Groups on the Threshold Energy for the Unimolecular Interch

Article pubs.acs.org/JPCA

Effects of CF3 and CH3 Groups on the Threshold Energy for the Unimolecular Interchange Reaction of Cl- and F‑Atoms in CF3CHFCH2Cl and CH3CHFCH2Cl Corey E. McClintock,† Kylie C. Smith,† George L. Heard,† D. W. Setser,‡ and Bert E. Holmes*,† †

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

ABSTRACT: The recombination reactions of CH2Cl radicals with CF3CHF and with CH3CHF radicals were used to generate CF3CHFCH2Cl and CH3CHFCH2Cl molecules with 90−92 kcal mol−1 of vibrational energy. The experimental rate constants for elimination of HCl and HF and the interchange of Cl and F atoms were measured and compared to RRKM calculated rate constants to assign the threshold energy for each unimolecular reaction channel. The Cl/F interchange reaction is approximately 18% of the total unimolecular reaction for both molecules. The product branching ratios and some rate constants also could be measured for the unimolecular reactions of the rearranged molecules, CF3CHClCH2F and CH3CHClCH2F. The most important result is that the CH3 group lowers the threshold for Cl/F interchange relative to CH2FCD2Cl, as expected for an electrondensity donating group, and the CF3 group, an electron-density withdrawing group, increases the threshold energy relative to CH2FCD2Cl. The CH3 and CF3 groups alter the threshold energies of the HCl and HF elimination reactions in such a way so as to maintain the same branching fraction for the interchange reaction. The results from density functional theory using the B3PW91 method with the 6311+G(2d,p) and G-31G(d′,p′) basis sets are used to discuss the trends in threshold energies for the Cl/F interchange and the HF and HCl elimination reactions.

I. INTRODUCTION The unimolecular interchange of a chlorine atom and a fluorine atom (or any other combination of F, Cl, and Br atoms) located on adjacent carbon atoms in a fluorochloroalkane molecule competes with the unimolecular elimination of HCl or HF.1−15 In recent work16 the threshold energy for the interchange reaction of Cl- and F-atoms in CH2FCD2Cl was assigned as 62 ± 2 kcal mol−1. In the present study the threshold energy for the halogen interchange reactions involving the second and third carbon atoms of CF3CHFCH2Cl and CH3CHFCH2Cl will be reported and compared to that of CH2FCD2Cl to illustrate the effects of the CF3 and CH3 groups on the threshold energy for the interchange reaction. These halogen atom interchange reactions belong to type-1 dyotropic rearrangement reactions.17−21 Computational studies18−20 of substituent effects on threshold energies for the model molecules, CH2ClCH2Cl, CH2BrCH2Br, and CH2ClCH2F, suggest that electron-density © 2014 American Chemical Society

donating groups should lower the threshold energy and that electron-density withdrawing groups should raise the threshold energy for these interchange reactions of halogen atoms. The present study, which uses chemically activated molecules with 90 ± 2 kcal mol−1 of vibrational energy formed by radical recombination at room temperature, provides an experimental test of these predictions. In addition to the experimental measurements, electronic−structure calculations using density functional theory (DFT) are employed to obtain calculated threshold energies for the rearangement reactions of CH2ClCH2F, CF3CHFCH2Cl, and CH3CHFCH2Cl plus the vibrational frequencies and moments of inertia of these molecules and their transition states. The trends in the calculated threshold energies with CF3 and CH3 substitution Received: December 16, 2013 Revised: March 14, 2014 Published: March 21, 2014 2886

dx.doi.org/10.1021/jp412299p | J. Phys. Chem. A 2014, 118, 2886−2896

The Journal of Physical Chemistry A

Article

can be compared to the experimental results to specifically check the effects of the CF3 and CH3 groups on the dyotropic Cl/F rearrangement threshold energy. In addition to observing the effects of CF3 and CH3 groups on the threshold energy for the rearrangement reaction, the results also provide information about the changes in threshold energies by these groups for HCl and HF elimination relative to CH2FCD2Cl. It is firmly established22−24 that electron-density donating groups on the CX atom lower the threshold energy for HX elimination from CH3CH2X (X = F, Cl, or Br), but such groups have little effect for substitution on the CH atom, where CX and CH denote the carbon atoms to which the halogen (X) and hydrogen atoms are bound in the four-membered ring of the transition state. This effect for the CH3 group was characterized many years ago in thermal activation studies22 of n-propyl chloride vs iso-propyl chloride and the explanation has been the subject of much discussion.23 However, the situation for 1,2-dihaloethanes is more complex because a halogen substituent on CH raises the threshold energy, by ∼5 kcal mol−1, relative to the monohalide reference molecule.15 Competing substituent effects exist for CF3CHFCH2Cl and CH3CHFCH2Cl, and the net effect on the threshold energy for HF and HCl elimination reactions can be unexpected. In anticipation of the results, the HF elimination reaction can be the preferred pathway for these molecules, whereas HCl elimination from alkyl halides normally has the lower threshold energy. Since the reactions of the isomerized molecules, CF3CHClCH2F and CH3CHClCH2F, also were observed, our results can be viewed as a study of substitution on each end of CH2FCH2Cl. The vibrationally activated molecules (denoted by an asterisk) were generated in a room temperature bath gas (M) by the recombination of CH2Cl radicals with CF3CHF and CH3CHF radicals that were formed by the photolysis of CH2ICl with either CF3CHFI or CH3CHFCl. The pathways of reaction are identified by numbering the carbon atoms 1, 2, and 3 from left to right as the formulas are written. The CF3CHFCH2Cl* molecules have three unimolecular reaction channels that are in competition with collisional deactivation, as outlined below; the fourth possibility, 2,1-HF elimination, was not observed due to the high threshold energy for this reaction.

