Free radical mechanism of the addition to acetyleneCl2

Stella M. Resende, Josefredo R. Pliego Jr. and Wagner B. De Almeida

de Computacional e Modelagem Molecular, Depto. de ICEx,L aborato� rio Qu•�mica Qu•�mica,UFMG, Belo Horizonte, MG, 31270-901, Brazil

26th May 1998, Accepted 28th July 1998Recei¿ed

The free radical mechanism for the addition of to acetylene in the gas phase has been studied. TheCl2structures and energies of reactants, transition states and products were determined through ab initiocalculations of the stationary points on the potential-energy surface (PES) for the interaction of these twomolecules. Using BD(T)/6-311] G(2df,2p)//CASSCF(6,6)/6-31G(d,p) level of theory, the reaction rate for theinitiation step was estimated as 10~18 l mol~1 s~1 (at 298.15 K). This leads to(Cl2 ] C2H2 ] Cl] C2H2Cl)the formation of a small quantity of Cl and radicals, the chain propagators, and the following stepsC2H2Clwill only occur to an appreciable extent after an induction period, which generates a measurable amount ofthese radicals. The following steps were studied at the UCCSD(T)/6-311 ] G(2df,2p)//UMP2/6-31G(d,p) levelof theory. The propagation reaction occurs with an activation energy of [1.22C2H2 ] Cl] C2H2Clkcal mol~1, and produces a radical where the two hydrogens are on opposite sides of the moleculeC2H2Cl,(trans-isomer). This reaction has a rate constant 2.85 ] 1010 l mol~1 s~1 at 298.15 K. The interconversion ofthe two isomers of the radical (cisÈtrans) is very fast, with a rate constant 4.75 ] 1010 s~1 and so theseC2H2Clspecies can be considered to be in equilibrium. The rate constants for the reaction C2H2Cl ] Cl2] C2H2Cl2

where the products trans- and cis-1,2-dichloroethylenes are formed, are 1.95 ] 1010 and 3.63] 109] Cl,l mol~1 s~1, respectively, and those for the two polymerization reactions C2H2] C2H2Cl] C2H2C2H2Clare ca. 102 l mol~1 s~1. Hence, the latter reactions will not compete with the formation of and theC2H2Cl2 ,polymerization products will not be produced in meaningful amounts. Analysis of the kinetics data gives97.3% of the trans-1,2-dichloroethylene and 2.7% of the cis-1,2-dichloroethylene products.

IntroductionThe addition of chlorine to a carbonÈcarbon double bond isdiscussed in standard organic chemistry textbooks1,2 and ithas been established that the reaction can proceed either by afree radical or by an ionic mechanism. However, alkynes seemto react only by a radical mechanism.1,2 The reaction betweenacetylene and molecules is a prototype for the(C2H2) Cl2study of addition chemical reactions of halogens to carbonÈcarbon triple bonds. Although this is the simplest model ofthis kind of reaction, we are not aware of any theoreticalanalysis of it.

The interaction of acetylene with chlorine to form a weaklybound complex has previously been studied experimentallyand theoretically. Bloemink et al.3 detected the formation ofthe complex in the gas phase, and have proposedC2H2É É ÉCl2that it has a T-shaped form, with the chlorine interacting withthe carbonÈcarbon p bond. The authors have interpreted thisstructure as a pre-reactive complex, where the chlorine acts asa Lewis acid and the acetylene as a Lewis base, and have alsospeculated on the possibility of the reaction proceeding by anionic mechanism in polar solvents, similar to that proposedfor chlorine addition to alkenes, as illustrated below:4

HCyCH] Cl2 H HCyCHÉ É ÉCl2] HClC`xCH] Cl~] products

In this scheme, represents the molecularHCyCHÉ É ÉCl2complex that is formed initially. These molecular complexeswere investigated theoretically by Resende and De Almeida.5They located six stationary points on the PES: a T-shapedform, where one chlorine atom is attached to the acetylene

triple bond (bpÈar type), a parallel form, a slipped parallelform, a crossed form, an inclined inverse T-shaped form and asymmetric form, where the van der Waals bond is betweenone of the hydrogen atoms of the acetylene and the ClwClbond. At the MP2/TZ2P//MP2/TZP level of calculation, onlythe T-shaped and the parallel forms are minimum-energystructures, and their stabilization energies are, respectively,2.002 and 0.422 kcal mol~1. The two inverse T-shaped struc-tures and the slipped parallel structure are predicted to beÐrst-order transition states at this level of calculation. Theirstabilization energies are 0.709 kcal mol~1 for the inclinedform, 0.694 kcal mol~1 for the symmetric form, and 0.624 kcalmol~1 for the slipped parallel form, which suggests that theintermolecular PES is very Ñat in this region. The crossedform is a second-order transition state and is stabilized by0.390 kcal mol~1. Both complexes are very weakly bound,except for the global minimum T-shaped structure. Thus,the bpÈar T-shaped form is the one that will be observed, asfound in the experimental work of Bloemink et al.3 and in amolecular analysis reported by Legon.6

