www.elsevier.com/locate/cplett

Chemical Physics Letters 442 (2007) 187–193

Theoretical studies on the reactions Cl + CH3COCCl2X (X = F, Cl, Br)

Hui Zhang a, Gui-ling Zhang a, Jing-yao Liu b, Miao Sun a, Bo Liu a,*, Ze-sheng Li b

a College of Chemical and Environmental Engineering, Harbin University of Science and Technology, Harbin 150080, PR Chinab Institute of Theoretical Chemistry, State Key Laboratory of Theoretical and Computational Chemistry, Jilin University, Changchun 130023, PR China

Received 15 March 2007; in final form 18 May 2007Available online 25 May 2007

Abstract

Theoretical investigations are carried out on the title reactions by means of direct dynamics method. The optimized geometries, fre-quencies and minimum energy path are obtained at the MP2/6-31+G(d,p) level, and energetic information is further refined at the MC-QCISD (single-point) level. The rate constants for both reactions are calculated by canonical variational transition-state theory with thesmall-curvature tunneling correction in a wide temperature range 200–3000 K. The theoretical rate constant is in good agreement withthe available experimental data. Furthermore, the effects of halogen substitution on the rate constants of this class of hydrogen abstrac-tion reactions are also discussed.� 2007 Elsevier B.V. All rights reserved.

1. Introduction

Acetone represents an important class of oxygenatedvolatile organic compounds (VOCs), which are emittedfrom a variety of anthropogenic and natural sources intothe atmosphere. In addition to these direct emissions,atmospheric oxidation of volatile hydrocarbons constitutesa significant source of various ketones. In the degradationof non-halogenated hydrocarbons, acetone is known to belong-lived (several months) [1]. The accumulation of ace-tone in the upper troposphere and lower stratosphere hasrecently been highlighted [2–4]. Acetone has been shownto be a potentially important source of HOx radicals(OH and HO2), resulting in an increased ozone production.Hence, there is a particular need to investigate the chemis-try of some halogenated acetones. The most likely fate ofhalogenated acetones in the Earth’s atmosphere would betheir reaction with Cl. However, there are very limitedexperimental values which are available in the literatureconcerning rate constants of the title reactions. For thereaction Cl + CH3COCCl3, only Carr et al. [5] measured

0009-2614/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.cplett.2007.05.074

* Corresponding author. Fax: +86 0451 86392708.E-mail address: hust_zhanghui1@hotmail.com (B. Liu).

the rate constant with (1.7 ± 0.3) · 10�14 cm3 mole-cule�1 s�1 at 298 K. While there is no experimental valueavailable for the reactions Cl + CH3COCCl2F and Cl +CH3COCCl2Br. No Arrhenius parameters were reportedfor both reactions.

The aim of this Letter is to make a systematic theoreticalinvestigation on the kinetic properties of the reactionsCl + CH3COCCl2F! CH2COCCl2F + HCl (R1), Cl +CH3COCCl3! CH2COCCl3 + HCl (R2), and Cl +CH3COCCl2Br! CH2 COCCl2Br + HCl (R3). To the bestof our knowledge, little theoretical work has addressed thesereactions.

Here, dual-level direct dynamics method [6–10] pro-posed by Truhlar and co-workers is employed to studythe kinetic nature of both reactions. The potential energysurface information, including geometries, energies, gradi-ents, force constants of all the stationary points (reactants,products, and transition states) and some extra pointsalong the minimum energy path (MEP) are obtaineddirectly from electronic structure calculations. Single-pointenergies are further carried out at the multi-coefficient cor-relation method based on quadratic configuration interac-tion with single and double excitations (MC-QCISD) level[11]. Subsequently, by means of POLYRATE 9.1 program[12], the rate constants are calculated using the variational

188 H. Zhang et al. / Chemical Physics Letters 442 (2007) 187–193

transition-state theory (VTST) proposed by Truhlar andco-workers [13,14]. The comparison between theoreticaland experimental results is discussed.

