Characterization of the 1, 1-HF Elimination Reaction from the

Apr 8, 2015 - Department of Chemistry, University of North Carolina, One University Heights, Asheville, North Carolina 28804-8511, United. States. ‡...
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Characterization of the 1,1-HF Elimination Reaction from the Competition between the 1,1-HF and 1,2-DF Unimolecular Elimination Reactions of CD3CD2CHF2 Leah N. Wormack, Meghan E. McGreal, Corey E. McClintock, George L. Heard, D. W. Setser,‡ and Bert E. Holmes* Department of Chemistry, University of North Carolina, One University Heights, Asheville, North Carolina 28804-8511, United States ‡ Kansas State University, Manhattan Kansas 66506, United States S Supporting Information *

ABSTRACT: The recombination of CHF2 and C2D5 radicals was used to produce CD3CD2CHF2* molecules with 96 kcal mol−1 of vibrational energy in a room temperature bath gas. The formation of CD3CDCHF and CD3CDCDF was used to identify the 1,2-DF and 1,1-HF unimolecular elimination channels; CD3CDCDF is formed by isomerization of the singlet-state CD3CD2CF carbene. The total unimolecular rate constant is 1.6 × 106 s−1, and the branching ratio for 1,1-HF elimination is 0.25. Threshold energies of 64 ± 2 and 73 ± 2 kcal mol−1 were assigned to the 1,2-DF and 1,1-HF reaction channels. The E and Z isomers of 1-fluoropropene were observed for each reaction; approximately 30% of the CD3CDCDF molecules derived from 1,1-HF elimination retained enough energy to undergo cis−trans isomerization. Electronic structure calculations with density-functional theory were used to characterize the transition-state structures and the H atom migration barrier for CD3CD2CF. Adjustment of the rate constants to account for kinetic-isotope effects suggest that the branching ratio would be 0.20 for 1,1-HF elimination from C2H5CHF2. The results from an earlier study of CD3CHF2 and CH3CHF2 are also reinterpreted to assign a threshold energy of 74 kcal mol−1 for the 1,1-HF elimination reaction. Because CHF2CHF2* is generated in the photolysis system, the 1,1-and 1,2-HF-elimination reactions of CHF2CHF2* are discussed. The 1,1-HF channel was identified by trapping the CF2HCF carbene with cis-butene-2.

I. INTRODUCTION In recent years we have studied the unimolecular 1,2-HX (X = F, Cl, Br) elimination reactions in conjunction with measuring the rates of the halogen interchange reactions of 1,2dihaloalkanes using chemical-activation techniques.1−4 Transition-state models, threshold energies, and substituent effects were characterized. The 1,1-dihalide class of haloalkanes were not studied because the competition with 1,1-HX elimination reactions made mechanistic interpretations more difficult. We now wish to present a study of chemically activated CD3CD2CHF2*; the 1,1-HF and 1,2-DF reactions can be identified, and the 1,1-HF reaction can be studied. The unimolecular 1,1-HX elimination reactions of dihalo- and trihalomethanes have been known for some time and continue to be of interest.5−9 However, to our knowledge 1,1-HX elimination has been documented for only a limited number of 1,1-dihaloethanes, namely, CD3CHF2 (the CF2CD2 + HD product proposed in this paper can be explained by the recombination of CF2 with CD3 followed by the decomposition of vibrationally excited CD3CF2)10,11 CH2ClCDCl2,12 and CH2FCDF2,13 although the 1,1-HX channel has been assumed to be important for CF 3 CHF 2 , CF 2 ClCHF 2 , and CF3CHCl2.14−16 Stabilization of the singlet carbene product © 2015 American Chemical Society

by the halogen atom is required for 1,1-HX elimination to be competitive with 1,2-HX elimination from 1,1-dihaloalkanes. Other methods to generate carbenes in the gas phase are thermolysis and photolysis of diazirines17 and thermal rearrangement reactions of certain organosilane molecules,18 such as CF3CFX-SiF3 and CHF2CFX-SiF3. Modern computational methods for electronic structures have provided reliable information about energies and isomerization barriers for carbenes, and CH3CCl and CH3CF have been extensively studied.19−25 The potential-energy barriers to H atom migration are 17 ± 2 and 12 ± 2 kcal mol−1 for CH3CF and CH3CCl, respectively, and tunneling has been proposed to explain the observed isomerization to vinyl fluoride and vinyl chloride at modest temperatures. Current understanding19−25 of the thermochemistry and potential-energy barriers for isomerization of CH2X−CX type carbenes (X = F, Cl) requires significant upward revision of the threshold energies assigned in earlier work11−13 to the 1,1-HF and 1,1-HCl unimolecular elimination processes in the gas phase. Therefore, the data from Received: February 3, 2015 Revised: April 3, 2015 Published: April 8, 2015 3887