In their gas-phase microwave study, Bloemink et al.observed the formation of the molecular complexes with anapparatus where the components remain separate until thepoint at which they expand simultaneously into the vacuumchamber of the spectrometer, because they have argued thatthis reaction may be explosive under certain conditions. Thus,in their experiment, there are no surfaces where reaction mightoccur between the mixing point and the collisionless super-sonic expansion, and only the formation of weakly boundcomplexes was observed.

A very interesting study of chlorine addition to but-1-ynewas reported by Poutsma and Kartch.7 They performed the

J. Chem. Soc., Faraday T rans., 1998, 94, 2895È2900 2895

Publ

ishe

d on

01

Janu

ary

1998

. Dow

nloa

ded

on 2

9/10

/201

4 15

:33:

12.

View Article Online / Journal Homepage / Table of Contents for this issue

experiments in solution in an inert solvent under(C2F3Cl3),three di†erent sets of conditions : in the dark and in the pres-ence of oxygen, in the dark without oxygen, and in the pres-ence of light. In the Ðrst case, no reaction was observed. In thesecond case, the reaction was initiated 5È10 min after mixing.In the last case, upon illumination the reaction proceededpromptly. In both situations where reaction occurred, the pro-ducts were produced with the same yield. About 90% of theproducts were a mixture of cis- and trans-1,2-dichlorobut-1-ene, with 97% trans and only 3% cis. These results givesupport to a free radical addition mechanism, and show thatthe reaction can be auto-initiated. The occurrence of the reac-tion in the dark after some initial time indicates an inductionperiod, when the initial radicals that will begin the chain reac-tion are formed. However, we could ask : which is the initialstep ; how is the corresponding transition state formed andwhich radicals are formed in the beginning of the reaction?Poutsma and Kartch did not address these questions. Theyassumed that the initial formation of Cl radicals initiates theprocess, but they did not propose a mechanism that explainsthe spontaneous reaction in the dark.

Therefore, here, we intend to give a general picture of thereaction mechanism and kinetics of a chlorine addition to acarbonwcarbon triple bond, studying the reaction of withCl2acetylene. Although this system is small, it may give informa-tion about this kind of reaction and provide answers to theabove questions. We also aim to analyze the possible explo-sive character mentioned in the work of Bloemink et al.

CalculationsThe ab initio calculations were performed with GAMESS8and Gaussian 949 programs. The Ðrst interaction of the twomolecules was investigated through a multiconÐgurationalmethodology, which is able to identify whether the reactionproceeds via free radical or ionic initiation. The stationarypoints were optimized at the CASSCF(6,6)/6-31G(d,p) level oftheory,10h14 including the four p electrons of the acetylene,and the pair of r electrons of the The single point energyCl2 .calculation by the Brueckner-doubles method,15 includingtriples in a perturbative form [BD(T)] was used to achieve a

high level of electronic correlation. To include the e†ect of amore extended basis set, we have used the additivity approx-imation, with the Mo� llerÈPlesset second order perturbativemethod (MP2)16 and the 6-311 ] G(2df,2p) basis set. We haveused the unrestricted MP2 procedure17,18 for geometry opti-mization for the remaining reactions. Thus, the geometrieswere obtained at the UMP2/6-31G(d,p) level of theory, andthe electronic correlation was included through the unre-stricted Mo� llerÈPlesset fourth-order perturbation method(UMP4)17,18 and unrestricted coupled cluster single anddouble with the inclusion of triple in a perturbative form[UCCSD(T)]19h21 calculations. Additivity was also used toachieve the results with the 6-311 ] G(2df,2p) basis set. The abinitio results for the absolute energies, vibrational frequencies,zero-point energies and moments of inertia for all stationarypoints are given in Table 1. All rate constants and equilibriumconstants were calculated by transition state theory and sta-tistical thermodynamics using the ab initio data obtained inthis work.

