Characterization of the 1,1-HCl Elimination Reaction of Vibrationally

Article pubs.acs.org/JPCA

Characterization of the 1,1-HCl Elimination Reaction of Vibrationally Excited CD3CHFCl Molecules and Assignment of Threshold Energies for 1,1-HCl and 1,2-DCl plus 1,1-HF and 1,2-DF Elimination Reactions Timothy M. Brown,‡ Matthew J. Nestler,‡ Samuel M. Rossabi,‡ George L. Heard,‡ D. W. Setser,† and Bert E. Holmes*,‡ ‡

Downloaded by CENTRAL MICHIGAN UNIV on September 10, 2015 | http://pubs.acs.org Publication Date (Web): September 1, 2015 | doi: 10.1021/acs.jpca.5b06638

Department of Chemistry, University of North Carolina−Asheville, One University Heights, Asheville, North Carolina 28804-8511, United States and † Kansas State University, Manhattan, Kansas 66506, United States S Supporting Information *

ABSTRACT: Vibrationally excited CD3CHFCl molecules with 96 kcal mol−1 of energy were generated by the recombination of CD3 and CHFCl radicals in a room-temperature bath gas. The four competing unimolecular decomposition reactions, namely, 1,1-HCl and 1,2-DCl elimination and 1,1-HF and 1,2-DF elimination, were observed, and the individual rate constants were measured. The product branching fractions are 0.60, 0.27, 0.09, and 0.04 for 1,2-DCl, 1,1-HCl, 1,2-DF, and 1,1-HF elimination, respectively. Electronic structure calculations were used to define models of the four transition states. The statistical rate constants calculated from these models were compared to the experimental rate constants. The assigned threshold energies with ±2 kcal mol−1 uncertainty are 60, 72, 65, and 74 kcal mol−1 for the 1,2-DCl, 1,1-HCl, 1,2-DF, and 1,1-HF reactions, respectively. The loose structure of the 1,1-HX transition states, which is exemplified by the order of magnitude larger pre-exponential factor relative to the 1,2-HX elimination reactions, compensates for the high threshold energy; thus, the 1,1-HX elimination reaction rates can compete with the 1,2-HX elimination reactions for high levels of vibrational excitation in CD3CHFCl. The 1,1-HCl and 1,1-HF reactions are observed via the CD2CDF and CD2CDCl products formed from isomerization of the CD3CF and CD3CCl carbenes. These D-atom migration reactions are discussed, and the possibility of tunneling is evaluated. The transition states developed from the 1,1-HCl and 1,1-HF reactions of CD3CHFCl are compared to models for the HCl and HF elimination reactions of CHF2Cl, CHFCl2, and CH2FCl.

I. INTRODUCTION The four competitive unimolecular HCl and HF elimination reactions from CD3CHFCl* were selected for study by the chemical activation technique. The molecules, which are formed by the recombination of CD3 and CHFCl radicals at room temperature, have 96 kcal mol−1 of vibrational energy. The primary objective of the study is to characterize the 1,1HCl elimination reaction. The 1,1-HF elimination process has already been studied for the C2D5CHF21 and CD3CHF22 molecules, and comparison with 1,1-HCl elimination in a competitive environment is useful. The fate of the carbenes formed in conjunction with 1,1-HX (X = F, Cl, Br) elimination from 1,1-dihaloalkanes provides another interesting question.3−10 The rate of D atom migration and the contribution from tunneling in the isomerization of CD3CF and CD3CCl will be addressed. The 1,1-HCl elimination from CH2ClCHCl2 (CD2ClCHCl2) has been reported,11 but interpretation of the © 2015 American Chemical Society

experimental data needs to be revised with a better model of the transition state. The thermochemistry of CD3CF and CD3CCl is sufficiently well-established that assignment of a lower limit to the threshold energy (E0) for 1,1-HX elimination can be made. The energy profile for the CD3CHFCl system shown in Figure 1 illustrates this point. Since the transition state for 1,1-HX elimination also applies to the reverse reaction, the addition of the carbenes to HCl or HF, some information can be deduced about the threshold energy for the addition reactions from the threshold energies for 1,1-HX elimination. The transition states for 1,1-HX elimination from the chlorofluoromethanes can be related to those of CD3CHFCl, and the branching fractions12,13 for CHF2Cl, CHFCl2, and Received: July 10, 2015 Revised: August 19, 2015 Published: August 20, 2015 9441

DOI: 10.1021/acs.jpca.5b06638 J. Phys. Chem. A 2015, 119, 9441−9451

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The Journal of Physical Chemistry A

Figure 1. Energy profile for the four reaction channels of CD3CHFCl. The listed energies are based on known thermochemistry or the E0 values assigned from experiments of this study. The calculated threshold energies from MP2/6-311+G(2d,p) are 59.1, 66.5, 62.6, and 72.1 kcal mol−1 for 1,2-DCl, 1,1-HCl, 1,2-DF, and 1,1-HF, respectively. The potential energy barriers for D atom migration in CD3C−Cl and CD3C−F are calculated values; see text.

addition of CF3CHCH2 as a scavenger. The concentration of the iodine atoms are controlled by reaction with mercury. The experimental rate constants kexp are compared to calculated statistical rate constants to assign the threshold energy for each reaction channel. The energy required for isomerization (1,2-D atom migration) of CD3C−Cl and CD3C−F relative to the available energy should be noted; see Figure 1. Electronic-structure calculations were done using the Gaussian-09 suite19 of codes to obtain geometries of the transition states and molecules. The vibrational frequencies and moments of inertia are needed for CD3CHFCl and the four transition states plus information to describe the isomerization of CD3CF and CD3CCl. In previous studies of 1,2-HX elimination,16−18 halogen atom interchange, and 1,1-HF elimination reactions, various density-functional theory (DFT) methods with basis sets of double- and triple-ζ quality have been used to define transition states. For the purpose of obtaining frequencies and moments of inertia to be used in the calculation of statistical rate constants with E0 to be defined by comparison to the experimental rate constant, we (and others) have found that the results are not very sensitive to the DFT method or basis set. However, in the current study finding a satisfactory transition state for 1,1-HCl elimination proved to be a challenge when using B3PW-91 with 6-31G(d′,p′), 6311+G(2d,p), and cc-pVTZ basis sets, and M06-2X with 6311+G(2d,p). We finally used MP2 with the 6-311+G(2d,p) basis set to locate a suitable transition state for the 1,1-HCl process, and the models for all four transition states were evaluated by this method. In the search for the 1,1-HCl transition state, calculations with the CASSCF(4,4) method also were employed to refine the structure. Different DFT methods and basis sets do not give the same calculated threshold energy for a given reaction. That is not a major concern, since we use the experimental rate constants to assign threshold energies. Nevertheless, the trends in the calculated

