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Chemical Physics Letters 432 (2006) 6–10

Theoretical studies on the reactions X + CHBrF2 (X = F, Br)

Hui Zhang a, Gui-ling Zhang a, Li Wang b, Bo Liu a,*, Xiao-yang Yu 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 9 June 2006; in final form 7 October 2006Available online 14 October 2006

Abstract

Theoretical investigations are carried out on the reactions F + CHBrF2! CBrF2 + HF (R1) and Br + CHBrF2! CBrF2 + HBr(R2) by means of direct dynamics method. The minimum energy path (MEP) is obtained at the BH&H-LYP/6-311G(d,p) level, and ener-getic information is further refined at the QCISD(T)/6-311+G(2df,2p) (single-point) level. The rate constants for both reactions are cal-culated by canonical variational transition state theory (CVT) with the small-curvature tunneling (SCT) correction in a wide temperaturerange 200–3000 K. The theoretical rate constant is in good agreement with the available experimental data. Furthermore, the rate con-stants of reaction Cl + CHBrF2! CBrF2 + HCl (R3) calculated in the other paper are added to discuss the effects of halogen substitu-tion on the rate constants of this class of hydrogen abstraction reactions.� 2006 Published by Elsevier B.V.

1. Introduction

Halons are used as fire-extinguishing agents. The activespecies in halon is bromine. When heated to high tempera-tures, halons decompose liberating bromine atoms, whichtrap the free radicals that propagate combustion. Sincebromine atoms have adverse effect on the ozone layer dele-tion [1–3], CHBrF2 has been proposed as a substitute forconventional fully halogenated halons. Further investiga-tion on this combustion process is important to elucidatethe mechanism of these reactions. However, there are verylimited experimental values which are available in the liter-ature concerning rate constants of the title reactions. Forthe reaction F + CHBrF2, only Bilde et al. [4] measuredthe rate constant with (9.0 ± 2.1) · 10�13 cm3 mole-cule�1 s�1 at 296 K. While there is no experimental valueavailable for the reaction Br + CHBrF2. No Arrheniusparameters were reported for both reactions.

The aim of this Letter is to make a systematic theoreticalinvestigation on the dynamic properties of the reactionsF + CHBrF2! CBrF2 + HF (R1) and Br + CHBrF2!

0009-2614/$ - see front matter � 2006 Published by Elsevier B.V.

doi:10.1016/j.cplett.2006.10.024

* Corresponding author. Fax: +86 451 86392708.E-mail address: hust_zhanghui1@hotmail.com (B. Liu).

CBrF2 + HBr (R2). To our best knowledge, little theoreti-cal work has addressed this reaction.

Here, dual-level direct dynamics method [5–9] proposedby Truhlar and co-workers is employed to study the kineticnature of both reactions. The potential energy surfaceinformation is obtained directly from electronic structurecalculations. Subsequently, by means of POLYRATE 9.1 pro-gram [10], the rate constants are calculated using the vari-ational transition state theory (VTST) proposed by Truhlarand co-workers [11,12]. The comparison between theoreti-cal and experimental results is discussed.

2. Computational method

In the present work, the geometries and frequencies ofthe stationary points (reactant, products, hydrogen-bondedcomplex, and transition states) are optimized using Becke’shalf and half (BH&H) [13] exchange with Lee–Yang–Parr(LYP) [14] correlation functional with the 6-311G(d,p)basis set (BH&H-LYP/6-311G(d,p)). The MEP is obtainedby intrinsic reaction coordinate (IRC) theory in mass-weighted Cartesian coordinates with a gradient step-sizeof 0.05 (amu)1/2 bohr. At the same level, the energy deriva-tives, including gradients and Hessians at geometries along

Fig. 1. Optimized geometries of the reactant, products, hydrogen-bondedcomplex, and transition states at the BH&H-LYP/6-311G(d,p) level. Thevalues in parentheses are the experimental values (Ref. [21] for HF, Ref.[22] for HBr). Bond lengths are in angstrom, and bond angles are indegree.

H. Zhang et al. / Chemical Physics Letters 432 (2006) 6–10 7

the MEP, are obtained to calculate the curvature of thereaction path. Furthermore, the energy profile is refinedby the quadratic configuration interaction with single anddouble substitutions with a triple contribution [QCISD(T)][15] with 6-311+G(2df,2p) basis set based on the BH&H-LYP/6-311G(d,p) geometries. Furthermore, the effect ofthe basis set superposition error on the energies for thereactant precursor complex is considered by means of thecounterpoise method proposed by Boys and Bernardi[16]. All the electronic structure calculations are performedby means of GAUSSIAN03 program package [17].