ResultsOur calculations show that the addition reaction of toCl2will occur via a free radical mechanism. We have identi-C2H2Ðed the following elementary reactions :

Initiation step :

Cl2 ] C2H2 ] Cl] C2H2Cl (1)

Cl2 ] 2Cl (2)

Isomerization step :

C2H2Cl (trans) % C2H2Cl (cis) (3)

Propagation step :

C2H2 ] Cl] C2H2Cl (4)

C2H2Cl] Cl2] C2H2Cl2 ] Cl (5)

C2H2] C2H2Cl] C2H2C2H2Cl (6)

Table 1 Calculated energies frequencies (in cm~1), ZPE (in kcal mol~1) and moments of inertia (in u for all stationary points obtained(Eh), a02)in this work, at the UMP2/6-31G(d,p) level of theory, except for TS1 and WCB, which are at the CASSCF/6-31G(d,p) level of theory

Species Absolute energy Frequencies ZPE Moments of inertia

Cl [459.552433 È È ÈAcetylene [77.081668 441, 441, 750, 750, 1999, 3502, 3588 16.40 0, 52, 52Cl2 [919.171395 547 0.78 0, 254, 254TS1 [995.775718 415i, 70, 78, 183, 342, 541, 721, 772, 1131, 1720, 17.98 37, 1385, 1422

3469, 3551WBC [995.782998 27, 41, 51, 385, 594, 665, 858, 976, 1326, 1646, 19.19 197, 1513, 1710

3417, 3438R1 [536.648031 380, 750, 826, 895, 1013, 1301, 1863, 3317, 3406 19.66 30, 277, 307TS3 [536.640474 675i, 424, 728, 868, 921, 1292, 1927, 3262, 357 18.57 26, 291, 316R2 [536.646218 412, 692, 762, 931, 974, 1303, 1861, 3262, 3401 19.44 23, 290, 313TS4 [536.621362 565i, 239, 756, 852, 920, 936, 2284, 3498, 3624 18.74 40, 334, 374TS5A [1455.816493 373i, 8, 46, 102, 131, 318, 483, 787, 854, 960, 20.99 64, 3245, 3310

1024, 1298, 1948, 3318, 3406TS5B [1455.814365 387i, 36, 41, 110, 196, 425, 490, 753, 775, 972, 20.95 323, 2022, 2345

979, 1285, 1950, 3248, 3398TS6A [613.707799 [743i, 64, 104, 138, 270, 393, 708, 756, 833, 841, 39.12 92, 1299, 1339

877, 936, 1000, 1075, 1319, 1940, 2305, 33133362, 3503, 3630

TS6B [613.705978 746i, 26, 124, 154, 317, 479, 708, 737, 780, 821, 38.99 219, 862, 1033876, 929, 999, 1034, 1303, 1927, 2303, 32613367, 3500, 3630

trans-DCE [996.359343 219, 245, 361, 777, 873, 898, 959, 1278, 1347, 21.83 34, 1176, 12101678, 3316, 3319

cis-DCE [996.360184 172, 422, 5906, 734, 751, 906, 910, 1261, 1373, 22.05 153, 733, 8871681, 3303, 3323

2896 J. Chem. Soc., Faraday T rans., 1998, 94, 2895È2900

Publ

ishe

d on

01

Janu

ary

1998

. Dow

nloa

ded

on 2

9/10

/201

4 15

:33:

12.

View Article Online

Termination step :

C2H2Cl] Cl] C2H2Cl2 (7)

2Cl] Cl2 (8)

2(C2H2Cl)] ClC2H2C2H2Cl (9)

C2H2C2H2Cl] Cl] ClC2H2C2H2Cl (10)

Reaction (1) of the initiation step involves the interaction ofand and the breaking of a ClwCl r bond and oneCl2 C2H2acetylene p bond to form two radical species : Cl and C2H2Cl.

This reaction produces a weakly bound complex (WBC),which dissociates quickly into the products, a Cl atom and aradical, where the two hydrogens are on opposite sides of themolecule (trans). The weakly bound complex has a high multi-conÐgurational character, which can be noted by its CI coeffi-cient (0.69) in the CASSCF wavefunction. Fig. 1 presents thestructural forms for the reactants, transition state (TS1) andWBC, where the principal geometrical parameters are alsogiven. The structure of the radical produced (R1) is shown inFig. 2. Both TS1 and WBC are planar, and the distancebetween the Cl atoms is 2.682 in TS1, but it increases toÓ3.825 in WBC. The energy values obtained are listed inÓ

Fig. 1 Structures and geometrical parameters for the reactants(MP2/6-31G(d,p) geometry optimization), transition state TS1 and thecomplex WBC (geometry optimization at the CASSCF/6-31G(d,p)level of calculation).

Fig. 2 Structures and relevant geometrical parameters for the trans-and cis-isomers and the transition state TS3 of the radical C2H2Cl,optimized at the MP2/6-31G(d,p) level.