2. Computational method

In the present work, the equilibrium geometries and fre-quencies of all the stationary points (reactants, products,and transition states) are optimized at the restricted orunrestricted second-order Møller–Plesset perturbation(MP2) [15–17] level with the 6-31+G(d,p) basis set. Molec-ular electrostatic potentials [18] of CH3COCCl2F,CH3COCCl3, and CH3COCCl2Br are calculated at thesame level, and plotted using GOPENMOL 2.32 [19]. TheMEP is obtained by intrinsic reaction coordinate (IRC)theory in mass-weighted Cartesian coordinates with a gra-dient step-size of 0.05 (amu)1/2 bohr. Then, the energyderivatives including gradients and Hessians are obtainedby calculating the curvature of the reaction path and thegeneralized vibrational frequencies along the reaction path.In order to obtain more accurate energies and barrierheights, a dual-level direct dynamics method [6–10] isapplied to study the title reaction. Single-point energiesare refined by multi-coefficient correlation method basedon quadratic configuration interaction with single and dou-ble excitations MC-QCISD [11] based on the MP2/6-31+G(d,p) geometries. All the electronic structure calcula-tions are performed by means of GAUSSIAN 03 programpackage [20].

The variational transition-state theory (VTST) [13,14] isemployed to calculate the rate constants by POLYRATE 9.1program [12]. The specific form of VTST that we used iscanonical variational transition-state theory (CVT) [21–24] with the small-curvature tunneling (SCT) [25,26] contri-butions proposed by Truhlar and co-workers. For the titlereaction, all vibrational modes are treated as separable har-monic oscillators, except for the lowest vibrational modethat is treated by using the hindered rotor model [27,28].In the calculation of the reactant electronic partition func-tion, two electronic states of Cl atoms, 2P1/2 and 2P3/2, areincluded, with an 881 cm�1 splitting due to spin-orbit cou-pling. During the kinetic calculations, the Euler single-stepintegrator with a step-size of 0.0001 (amu)1/2 bohr isadopted to follow the MEP, and the generalized normal-mode analysis is performed every 0.01 (amu)1/2 bohr. Thecurvature components are calculated by using a quadraticfit to obtain the derivative of the gradient with respect tothe reaction coordinate.

3. Results and discussion

3.1. Stationary points

The optimized geometric parameters of the reactants(CH3COCCl2F, CH3COCCl3, and CH3COCCl2Br), prod-ucts (CH2COCCl2F, CH2COCCl3, CH2COCCl2Br, andHCl), and transition states (TS1, TS2, and TS3) calculated

at the MP2/6-31+G(d,p) level along with the availableexperimental data [29] are presented in Fig. 1. It can beseen that the theoretical geometric parameter of HCl is ingood agreement with the corresponding experimentalvalue. In TS1, TS2, and TS3 structures, the breaking bondsC–H increase by 31%, 29%, and 29% compared to the reg-ular bond lengths in CH3COCCl2F, CH3COCCl3, andCH3COCCl2Br; the forming bonds H–Cl stretch by 11%,11%, and 11% over the equilibrium bond length in isolatedmolecule HCl, respectively. The elongation of the breakingbond is greater than that of the forming bond, indicatingthat reactions R1, R2, and R3 are product-like, i.e., thereactions will proceed via late transition states.

Table 1 lists the harmonic vibrational frequencies of allthe stationary points involved the reactants, products, andtransition states at the MP2/6-31+G(d,p) level as well asthe corresponding available experimental results [5,30].Our calculated frequencies agree well with the experimentalvalues with the largest deviation within 4%. All the transi-tion states in Table 1 are confirmed by normal-mode anal-ysis to have one and only one imaginary frequencycorresponding to the stretching modes of the couplingbreaking and forming bonds. And the values of those imag-inary frequencies are 1270i cm�1 for TS1, 1392i cm�1 forTS2, and 1368i cm�1 for TS3.