CH2FCl can be compared to those from CD3CHFCl. The difference in threshold energies for HCl and HF elimination from CHF2Cl can be combined with the measured E0(HCl) from thermal activation experiments14 to estimate E0(HF). The CHF2Cl molecule has been a favorite for detailed studies of infrared-multiphoton excitation,13,15 and an assignment to E0(HF) will aid in establishing an upper bound to the energy distribution. Although most aspects of 1,2-HX elimination reactions from haloalkanes are understood, the variation of the experimental E0(HCl) and E0(HF) with substitution of a F atom on CCl and a Cl atom on CF do not follow the trends from electronicstructure calculations (the Cl and F subscripts denote the carbon atom from which the halogen atom is leaving). The present study with CD3CHFCl complements our studies of a series of 1,1,1-trihaloethane molecules CH3CCl3,16 CH3CF3,17 CH3CF2Cl, and CH3CFCl2,18 and this study with CD3CHFCl provides a direct comparison of 1,2-DCl and 1,2-DF elimination, which enables a better understanding of the role of the F and Cl substituents. Mercury photosensitization of a CD3I and CHFCl2 mixture was used to generate CD3 and CHFCl radicals in a roomtemperature bath gas; these radicals combine to produce chemically activated CD3CHFCl*. The unimolecular reactions produce CD2CHF (+DCl), CD2CHCl(+DF), CD3C−F (+HCl), and CD3C−Cl (+HF) as products. The carbenes isomerize to CD2CDF and CD2CDCl, and each reaction product can be identified by gas chromatography with a mass spectrometer for the detector. Experimental rate constants are measured for each reaction by comparing the ratio of decomposition product (Di) to the collisionally stabilized molecule, CD3CHFCl, as a function of pressure (kexp/kM[M] = [D]/[S], where kM is the rate constant for collisions of CD3CHFCl* with M). The vinyl chloride and vinyl fluoride products were protected from attack by Cl atoms by the 9442


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The Journal of Physical Chemistry A Table 1. Summary of Rate Constants and Threshold Energies for CD3CHFCl reactions

rate constant, Torr

kexp,a,b s−1

k⟨E⟩, s−1

E0,c kcal mol−1

CD3CHFCl → CD2CHF + DCl

62 ± 5d

8.0 ± 0.8 × 108

CD3CF: + HCl

29 ± 3d

3.7 ± 0.4 × 108

CD2CHCl + DF

9.4 ± 0.8d

1.2 ± 0.2 × 108

CD3CCl: + HF

4.6 ± 0.4d

0.58 ± 0.6 × 108

8.0 × 108 5.9 × 108 4.3 × 108 2.9 × 108 1.3 × 108 0.96 × 108 0.70 × 108 0.47 × 108

60 61 71 72 64 65 73 74

33.6 7.4

4.8 × 108 1.0 × 108

CD3CHF2 → CD2CHF + DFe CD3CF: + HFe

64 73

The collision constants were calculated from the following collision diameters, Å, and ε/k, K, values: CF3CHCH2 (4.90 and 250), CD3I (4.66 and 406), CHFCl2 (4.57 and 405), CD3CHFCl (4.49 and 370). The collision constants were 4.3 ± 0.1 × 10−10 cm3 molecule−1 s−1 for each of these three bath gases. The major bath gas is SF6 with a collision diameter of 5.20 Å and ε/k = 212 K, which give a collision constant of 3.9 × 10−10 cm3 molecule−1 s−1. Thus, the effective collision rate constant is 4.0 × 10−10 cm3 molecule−1 s−1. The collisional model for SF6 has been assigned20,21 as stepladder deactivation with ⟨ΔE⟩ = 6 kcal mol−1. Therefore, the experimentally measured rate constants were divided by 1.2 to obtain the experimental rate constant for the strong collision limit. bThe overall uncertainty was increased at least to ±10% to allow for the additional uncertainty associated with the collision rate constants. cThe calculated E0 were 59.1, 66.5, 62.6, and 72.1 kcal mol−1 for 1,2-DCl, 1,1-HCl, 1,2-DF, and 1,1-HF, respectively. dThe experimental rate constant in pressure units based on the strong collision limit; total rate = 105 ± 8 Torr. eThis information was taken from refs 1 and 2.


a

threshold energies and the calculated structures of the transition states provide insight at the molecular level. DFT methods were used to describe the isomerization reactions of CD3CF and CD3CCl.

CD3 + CHFCl → → CD3 + CD3 → CHFCl + CHFCl → →

II. EXPERIMENTAL METHODS Samples of CD3I, CHFCl2, and CF3CHCH2 plus a droplet of Hg were loaded into quartz vessels ranging in size from 3.285 to 1050 cm3 and irradiated with the 253.7 nm resonance line of a 200 W Hg germicidal lamp. Sulfur hexafluoride was added to the vessels to achieve higher pressure. The background regarding the use of the Hg sensitization technique to generate radicals from chlorine- and iodine-containing molecules and the use of CF3CHCH2 as a Cl atom scavenger is described in ref 16. The molar ratios of CD3I/CHFCl2/CF3CHCH2/SF6 were 8:3:4:40. Irradiation times were usually 10 min or less, and the vessels were cooled during irradiation to maintain room temperature. The Hg(3P1) atoms mainly form Hg + Cl and HgCl in the interaction with CHFCl2. The CD3 radicals are formed from interaction with Hg(3P1) and from I atom abstraction by CHFCl radicals. Chlorine atoms react more rapidly with CF3CHCH2 than do CD3 or CHFCl radicals. Normally less than 5% of the CHFCl2 was converted into CHFCl radicals and either HgCl or Cl. The conversion of CD3I to CD3 radicals was typically 15% depending on pressure in the reaction vessel. Thus, for most trials the CF3CHCH2 was much more than 25 times greater than the concentration of atomic chlorine, effectively protecting the alkene products from attack by Cl. After irradiation the contents of the vessel were transferred to the vacuum line of the gas chromatograph, which had a mass spectrometer (Shimadzu QP5000) as detector, and analyzed with an RTX-1701 column. Commercial samples of CH3CHFCl, CH2CHCl, and CH2CHF were available for identification and calibration. The calibration factors for the CH2CHCl/CH3CHFCl and CH2CHF/CH3CHFCl ratios were 2.53 ± 0.14 and 5.37 ± 0.22, respectively. The principal reactions of the CD3 and CHFCl radicals, which are combination reactions at room temperature, are listed below. The asterisk denotes vibrational excitation.