DOI: 10.1021/acs.jpca.5b01129 J. Phys. Chem. A 2015, 119, 3887−3896

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Figure 1. Energy profile for the C2D5CHF2 system. The minimum value of the threshold energy for 1,1-HF elimination is the enthalpy of reaction for C2D5CHF2 → HF + CD3CDCDF plus the enthalpy of isomerization of CD3CD2CF. The activation energy for the addition of C2H5CF to HF has not been studied; our results suggest a value of ≈2 kcal mol−1. The calculated9 activation energy for the HCF carbene + HF reaction is about 10 kcal mol−1. The DFT calculated threshold energies are 62 and 70 kcal mol−1 for 1,2-DF and 1,1-HF elimination, respectively. On the basis of the thermochemistry,28 the minimum threshold energy for formation of CHF2CF + HF from CHF2CHF2 is 79 kcal mol−1. The calculated energy barrier for H atom migration in CHF2CF is 9.9 kcal mol−1.

the CD3CHF2* system11 will be reconsidered with this new study of C2D5CHF2*. Because CF2HCF2H* molecules are generated in the experiment, we have also taken this opportunity to discuss the 1,1- and 1,2-HF elimination reactions of this molecule. We have used the chemical activation technique to measure the experimental rate constants for CD3CD2CHF2* with an average energy of 96 kcal mol−1. The molecules are generated by the recombination of C2D5 and CHF2 radicals at room temperature. The radicals are produced by the cophotolysis of C2D5I and CHF2I at room temperature. The reaction scheme is outlined below, and the energy profile of the system is shown in Figure 1. The vibrational energy is denoted by the asterisk and M represents the bath gas molecules.

The CD3CD2CF* product will retain sufficient vibrational energy to isomerize to 1-fluoropropene-d5 at the pressures of these experiments and we do not expect collisional stabilization to be important. This isomerization may proceed, in part, by tunneling through the potential-energy barrier. CD3CD2 CF* → Z ‐CD3CDCDF (cis) → E‐CD3CDCDF (trans) + M → CD3CD2 CF + M

The ratio of CD3CDCHF/CD3CDCDF can be used to determine the branching ratio for 1,2-DF and 1,1-HF elimination channels, and the total rate constant, kexp, is obtained by measuring the total 1-fluoropropene/1,1-difluoropropane ratio vs bath gas pressure−1, i.e., from the competition between collisional deactivation and decomposition (kexp/ kM[M] = [D]/[S]; kM is the rate constant for collisions). The rate constant for loss of HF from CHF2CHF2* by either 1,1HF or 1,2-HF reaction also was determined by measuring the ratio of CF2CHF/CHF2CHF2 vs the inverse pressure. The H atom migration reaction of carbenes is known to favor formation of the Z-isomer of the alkene17,21,22 and that is the case for CD3CD2CF*, which preferentially gives cis-CD3CD CDF. Depending upon how the 25 kcal mol−1 excess energy is divided between HF and CD3CD2CF, cis-2-fluoropropene-d5 may have enough energy to isomerize to the trans isomer; see Figure 1 for the energy profile. The cis- and trans-CD3CD CHF molecules from 1,2-DF elimination do not retain enough energy to isomerize

C2D5 + CHF2 → CD3CD2 CHF2* 2CHF2 → CHF2CHF2* 2C2D5 → C4 D10*

(1)

The disproportionation reactions26 of C2D5 and CHF2 were observed, but those products are not of direct interest. The C2D5CHF2* and CHF2CHF2* molecules have 96 kcal mol−1 of energy and will lose DF or HF unless stabilized by collisions with bath gas molecules, M. CD3CD2 CHF2* → CD3CD2 CF* + HF → Z ‐ and E‐CD3CDCHF + DF + M → CD3CD2 CHF2 + M

(3)

(2) 3888

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The Journal of Physical Chemistry A Electronic structure calculations were done with the Gaussian-09 suite of codes.27 Density-functional theory, DFT, calculations were done to establish the structures and relative energies of the molecules and transition states. After some survey calculations, we selected the B3PW91/cc-pDVZ method to describe the 1,1-HF and 1,2-DF transition states. The B3PW91/6-311+G(2d,p) method also was used to describe the properties of CD3CD2CF. The calculated frequencies and moments of inertia of the molecules and transition states were employed to calculate the statistical rate constants that were matched to the experimental values to obtain threshold energies for 1,2-DF and 1,1-HF elimination. Evaluation of the kinetic-isotope effects permits the 1,1-HF product branching ratio to be estimated for CH3CH2CHF2 based on the results from CD3CD2CHF2. A major goal is to characterize the transition state for 1,1-HF elimination as a reference for future work involving 1,1-HCl elimination reactions. Unless stated otherwise, we assume that the total carbene concentrations from 1,1-HF elimination were measured from their rearranged alkene counterpart.

Figure 2. Ratios of product to reactant vspressure−1 from GC−FID data. The total rate constant for C2D5CHF is derived from the 1fluoropropene/1,1-difluoropropane ratios (○); the slope and intercept of the plot are 0.107 ± 0.006 and 0.030 ± 0.033, respectively, with a correlation coefficient of 0.962. The overall cis/trans ratio of 1fluoropropene (◆) is 1.35.