Table 2 Calculated values (in kcal mol~1) for the stationary pointsobtained for reaction (1)a

TS1 WBC Products

6-31G(d,p)CASSCF 32.19 27.62 28.08*ZPE 1.40 2.61 2.47MP2 36.80 72.96 33.99MP4(SDQ) 37.80 [42.44 27.26CCSD 38.34 48.98 22.22BD 38.28 46.17 21.89MP4 26.16 [86.44 31.17CCSD(T) 22.55 [204.78 24.45BD(T) 25.22 12.88 23.94

6-311 ] G(2df,2p)MP2 41.83 È 47.59CCSD(T)b 27.58 È 38.05BD(T)b 30.24 È 37.54

a Geometry optimizations were performed at the CASSCF/6-31G(d,p)level of theory. b Obtained by additivity approximation.

Table 2. Using the 6-31G(d,p) basis set, the classical energybarrier to TS1 formation is 32.19 kcal mol~1 at the CASSCFlevel, but is increased when dynamical electron correlation isincluded, as in the MP4(SDQ), CCSD and BD methods. Inlevels of calculation where the perturbative inclusion of triplesexcitation contribution to electronic correlation is considered[MP4, CCSD(T), BD(T)], the energy barrier is not so high. Inour best result, BD(T)/6-311 ] G(2df,2p), the classical energybarrier is 30.24 kcal mol~1. For the weakly bound complex,the behavior is erratic for all high-level single referencemethods, except for the most sophisticated one, BD(T), whichgives more reasonable values. However, the value is very lowwhen compared with the CASSCF values. This is due to thepresence of a strong non-dynamical electron correlation inthis structure, which reduces the quality of the results of thesingle-reference-based methods. This molecular complex isvery weakly bound at the CASSCF level and will dissociatequickly into the products. The results for the products show agood agreement between the CCSD(T) and BD(T) values, andthe classical reaction energy is 37.54 kcal mol~1 at the BD(T)/6-311 ] G(2df,2p) level of calculation. Tables 3 and 4 presentthermodynamic and kinetics results, such as the activationenergy, the Arrhenius activation energy the Gibbs ener-(Ea),gies of activation (denoted with the symbol and reaction()free energies (*G¡, standard state of 1 atm pressure), the Arr-henius factors (A) and rate constants (k). The variations inactivation and reaction enthalpy and entropy are also given.The activation energy for this reaction is 31.64 kcal mol~1,and the Gibbs energy of activation is 38.66 kcal mol~1. TheGibbs energy of reaction is 39.66 kcal mol~1, showing that theformation of these radicals is not spontaneous. The fact that

Table 3 Thermodynamic activation properties (in kcal mol~1, standard state 1 atm pressure) and rate constants (in l mol~1 s~1) calculated forthe reactions of the free radical mechanism of addition to acetyleneaCl2

1 3 4 5a 5b 6a 6b

*Eb 31.64 2.84 [1.22 [2.04 [1.78 7.59 7.09*H¡º 31.24 2.79 [2.39 [2.07 [1.97 6.88 6.32[T *S¡º 7.42 0.10 7.48 7.38 8.28 9.60 9.25*G¡º 38.66 2.89 5.09 5.31 6.31 16.48 15.57Ea [ 3.38 [1.21 [0.89 [0.79 8.06 7.50A [ 1.43] 1013 3.70] 109 4.34] 109 9.58] 108 1.03] 108 1.86] 108k 10~18 c 4.75] 1010 2.85] 1010 1.95] 1010 3.63] 109 1.28] 102 5.93] 102

a T \ 298.15 K. Rate constants obtained using transition state theory. The degeneracy of the electronic energy levels of the chlorine atoms wasconsidered. b Activation energy, which corresponds to classical activation energy plus ZPE correction. c The calculation of this parameter wasdiscussed in the text.

J. Chem. Soc., Faraday T rans., 1998, 94, 2895È2900 2897

Publ

ishe

d on

01

Janu

ary

1998

. Dow

nloa

ded

on 2

9/10

/201

4 15

:33:

12.

View Article Online

Table 4 Thermodynamic reaction parameters (in kcal mol~1, standard state 1 atm pressure) calculated for the reactions of the free radicalmechanism of addition to acetyleneaCl2

1 2 3 4 5a 5b 7a 7b

*Eb 40.01 55.43 1.06 [14.36 [38.70 [40.09 [94.12 [95.53*H¡ 39.70 56.20 1.07 [15.63 [38.76 [40.32 [94.95 [96.52[T *S¡ [0.04 [7.82 0.06 7.90 1.92 1.92 8.13 [9.97*G¡ 39.66 48.38 1.13 [7.73 [36.84 [38.40 [86.82 [86.55

a The degeneracy in the energy levels of the chlorine atoms was considered. T \ 298.15 K. b Reaction energy, which corresponds to classicalreaction energy plus ZPE correction.

the Gibbs energy of activation is lower than that of reaction isdue to the inclusion of a more extended basis set, thatincreases the reaction energy more than the activation barrier.This Ðnding indicates that the transition state should be dis-located to a longer ClwCl bond, increasing the activationenergy and also the Gibbs energy of activation to a valuegreater than the Gibbs energy of reaction. In consequence, theGibbs energy of activation should be greater than 39.66kcal mol~1. The upper limit for this parameter can also beestimated. Considering the activation enthalpy to be equiva-lent to the reaction enthalpy (39.70 kcal mol~1), and addingthis value to the result for reaction (1) (7.42[T *S¡ºkcal mol~1) we can obtain the maximum value for *G¡º,47.12 kcal mol~1. Thus, a reasonable estimate of the Gibbsenergy of activation is kcal mol~1, and the*G¡º\ (43 ^ 3)rate constant will be ca. 10~18 l mol~1 s~1. This valuek1is given in Table 3.