CH3CHFCH 2Cl* → CH3CHClCH 2F* → HF + CH 2CFCH 2Cl → HF + CH3CHCHCl (cis and trans) → HCl + CH3CFCH 2 + M → CH3CHFCH 2Cl + M (2)

The main reaction of CH3CHClCH2F* is 1,2-HCl and 3,2-HCl elimination, but some 2,3-HF elimination was observed. The experimental rate constants are obtained from measurements of the ratios of the relative concentrations of the decomposition product (Di) for a specific channel, i, to the stabilized molecule (S) for a range of pressure. The experimental rate constants25 will be compared to the calculated statistical unimolecular rate constants to assign experimental threshold energies. Electronic structure calculations (density-functional theory with the B3PW91 method and the 6-311+G(2d,p) basis set) were used to obtain the vibrational frequencies and moments of inertia of the molecules and the transition states. Calculations also were done with the 6-31G(d′,p′) basis set for comparison. These calculations also provide theoretical threshold energies, which tend to be close to the experimental values for HF elimination reactions.1−15 The theoretical values are usually lower than the experimental values for HCl elimination and Cl/F-interchange processes. As an aid to the reader, the energy profiles of the reactions for the CF3CHFCH2Cl and CH3CHFCH2Cl systems are summarized in Figure 1. The Cl/F interchange reactions are just slightly endothermic. The calculated threshold energies from both basis sets are listed in Figure 1; the experimentally assigned values are given in Table 2. Casual inspection of Figure 1 shows that the calculated threshold energies are substantially higher for CF3CHFCH2Cl than for CH3CHFCH2Cl. This trend, plus the statistical effect on the density of states from substitution of three H-atoms by three F-atoms, ensures that the rate constants for the CF3CHFCH2Cl system will be smaller than those for CH3CHFCH2Cl system.

II. EXPERIMENTAL METHODS The CF3CHFCH2Cl* experiments consist of placing measured quantities of CH2ClI and CF3CHFI in Pyrex vessels of known volume followed by photolysis at room temperature with a high pressure 200 W mercury lamp (Oriel). The contents of the vessels were recovered and analyzed by gas chromatography using either flame-ionization or mass-spectrometric detectors. The ratio of CH2ClI and CF3CHFI was typically 1:4, and the normal time for photolysis was 10 min. A small quantity of solid mercury(I) iodide was added to each vessel to aid in the generation of radicals.1,2,6−12 Gas handling was done on an allglass, grease-free, high-vacuum line, and pressures were measured with a MKS-270 electronic manometer. Low pressures were needed for the CF3CHFCH2Cl* system; therefore, large photolysis vessels ranging in size from 34.71 to 4900 cm3 were used. Commercial samples of all products were available except for CF3CHFCH2Cl and the rearranged product, CF3CHClCH2F. For all other products, identification of the gas chromatographic signals was straightforward. Mixtures of known composition were prepared to obtain calibration factors to convert the raw product ratios to ratios of actual concentrations. It was assumed that the total ion-count, TIC, from the structural isomers CF 3CHFCH 2Cl and

CF3CHFCH 2Cl* → CF3CHClCH 2F* → HF + CF3CHCHCl (cis and trans) → HCl + CF3CFCH 2 + M → CF3CHFCH 2Cl + M (1)

The important reactions for CF3CHClCH2F* are 2,3-HF and 3,2-HCl elimination. The reverse of the Cl/F-interchange step is a minor component, and it can be ignored in the analysis. As shown in eq 2, the reactions of CH3CHFCH2Cl* do include 1,2-HF elimination plus Cl/F-interchange and 3,2-HF and 2,3HCl elimination. 2887



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Figure 1. Schematic representation of the calculated energy profiles for the CF3CHFCH2Cl and CH3CHFCH2Cl systems. The calculated threshold energies are listed for the 6-31G(d′,p′) and the 6-311+G(2d,p) basis sets (the latter in parentheses and the former in brackets). The experimentally assigned E0 values are given in Table 2. The calculated E0 for Cl/F interchange in CH2ClCH2F are 60.0 and 56.4 kcal mol−1 for the 6-31G(d′,p′) and 6-311+G(2d,p) basis sets, respectively.3,12 Note the slight distortion of the positions of the Cl and F atoms in the sketchs of the transition states; the numbers are in units of Angstroms.

molecules. The CH2CHCl produced from the decomposition of CH2ClCH2Cl* formed from the recombination of the CH2Cl radicals seemed to protect the alkenes from reaction with Cl-atoms, but in accordance with the procedure in similar Hg photosensitization experiments an additional scavenger, CF3CHCH2, which did not interfere with the analysis of any products, was used to protect the chloro- and fluoropropenes from Cl-atom reactions. The typical composition of a sample was 0.325 μmol of CH2ClI, 0.650 μmol of CH3CHFCl and 0.244 μmol of CF3CHCH2. Commercial samples of all the halogenated propenes other than E- and Z-CH3CHCHF

CF3CHClCH2F were the same and were the same as another isomer, CHF2CF2CH2Cl, which was used to obtain the calibration factor. The rate constants for the CH 3 CHFCH 2 Cl* and CH3CHClCH2F* molecules are 2−3 orders of magnitude larger than for CF3CHFCH2Cl*, and correspondingly smaller vessels were used for photolysis. Since CH3CHFI was not available, the experiments for the CH3CHFCH2Cl system utilized mercury photosensitization of CH3CHFCl and CH2ClI in quartz vessels to produce the CH3CHF and CH2Cl radicals, which in combination produced the desired CH3CHFCH2Cl* 2888



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ion component of CH2CHCl and CH3CHCH2Cl in the total-ion counts. In another approach, several photolyses were done with analysis by flame-ionization detection, FID, and the ratio of signals from the chloropropene and CH3CHFCH2Cl were measured. On the basis of previous experience in this laboratory, the response for these compounds would be similar when FID is the detection method, i.e., the corection factor to obtain relative concentrations would be close to unity. These experiments confirmed the calibration based on the CH2 CHCl/CH2FCH2Cl analogy.

were available to enable identification of gas chromatograph peaks. Carefully prepared mixtures were used to obtain relative calibration factors for the chloro- and fluoropropenes, and it was assumed that the TIC for CH3CHCHF and CH3CF CH2 would be the same. Commercial samples were unavailable for CH3CHFCH2Cl and CH3CHClCH2F. Identification of