II. EXPERIMENTAL METHODS AND RESULTS The experiments consisted of photolysis of CHF2I and C2D5I mixtures in a 3:8 molar ratio together with a small amount of solid Hg2I2 followed by analysis with gas chromatography using mass spectrometric (GC−MS) or flame ionization (GC−FID) detectors. The photolysis source was a 200 W Xe/HgXe ultraviolet Oriel lamp, and the photolysis times were 2−10 min depending on the size of the Pyrex vessels, which ranged from 15 to 1000 cm3. Samples were prepared and transferred using standard procedures with a grease-free, all-glass, vacuum system. The response of the GC−FID was calibrated from prepared calibration mixtures of CH 3 CFCH 2 and CH3CH2CHF2; 2-fluoropropene was used because a sample of 1-fluoropropene was not available. The response of the GC− FID for 2-fluoropropene and 1-fluoropropene should be similar. The cis-1-fluoropropene eluted before the trans isomer. The total rate constant was determined from experiments using GC−FID analysis with a MXT-624 column with a starting temperature of 28 °C. The pressure range was 2−0.05 Torr; the ratios of 1-fluoropropene-d4 and -d5/1,1-difluoropropane-d5 and cis-1-fluoropropene/trans-1-fluoropropene are shown in Figure 2. The slope of the decomposition/ stabilization (D/S) vs inverse pressure plot is 0.107 ± 0.006 Torr with an intercept of zero. The slope is converted to a rate constant in s−1 units after multiplication by the collision rate constant; the result is 1.6 × 106 s−1. The overall cis-1fluoropropene/trans-1-fluoropropene ratio, as measured by GC−FID, is 1.35, and the data are shown in Figure 2. The 1,1-HF and 1,2-DF branching ratio was determined in experiments using GC−MS detection over a wide pressure range. The Shimadzu QP2010 GC−MS used a Restek 105 m RTX-200 column for isotopic analysis of the 1-fluoropropenes. The parent mass peaks were integrated separately for cis-1fluoropropene-d4 and -d5 and trans-1-fluoropropene-d4 and -d5. The branching ratio was determined by adding together the cisand trans-d4 signals and the cis- and trans-d5 signals. The result is shown in Figure 3; the 1,2-DF/1,1-HF branching ratio is 4.09 ± 0.02, and it is independent of pressure. The individual rate constants for 1,2-DF and 1,1-HF elimination are summarized in Table 1. After selection of the parameters for the collision partners, which are given in the footnotes of Table 1, the uncertainty in the rate constants was increased to ±20%. The

Figure 3. Product branching ratios from GC−MS data plotted vs pressure−1. 1-Fluoropropene-d5 is monitored at mass 65 and 1fluoropropene-d4 at mass 64. Key: (○) 1-fluoropropene-d4/1fluoropropene-d5, i.e., the ratio of 1,2-DF/1,1-HF elimination (the product branching ratio is 4.09 ± 0.02); (□) ratio of cis-CD3CD CHF/cis-CD3CDCDF; (◆) ratio of trans-CD3CDCHF/transCD3CDCDF. The decline in the trans-CD3CDCHF/transCD3CDCDF ratio is a consequence of the cis → trans isomerization of CD3CDCDF; the loss of cis-CD3CDCDF is too small to affect the cis-CD3CDCHF/cis-CD3CDCDF ratio on the scale of the plot.

overall cis/trans-1-fluoropropene ratio from the GC−MS measurements for the 0−50 Torr−1 pressure range is in agreement with the GC−FID data in Figure 2. However, the 3889

DOI: 10.1021/acs.jpca.5b01129 J. Phys. Chem. A 2015, 119, 3887−3896

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The Journal of Physical Chemistry A Table 1. Rate Constants for ⟨E⟩ = 96 kcal mol−1 and Threshold Energies experimental resultsa reaction

rate constants, s−1

C2D5CHF2 → CD3CDCHF + DF

1.28 ± 0.24 × 106 cis/trans = 1.3 ± 0.1b 0.32 ± 0.06 × 106 cis/trans = 4.1 ± 0.2c

C2D5CHF2 → CD3CDCDF + HF C2H5CHF2 → CH3CHCHF + HF CHF2CHF2 → CF2CHF + HF

1.9 × 105

calculated results E0, kcal mol−1 64 65 73 72 64 73 80 85

(1,2-HF)d (1,1-HF) (1,2-HF)e (1,1-HF)e

kE, s−1 1.9 × 106 1.2 × 106 0.29 × 106 0.47 × 106 5.9 × 106 1.2 × 106 2.2 × 105 1.7 × 105

