 6.85 95.67 21.13 10.64 30.06 14.78 13.12 91.61 102.81 37.78 1.23 25.12 23.27 93.02 108.35

0.0 43.55 46.85 30.90 7.97 15.10 15.52 84.96 40.21 6.51 95.27 21.21 10.53 29.80 14.94 13.02 91.39 103.08 37.89 1.19 24.98 23.94 93.37 108.48

38.19 25.72 18.07 102.73

Frequencies are scaled by 0.9679. The scale factor is taken from Ref. [32]. Frequencies are scaled by 0.96. The scale factor is taken from Ref. [21]. Df H298:15 ðCF3 OÞ is taken from Ref. [33]. Df H298:15 ðFONOÞ is taken from Ref. [34]. Other available Df H298:15 values are taken from Ref. [31].

rable with that between trans-CF3OON and trans-CF3ONO, i.e. 31.36 kcal/mol at the G3B3//B3LYP/6-311 + G(3df) level.

Another reaction channel for IM2 is the barrierless unimolecular decomposition to products CF3 + NO2 via the scission of 1C–

59

G. Xu et al. / Journal of Molecular Structure: THEOCHEM 948 (2010) 55–60 Table 2 Calculated enthalpies of formation (kcal/mol) of CF3NO2, trans-CF3ONO and cis-CF3ONO. CF3NO2

G3B3//B3LYP/6-311 + G(3df) G4//B3LYP/6-311 + G(3df) Mean

trans-CF3ONO

cis-CF3ONO

Df H0

Df H298:15

Df H0

Df H298:15

Df H0

Df H298:15

158.83 158.80 158.82

160.97 161.00 160.99

175.16 174.77 174.97

176.92 176.60 176.76

171.82 170.99 171.41

173.62 172.85 173.24

5O bond. IM2 can also evolve into IM3 (CF3NO2) via a three-center transition state TS6, which involves the 1C–5O bond fission and the 1C–6N bond formation. In TS6, the 1C–5O bond is lengthened from 1.353 Å in IM2 to 1.975 Å, and the forming 1C–6N bond is 1.955 Å, which is 0.388 Å longer than that in CF3NO2. This process needs to surmount an amount of energy of 76.89 kcal/mol, thus it is not competitive with the channels to form CF2O + FNO above-mentioned. The calculated 1C–3F, 1C–6N and 6N–7O bond lengths of CF3NO2 are 1.318, 1.567 and 1.208 Å, respectively, which accord with the experiment values of 1.325, 1.56 and 1.21 Å [28] well. CF3NO2 can further decompose to CF3 + NO2 without barrier. 3.1.4. Channels of no importance It could be seen immediately from Fig. 3 that the production of CF2O + F + NO from IM1 via TS3 is negligible due to its high barrier of 139.17 kcal/mol. The product channels to form FONO + CF2 and F2CNO(2A0 ) + FO are endothermic by 93.02 and 108.35 kcal/mol, respectively. Obviously, these channels can not play roles in the CF3O + NO reaction.

tively, while the counterparts at 0 K are 158.82, 174.97 and 171.41 kcal/mol, respectively. 3.3. Comparison with experiments According to the potential energy surface aforementioned, we can conclude that the reaction pathway, CF3O + NO ? IM1 ? TS1 ? IM2 ? TS4 ? CF2O + FNO, is the most accessible. The scheme CF 3 O + NO ? IM1 ? TS1 ? IM2 ? TS5 ? IM5 ? TS7 ? IM6 ? TS8 ? CF2O + FNO provides another thermodynamically facile route that evolves into CF2O + FNO. Thus CF2O + FNO are the dominant products. Indeed, both FNO and CF2O were observed as products in the FTIR spectroscopy [15] and the laser flash photolysis/ transient diode laser absorption [16], while either FNO or CF2O was detected in different experimental studies [11–14]. Since all transition states involved in the two pathways lie below the CF3O + NO reactants, it is expected that the title reaction proceeds fast, and the overall rate constant may show a negative temperature dependence, which has been observed in different experimental studies reported in the literature [6,16,20].