The variational transition-state theory (VTST) [11,12]are employed to calculate the rate constants by POLYRATE

9.1 program [10]. The specific form of VTST that we usedis canonical variational transition-state theory (CVT) [18–20] with the small-curvature tunneling (SCT) [21,22] contri-butions proposed by Truhlar and co-workers. All of thevibrational modes were treated as quantum-mechanicalseparable harmonic oscillators. During the kinetic calcula-tions, the Euler single-step integrator with a step size of0.0001 (amu)1/2 bohr is adopted to follow the MEP, andthe generalized normal-mode analysis is performed every0.01 (amu)1/2 bohr. The curvature components are calcu-lated using a quadratic fit to obtain the derivative of thegradient with respect to the reaction coordinate.

3. Results and discussion

3.1. Stationary points

The optimized geometric parameters of the reactant(CHBrF2), products (CBrF2, HF, and HBr), hydrogen-bonded complex (HBC), and transition states (TS1 andTS2) calculated at the BH&H-LYP/6-311G(d,p) levelalong with the available experimental data [23,24] are pre-sented in Fig. 1. It can be seen that the theoretical geomet-ric parameters of HF and HBr are in good agreement withthe corresponding experimental values. For the transitionstate structure of reaction R1, TS1, the length of C–H bondwhich will be broken stretches by 5% over the equilibriumlength C–H bond in CHBrF2, and the forming H–F bond iselongated about 54% over the equilibrium bond length inisolated molecule HF. On the other hand, the reactive C–H bond in TS2 that will be broken increases by 45% com-pared to the C–H equilibrium bond lengths in CHBrF2,and the forming H–Br bond is about 7% longer than theregular bond length in isolated molecule HBr. For the reac-tion R1, the elongation of the breaking bond is greaterthan that of the forming bond, indicating that transitionstate TS1 is reactant-like i.e., the H-abstraction channelprocess via early transition state. However, the structureof transition state TS2 is near the products, and the reac-tion R2 will process via late transition state.

Table 1 lists the harmonic vibrational frequencies of allthe stationary points involved the reactant, products,hydrogen-bonded complex, and transition states at theBH&H-LYP/6-311G(d,p) level as well as the correspond-

ing available experimental results [24–26]. Our calculatedfrequencies agree well with the experimental values withthe largest deviation within 4%. All the transition statesare confirmed by normal-mode analysis to have only oneimaginary frequency, which take the values of 316i cm�1

for TS1 and 493i cm�1 for TS2.

3.2. Energetics

The reaction enthalpies (DH 0298Þ and potential barrier

heights (DETS) with zero-point energy (ZPE) correctionsfor reaction R1 and R2 calculated at the QCISD(T)/6-311+G(2df,2p)//BH&H-LYP/6-311G(d,p) level as well asthe available experimental reaction enthalpies are listed inTable 2. The calculated reaction enthalpy of reactionR1 (�33.9 kcal/mol) is in good agreement with the

Table 1Calculated and experimental frequencies (cm�1) for the reactant, products, hydrogen-bonded complex, and transition states at the BH&H-LYP/6-311G(d,p) level

Species BH&H-LYP/6-311G(d,p) Experiments

CHBrF2 3255, 1448, 1360, 1218, 1176, 741, 608, 333, 328 3148,a 1435, 1355, 1275, 1125, 737, 590CBrF2 1299, 1221, 713, 602, 342, 323 1198,b 1138, 684HF 4310HBr 2720 2649c

HBC 3275, 1457, 1368, 1216, 1175, 742, 608, 333, 328, 70, 16, 9TS1 1967, 1336, 1240, 1202, 1123, 726, 617, 339, 327, 74, 67, 316i

TS2 1314, 1238, 1043, 801, 778, 650, 382, 326, 320, 92, 57, 493i

a Ref. [23].b Ref. [24].c Ref. [22].