III. EXPERIMENTAL RATE CONSTANTS III-A. CF3CHFCH2Cl System. The decomposition to stabilization ratios (Di/S) for the three unimolecular reactions are plotted vs inverse pressure in Figure 2. Low pressures were required to observe appreciable yields of decomposition products and most data are for experiments below 0.02 Torr. The 2,3-HCl elimination process was the most important reaction; the Cl/F interchange reaction was observed, although it is the least important of the three possibilities. The yields of cis- and trans-CF3CHCHCl were combined to make the Di/ S plot for 3,2-HF elimination. The Di/S vs pressure−1 plots are linear with acceptable correlation coefficients, and the slopes with their least-squares uncertainties are summarized in Table 1. These slopes become the experimental rate constants when they are multiplied by the collisional rate constant, which is given in the footnote of the table. The unimolecular rate constants are in the 1−4 × 104 s−1 range, which resemble the magnitude of the rate constants for the CF3CFClCH2Cl*, CF2ClCFClCH2F*, and CF2ClCF2CH2Cl* molecules,10,11 which had similar average energies. The product branching ratios can be obtained from the ratios of the rate constants or they can be obtained from the ratios of the decomposition products. The latter has some experimental advantage because lower pressure experiments with higher yields of decomposition products can be studied. Branching ratio plots are shown in Figure 3. The average branching ratio for HCl vs HF elimination is 1.6 ± 0.1, which compares favorably with the ratio of 1.7 derived from the rate constants. The E/Z ratios from 3,2-HX elimination also are summarized

Figure 2. Plots of the decomposition to stabilization product ratios for CF3CHFCH2Cl* vs pressure−1; ◆ CF3CFCH2/CF3CHFCH2Cl; □ E- and Z-CF3CHCHCl/CF3CHFCH2C; ■ (CF3CClCH2 + Eand Z-CF3CHCHF + CF3CHClCH2F)/CF3CHFCH2Cl, e.g., the rate for Cl/F interchange. The lines are least-squares fits to the data points. The correlation coefficients are between 0.96 and 0.93, and the intercepts are effectively zero.

their gas chromatography peaks was possible from their mass spectra and the dependence of their relative yields with reduced pressure. Calibration factors for Di/S ratios were obtained from the assumption that the ratio of the total ion-count for CH2 CHCl to the total ion-count for CH2FCH2Cl would be the same as that for the CH3CHCHCl/CH3CHFCH2Cl ratio, and prepared mixtures of CH2CHCl and CH2FCH2Cl were used for calibration. Since parent-ion counts actually were used for the halopropenes, the ratio was then adjusted for the parentTable 1. Experimental Rate Constantsa reaction 3,2-Cl/F 2,3-HCl 3,2-HCl 3,2-HF 2,3-HF 1,2-HF 1,2-HCl

kexpt s−1

⟨E⟩ kcal/mol

process

b

−3

CF3CHFCH2Cl 10

4

Torr, 10 s

−1

b

CF3CHClCH2F 10

−3

k⟨E⟩ s−1 4

Torr, 10 s

0.96 ± 0.1, 1.3 ± 0.2 2.4 ± 0.1, 3.4 ± 0.4

−1

c

E0 kcal/mol 7

CH3CHFCH2Cl Torr, 10 s

CH3CHClCH2Fc Torr, 107 s−1

0.47 ± 0.05, 0.70 ± 0.08 0.25 ± 0.02, 0.39 ± 0.03 0.72 ± 0.30, 1.0 ± 0.4d

1.5 ± 0.1, 2.1 ± 0.2d f

−1

0.76 ± 0.10, 1.1 ± 0.2e 0.67 ± 0.05, 1.0 ± 0.1e

4.2 ± 0.5, 5.9 ± 0.7 f

0.038 ± 0.005, 0.057 ± 0.007 1.01 ± 0.09, 1.5 ± 0.2 2.1 ± 0.3, 3.2 ± 0.4

a The top entry lists the slopes obtained from the plots of D/S vs pressure−1 and immediately beside the slope is the rate constants in s−1 units. bThe following collision diameters (cm) and ε/k (K) were used to calculate the collision constant; CF3CHFCH2Cl (5.6 × 10−8 and 410), CF3CHFI (5.3 × 10−8 and 300), and CH2ClI (5.1 × 10−8 and 400). The collision frequency for CF3CHFCH2Cl* was 1.4 × 107 s−1/Torr. The same value was used for CF3CHClCH2F*. The collision diameters and ε/k values were taken from ref 25. In some cases analogies to similar molecules were used to estimate the values. cThe following collision diameters (cm) and ε/k (K) were used to calculate the collision constant; CH3CHFCH2Cl (5.5 × 10−8 and 350), CH3CHFCl (5.3 × 10−8 and 300), and CH2ClI (5.1 × 10−8 and 400). The collision frequency for CH3CHFCH2Cl* was 1.5 × 107 s−1/ Torr. The same value was used for CH3CHClCH2F. The collision diameters and ε/k values were taken from ref 25. In some cases analogies to similar molecules were used to estimate the values. dThe trans/cis ratios for CF3CHCHCl and CF3CHCHF were 3.1 and 1.5, respectively. e The trans/cis ratios for CH3CHCHCl and CH3CHCHF were 0.66 and 0.60, respectively. fThe E0 for 2,1-HF elimination from CF3CHFCH2Cl and CF3CHClCH2F is expected to be higher than 70 kcal mol−1, and this reaction is not competitive with the observed elimination reactions.

