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The Unimolecular Reactions of CFCHF Studied by Chemical Activation: Assignment of Rate Constants and Threshold Energies to the 1,2-H-Atom Transfer, 1,1-HF Elimination and 1,2-HF Elimination Reactions and the Dependence of Threshold Energies on the Number of F-Atom Substituents in the Fluoroethane Molecules Caleb A Smith, Blanton R. Gillespie, George L. Heard, Donald W. Setser, and Bert E. Holmes J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b06769 • Publication Date (Web): 19 Sep 2017 Downloaded from http://pubs.acs.org on September 19, 2017

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The Journal of Physical Chemistry

The Unimolecular Reactions of CF3CHF2 Studied by Chemical Activation: Assignment of Rate Constants and Threshold Energies to the 1,2-H-Atom Transfer, 1,1-HF Elimination and 1,2-HF Elimination Reactions and the Dependence of Threshold Energies on the Number of F-Atom Substituents in the Fluoroethane Molecules Caleb A. Smith, Blanton R. Gillespie, George L. Heard, D. W. Setser# and Bert E. Holmes* Department of Chemistry, University of N. Carolina – Asheville, One University Heights, Asheville, N. Carolina, 28804-8511, United States. #

Kansas State University, Manhattan, Kansas, 66506, United States. ABSTRACT

The recombination of CF3 and CHF2 radicals in a room temperature bath gas was used to prepare CF3CHF2* molecules with 101 kcal mol-1 of vibrational energy. The subsequent 1,2-H-atom transfer, 1,1-HF elimination and 1,2-HF elimination reactions were observed as a function of bath gas pressure by following the CHF3, CF3(F)C: and C2F4 product concentrations by gas chromatography using a mass spectrometer as the detector. The singlet CF3(F)C: concentration was measured by trapping the carbene with trans-2-butene. The experimental rate constants are 3.6 x 104, 4.7 x 104 and 1.1 x 104 s-1 for the 1,2-H-atom transfer, 1,1-HF elimination and 1,2-HF elimination reactions, respectively. These experimental rate constants were matched to statistical RRKM calculated rate constants to assign threshold energies (E0) of 88 ± 2, 88 ± 2 and 87 ± 2 kcal mol-1 to the three reactions. Pentafluoroethane is the only fluoroethane that has a competitive H-atom transfer decomposition reaction, and it is the only example with 1,1-HF elimination being more important than 1,2-HF elimination. The trend of increasing threshold energies for both 1,1-HF and 1,2-HF processes with the number of F-atoms in the fluoroethane molecule is summarized and investigated with electronic-structure calculations. Examination of the Intrinsic Reaction Coordinate (IRC) associated with the 1,1-HF elimination reaction found an adduct

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between CF3(F)C: and HF in the exit channel with a dissociation energy of about 5 kcal mol-1. Hydrogen-bonded complexes between HF and the H-atom migration transition state of CH3(F)C: and the F-atom migration transition state of CF3(F)C: also were found by the calculations. The role that these carbene-HF complexes could play in 1,1-HF elimination reactions is discussed. 1. INTRODUCTION The four-centered, 1,2-HF elimination reactions of fluoroethanes, which are an important subset of unimolecular reactions, have been recognized as typical gasphase unimolecular reactions of alkyl halides for many years.1 Both thermal2-5 and chemical activation methods6-8 were used to characterize the Arrhenius parameters and the nature of the four-centered transition state. Electronicstructure calculations9-11 have recently provided additional understanding of the transition states for C2H5F, C2H4F2, and CH3CF3, which permit more reliable assignments of threshold energies from rate constants measured at a specific energy.12-14 High temperature studies of CH3CH2F, CH3CF3 and CF3CHF2 continue to receive attention with an emphasis on the collisional activation and deactivation models in the fall-off region.15-18 The 1,2-HF elimination reactions of fluoroethanes can be adequately described by statistical RRKM models for the vast majority of experimental conditions.16,17,19 As H-atoms are replaced by Fatoms in the fluoroethane series, the threshold energy, E0, for 1,2-HF elimination increases; however, the correct E0 values for the molecules with 4 and 5 fluorine atoms remain to be firmly established. Our laboratory has used the chemical activation technique to study CH2FCH2F13, CH2FCHF220, and CHF2CHF221, and in the present work we report experiments for CF3CHF2. We will show that E0(1,2-HF) increases from 55 to 87 kcal mol-1 from C2H5F to C2F5H. The E0(1,2-HF) assignments from chemical-activation experiments for C2H2F4 and C2HF5 are higher than assignments based on early shock-wave experiments.22,23 The dissociation reaction giving CF3 and CHF2 radicals was recognized as being in competition with 1,2-HF elimination in high temperature and in infrared multiphoton excitation experiments.20-25 of CF3CHF2. A recent shock-wave study18 monitored the CF2 concentration as a measure of the decomposition rate of CF3CHF2, since most of the secondary reactions lead to CF2 at high temperatures. ACS Paragon Plus Environment

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These authors also employed high-level electronic-structure calculations to explore primary reactions in addition to 1,2-HF elimination. As the threshold energy for 1,2-HF elimination increases, 1,1-HF elimination with formation of a carbene as a primary product can become competitive for fluoroalkane molecules with two F-atoms on the terminal carbon atom. The second F-atom is required to stabilize the singlet carbene and lower the E0(1,1HF). The competition between 1,2-HF and 1,1-HF elimination processes has been demonstrated by isotopic labeling for CD3CHF28, C2D5CHF226, and CD2FCHF2 20 and the carbene in all three cases rearranged to CD2=CDF, CD3CD=CDF and CDF=CDF, respectively. However, the carbenes from CHF2CHF221, CHF2(F)C:, and from CF3CHF2, CF3(F)C:, have high threshold energies for rearrangement, and they can be trapped by reaction with an alkene in room temperature chemical-activation experiments. In the present work, CF3CHF2* molecules were generated with 101 kcal mol-1 of vibrational energy in a room temperature bath gas by recombination of CF3 and CHF2 radicals. The 1,2-HF and 1,1-HF channels were identified by measuring the CF2=CF2 product and the adduct between CF3(F)C: and trans-2butene, respectively. A third unimolecular pathway from CF3CHF2 has been identified27 from the photoelectron spectra of CF3H in a high temperature flow reactor and in conventional product analysis25 from a flow reactor. Computational studies18,25 also have suggested that (H-atom transfer) formation CF3H + :CF2 could compete with 1,1-HF and 1,2-HF elimination. In the current study the three unimolecular rate constants were determined by comparing ratios of the three decomposition products to collisionally stabilized C2F5H as a function of bath gas pressure. Chemical-activation experiments with CF3CHF2* at room temperature provide the means to identify and study 1,2-HF, 1,1-HF and 1,2-H-atom transfer primary reactions with minimum interference from secondary process. Because we form CF3CHF2 by combination of fluorocarbon radicals the fourth unimolecular channel, C-C rupture, will not be observed. The experiments consist of photolysis of CF3I and CHF2I mixtures at room temperature in the presence of trans-2-butene followed by gas chromatographic analysis of the product mixture. The following reactions summarize the principal chemical reactions in this photolytic system. The combination/disproportionation