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 at theQCISD(T)/6-311+G(2df,2p)//BH&H-LYP/6-311G(d,p) level together with the experimental values, the reaction enthalpies is also calculated at theQCISD(T)/6-311+G(2df,2p)//MPWB1K/6-311G(d,p) and QCISD(T)/6-311+G(2df,2p)//MP2/6-311+G(d,p) level

QCISD(T)/6-311+G(2df,2p)//BH H-LYP/6-311+G(d,p)

QCISD(T)/6-311+G(2df,2p)//MPWB1K/6-311G(d,p)

QCISD(T)/6-311+G(2df,2p)//MP2/6-311+G(d,p)

Experiments

DH 0298 F + CHBrF2! CBrF2 + HF �33.9 �33.4 �33.8 �32.1

Br + CHBrF2! CBrF2 + HBr 11.9 12.3 12.1 16.5DETS+ZPE F + CHBrF2! CBrF2 + HF �1.7

Br + CHBrF2! CBrF2 + HBr 12.2

Experimental value derived from the standard heats of formation: F, 19.0 kcal/mol [22]; Br, 26.8 kcal/mol [22]; CHBrF2, �109.0 kcal/mol [4]; CBrF2,�57.0 kcal/mol [4]; HF, �65.1 kcal/mol [22]; HBr, �8.7 kcal/mol [22].

8 H. Zhang et al. / Chemical Physics Letters 432 (2006) 6–10

corresponding experimental value (�32.1 kcal/mol). Whilefor the reaction R2, the calculated value (11.9 kcal/mol) isslightly lower than that of the experimental one (16.5 kcal/mol), which was derived from the experimental standardheats of formation (F, 19.0 kcal/mol [24]; Br, 26.8 kcal/mol [24]; CHBrF2, �109.0 kcal/mol [4]; CBrF2,�57.0 kcal/mol [4]; HF, �65.1 kcal/mol [24]; HBr,�8.7 kcal/mol [24]). For the reaction R2, the differencebetween the calculated and experimental value is large.So the reaction enthalpies for reaction R1 and R2 arecalculated at QCISD(T)/6-311+G(2df,2p)//MPWB1K[27]/6-311G(d,p) and QCISD(T)/6-311+G(2df,2p)//MP2[28–30]/6-311+G(d,p) levels. The corresponding valuesare also listed in the Table 2. The values calculated atvarious levels agree well with each other. So the values cal-culated at QCISD(T)/6-311+G(2df,2p)//BH&H-LYP/6-311G(d,p) level are expected to be reliable. Thus, in thepresent study, we use QCISD(T)/6-311+G(2df,2p)//BH&H-LYP/6-311G(d,p) method to calculate the poten-tial energy barriers as well as the energies along the MEPin the following studies.

Note that the energy of reactant is set to be zero for ref-erence. For the reaction R1, one complex with the relativeenergy 0.6 kcal/mol lower than the reactants F + CHBrF2

is found on the reactant side. The corrected complex energywith basis set superposition error is 0.1 kcal/mol lowerthan the reactants; it means that the hydrogen-bondedcomplex is existent. The result is consistent with the Bilde’s

conclusion [4] that the reaction of F atom with CHBrF2

gave an adduct in the gas phase, the adduct was in dynamicequilibrium with CHBrF2 and F atom. The potential bar-rier heights are �1.7 kcal/mol for reaction R1 and12.2 kcal/mol for reaction R2 at QCISD(T)//BH&H-LYPlevel. On the basis of above calculation, the reaction R1is more favorable than reaction R2 both thermodynami-cally and kinetically.

3.3. Rate constants

Dual-level dynamics [5–9] calculations of theF + CHBrF2 and Br + CHBrF2 are carried out at theQCISD(T)/6-311+G(2df,2p)//BH&H-LYP/6-311G(d,p)level. The rate constants, k1 for R1 and k2 for R2, are eval-uated by conventional transition state theory (TST),canonical variational transition state theory (CVT), andthe CVT with the small-curvature tunneling (SCT) contri-butions in a wide temperature range from 200 to 3000 K.The calculated rate constants of the two reactions are plot-ted against the reciprocal of temperature in Fig. 2. It isshown that for reaction R1, the CVT and TST rate con-stants are nearly the same in the whole temperature range,which indicates that the variational effect is small andalmost negligible. The CVT/SCT rate constants are muchgreater than the CVT ones in the range 200–1500 K. Forexample, the kCVT/SCT: kCVT ratios are 5.46 · 103 at 300,1.17 · 102 at 500, and 14.6 at 1500 K, respectively. Thus,

0 1 2 4 5

1E-26

1E-24

1E-22

1E-20

1E-18

1E-16

1E-14

1E-12

1E-10

k1(TST)

k1(CVT)

k1(CVT/SCT)

k2(TST)

k2(CVT)

k2(CVT/SCT)R

ate

cons

tant

s (c

m3 m

olec

ule-1

s-1)

1000/T (K-1)

3

Fig. 2. The TST, CVT and CVT/SCT rate constants calculated at theQCISD(T)/6-311+G(2df,2p)//BH&H-LYP/6-311G(d,p) level for the reac-tions R1(k1) and R2 (k2) (in cm3 molecule�1 s�1) versus 1000/T between200 and 3000 K.