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pressures. According to the ratio of rate constants, 2,3-HF elimination is 6 times faster than 3,2-HCl elimination, even though the latter has a 2-fold higher reaction path degeneracy. The branching ratio plot in Figure 3 gives a similar ratio for HF to HCl elimination. Evidently the threshold energy is lower for 2,3-HF elimination than for 3,2-HCl elimination. It should be noted that the effect of the CF3 group is to retard the rate of 3,2-HX elimination for both molecules. The trans/cis ratio for CF3CHCHF, Figure 3, is 1.5 ± 0.1, which is one-half that for CF3CHCHCl. The Cl/F interchange component from CF3CHClCH2F* is sufficiently small that the interchange reaction need not be considered in the kinetic analysis of the CF3CHFCH2Cl system. III−B. CH3CHFCH2Cl System. The rate constants for CH3CHFCH2Cl* were 100−1000 times larger than for CF3CFHCH2Cl*, and higher pressures were used to obtain reliable Di/S vs pressure−1 plots, which are shown in Figure 5

Figure 3. Plots of the product branching ratios from CF3CHFCH2Cl* and CF3CHClCH2F* vs pressure−1. □ ratio of trans(E)-CF3CH CHCl/cis(Z)-CF3CHCHCl for CF3CHFCH2Cl; ■ ratio of CF3CFCH2/cis- + trans-CF3CHCHCl, e.g., the ratio of HCl elimination to HF elimination for CF3CHFCH2Cl; ▲ ratio of cis(Z)CF3CHCHF/trans(E)-CF3CHCHF for CF3CHClCH2F; and ○ ratio of E- + Z-CF3CHCHF/CF3CClCH2, e.g., the ratio of HCl elimination to HF elimination for CF 3 CHClCH 2 F. The CF3CHClCH2F was not observed until 1/P > 25, and the yield of some decomposition products was very small until 1/P > 80, so no results are available for the CF3CHClCH2F system at the highest pressures.

in Figure 3. The trans/cis (or E/Z) ratio of CF3CHCHCl from 3,2-HF elimination is 3.1 ± 0.1, which indicates that the trans-conformation of the transition state has a lower threshold energy than the cis-conformation. The yields of CF3CHClCH2F and its decomposition products were small, but Di/S plots for CF3CHClCH2F* could be constructed, see Figure 4, and the slopes of the linear plots and the corresponding rate constants are summarized in Table 1. The plots in Figure 4 have points only for 1/P greater than 30 because CF3CHClCH2F* is not formed at higher

Figure 5. Plots of the decomposition to stabilization product ratios from CH3CHFCH2Cl* and from CH3CHClCH2F* vs pressure−1. ● CH2CHCH2Cl + E- and Z-CH3CHCHCl/CH3CHFCH2Cl; □ CH3CFCH2/CH3CHFCH2Cl. The lines are least-squares fits to the data points; the correlation coefficients are 0.96 and 0.97, respectively. The bottom set of data points, ◇, is for 2,3-HF elimination from the interchanged molecule, CH3CHClCH2F, e.g., CH3CClCH2/ CH3CHClCH0F; the correlation coefficient is 0.86.

and the branching ratio plots are in Figure 6. Four reaction channels were observed with 1,2-HF elimination being the most important followed by 3,2-HF elimination, as demonstrated by the product branching plots of Figure 6. The Cl/F interchange reaction was identified from the isomerized molecule and its decomposition products, which include mainly 3,2- and 1,2-HCl elimination plus a small 2,3-HF elimination component. The Cl/F interchange reaction is more important than HCl elimination. The Di/S plots from CH3CHFCH2Cl* are linear with correlation coefficients of 0.96, and the slopes with their least-squares uncertainties are summarized in Table 1. The slopes in units of Torr are converted to rate constants by multiplication by the collision rate constant. The unimolecular rate constants in units of s−1, which also are shown in Table 1, are in the range of 0.5−1.5 × 107 s−1. It should be noted that the yields of the cis- and trans-isomers of CH3CHCHCl from 3,2-HF elimination have been combined for that Di/S plot. The branching ratio of HCl elimination to F/Cl interchange is 0.55 ± 0.15, as shown in Figure 6; this corresponds to an overall branching fraction for isomerization

Figure 4. Plots of the decomposition to stabilization product ratios for CF3CHClCH2F* vs pressure−1. □ CF3CClCH2/CF3CHClCH2F, ● E- + Z-CF3CHCHF/CF3CHClCH2F. The lines are least-squares fits to the data points; the correlation coefficients are 0.92 (upper line) and 0.56 (lower line). In spite of the scatter of the data for HCl elimination, the branching ratio based on the rate constants is in good agreement with the ratio from Figure 3. 2890



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Figure 7. Plots of product branching ratios from CH3CHClCH2F* vs pressure−1. ■ CH2CHCH2F + CH3CHCHF(E and Z)/ CH3CClCH2, e.g., the ratio of 1,2-HCl + 3,2-HCl elimination to the 2,3-HF elimiantion; ◇ CH2CHCH2F/CH3CHCHF(E and Z), e.g., the ratio of 1,2-HCl/3,2-HCl elimination; and ● trans(E)/ cis(Z) ratio for CH3CHCHF.

Figure 6. Plots of product branching ratios from CH3CHFCH2Cl* vs pressure−1. ■ CH2CHCH2Cl + CH3CHCHCl (E and Z)/ CH3CFCH2, e.g., the ratio of HF elimination to HCl elimination; ● CH3CFCH2/CH3CHClCH2F + CH2CHCH2F + CH3CH CHF (E and Z) + CH3CClCH2, e.g., the ratio of HCl elimination to F/Cl interchange; □ CH2CHCH2Cl/CH3CHCHCl (E and Z), e.g., the ratio of 1,2-HF elimiantion to 3,2-HF elimaintion; and ◇ trans(E)-CH3CHCHCl/cis(Z)-CH3CHCHCl.

sysematic uncertainty in the rate constants for CH3CHFCH2Cl and CH3CHClCH2F should be remembered.