Table 5 presents the energetics for the activation of theother reactions, for which the structures were optimized at theUMP2 level. The energies of activation of the reactions thatwill occur to a relevant extent are shown in Table 5, and theresults for the reaction energies are given in Table 6.

The other reaction of the initiation step is the dissociationof into Cl atoms [reaction (2)]. This occurs without anCl2activation energy barrier above the dissociation limit, and the

reaction energy is 55.43 kcal mol~1. It is very endothermic,and the Gibbs energy of reaction is 48.38 kcal mol~1, higherthan the value found for reaction (1) (39.66 kcal mol~1).Therefore, the reaction of dissociation of into chlorineCl2atoms will be considerably slower than reaction (1) and willnot be competitive in the generation of chlorine radicals.

Reaction (3) is the isomerization of the trans-radical(R1) to the cis-isomer, the transition state (TSR) isC2H2Cl

shown in Fig. 2, together with the cis-isomer (R2). In the TSR,the carbon atoms and one of the hydrogen atoms are almostcollinear. It has a small energy barrier of 2.84 kcal mol~1, andthe reaction energy is 1.06 kcal mol~1. Thus, the trans-isomeris more stable than the cis-isomer. The interconversion rateconstant is 4.75] 1010 s~1 which means that once the trans-radical is formed, the cis-radical will be produced quickly. TheGibbs energies of activation and reaction are 2.89 and 1.13kcal mol~1, respectively.

The structural forms obtained for the transition states of thepropagation step are depicted in Fig. 3, together with the rele-vant geometrical parameters for the reactions of the twoisomers of the radical. The Ðrst reaction of the propa-C2H2Clgation step, reaction (4), is the addition of Cl atom to acety-lene. The structure of the transition state (TS4) is shown inFig. 3. It can be seen that the approach of the chlorine atomforces a distortion in the acetylene molecule that will lead only

Table 5 Calculated classical activation energies (in kcal mol~1) for the other reactions of the free radical addition to acetyleneaCl23 4 5a 5b 6a 6b

6-31G(d,p)UMP2 4.74 8.00 1.84 2.04 13.74 13.75*ZPE [1.09 2.34 0.55 0.73 3.06 3.15UMP4(SDQ) 4.85 4.85 2.59 2.82 10.65 10.55UCCSD 5.15 1.36 1.80 2.10 7.20 7.04UMP4 4.68 5.49 1.42 1.58 10.96 10.87UCCSD(T) 5.09 0.52 0.33 0.57 6.34 6.15

6-311 ] G(2df,2p)UMP2 3.58 3.92 [1.08 [1.04 11.93 11.54UCCSD(T) 3.93 [3.56 [2.59 [2.51 4.53 3.94

a Geometry optimizations were performed at the UMP2/6-31G(d,p) level of theory.

Table 6 Calculated classical reaction energies (in kcal mol~1) for the other reactions of the free radical addition to acetyleneaCl22 3 4 5a 5b 7a 7b

6-31G(d,p)UMP2 41.75 1.14 [8.74 [57.95 [59.62 [99.70 [101.36*ZPE 0.78 [0.22 3.26 1.39 1.83 2.17 2.61UMP4(SDQ) 38.20 1.18 [11.64 [53.72 [55.11 [91.94 [93.39UCCSD 37.94 1.18 [15.06 [49.71 [50.89 [87.65 [89.04UMP4 40.62 1.26 [10.13 [55.24 [56.90 [95.87 [97.53UCCSD(T) 40.48 1.28 [15.18 [49.88 [51.43 [90.36 [91.91

6-311 ] G(2df,2p)UMP2 57.48 1.14 [11.18 [48.16 [50.11 [105.63 [107.59UCCSD(T) 56.21 1.28 [17.62 [40.09 [41.92 [96.29 [98.14

a Geometry optimizations were performed at the UMP2/6-31G(d,p) level of theory.

2898 J. Chem. Soc., Faraday T rans., 1998, 94, 2895È2900

Publ

ishe

d on

01

Janu

ary

1998

. Dow

nloa

ded

on 2

9/10

/201

4 15

:33:

12.