The collision diameters, Å, and (ε/k) values used to calculate the collision rate constant, kM: C2D5I, −5.0 (394 K); CHF2I, −5.4 (298 K); C2D5CHF2, −5.3 (250 K); CHF2CHF2, −5.2 (201 K). These give collision rate constants of 4.6 × 10−10 and 4.1 × 10−10 cm3 molecule−1 s−1, respectively, for C2D5CHF2 and CHF2CHF2, kM = πdM2(8kT/πμM)1/2Ω22*(T). bThe cis/trans ratio from 1,2-DF elimination, which is invariant with pressure. cThe cis/trans ratio from D atom migration of C2D5CF; the observed ratio changes with pressure because of the isomerization of 1fluoropropene-d5; see text. dThis rate constant should be compared to the E0 = 65 kcal mol−1 entry of C2D5CHF2. eThe two entries for E0 are for either exclusively 1,2-DF or 1,1-HF elimination reactions. The Arrhenius expressions are discussed in the Discussion. a

85 kcal mol−1 of energy, and the majority of the CD3CD CDF molecules must not have sufficient energy to isomerize. The threshold energy is expected to be 63 ± 3 kcal mol−1 for cis−trans isomerization of 1-fluoropropene.30 The high and low pressure limits suggest that approximately 30% of the 1fluoropropene molecules have enough energy to isomerize. The decomposition to stabilization plot for elimination of HF from CHF2CHF2 is shown in Figure 5. The measurements

decline in the trans-CD3CDCHF/trans-CD3CDCDF ratio with decreasing pressure suggests that conversion of cis to trans isomers of CD3CDCDF may occur. The cis/trans-ratios for each reaction channel are shown separately in Figure 4. The ratio for 1,2-DF elimination, i.e., 1-

Figure 4. Plots of the cis/trans ratios of 1-propene-d4 from 1,2-DF elimination (●) and 1-fluoropropene-d5 from 1,1-HF elimination (■). The data for 1,1-HF elimination also are shown plotted vs pressure for the 0−0.1 Torr range (◆).

Figure 5. Plot of the decomposition to stabilization ratio for CF2HCF2H. The slope and intercept of the linear fit are 0.0137 ± 0.0004 and 0.0018 ± 0.017, respectively, with a correlation coefficient of 0.987.

fluoropropene-d4, is independent of pressure and has a value of 1.3. This ratio reflects the small difference in the threshold energies of the cis and trans transition states for 1,2-DF elimination. However, the cis/trans ratio from 1,1-HF elimination, i.e., for 1-fluoropropene-d5, is much larger and declines from a ratio of 4.1 ± 0.2 to 2.4 ± 0.2 as the pressure is reduced. The high pressure cis/trans ratio of 4.1 is governed by the preference for cis-1-fluoropropene-d5 formation in the isomerization of C2D5CF. The pressure dependence of the ratio indicates that a certain fraction of the CD3CDCDF molecules have sufficient energy to isomerize. The equilibrium ratio of cis/trans should be close to 1.0 for molecules with 80−

were made with the GC−MS with calibration from samples of CHF2CHF2 and CF2CHF. The data appear to be of good quality and give a slope of 0.014 Torr. The corresponding rate constant, which represents the total formation of CHFCF2, is 1.9 × 105 s−1; see Table 1. The small rate constant, relative to those for C2D5CHF2* or CH3CHF2*, must be a consequence of elevated threshold energies for both 1,2- and 1,1-HF elimination reactions. Inspection of Figure 1 shows that higher enthalpies of reaction for 1,1-HF elimination reduce the energy 3890

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of inertia of 19.6 amu Å2 to represent the molecule. The C2D5 torsional frequency (40−80 cm−1 depending on DFT method and basis set) in the transition state for 1,1-HF elimination was very low and the barriers to internal rotation of C2D5CF are very small. Therefore, we treated this motion as a free-rotor with a reduced moment of 25.1 amu Å2. The torsional motion in the 1,1-HF transition state of CHF2CHF2 also was treated as a free rotor (Ired = 26.1 amu Å2), or with a barrier of 2 kcal mol−1 for comparison. The anti conformer of CHF2CHF2 with an internal rotational barrier of 4.0 kcal mol−1 and Ired = 26.1 amu Å2 was used as the model to calculate the density of states for CHF2CHF2. The transition states for 1,1-HF and 1,2-DF elimination were easily identified and the frequencies and moments of inertia are tabulated in the Supporting Information. 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.31 The rate constants were obtained from the usual RRKM expression.

released to CHF2CF and introduce the possibility that H atom migration may not readily occur. Therefore, some experiments with added cis-butene-2 were conducted in an attempt to trap CHF2CF molecules that lacked sufficient energy to isomerize to CF2CHF. These qualitative trapping experiments did identify CHF2CF molecules from the addition product to butene-2. Therefore, some 1,1-HF elimination from CHF2CHF2 does occur. Further analysis of the CHF2CHF2* reaction is delayed for the Discussion.