CD3CHFCl∗ a. CD3H + CFCl CD3CD3∗ b. ∗ CHFClCHFCl c. CH 2FCl + CFCl

(1)

The CHFCl−CHFCl recombination product, which consisted of meso- and d,l-stereoisomers, was the lowest yield of the three recombination products, because the concentration of CD3 was higher than that of CHFCl. The CHFClCHFCl* molecules can isomerize by Cl/F interchange18 to give CHF2CHCl2*, as well as undergo several HX elimination reactions. Because of the chemical complexity and small yield, no attempt was made to study the unimolecular reactions of CHFClCHFCl*. The CFCl carbene can recombine, interact with CD3 and CHFCl radicals to give CD2CFCl (+ D atom) and CFClCFCl (+ H atom), or be scavenged by CF3CHCH2, CD3I, or CHFCl2. These processes do not interfere with observation of the decomposition reactions of CD3CHFCl*, which are listed next. CD3CHFCl∗ → → → →

DCl + CD2 CHF DF + CD2 CHCl HCl + CD3CF HF + CD3CCl

a. b. c. d.

(2)

The CD3CF and CD3CCl carbenes isomerize by D atom migration to give CD2CDF and CD2CDCl, which can be differentiated from the products of reactions 2a,b with a mass spectrometer as the detector of the gas chromatograph. The experimental rate constants are measured relative to the collisional deactivation rate. At a given bath gas pressure, the ratio of the concentration of a decomposition product Di to the concentration of the stabilized molecule S is equal to the ratio of the rate constant kexp, to the collision frequency kM[M]. This simple formulation is true for efficient collisional deactivation, which should apply to collisions of CD3CHFCl* with CD3I and CF3CHCH2 at room temperature.20−22 However, the deactivation by SF6 and CFCl2H are likely to be less efficient 9443


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than unit deactivation, and a 6 kcal mol−1 stepladder model has been found for the deactivation of similar excited molecules.20,21 This minor complication will be included in the analysis of the data. The collision rate constant for each collision pair is given by the standard expression kM = πd2(8kT/ πμ)1/2Ω(2,2)*; the collision diameters d and the ε/k values used to calculate kM are given in a footnote of Table 1. Fitting linear plots of the Di/S ratios versus pressure−1 is a common way to obtain average rate constants.16−18 The product branching fractions from reaction 2 are equivalent to the ratios of the rate constants, and experimental product-branching ratios and fractions also can be used to help define the best average rate constant for each reaction channel.

III. EXPERIMENTAL RESULTS The experimental measurements of the decomposition and stabilization product ratios and branching fractions are presented in Figures 2−4. The plots display the results of Figure 3. Plots of the branching fractions for (1,2-DCl + 1,1-HCl elimination)/(total decomposition) (●) and (1,2-DF + 1,1-HF elimination)/(total decomposition) (□) vs pressure−1.

Figure 2. Plot of the ratio of the sum of the four decomposition products divided by the stabilized CD3CHFCl product vs pressure−1. The slope and intercept of the linear least-squares fit to the data are 126 ± 9 and 0.005 ± 0.163, and the correlation coefficient is 0.95.

29−36 separate experiments over the 8−80 Torr pressure range. We decided first to obtain the total unimolecular rate constant, in pressure units, by plotting the sum of the yields of the four decomposition products divided by the stabilized CD3CHFCl yield versus pressure−1, and this plot is shown in Figure 2. We also examined the individual rate constant (kexp = pressure (D/S)) from each experiment, since the data of Figure 2 do not extend to the low range of D/S. From these considerations, 126 ± 9 Torr was selected as the average total rate constant. Since this rate constant is for SF6 as the major bath gas, this number needs to be reduced by a factor of 1.2 to account for a 6−8 kcal mol−1 deactivation model.20,21 Thus, the strong collision limit would be 105 ± 8 Torr. The next step is to divide the rate constant into its components using the product-branching fractions of Figure 3. The branching fractions for the CD2CHF + CD2CDF and CD2CHCl + CD2CDCl products shown in Figure 3 do not show any dependence on pressure, and the average values are 0.87 ± 0.05 and 0.13 ± 0.04. The rate constant ratios

Figure 4. Plots of the branching ratios of the 1,2-DCl/1,1-HCl reactions (●) (CD2CHF/CD2CDF) and 1,2-DF/1,1-HF reactions (□) (CD2CHCl/CD2CDCl) vs pressure−1; these product ratios are derived from comparison of the mass ratios (48/49 and 64/ 65) of the parent ions.

for the DCl/HCl and DF/HF elimination reactions are just the ratios of the masses of vinyl fluoride-d2/vinyl fluoride-d3 (m/z = 48/49) and vinyl chloride-d2/vinyl chloride-d3 (m/z = 64/65), and no calibration of the detection system is required. The plots in Figure 4 for both ratios follow the same pattern. The data seem to fall into a low-pressure regime, p−1 > 0.05, with ratios of 2.2 ± 0.1 and a higher-pressure regime with limiting ratios of 2.7 ± 0.4. There could be three explanations of the pressure dependence. The first could be just experimental uncertainty, especially for the higher-pressure data because of the low yields of vinyl chloride-d3 and vinyl fluoride-d3. The second explanation could be that some of the CD3CF and CD3CCl do not isomerize at the higher pressures. The third 9444


