Transition State for 1,2 Hydrogen Halide Elimination from Ethyl

Aug 1, 1994 - Caleb A. Smith , Blanton R. Gillespie , George L. Heard , D. W. Setser , and Bert E. Holmes. The Journal of Physical Chemistry A 2017 12...
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8359

J. Phys. Chem. 1994, 98, 8359-8370

Transition State for 1,2 Hydrogen Halide Elimination from Ethyl Halides Joseph L. Toto, Glyn 0. Pritchard, and Bernard Kirtman' Department of Chemistry, University of California, Santa Barbara, California 91 306 Received: January 21, 1994; In Final Form: May 26, 1994"

On the basis of extensive quantum chemical calculations for 1,2 elimination of H X from CzHsX (X = F, C1, Br, and I) we have obtained a strongly asymmetric transition state that differs greatly from previous models for this reaction. The effect of a-chloro/fluoro substitution was also investigated, specifically for HF and H C l elimination. W e confirm the electron donor/acceptor property of these substituents but find the conventional explanation of their effect on the activation energy to be unsatisfactory.

I. Introduction The unimolecular decomposition of an alkyl halide R X to form an olefin and the 1,2 elimination product H X has been extensively studied. Prior to 1955 it was generally thought' that this reaction proceeded via a four-center transition state (TS) and that the activation energy (E,) for elimination was proportional to the carbon-halidebondstrength. Thisview was modified by Maccoll and Thomas,2 who showed that a correlation existed between E, and the heterolytic bond dissociation energy (BDE) for R-X R+ X:-, rather than the homolytic BDE for R-X R. X-. Their observation was based on data for elimination reactions of primary, secondary, and tertiary alkyl halides. On the basis of their observations Maccoll and Thomas2 suggested an analogy between gas-phase elimination reactions and S N(or ~ El) reactions in polar solvents. Thus, it was proposed in the former case that the leaving, partially charged, positive hydrogen atom could play a role similar to that of the solvent by stabilizing the stretched and polarized CX bond. This model was subsequently refinedl~3.~ so as to have complete heterolytic cleavage of R X into an intimate R+X-ion pair and a somewhat less polarized C H bond. At first glance such a TS might seem energetically unlikely because, in most cases, the heterolytic cleavage energy is more than 100 kcal/mol larger than the corresponding energy for homolytic cleavage. However, the Coulombic stabilization of the intimate ion pair can more than account for this difference depending upon the separation of the ions. Assuming a separation, r f , of 2.5 8,at the transition state, Maccolll estimated an E, for ethyl bromide quite close to the experimental5 value. Benson and Bose6 (BB) subsequently suggested that the close agreement between theory and experiment was fortuitous due to an underestimate of r+. They felt that a value of 2.9 8, would be more realistic for the latter quantity. This gives a theoretical E , which is markedly larger than experiment (addition of a polarization correction does not significantly affect the result) and led BB to propose a four-center transition state consisting of two interacting semiion pairs. One of these pairs is a polarized X H bond and the other a polarized olefinic C-C bond. The magnitude of the charge separation was taken to be 0.5e in either case, with the dipoles pointing in opposite directions as shown in Figure 1. Thus, the halide X has a charge of -0.5e rather than -1.0e, as in the ion pair model. Using primarily electrostatic calculations, BB determined activation energies in reasonable agreement with experiment, although the effect of a-methyl substitution was underestimated. The effect of replacing C1 by Br or I was also underestimated, but to a lesser extent. A further elaboration of the semiion pair theory, with an extension to include polyatomic X groups, was later provided by

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*Abstract published in Aduance ACS Abstracts, July 15, 1994.

Figure 1. The semiion pair transition state for 1,2 HX elimination. Ordinarily, it is assumed that 6' = 6. In the BB model6 6' = 6 = OSe, whereas in the MTJ treatmentI7 6' = 6 = variable.

Benson and H a ~ g e n .For ~ X = OH, SH, NH2, and PH2 they obtained an average error in the calculated activation energy of f 2 kcal/mol (compared to experiment). However, the model was later found to be unsuccessful for fluoro-substituted polar olefinsg-9and for four-centered transition state reactions of the type AB CD = AC BD.10 The general features of the Benson, Bose, and Haugen (BBH) transition state have proved useful in explaining a-halogen substituent effects observed in a series of ethyl halide elimination reactions.11J2 Increased chlorine substitution on the a-carbon slightly decreases the threshold energy for elimination of HCl (E, is uniformly larger than the threshold energy by about 1.5 kcal/mol) in the following order, CH3CH2Cl = 55, CH3CHC12 = 52, and CH3CC13 = 50 kcal/mol, while the opposite effect is found for H F elimination with successive fluorine substitution, CH~CHIF= 58, CH3CHF2 = 61, andCH3CF3 = 68 k c a l / m ~ l . Q ~ ~ The latter trend was attributed"-13 to the increased electron withdrawal by additional fluorines, which tends to destabilize the developing positive a-carbon charge. Additional chlorines, on the other hand, were thought to induce a resonance effect by delocalizing an electron lone pair into the developing r-bond. This would stabilize the partial positive charge on the or-carbon and lower the activation barrier. In passing, we note that the above observed trends are probably correct (as supported by our calculations herein), but there is significant uncertainty in the experimental data. The experimental situation will be discussed in section 111. The BBH6v7electrostatic calculations are based on a geometry for the TS wherein the C-H, C-X, and H-X bonds are elongated from their normalvalues, while the ethanic C-C bond is shortened. This effect is assumed to be less for the H-X and C-C bonds, corresponding to a change in the bond order, n, of 0.5 in either case. For the more highly (and equally) stretched C-H and C-X bonds n is only 0.18 in their model. Setser and co-workers14J5 have pointed out that this TS is too loose to reproduce the experimental kinetic data for chloroethane and bromoethane. Therefore, they suggested a (covalent) asymmetric TS complex with the C-H and H-Cl(Br) bonds nearly broken ( n = 0.2 in both instances), while the olefinic and C-CI(Br)