III. COMPUTATIONAL METHODS AND RESULTS The average energy of C2D5CHF2* and CHF2CHF2* can be obtained from reliable thermochemistry. The enthalpies of formation of CHF2 (−57.2 kcal mol−1), C2H5 (28.7 kcal mol−1), and CF2HCF2H (−211.0 kcal mol−1) were taken from Haworth et al.28 and the enthalpy of formation of C2H5CHF2 (−124 kcal mol−1) was obtained from the compilation by Khursan.29 The enthalpy of the recombination reactions are both −95 kcal mol−1 at 298 K. Converting to 0 K and adding the average thermal energies of the reactants increases the average energy to 96 kcal mol−1 for both reactions. These values have an uncertainty of ±2 kcal mol−1. The energy of C2D5CF + HF relative to C2D5CHF2 can be estimated as 71 ± 2 kcal mol−1 from the enthalpy change for the formation of 1fluoropropene-d4 + HF plus the isomerization energy of C2D5CF. The energy of isomerization was calculated from B3PW91/6-311+G(2d,p) to be 55.3 and 54.8 kcal mol−1 for the cis and trans isomers, respectively; the values were 54.4 and 53.7 kcal mol−1 with the cc-pVDZ basis set. The threshold energies of the transition states for H atom migration were 9.0 (and 9.3) and 9.9 (and 10.8) kcal mol−1 for the cis and trans geometries, according to the 6-311+G(2d,p) (and cc-pVDZ basis sets). Similar differences in the energies for cis and trans geometries of the transition states were found for other DFT methods, as well as in published reports.21−25 The minimum threshold energy28 for CHF2CF formation from CHF2CHF2 is 79 kcal mol−1, and the calculated barrier (B3PW91/6311+G(2d,p)) for H atom migration of 9−10 kcal mol−1 implies that H atom tunneling must be important for CHF2CF, if CHFCF2 is formed via 1,1-HF elimination. Calculations of molecular structures associated with the C2D5CHF2 and CHF2CHF2 reactions were done using the Gaussian-09 suite27 of codes. The B3PW91 method with the cc-pVDZ basis set was adopted to describe the molecules and their transition states. Calculations were done for C2H5CHF2 and C2H5CDF2, as well as for C2D5CHF2, to account for kinetic-isotope effects. Intrinsic reaction coordinate tests (IRC) were made to ascertain that the transition states were true saddle points that connected reactants and products. The vibrational frequencies and moments of inertia are listed in the Supporting Information. The C2D5 torsional motion in C2D5CHF2, the CHF2 torsional motion in CHF2CHF2, and the C2D5 and CHF2 torsional motions in the 1,1-HF transition states were treated as internal rotations and those descriptions are presented in the paragraph below. Because the CD3 torsion remains the same motion in the molecule and transition states, it was treated as a vibration. The gauche and anti conformers associated with the C2D5 internal rotation in the molecule differed in energy by only 0.13 kcal mol−1 with the anti conformer having the lower energy. The potential-energy barriers to internal rotation are 3.5 and 3.9 kcal mol−1. We adopted the anti conformer with an average potential-energy barrier of 3.7 kcal mol−1 and reduced moment

kE = (s†/h)(I †/I )1/2

∑ P†(E − E0)/N *(E)

(4)

The I†/I term is the ratio of overall moments of inertia, and s† is the reaction path degeneracy (2 for 1,1-HF and 4 for 1,2-DF elimination). The (I†/I)1/2 favors the 1,1-HF rate constant over the 1,2-DF rate constant by a factor of 1.05. Because the frequencies of the two geometric isomers of the 1,2-DF transition state were nearly identical, the sums of states for the 1,2-DF rate constant were calculated with the frequencies of the trans-isomer. The threshold energy, E0, was varied until the calculated rate constant from eq 4 matched the experimental rate constant. The assigned threshold energies are listed in Table 1. Given the uncertainties in the calculated and experimental rate constants, the assigned E0 have an uncertainty of ±2 kcal mol−1. We prefer 64 ± 2 kcal mol−1 for 1,2-DF because of the results11,32 for CD3CHF2 (vide inf ra). The E0 for 1,1-HF elimination is 73 ± 2. The ≈10 kcal mol−1 difference in threshold energies between 1,2-DF and 1,1-HF elimination is especially worthy of note. For the same internal energy (22 kcal mol−1), the ratio of the ∑P†(E − E0) terms is 19, and the low frequencies of the transition state for 1,1-HF elimination compensates for the 10 kcal mol−1 difference in E0 values. The DFT calculated threshold energies were 62 and 70 kcal mol−1 for 1,2-DF and 1,1-HF elimination from C2D5CHF2. Two threshold energies are listed in Table 1 for CH2FCH2F corresponding to reaction by either 1,2-HF elimination (80 kcal mol−1) or 1,1-HF (85 kcal mol−1) elimination. High values are required to match the small experimental rate constant. Early qualitative chemical-activation studies32 using photolysis of (CHF2)2CO at 250 °C also reported small rate constants (0.1 ± 0.04 Torr) for CHF2CHF2; all of the experimental evidence supports small rate constants with high E0 values. The calculated E0 values of 75 (1,2-HF) and 77 (1,1-HF) kcal mol−1 also are quite high. Additional interpretation of the CHF2CHF2 reaction is reserved until the Discussion.