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of the CD3 and CHFCl radicals. The enthalpies of formation at 298 K for CH3 (35.1 kcal mol−1),27 CHFCl (−14.5 kcal mol−1),27 and CH3CHFCl (−74.9 kcal mol−1)28 give −95.5 kcal mol−1 as the enthalpy change for the recombination. Conversion to 0 K and adding the thermal energy of the radicals gives ⟨E⟩ = 96.3 kcal mol−1. The uncertainty is ±2−3 kcal mol−1. However, the average energy for CH3CHF2* from recombination of CH3 and CHF2 is also 96 kcal mol−1, and that value is based on self-consistent enthalpies of formation.29 Thus, ⟨E⟩ = 96 kcal mol−1 seems to be reliable for CH3CHFCl* or CD3CHFCl*, and this energy will be used to assign the E0 values from the calculated rate constants using the relationship k⟨E⟩ = kexp. The minimum values for threshold energies shown in Figure 1 for 1,1-HCl and 1,1-HF elimination were assigned from the enthalpies of the 1,2-DF and 1,2-DCl elimination reactions plus that for the H-atom rearrangement reactions. Electronic structure calculations have given −50.7 kcal mol−1 for CH3CF3 and −58 kcal mol−1 for CH3CCl4. We also did calculations with several DFT methods; the isomerization energies from calculations with B3PW-91/6-311+G(2d,p) were −52.5 and −56.6 kcal mol−1 for CD3CF and CD3CCl, respectively. We adopted values of 52 and 57 kcal mol−1 as shown in Figure 1; the estimated uncertainty is ±2 kcal mol−1. We also calculated threshold energies for the isomerization of CD3CF and CD3CCl, and the values were 14.0 and 10.2 kcal mol−1, respectively. Hu5 has reported 14.6 and 11.0 kcal mol−1; Bacskay3 found 16.9 kcal mol−1 for CH3CF, and Albu and coworkers4 used 12.0 kcal mol−1 in their study of the thermal isomerization rate of CH3CCl. We selected 15 and 11 kcal mol−1 in Figure 1 as the threshold energies for CD3CF and CD3CCl, respectively. B. Calculation of kE and Assignment of E0 Values. To calculate the RRKM rate constants kE as a function of energy, the transition-state structures of the four reaction channels must be identified. Then the vibrational frequencies and moments of inertia are used to obtain kE. It is desirable to use the same computational method and basis set for each transition state. In past work involving mainly 1,2-HX (X = F, Cl, Br) elimination and halogen-atom interchange reactions,16−18,30,31 we used various DFT methods. However, finding a satisfactory transition state for 1,1-HCl elimination proved to be a challenge when using DFT methods (B3PW-91 with 6-31G(d′,p′), 6-311+G(2d,p), or cc-pVTZ basis sets) and M06-2X with 6-311+G(2d,p). We found that the MP2 approach with the 6-311+G(2d,p) basis set located the 1,1HCl transition state, as well as the other three transition states. Each transition state was verified by the intrinsic reaction coordinate test. Previous surveys32,33 of computational methods have found that MP2 calculations tend to overestimate the threshold energies of 1,2-HX elimination reactions, and that is why DFT methods have been favored. However, vibrational frequencies from DFT and MP2 methods are very similar, and frequencies are our principal concern. Diagrams of the four transition states are presented in Figure 5. The transition states for 1,2-DF and 1,1-HF elimination closely resemble those recently reported1 for C2D5CHF2. The three-centered transition state has lower frequencies than the four-centered case because the in-ring C−F distance is longer, and the structure retains an internal rotation. Comparison of the 1,1-HF and 1,1HCl transition states shows that the latter has a much smaller in-ring H−C−Cl angle, 9.9°, than the corresponding angle, 28°, in the 1,1-HF transition state. The basic structure for the 1,1-

explanation, which is the most probable, is that the ratio is intrinsically pressure dependent23,24 because of the stepwise deactivation of CD3CHFCl* and the stronger energy dependence of the 1,1-HX elimination rate constants. Evaluation of the 1,2-DCl/1,1-HCl ratio versus pressure using a simple stepladder deactivation model of 6 kcal mol−1 and the statistical rate constants developed in section B showed that the ratio increased by ∼20% from the low-pressure limit to the highpressure region. Irrespective of the correct explanation, the lower-pressure data provide the best measure for the relative rate constants. We will use 2.2 for both branching ratios, and the recommended product branching fractions are 0.60, 0.27, 0.09, and 0.04 for 1,2-DCl, 1,1-HCl, 1,2-DF, and 1,1-HF, respectively. The individual rate constants in pressure units are 62, 29, 9.4, and 4.6 Torr; these values are converted to s−1 units in Table 1. In preliminary work, a separate set of experiments was done to identify the product branching ratios for the DCl/HCl and DF/HF processes. For these experiments the very low-pressure range (less than 5 Torr) was emphasized, and all the CD3CHFCl* molecules were converted to products. The 1,2DCl/1,1-HCl ratio was 1.9 ± 0.2, that is, virtually the same as for the plot in Figure 4. However, the 1,2-DF/1,1-HF ratios were very scattered and tended to be less than 2.0. Furthermore, the ratio showed a dependence on the amount of CF3CHCH2 scavenger added to the photolysis vessel. The implication is that another source of CD2CDCl, but not CD2CHCl, exists in the photolysis system. One possibility involves the following set of reactions that includes C2D6, C2D4, and radicals, R. Since CD2CDCl has the smallest yield of the four products, it is especially susceptible to side reactions. C2D6 + Cl (or Hg ∗) → C2D5 + DCl (or Hg + D) C2D5 + R → C2D4 + RD C2D4 + Cl → CD2 ClCD2 CD2 ClCD2 + R → CDClCD2 + RD

(3)

With sufficient addition of CF3CHCH2 to control the Cl atom concentration, the 1,2-DF/1,1-HF product ratio was close to 2.0, and that information was used to design the experiments that are displayed in Figures 2, 3, and 4. In summary, the branching fractions assigned to the four elimination reactions seem quite reliable. The absolute values of the rate constants have more uncertainty because of the absence of data at sufficiently high pressures to reach the limiting values of the rate constants. The sum of the HF and DF elimination rate constants from CD3CHFCl* are about one-half of those2 for CD3CHF2* after adjustment to the same reaction path degeneracy. We found no experimental evidence for trapping of either CD3CF or CD3CCl, and we analyzed the system assuming that the measured CD2CDF and CD2 CDCl yields represent the total 1,1-HCl and 1,1-HF elimination reactions. The average vibrational energy of the CD2CDCl molecules will be ∼74 kcal mol−1 of energy following the isomerization of CD3CCl; however, DCl elimination to give C2D2 was not observed and would not be expected, since the threshold energy25,26 is ∼70 kcal mol−1.