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8360 The Journal of Physical Chemistry, Vol. 98, No. 34, 1994

bonds are almost completely formed (n = 1.8 for the former and n = 0.8 for the latter). For other haloethanes16 different, but very similar, bond orders were chosen. A somewhat different modificationI7 of the semiion pair theory was proposed by Maltman, Tschuikow-Roux, and Jung (MTJ). They retained the BBH H-X and C-C bond orders as well as the equality of the formal charge separation, 6, for both bonds. However, 6 was treated as a variable parameter which determines the value of n for the C-X and C-H bonds through a conservation rule. The parameter 6, in turn, was determined empirically starting with a value for ethylene and then adding olefin substituent corrections arising from steric and inductive effects. MTJ find a much smaller 6, and corresponding larger C-H and C-X bond orders, than the original semiion pair theory. This leads to a tighter TS, as required by the kinetic data. From the bond orders MTJ calculate bond energies and, ultimately, E,. Although, on the average, the resulting activation energies lie within f1.7 kcal/mol of experiment for a large set of reactions, one must bear in mind that the treatment is heavily parametrized. Beyond these models, there have been just a few ab initio treatments that characterize theTS for H X elimination. As part of a dynamical study on energy partitioning, Sato and MorokumaI8 optimized the TS geometry for HFelimination from CH3-CH2F at the Hartree-Fock 4-31G level. The E, was then determined using single-point SDCI calculations with a Davidson correction19 and with zero-point vibrations taken into account. These authors did not examine the charge distribution or bond orders in the TS. A set of Hartree-Fock 3-21G calculations comparing (HX)2 addition to ethylene with H X addition for X = F, C1 have been carried out by Clavero and co-workers.20 Mulliken bond populations, electron charge transfer from ethylene to HX, and isodensity contour maps revealed important differences in the H F and HCl TS structures. The TS involving H F was shown to be characterized by strong C F bond formation, while in the HCl case it is the C-H bond that is more completely formed as expected for an electrophilic reaction. According to this analysis, the H F transition state is correctly characterized as four-centered, but the HCl transition state is 'bicentric". Since neither basis set variation nor electron correlation was considered, these conclusions were recognized to be preliminary in nature. No results were reported for X = Br or I. Recently, Sola et aL2I have reported on the reverse reaction of H F addition to C2H+,,)Fn with n = 0-4. Optimized TS geometries were obtained, generally a t the Hartree-Fock 3-21G level but, in some cases, also at the 6-31G** level. The change in basis set was found to have an important effect on the calculated Ea's, which is not due to the difference in geometry. Including electron correlation, at the MP2 (and MP3) level, led to a substantial lowering of barrier heights. The TS bond orders, charge transfer from olefin to HF, and variation in E, with the number of fluorines were analyzed in terms of an increase in the electrophilicity of the reaction with increasing substitution. Finally, we wish to take particular note of the recent experimental study by Holmes and co-workers,I3 who determined branching ratios and threshold energies for H F and HC1 elimination from CH3CF2CI by the chemical activation method. On the basis of the trends in threshold energies for a-chloro/ fluoro substitution given above they estimated beforehand that the barrier for HCl loss would be greater (-65 kcal/mol) than that for elimination of HF (-60 kcal/mol). Instead, for internal energies of about 100 kcal/mol, they found a branching ratio favoring HCl by 25:l (in general accord with most prior observations on this molecule13) from which threshold energies of 55 f 2 for HCl loss and 69.5 f 2 kcal/mol for HF loss were determined. Thus, the measured order of activation energies turned out to be the reverse of their prediction, and the marked preference for HCl elimination was in agreement with other studies

.

1010et

t

I

ai.

I

Figure 2. Geometrical parameters of the transition state for 1,2 HX elimination from C2H5X (X = F, CI, Br, I). The assumed C, symmetry plane corresponds to the plane of the paper.

on a variety of fluorochloroethanes.~*~23 In a very recent chemical activation study24 a branching ratio of 45:l in favor of HC1 elimination was reported for CH3CFC12 formed with an internal energy of approximately 100 kcal/mol. The purpose of this paper is 2-fold. First, we wish to present extensive ab initio quantum chemical calculations-carefully tested for basis set and correlation effects-that provide reliable trends in TS geometry, atomic charges, bond orders, and energy barriers for a series of 1,2 H X elimination reactions from halogenated ethanes including Br and I. The second goal is to provide our own characterization of the TS for these reactions and to compare with the several previous models (Maccoll, BBH, Setser, MTJ, etc.) that have been proposed. 11. 1,2 HX Elimination from CzH$

We considered, first, 1,2 H X elimination from the set of ethyl halides C2H4-HX, where X = F, C1, Br, or I. A. TS Geometry. By maintaining C,symmetry, the 18 internal degrees of freedom in the nuclear motion of the atoms is reduced to 1 1 independent internal coordinates, which may be chosen as shownin Figure 2. From the viewpoint of the elimination products, there are three intermolecular coordinates, Rx, a,and 0, which give the position of H X (apart from the H X bond length) with respect to C2H4. Here Rx is the distance between the midpoint, m,of the C-C bond and the X atom, a is the mXH angle, and /3 is the CxmX angle, where CX is the carbon originally bonded to X. The remaining intramolecular coordinates consist of four bond lengths (RHx,Rcc, R c ~ Hand ~ ,RC"H~) and four bond angles (aH'CxH',( I H Q C ~ , a c x c H ~and ? , U H ~ C , , H ~ )A. prime is used here to distinguish the hydrogens of the nascent ethylene from the leaving hydrogen. In the case of HF elimination, a search was conducted for a nonplanar TS by following separately the steepest descents and the linear synchronous transit paths to the reactant, but none was found. In addition, several runs were made starting with an outof-plane geometry and, in every case, the TS was found to be planar. For all the other halogens it was assumed that the TS has C, symmetry. Our study was carried out using the Gaussian92 program.25 For the [C2H4--HF] TS Table 1 gives optimized geometrical parameters at the Hartree-Fock level of theory using the 3-21G, 4-31G, 6-31G**, and 6-311G** basis sets. (The 3-21G and 6-31G**calculationsreproduce theresultsgiven inref 21 .)There is close agreement between the four basis sets for all parameters other than R H Xa, , 8, and Rx. The latter, together with Rcc, characterize the geometry of the reaction complex. As far as these four parameters are concerned, the difference between the 4-31G basis and the larger basis sets is less than 4' in the two angles and 0.04 A in the two lengths. This may be contrasted with the 3-21G basis, which shows substantially larger discrepancies (compared to, say, 6-3 1 lG**) of over 9' in one of the angles and almost 0.1 1 A in both lengths. Table 2 shows the optimum TS geometrical parameters when