IV. DISCUSSION IV-A. C2D5CHF2. The 1,2-DF reaction is typical for 1,2-HF elimination reactions1,2,4 and only the kinetic-isotope effect merits additional analysis. Thus, attention will be focused on the 1,1-HF channel, which is clearly defined by the present experiment with C2D5CHF2 in which 20% of the overall 3891

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Figure 6. Diagrams of the transition states for 1,2-DF and 1,1-HF elimination from C2D5CHF2. The structures of C2D5CF and the 1,1- and 1,2-HF transition states for CHF2CHF2 also are shown for comparison. Standard bond lengths from molecules that can be used for reference are C−H = 1.088 Å, C−F = 1.376 Å, and H−F = 0.917 Å. The angles of C−C−F = 104.3° and C−C−H = 120.5° for the F and H in the three-membered ring for 1,1-difluoropropane and the same angles are 98.5° and 116.3° for CHF2CHF2.

unimolecular reaction proceeds via 1,1-elimination. These conclusions for C 2 D 5 CHF 2 are similar to those for CD3CHF2; see below. The assignment of E0 = 73 ± 2 kcal mol−1 is consistent with the currently accepted thermochemistry for C2H5CF (and CH3CF), which provides a rigorous lower limit to the E0 obtained from analysis of the kinetics. In general, the 10 ± 2 higher threshold energy for 1,1-HX processes can be compensated by a greater number of internal

states in the 1,1-transition state, and competition will exist with the 1,2-HX process for most 1,1-dihaloalkanes at high levels of excitation (or high temperature). We used a free-rotor model for the internal rotation of C2D5−CHF2 in the 1,1-HF transition state; the rate constant decreases by 20−30%, if a barrier of 2 kcal mol−1 is assumed. Other basis sets or DFT methods give similar frequencies to the method used here, and those assignments of E0 should fall into the ±2 kcal mol−1 3892

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that the majority of the C2D5CF molecules will have isomerized, but additional work is needed to quantify the probability for D atom tunneling. This conclusion is at variance with the claim that only 30−40% of the 1-fluoropropene-d4 molecules have enough energy for cis/trans isomerization. However, the threshold energy for cis/trans isomerization of 1fluoropropene 30 has not been measured, the cis/trans equilibrium ratio at 85 kcal mol−1 might be larger than 1.0,34,35 and the high and low pressure experimental limits for the ratio have some uncertainty. Thus, several factors are not known precisely. The current experiments define the minimum product branching fraction for 1,1-HF elimination from C2D5CHF2. The calculated kinetic-isotope effects for 96 kcal mol−1 can be used to scale the rate constants for C2D5CHF2 to obtain rate constants for C2H5CHF2 and C2H5CDF2. The kinetic-isotope effect for 1,1-HF elimination from C2H5CHF2 is a pure secondary effect with no changes in threshold energy, and the C2D5CHF2 rate constant can be scaled by the ratios of the density of states (a factor of 27.3) multiplied by the ratio of the sums of states of the transition states (a factor of 6.78) to obtain a rate constant ratio of 4.0, and the 1,1-HF rate constant becomes 1.2 × 106 s−1 based on the E0 = 73 kcal mol−1 entry of Table 1 for C2D5CHF2. For 1,2-HF elimination from C2H5CHF2, the primary kinetic-isotope effect must be recognized, and the threshold energy for HF elimination from C2H5CHF2 is 1.0 kcal mol−1 lower (i.e., 64 kcal mol−1) than for DF elimination from C2D5CHF2 for E0 = 65 kcal mol−1. The ratio of the sums of states of the transition states decreases to 5.68; the overall scaling factor is 4.8 and the rate constant for 1,2-HF elimination from C2H5CHF2 is 9.3 × 106 s−1 based on the E0 = 65 kcal mol−1 entry for C2D5CHF2. Based on these scaled rate constants, the branching ratio for 1,1-HF elimination from C2H5CHF2 would be 0.20. Because the 1,1channel for C2H5CDF2 includes a primary kinetic-isotope effect, the threshold energy increases by 0.85 kcal mol−1 and the branching ratio for 1,1-DF elimination declines to 0.13. The rate constants for C2H5CHF2 are summarized in Table 1. IV-B. CD3CHF2 and CH3CHF2. The reactions of chemically activated CD3CHF2 and CH3CHF2 were studied previously10,11 using the photolysis of acetone-d6 and 1,1,3,3-tetrafluoroacetone as the source of radicals. The experimental data are reliable and those rate constants can be fitted with improved thermochemistry and models for the transition states. The average energy of the molecules is 96 kcal mol−1. For the collision diameters used in the current work, the rate constants for CD3CHF2 are 1.0 × 108 and 4.8 × 108 s−1 for 1,1-HF and 1,2-DF elimination, respectively. These rate constants correspond to a branching ratio of 0.21, which is nearly the same as that for C2D5CHF2. We will assume that all of the CD3CF concentration isomerizes to CD2CDF, even though the barrier to D atom migration (15−17 kcal mol−1)19 is rather high. New calculations were done for CH3CHF2 and these will be compared to the published rate constants (adjusted to our collision diameters) of 1.4 × 109 and 0.16 × 109 s−1 for 1,2-HF and 1,1-HF elimination. Fitting these rate constants using the same methods described for C2D5CHF2 gave threshold energies of 63 ± 2 and 74 ± 2 kcal mol−1 for the 1,2-HF and 1,1-HF reactions. The assignment of 74 kcal mol−1 is consistent with the minimum threshold energy (71 kcal mol−1) on the basis of the sum of the isomerization enthalpy of CD3CF and the enthalpy of reaction for formation of HF + CD2 CDF.19 In the former analysis,11 the transition state that was

