Ab initio and RRKM studies of the unimolecular reactions of CH₂XCHFO (X = H, F) radicals

Abstract

The unimolecular reaction mechanism of the CH₂XCHFO (X = H, F) radicals was studied using the ab initio G2(MP2, SVP) theory. Three kinds of reaction pathways, namely bond scission, three-center elimination of HF and isomerization, were examined. Both the energy-specific rate constant [k(E)] and the thermal rate constant [k(T, P)] were evaluated using the RRKM theory and the ab initio data. These theoretical calculations support the proposal that the C–C bond scissions dominate the decomposition of CH₂XCHFO (X = H, F). The major products of the unimolecular reactions should be CH₂X and CHFO. Furthermore, it is concluded that the lifetimes of CH₃CHFO and CH₂FCHFO are both very short in the atmosphere.

---

I. Introduction

Alkoxyl radicals are important intermediates in atmospheric chemistry. Hydrofluorocarbons (HFCs) and hydrochlorofluorocarbons (HCFCs), which have been widely used as replacements for chlorofluorocarbons (CFCs),¹ react with atmospheric OH radicals to produce halogenated alkyl radicals. These species add molecular oxygen to give peroxyl (RO₂). The subsequent reaction of peroxyl with NO or other peroxyl radicals leads to the formation of an alkoxyl radical.² It has been shown that alkoxyl radicals play an important role in the degradation mechanism of organic compounds in the troposphere.³

The alkoxyl radical could be depleted in two kinds of manner, oxidation by O₂ and unimolecular decomposition,⁴ and its fate is determined by the competition between these two pathways. The alkoxyl and substituted alkoxyl radicals are unlikely to undergo self-reactions in the atmosphere where their concentration will be very low. The reactions of alkoxyl radicals with O₂ have been more or less investigated experimentally.⁵ Despite being more important, the unimolecular decomposition reactions of alkoxyl, in particular halogen-substituted alkoxyl radicals, have rarely been studied.

CH₂XCHFO (X = H, F) radicals are of considerable interest in the degradation mechanism of two CFC alternatives CH₃CH₂F (HFC-161) and CH₂FCH₂F (HFC-152). There has been no direct experimental study of the reactions of CH₂XCHFO. In a study of the atmospheric chemistry of HFC-152,⁶ a few characteristics of the CH₂FCHFO radical were inferred tentatively from indirect kinetic experiments. The unimolecular decomposition of CH₂FCHFO, which mainly undergoes C–C bond scission, may dominate its fate. The corresponding rate constant was found to be >6×10⁴ s⁻¹.

In this paper, we present a theoretical study of CH₂XCHFO (X = H, F) using the high-level ab initio molecular orbital (MO) method and RRKM theory. We confined ourselves to the investigation of the following six reaction channels, which are of most atmospheric concern:

CH₂XCHFO→CH₂X+CHFO (1) →H+CH₂XCFO (2)→F+CH₂XCHO (3)→HF+CH₂XCO (4) →CH₂X CF(OH) (5) →CHXCHF(OH) (6) (1)

where reactions (1)–(3) are the bond scission channels, reaction (4) is the three-center elimination of HF and reactions (5) and (6) are the hydrogen rearrangement channels. Our calculations not only provide theoretical evidence for the experimental findings in the case of CH₂FCHFO but also predict a reasonable reaction mechanism for the CH₃CHFO radical. We also report the unimolecular rate constants for both radicals over a wide range of temperatures and pressures. The implications of our results are discussed in terms of understanding the tropospheric chemistry of CH₂XCHFO (X = H,F).

II. Computational details

For the present relatively large system containing 4–5 heavy atoms, the most inexpensive and reliable G2(MP2, SVP) theory⁷ was employed in the ab initio calculations. Geometries of the reactants, products and transition states were fully optimized at the UMP2(full)/6–31G(d) level. Vibrational frequencies calculated at the same level were used for the characterization of stationary points and zero-point energy (ZPE) corrections (scaled by a factor of 0.93).⁸ The minimum has no imaginary frequency and the transition state has only one imaginary frequency. Moreover, all transition states were subjected to IRC⁹ calculations to confirm the connection between reactants and products.