1,2 Hydrogen Halide Elimination from Ethyl Halides

TABLE 1: Optimized Hartree-Fock TS Geometry' for [CzH4--HFl RHF/3-21G RHF/4-31G RHF/6-31G** RHF/6-311GS*

RHX

1.1990 45.556 B 69.061 1.9877 Rx Rcc 1.4062 &,,HI 1.0745 1.0694 Rc~H, aH'CHH' 115.957 aH'CxH' 116.030 ( I C ~ ~ , , H < 118.073 (IH~C~C,, 121.226 CY

1.2574 38.152 68.817 2.0502 1.3962 1.0763 1.0719 116.550 116.003 118.213 121.673

1.2826 40.239 72.568 2.0868 1.3952 1.0736 1.0682 115.563 116.175 118.458 121.798

1.3082 36.331 69.546 2.096 1 1.3944 1.0761 1.0718 116.924 118.250 118.276 120.704

The geometrical parameters are shown in Figure 2. Angles are in degrees and distances in angstroms.

TABLE 2 Optimized TS Geometry* for [C2H4-HF] Including Correlation at the MP2 Level MP2/4-3 1G

MP2/6-31G**

1.2833 42.295 69.912 2.0683 1.4108 1.0868 1.0843 115.701 115.651 118.648 121.648

1.2326 39.466 66.043 2.0155 1.3992 1.0785 1.0793 115.524 117.094 118.607 121.240

RHX CY

B

Rx Rcc Rc~H~ Rc~H~ OH'C,,H'

~H'C~H? aCXCHH' OH'CXCH

The geometricalparameters correspond to those shown in Figure 2. Angles are in degrees and distances in angstroms.

TABLE 3: Optimized TS Geometry' for [C~HI-HCI] RHX (Y

B Rx Rcc RC~H' Rc~H~ UH'CHH'

aH'CxH' ~CXCHH' aH'CxCn

RHF/4-3 1G

RHF/6-3 1G**

MP2/4-31G

1.8697 25.029 80.799 2.8373 1.3822 1.0739 1.0700 115.989 116.514 118.779 121.605

1.9613 20.811 72.618 2.861 1 1.3770 1.0754 1.0730 116.789 117.883 119.510 121.513

1.8360 29.008 77.503 2.7291 1.4013 1.0883 1.0844 115.846 116.319 118.498 121.832

The geometrical parameters are shown in Figure 2. Angles are in degrees and distances in angstroms. correlation is included at the MP2 level of theory using either a 4-31G or 6-31G** basis. In general, the corrections due to correlation (within a given basis) are a bit smaller than the corrections due to increasing the size of the basis (at the HartreeFock level) beyond 4-3 1G. The effect of correlation is to reduce Rx. However, it is not clear that the TS is tighter since the stronger C-H bond (see later) is lengthened, while the weaker C-F bond is shortened. Not as many calculations were done for the [CzH4-HCl] system (cf. Table 3), but we see, as in the above case, that the C2H4 parameters are relatively insensitive to basis set or level of theory. However, the variance in the remaining intermolecular parameters for X = C1 is larger than X = F (for the same level and basis set) by roughly a factor of 2 in the angles (a,8) and 4 in the lengths ( R H x Rx). , Rx, for example, changes by 0.1 1 A between RHF/4-31G and MP2/4-31G for X = C1, whereas the change is 0.02 8, for X = F. Again, this distance decreases in the correlated structure. In comparing the two halogens it should be noted that the difference in Rx between F and C1 is much greater than the variance for the several calculations of either halide separately. For the heavier halogens, Br and I, an effective core potential

The Journal of Physical Chemistry, Vol. 98, No. 34, 1994 8361

TABLE 4 RHF Transition-State Geometry' for [C2&-HX] with X = C1, Br, and I Obtained Using the LANL Effective Core Potential and the LANLlDZ Basis' LANLlDZ

RHX CY

B Rx Rcc &,,HI

Rc~H, LIH~C~H' UH~C~H, UC~C,,HI

UH~C~C,,

ab initio C1 1.8697 25.029 80.799 2.8373 1.3822 1.0739 1.0700 115.990 116.514 118.779 121.605

CI

Br

I

1.8745 24.111 83.258 2.8678 1.3982 1.0748 1.0729 115.896 116.468 118.339 121.593

2.0521 22.038 86.258 3.0817 1.4008 1.0752 1.0735 115.585 116.571 118.054 121.526

2.2718 20.058 89.303 3.3321 1.4060 1.0759 1.0740 115.188 116.660 117.538 121.482

a The geometrical parameters correspond to those shown in Figure 1. Angles are in degrees and distances in angstroms. An ab initio 4-31G calculation for X = C1 is also included for comparison purposes.