H. Zhang et al. / Chemical Physics Letters 432 (2006) 6–10 9

SCT correction plays an important role for reaction R1.While for the reaction R2 both the variational effect andsmall tunneling correction are negligible in the whole tem-perature range.

The CVT/SCT rate constants for the reactionsF + CHBrF2! CBrF2 + HF (k1), Br + CHBrF2!CBrF2 + HBr (k2) and Cl + CHBrF2! CBrF2 + HCl(k3) [31] calculated in the other published article are dis-played in Fig. 3 along with the corresponding experimentaldata [4]. The CVT/SCT rate constants of k1 (6.66 · 10�13)and k3 (2.27 · 10�15) cm3 molecule�1 s�1, are in goodagreement with the corresponding experimental values[4], respectively. The deviation between the theoreticaland experimental values remains within a factor of approx-imately 0.74. Thus, the present calculations may provide

0 1 2 3 4 5

1E-26

1E-24

1E-22

1E-20

1E-18

1E-16

1E-14

1E-12

1E-10

k1(CVT/SCT)

k3(CVT/SCT)

k2(CVT/SCT)

Ref. 4 Ref. 27R

ate

cons

tant

s (c

m3 m

olec

ule-1

s-1)

1000/T (K-1)

Fig. 3. The CVT/SCT rate constants calculated at the QCISD(T)/6-311+G(2df,2p)//BH&H-LYP/6-311G(d,p) level for three reactions, R1(k1), R2 (k2) and R3 (k3) (in cm3 molecule�1 s�1), versus 1000/T between200 and 3000 K, together with the experimental value.

reliable prediction of the rate constants for the title reac-tions over a wide temperature range.

Seen from Fig. 3, the rate constants of reaction R1 areabout 13–1 orders of magnitude higher than those of reac-tion R2 from 200 to 3000 K. This is consistent with a qual-itative assessment based on the potential energy barrierheights and the reaction enthalpies of these two reactions.

For convenience of future experimental measurements,three-parameter fits of the CVT/SCT rate constants ofthe title reactions in the temperature range 200–3000 Kare performed and the expressions are given as follows:(in unit of cm3 molecule�1 s�1)

k1ðT Þ ¼ 7:31� 10�18T 1:98 expð41:00=T Þk2ðT Þ ¼ 1:40� 10�19T 2:67 expð�5844:95=T Þ

3.4. Reactivity trends

The difference of the rate constants of reactions of halo-gen (F, Cl, and Br) with CHBrF2 can be qualitative illus-trated by the difference of energy gap between the highestoccupied MOs (HOMO) of CHBrF2 and halogen (F, Cl,and Br). The results of theoretical calculation at theBH&H-LYP/6-311G(d,p) level show that the HOMOenergy of CHBrF2 is �0.37 hartree, which are 0.20, 0.05and 0.01 hartree higher than that of np atom orbital energyfor F, Cl and Br, respectively. It means that the energy gapbetween the HOMO of CHBrF2 and halogen (F, Cl, andBr) are 0.20, 0.05 and 0.01 hartree, respectively. As a resultof negative energy gap, the reactions of halogen withCHBrF2 are exothermic once, and the value of exothermicof the reaction F + CHBrF2 is the maximum, so the reac-tion rate is the fastest. This means that for the above-men-tioned three reactions, with the n increase for the attackatoms F, Cl, Br, the reaction rate constants decrease inthe order of F + CHBrF2>Cl + CHBrF2 > Br + CHBrF2.This is consistent with a qualitative assessment based onthe potential energy barrier heights by the present workand the previous experimental investigation [4].

4. Conclusions

In this Letter, the title reactions F + CHBrF2!CBrF2 + HF and Br + CHBrF2! CBrF2 + HBr havebeen studied by theoretical methods. The potential energysurface information is obtained at the BH&H-LYP/6-311G(d,p) level, and higher-level energies for the stationarypoints and a few extra point along the minimum energypath are further refined by the QCISD(T) theory. The the-oretical rate constants are calculated by canonical varia-tional transition state theory (CVT) incorporating thesmall-curvature tunneling (SCT) contributions method inthe temperature range 200–3000 K. The calculated rateconstant k1 is in good agreement with the available exper-imental value. Owing to the good agreement between thetheoretical and experimental values, it is reasonable to

10 H. Zhang et al. / Chemical Physics Letters 432 (2006) 6–10

believe that our calculated results will provide a good esti-mate for the kinetics of the reactions in the high tempera-ture range.