of 0.19 for CH3CHFCH2Cl. The trans/cis ratio for CH3CH CHCl is 0.66, and the cis-isomer is favored for 3,2 HF elimination in contrast to the CF3CHFCH2Cl analogue. Since Cl/F interchange from CH3CHFCH2Cl* was only 19% of the total reaction, the yields of the individual decomposition products from CH3CHClCH2F* were small. Furthermore, the rate constant for CH3CHClCH2F* is larger than for CH 3 CHFCH 2 Cl*, so the yield of stabilized CH3CHClCH2F was very small, and the Di/S data from most reactions of CH3CHClCH2F* do not cover the Di/S range that is best for assigning rate constants, i.e., the HCl elimination rates are too fast to observe stabilized product. Fortunately the rate constant for 2,3-HF elimination from CH3CHClCH2F* is slow enough to be in the same pressure range as the unimolecular reactions of CH3CHFCH2Cl* and the D/S data for 2,3-HF loss are in Figure 5. However, the product branching ratios for CH3CHClCH2F* are reliable; see Figure 7. The 3,2-HCl and 1,2-HCl elimination processes are the most important, with the latter being favored by a factor of 2.8. These rate constants were obtained from the Di/S plot for 2,3-HF elimination from CH3CHClCH2F* shown in Figure 5 and scaled by the branching factor of 75 ± 25 to obtain the rate constant for HCl elimination. Ther rate constant for HCl elimination was divided into its components using the branching ratio of 2.8 ± 0.8. The absolute rate constants for CH 3 CHClCH 2 F have more uncertainty than for CH3CHFCH2Cl because they are based upon the Di/S measurements for the smallest rate constant, and the true uncertainty is larger than the least-squares value of ±20% shown in Table 1. For both CH3CHFCH2Cl* and CH3CHClCH2F*, the HX elimination process with the Cl- or F-atoms leaving the central carbon atom is favored. The ratio of 1,2-HX to 3,2-HX is 1.4 and 2.8, respectively, for CH 3 CHFCH 2 Cl* and CH3CHClCH2F*, and both CH3 and CH2X groups are effective in promoting the HX elimination reactions. Because of the necessity for indirect calibration of the response of the GC−MS measurements for CH3CHFCH2Cl, a possible

IV. CALCULATED RATE CONSTANTS IV-A. Thermochemistry. The calculated statistical rate constants at energy E, which are obtained in the usual way from eq 3, are matched to the experimental rate constant with E set to ⟨E⟩, the average energy of the molecules. kE = (s†/h)(I†/I )1/2

∑ P†(E − E0)/N *(E)

(3)

†

The sums of states of the transition state, ∑P (E − E0), and the density of states of the molecule, N*(E), were calculated in the harmonic approximation; (I†/I) is the ratio of the overall moments of inertia, and s† is the reaction path degeneracy. If ⟨E⟩ is reliably defined, the only remaining factor in making the comparison to the experimental rate constant is E0. These rate constants are sensitive to the energy. For example increasing E from 92 to 94 kcal mol−1 for CF3CHFCH2Cl* increases kE by a factor of 1.8. Therefore, the thermochemical information used for the assignment of ⟨E⟩ is important, and the details are given below. The average energy of the molecules is obtained from eq 4; the enthalpy of ⟨E⟩ = ΔH 0(0 K) + 3RT + ⟨Evib(CH 2Cl)⟩ +⟨Evib(CF3CFH or CH3CFH)⟩

(4)

the recombination reaction at 0 K is the important term. The average vibrational energy of the two radicals, which is small, can be calculated from the vibrational frequencies; 3RT is the energy of three translational and three rotational motions of the radicals that become vibrations in the molecule. The enthalpy of formation of CH2Cl is established26 as 28.0 ± 0.7 kcal mol−1. The enthalpies of formation of CF3CFH and CH3CFH, which are in the computational compilation of C1 and C2 hydrofluorocarbon molecules and radicals by Haworth et al,27 are −166.7 and −17.3 kcal mol−1, respectively. The latter agrees with the recommended experimental value of −18.2 kcal mol−1. Unfortunately, the −166.7 kcal mol−1 value differs by 4 kcal mol−1 from the quoted experimental (−162.7 kcal mol−1)28 2891



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2,3-HCl and 3,2-HF reactions are observed. The CH3 or CH2Cl torsion in the transition states of CH3CHFCH2Cl also were treated as hindered internal rotations. The calculated properties of the models of the molecules and transition states are summarized in the Supporting Information. However, the features associated with the conformers of the molecules are outlined below. The approximation of using an average barrier to represent the asymmetric rotor was evaluated for CH2XCH2Y molecules in ref 15. The three conformers of CF3CHFCH2Cl were identified using the Gaussian codes. The lowest energy conformer has the CF3-group and the Cl-atom in trans positions; the next conformer, which has the F- and Cl-atoms in the trans position, has 1.3 kcal mol−1 higher energy; the third conformer with the H-atom trans to the Cl atom is 2.0 kcal mol−1 above the most stable conformer. The barriers to internal rotation are 2.2, 5.8, and 6.8 kcal mol−1, measured from the lowest energy conformer. The highest barrier is for the Cl-atom to pass the CF 3 group. The reduced moments of inertia of the CF3CHFCH2Cl conformers and the geometries at the barrier positions were averaged. The potential energy barriers also were averaged, and the CH2Cl torsion was treated as antisymetric rotor. In summary, the sum of states for the transition states was calculated from vibrational models, and the density of states for CF3CHFCH2Cl* with 90 kcal mol−1 was calculated from the averaged frequencies of the 6 positions corresponding to the conformers and barrier geometries with the CH2Cl torsional frequency replaced by the parameters for an average hindered rotor. The same procedure was followed for CF3CHClCH2F*. In this case the conformers differ in energy only by 0.35 and 0.95 kcal mol−1; the average barrier and reduced moment were 3.9 kcal mol−1 and 20.8 amu Å2. Since 1,2-HF and 1,2-HCl elimination were observed from CH3CHFCH2Cl* and CH3CHClCH2F*, respectively, the CH3-torsional frequency was replaced by a symmetric internal rotor, and the CH2Cl (or CH2F) torsional frequency was replaced by the average asymmetric internal rotor. The three conformers were identified, and the frequencies and overall moments of inertia were averaged as described above. The conformers of CH3CHFCH2Cl differ in energy by only 0.41 and 0.60 kcal mol−1 and the barriers to internal rotation of the CH2Cl group are 2.9, 4.4, and 6.9 kcal mol−1. The average barrier and reduced moment for CH2Cl are 4.7 kcal mol−1 and 20.3 amu Å2. The values for CH3 are 2.6 kcal mol−1 and 3.1 amu Å2, respectively. The models for CH3CHClCH2F were evaluated in the same way as for CH3CHFCH2Cl, and the results can be found in the Supporting Information. IV−C. Calculated Results and Assignment of Threshold Energies. The rate constants at energy ⟨E⟩ were calculated with the multiwell code provided by Professor Barker36 for several values of E0, and the calculated values were compared to the experimental rate constants from Table 1 to select the best value for E0. As already noted, the sums of states of the transition state and the density of states for the molecule were calculated in the harmonic approximation from the models defined above; additional details are provided in the Supporting Information. Since anharmonicity has not been included in the models, the assigned E0 may be upper limits because anharmonicity would increase the density term more than the sum of states in eq 3, and the calculated anharmonic rate constants would be reduced. In addition to the experimental rate constant for a given reaction channel, the assigned threshold energies for a specific molecule depend on the