(ECP) was introduced to make the calculations feasible. In this regard, we used the LANL formulation of Wadt and Hay26 with thedouble-{LANLlDZ basis, which is a (3s3p)/[2s2p] valence electron basis for the halogen along with a D95V27 basis oncarbon. For [C2H4-HCl] the calculations can be done with or without the ECP, which provides a useful check. The first two columns of Table 4 present Hartree-Fock results for an ab initio 4-31G, and an LANLlDZ, treatment of the [C2€14-HCl] TS geometry. The agreement between these calculations, both of which employ a double-!: basis, is satisfactory since geometry differences for the characteristic parameters of the reaction complex are, on the whole, substantially less than those asssociated with extending the basis or including electron correlation. Although the analogous calculations were not feasible for Br and I, we will assume that they would give similar results. In that event, the change in Rx reported in the last three columns of Table 4 for X = C1, Br, and I is considerably larger than the error due to using an ECP. B. ActivationEnergy. Besides the calculations described above for the TS, we also obtained optimum geometries for three additional stationary points: CzH5X (staggered), C2HsX (eclipsed), and C2H4 HX. For X = F and C1, single-point energies were, then, determined for all stationary points at the HF, MP2, and MP4 levels of theory using the 4-31G, 6-31G**, and 6-31 1G** basis sets. Not all possible combinations were considered, only those needed to draw the general conclusions given below. Finally, zero-point vibrational energy corrections, obtained from RHF/4-3 1G calculations, were added to the computed electronic energy differences in order to compare directly with experiment. (Often the R H F ZPVEs are scaled by 0.89, but this was not done here since it would result in an insignificant additive factor of about 0.5 kcal/md in each case.) Calculated single-point energies at the four stationary points are reported for X = F in Table 5 and X = C1 in Table 6. Given the particular basis set and level of correlation treatment, we see that E, is little affected by the choice of optimized geometry. For example, consider the value of E, obtained from the set of RHF/ 6-31G** single-point energy calculations. At the RHF/4-3 1G geometry (Le. RHF/6-31G**//RHF/4-31G) E , = 76.2 kcal/ mol for X = F. Switching to the RHF/6-31G** geometry (keeping everything else the same), we obtain 76.0 kcal/mol, a differenceof only 0.2 kcal/mol, while at the MP2/4-3 1G geometry (again, keeping everything else the same) E, = 74.8 kcal/mol. For X = C1, the analogous values are 61.4,61.8, and 62.5 kcal/ mol, respectively. Similarly, we may compare MP2/4-3 1G// RHF/4-31G with MP2/4-31G//MP2/4-31G, as well as MP2/ 6-3 lG**//RHF/4-31G with MP2/6-31G**//MP2/4-3 1G and MP4/6-31G**//RHF/4-31G with MP4/6-31G**//MP2/431G. The maximum difference in any of these cases is 1.3 kcal/

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8362 The Journal of Physical Chemistry, Vol. 98, No. 34, 1994

Toto et al.

TABLE 5 Relative Energies. (in kcal/mol) of Stationary Points on the Potential Energy Surfnce for Concerted Elimination of HF from C a s F A = Staggered; B = Eclispsed; C = Transition State; and D = Products geometry single-point energy RHF/4-31G

mF/6-31G**

RHF/6-3 1G

MP2/4-31G

A B C D A B C D A B C D A

B C D MP2/6-3 1G**

A

MP2/6-311GS*

B C D A B C D

MP4/6-31G1*

A

MP4/6-311GS*

B C D A B C D

RHF/4-31G 0.0 (-177.845 03) 3.2 69.5 16.9 0.0 (-178.083 90) 3.6 76.2 15.9 0.0 (-178.128 38) 3.6 73.8 12.0 0.0 (-178.150 23) 3.5 61.2 15.0 0.0 (-178.548 40) 3.9 66.2 17.9 0.0 (-178.638 331 3.9 . 66.2 17.9 0.0 (-178.591 63) 3.8 65.2 18.0 0.0 (-178.684 40) 3.8 62.9 13.0

MP2/4-3 1G

RHF/6-31GS*

0.0 (-178.080 50) 3.6 74.8 15.9

0.0 (-178.085 40) 3.5 76.0 16.5

0.0 (-178.155 99) 3.5 61.4 14.8 0.0 (-178.546 81) 3.9 64.9 17.1

0.0 (-178.590 53) 3.7 64.1 17.3

0.0 (-178.518 90) 63.8

a The total energy in au is given in parentheses for the staggered configuration, Zero-point vibrational corrections, taken from an RHF/4-3 1G treatment, have been included. All correlation calculations except MP2/4-31G were performed with the core orbitals frozen.

TABLE 6 Relative Energies. (in kcal/mol) of Stationary Points on the Potential Energy Surface for Concerted Elimination of HCI from C~HSCI:A = Staggered; B = Eclipsed; C = Transition State; and D = Products geometry single-point energy RHF/4-3 1G

RHF/6-31G**

A B C D A B C

D RHF/6-311G**

A

B C

D MP2/4-31G

A

B C

D MP2/6-31G**

A

B C

D MP2/6-311GS*

A

B C

D MP4/6-3 1G**

A

B C

D MP4/6-311G**

A

B C

D

RHF/4-31G 0.0 (-537.526 11) 3.5 58.0 19.5 0.0 (-538.136 16) 3.7 61.4 15.7 0.0 (538.175 741 3.8 58.9 10.8 0.0 (-537.757 05) 3.7 60.6 18.2 0.0 (-538.559 80) 4.0 65.9 17.8 0.0 (-538.621 21) 4.2 63.9 15.3 0.0 (-538.612 43) 3.9 65.0 16.4 0.0 (-538.676 32) 4.1 63.0 14.4