Acknowledgements

The authors thank Professor Donald G. Truhlar forproviding POLYRATE 9.1 program. This work is supportedby the National Natural Science Foundation of China(20333050, 20303007 and 20272011), the Doctor Founda-tion by the Ministry of Education, the Foundation for Uni-versity Key Teacher by the Department of Education ofHeilongjiang Province (1151G019), the Key subject of Sci-ence and Technology by the Ministry of Education of Chi-na, the Key subject of Science and Technology by JilinProvince, and Natural Science Foundation of HeilongjiangProvince (TA2005–15).

References

[1] World Meteorological Organization (WMO), Scientific Assessment ofOzone Depletion, 1994, Report No. 37, WMO, Geneva, 1995.

[2] T. Tang, J.C. McConnell, Geophys. Res. Lett. 23 (1996) 2633.[3] G.P. Brasseur, J.J. Orlando, G.S. Tyndall (Eds.), Atmospheric Chem-

istry and Global Change, Oxford University Press, Oxford, 1999.[4] M. Bilde, J. Sehested, T. Møgelberg, T.J. Wallington, O.J. Nielsen, J.

Phys. Chem. 100 (1996) 7050.[5] R.L. Bell, T.N. Truong, J. Chem. Phys. 101 (1994) 10442.[6] 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.

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

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

[9] W.-P. Hu, D.G. Truhlar, J. Am. Chem. Soc. 118 (1996) 860.

[10] J.C. Corchado et al., POLYRATE version 9.1, Department of Chemistryand Supercomputer Institute, University of Minnesota, Minneapolis,Minnesota, 2002.

[11] D.G. Truhlar, B.C. Garrett, Acc. Chem. Res. 13 (1980) 440.[12] D.G. Truhlar, A.D. Isaacson, B.C. Garrett, Generalized Transtion

State Theory, in: M. Baer (Ed.), The Theory of Chemical ReactionDynamics, vol. 4, CRC Press: Boca Raton, FL, 1985, p. 65.

[13] A.D. Becke, J. Chem. Phys. 98 (1993) 1372.[14] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785.[15] J.A. Pople, M. Head-Gordon, K. Raghavachari, J. Chem. Phys. 87

(1987) 5968.[16] S.F. Boys, F. Bernardi, Mol. Phys. 19 (1970) 553.[17] M.J. Frisch et al., Gaussian, Inc., Pittsburgh PA, 2003.[18] B.C. Garrett, D.G. Truhlar, J. Chem. Phys. 70 (1979) 1593.[19] B.C. Garrett, D.G. Truhlar, J. Am. Chem. Soc. 101 (1979) 4534.[20] (a) B.C. Garrett, D.G. Truhlar, R.S. Grev, A.W. Magnuson, J. Phys.

Chem. 84 (1980) 1730;(b) D.G. Truhlar, A.D. Issacson, R.T. Skodje, B.C. Garrett, J. Phys.Chem. 87 (1983) 4554.

[21] D.H. Lu et al., Comput. Phys. Commun. 71 (1992) 235.[22] 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.[23] In NIST Chemistry WebBook, NIST Standard Reference Database

Number 69, June 2005 Release. Date Compiled by K.P. Huber and G.Herzberg.

[24] M.W. Chase, NIST-JANAF, Thermochemical Tables, fourth edn.,Monograph 9, J. Phys. Chem. Ref. Data 1998, 1–1951.

[25] In NIST Chemistry WebBook, NIST Standard Reference DatabaseNumber 69, March 2003 Release. Vibrational frequency date com-piled by Coblentz Society, Inc.

[26] In NIST Chemistry WebBook, NIST Standard Reference DatabaseNumber 69, March 2003 Release. Vibrational frequency date com-piled by M.E. Jacox.

[27] Y. Zhao, D.G. Truhlar, J. Phys. Chem. A 108 (2004) 6908.[28] W.T. Duncan, T.N. Truong, J. Chem. Phys. 103 (1995) 9642.[29] M.J. Frisch, M. Head-Gordon, J.A. Pople, Chem. Phys. Lett. 166

(1990) 275.[30] M. Head-Gordon, J.A. Pople, M.J. Frisch, Chem. Phys. Lett. 153

(1988) 503.[31] H. Zhang, Z.S. Li, J.Y. Liu, L. Sheng, C.C. Sun, J. Mol. Struc.

Theochem. 674 (2004) 23.