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ratio for CF3 + CHF2 is 0.0928, and the small amount of singlet-state :CF2 will be removed by reaction with trans-2-butene. An asterisk denotes vibrational excitation of CF3CHF2*, and M represents a bath gas molecule (CF3I, CHF2I or trans2-C4H8, which are efficient colliders). 2 CF3 CF3 + CHF2

CF3CHF2*

M

→ C2F6*

ΔHo298 = - 101 kcal mol-1

1.

→ CF3CHF2*

ΔHo298 = - 99 kcal mol-1

2a.

→ CF2 + CF3H

ΔHo298 = -44 kcal mol-1

2b.

→ HF + C2F4

ΔHo298 = 40 kcal mol-1

3a.

→ HF + CF3CF


3b.

→ CF3H + CF2


3c.

→ CF3CHF2 + M

CF3(F)C: + trans-CH3CH=CHCH3 → C4H8-CFCF3

3d. 4.

(+/-)-1-fluoro-1-(trifluoromethyl)-2,3-dimethylcyclopropane The thermochemical values for reactions 1-3 were taken from the systematic compilation of the enthalpies of formation of C1 and C2 fluorocarbon species by Haworth, et al.29 The enthalpies of formation of CF3 and CHF2 from the more recent calculations of Csontos et al.30 agree with those of reference 29. Converting 99 kcal mol-1 to 0 K and adding the thermal energy of recombination gives = 101 kcal mol-1 as the average vibrational energy of CF3CHF2*; this number should be reliable to ± 2 kcal mol-1. At 298 K the thermal distribution of the CF3CHF2* molecules is narrow and symmetric and the average energy is sufficient to define the rate constant, i.e. = k. The threshold energy31 for isomerization of singlet-state CF3(F)C: to C2F4 is 37 kcal mol-1 and CF3(F)C: will not isomerize under the conditions used in these experiments. The enthalpy of reaction for 3b provides a lower limit to E0(1,1-HF). We are not aware of a measurement for the activation energy for CF3(F)C: + HF, but calculations18 suggest ≈ 5 kcal mol-1. Threshold energies for each channel were determined by comparing the experimental rate constants to calculated statistical RRKM rate constants. The E0(1,2-HF) is high ACS Paragon Plus Environment

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enough (≥ 85 kcal mol-1) for CF3CHF2* that H-atom transfer and 1,1-HF elimination become important alternative processes. It can be noted that 1,1-HF elimination from C2HF5 had been suspected based upon the energy disposal to HF as measured from infrared chemiluminescence32,33 of the HF product. Reactions 2b and 3c give the same products, and two different pathways on the potential surface may exist for H-atom transfer. Decomposition reactions of CH2O34, CH3CHO35,36 and C3H837 leading to H2 + CO, CH4 + CO, and CH4 + C2H4 have received extensive theoretical analysis in terms of roaming radicals. Disproportionation reactions between two radicals, such as reaction 2a, probably occur via roaming radicals38,39 during the recombination event. The possibility of two different pathways for H-atom transfer, one a more-or-less conventional molecular transition state and the other a roaming radical process34-39, resembles the description for CH2O34 and CH3CHO36 reactions. From the point of view of the reverse of reactions 2b and 3c, the two pathways correspond to H-atom abstraction by CF2 from H-CF3 and CF2 insertion into the C-H bond of H-CF3. With the recent results for CHF2CHF221 and this study of C2HF5, the unimolecular reactions of the entire fluoroethane series have been experimentally characterized, and the threshold energies can be compared to results from electronic-structure calculations. Toto and co-workers9 first demonstrated that electronic-structure calculations could be used to describe the transition-state structures for HF-elimination reactions. Their work was followed by calculations with a variety of methods and basis sets for C2H5F, C2H4F2, and CH3CF3 and several fluoropropanes.10-14,26 Density functional methods with modest basis sets gave transition states that matched the major aspects of the experimental data, including Arrhenius parameters, rate constants at specific energies, kinetic-isotope effects, and increase in E0(1,2-HF) with the number of Fatoms in the molecule. Extending the calculations with satisfactory agreement to the experimental results for 1,2-HF and 1,1-HF elimination and for H-atom transfer for CHF2CHF2 and CHF2C HF2 presents a challenge, and we will summarize some computational efforts in this work. Since experimental data exists for 7 of the 8 fluoroethane molecules, the efficacy of the computational methods can be judged according to the following criteria: i) Satisfactory transition-state