MP2/4-31G

RHF/6-3 1G**

0.0 (-538.135 09) 3.8 62.5 14.5

0.0 (-538.139 34) 3.7 61.8 16.3

0.0 (-537.7580) 3.6 60.2 17.8 0.0 (-538.559 24) 4.0 65.7 17.7

0.0 (-538.612 24) 3.9 64.5 16.2

The total energy in au is given in parentheses for the staggered configuration. Zero-point vibrational corrections, taken from an RHF/4-31G treatment, have been included. All correlation calculations except MP2/4-31G were performed with the core orbitals frozen. a

1,2 Hydrogen Halide Elimination from Ethyl Halides

The Journal of Physical Chemistry, Vol. 98, No. 34, 1994

TABLE 7: MP2 and MP4 Relative Energiess (in kcal/mol) of Stationary Points on the Potential Energy Surface for Concerted Elimination of HX (X = CI, Br, I) from CzHsX: A = Staggered; B = Eclipsed; C = Transition State; and D = Products LANLIDZb LANLlDZ**' X/3-21G*&6-31G**d MP2 MP4 MP2 MP4 MP2 MP4

x = CI

A

0.0

0.0

B

D

3.8 60.4 16.8

3.7 59.6 15.4

A

0.0

0.0

B

3.7 61.6 15.0 0.0

C

0.0 4.0

68.4 14.8

0.0

3.9 67.6 13.6

0.0 4.1

66.8 14.8

0.0

3.9 65.8 13.7

X = Br C

D A B C

3.6 59.6 18.3

0.0 3.7

0.0 3.5

65.4 18.9

64.1 16.7 X=I

0.0

0.0

0.0

0.0

3.9 62.3 19.4

0.0 3.6

60.9 17.3

3.8 3.9 3.9 3.7 60.4 67.4 64.4 63.7 19.3 D 21.8 20.9 18.5 The energy in au of the staggeredconfiguration,including the RHF/ LANL 1DZ zero-point vibrationalcorrectionis (reading from left to right and,then,toptobottom)-93.532 32,-93.568 15,-93.792 25,-93.844 50, -536.393 34,-536.446 16,-91.751 13,-91.786 29,-92.001 84,-92.050 78, -2649.203 06, -2649.251 90, -89.976 65, -90.010 85, -90.201 57, and -90.249 17 au, respectively. All geometry calculations were performed at the RHF/LANLlDZ geometry. *The LANLlDZ basis in the Gaussian92 program is taken from ref 30 and is described in the text. This calculation used an effective core potential. LANLlDZ plus polarization function on X and a 6-31G** basis on C&. The d orbital exponents on CI, Br, and I are 0.75, 0.39, and 0.39, respectively. This calculationusedaneffectivecore potential. Thisisanabiniriotreatment. The 3-21G* basis for CI was taken from Gaussian92 and the 3-21G* basis for Br from ref 32. A 6-31G**basis was used for the C2H5 moiety.

mol for X = F and 0.5 kcal/mol for X = C1. Although a similar study was not done for X = Br and I, it seems reasonable to assume that E, will be insensitive to geometry for these halogens as well. The basis set dependence in the single-point determination of E, can be illustrated by comparing values taken from calculations using the RHF/4-3 1G geometry (changing the geometry will have little effect, as seen above). For X = F (Table 5), E, increases by 6.7 kcal/mol from RHF/4-31G to RHF/6-31G** and then decreases by 2.4 kcal/mol on going to RHF/6-3 1lG**, while the corresponding changes (at the same geometry) in the series MP2/ 4-31G MP2/6-31G** MP2/6-311G** are +5.0 and -2.3 kcal/mol. At the MP4 level the difference between the 6-31G** and the 6-311G** basis is, again, -2.3 kcal/mol. The same comparisons can be made for X = C1 (Table 6). For 4-31G 6-31G** 6-31 1G** the successive AE,'s are +3.4 and -2.5 at the R H F level and +5.3 and -2.0 at the MP2 level. At the MP4 level AE, = -2.0 for 6-31G** 6-31 1G**. So there can be a significant difference associated with including polarization functions, but further splitting of the valence shell from double-{ to triple-{ causes a relatively small effect. Note also that the basis set effect varies little from R H F to MP2 to MP4 and, furthermore, that X = F and X = C1 behave in a parallel fashion. Given the geometry and the basis set for the single-point calculations, we find, just as Sola et n1.21 did, that correlation substantially decreases the barrier height for elimination of HF. For X = Cl, on the other hand, correlation generally leads to a small increase in E,. In order to compare X = Br and I with X = F and C1, we carried out the set of calculations reported in Table 7. This table gives MP2 and MP4 single-point energies, obtained a t the RHF/ LANLlDZ optimized geometry, for the same four stationary points as above. Several different calculations, both with and without an ECP, were carried out. These include an ECP with