View Article Online

Fig. 3 Structures and relevant geometrical parameters for the tran-sition states involved in the reactions (4), (5) and (6). Geometry opti-mizations were performed at the MP2/6-31G(d,p) level of theory.

to a radical where the hydrogen atoms are onC2H2Clopposite sides of the radical. The classical energy barrier to thisreaction is positive with the 6-31G(d,p) basis set but, using alarger basis set, it is negative in the UCCSD(T) level of calcu-lation. These results show that the MPn calculations do notgive good results for systems where there is an open-shellspecies. This reaction has an activation energy of [1.22kcal mol~1, with a rate constant of 2.85 ] 1010 mol~1 s~1.The Gibbs energies of activation and reaction are 5.09 and[7.73 kcal mol~1, respectively. An experimental study of thisreaction has been carried out by Kaiser and Wallington.22They obtained a rate constant 12.0 ] 1010 l mol~1 s~1, whichis in good agreement with our result. In a previous study,23Kaiser reported an expression for the rate constant of thisreaction as a function of temperature. Using this relation, wehave obtained : kcal mol~1,*H¡º \ [3.26 [T *S¡º\ 7.44kcal mol~1 and kcal mol~1, so that the di†er-*G¡º\ 4.18ences between theoretical and experimental values are lessthan 1 kcal mol~1, indeed a very good result. In particular,the values of di†er by just 0.04 kcal mol~1, which[T *S¡ºmeans that the error is mainly in our determination of theactivation enthalpy.

The following reaction [reaction (5)] can proceed via eitherform of the radical. Reaction (5a) refers to the reac-C2H2Cltion with the trans-isomer, and reaction (5b) to that with thecis-isomer. The transition states involved, TS5A and TS5B,are depicted in Fig. 3. The approach of the chlorine moleculetakes place in the same way in either case, and the two struc-tures are planar. The classical energy barriers are small forboth reactions, and are negative with the larger basis set. Thevalues are [2.59 and [2.51 kcal mol~1, respectively. Theclassical reaction energies are also negative and close, [40.09and [41.92 kcal mol~1, respectively. These reactions alsohave similar activation energies, rate constants and Gibbsenergies of activation and reaction. Reaction (5a) has an acti-vation energy of [2.04 kcal mol~1, with a rate constant of1.95] 1010 l mol~1 s~1. The Gibbs energy of activation is

5.31 kcal mol~1 and that of reaction is [36.84 kcal mol~1.The respective values for reaction (5b) are [1.78 kcal mol~1,3.63] 109 l mol~1 s~1, 6.31 kcal mol~1 and [38.40 kcalmol~1. These values show that reaction (5a) is a little fasterthan reaction (5b), but the products of reaction (5b) will bemore stable.

The last reaction in the propagation step is the reaction ofthe radical with acetylene [reaction (6)]. This can alsoC2H2Cloccur via both isomers, reaction (6a) being for the trans-isomer and reaction (6b) for the cis-isomer. The transitionstates involved also have similar structures, as shown in Fig. 3.They are not planar, and the acetylene is approaching in di†er-ent ways in the two transition states, TS6A and TS6B. Theclassical activation energies are 4.53 and 3.94 kcal mol~1using our best level of calculation. However, the Gibbs ener-gies of activation are, respectively, 16.48 and 15.57 kcal mol~1.The activation energies are 7.59 and 7.09 kcal mol~1, whichleads to rate constants of 1.28 ] 102 l mol~1 s~1 for reaction(6a) and 5.93] 102 l mol~1 s~1 for reaction (6b). Hence, thesereactions proceed at a very low rate, and we have not studiedthe product formed.

The reactions of the termination step proceed without anactivation energy barrier, and are very exothermic for each ofthe isomers. Reaction (7a) corresponds to the formation oftrans-dichloroethylene, and reaction (7b) to the formation ofthe cis-isomer. The relevant geometrical parameters and thestructures of the products are given in Fig. 4. The formation ofthe cis-isomer is more exothermic by 1.57 kcal mol~1. TheGibbs energies of reaction are [86.82 kcal mol~1 for reaction(7a) and [86.55 kcal mol~1 for reaction (7b), showing thatthese two reactions are equally spontaneous.

Reaction (8) is the inverse of reaction (2) and will occurwithout an energy barrier. The possibility of reaction betweentwo radicals is assessed in reaction (9). This wasC2H2Clneglected since the concentration of the radicals willC2H2Clnot reach high values, due to the slow rate of reaction (1) andthe fast rate of reactions (5) and (7). Finally, reaction (10)shows the reaction of the radical formed in reaction (6) withCl atoms. We have shown that reaction (6) will not be impor-tant and, consequently, reaction (10) can be neglected in ourstudy.