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geometries for both 1,1-HF and 1,2-HF elimination reactions. ii) Satisfactory E0(1,2-HF) for the series of molecules, including the 30 kcal mol-1 increase from C2H5F to C2HF5. iii) Satisfactory E0(1,1-HF) for molecules with two F-atoms on a terminal carbon atom. iv) A satisfactory description of the 1,2- H-atom transfer transition state. In general, molecular models (vibrational frequencies and moments of inertia) for the molecules and their transition state that were obtained from the majority of electronic-structure calculations have been adequate for the calculation of the densities and sums of vibrational states that were needed for evaluation of the statistical rate constants. The agreement between experimental and calculated threshold energies has been less satisfactory. 2. EXPERIMENTAL METHODS. The experiments consisted of photolysis of mixtures of CF3I, CHF2I and trans-2butene with light from an Oriel 8510-4 high pressure mercury lamp, in Pyrex vessels with effective λ = 290-340 nm, followed by gas chromatography analysis (Shimadzu QP-5000 GCMS with a 105 meter RTX-624 column and a mass spectrometer detector). A small amount of Hg2I2 was added to each vessel to control free I2. Since the rate constants are small, large Pyrex vessels were required to observe measurable quantities of decomposition products, and the volumes of the vessels ranged from 113 to 1168 cm3. Photolysis times were typically 3-10 minutes, and the loss of CF3I and CHF2I was less than 3%. The ratio of decomposition to stabilization product concentrations was obtained from calibration mixtures prepared with known composition. A more complete description of the experimental techniques can be found in ref. 21. Two series of experiments were done to identify and measure the decomposition products. The first series was designed to measure CF3(F)C: carbene and C2F4 products; it utilized a 5:1:5 mixture of CF3I:CHF2I:trans-2-butene and a photolysis time of 10 minutes. The CHF2I component was reduced in order to minimize the CF2H concentration, which can lead to the formation of CF2 and CHF3 via reaction 2b. The desired pressure range was obtained by selection of the size of the photolysis vessel while keeping the amounts of starting materials


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constant. The CF3CHF2 was monitored from the integrated m/z = 101 and 51 signals; C2F4 was monitored by the integrated signal from m/z = 81, and the cyclopropane adduct was monitored by the integrated total ion-count. Experiments to measure the CF3H product required a separate set of photolysis data without trans-2-butene because CF3H was formed from the disproportionation reaction between CF3(CH3)CHCHCH3 and CF3 radicals. Addition of a CF3 radical to trans-2-butene forms the CF3(CH3)CHCHCH3 radical. The second set of experiments utilized a 10:1 mixture of CF3I:CHF2I. Photolysis time varied from 3-10 minutes; longer times were required to obtain sufficient products for analysis at high pressures. Calibration of the GCMS response was straightforward for CF3CHF2, C2F4, and CHF3 because pure samples were available. Several mixtures resembling the photolyzed samples were prepared and analyzed to obtain an average for the calibration factors. Since a pure sample of the cyclopropane adduct [(+/-)-1fluoro-1-(trifluoromethyl)-2,3-dimethylcyclopropane] was not available, proxy molecules were needed to obtain a calibration factor. Thus, mixtures were prepared with either 1,1,1-trifluoropentane or 1,1,1-trifluorohexane as the proxy molecule to obtain the calibration factor for the ratio of adduct/CF3CHF2. The use of these proxy molecules for the cyclopropane adducts is discussed in detail in ref. 21. 3. EXPERIMENTAL RATE CONSTANTS. Rate constants for reaction 3a and 3b were obtained by the usual method for chemical activation experiments, which consist of measuring the decomposition products (CF3(F)C: and CF2=CF2) and the collisionally stabilized product (CF3CHF2) over a range of pressure. The ratio of decomposition to stabilization, Di/S, for each product is plotted vs P-1 and the slope of the linear plot gives the average rate constant after conversion from pressure units to collision frequency, i.e., D/S = kexp/kM[M]. The information needed to calculate kM for the photolysis mixture is given in the footnotes of Table 1. Efficient deactivation for C2F5H* with 101 kcal mol-1 of vibrational energy by collisions at room temperature with CF3I, CHF2I and trans-butene-2 should apply for the following reasons. The density of vibrational


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states is very high, approximately 2 x 1014 states/cm-1, and an internal bottleneck to loss of energy during a collision is not expected. The high density of states and the relatively small rate constants also ensure that the three reactions can be treated independently. The threshold energies for each reaction are rather high; therefore E-E0 is small and the RRKM rate constants decline sharply with energy. Collisions that remove 4-6 kcal mol-1 on average effectively deactivate CF3CHF2 for further reaction at the pressures of the experiments. Each experimental rate constant is defined as kexp = (Di/S)kM[M] at a given pressure or concentration of bath gas. The data from photolysis of the 5:1:5 CF3I:CHF2I:C4H8 mixture are shown in Figure 1 for the pressure range 0.1 to 0.008 Torr; low pressures were required to observe decomposition products and the rate constants clearly are quite small. The least-squares slopes of the two plots are 2.7 ± 0.2 x 10-3 and 0.88 ± 0.14 x 10-3 Torr for the 1,1-HF and 1,2-HF reactions, respectively. The intercept of the plots are 0.07 ± 0.02 and - 0.005 ± 0.010, respectively. According to the proposed mechanism, the intercept is expected to be zero. Another possible interpretation of the data is to constrain the linear fit to pass through the origin. Those linear fits give 3.54 x 10-3 and 0.88 x 10-3 for 1,1-HF and 1,2-HF reactions, respectively. We prefer the latter values because of the small number of experimental points at pressure above 0.05 Torr, and the slopes from these plots are reported in Table 1. Although there is significant scatter in the Di/S plots, the systematic uncertainty associated with calibration of the GCMS response for 1,1-trifluoromethyl-fluoro2,3-dimethylcyclopropane is likely to be the source of the greatest uncertainty for the 1,1-HF rate constant. Nevertheless, the data clearly show that the 1,1-HF elimination rate constant is 4-6 times larger than that for 1,2-HF elimination. A few experiments with the concentration of trans-2-butene doubled were done, which confirmed that all of the CF3(F)C: was trapped using a lower concentration of the butene. The experiments with trans-2-butene in the photolyzed mixtures could not be used to monitor CF3H because of the contribution from the interaction of CF3 with the addition product of CF3 with 2-butene, CF3(CH3)CHCHCH3. Therefore, a separate set of experiments was done with a 10:1 mixture of CF3I:CHF2I. The ACS Paragon Plus Environment