3.2. Energetics

The reaction enthalpies ðDH 0298Þ and potential barrier

heights (DETS) with zero-point energy (ZPE) correctionsfor reaction R1, R2, and R3 calculated at the MC-QCISD//MP2/6-31+G(d,p) level are listed in Table 2. It isshown that the three individual reactions are all exothermicreaction, which is consistent with the discussion of Ham-mond’s postulate [31]. Due to lack of the experimental heatsof formation for the title reaction species, it is difficult tomake a direct comparison between theory and experimentfor the enthalpy of the three reactions. For comparison,the calculated reaction enthalpy of reaction CH3COCH3

with Cl at the MC-QCISD//MP2/6-31+G(d,p) level as wellas the available experimental reaction enthalpies is alsolisted in Table 2. The theoretical value of DH 0

298 for reactionCH3COCH3 with Cl is �7.60 kcal/mol which is in goodagreement with the corresponding experimental value of�7.73 ± 0.14 kcal/mol, which was derived from thestandard heats of formation (Cl, 28.97 kcal/mol [32];CH3COCH3, �51.90 ± 0.14 kcal/mol [33]; CH2COCH3,�8.61 kcal/mol [34]; HCl, �22.05 kcal/mol [32].). In viewof the good agreement obtained above, it is expected thatthe enthalpy of the title reactions calculated at the same levelis reliable.

A schematic potential energy surface of the title reac-tions with ZPE corrections obtained at the MC-QCISD//MP2/6-31+G(d,p) level are described in Fig. 2. Note thatthe energy of reactant is set to zero for reference. The val-ues in parentheses are calculated at the MP2/6-31+G(d,p)level and include the ZPE corrections. The barrier heights

Fig. 1. Optimized geometries of the reactants, products, and transition states at the MP2/6-31+G(d,p) level. The value in parentheses is the experimentalvalue (Ref. [27] for HCl). Bond lengths are in angstroms, and bond angles are in degrees.

Table 1Calculated and experimental frequencies (cm�1) for the reactants, products, and transition states at the MP2/6-31+G(d,p) level

Species MP2/6-31+G(d,p) Expt.

CH3COCCl2F 3263, 3225, 3132, 1782, 1512, 1508, 1433, 1266, 1085, 1069, 1043, 921, 879, 612, 575, 544, 434, 380, 339,279, 218, 180, 145, 45

CH3COCCl3 3267, 3236, 3140, 1777, 1521, 1511, 1434, 1223, 1066, 1040, 901, 885, 813, 596, 570, 447, 407, 299, 291, 283,193, 185, 121, 52

1826a, 849a

CH3COCCl2Br 3264, 3233, 3136, 1774, 1518, 1510, 1434, 1223, 1065, 1036, 898, 881, 751, 596, 546, 412, 396, 291, 245, 235,186, 179, 133, 64

CH2COCCl2F 3413, 3274, 2041, 1500, 1292, 1082, 1039, 942, 926, 775, 631, 595, 546, 436, 382, 347, 302, 278, 220, 178, 49CH2COCCl3 3412, 3275, 2116, 1505, 1253, 1031, 907, 893, 863, 728, 603, 596, 448, 410, 298, 294, 284, 249, 191, 170, 61CH2COCCl2Br 3413, 3275, 2143, 1501, 1249, 1031, 908, 888, 827, 700, 600, 589, 409, 402, 291, 282, 244, 234, 179, 150, 78HCl 3112 2991b

TS1 3312, 3205, 2491, 1466, 1259, 1128, 1082, 1072, 938, 923, 909, 878, 641, 594, 547, 515, 430, 385, 364, 314,236, 203, 175, 72, 49, 22, 1270i

TS2 3341, 3222, 2712, 1476, 1236, 1131, 1042, 942, 916, 894, 880, 816, 647, 594, 526, 451, 402, 350, 293, 290, 268,188, 151, 90, 49, 7, 1392i

TS3 3344, 3225, 2684, 1477, 1234, 1138, 1038, 946, 912, 888, 880, 769, 623, 597, 534, 403, 398, 365, 282, 244, 234,179, 125, 94, 51, 19, 1368i

a Ref. [5].b Ref. [28].