Despite the good performance of the G2(MP2, SVP) theory,^10,11 the calculated energy barriers might have significant uncertainty (at worst, >2 kcal mol⁻¹) for two major reasons. First, the UMP2(full)/6–31G(d) level of theory may not be quantitatively adequate enough to determine the ‘‘ true’’ geometries of stationary points in particular transition states. Second, spin contamination was inevitably encountered in the application of the unrestricted Hartree–Fock (UHF) reference wavefunction for the open-shell system. For doublets, the expectation values of S² are always in the range 0.750–0.936 before projection, where 0.750 is the correct value. However, the agreement of our G2(MP2, SVP) theoretical results in the following section with the experimental observation in the case of the CH₂FCHFO system provides confidence that this is a reasonable level, at least qualitatively, to study the unimolecular reactions of CH₂XCHFO (X = H, F).

The energy-specific rate constants k(E) for different reaction channels were evaluated using the Rice–Ramsperger–Kassel–Marcus (RRKM) theory. Subsequently these data were utilized to deduce the thermal rate constants k(T, P) at various temperatures and pressures through the numerical solution to the master equation for the multi-channel reactions. The basic procedure has been detailed elsewhere.¹² Note that the angular momentum conservation is included only in the high-pressure limit, which is a reasonable approximation for the tight transition state.¹² In view of the inherent errors in the calculated barrier heights, the rate constants easily have 50% or larger uncertainty.

All the ab initio calculations were performed using the GAUSSIAN 94 program.¹³ The RRKM calculations were carried out using the UNIMOL program package¹⁴ and the obtained ab initio data.

III. Results and discussion

The geometrical parameters for the two reactants and all the transition states are shown in Fig. 1. The corresponding moments of inertia and vibrational frequencies are listed in Table 1. The barrier heights and heats of reaction for various product channels are summarized in Table 2.

Fig. 1 Selected UMP2(full)/6–31G(d) geometric parameters for the reactants and transition states for reaction channels (1)–(6). Bond distances are in ångströms and the XCCO dihedral angles are in degrees. The first entry in each pair is for the CH₃CHFO system and the second entry that for the CH₂FCHFO system.

Table 1 Moments of inertia (I_A, I_B, I_C) and scaled vibrational frequencies for various species involved in the decomposition of CH₃CHFO and CH₂FCHFO (in italics)

Species	IA, IB, IC/u	Frequency^a/cm^−1
a i represents imaginary frequency.
CH3CHFO	180.8, 199.2, 339.3	231, 341, 417, 526, 832, 898, 1011, 1036, 1105, 1223,
1296, 1354, 1440, 1446, 2853, 2919, 3015, 3021
CH2FCHFO	199.1, 460.9, 611.0	120, 232, 386, 451, 540, 840, 979, 1043, 1060, 1094,
1139, 1212, 1298, 1354, 1459, 2841, 2928, 2999
TS1	185.2, 224.6, 365.2	728i, 179, 255, 394, 585, 673, 718, 918, 992, 1103,
1295, 1385, 1395, 1617, 2858, 2957, 3116, 3129
TS1	205.3, 487.9, 638.8	650i, 105, 188, 352, 379, 588, 731, 899, 989, 1098,
1147, 1158, 1294, 1439, 1584, 2846, 2981, 3112
TS2	179.2, 196.3, 343.5	1740i, 220, 373, 504, 608, 677, 703, 817, 978, 1056,
1144, 1350, 1429, 1436, 1677, 2917, 3009, 3039
TS2	194.1, 458.5, 604.4	1699i, 131, 233, 435, 496, 637, 657, 689, 831, 1027,
1062, 1143, 1210, 1334, 1450, 1693, 2920, 3002
TS3	163.9, 248.5, 361.8	816i, 180, 229, 336, 487, 829, 894, 1054, 1102, 1343,
1363, 1415, 1427, 1581, 2850, 2903, 2988, 3030
TS3	206.8, 515.0, 653.8	844i, 78, 210, 322, 356, 504, 806, 1006, 1053, 1060,
1180, 1300, 1347, 1439, 1589, 2874, 2911, 2996
TS4	187.9, 215.6, 378.7	656i, 149, 326, 458, 527, 678, 903, 941, 1007, 1069,
1342, 1418, 1431, 1452, 1923, 2920, 3013, 3040
TS4	226.9, 449.7, 635.1	584i, 118, 221, 400, 429, 543, 819, 902, 985, 1059,
1133, 1206, 1334, 1438, 1670, 2123, 2924, 2996
TS5	184.6, 197.2, 357.1	2100i, 199, 363, 449, 510, 671, 824, 957, 1047, 1174,
1255, 1363, 1432, 1435, 2399, 2897, 2986, 3021
TS5	194.6, 476.5, 632.0	2106i, 104, 219, 414, 442, 555, 686, 849, 1016, 1054,
1175, 1219, 1226, 1364, 1453, 2404, 2897, 2981
TS6	145.6, 223.4, 319.5	2271i, 361, 404, 494, 731, 855, 943, 981, 1054, 1099,
1115, 1230, 1338, 1367, 1945, 2969, 2985, 3102
TS6	231.2, 387.6, 545.6	2364i, 192, 232, 474, 567, 663, 844, 963, 1002, 1068,
1132, 1165, 1236, 1321, 1353, 1960, 2971, 2998