IV. COMPUTATIONAL RESULTS A. Thermochemistry. The average energy of the CD3CHFCl* molecules was assigned from the enthalpy of the radical combination reaction at 0 K plus the thermal energy 9445


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atom and the Cl atom leads to a large (I†/I)1/2 ratio of 1.85, whereas that for 1,1-HF elimination is 1.41, and those for 1,2HX elimination are 1.10 (DF) and 1.29 (DCl). The vibrational frequencies (see the Supporting Information) were used to calculate sums of internal states for the transition states and the density of states for the molecule. These were used in the standard expression for the statistical rate constant, eq 4, at an energy E for the molecule and E − E0 for the transition state. The sums of internal states of the transition states, ∑P†(E − E0), and the density of internal states of the molecule, N*(E), were computed from harmonic frequencies with the Multiwell code of Barker.34


kE = (s†/h)(I †/I )1/2

∑ P†(E − E0)/N *(E)

(4)

The I†/I term is the ratio of overall rotational moments of inertia, and s† is the reaction path degeneracy. The threshold energy for each reaction channel was assigned by matching k⟨E⟩ to the kexp, which are listed in Table 1. The fitting of the individual kE to kexp depends on the properties of each transition state and E − E0, since N*(E) is constant. The relative values for (I†/I)1/2∑P†(E − E0) at E − E0 = 22 kcal mol−1 for the 1,2-DF, 1,2-DCl, 1,1-HF, and 1,1-HCl transition states are 1.0, 1.78, 12.9, and 36.1. The closest match to kexp were obtained with E0 = 60, 72, 65, and 74 kcal mol−1 for 1,2DCl, 1,1-HCl, 1,2-DF, and 1,1-HF, respectively. Additional kE are given in Table 1 to illustrate the effect from changing E0 by 1 kcal mol−1, which alters the rate constant by a factor of 1.32. The uncertainty in the assigned E0 values is ±2 kcal mol−1. The assigned E0 for the 1,2-DF and 1,1-HF for CD3CHFCl are nearly identical to those previously1 assigned to CD3CHF2. At first glance, the similar E0 for both 1,1-HF and 1,1-HCl elimination seems strange given the 6 times larger rate constant for 1,1-HCl elimination. However, the lower frequencies for the HCl transition state give higher sum of states in eq 4; the ratio for 20 kcal mol−1 of energy in each transition state is 2.1. Finally, we note that the assigned E0 for the 1,1-HX transition states meet the minimum requirement imposed by the thermochemistry given in Figure 1. The calculated rate constants for 1,1-HX elimination from the MP2 models of the transition state and CD3CHFCl were compared to those from the CASSCF models. The rate constants for a common E0 were the same to within 10%; however, this was largely fortuitous because of counter-balancing effects in the sums and densities of states from the two computational methods. The sums of states for the two 1,1-HX transition states were actually 1.35 larger for the MP2 model. The MP2 calculated E0 values are 59.1, 66.5, 62.6, and 72.1 kcal mol−1 for 1,2-DCl, 1,1-HCl, 1,2-DF, and 1,1-HF elimination, respectively. The moderately good agreement with the experimental values will be compared to the trends in the calculated E0 for C2H5F, C2H5Cl, CH3CHCl2, and CH3CHF2 in the Discussion Section before judging the reliability of the MP2 method for the computation of threshold energies. The product-branching ratio for CHF2Cl* with an energy of 102 kcal mol−1 was measured from infrared chemiluminescence as 0.24 in favor of HCl elimination.12 This branching ratio corresponds to a difference in E0(HF) − E0(HCl) of 12 kcal mol−1, according to the ratio of rate constants calculated for HF and HCl elimination. Combining this information with the preferred threshold energy14 for HCl elimination of 54.9 kcal mol−1 gives E0(HF) = 66.9 kcal mol−1. Within the experimental uncertainty of the branching ratio for CHF2Cl, the difference in

Figure 5. Diagrams of the transition states for the four reaction channels of CD3CHFCl from MP2 calculations. For reference the bond lengths in CH3CHCFCl are 1.088 (C−H), 1.376 (C−F), and 1.793 (C−Cl) Å, and in CFClCHF they are 1.32 (C−F) and 1.72 (C−Cl) Å. The bond lengths of the HCl and HF molecues are 1.274 and 0.917 Å, respectively.

HCl transition state was confirmed by extensive calculations with the CASSCF(4,4) method using the 6-311+G(2d,p) basis set. The 1,1-HX transition states also are the transition states for the addition of carbenes to HX, and in fact, they resemble the addition step more than a traditional elimination reaction. Calculations also were done for CHFCl2 and CHF2Cl to characterize the structures of the transition states for HCl and HF elimination. Although experimental rate constants from chemical activation experiments are not available, branching ratios can be used to assign differences in threshold energies. Further discussion about the structure of the transition states is reserved until the threshold energies are assigned. The models (vibrational frequencies and moments of inertia) for the CD3CHFCl system plus those for CHF2Cl, CHFCl2, and CH2FCl are summarized in the Supporting Information. The CD3 torsional frequencies of CD3CHFCl and the 1,1HX transition states were replaced by internal rotors. The potential energy barrier to internal rotation in the carbenes is very low, and free-rotors were used in the 1,1-HX transition states. The calculated potential barrier for CD3CHFCl was 3.81 kcal mol−1. The reduced moments of inertia were 5.92 amu Å2 for CD3CHFCl and 6.09 and 6.10 amu Å2 for the 1,1-HF and 1,1-HCl transition states, respectively. Low frequencies make the most important contributions to the number of internal states. The three lowest frequencies for the 1,1-HF transition state, excluding the CD3 torsion, are 142, 223, and 357 cm−1. These values were compared to results from several DFT calculations, and the differences were between 1 and 4%. The corresponding three frequencies for the 1,1-HCl transition state are 72, 119, and 458 cm−1; these can be compared to the CASSCF results, which were 102, 110, and 487 cm−1. Given the difficulty in defining the 1,1-HCl transition state, the uncertainty in these frequencies may be larger than for the 1,1-HF transition state. The long distance between the carbon 9446


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threshold energies from the MP2 calculations, 13.3 kcal mol−1, would also match the data. Experimental data for the branching ratio are not available for CHFCl2. However, the calculated difference in threshold energies for CHFCl2 of 10 kcal mol−1 predicts a branching ratio of 0.054 for a excitation energy of 102 kcal mol−1. The difference in branching ratios for CHF2Cl and CHFCl2 arises mainly from the changes in reaction path degeneracy. These differences in threshold energies are consistent with the observation of only HCl elimination in infrared-multiphoton excitation experiments.13,15 The calculated (MP2) difference in threshold energies for CH2FCl is only 2 kcal mol−1, and HF elimination may be more competitive than for CHF2Cl and CHFCl2.