H. Zhang et al. / Chemical Physics Letters 442 (2007) 187–193 189

Table 2The reaction enthalpies at 298 K (DH 0

298Þ and the barrier height TSs (DETS) with zero-point energy (ZPE) correction (kcal/mol) for the title reactions andCH3COCH3 reaction with Cl at the MC-QCISD//MP2/6-31+G(d,p) level together with the experimental value

MC-QCISD//MP/6-31+G(d,p) Expt.

DH 0298 Cl + CH3COCCl2F! CH2COCCl2F + HCl (R1) �7.05

Cl + CH3COCCl3! CH2COCCl3 + HCl (R2) �7.14Cl + CH3COCCl2Br! CH2COCCl2Br + HCl (R3) �6.82Cl + CH3COCH3! CH2COCH3 + HCl �7.60 �7.56 ± 0.14

DETS + ZPE Cl + CH3COCCl2F! CH2COCCl2F + HCl (R1) 7.08Cl + CH3COCCl3! CH2COCCl3 + HCl (R2) 3.90Cl + CH3COCCl2Br! CH2COCCl2Br + HCl (R3) 3.72Cl + CH3COCH3! CH2COCH3 + HCl 0.81

Experimental value derived from the standard heats of formation: Cl, 28.97 kcal/mol [30]; CH3COCH3, �51.90 ± 0.14 kcal/mol [31]; CH2COCH3,�8.61 kcal/mol [32]; HCl, �22.05 kcal/mol [30].

Cl + CH3COCCl2X

(X = F, Cl, and Br)

TS17.08 (14.67)

TS23.90 (14.20)

TS33.72

(13.67)

CH2COCCl2F + HCl-7.49(6.24)

CH2COCCl2Br + HCl-7.30(6.49)

CH2COCCl3 + HCl-7.62(5.84)

2.5

0.0

5.0

7.5

10.0

-2.5

-5.0

-7.5

-10.0 -

-

-

-

-

-

-

-

-

Fig. 2. Schematic potential energy surface for the title reactions. Relativeenergies (in kcal/mol) are calculated at the MC-QCISD//MP2/6-31+G(d,p)+ZPE level. The values in parentheses are calculated at theMP2/6-31+G(d,p)+ZPE level.

190 H. Zhang et al. / Chemical Physics Letters 442 (2007) 187–193

of reactions R1 (7.08 kcal/mol) and R2 (3.90 kcal/mol) areabout 3.4 and 0.2 kcal/mol higher than that of reaction R3(3.72 kcal/mol), respectively. And as a result, the later reac-tion path R3 is more kinetically favorable than the formers,it is expected to have larger rate constants.

3.3. Rate constants

Dual-level dynamics [6–10] calculations of theCl + CH3COCCl2X (X = F, Cl, and Br) are carried outat the MC-QCISD//MP2/6-31+G(d,p) level. The rate con-stants, k1 for R1, k2 for R2, and k3 for R3, are evaluated byconventional transition-state theory (TST), canonical vari-ational transition-state theory (CVT), and the CVT withthe small-curvature tunneling (SCT) contributions in awide temperature range from 200 to 3000 K. The calcu-lated rate constants TST, CVT, and CVT/SCT of the threereactions are displayed in Table 3. From Table 3, it isshown that for the reactions R1 and R3, the tunnelingeffect, i.e., the ratio between CVT and CVT/SCT rate con-stants, plays a significant role at the temperature range200–600 K. The ratios of k1(CVT)/k1(CVT/SCT) are

0.20, 0.64, and 0.82 at 200, 400, and 600 K for R1, 0.02,0.41, and 0.69 at 200, 400, and 600 K for R3, respectively.While the variational effect, i.e., the ratio between CVT andTST rate constants, are nearly the same in the whole tem-perature region for reaction R1 and R3. The ratios ofk1(CVT)/k1(TST) are 0.78, 0.82, and 0.83 at 500, 1000,and 3000 K for R1, respectively, and the ratios ofk3(CVT)/k3(TST) are 0.94, 0.92, and 0.90 at 500, 1000,and 3000 K for R3, respectively, which indicates that thevariational effect is almost negligible for these two reac-tions. For reaction R2, the TST, CVT and CVT/SCT rateconstants are almost the same over the whole temperaturerange, which means that both of the variational effect andthe tunneling effect are very small.