DiscussionAccording to our calculations, addition to acetyleneCl2begins with the formation of a radical (trans) andC2H2Clchlorine atoms through the transition state TS1. The disso-ciation of molecules into Cl radicals has a smaller rateCl2constant and will not be important for the production of Clatoms. The rate constant of the reaction (1) is not very high,and it takes a period of time until the concentration of chlo-rine radicals reaches a value where the reactions of the propa-gation step can take place at a reasonable rate. We canestimate this time considering real reaction conditions. If wetake concentrations of acetylene and of 3.7 mol l~1 andCl20.29 mol l~1 (as used by Poutsma and Kartch in chlorineaddition to but-1-yne) respectively, and the rate constant is ca.

Fig. 4 Structures and geometrical parameters for the principal pro-ducts of the addition reaction of to acetylene, i.e. cis- and trans-Cl2dichloroethylenes.

J. Chem. Soc., Faraday T rans., 1998, 94, 2895È2900 2899

Publ

ishe

d on

01

Janu

ary

1998

. Dow

nloa

ded

on 2

9/10

/201

4 15

:33:

12.

View Article Online

10~18 l mol~1 s~1, after 1 h reaction (1) will be in equilibrium,and the concentration of Cl radicals will be 3] 10~15 moll~1, a quantity sufficient to consume 0.29 mol l~1 of the acety-lene in 15 min. Comparing this result with the Poutsma andKartch work, we can see they are in good agreement, after, intheir experiment with but-1-yne the reaction has proceededsigniÐcantly after 5È10 min in the dark.

The trans-radical produced in reactions (1) and (4) can beinterconverted to the cis-isomer via a small energy barrier,with a rate constant of 4.75 ] 1010 s~1. Thus, we can considerthese species to be in equilibrium. Also, considering the reac-tion rate constants of reactions (5a) and (5b), we can estimatethe proportion of cis- and trans-dichloroethylenes formedfrom:

[trans][cis]

\k5a

k5bKeq\ 3.61

where is the equilibrium constant for trans- to cis-Keqisomerization of the radical Thus, theC2H2Cl (Keq\ 0.149).trans-1,2-dichloroethylene will correspond to 97.3% of theyield and the cis-1,2-dichloroethylene to 2.7%. This result is inexcellent agreement with the experimental Ðndings ofPoutsma for but-1-yne, i.e. 97% for the trans- and 3% for thecis-isomer.

Reaction of radicals with acetylene is also possible,C2H2Clbut the rate constants are smaller than for the reaction with

by a factor of 108. Therefore, the products of these reac-Cl2,tions will not be formed in signiÐcant amounts when the con-centration of is high. After almost complete consumptionCl2of the the remaining radicals will react via theCl2, C2H2Clpolymerization reactions (6a) and (6b), but at a very slow rate.

Now, we can consider whether this reaction could be explo-sive. In accordance with our discussion, the generation ofchain propagators will reach equilibrium in 1 h (discountingother reactions), resulting in a concentration that willconsume 0.29 mol l~1 of the acetylene in 15 min. Therefore, atroom temperature and in the absence of light, this reactionshould not be explosive under conditions where the pro-duction of radicals on the walls is not signiÐcant. Indeed,Poutsma and Kartch carried out the reaction of andCl2but-1-yne at [9 ¡C without explosion. Nevertheless, at highertemperatures, the rate constant of reaction (1) and the concen-tration of radicals can be increased and, as a result, the reac-tion will proceed at a greater rate. If the generated heatcannot be quickly dissipated, it will result in an increase intemperature, accelerating the formation of radicals and poss-ibly leading to an explosion.

Analyzing the overall mechanism, we can extract informa-tion about the stability and heat of formation of the products.From the results reported in Table 4, we are able to calculate*H¡ of trans- and cis-dichloroethylene formation from acety-lene and [55.26 kcal mol~1 for trans and [55.76Cl2 :kcal mol~1 for cis. Comparing this with the experimentalvalues available :24 [53.1 and [53.4 kcal mol~1, respectively,it can be seen that the di†erence in enthalpy for the isomers is0.5 kcal mol~1 in our calculation and 0.3 kcal mol~1 in theexperimental results. In both cases the cis-isomer is predictedto be the most stable, and the theoretical and experimentalresults are in excellent agreement.

ConclusionsThe mechanism of addition to acetylene has been studied.Cl2We have shown that the reaction proceeds by a free radicalmechanism, with an initiation step that generates Cl and

radicals, which also propagate the chain reaction.C2H2Cl

There is an induction period, while the concentration of theseradicals increases, and the reaction only proceed at an appre-ciable rate when a sufficient concentration is reached. Theprincipal products are trans- and cis-1,2-dichloroethylenes,97.3% and 2.7%, respectively. The reaction should proceed inless than 1 h for concentrations of 3.7 mol l~1 acetylene and0.29 mol l~1 and it is unlikely to be explosive at roomCl2,temperature in the absence of a signiÐcant rate of productionof radicals on surfaces.