range. The Arrhenius expressions calculated at 800 K for the thermal rate constants [k(T) = 1.03 × 1014 exp(−65900/RT) and 13.6 × 1014 exp(−75300/RT)] for the 1,2-DF and 1,1-HF channels with E0 values of 64 and 73 kcal mol−1) provide an overall comparison of the two reactions. The structure of the 1,1-HF transition state will be examined by considering the structures in Figure 6. According to microscopic reversibility, the transition state for 1,1-HF elimination also applies to the addition reaction of C2D5CF (or CHF2CF) to HF; thus it has some general interest. The structure of the transition states for both C2D5CHF2 and CHF2CHF2 are shown in Figure 6, but they are similar and only that for C2D5CHF2 will be discussed. The C−F distance increases by 52% in the 1,1-HF transition state and 42% in the 1,2-DF transition state relative to the C−F distance in the molecule. However, the C−H and H−F distances are shorter in the 1,1-transition state than in the 1,2-transition state. The C− H distance is only 17% longer than in the molecule, and the H−F distance is just 22% longer than in free HF. The F atom is displaced much further from its parent C atom than is the H atom in forming the three-membered ring for 1,1-HF elimination. According to Figure 6, the C−C and out-of-ring C−F bonds of the transition state have approached the geometry of the free carbene. Other computational methods and basis sets gave geometries that are similar to those shown in Figure 6 for these transition states. The H−C−F angle and the C−F length in the three-centered ring are important indices for 1,1-HX transition states, because as the angle becomes smaller the three-atom structure tends to become more collinear. Given the unusual structure and the small release of potential energy in passing the transition-state geometry, it is advisible to check explicitly that the transition state meets the test for a sensible imaginary frequency and the forward− backward IRC test. In terms of the reverse reaction, the carbene would interact mainly with the H atom of HF in forming the transition state. Measurements of the activation energies for reactions of carbenes with HX molecules would aid in defining the 1,1-HX elimination reactions. The 2 kcal mol−1 that is implied in Figure 1 for the activation energy of C2D5CF + HF may be an underestimate. In our experimental analysis we assumed that all of the C2D5CF isomerized to 1-fluoropropene-d5. The fact that the branching ratio for 1,2-DF/1,1-HF is constant for a wide range of pressure supports this claim. Also, the addition of butene-2 to the photolysis vessel gave no discernible addition product with the carbene, and the addition of butene-2 did not change the product branching ratio. Experiments under thermal equilibrium conditions for C2H5C−Cl report rapid (a lifetime of less than 10 ns is quoted in solution23) conversion to 1chloropropene. Extensive experiments33 with CH3CCl report a lifetime of 312 ns in hexane. The explanation for the short lifetimes for both ethyl- and methylchlorocarbene has been tunneling through the H atom migration barrier.20,23−25,33 The barrier is higher for fluorocarbenes and the deuterium atom will reduce the tunneling rate for C2D5CF. Analysis of the vibrational and rotational distributions of HF from 1,1-HF elimination reactions8,15 suggests that the available energy is partitioned statistically (because the release of the potential energy is very small). The mean internal energy of C2D5CF, assuming statistical partitioning, would be 17 kcal mol−1, and the time between collisions at 0.1 Torr is 1 μs. Furthermore, inspection of the statistical energy distribution shows that 80% of the distribution has ≥10 kcal mol−1 of energy. We conclude 3893

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needed to measure the actual product branching ratio and to understand the tunneling rate for CHF2CF. The activation energy of 69 ± 3 kcal mol−1 reported from high temperature shock-tube experiments40 is clearly too low; separation of the effects of radical reactions from the molecular decomposition steps is difficult in such experiments. The systematic increase in threshold energies for 1,2-HF elimination as the number of F atoms is added to the ethane structure has been noted by several investigators.10,13,32,40 One explanation for this trend is simply the decrease in the CC bond dissociation energy with fluorine substitution. As shown in Figure 6, the 1,2-DF transition state develops a partial double bond; a less strong double bond with F atom substitution would raise the threshold energy.