value. However, the latter is based upon an estimate for D(CF3CHF-H) at 298 K of 103.5 ± 1.0 kcal mol−1 and ΔHof(CF3CH2F) = −214.1 ± 2.0 kcal mol−1 from a 1975 compilation.29 If the recommended ΔHof(CF3CH2F) = −218.0 kcal mol−1 from the computational compilation27 is used, then the derived ΔHof(CF3CHF) would agree with that from the computational result. Thus, the question becomes what is the true ΔHof(CF3CH2F) because other30,31 computational efforts support D(CF3CFH-H) of ∼102 kcal mol−1. The 1975 value actually is not from an experimental measurement but rather from a thermochemical cycle plus a reasonable assumption. Therefore, the ΔHof(CF3CHF) recommended by Haworth et al. was adopted. The enthalpy of formation at 298 K for CF3CHFCH2Cl was obtained (−225.8 kcal mol−1) from the energy of isomerization (4.0 kcal mol−1) of CF3CFClCH3 as calculated from the difference in the two calculated energies together with ΔHof (CF3CFClCH3) = −229.8 kcal mol−1. The latter32 is based upon an extensive series of isodesmic calculations. These enthalpies of formation give −87.0 kcal mol−1 for the enthalpy of radical recombination at 298 K; converting to 0 K and adding the vibrational energy gives ⟨E⟩ = 90 kcal mol−1. This value can be compared to ⟨E⟩ = 91 kcal mol−1 for CH2FCH2Cl.15,16 The ΔHof (CH3CHFCH2Cl) was obtained from isodesmic calculations for the reactions below. Combining the calculated energy of reaction (2.5 kcal mol−1 for both reactions according to the 6-311+G(2d,p) basis set) and the known enthalpies of formation26,27,33,34 gave CH3CHFCH3 + CH3CH 2Cl → CH3CHFCH 2Cl + CH3CH3

(5a)

CH3CH 2CH 2Cl + CH3CHFCH3 → CH3CHFCH 2Cl + CH3CH 2CH3

(5b)

−1

ΔH f (CH3CFClCH3) = −80 kcal mol . Combining this value with the enthalpies of formation of the radicals gave an enthalpy of reaction of 90 kcal mol−1 for the radical recombination at 298 K; conversion to 0 K and using eq 4 gave ⟨E⟩ = 92 kcal mol−1. The uncertainty in both ⟨E⟩ values is, at least, 2 kcal mol−1. The average energies of the chemically activated CH2FCH2Cl, CF3CHFCH2Cl, and CH3CHFCH2Cl molecules formed by radical recombination are the same to within the combined uncertainties of the thermochemistry. IV−B. Models for Molecules and Transition States. The molecular structure calculations using the Gaussian35 suite of codes with the DFT methods provide reliable vibrational frequencies and moments of inertia for these halocarbon systems.1−15 However, it is necessary to decide whether to treat the torsional motions of the CF3 (or CH3) and CH2Cl (or CH2F) groups as vibrations or as hindered internal rotations. Since 2,1-HF elimination from CF3CHFCH2Cl was not observed because of the high E0, the torsion motion of the CF3 group remains similar in both the molecule and the 2,3-HX (or 3,2-HX) and Cl/F-interchange transition states, and the CF3 torsion can be treated adequately as a vibrational mode in both structures. However, the CH2Cl (or CH2F) torsional motions become vibrational modes in the transition state structures, and it is better to treat these motions as hindered rotors in the CF3CHFCH2Cl and CF3CHClCH2Cl molecules. The CH3 and CH2Cl torsional motions in CH3CHFCH2Cl were both treated as hindered rotors since 1,2-HF as well as o

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The preference for 2,3-HF elimination from CF3CHClCH2F rather than 3,2-HCl elimination is supported by the DFT calculations. On the basis of the available evidence, it seems that the combination of DFT calculations of the transition-state structures and conventional application of statistical unimolecular reaction theory provides satisfactory explanations for the unimolecular reactions of CH2FCD2Cl, CH3CHFCH2Cl, and CF3CHFCH2Cl with 90 kcal mol−1 of vibrational energy. The threshold energies for CH3CHFCH2Cl range from 56 to 60 kcal mol−1; 1,2- and 3,2-HF elimination have a 2 kcal mol−1 lower E0 than 2,3-HCl elimination, which has the highest value. The 56 kcal mol−1 assignment for Cl/F interchange indicates a definite reduction in threshold energy relative to CH2FCD2Cl. The rate constants for CH 3 CHClCH 2 F have a large uncertainty; however, E0 values can be asigned to establish the trends. Clearly the E0 for HCl elimination from the two channels are comparable and both are several kcal mol−1 lower than that for HF elimination.The difficulty in devising a reliable calibration for the D/S ratios for the CH3CHFCH2Cl system should be remembered; a change in the calibration factor would systematically change the rate constant and the E0 assignments.