Acknowledgementsauthors would like to thank the Conselho Nacional deThe

Desenvolvimento Cienti� Ðco e Tecnolo� gico (CNPq) for provid-ing the research grants, and the de Amparo a Pes-FundacÓ a8 oquisa no Estado de Minas Gerais (FAPEMIG) and thePrograma de Apoio ao Desenvolvimento Cienti� Ðco e Tecnol-o� gico (PADCT[ Proc No 620241/95.0) for supporting thisproject.

References1 J. March, Advanced Organic ChemistryÈReactions, Mechanisms

and Structure, Wiley, New York, 1985.2 D. Barton and D. W. Ollis, in Comprehensive Organic Chemistry,

ed. J. F. Stoddart, Pergamon Press, 1979, vol. I.3 H. Bloemink, S. A. Cooke, K. Hinds, A. C. Legon and J. C.

Thorn, J. Chem. Soc., Faraday T rans., 1995, 91, 1891.4 H. Bloemink, K. Hinds, A. C. Legon and J. C. Thorn, Chem.

Phys. L ett., 1994, 223, 162.5 S. M. Resende and W. B. De Almeida, Mol. Phys., 1997, 91, 635.6 A. C. Legon, Chem. Phys. L ett., 1995, 237, 291.7 M. L. Poutsma and J. L. Kartch, T etrahedron, 1966, 22, 2167.8 M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S.

Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S.Su, T. L. Windus, M. Dupuis and J. A. Montgomery Jr. ;GAMESS, J. Comput. Chem., 1993, 14, 1347.

9 Gaussian 94, Revision D.2, M. J. Frisch, G. W. Trucks, H. B.Schlegel, P. M. W. Gill, B. G. Johnson, M. A. Robb, J. R.Cheeseman, T. Keith, G. A. Petersson, J. A. Montgomery, K.Raghavachari, M. A. Al-Laham, V. G. Zakrzewski, J. V. Ortiz,J. B. Foresman, J. Cioslowski, B. B. Stefanov, A. Nanayakkara,M. Challacombe, C. Y. Peng, P. Y. Ayala, W. Chen, M. W.Wong, J. L. Andres, E. S. Replogle, R. Gomperts, R. L. Martin,D. J. Fox, J. S. Binkley, D. J. Defrees, J. Baker, J. P. Stewart, M.Head-Gordon, C. Gonzalez and J. A. Pople, Gaussian, Inc., Pitts-burgh PA, 1995.

10 K. Ruedenberg, M. W. Schmidt, M. Gilbert and S. T. Elbert,Chem. Phys., 1982,.71, 41.

11 K. Ruedenberg, M. W. Schmidt, M. Gilbert and S. T. Elbert,Chem. Phys., 1982, 71, 51.

12 K. Ruedenberg, M. W. Schmidt, M. Gilbert and S. T. Elbert,Chem. Phys., 1982, 71, 65.

13 P. E. M. Siegbahn, J. Almlof, A. Heiberg and B. O. Roos, J.Chem. Phys., 1982, 74, 2384.

14 B. O. Roos, Advances in Chemical Physics, Wiley, New York,1987, vol. 69.

15 N. C. Handy, J. A Pople, M. Head-Gordon, K. Raghavachariand G. W. Trucks, Chem. Phys. L ett., 1989, 164, 185.

16 C. Moller and M. S. Plesset, Phys. Rev., 1934, 46, 618.17 J. A. Pople, J. S. Binkley and R. Seeger, Int. J. Quantum Chem.,

1976, 10, 1.18 R. Krishnan, M. J. Frisch and J. A Pople, J. Chem. Phys., 1980,

72, 4244.19 J. Cizek, J. Chem. Phys., 1966, 45, 4256.20 J. Paldus, J. Cizek, I. Shavitt, Phys. Rev. A, 1972, 5, 50.21 R. J. Bartlett, J. Phys. Chem., 1989, 93, 1697.22 E. W. Kaiser and T. J. Wallington, J. Phys. Chem., 1996, 100,

4111.23 E. W. Kaiser, Int. J. Chem. Kinet., 1992, 24, 179.24 D. R. Lide, in CRC Handbook of Chemistry and Physics, 73rd

edn., CRC Press, New York, 1993.

Paper 8/03923B

2900 J. Chem. Soc., Faraday T rans., 1998, 94, 2895È2900

Publ

ishe

d on

01

Janu

ary

1998

. Dow

nloa

ded

on 2

9/10

/201

4 15

:33:

12.

View Article Online