selected to represent 1,1-HF elimination had frequencies that were similar to those of the 1,2-HF transition state, and this led to an erroneous assignment of a low threshold energy for 1,1HF elimination, which is inconsistent with the presently established thermochemistry. The principal question that remains is whether the measurement of the CD2CDF product accurately reflects the fraction of CD3CF that was formed from CD3CHF2. If the excess energy is divided statistically, CD3CF would have an average energy of 17 kcal mol−1 and a significant fraction of the energy distribution must be below the isomerization barrier and tunneling must be operative. Additional work is needed to measure and understand the isomerization rate of CD3CF. The existing experimental measurements11 may represent a lower limit to the branching fraction for 1,1-HF elimination for CD3CHF2. The threshold energy of 63 ± 2 kcal mol−1 for 1,2-HF elimination from CH3CHF2 is consistent with the activation energy of 63.4 ± 1.1 kcal mol−1 reported in a conventional thermal activation study from 703 to 808 K36 and 61.9 ± 1.8 kcal mol−1 from a shock-tube study (1040−1320 K).37 The preexponential factors from these two studies are (4.0 ± 2.0) × 1013 and (7.9 ± 2.0) × 1013 s−1. The Arrhenius expression at 800 K from our model for 1,2-HF elimination is 12.0 × 1013 exp(−64900/RT). The Arrhenius expression at 800 K from our model for 1,1-HF elimination is 11.5 × 1014 exp(−76500/RT) for E0 = 74 kcal mol−1. Xu and co-workers38 have studied CH3CHF2 and CH2CHF in shock-tube experiments at 1500−2000 K. They developed models for calculations of the 1,2-HF elimination RRKM rate constants using the G3B3 method to evaluate their results in the falloff region of pressure. Their calculated E0(1,2-HF) of 64.4 kcal mol−1 agrees with our assignment from the chemical activation data, and their model of the transition state closely matches the vibrational frequencies of our calculations. However, at these high temperatures the 1,1-HF elimination reaction should be included in the fitting of the experimental data. IV-C. CHF2CHF2. Although analysis of the kinetics for the CHF2CHF2* molecule was not intended to be an important part of this work, this molecule presents several interesting questions. First, the high threshold energy associated with the small rate constant for 1,2-HF elimination offers the possibility that 1,1-HF elimination may be significant relative to 1,2-HF elimination. Second, the potential-energy barrier for H atom migration for CHF2CF is 9.9 kcal mol−1, and the available excess energy is less than that required for complete isomerization to CF2CHF (without extensive tunneling). Third, extensive gas-phase studies of the competition between unimolecular isomerization and bimolecular reaction of CHF2CF with an added substrate have been made under thermal equilibrium conditions.39 Therefore, we attempted to trap CHF2CF in our system by adding variable amounts of cisbutene-2 to the photolysis vessel. The two addition products were identified by comparison to MS data of ref 39, and the yield was significant; however, calibration of the GC−MS was not possible because a sample of the six-carbon trifluorocyclopropane products was not available. The addition of cis-butene2 did not affect the D/S plot shown in Figure 5; i.e., the data points with added butene-2 were the same as those without added butene-2 at the same total pressure. The qualitative observations are consistent with assigning the majority of the CF2CHF in the D/S plot of Figure 5 to 1,2-HF elimination with a probable matching component for 1,1-HF elimination that yielded CHF2CF, which did not isomerize. Further work is

V. CONCLUSIONS The product branching ratio for 1,1-HF elimination from C2D5CHF2* has been measured as 0.25, and the 1,1-HF channel competes with the 1,2-DF channel. Comparison of the experimental rate constant with calculated statistical rate constants gave a threshold energy of 73 ± 2 kcal mol−1 for 1,1-HF elimination and 64 ± 2 kcal mol−1 for 1,2-DF elimination. These results are very similar to previous experimental studies of CD3CHF2*. DFT electronic-structure calculations provide structures for the transition states, and 1,1HF elimination reactions from 1,1-difluoroalkanes have now been characterized. The calculated threshold energies by the B3PW91/cc-pVDZ method were 62 and 70 kcal mol−1 for 1,2DF and 1,1-HF elimination, respectively. Although the threshold energies for the 1,1-HF and 1,2-HF reactions differ by ≈10 kcal mol−1, the competition can be effective because of the higher entropy of the 1,1-HF transition state. The carbene formed by 1,1-HF (or 1,1-HX in general) elimination has interesting properties because of the possibility for tunneling of the H- or D atom through the H atom migration barrier. In some cases the H atom migration rate may be so slow that the carbene will undergo bimolecular reactions with components in the gas mixture. In fact, CHF2CF formed from CHF2CHF2* provides an example in which the carbene was trapped by the addition of cis-butene-2 to the photolysis mixture. The evidence indicates that the majority of the C2D5CF carbene molecules did isomerize to CD3CDCDF, but the measurements could represent a lower limit to the 1,1-HF product branching ratio, if a small fraction of the C2D5CF molecules did not isomerize.

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ASSOCIATED CONTENT

S Supporting Information *

Supporting Information contains calculated vibrational frequencies, cm−1, overall moments of inertia (Ix, Iy, and Iz), amu Å2, and reduced moments of inertia for internal rotors using B3PW91/cc-pvDZ for the transition states for the 1,2-DF and 1,1-HF elimination from CD3CD2CHF2 and the 1,2- and 1,1HF elimination from CHF2CHF2 and a Newman projection. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest. 3894

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

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