V. DISCUSSION A. Transition States for 1,1-HCl and 1,1-HF Elimination. The assigned E0 (1,1-HCl and 1,1-HF) values meet the minimum requirement defined by the thermochemistry shown in Figure 1 and allow 1−3 kcal mol−1 threshold energy for the addition of the carbenes to HCl and HF. These may be lower limits to the actual threshold energies for addition, since the thermochemistry and the assigned E0 have uncertainties of ±2 kcal mol−1. The assigned E0 are sufficiently good that some confidence can be placed in the structures of the transition states, which are examined in the following paragraph. The low frequencies of the 1,1-HX elimination transition states compensate for the higher threshold energy, and 1,1-HX can be competitive with 1,2-HX elimination at high excitation energy and high temperature. The latter is demonstrated by the thermal rate constants in Arrhenius form (s−1) at 1000 K; the rate constants are 11.0 × 10 13 e −(62 100/RT) , 13.9 × 10 14 e −(73 000/RT) , 6.47 × 10 13 e −(67 150/RT) , and 6.97 × 1014e−(75 500/RT) for 1,2-DCl (E0 = 60 kcal mol−1), 1,1-HCl (E0 = 71 kcal mol−1), 1,2-DF (E0 = 65 kcal mol−1), and 1,1-HF (E0 = 73 kcal mol−1), respectively. The larger pre-exponential factor for 1,1-HCl than for 1,1-HF elimination is a consequence of lower vibrational frequencies for the HCl elimination transition state. Low-temperature pyrolysis experiments35 in a flow reactor with CH3CHFCl reported k(T) = 8.7 × 1013e−(57 000/RT) for 1,2-HCl elimination, which is in modest agreement with our model, since HCl elimination has a 1.1 kcal mol−1 lower Ea than DCl elimination. At elevated temperatures, the 1,1-HX elimination channel will augment 1,2-DX elimination and add to the total unimolecular decomposition reaction of CD3CHFCl or CH3CHFCl. The carbene-like structure for the CD3C-X fragment is evident in Figure 5 for both 1,1-HF and 1,1-HCl transition states. However, the HCl fragment is closer to a free HCl molecule than the HF fragment is to the HF molecule, which can be shown by examination of the C−H and H−X bond lengths. The C−H extension is 34% for 1,1-HCl and only 14% for 1,1-HF, and the H−Cl bond extension is just 15%, whereas it is 30% for H−F, relative to the free molecules. The extension of the C−F (55%) and C−Cl (60%) bonds are similar in both transition states. The H−C−Cl angle is just 9.9° for the 1,1HCl transition state, whereas the H−C−F angle is 28°, and the C, H, and Cl atoms are more nearly colinear in the 1,1-HCl transition state. The MP2 calculated E0 for 1,1-HF elimination is close to our assigned value; however, the calculated value for 1,1-HCl elimination is too low by 5 kcal mol−1. The structures of the transition states for HF and HCl elimination from CHF2Cl and CHFCl2 are shown in Figure 6. Our model for the HCl elimination transition state from

Figure 6. Diagrams of the HF and HCl elimination transition states for CHF2Cl and CHFCl2 from MP2 calculations. The enthalpies of reaction28,36 for HF and HCl elimination from CHF2Cl are 55 and 47 and from CHFCl2 are 57 and 53 kcal mol−1, respectively. On the basis of the E0 values assigned in the text, the threshold energies for :CFCl + HF and :CF2 + HCl are 13 and 9 kcal mol−1, and for :CCl2 + HF and :CFCl + HCl, they are 10 and 4 kcal mol−1. Note the correlation of these threshold energies with the structures of the transition states.

CHF2Cl is very similar to that of ref 14. The C−H and C− F(Cl) distances are less extended, and the H−Cl and H−F distances are longer than in the corresponding transition states from CD3CHFCl. The calculated (MP2) E0 in kcal mol−1 were 58.5 and 59.1 for HCl elimination and 71.8 and 69.0 for HF elimination from CHF2Cl and CHFCl2, respectively. The best experimental14 E0(HCl) value for CHF2Cl is 56.3 kcal mol−1, and based upon this number our assignment for E0(HF) is ∼67 kcal mol−1. Combining these threshold energies with the thermochemistry36 of CF2 and CClF gives 9 and 13 kcal mol−1 for the threshold energies for CF2 + HCl and CFCl + HF, respectively. Assuming that the E0 for CHFCl2 from the MP2 calculations also are ∼3 kcal too high, the threshold energies for CFCl + HCl and CCl2 + HF would be ∼4 and 10 kcal mol−1, respectively. The threshold (or activation) energy for CCl2 + HCl seems to be established37,38 as 3−4 kcal mol−1. As judged by these examples, the threshold energy for carbene addition to HCl and HF seems to correlate with the structure of the transition states. The threshold energy for the carbene addition reactions to HCl decrease as the H−C−Cl angle becomes smaller, and the structure becomes more colinear in the transition states for the CHF2Cl, CHFCl2, CD3CHFCl series. As a final point, we note that the pre-exponential factors for the thermal unimolecular elimination of HCl and HF are large, and HF elimination, as well as C−Cl bond rupture, should be included in modeling high-temperature reactions of CHF2Cl, CHFCl2, and CH2FCl. The MP2 calculations for CH2FCl gave E0 values of 75.3 and 77.3 for HF and HCl elimination, respectively. We were initially surprised by the high value for E0(HCl), and we used the geometry of the MP2 calculation with a single point calculation by DFT methods to obtain another estimate. Both threshold energies were reduced by ∼4 kcal mol−1. The similar threshold energies combined with similar enthalpies of reaction36 imply that the CHF + HCl and CHCl + HF addition reactions will have threshold energies of ∼20 kcal mol−1. We are not aware of any definitive experimental studies of either the unimolecular decomposition or the bimolecular addition reactions for the CH2FCl system that would test these expectations. Infrared 9447