reaction path degeneracies and the sum of states of the transition state for that process. At a common energy of 30 kcal mol−1, the relative values for the ∑P†(E − E0) are 1.0:1.4:2.0 for the interchange, HF-elimination, and HCl-elimination transition states, respectively, from CF3CHFCH2Cl. The ratios of the sums of states are similar for the transition states of the other three molecules. The reaction path degeneracies are 1, 2, and 1 for interchange, 3,2-HF (cis- and trans-geometries) and 2,3-HCl elimination, respectively, for CF3CHFCH2Cl. A common E0 was assigned to the 3,2-HX elimination process based on the sum of the calculated rate constants for cis- and trans-geometries. The experimentally based assignments of the E0 values are summarized in Table 2. The overall uncertainty in the absolute Table 2. Assignment of Threshold Energies process CF3CHFCH2Cl* 3,2-Cl/F 2,3-HCl 3,2-HF CF3CHClCH2F* 2,3-HF 3,2-HCl CH3CHFCH2Cl* 3,2-Cl/F 2,3-HCl 1,2-HF 3,2-HF CH3CHClCH2F* 1,2-HCl 3,2-HCl 2,3-HF CH2FCH2Cl*a 2,1-Cl/F 1,2-HCl 2,1-HF

⟨E⟩ kcal/mol

kexpt s−1

k⟨E⟩ s−1

E0 kcal/mol

1.3 × 104 3.4 × 104 2.1 × 104

1.4 × 104 4.2 × 104 2.2 × 104

64 ± 2 64 ± 2 65 ± 2b

5.9 × 10 1.0 × 104

6.0 × 10 0.92 × 104

61 ± 2 67 ± 3

0.70 × 107 0.38 × 107 1.5 × 107 1.0 × 107

0.72 × 107 0.48 × 107 1.5 × 107 1.0 × 107

56 60 58 58

3.2 × 107 1.1 × 107 0.057 × 107

2.6 × 10 7 1.0 × 107 0.052 × 107

58 ± 3c 59 ± 3 62 ± 3

0.40 × 108 0.82 × 108 1.1 × 108

0.62 × 108 1.4 × 108 1.3 × 108

62 ± 3 65 ± 2 63 ± 2

90

V. DISCUSSION V-A. Substituent Effects on Threshold Energies for Cl/ F Interchange. The most striking result for the CH2FCD2Cl, CF3CHFCH2Cl, and CH3CHFCH2Cl series is the similarity of the branching fraction for the Cl/F interchange reaction, which is approximately 0.18 for all three cases. Thus, whatever the nature of the substituent effect, it seems to affect the interchange reaction and the HX-elimination reactions in a similar way. The experimentally assigned threshold energies are 62, 64, and 56 kcal mol−1 for CH2FCD2Cl, CF3CHFCH2Cl, and CH3CHFCH2Cl, respectively, which follows the trend from the DFT calculations illustrated in Figure 1. Evidently the CF3 group increases E0 for Cl/F interchange, whereas the CH3 group lowers E0. Furthermore, the effect is more pronounced for CH3 than for CF3. These trends are in accord with expectations for the effects of electron-releasing and electronwithdrawing groups on the threshold energies of dyotropic rearrangement reactions involving halogen atoms.18,19 Fernández and co-workers found a linear correlation between the calculated threshold energies and the Hammett σp. Those constants37 are −0.17 for CH3 and 0.54 for CF3, and a quantative correlation does not seem to hold for the CF3 group.The correlation is better for the calculated E0 values, which are 57, 60, and 65 kcal mol−1 for CH3CHFCH2Cl, CH2FCH2Cl, and CF3CHFCH2Cl, respectively, according to the 6-31G(d′,p′) calculations. The CF3 and CH3 groups do distort the geometry of the bridged transition state without changing the C−C distance appreciably, as illustrated in Figure 1. The C−F and C−Cl distances closer to the C(H) (CF3 or CH3) end are lengthened, and the halogen atoms are displaced slightly toward the CH2 end of the structure. This effect is more noticeable for the CH3 group than for the CF3 group. The initial discovery6 of the Cl/F interchange reaction was with the CF2ClCF2CH3 molecule, which had the benefit of the effect of the CH3 group, but the unfavorable effect was associated with an F-atom on the same carbon atom as the methyl group in the transition state, and the E0 was8 67 kcal mol−1. In contrast the E0 for CF2ClCHFCH3 was8 just 57 kcal mol−1, and the full electron donating effect of the methyl group is realized. V−B. Substituent Effects on Threshold Energies for HCl and HF Elimination Reactions. Before considering

88 4

4

92 ± ± ± ±

3c 3 3 3

91

91

a

The E0 for the interchange rate constant is from the study of CH2FCD2Cl in ref 16. The E0s for the elimination reactions are from ref 15. bThis value was assigned by using the sum of rate constants for the cis- and trans-isomers. If the E0 are assigned separately, the values would be 64.5 (trans) and 66.0 (cis) kcal mol−1. cThe large uncertainty is associated with the difficulty in the calibration for the relative concentrations of CH3CHFCH2Cl and CH3CHClCH2F, see text.

value of the threshold energies is ±2−3 kcal mol−1. However, the relative values should be more reliable. The assigned E0 values for CF3CHFCH2Cl are 64, 65, and 64 kcal mol−1 for interchange, HF elimination, and HCl elimination, respectively. The striking aspect is their similarity. Interchange and HCl elimination both have a reaction path degeneracy of one, but the larger sums of states and moment of inertia ratio for HCl elimination combine to provide a rate constant ratio of 2.4 for the same E0. The best measure of E0 for the interchange reaction in CF3 CHClCH2 F is to use the value from CF3CHFCH2Cl and subtract the endoergicity (∼2 kcal mol−1; see Figure 1) of the isomerization. The E0 for the principal reaction from CF3CHClCH2F, which is 2,3-HF elimination, was assigned as 61 kcal mol−1. The 3,2-HCl elimination rate is 6 times slower than for HF elimination. This difference corresponds to an increase of E0 by ∼5 kcal mol−1 and E0 for 3,2-HCl elimination must be close to 68 kcal mol−1. 2893



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exists between the isomers of the CF3CHCHX and CH3CHCHX propenes also exists for the geometric isomers of the precursor transition states.