The CVT/SCT rate constants for the three reactionsCl + CH3COCCl2F! CH2COCCl2F + HCl (k1), Cl +CH3COCCl3! CH2COCCl3 + HCl (k2), and Cl + CH3-COCCl2Br! CH2COCCl2Br + HCl (k3) are plottedagainst the reciprocal of temperature in Fig. 3 as well asthe corresponding experimental data [5]. The CVT/SCTrate constant of k2 (2.27 · 10�14) cm3 molecule�1 s�1, is ingood agreement with the corresponding experimental onesgiven by Carr [5] at 298 K. The deviation between the the-oretical and experimental values remains within a factor ofapproximately 1.34. Thus, the present calculations mayprovide reliable prediction on the rate constants for thetitle reactions over the wide temperature range.

As shown in Fig. 3, the rate constants of reaction R1 areabout 4–1 and 5–1 orders of magnitude lower than those ofreaction R2 and R3 from 200 to 3000 K, respectively. Thisis consistent with a qualitative assessment based on thepotential energy barrier heights and the reaction enthalpiesof these two reactions.

As a result of the limited experimental knowledge of thekinetic nature of the title reactions, we hope that our presentstudy may provide useful information for future laboratoryinvestigations. For convenience of future experimentalmeasurements, the three-parameter fits for the CVT/SCTrate constants of the title reactions in the temperature range200–3000 K are performed and the expressions are given asfollows: (in unit of cm3 molecule�1 s�1)

Tab

le3

Th

eT

ST

,C

VT

and

CV

T/S

CT

rate

con

stan

tsca

lcu

late

dat

the

MC

-QC

ISD

//M

P2/

6-31

+G

(d,p

)le

vel

for

thre

ere

acti

on

s,R

1,R

2,an

dR

3,b

etw

een

200

and

3000

K(c

m3

mo

lecu

le�

1s�

1)

T(K

)C

l+

CH

3C

OC

Cl 2

F!

CH

2C

OC

Cl 2

F+

HC

l(R

1)C

l+

CH

3C

OC

Cl 3!

CH

2C

OC

Cl 3

+H

Cl

(R2)

Cl

+C

H3C

OC

Cl 2

Br!

CH

2C

OC

Cl 2

Br

+H

Cl

(R3)