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8363

TABLE 8: Best Calculated Activation Energies (kcal/mol) for RX Elimination from CzH& Where X = F, CI, Br, and 1' experiment average* preferredc theory this work 59.533 61.5 QHsF 60.0 CzHsCl 56.9 (57.8) 56.55J4 61.6 C2HsBr 53.0 53.85J5 56.7 51.4 50.05 57.0 C2HsI a The experimentalvalues are inciuded for comparison. Average of literaturevalues,see text. Estimated errors for individual measurements are generally 1-2 kcal/mol. Two earlier, less reliable, results for C2HsCl are included in the parentheses. The preferred values for X # F are J 5 C2HsF see text. those recommended by the cited a ~ t h o r s . ~ J ~For the LANLlDZ basis, as described previously, and with a LANLlDZ** basis (which contains a d polarization function on X-where the exponents on C1, Br, and I are 0.75,0.39, and 0.39, respectively-as well as a 6-31G** basis on the C2H5 moiety). An ab initio treatment was also done with a 3-21G* basis for X = C1 and BrZSalong with a 6-31G** basis for C2H5 (designated as X/3-21G*&6-31G**). As we have already found, in the case of X = F and C1, it is important for the heavier halogens to include polarization functions in the basis, and, in addition, the effect of these functions is quite similar for MP2 and MP4. We note that, for elimination of HC1, the E,obtainedin theall-electron MP4 treatment (=65.8 kcal/mol) is within 1 kcal/mol of the MP4/6-3 lG**//RHF/ 4-3 1G result (=65.0 kcal/mol). Furthermore, as far as the trend from C1 to Br is concerned, the LANLlDZ** calculation mimics the all-electron treatment fairly well; AE, is reproduced to within 1.5 kcal/mol. This gives us some confidence in using the LANLlDZ** value for comparing Br and I. Our best values for E, are reported in Table 8. They were obtained in the following manner. A set of MP4/6-31G**j/ RHF/6-31G** calculations was carried out for C ~ H S Fand , the resulting E, was reduced by 2.3 kcal/mol to account for the predictedeffectofemployinga 6-31 1G** basisinsteadof6-31G** in the MP4 single-point energy determination. (We used the RHF/6-31G** geometry instead of MP2/4-31G because the corrections compared to RHF/4-3 1G are greater in the former case as noted earlier.) This yields the reference value for X = F. For the remaining halogens we used the differences in E, taken from the best calculations that were done in common for the two halogens being compared. Thus, the MP4/6-31G**/ /RHF/4-31G results provide AE, for F C1; for C1 Br the MP4/(X/3-21G*&6-31G**) calculations (at the RHF/ LANL 1DZ geometry) were utilized; and for Br I we employed

-

MP4/LANLlDZ**//RHF/LANLlDZ.

-

-+

The experimental Ea'sfor X = C1, Br and I listed in Table 8 were simply obtained by averaging all literature values reported in various tabulations through 1967,1,5J4J5929 except for C1, in which case two earlier, less reliable, results were discounted (although they are included parenthetically). Two more recent studies on C2H#330J1 give E, values of 56.3 and 57.8 kcal/mol, respectively, and they are included in the average value of 56.9 kcal/mol. The first successful pyrolysis of C ~ H Swas F reported in 1968;32this and subsequent results are tabulated in the shocktube study of Tschuikow-Roux and co-workers in 1980.33 Their value of E, = 59.5 kcal/mol is taken as the preferred value. (Prior to 1968, data on alkyl fluorides were restricted to chemical activation studies,' which had been quite successful in predicting energy barriers for H F elimination, with a value of -60 kcal/ mol for C ~ H S Ffor , example.34) According to our theoretical calculations, the halogens F and CI have essentially the same E, as do the halogens Brand I. The decrease between the former and the latter value is 4.5-4.9 kcal/ mol. On the other hand, the experimental results show a steady decrease from F to I. One should not place too much stock in this difference, however, since it could be accounted for by the

Toto et al.

8364 The Journal of Physical Chemistry, Vol. 98, No. 34, 1994 TABLE 9 Calculated Atomic Charges at the Transition State in GHI-HFP F H CF CH A. Mulliken Population Analysis RHF/4-3 1Gb MP2/4-3 lGb MP2/4-31G//RHF/4-31G RHF/6-31G**b RHF/6-3lGZ*//RHF/4-31G MP2/6-31G**' MP2/6-31G**//RHF/4-31G

0.4362 0.2973 0.3025 0.4453 0.4516 0.3080 0.3140

-0.2758 -0.2069 -0.2054 -0.2451 -0.2475 -0.1962 -0.1800

-0,6021 -0.4564 -0.4774 -0.6084 -0.6208 -0.4501 -0.4823

0.4597 0.3660 0.3804 0.4082 0.4168 0.3383 0.3483

B. Electrostatic Potential (ESP) RHF/4-3 1Gb MP2/4-3 1Gb MP2/4-31G//RHF/4-31G RHF/6-3lGSSb RHF/6-31GS* RHF/4-31G MP2/6-31G**I' MP2/6-3lG**//RHF/4-3lG

0.4898 0.3518 0.3476 0.4563 0.4585 0.3374 0.3292

-0.2482 -0.2012 -0.1797 -0.2406 -0.2190 -0.2227 -0.1621

-0.5919 0.3502 -0,4429 0.2923 -0.4701 0.3022 -0.5223 0.3066 -0.5475 0.3080 -0,3848 0.2701 -0,4372 0.2700

For H atoms not involved in the four-center TS the charges have been summed into the carbon atom to which they arebonded. The carbon atoms are designated CFor CH depending upon whether initially bonded to F or H. The double diagonal line is omitted whenever the geometry and single-point energies are determined in the same basis. (1

experimental uncertainties of 1-2 kcal/mol on each measurement. The average discrepancy between theory and experiment is 4.2 kcal/mol which is reasonable for the level of calculations performed. C. Atomic Charges at the Transition State. Atomic charges for the [C2H4-HF] TS were obtained using both a Mulliken population analysis and theelectrostatic potential (ESP) method,35 with the results shown in Table 9. For convenience the charges on the H atoms of the nascent ethylene have been summed into the carbon atom to which they are bonded. For the effect of geometry, we may compare the MP2/4-31G and MP2/4-31G//RHF/4-31G calculations or RHF/6-31G** and RHF/6-3 1G* *//RHF/4-3 1G or MP2/6-3 1G* * and MP2/ 6-31G**//RHF/4-31Gn Except for thecorrelated ESP results, the difference in atomic charges, in each case, is less than 0.033e at each center. In order to get some idea of the basis set dependence, we compare the RHF/4-3 1G calculationwith RHF/ 6-31G**//RHF/4-31G and the MP2/4-31G//RHF/4-31G calculation with MP2/6-3 lG**//RHF/4-3 1G. The largest difference in atomic charges in either instance is less than 0.045e. Overall, the Mulliken populations are less sensitive to basis set than the ESP results and the correlated values are more consistent