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results are shown in Figure 1. The data can be fit to a linear plot with an intercept of 0.066 ± 0.051. In principle the intercept should be the disproportionationcombination ratio (kd/kC) for reaction 2, which is reported28 to be 0.09 ± 0.01. A steady-state analysis of the rate equations shows that the slope of this plot should be equal to kH(1 + kd/kc ) + kd/kc(kHF ). This equation with kHF equal to the sum of the HF elimination rate constants and the slope of the plot, 4.06 ± 0.64 x 10-3 Torr, gives kH = 3.4 x 10-3 Torr for the H-atom transfer rate constant (in pressure units) and this value is entered in Table 1. The H-atom transfer and 1,1HF elimination reactions have comparable importance. Inspection of Table 1 shows that the rate constants for CF3CHF2* are an order of magnitude smaller than those for CHF2CHF2*, which implies that the threshold energies will be much higher for CF3CHF2 than for CHF2CHF2. 4. COMPUTATIONAL RESULTS. 4A. Transition-state models and rate constants. In order to evaluate the statistical rate constants, molecular models of CF3CHF2 and transition states for the three reactions are required. Electronic-structure calculations using several methods and basis sets available in the Gaussian suite40 of codes were used to survey the C2F5H system. Several methods, such as B3PW91/cc-pVDZ and M06-2X/cc-pVDZ, were able to provide valid descriptions of the transition states for the three reaction pathways, as judged by the intrinsic reaction coordinate (IRC) test. Our survey also was consistent with results from a larger set of calculations18 for the CF3CHF2 system. We decided to compare the rate constants from the B3PW91/cc-pVDZ and M06-2X/aug-cc-pVTZ calculations. Frequencies and moments of inertia were not sensitive to the method or basis set, except for the twisting mode of the transition state for H-atom transfer, which has a very low value. Since M06-2X calculations should treat long-range interactions better than the B3PW91 method, we decided in favor of the M06-2X results for calculation of the RRKM rate constants. The structures of the transition states are shown in Figure 2 and the frequencies and moments of inertia are given in Supporting Information. The 1,2-HF and 1,1-HF transition-state


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structures closely resemble21 those for CHF2CHF2; the unusual character of the transition state for H-atom transfer is considered in the Discussion. The RRKM rate constant, eq. 5, was calculated41 using harmonic-oscillator rigid-rotor models to evaluate the density of states, N*(E), of the molecule and the sum of states of the transition state, ΣP‡ (E-E0). The reaction path degeneracy is s‡, and (I‡/I) is the ratio of the three overall rotational moments of inertia. kE = s‡/h (I‡/I)1/2(ΣP‡(E-E0)/N*(E))

(5)

The CF3 torsional mode was treated as a hindered internal rotation in the molecule (Ired = 33.6 amu Å2; V = 3.9 kcal mol-1) and as a free internal rotation for the 1,1-HF transition state (I‡ = 42.4 amu Å2). In fact, the density of states for the molecule is nearly the same for the torsion treated either as a vibration or as a hindered rotation at the high energy of 101 kcal mol-1. The difference in the sum of states for a free rotor and a 3.9 kcal mol-1 hindered rotor for the 1,1-HF transition state was a factor of 2.2. Treating the CF3 torsion as an internal rotation reduces the difference between the B3PW91 and M06-2X calculated rate constants. The threshold energies were assigned by matching the calculated kE for E= 101 kcal mol-1 to the kexp, and the results are given in Table 1. Since E is high and E-E0 is rather low, ≈ 15 kcal mol-1, the rate constants are sensitive to E and to E0, and one kcal mol-1 difference in E changes kE by a factor of ≈ 1.6 and a similar change in E0 alters kE by a factor of ≈ 1.9. The rate constants are more sensitive to E and E0 than to changing one frequency, except for the very low frequency in the H-atom transfer transition state. For example, increasing the twisting frequency in the transition state for H-atom transfer from 18.4 (B3PW91) to 37.4 (MO6-2X) cm-1 reduced the sums of states by a factor of 2.1. The sums and density of states were calculated with the harmonic frequencies. If anharmonicity was introduced for calculating the sums and densities, the effect would be more pronounced for the densities than the sums of states because of the differences in vibrational energies, and the anharmonic rate constants would be smaller than the harmonic ones. Smaller rate constants would result in selection of slightly lower threshold energies.


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The assigned E0 values matched to rate constants calculated at M06-2X/augcc-pVTZ are listed in Table 1. Within the combined experimental and computational uncertainties all three E0 are 87 ± 2 kcal mol-1. The ratios of sums of states for the three transition states at 14 kcal mol-1 are 1.0:5.0:4.9 for 1,2-HF, 1,1-HF and 1,2-H-atom transfer, respectively, for a free-rotor in 1,1-HF and a 37.4 cm-1 frequency in H-atom transfer. It should be noted that nearly a twofold change in kexp is needed to alter E0 by 1 kcal mol-1; thus, the threshold energies are not very sensitive to the uncertainty of kexp. Depending on the choices for the twisting frequency of the H-atom transfer model and the barrier for internal rotation in the 1,1-HF transition state, those E0 could be somewhat different than the values given in Table 1. The uncertainty in the threshold energies is 2-3 kcal mol-1, which is more than for traditional chemical-activation experiments, because of the sensitivity to and to the low frequencies in the transition states for 1,1-HF and 1,2-H-atom transfer. The assignment of E0(1,1-HF) = 88 kcal mol-1 implies that the threshold energy for addition of CF3(F)C: to HF is ≈ 9 kcal mol-1; the calculated43 barrier for addition of CF2 to HF is 18 kcal mol-1. 4B. Threshold energies for unimolecular reactions of fluoroethanes. A summary of the threshold energies for C2F5H that have been calculated by various methods will be presented first. In addition to the four calculations for the E0 values given in Table 2, we have results from M06-2X/aug-cc-pVTZ, which are 84, 88 and 95 kcal mol-1 for 1,1-HF, 1,2-HF and H-atom transfer, respectively. Cobos and coworkers18 did several calculations, and their results from M06-2X/6311++G(3df,3pd), CBS-QB3, Q3B3 and G4 are 84.8, 83.2, 81.5 and 81.5 for E0(1,1HF); 88.2, 89.1,87.7 and 87.9 for E0(1,2-HF); and 95.6, 91.1, 90.6 and 90.6 kcal mol-1 for E0(1,2-H-atom). The more extended basis sets for the M06-2X calculations gave nearly the same results as for the calculations listed in Table 2. The E0 values from model chemistry methods tend to be 1-2 kcal mol-1 lower than the M06-2X values. All of the calculations give E0(1,1-HF) values that are too low (3-6 kcal mol-1) relative to the experimental 88 kcal mol-1 result, whereas all of the calculations give E0(1,2-HF) values that are close to the experimental result. The model chemistry calculations are in better accord with the experimental E0(1,2-Hatom), but the values are still 2-3 kcal mol-1 too high. Additional computational