---

Table 2 Barrier heights (E_a) and heats of reaction (Δ_rH^°) calculated at the G2(MP2, SVP) level for the product channels (1)–(6) of CH₂XCHFO (X = H, F)

CH3CHFO^a		CH2FCHFO^a
No.	Product channel	Ea/kcal mol^−1	ΔrH^°/kcal mol^−1	Ea/kcal mol^−1	ΔrH^°/kcal mol^−1
a The total energies at the G2(MP2, SVP) level are −253.261 54 Eh for CH3CHFO and −352.40597 Eh for CH2FCHFO.
1	CH2X+CHFO	11.6	0.1	8.3	−1.4
2	H+CH2XCFO	14.7	3.0	16.0	6.1
3	F+CH2XCHO	39.1	37.3	39.4	36.9
4	HF+CH2XCO	27.5	−10.6	30.9	−10.0
5	CH2XCF(OH)	28.5	−8.3	29.5	−8.1
6	CHXCHF(OH)	31.7	−2.1	32.6	−5.8

---

III.1. Reaction mechanism

The preferred ground-state configurations of both CH₃CHFO and CH₂FCHFO have C₁ symmetry (gauche structures). As shown in Fig. 1, the XCCO dihedral angles are 181.9° for CH₃CHFO and 184.9° for CH₂FCHFO. The other conformations corresponding to the rotamers about the C–C bond were found to be saddle points, as characterized by the imaginary vibrational frequencies. Spin density analysis shows that the unpa ired electron is located at the oxygen atom, leading to a long C–O single bond (∽1.35 Å).

III.1.A. Bond scission mechanism.. Three bond scission channels, namely the extrusion of CH₂X, H and F from the α-carbon of CH₂XCHFO, are conceivable. Note that the elimination of H or F from the β-carbon is extremely difficult because of the significant endothermicity (e.g., >100 kcal mol⁻¹).

The energetically most favorable bond scission channel for CH₂XCHFO (X = H, F) is the C–C bond cleavage (channel 1). This reaction pathway is nearly thermoneutral. The transition state involved is illustrated as TS1 (Fig. 1). In view of the significantly elongated CC bond and the shortened CO bond, TS1 appears to be product-like. It is noted that the monofluorination of the β-carbon shortens the dissociating CC bond of TS1, and also lowers the barrier height (11.6 kcal mol⁻¹ for CH₃CHFO vs. 8.3 kcal mol⁻¹ for CH₂FCHFO).

The second feasible bond scission channel involves the hydrogen extrusion via transition state TS2. In this case, the fluorination of β-carbon has little influence upon the structural parameters of TS2. For example, the dissociating CH bond is stretched to about 1.50 Å. The CO bond is shortened by about 0.14 Å and the CC bond barely changes. As a result, the barrier heights of the CH ruptures, 14.7 kcal mol⁻¹ for CH₃CHFO and 16.0 kcal mol⁻¹ for CH₂FCHFO, are very close. The calculated heats of reaction indicate that channel (2) is slightly endoergic.