than RHF. From this analysis, we conclude that polarization functions are of borderline significance and expect that further augmentations of the basis set beyond 6-31G** would have negligibleeffect. On theother hand, correlation isquiteimportant, as may be ascertained from examining the RHF/6-31G1*// RHF/4-31G vs MP2/6-3lG**//RHF/4-31G or RHF/4-31G vs MP2/4-3 lG//RHF/4-31G calculations. Finally, comparing Mulliken populations with charges obtained by fitting electrostatic potentials, we find significant differences in the range 0.07-0.1 le. Since Mulliken populations show less dependence on geometry and basis set, this is the method we prefer to use in this paper. For the [C2H4-HF] TS we take the MP2/6-31G** charges as the best values available. For the heavier (than F) halogens the basis set and ECP dependence were ascertained by inspecting the atomic charges obtained from an MP2 Mulliken population analysis and are reported in Table 10. Note, first, that the RHF/4-31G and LANLlDZ optimized geometries give MP2/6-31G** atomic charges for X = C1 that differ from one another by less than 0.005e. On this basis, we feel confident in using the LANLlDZ geometry for X = Br and I. When polarization functions are included within the ECP framework (i.e. LANLlDZ** vs LANLlDZ), the largest effect on the charge at any center is 0.03e, 0.06e, and 0.03efor C1, Br, and I, respectively. As expected, the LANLlDZ** values are, by and large, closer to those of the other two polarized basis sets (6-31G** and X/3-21G*&631G**). The maximum difference between LANLlDZ** and X/3-21GZ&6-31G** is 0.034e for X = C1 and 0.055e for X = Br, which we consider to be of borderline significance. However, the LANLlDZ** calculation reproduces the change from C1 to Brtowithin0.02e. We, therefore,assumethat theLANLlDZ** MP2 charges will give comparisons between Br and I with satisfactory accuracy. In the case of C1, the difference between X/3-21GS&6-31G** and 6-31G** is less than about 0.02e at each center. Hence, for the comparison between C1 and Br we feel that the MP2 X/3-21G*&6-31G** results are satisfactory. A summary of atomic charges at the [C2H4-HX] transition state is given in Table 1 1. These results were determined by the same general procedure employed in the previous section for activation energies. In this case an MP2/6-31G** treatment yields the reference value for X = F. The difference F C1 is obtained from common MP2/6-31G**//RHF/4-3lG calculations; C1 Br from MP2/(X/3-21G*&6-31G**)// RHF/LANLlDZ** calculations; and Br I from MP2/ LANLl DZ**//RHF/LANLlDZ calculations. A discussion of

-

-

-

TABLE 1 0 Atomic Charges from an MP2 Mulliken Population Analysis at the Transition State in [CZHd-HXl, Where X = CI, Br, and 1' 6-31G**b

LANL 1DZC

0.3578 (0.3530) -0.0044 (-0.0083) -0.5725 (-0.5681) 0.2191 (0.2233)

0.3167 -0,0366 -0.5058 0.2257

LANLIDZ*ld

X/3-2 1G* 8 6 - 3 1G**'

0.3418 -0,0204 -0.5390 0.2176

0.3519 -0.0182 -0.5733 0.2396

0.3435 -0.0072 -0.5390 0.2026

0.3731 -0.0056 -0.5935 0.2260

x = CI CCl CH C1 H

X = Br CBr

CH Br H

0.3064 -0.0133 -0.4752 -0,1821

X=I

CI CH I H

0.2788 0.0045 -0.4225 0.1392

0.3077 0.0225 -0.4562 0.1260

a All calculations (except those in parentheses) were done at the RHF/LANLlDZ optimized geometry. For H atoms not involved in the four-center TS the charges have been summed into the carbon atom to which they are bonded. The carbon atoms are designated CXor CH depending upon whether initially bonded to X or H. The MP2/6-3 1G** charges at the RHF/4-31G geometry are given in parentheses. e The LANLlDZ basis in the Gaussian92 program is taken from ref 30 and is described in the text. This calculation used an effective core potential. LANLlDZ plus polarization function on X and a 6-31G** basis on CZHJ.The d orbital exponents on CI,Br, and I are 0.75,0.39, and 0.39, respectively. This calculation used an effective core potential. e The 3-21G* basis on X was taken from Gaussian92 for CI and from ref 32 for Br. A 6-31G** basis was used for the C2H5 moiety.

The Journal of Physical Chemistry, Vol. 98, No. 34, 1994 8365

1,2 Hydrogen Halide Elimination from Ethyl Halides

TABLE 11: Best Calculated Atomic Charges at the Transition State for HX Elimination from C2H&, Where X = F, C1, Br, and I C2HsF C2HsCl C2HsBr C2HsI

cx

CH

X

H

0.3080 0.3470 0.3682 0.3324

4,1962 -0,0245 -0.0119 0.0178

-0.4501 -0.5359 -0.5561 -0.4733

0.3383 0.2133 0.1997 0.1231

TABLE 1 2 Transition State Bond Orders for HX Elimination (X = F, C1, Br, I) from C2H& Calculated Using Eql F(RHF/4-3 1G) F(RHF/6-3 1G**) CI(RHF/4-3 1G) Cl(RHF/LANLlDZ) Br(RHF/LANLlDZ) I(RHF/LANLl DZ)

HX

cx

CH

cc

0.25 0.25 0.11 0.11 0.10 0.08

0.11 0.13 0.03 0.02 0.02 0.01

0.39 0.41 0.51 0.55 0.58 0.62

1.54 1.56 1.63 1.60 1.60 1.59

the charges with reference to the various transition-state models is given in the next section. D. Comparison of TS Properties with Previous Models. In addition to the charge distribution in the TS there are two other important properties that characterize the various models for 1,2 H X elimination. One is the set of bond orders for the four bonds either broken or formed in the reaction, and the other is the TS geometry shown in Figure 3. In this figure we compare the RHF/ 4-31GTSgeometriesforX = FandCland theRHF/LANLlDZ geometries for X = C1, Br, and I. For X = F and C1 adding correlation at the MP2 level makes a relatively unimportant difference in the shift of TS bond lengths and angles from one halide to the other. A similar situation exists for adding polarization functions to the basis set. Thus, for the trends discussed below, it is sufficient to examine the geometries in Figure 3. Wherever possible, we have verified that our general conclusions remain valid at higher levels of treatment.