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effort is needed, especially for 1,1-HF elimination, to describe threshold energies for unimolecular reaction of C2F5H. According to the thermochemistry used here29, the threshold energy for dissociation of CF3-CF2H would be ≈100 kcal mol-1. The experimental threshold energies for HF elimination from the fluoroethane series of molecules are compared with the calculated results from two commonly used methods, M06-2X and B3PW91, in Table 2 to illustrate trends, rather than attempt to obtain the best agreement between experimental and calculated threshold energies. The identification of computational methods to obtain reliable threshold energies also is relevant for selection of methods that are suitable for direct-dynamic treatments44-47 of the exit channel. Thermal- and chemical-activation studies are in agreement for the threshold energy assignments for the first four members of the series. The remaining experimental values are mainly based on chemical activation results. Although all of the experimental uncertainties are listed as ± 2 kcal mol-1, the actual limits are generally smaller for molecules with three or less F-atoms than those with 4 and 5 F-atoms. The obvious trend is the systematic increase in E0(1,2-HF) from 58 to 87 kcal mol-1 and E0(1,1-HF) from 74 to 88 kcal mol-1 as the number of F-atoms increase. There is no obvious difference in E0(1,2-HF) with respect to location of the F-atoms on the carbon atoms. Both computational methods capture the main trends of the threshold energies; however, both underestimate the overall increase in E0(1,2-HF) for the series. The M06-2X method overestimates E0(1,2-HF) for the first 5 fluoroethanes. The B3PW91 method severely underestimates the E0 for 1,1-HF elimination reactions. The M06-2X method gives E0(1,1-HF) that are too high for CH3CF2H and CH2FCHF2 and somewhat too low for CHF2CHF2 and C2F5H. Larger basis set with M06-2X did not give appreciably better results. Higher level treatments seem to be required for satisfactory analysis of the whole fluoroethane series by a single computational method. The threshold energy for 1,2-H-atom transfer is so high that the reaction is only competitive for C2F5H. It is not even important for CF3CHFCF3.48 It is of interest to note48 that replacing an Fatom by a CF3-group lowers E0(2,1-HF) of CF3CHFCF3 to 75 kcal mol-1. There is a strong correlation of increased threshold energies with the reduced dissociation energies of the product fluoroethenes.


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5. DISCUSSION. 5A. Transition-state structures and Intrinsic Reaction Pathways. The current work establishes that 1,1-HF elimination and 1,2-H-atom transfer are dominant, and nearly equivalent, decomposition pathways for chemicallyactivated CF3CF2H*. The conventional 1,2-HF elimination pathway for fluoroethanes contributes only about 12% to the reaction rate for molecules with 101 kcal mol-1 of energy. Since the threshold energies are similar, the product branching ratios are not sensitive to the energy (or temperature). The decomposition mechanism for high temperature conditions, which would include the dissociation reaction, is addressed in the following section. The structure of the transition states for 1,2-HF elimination given by several levels of electronic-structure calculations are very similar and the transition-state structures seem to satisfy the majority of the experimental data, including kineticisotope effects10,14 and energy disposal.44-47 One notable feature is the more nearly planar geometry around the carbon atom attached to the leaving F-atom and this is clearly the case for C2F5H shown in Figure 2. In fact, for the C2H5F reaction, relaxation of the CH2 group associated with the leaving H-atom is responsible for a significant part of the vibrational energy acquired by C2H4.46, 47 The influence of the mass of the atoms attached to the carbon atoms on the energy disposal is still the subject of research45, but the 128.4° and 170.2° out-ofplane CF2 angles suggest that C2F4 also would acquire vibrational energy as it become planar, see Figure 2. The transition states and the results of IRC calculations for 1,1-HF elimination and 1,2-H-atom transfer are more unusual and they can be fruitfully discussed. The H-C-F angle in the three-membered ring for 1,1-HF elimination is about 35° and the extensions of the C-F, C-H and H-F distances, relative to typical bond lengths in stable molecules, is 36%, 21% and 18%, respectively. The 1,1-HF transition state actually has shorter C-F, C-H and H-F distances than the 1,2-HF elimination transition state in Figure 2. However, the C-F distance in the 1,1-HF transition state is dependent on the computational method. The F-C-C angle of


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108.6° indicates that the carbene structure (120° angle) has not developed. The imaginary frequency [-632 cm-1 (B3PW91) and -1145 cm-1 (M06-2X) cm-1] mimics the anticipated reaction coordinate and involves motions of both the F- and Hatoms away from the carbon atom. In order to explore the exit channel of 1,1-HF elimination reactions, calculations were extended to include CH3CHF2. Calculations with the M06-2X method identified adducts between HF and the carbenes, CF3(F)C: and CH3CF:. Similar calculations of the stationary points for potentials49-51 describing the reaction of OH radicals with molecules containing oxygen or nitrogen atoms found potential wells before and after the transition state. These attractive interactions are associated with hydrogen-bonding type forces of OH radicals and the molecule or with H2O and the radical resulting from removal of the H-atom. The post-transition state complex (PTSC) shown in Figure 2 certainly resemble a hydrogen-bonded complex between the electron pair of the carbene and HF. According to CBS-QB3 calculations, the dissociation energies at 0 K of the complex to the free carbene and HF are 5.0 (CF3(F)C:) and 9.3 (CH3(F)C:) kcal mol-1 when the zero-point energy is included; the larger attraction between CH3(F)C: and HF is expected based on the electron density donating properties of the CH3 group. For comparison, the dissociation energy43 for F2C:HF is 5.1 kcal mol-1 from G3B3 calculations. Threshold energy barriers for isomerization of the free carbene to the alkene are calculated (M062X) to be 34.8 and 14.6 kcal mol-1 for CF3(F)C: and CH3(F)C:, respectively, see Figure 3. Similar result were reported by Bacskay31; 37.5 and 16.9 kcal/mol from CCSD(T)/cc-pVTZ calculations for CF3(F)C: and CH3(F)C:. A novel finding is the prediction of a hydrogen-bonded complex between HF and the transition state for F-atom migration (see Figure 2e and f); the threshold energy is 9.9 kcal/mol (see Figure 3b) lower for F-migration for the complexed transition state versus the free carbene. The complex-aided H-migration transition state is 9.2 kcal mol-1 lower for the CH3CHF2 system, see Figure 3, than for the free carbene. The importance of the hydrogen-bonded complex and its hydrogen-bonded migration transition state will likely change with the nature of