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The Journal of Physical Chemistry A multiphoton-excitation experiments39 found a 2−5% contribution from HF elimination, and a qualitative thermal pyrolysis study40 reported Arrhenius parameters of 1.1 × 1013 exp(−66500/RT) for loss of HCl. These Arrhenius values do not seem compatible with the calculated models for CH2FCl, but the rate-constant measurements certainly were in the falloff region. More experimental and computational work is needed for CH2FCl. B. Threshold Energies for 1,2-DCl and 1,2-DF Elimination and the MP2 Method. The MP2/6-311+G(2d,p) calculations32,33 gave E0 values that are 2−3 kcal mol−1 higher than the accepted experimental values for C2H5F, CH3CHF2, CH2FCH2F, and CH3CF3, and the calculated values reproduce the trend of higher E0 with additional F atom substitution. Thus, agreement between the calculated and experimental E0 for 1,2-DF elimination from CD3CHFCl is expected. However, the MP2 calculations of Rajakumar and Arunan32 overestimated the threshold energies for 1,2-HCl elimination from C2H5Cl by 10 kcal mol−1, and the method has not been employed to model HCl elimination processes. Our MP2-calculated E0 values for C2H5Cl, CH3CHCl2, and CH2ClCH2Cl are 59.9, 58.3, and 64.5 kcal mol−1, respectively, which also are high relative to the experimental results, but they have the correct trend for 1,1- and 1,2-dichloroethane.41 DFT calculations16,41 give results for this series of molecules that are closer to the experimental E0 values and also follow the trends with Cl atom substitution. For 1,2-HCl elimination reactions, the E0 correlate with the relative stability of the carbocation,16 for example, CH3CH2+ for C2H5Cl, CH3CHCl+ for CH3CHCl2, and CH2ClCH2+ for CH2ClCH2Cl. Comparison of the experimental results for CH2FCH2Cl41 and CH3CHFCl is of interest. The rate constants for similar excitation energies are (1.1 ± 0.3) × 108 and (0.82 ± 0.25) × 108 s−1 for elimination of HF and HCl, respectively, from CH2FCH2Cl,41 which are ∼2 and 10 times smaller than those for CH3CHFCl after accounting for the kinetic-isotope effects for CD3CHFCl. The assigned E0 for CH2FCH2Cl were 63 ± 2 (HF) and 65 ± 2 (HCl) kcal mol−1. The enthalpies of formation for CH2FCH2Cl and CH3CHFCl differ by 6 kcal mol−1; the latter is more stable. Thus, the energies (kcal mol−1) of the transition-state isomers, relative to CH3CHFCl, are 59 (HCl) and 64 (HF) from CH3CHFCl and 69 (HF) and 71 (HCl) from CH2FCH2Cl. The higher energies of the transition states with a halogen atom on the CH end rather than the CX end of the transition state can be associated with the destabilization effect of the CH2XCH2+ carbocation.16 The 4−6 kcal mol−1 elevation of the E0 values for CH3CHFCl relative to C2H5Cl (55 kcal mol−1) and C2H5F (58 kcal mol−1) is probably associated with the lowered bond dissociation energy of D(CH2CHF or Cl) versus D(CH2CH2), which negates the effect16 of the stability of the CH3CHF(or Cl)+ carbocations. The calculated E0(HCl) values for the 1,1-chlorofluoroethane class of molecules do not follow the experimental results. The E0 (kcal mol−1) have been assigned for CH3CHFCl (59 and 64), CH3CF2Cl (57 and 68),18,42 and CH3CFCl2 (55 and 65)18,42 from chemical activation experiments; the smaller number applies to HCl elimination. The Cl atom clearly elevates E0(HF), even though the CH3CHCl+ ion, in principle, could have a stabilizing effect; the transition state for HF elimination evidently is not dominated by the carbocation contribution to the structure.16 In fact, the additional Cl atom elevates the E0(HF) as much as an F atom. The MP2 (and the

DFT16) calculations are consistent with these E0 values for HF elimination reactions. The experimental effect of F atom substitution upon 1,2-HCl elimination from CD3CHFCl, relative to C2H5Cl, is to elevate the experimental E0 by ∼4 kcal mol−1; however, DFT and MP2 calculations all predict a reduction in E0 relative to C 2H5Cl (2 kcal mol−1for CH3CHFCl with MP2), because of the stability provided by the CH3CHF+ ion to the transition-state structure. This contribution can be identified in Figure 5 by the shorter C− F out-of-ring distance16 relative to typical C−F bonds. Thus, the apparent agreement by MP2 calculations with E0(DCl) for CD3CHFCl is a fortuitous cancellation of the overestimation of E0(HCl) in general and the specific reduction for CD3CHFCl. The DFT-calculated threshold energies18 for 1,2-HF elimination from CH3CF2Cl and CH3CFCl2 are in accord with the experimental results,42 but the calculated E0(HCl) are always too small. The E0(HCl) for these two molecules are in modest agreement from thermal43,44 and chemical-activation experiments,18,42 and the experimental values seem to be established. The inability of the computational methods to match the experimental E0(1,2-HCl) from the CH3CHFCl, CH3CFCl2, and CH3CF2Cl series is a consequence of the overweighting of the carbocation contribution to the transition states, but the explanation of why this occurs remains to be discovered. This discussion of threshold energies has no significant impact on the vibrational frequencies of the 1,2-DX transition states, which are very similar for all computational methods. C. Isomerization Reactions of CD3CF and CD3CCl. Our analysis of the 1,1-HCl and 1,1-HF elimination reactions from CD3CHFCl was based on the assumption that the CD3CF and CD3CCl carbenes isomerize to CD2CDF and CD2CDCl. The energy to be released to the carbenes is 96 ± 2 minus 73 ± 2 kcal mol−1. Since the threshold energy for the addition of the carbenes to HCl or HF is small, statistical partitioning of the 26 kcal mol−1 should be a good assumption. The average vibrational energy of the carbenes should be approximately two-thirds of 26 kcal mol−1 or 17 kcal mol−1 with a distribution corresponding to a half-width of ∼8 kcal mol−1. Since the threshold energy for isomerization of CD3Cl is 11 kcal mol−1, the majority of the CD3CCl distribution will be above the threshold energy, and the rate constants are sufficiently large that CD2CDCl should be the observed product. However, the threshold energy for isomerization of CD3CF is 15 kcal mol−1, and a significant fraction of the distribution may be below the threshold energy. Therefore, the role of tunneling needs to be evaluated. The tunneling treatment discussed by Baer and Hase45 was used to estimate RRKM rate constants that include the possibility of tunneling for the D atom isomerization reaction of CD3CF. The method is based on the Eckart potential with its probability for tunneling. The calculation of the tunneling probability requires the potential energy barriers in the forward and reverse directions and the imaginary frequency of the transition state. The frequencies of CD3CF and its transition state were evaluated using both MP2 and DFT calculations. The results were very similar for all the methods with an imaginary frequency of 1000 ± 100 cm−1. The conventional rate constant without tunneling is ∼2 × 109 s−1 at 17 kcal mol−1, that is, 2 kcal mol−1 above the threshold energy.46 The inclusion of tunneling enhances those rate constants by a factor of 3−4, and the CD3CF distribution above 15 kcal mol−1 will isomerize at the pressures of our experiments. However, the rate constant at 13 kcal mol−1, that is, 2 kcal mol−1 below the 9448