TS

TC

VT

CV

T/S

CT

TS

TC

VT

CV

T/S

CT

TS

TC

VT

CV

T/S

CT

200

2.88

·10�

19

1.85

·10�

19

9.37

·10�

19

5.68

·10�

16

4.15

·10�

16

1.13

·10�

15

4.84

·10�

16

4.17

·10�

16

2.10

·10�

14

250

1.29

·10�

17

8.92

·10�

18

2.58

·10�

17

5.11

·10�

15

4.34

·10�

15

6.52

·10�

15

4.78

·10�

15

4.37

·10�

15

5.52

·10�

14

298

1.59

·10�

16

1.15

·10�

16

2.47

·10�

16

2.22

·10�

14

2.04

·10�

14

2.27

·10�

14

2.20

·10�

14

2.07

·10�

14

1.11

·10�

13

350

1.17

·10�

15

8.71

·10�

16

1.53

·10�

15

7.27

·10�

14

7.02

·10�

14

6.38

·10�

14

7.55

·10�

14

7.12

·10�

14

2.34

·10�

13

400

5.07

·10�

15

3.86

·10�

15

5.99

·10�

15

1.77

·10�

13

1.74

·10�

13

1.41

·10�

13

1.89

·10�

13

1.79

·10�

13

4.36

·10�

13

450

1.64

·10�

14

1.27

·10�

14

1.80

·10�

14

3.63

·10�

13

3.62

·10�

13

2.64

·10�

13

3.99

·10�

13

3.76

·10�

13

7.49

·10�

13

500

4.29

·10�

14

3.36

·10�

14

4.46

·10�

14

6.62

·10�

13

6.59

·10�

13

4.75

·10�

13

7.41

·10�

13

6.97

·10�

13

1.21

·10�

12

550

9.61

·10�

14

7.59

·10�

14

9.63

·10�

14

1.10

·10�

12

1.10

·10�

12

7.91

·10�

13

1.26

·10�

12

1.18

·10�

12

1.84

·10�

12

600

1.91

·10�

13

1.52

·10�

13

1.86

·10�

13

1.72

·10�

12

1.71

·10�

12

1.23

·10�

12

1.98

·10�

12

1.85

·10�

12

2.67

·10�

12

650

3.48

·10�

13

2.79

·10�

13

3.31

·10�

13

2.53

·10�

12

2.53

·10�

12

1.83

·10�

12

2.95

·10�

12

2.76

·10�

12

3.74

·10�

12

800

1.41

·10�

12

1.15

·10�

12

1.28

·10�

12

6.41

·10�

12

6.40

·10�

12

4.75

·10�

12

7.64

·10�

12

7.11

·10�

12

8.61

·10�

12

1000

5.20

·10�

12

4.25

·10�

12

4.57

·10�

12

1.56

·10�

11

1.56

·10�

11

1.20

·10�

11

1.90

·10�

11

1.75

·10�

11

1.96

·10�

11

1500

3.59

·10�

11

2.96

·10�

11

3.06

·10�

11

6.16

·10�

11

6.16

·10�

11

5.05

·10�

11

7.70

·10�

11

7.03

·10�

11

7.33

·10�

11

2000

1.08

·10�

10

8.98

·10�

11

9.14

·10�

11

1.40

·10�

10

1.40

·10�

10

1.19

·10�

10

1.77

·10�

10

1.60

·10�

10

1.63

·10�

10

2400

1.99

·10�

10

1.65

·10�

10

1.67

·10�

10

2.22

·10�

10

2.22

·10�

10

1.94

·10�

10

2.83

·10�

10

2.55

·10�

10

2.58

·10�

10

3000

3.85

·10�

10

3.21

·10�

10

3.23

·10�

10

3.73

·10�

10

3.72

·10�

10

3.33

·10�

10

4.77

·10�

10

4.29

·10�

10

4.31

·10�

10

0 1 2 3 4 5

1E-19

1E-18

1E-17

1E-16

1E-15

1E-14

1E-13

1E-12

1E-11

1E-10

1E-9

Rat

e co

nsta

nts

(cm

3 mol

ecul

e-1s-1

)

1000/T (K-1)

k1(CVT/SCT)

k2(CVT/SCT)

k3(CVT/SCT)

Ref. 5

Fig. 3. The CVT/SCT rate constants calculated at the MC-QCISD//MP2/6-31+G(d,p) level for three reactions, R1 (k1), R2 (k2) and R3 (k3) (incm3 molecule�1 s�1), versus 1000/T between 200 and 3000 K, togetherwith the experimental value.

H. Zhang et al. / Chemical Physics Letters 442 (2007) 187–193 191

k1ðT Þ ¼ 1:18� 10�17T 2:27 exp ð�2939:42=T Þk2ðT Þ ¼ 1:32� 10�18T 2:49 exp ð�1309:06=T Þk3ðT Þ ¼ 8:53� 10�20T 2:84 exp ð�576:59=T Þ