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the carbene and the hydrogen halide. One interesting general point is that the electron pair of the carbene seems to remain attracted to HF as the H- or F-atom is being transferred, according to the structures of Figures 2 and 3. The difference in the E0(1,1-HF) values and the 0 K enthalpy of reaction for CF3CHF2 and CH3CHF2 are 4 and 1.7 kcal mol-1 from calculations or 8 and 3 kcal mol-1 from experiments, respectively, and this energy would be released to products. The majority of this energy would be expected to be released as vibrational energy of the carbene moiety and relative translational energy as the HF moves away from the carbon atom. The trajectories may largely follow the minimum energy path, see Figure 3, and then the additional potential energy associated with the hydrogen-bond formation would be released as vibrational energy. Finally, the excess vibrational energy above the energy of the 1,1-HF elimination transition state (101-88 = 13 kcal mol-1 for C2F5H and 96-72 = 24 kcal mol-1 for CH3CHF2) must be included. The total energy will relax to a statistical distribution, and the complex will dissociate to the carbene and HF. Two geometries from the IRC calculation as the 1,1-HF transition state evolves to the PTSC (Figure 3a for CF3CHF2) illustrate how the HF moves from the transition state and evolves to the carbene-HF adduct. The H and F-atoms move toward each other while both move away from the pair of electrons on the carbene to achieve the expected linear arrangement for a hydrogen-bonded complex. The H-atom transfer transition state, Figure 2c, is also a three-membered ring with the C-C distance increased by 50% and the C-H distance in CHF2 increased by only 5%. The CF3 and CHF2 groups still have sp3 geometry. The B3PW91 and M06-2X methods give very similar structures and vibrational frequencies, except for the CF2H twisting mode that moves the H-atom out of the C-C-H plane. That frequency may be sensitive to the C-H distance of the CF3 group, which was 1.56 and 1.61 Å from M06-2X and B3PW91, respectively. The imaginary frequency is close to -1200 cm-1 from several calculations and show that the reaction coordinate involves motion of the H-atom toward the CF3 group. After the H-atom is transferred, the CF2 and CHF3 groups separate with repulsive


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energy release. The H-atom transfer transition state is also the transition state for the reverse reaction, which is the insertion of CF2 into the C-H bond of CF3H. A similar transition state exists21 for the insertion of CF2 into the C-H bond of CH2F2. The calculated E0(1,2-H-atom) for CHF2CHF2 is 95 kcal mol-1, which is the same as for CF3CHF2; however, even after reduction to the expected experimental value, the rate would not compete with HF elimination reactions for = 96 kcal mol-1. A second reaction pathway for the formation of CF2 + CHF3 exists from the disproportionation reaction of CF3 + CHF2 and the energy of this transition state must be similar to the bond dissociation energy of CHF2-CF3, which would be ≈ 12 kcal mol-1 higher than the transition state for H-atom transfer. In terms of the reverse reaction, this transition state represents the abstraction of the H-atom by CF2 from CHF3. Modeling the dissociation and disproportionation reactions requires advanced computational methods to generate the potential surface and to evaluate the rate constants. Such computations exceed our resources; however, the disproportionation reactions of CF3 + CHF2 and of 2CHF2 seem likely candidates for roaming radical mechanisms.34-39 5B. High temperature decomposition of CF3CHF2 Two recent studies18,25 of the high temperature decomposition of CF3CHF2 have attempted to relate their observations to the three primary reactions. Despite quite different experimental conditions (turbulent flow reactor25 at 1 atm of N2 and 1273-1373 K versus shock wave18 at ≈ 6 atm of Ar and 1400-2000 K) similar Arrhenius parameters of 1014 exp (-75000 kcal mol-1/RT) s-1 were reported. Even with allowance for fall-off effects, the activation energy is less than the threshold energies of the primary reactions, and the authors included dissociation to CF3 + CHF2 in the mechanism followed by secondary reactions of the radicals. At high temperatures, the contribution of a chain reaction based on C2F5 radicals is possible. The D298(H-C2F5) is 105 kcal mol-1 and D298(H-CF3) is 108 kcal mol-1 and CF3, F or H radicals could initiate the formation of C2F5, which could be followed by reactions 6 and 7. CF3CF2 → CF3 + CF2

∆H298 = 57 kcal mol-1


6.

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CF3 + CF3CHF2 → CHF3 + CF3CF2 ∆H298 = -3.3 kcal mol-1

7.

At high temperatures CF3H can eliminate HF and give :CF2 (E0 = 73 kcal mol-1)43, the net result of the cycle would be HF + 2CF2. The enthalpy of reaction 6 is 15 kcal mol-1 lower than dissociation to F + C2F4 and reaction 6 is dominant. The importance of dissociation giving CF3 + CHF2 will depend on the temperature and pressure of the experiments. Modeling of the system will need to employ a reliable bond dissociation energy and advanced treatment of the rate constant for dissociation. Calculated Arrhenius expressions from models similar to those used in our work for the decomposition reaction of CF3CHF2 are given in ref. 18 and those pre-exponential factors can be consulted. The transition state for H-atom transfer has low frequencies and the pre-exponential factor is larger than those for 1,1-HF and 1,2-HF elimination. 6. CONCLUSIONS The total unimolecular rate constant for CF3CHF2 with 101 kcal mol-1 of vibrational energy is 9.4 x 104 s-1; the product branching ratios are 0.50, 0.38 and 0.12 for 1,1HF elimination, 1,2-H-atom transfer and 1,2-HF elimination, respectively. Electronic-structure calculations with the M06-2X/aug-cc-pVTZ method provided transition-state models that enabled RRKM rate constants to be calculated; comparison with experimental values assign threshold energies of 88, 88, and 87 kcal mol-1 with an uncertainty of ± 2 kcal mol-1 for 1,1-HF elimination, 1,2-H-atom transfer and 1,2-HF elimination, respectively. These results should be useful in understanding the mechanism for the high temperature chemistry of C2F5H. Electronic-structure calculations with B3PW91 and M06-2X methods were compared to experimental 1,2-HF and 1,1-HF threshold energies of the other members of the fluoroethane series, as well as for C2F5H, and it was concluded that high level ab initio methods would be required for a single method to provide reliable threshold energies for the entire series. The unusual transition state for the 1,2-H-atom transfer reaction, which also is the transition state for the insertion of CF2 into the C-H bond of CF3H, was discussed. According to calculations, a hydrogen-bonded complex exist in the exit channel for 1,1-HF elimination with a binding energy of about 5 kcal mol-1 between HF and CF3(F)C:..