CF3CHFCH2Cl and CH3CHFCH2Cl, the threshold energies of some simpler, but related, molecules should be reviewed. The thermal activation studies for CH3CHClCH3 have been recently reviewed,38,39 and the Ea value of 52.1 ± 0.3 kcal mol−1 corresponds to a threshold energy of 50.1 kcal mol−1. The CH3CHFCH3 molecule has been less extensively studied, but thermal and chemical activation studies40 favor E0 = 54 ± 1 kcal mol−1. The CH3 group on CX lowers the threshold energy by 4 ± 1 kcal mol−1 relative to CH3CH2CH2Cl and CH3CH2CH2F. A chemical activation study32 of CF3CFClCH3 established that the CF3 group raised the threshold energies for HF or HCl elimination by 7−8 kcal mol −1 . The CH3CHClCH2Cl molecule provides an example,41 which illustrates the elevation of E0 for 2,3-HCl elimination by the presence of adjacent chlorine atoms. The favored product is 3chloropropene (1,2-HCl elimination with Ea = 54 kcal mol−1) followed by 1-chloropropene (3,2-HCl elimination with Ea = 54 kcal mol−1 for the average of the cis- and trans-isomers). The least favored product is 2-chloropropene (2,3-HCl elimination with Ea = 59 kcal mol−1); the transition state has the second Cl atom on the CH atom. The intermolecular comparison12,15 between CH3CH2X and CH2XCH2X molecules shows a similar increase in E0 of ∼5 kcal mol−1 for the 1,2-dihalide series of molecules. The second lesson from the CH3CHClCH2Cl molecule is that the CH3 and CH2Cl groups on CX both lowered the Ea (or threshold energy) for loss of HCl. The similar reduction in E0 by the CH3 and CH2Cl (or CH2F) groups for CH3CHFCH2Cl (or CH3CHClCH2F) for 1,2- or 3,2-HX elimination is clearly demonstrated by the results of the present study. The effect of the CH3 group to reduce E0 seems to overcome the expected effect of the F (or Cl) atom on CH to increase the E0 for 3,2-HX elimination. However, the presence of the F (or Cl)-atom on CH does increase the E0 for 2,3-HCl (or 2,3-HF) elimination. Relative to CH2ClCH2F, substitution of a methyl group on either end of the molecule certainly lowers the threshold energies for unimolecular reaction. The CF3 group and the adjacent halogen-atom effect act with the same tendency, and except for 2,3-HF elimination from CF3CHClCH2F, all threshold energies are increased for CF3CHFCH2Cl and CF3CHClCH2F relative to CH2ClCH2F. The combined effect is especially strong for 3,2-HCl elimination from CF3CHClCH2F because the CF3 group and the F atom both attract electron density and E0 = 67 kcal mol−1 is exceptionally high for elimination of HCl. As a final point, the inversion of the trans- to cis-CF3CH CHX and CH3CHCHX product ratios formed by 3,2-HX elimination reactions of the CF 3 CHFCH 2 Cl and CH3CHFCH2Cl systems should be considered. For most substituted 1-halopropenes, the trans-isomer is the more stable, and this is consistent with the trans/cis product ratios from CF3CHFCH2Cl and CF3CHClCH2F. However, the cis-isomer is favored for the 1-bromo, 1-chloro, and 1-fluoropropenes,42 and this also is the case for the 1-halopropene products from the CH3CHFCH2Cl and CH3CHClCH2F reactions. These trans/cis ratios are consistent with the development of the C− C olefinic structure in the transition state for 3,2-HF or 3,2-HCl elimination, especially for the CX carbon atom in the fourmembered ring,1,15 which is attached to the CH3 or CF3 groups. This indicates significant3 alkene character at the CX carbon; thus, the relative energy of the cis- and trans-products is reflected in the difference in energy of the corresponding cisand trans-transition state structures. The energy difference that

VI. CONCLUSIONS The influence of the CF3 and CH3 groups on the threshold energies of the dyotropic halogen-atom rearrangement reaction has been measured for vibrationally activated CF3CHFCH2Cl and CH3CHFCH2Cl molecules. The threshold energies are 64 and 56 kcal mol−1; the CF3 group raises and the CH3 lowers the threshold energy relative to CH2FCD2Cl (E0 = 62 kcal mol−1) . The DFT calculations with the B3PW91 method also support this trend for the threshold energies. On the basis pf these two examples and other electronic structure calculations,18−20 electron-density donating groups lower the threshold energy and electron-density withdrawing groups raise the threshold energy for the unimolecular halogen-atom interchange reaction. The HF and HCl elimination reactions in the CF3CHFCH2Cl and CH3CHFCH2Cl systems are in competition with the rearrangement reaction, and rate constants also were measured for these unimolecular reactions. The branching fraction for rearrangement was nearly constant, 0.18 ± 0.03, in the these systems, as well as for CH2FCD2Cl, and the substituents affect the elimination and rearrangement reactions is similar ways, although specific effects can be identified for certain HCl and HF elimination reactions. In particular, the electron-density releasing character of the CH2Cl and CH2F groups is nearly as strong as for the CH3 group in promoting HF elimination from CH3CHFCH2Cl and HCl elimination from CH3CHClCH2F. For CF3CHClCH2F and CH 3 CHFCH 2 Cl, HF elimination dominates over HCl elimination. The higher threshold energies and the statistical effect associated with exchange of three H-atoms by three Fatoms reduces the rate constants of CF3CHFCH3 by 3 orders of magnitude relative to CH3CHFCH2Cl.

■

ASSOCIATED CONTENT

S Supporting Information *

Tables of the molecular and transition state structure vibrational frequencies, overall moments of inertia, and the reduced moments of inertia for the internal rotors calculated using B3PW91/6-31G(d ′,p′) for CF 3 CH ClCH 2 F, CF3CHFCH2Cl, CH3CHFCH2Cl, and CH3CHClCH2F. This material is available free of charge via the Internet at http:// pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*(B.E.H.) Phone: 828-232-5168. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■ ■

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

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Groups on the Threshold Energy for the Unimolecular Interch

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