One of the salient geometrical features of the TS is the constancy of the C-C bond length, which is 1.397 f 0.015 A regardless36 of X. From the geometrical perspective, then, the degree of double-bond formation in the TS does not vary throughout the halogen series. On the other hand, the C-H bond decreases in length noticeably from X = F to X = C1 and continues to decrease, but much more slowly, thereafter. This means that, using geometry as a criterion, the C-H bond in the TS is weakest for X = F and approximately the same strength for the remaining three halogens with C1 < Br < I. As expected, the C-X and H-X bonds in the TS lengthen in the order F < C1 < Br < I. In fact, for all X other than F, rcx is given remarkably well by rcx = 1.63(rc + rx), where rc and rx are atomic covalent radii for carbon and X, respectively. This result may be rationalized by assuming a constant stretching factor for the TS and by noting27 that bond distances between atoms of opposite charge are not significantly altered from their covalent values, since the effect of the charge is to increase the radius of one atom while decreasing the radius of the other. A similar relation with a stretching constant of 1.42 applies almost as well to rHx. The four bond lengths discussed above determine the quadrilateral geometry of the four atoms directly involved in bond breaking or bond formation except for addition of any one of the bond angles.37 Looking at the CH-CX-X bond angle, we see that it decreases from approximately tetrahedral in the reactant to slightly less than 90' in the TS for X = F. From X = F to I, this TS angle closes down 2-3' between rows of the periodic table. The CX-CH-H angle varies in the opposite manner for all the transition states so that LCH-CX-X + LCX-CH-H = 170'. Along with the above bond angle at the CX carbon, we find that the three dimensional geometry is nearly planar; that is to say, the dihedral angle between the H2Cx plane and the plane perpendicular to the C-C bond turns out to be 84.5 f 4.3' (the H2Cx plane is tipped toward X) for all X. From this perspective,

a F

I

b

Br

I\

Figure 3. Transition state geometry for 1,2 HX elimination from C2HsX (X = F, C1, Br, I): (a) RHF/4-31G, (b) RHF/LANLlDZ. Only those bonds broken or formed during the reaction are shown.

8366 The Journal of Physical Chemistry, Vol. 98, No. 34, 1994 Cx is almost ethylenic. The CH carbon, on the other hand, is substantially more pyramidal with the corresponding dihedral angle equal to 117.6 f 2.9O. If the HZCHgroup were perfectly tetrahedral, the latter angle would be 1 18.1O. From the bond lengths in the TS, r(n), one can determine a set of geometry-based bond orders utilizing the Pauling relation:

n = exp([r, - r(n)]/0.26) where rs is the ordinary single-bond length.36 Since our purpose is to test the semiquantitative models of the TS discussed in the Introduction, it suffices here to use HartreeFock-calculated values for r, and r(n) as long as the same basis set is utilized to obtain both parameters. This geometric definition of n is the one that has been used in prior models; the various wave function definitions should lead to a similar picture. Our resulting bond orders are reported in Table 12. For X = F and C1 there is little variation between basis sets. The qualitative picture that emerges from the calculated bond orders is very different from either the BBH or the Setser models. As in the Setser model, the TS complex is very asymmetric, but it is the C-X and H-X bonds (rather than C-H and H-X) that are nearly broken, while the olefinic and C-H bonds are more strongly formed. For X = C1, but not X = F, Clavero et al.20 focus on the C-H bond and describe the TS as “bicentric”. Clearly, the TS is much better described as tricentric with the olefinic and C-H bonds a good deal less completely formed (roughly 5 6 6 0 % for C1, Br, and I) than Setser has suggested. The asymmetric (or tricentric) TS we have found in terms of bond orders is consistent with the near planarity or ethylenic character of CX as contrasted with the substantial pyramidalization of CH. It is also somewhat reminiscent of the carbocation picture, Le., the Maccoll model, which applies to electrophilic reactions in solution. As far as the semiion pair model is concerned, we observe that the C-C bond order assumed by BBH agrees fairly well with our calculations but all their other assumed bond orders are quite different from ours and the same is true of the MTJ modification. Although the general description of bond orders in the TS just provided is valid for all X, there is a distinct difference between F and the remaining halogens. For X # F, the TS is more like the carbocation of electrophilic addition in solution; the H X and CX bond orders are smaller than for X = F whereas the C H and CC bond orders are larger. The differences in n are in the range 0.05-0.20. Next we turn to the transition-state atomic charges presented in Table 11. Again the asymmetry of the TS is obvious, which contrasts sharply with the semiionic model either in the BBH form or in the MTJ modification. Although the character of the CH-H bond is sensitive to the particular halogen, it tends to be covalent, in general, whereas the character of the CX-X bond is insensitive to X and tends to be semiionic. The magnitude of the partial charge on the halogen is 0.50 f 0.05 in every case, which is consistent with the BBH treatment. However, the remaining atomic charges are much smaller in magnitude. The positive charge on CXis 0.34 0.03 and, except for X = F, CH is essentially neutral, while hydrogen has a partial charge of 0.17 0.05. X = F is, again, distinctly different from the other halogens. The latter are more carbocationic, as judged by the larger electronic charge on X, although the differences are modest, especially for I. Nevertheless, X is far from being a pure cation (Maccoll model) since its partial charge is much less than unity. The distinction between F and the remaining halogens is more striking when one compares the TS with the reactant. In the reactant the partial charge on X # F is relatively small in magnitude (