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Similar hydrogen-bonded complexes can be expected for all 1,1-HF elimination reactions of 1,1-difluoroalkanes. Calculations also predict that a hydrogenbonded complex exists between HF and the transition state for H- or F-atom migration converting the carbenes (:CFCH3 and :CFCF3) into CHF=CH2 and CF2=CF2. Neither complex-assisted transition states are important for these examples, since dissociation of the PTSC is faster than the F- or H-atom assisted migrations. Since H-atom migration from other carbenes can have low threshold energies, the role of complex-assisted reactions needs to be evaluated for each case. The influence of carbene adducts with hydrogen-bond donor molecules may be of importance for carbene bimolecular addition reactions.

7. AUTHOR INFORMATION Corresponding Author. * BEH E-mail: [email protected] Telephone: 828-2325168 8. ACKNOWLEDGEMENTS Financial support from the National Science Foundation (CHE-1111546 and CHE1229406) is gratefully acknowledged. 9. SUPPORTING INFORMATION. Supporting Information contains the vibrational frequencies and moments of inertia for the calculated molecular and transition state geometries using B3PW91/cc-pVDZ and M06-2X/aug-cc-pVTZ for the unimolecular reactions of CF3CHF2. This information is available free of charge via the Internet at http://pubs.acs.org.


18

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FIGURE CAPTIONS Figure 1. Plot of the decomposition (Di) to stabilization (S) ratio vs pressure-1. ()(+/-)-1-fluoro-1-(trifluoromethyl)-2,3-dimethylcyclopropane/C2F5H with leastsquares slope and intercept of 2.70 ± 0.22 x 10-3 and 0.072 ± 0.016; (♦) CHF3/C2F5H with least-squares slope and intercept of 4.06 ± 0.64 x 10-3 and 0.066 ± 0.051; (•) C2F4/C2F5H with least-squares slope and intercept of 0.88 ± 0.14 x 10-3 and – 0.004 ± 0.010. The fourth (solid) line shows a forced fit of the cyclopropane/C2F5H data to a line through the origin; see text for explanation of the preference for this slope. Figure 2. Diagrams of the transition states geometries for (a) 1,1-HF elimination, (b) 1,2-HF elimination, (c) 1,2-H-atom transfer from C2F5H, (d) the hydrogen bonded adduct between CF3(F)C: and HF, (e) F-atom migration for the free carbene, and (f) F-atom migration with HF hydrogen-bonded adduct. All structures are from calculations with M06-2X/aug-cc-pVTZ. Vibrational frequencies are listed in Supporting Information. The out-of-plane angles relative to the C-C axis for the two CF2 groups of the 1,2-HF transition states are 128.4° and 170.2° degrees. For reference the bond distances for H-F is 0.92 Å, and for C2F5H the H-C, F-C and C-C are 1.08, 1.38 and 1.52Å. The H-atom transfer transition state is also the transition state for insertion of CF2 into the C-H bond of CHF3. Figure 3 a and b. Calculated relative energies with zero point energies included for (a) CH3CF2H and (b) CF3CHF2 systems. The dissociation energies of the complexes were calculated with CBS-Q3, which uses the optimized geometry from B3LYP. The other energies are based on calculations from M06-2X, i.e., the energy of the transition states is derived from the calculated energy difference between the complex and the transition state using the M06-2X results. The free carbene + HF is assigned zero energy. Motion of the H, F and C for the reaction coordinate are shown using arrows for the 1,1-HF elimination transition states. The vectors, illustrating motion of the H, F and C, are mass weighted representations of the forces on each atom as it moves from the 1,1-HF elimination transition state towards the complex. The vector for H-atom motion was reduced by a factor of 6 relative to motion of the F and C atoms. For CH3CF2H two snapshots are shown of


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the geometry of CH3(F)C: and HF along the IRC connecting the 1,1-HF elimination transition state to the hydrogen-bonded complex. Two geometries are shown for the atom-migration transition states converting the carbene into an alkene for both systems: the lower energy is the complex-assisted transition state the other is for isomerization of the free carbene.


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Table 1. Summary of rate constants and threshold energies for CF3CHF2 and CHF2CHF2 Reaction