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The Journal of Physical Chemistry A threshold energy, is only ∼1% of the rate constant at the threshold energy. According to this model, carbenes with less energy than 13 kcal mol−1 would be deactivated by collisions with the bath gas and ultimately would be trapped by bimolecular chemical reactions in our experiments. We estimate that this fraction could be approximately one-third of the distribution below 15 kcal mol−1 or 10−15% of the total distribution of CD3CF. The threshold energy for isomerization of C2D5CF is 10 kcal mol−1, and tunneling is less important for analysis1 of 1,1-HF elimination from C2D5CHF2. However, the question of tunneling is important for analysis of 1,1-HF elimination from CD3CHF2. The tunneling probability is very sensitive to the imaginary frequency, and tunneling would be much more important for a frequency of 2000 cm−1. However, the reaction coordinate for the isomerization is a bending motion and, hence, the low value for CD3CF. Experimental tests to trap CD3CF were done with CF3CHCH2 and with cis-butene-2 as scavengers, but no evidence was found for the expected cyclopropane products. The CD3CF carbene also could abstract a Cl atom47,48 from CHFCl2 (or an I atom from CD3I), but no evidence was found for products from CD3CFCl radicals. We conclude that the majority of the CD3CF must have isomerized to CD2CDF. Tunneling has often been invoked4−9 to explain the formation of CH2CHCl from CH3CCl in low-temperature experiments. An attempt4 to calculate the thermal isomerization rate constants of CH3CCl with a model that included an advanced treatment of tunneling did not reproduce the temperature dependence of the experimental rate constants measured in 1,2-dichloroethane or n-heptane solvents. Explanation of the discrepancy for CH3CCl awaits further studies with direct monitoring of the CH3CCl concentration,10 but tunneling must be included in the analysis. The threshold energies for elimination of DCl and DF from CD2CDCl and CD2CDF are sufficiently high25,26 that additional reactions should be negligible in our experiments. However, photolysis of 3-methyl-3-chlorodiazirine49 has been used to prepare CH3CCl with enough energy such that the vinyl chloride molecules formed from isomerization do have enough energy to react mainly by 1,1-HCl elimination.

311+G(2d,p) basis set was used for the electronic structure calculations because DFT methods were not successful for identifying the transition state for 1,1-HCl elimination. The elevation of the threshold energy (4−5 kcal mol−1) for 1,2-HCl elimination from CH3CHFCl, relative to C2H5Cl, is not reproduced by either MP2 or DFT computational methods. Calculations of the statistical rate constants were extended to CHFCl2 and CHF2Cl to examine the product branching ratios for HCl versus HF elimination. The difference in threshold energies is 10−12 kcal mol−1 in favor of HCl elimination, which is larger than the 2−3 kcal mol−1 difference for CD3CHFCl. However, according to the calculations, the difference in E0(HF) and E0(HCl) for CH2FCl should resemble the CD3CHFCl example. The 1,1-HF elimination reactions should be included together with 1,1-HCl elimination reactions in models for the high-temperature decomposition reactions of CH2FCl, CHF 2Cl, and CHFCl2 and longer-chain 1,1chlorofluoroalkanes.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b06638. Calculated vibrational frequencies, overall moments of inertia (Ix, Iy, and Iz), and reduced moments of inertia for internal rotors using MP2/6-311+G(2d,p) for the 1,1HX, 1,2-DX, and 1,2-HX (X = F, Cl) elimination reactions from CH3CHFCl and CD3CHFCl. The calculated transition-state geometries using MP2/6311+G(2d,p) for the 1,1-HX (X = F, Cl) elimination reaction from CH2FCl are also shown. (PDF)

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS Financial support from the National Science Foundation (CHE-1111546 and CHE-1229406) is gratefully acknowledged.

VI. CONCLUSIONS Rate constants for the four unimolecular reaction channels of CD3CHFCl* with 96 kcal mol−1 of vibrational energy were measured by the chemical activation technique. The branching fraction for 1,2-DCl, 1,1-HCl, 1,2-DF, and 1,1-HF reactions are 0.60, 0.27, 0.09, and 0.04. The experimental rate constants were compared to calculated statistical rate constants to assign threshold energies to each reaction channel. Although the threshold energies for 1,1-HCl and 1,1-HF elimination are 8− 10 kcal mol−1 higher than for 1,2-DF or 1,2-DCl elimination, the 1,1-elimination reactions are competitive at high excitation energies, because the frequencies of the transition states are much lower, especially for 1,1-HCl elimination. The assigned threshold energies for the 1,1-HX elimination reactions are slightly higher than the thermochemical requirements for formation of CD3CF (+HCl) and CD3CCl (+HF), which provides an independent confirmation for the low vibrational frequencies of these transition states, that is, higher frequencies would lead to assignment of lower threshold energies. The structures of the 1,1-HX transition states resemble the intuitive expectation for addition reactions of carbenes to HCl and HF with low threshold energies. The MP2 method with the 6-

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The Journal of Physical Chemistry A (42) McDoniel, J. B.; Holmes, B. E. Substituent Effects and Threshold Energies for the Unimolecular Elimination of HCl(DCl) and HF(DF) from Chemically Activated CFCl2CH3 and CFCl2CD3. J. Phys. Chem. 1996, 100, 3044−3050. (43) Huybrechts, G.; Hubin, Y. Pyrolysis of 1-Chloro-1,1-Difluoroethane in the Absence and Presence of CCl4 and Mixtures of CCl4 + HCl. Int. J. Chem. Kinet. 1985, 17, 157−165. (44) Huybrechts, G.; Eerdekens, K. Pyrolysis of 1,1-Dichloro-1Fluoroethane in the Absence and Presence of Added Propene or CCl4: A Computer-Aided Kinetic Study. Int. J. Chem. Kinet. 2001, 33, 191− 197. (45) Baer, T.; Hase, W. L. Unimolecular Reaction Dynamics: Theory and Experiments; Oxford University Press: Oxford, U.K., 1996; pp 264−270. (46) The lowest three frequencies of the transition state for CD3CF are 425, 558, and 797 cm−1; therefore, only four vibrational states exist below 2.3 kcal mol−1, and the rate constant is not a smooth function of energy. (47) Dees, K.; Setser, D. W. Kinetic Isotope Effects in the Unimolecular Reactions of Chemically Activated Chloroethane-d0 and -d5 and 1,2-Dichloroethane-d0 and-d4 Molecules. J. Chem. Phys. 1968, 49, 1193−1206. (48) Hayes, F.; Lawrance, W. D.; Staker, W. S.; King, K. D. Singlet Methylene Removal by Halogen-containing Organic Species. Chem. Phys. Lett. 1994, 231, 530−535 These authors measured the rate constants for the reactions of singlet CH2, but they did not recognize the Cl- and Br-atom abstraction mechanism.. (49) Cho, S. H.; Park, W.-H.; Kim, S. K.; Choi, Y. S. Unimolecular Dissociation Dynamics on the Ground Potential Energy Surface: the Method of Excitation and Product State Distributions of HCl and Cl Fragments. J. Phys. Chem. A 2000, 104, 10482−10488.

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Characterization of the 1,1-HCl Elimination Reaction of Vibrationally

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