3.2. Thermochemistry of relevant species 4. Conclusions In view of lack of thermochemistry data of CF3NO2, cis-CF3ONO and trans-CF3ONO in title system, the enthalpies of formation for the three adducts were evaluated using atomization reaction method [29]. Two multilevel scheme G3B3 [21] and G4 [30] were performed based on the B3LYP/6-311 + G(3df) geometries. The frequencies are scaled by 0.96 [21] and 0.9854 [30] for G3B3 and G4 methods, respectively. For any molecule M, the enthalpy of formation at 0 K is given by

Df H0 ðMÞ ¼

atoms X

Df H0 ðXi Þ 

X

D

ð1aÞ

i

where Df H0 ðXi Þ is the experimental enthalpy of formation of the isolated atom Xi taken from reference [31], and RDs is the calculated atomization energy of M. Theoretical enthalpies of formation at 298.15 K are computed as follows,

In present work, the CF3O + NO reaction mechanism has been modeled at the G3B3//B3LYP/6-311 + G(3df) and the CCSD(T)/ aug-cc-pVDZ//B3LYP/6-311 + G(3df) levels of theory. The calculations indicate that the reaction starts with barrierless addition of NO to CF3O to form cis-CF3ONO, which can undergo further isomerization or decomposition to various products. CF2O + FNO are identified as the most feasible products, since the reactants can access CF2O + FNO via two energetically favorable pathways. This is in line with previous experimental observations reported in the literature. The calculated potential energy surface suggests that the rate constant of the title reaction may exhibit a negative temperature dependence, according with previous experimental consensus. Additionally, enthalpies of formation of CF3NO2, cis-CF3ONO and trans-CF3ONO were also estimated using high level quantum chemical calculations.

Df H298:15 ðMÞ ¼ Df H0 ðMÞ þ ½H298:15 ðMÞ  H0 ðMÞ 

atoms X

½H298:15 ðXi Þ  H0 ðXi Þref

Acknowledgements

ð1bÞ

i

½H298:15 ðMÞ

H0 ðMÞ

where  is the calculated heat capacity correction for the molecule [29], and ½H298:15 ðXi Þ  H0 ðXi Þref is the heat capacity correction for the reference state of the atom Xi (denoted as ‘‘ref’’ in Eq. (1b)) taken directly from reference [31], which is 0.25, 1.04, 1.04 and 1.05 kcal/mol for carbon, nitrogen, oxygen, and fluorine atom, respectively. The calculated formation enthalpies of CF3NO2 and two conformers of CF3ONO are given in Table 2. For each species, the calculated values at both levels show good agreement. Taking the mean between the value at the G3B3//B3LYP/6-311 + G(3df) level and that at the G4//B3LYP/6-311 + G(3df) level, the enthalpies of formation at 298.15 K for CF3NO2, trans-CF3ONO and cis-CF3ONO are estimated as 160.99, 176.76 and 173.24 kcal/mol, respec-

Partly financial support by the National Natural Science Found of China (20577049, 20707025), the Excellent Youth Foundation of Auhui Scientific Committee (06045098), and the Natural Science Foundation of Anhui Province (070411026) is greatly acknowledged. Appendix A. Supplementary data The optimized geometries of all species involved in the CF3O + NO reaction at the B3LYP/6-311 + G(3df) level are listed. Tables S1 and S2 contain the absolute energies and vibrational frequencies of all species referred. Supplementary data associated with this article can be found, in the online version, at doi:10.1016/ j.theochem.2010.02.019.