3.4. Reactivity trends

The difference of the rate constants of the three reactionsof Cl with CH3COCCl2X (X = F, Cl, and Br) can be con-sidered as a qualitative relationship by the difference of thehighest occupied MOs (HOMO) of CH3COCCl2X (X = F,Cl, and Br). The results of theoretical calculation at theMP2/6-31+G(d,p) level show that the HOMO energy ofCH3COCCl2F is �0.451 hartree, which are 0.006 and0.017 hartree higher than that of CH3COCCl3 andCH3COCCl2Br, respectively. As a result, the reaction rateof Cl + CH3COCCl2Br is the fastest one. This means thatfor the above-mentioned three reactions, with the n

increase for the substitution atoms F, Cl, and Br onCH3COCCl2X, the reaction rate constants increase in theorder of Cl + CH3COCCl2F < Cl + CH3COCCl3 < Br +CH3COCCl2Br. This is consistent with a qualitative assess-ment based on the potential energy barrier heights by thepresent work.

The molecular electrostatic potential is an importanttool to analyze molecular reactivity because it can providethe information about local polarity. Fig. 4 gives the distri-bution of the molecular electrostatic potential. There, themost negative and positive potentials are assigned to beblue1 and red, respectively, and the color spectrum ismapped to all other values by linear interpolation. The lesspositive potential bond (less red) will be more helpful for

1 For interpretation of color in Fig. 4, the reader is referred to the webversion of this article.

Fig. 4. The calculated electrostatic potential textured vDW surfaces forthe reactants.

192 H. Zhang et al. / Chemical Physics Letters 442 (2007) 187–193

the electrophile to attack at. By comparison mole-cules CH3COCCl2F, CH3COCCl3, and CH3COCCl2Br,the positive potential around the C–H bond is the strongest(more red) in CH3COCCl2F and is the weakest (less red) inCH3COCCl2Br. Therefore, Cl, serving as an electrophile, ispreferably to attack the C–H bond of CH3COCCl2Br.

4. Conclusions

In this Letter, the title reactions Cl + CH3COCCl2X!products (X = F, Cl, and Br) have been studied by adual-level direct dynamics method. The potential energysurface information is obtained at the MP2/6-31+G(d,p)level, and higher-level energies for the stationary pointsand a few extra points along the minimum energy pathare refined at the MC-QCISD level. The theoretical rateconstants for R1, R2, and R3 are calculated by CVT incor-porating the SCT contributions in the temperature regionof 200–3000 K. The calculated rate constant k2 is in goodagreement with the available experimental value given byCarr and co-workers. Owe to the good agreement betweenthe theoretical and experimental values, we expect that thetheoretical results may be useful for estimating the kineticsof the title reactions over a wide temperature range whereno experimental data is available.

Acknowledgements

The authors thank Professor Donald G. Truhlar forproviding POLYRATE 9.1 program. This work is supported

by the National Natural Science Foundation of China(20333050, 20303007 and 20272011), the Doctor Founda-tion by the Ministry of Education, the Foundation forUniversity Key Teacher by the Department of Educa-tion of Heilongjiang Province (1151G019, 1152G010),the Key subject of Science and Technology by the Minis-try of Education of China, the Key subject of Scienceand Technology by Jilin Province, and Natural ScienceFoundation of Heilongjiang Province (TA2005-15,B200605).

References

[1] H.B. Singh et al., J. Geophys. Res. 99 (1994) 1805.[2] H.B. Singh, M. Kanakidou, P.J. Crutzen, D.J. Jacob, Nature 378

(1995) 50.[3] F. Arnold, G. Knop, H. Zierens, Nature 321 (1986) 505.[4] F. Arnold, V. Burger, B. Drost-Fanke, F. Grimm, J. Schneider, A.

Krieger, T. Stile, Geophys. Res. Lett. 24 (1997) 3017.[5] S. Carr, D.E. Shallcross, C.E. Canosa-Mas, J.C. Wenger, H.W.

Sidebottom, J.J. Treacy, R.P. Wayne, Phys. Chem. Chem. Phys. 5(2003) 3874.

[6] R.L. Bell, T.N. Truong, J. Chem. Phys. 101 (1994) 10442.[7] T.N. Truong, W.T. Duncan, R.L. Bell, in: Chemical Applications of

Density Functional Theory, American Chemical Society, Washing-ton, DC, 1996, p. 85.