Slope D/S plot, Torr

kexp a,b s-1

CF3CHF2* →

k

s-1

E0 kcal/mol

= 101 kcal

CF3H + :CF2

3.38 ± 0.50 x 10-3

3.61 ± 0.52 x 104

3.1 x 104

88c

CF3(F)C: + HF

3.54 ± 0.22 x 10-3

4.67 ± 0.45 x 104

5.8 x 104

88d

5.1 x104

87d

1.6 x 104

87

CF2=CF2 + HF

0.88 ± 0.14 x 10-3

1.10 ± 0.16 x 104

CF2H-CHF2e →

= 96 kcal

CF2=CHF + HF

4.6 ± 0.5 x 105

6.9 x 105

78

CF2H(F)C: + HF

1.4 ± 0.3 x 105

1.7 x 105

≤ 85e

a. The collision constants were calculated from the following collision diameters, Å, and ε/k ,oK, values: CF3CHF2 (5.2 and 201), CF3I (5.1 and 288), CHF2I (4.6 and 298), CH3CH=CHCH3 (5.3 and 312). The collision rate constants are 4.1 x 10-10 and 3.3 x 10-10 cm3 molecule-1 s-1 for the butene:CF3I:CHF2I and CF3I:CHF2I mixtures ,respectively b. The uncertainty was increased at least to ± 10% for CF3(F)C: + HF to allow for the additional uncertainty associated with the collision rate constants. c. This assignment is for a twisting frequency in the transition state of 37 cm-1. If the frequency of 18 cm-1 from the B3PW9 calculation is used, the threshold energy would be ≈89 kcal mol-1. The calculated rate constants also are sensitive to the threshold energy because the energy in the transition state, - E0, is low. A one kcal mol-1 variation in E0 changes the rate constant by a factor of 2; see text for discussion. d. The 87 kcal mol-1 assignment is for a CF3 internal rotational barrier of 3.9 kcal mol-1; the threshold increases to 88 kcal mol-1 for a CF3 free rotor. If the trapping of CF3CF was incomplete, the true experimental rate constant would be larger and E0 would be reduced. e. The information for CHF2CHF2 was taken from reference 21; the upper limit to E0(1,1HF) allows for possible isomerization of some CHF2(F)C: to CFH=CF2.


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Table 2. Summary of threshold energies for fluoroethanes Experimental

Molecule

Kcal mol-1

B3PW91/cc- M06-2X/ pVDZ cc-pVDZ

M062X/6311G(2d,p)

MP2/631G(d’,p’) Kcal mol-1

Kcal mol-1

Kcal mol-1

Kcal mol-1

CH3-CH2F (1,2-HF)

58 ±2 (a)

57

62

62

65

CH2F-CH2F (1,2-HF)

63 ±2 (b)

59

65

66

69

CH3-CHF2 (1,2-HF)

62 ±2 (b)

61

66

70

69

(1,1-HF)

74 ±2 (c)

70

77

78

79

CH3-CF3 (1,2-HF)

69 ±2 (a)

66

72

73

74

CH2F-CHF2 (1,2-HF)

68 ±3 (d)

66

73

73

76

(1,1-HF)

77 ±2 (d)

72

80

80

81

CH2F-CF3 (1,2-HF)

>69 (e)

72

78

79

81

CHF2-CHF2 (1,2-HF)

78 ±2 (f)

75

77

84

86

≤ 85 ±2 (f)

77

83

84

84

87 ± 2 (g)

80

88

89

91

≤ 88 ± 2 (g)

78

84

85

85

88 ± 2 (g)

88

95

96

h

(1,1-HF) CF3-CHF2 (1,2-HF) (1,1-HF) 1,2-H-atom trans.

a. See appendix of ref. 12 for a summary. Ref. 10 presents a summary of computational studies of CH3CF3. b. See ref. 11 for a summary of experimental studies. c. See ref. 26 for assignment of E0(1,1-HF) based on data from ref. 8. d. Interpretation of the analysis given in ref. 20. e. Derived from the Arrhenius activation energy (70.7 kcal mol-1) of ref. 42. The early shock-tube studies of the fluoroethanes frequently give lower limits to the activation energies of the primary reactions because of free-radical secondary reactions. Thus, 69 kcal mol-1 is listed as a lower limit.


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f. See ref 21. Lower limits are listed because all of the carbene product may not have been trapped by trans-butene. g. This work. Lower limits are listed because all of the carbene product may not have been trapped by trans-butene. h. The calculated energy was not reasonable.


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REFERENCES 1. Robinson, P. J.; Holbrook, K. A. Unimolecular Reactions, 1972, Table7.20 WileyInterscience, N. Y. 2. Day, M.; Trotman-Dickenson; A. F. Kinetics of the Thermal Decomposition of Ethyl Fluoride, J. Chem. Soc. A 1969, 233- 235; 1970, 2498-2503. 3. Kerr, J. A.; Timlin, D. M. A Kinetic Study of the Thermal Elimination of HF from 1,2-Difluoroethane, Int. J. Chem. Kinet. 1971, 3, 427-441. 4. Tschuikow-Roux, E.; Quiring, W. J.; Simmie, J. M. Kinetics of the Thermal Decomposition of 1,1-Difluoroethane in Shock-Waves. A Consecutive First-Order Reaction, J. Phys. Chem. 1970, 74, 2499-2455. 5. Tschuikow-Roux, E.; Quiring, W. J. Kinetics of the Thermally Induced Dehydrofluorination of 1,1,1-Trifluoroethane in Shock Waves, J. Phys. Chem. 1971, 71, 295-300 . 6. Kerr, J. K.; Timlin, D. M. Application of the RRKM Theory to the Unimolecular Decomposition of 1,2-Difluoroethane, Trans. Faraday Soc.1971, 67, 1376-1383. 7. Chang, H. W.; Craig, N. L.; Setser, D. W. Nonequilibrium Unimolecular Reactions and Collisional Deactivation of Chemically Activated C2H5F and CH3CF3, J. Phys. Chem. 1972, 76, 954-963. 8. Kim, K. C.; Setser, D. W.; Holmes, B. E. Hydrogen Fluoride and Deuterium Fluoride Elimination Reactions of Chemically Activated CD3CHF2, CH3CHF2, and CD3CH2F, J. Phys. Chem. 1973, 77, 725-733. 9. Toto, J. L.; Pritchard, G. O.; Kirtman, B. Transition States for 1,2-Hydrogen Halide Elimination from Ethyl Halides, J. Phys. Chem. 1994, 98, 8359-9370. 10. Martell, J. M.; Beaton, P. T.; Holmes, B. E. Comparison between Density Functional Theory and Conventional ab Initio Methods for 1,2-HF Elimination from CH3CF3: Test Case for HF Elimination from Fluoroethanes, J. Phys. Chem. A 2002, 106, 8471-8478.


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Figure 1



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

a.)

d.)

b.)

e.)

c.)

f.)


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Energy (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


+ HF

Figure 3

14.6

5.4

1.7

+ HF

-9.9


0


Energy (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

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+ HF 34.8

24.9

4.0

+ HF

0

-5.4


The Unimolecular Reactions of CF - ACS Publications

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