60

G. Xu et al. / Journal of Molecular Structure: THEOCHEM 948 (2010) 55–60

References [1] M.K.W. Ko, N.-D. Sze, J.M. Rodriguez, D.K. Weistenstein, C.W. Heisey, R.P. Wayne, P. Biggs, C.E. Canosa-Mas, H.W. Sidebottom, J. Treacy, Geophys. Res. Lett. 21 (1994) 101. [2] J.S. Francisco, M.M. Maricq, Acc. Chem. Res. 29 (1996) 391. [3] S.v. Ahsen, H. Willner, G.A. Arguello, J. Fluorine Chem. 125 (2004) 1057. [4] C. Bourbon, C. Fittschen, J.P. Sawerysyn, P. Devolder, J. Phys. Chem. 99 (1995) 15102. [5] A.A. Turnipseed, S.B. Barone, N.R. Jensen, D.R. Hanson, C.J. Howard, A.R. Ravishankara, J. Phys. Chem. 99 (1995) 6000. [6] A.A. Turnipseed, S.B. Barone, A.R. Ravishankara, J. Phys. Chem. 98 (1994) 4594. [7] R. Meller, G.K. Moortgat, Int. J. Chem. Kinet. 29 (1997) 579. [8] K. Brudnik, J.T. Jodkowski, E. Ratajczak, R. Venkatraman, A. Nowek, R.H. Sullivan, Chem. Phys. Lett. 345 (2001) 435. [9] B. Jing, J.Y. Liu, Z.S. Li, Y. Wang, L. Wang, H.Q. He, C.C. Sun, J. Mol. Struct. (THEOCHEM) 732 (2005) 225. [10] G.H. Xu, C.Y. Shen, H.Y. Han, J.Q. Li, H.M. Wang, Y.N. Chu, J. Mol. Struct. (THEOCHEM) 910 (2009) 34. [11] T.J. Bevilacqua, D.R. Hanson, C.J. Howard, J. Phys. Chem. 97 (1993) 3750. [12] J. Sehested, O.J. Nielsen, Chem. Phys. Lett. 206 (1993) 369. [13] Z. Li, J.S. Francisco, Chem. Phys. Lett. 186 (1991) 336. [14] C. Fockenberg, H. Somnitz, G. Bednarek, R. Zellner, Ber. Bunsenges. Phys. Chem. 101 (1997) 1411. [15] J. Chen, T. Zhu, H. Niki, J. Phys. Chem. 96 (1992) 6115. [16] T.S. Dibble, M.M. Maricq, J.J. Szente, J.S. Francisco, J. Phys. Chem. 99 (1995) 17394. [17] R. Zellner, H. Saathoff, Presented at the 12th International Symposium on Gas Kinetics, Reading, UK, 1992. [18] A. Bhatnagar, R.W. Carr, Chem. Phys. Lett. 231 (1994) 454. [19] C. Bourbon, M. Brioukov, B. Hanoune, J.P. Sawerysyn, P. Devolder, Chem. Phys. Lett. 254 (1996) 203. [20] N.R. Jensen, D.R. Hanson, C.J. Howard, J. Phys. Chem. 98 (1994) 8574.

[21] A.G. Baboul, L.A. Curtiss, P.C. Redfern, K. Raghavachari, J. Chem. Phys. 110 (1999) 7650. [22] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, J.A. Pople, Gaussian03(Revision B.05), Gaussian, Inc., Pittsburgh, PA, 2003. [23] S.P. So, Chem. Phys. Lett. 313 (1999) 307. [24] S.F. Boys, F. Bernardi, Mol. Phys. 19 (1970) 553. [25] S. Simon, M. Duran, J.J. Dannenbery, J. Chem. Phys. 105 (1996) 11024. [26] T. Fueno, K. Yokoyama, S. Takane, Theor. Chim. Acta 82 (1992) 299. [27] Y. Miller, G.M. Chaban, B.J. Finlayson-Pitts, R.B. Gerber, J. Phys. Chem. A 110 (2006) 5342. [28] I.L. Karle, J. Karle, J. Chem. Phys. 36 (1962) 1969. [29] L.A. Curtiss, K. Raghavachari, P.C. Redfern, J.A. Pople, J. Chem. Phys. 106 (1997) 1063. [30] L.A. Curtiss, P.C. Redfern, K. Raghavachari, J. Chem. Phys. 126 (2007) 084108. [31] M.W. Chase Jr., NIST-JANAF Thermochemical Tables, fourth ed., J. Phys. Chem. Ref. Data Monograph No. 9 NIST, Gaithersburg, 1998. [32] M.P. Andersson, P. Uvdal, J. Phys. Chem. A 109 (2005) 2937. [33] R. Janoschek, W.M.F. Fabian, J. Mol. Struct. 780–781 (2006) 80. [34] R. Atkinson, D.L. Baulch, R.A. Cox, R.F. Hampson Jr., J.A. Kerr, M.J. Rossi, J. Troe, J. Phys. Chem. Ref. Data 29 (2000) 167.