[8] D.G. Truhlar, in: D. Heidrich (Ed.), The Reaction Path in Chemistry:Current Approaches and Perspectives, Kluwer, Dordrecht, TheNetherlands, 1995, p. 229.

[9] J.C. Corchado, J. Espinosa-Garcia, W.-P. Hu, I. Rossi, D.G. Truhlar,J. Phys. Chem. 99 (1995) 687.

[10] W.-P. Hu, D.G. Truhlar, J. Am. Chem. Soc. 118 (1996) 860.[11] P.L. Fast, D.G. Truhlar, J. Phys. Chem. A 104 (2000) 6111.[12] J.C. Corchado et al., POLYRATE version 9.1, Department of Chemistry

and Supercomputer Institute, University of Minnesota, Minneapolis,Minnesota, 2002.

[13] D.G. Truhlar, B.C. Garrett, Acc. Chem. Res. 13 (1980) 440.[14] D.G. Truhlar, A.D. Isaacson, B.C. Garrett, in: M. Baer (Ed.), The

Theory of Chemical Reaction Dynamics, vol. 4, CRC Press, BocaRaton, FL, 1985, p. 65.

[15] W.T. Duncan, T.N. Truong, J. Chem. Phys. 103 (1995) 9642.[16] M.J. Frisch, M. Head-Gordon, J.A. Pople, Chem. Phys. Lett. 166

(1990) 275.[17] M. Head-Gordon, J.A. Pople, M.J. Frisch, Chem. Phys. Lett. 153

(1988) 503.[18] B. Boris, B. Petia, J. Phys. Chem. A 103 (1999) 6793.[19] D.L. Bergman, L. Laaksonen, A. Laaksonen, J. Mol. Graph. Model.

15 (1997) 301.[20] M.J. Frisch et al., Gaussian 03, Gaussian, Inc., Pittsburgh, PA, 2003..[21] B.C. Garrett, D.G. Truhlar, J. Chem. Phys. 70 (1979) 1593.[22] B.C. Garrett, D.G. Truhlar, J. Am. Chem. Soc. 101 (1979) 4534.[23] B.C. Garrett, D.G. Truhlar, R.S. Grev, A.W. Magnuson, J. Phys.

Chem. 84 (1980) 1730.[24] D.G. Truhlar, A.D. Issacson, R.T. Skodje, B.C. Garrett, J. Phys.

Chem. 87 (1983) 4554.[25] D.H. Lu et al., Comput. Phys. Commun. 71 (1992) 235.[26] Y.-P. Liu, G.C. Lynch, T.N. Truong, D.-H. Lu, D.G. Truhlar, B.C.

Garrett, J. Am. Chem. Soc. 115 (1993) 2408.[27] D.G. Truhlar, J. Comput. Chem. 12 (1991) 266.[28] Y.Y. Chuang, D.G. Truhlar, J. Chem. Phys. 112 (2000) 1221.[29] K.P. Huber, G. Herzberg, Molecular Spectra and Molecular Struc-

ture IV. Constants of Diatomic Molecules, Van Nostrand Reinhold,New York, 1979.

[30] K. Kuchitsu, in: Structure of Free Polyatomic Molecules Basic Data,vol. 1, Springer-Verlag, Berlin Heidelberg, 1998, p. 102.

H. Zhang et al. / Chemical Physics Letters 442 (2007) 187–193 193

[31] G.S. Hammond, J. Am. Chem. Soc. 77 (1955) 334.[32] M.W. Chase, NIST-JANAF, Thermochemical Tables, fourth edn.,

Monograph 9, J. Phys. Chem. Ref. Data, 1998, p. 1-1951.[33] K.B. Wiberg, L.S. Crocker, K.M. Morgan, J. Am. Chem. Soc. 113

(1991) 3447.

[34] A. Burcat, B. McBride, 1997 Ideal Gas Thermodynamic Data forCombustion and Air-Pollution Use, Technion Aerospace Engineering(TAE) Report # 804, June 1997.