The third bond scission channel is the elimination of fluorine from CH₂XCHFO (X = H, F) via transition state TS3. Similarly to TS2, the fluorination of the β-carbon barely changes the geometry of TS3. Two geometric features of TS3 are noteworthy. First, the dissociating CF bond is significantly stretched by about 33%, so TS3 has a late character, as could be expected from the considerable endothermicity of reaction (∽37.0 kcal mol⁻¹). Second, the FCO bond angle decreases from 112.3° to 82.7° for CH₃CHFO and from 107.6° to 84.1° for CH₂FCHFO. The energy barriers of these two fluorine extrusion reactions are nearly identical (39.1 vs. 39.4 kcal mol⁻¹). Note that among the six reaction channels examined, the C–F scission channel possesses the highest energy barrier and it is therefore difficult for it to occur to any extent.

III.1.B. Three-cen ter HF elimination mechanism.. By analogy with the well-characterized three-center elimination of HCl from the α-chloroalkoxyl radicals,^15–21 the three-center elimination of HF might be a feasible decomposition channel for α-fluoroalkoxyl radicals such as CH₂XCHFO (X = H, F). Moreover, this kind of reaction pathway is significantly exothermic. In fact, we have located the desired three-center transition state (TS4) for this mechanism. Generally, the geometric parameters of the transition state for CH₃CHFO are not different from those of CH₂FCHFO, reflecting the weak influence of β-carbon fluorination. However, the forming HF bonds still have a 0.1 Å difference in distance. The barrier heights are calculated to be 27.5–30.9 kcal mol⁻¹, which are lower than those for channel (3) but much higher than those for channels (1) and (2). Hence we can expect that the three-center HF elimination might make little contribution to the decomposition of CH₂XCHFO (X = H, F). It is worth noting that this mechanism is different from the decomposition of α-chloroalkoxyl radicals. It has been demonstrated that the three-center elimination of HCl from α-chlorinated alkoxyl radicals (e.g., CH₂ClO, CH₃CHClO, CH₂ClCHClO) has the lowest energy barrier and is the dominant reaction channel.^15–21

III.1.C. Isomerization mechanism.. Two pathways of rearrangement of CH₂XCHFO (X = H, F) are conceivable. The first (channel (5)) involves a 1,2-H shift from the α-carbon to the terminal oxygen via transition state TS5. During the hydrogen migration, the radical center is moved in the opposite direction, from O to α-C. The fluorination of β-carbon seems to have little impact on either the structure of TS5 or the barrier height for the 1,2-hydrogen shift pathway. The second mechanism (channel (6)) involves the rupture of one of the β-CH bonds and simultaneously the formation of an OH bond. The radical center is moved to β-carbon. The energy barriers of the 1,3-hydrogen shift pathways are 31.7 and 32.6 kcal mol⁻¹ for CH₃CHFO and CH₂FCHFO, respectively. All the products of isomerization reactions, namely CH₂XCF(OH) and CHXCHF(OH) (X = H, F), are lower in energy than the reactants CH₂XCHFO (X = H, F), resulting in exoergic hydrogen migrations.

In summary, since the energy barriers for the reaction channels (1)–(6) appear to be well separated, it can be expected that channel (1), i.e., the C–C bond scission of CH₂XCHFO (X = H, F), would be the dominant decomposition pathway because it has the lowest energy barrier. The major products of unimolecular reaction should be CH₂X and CHFO. The following kinetic calculations confirm this prediction.

III.2. Reaction kinetics

To assess the relative importance of the different reaction channels, we performed multi-channel RRKM calculations using our ab initio data (Tables 1 and 2). As will be shown below, both microscopic and thermal rate constants are obtained from first principles.

I II.2.A. Microscopic rate constants.. Figs. 2 and 3 show the microscopic rate constants as a function of internal energy E for the six unimolecular reaction channels of CH₃CHFO and CH₂FCHFO, respectively. Evidently, the rate constants for various reaction channels are well separated. The C–C bond scission pathway (channel (1)) has the largest rate constants over the whole energy range considered in this study, mainly resulting from channel (1) having the lowest energy barrier. This calculation supports the experimental proposal that C–C bond rupture dominates the decomposition of CH₂FCHFO.⁶ At higher energies, CH bond scission (channel (2)) might be competitive. The rate constants for other unimolecular reactions (channels (3)–(6)) are significantly lower than those for channels (1) and (2), and are negligible.

Fig. 2 Microscopic rate constants for the unimolecular reaction channels (1)–(6) of the CH₃CHFO radical.

Fig. 3 Microscopic rate constants for the unimolecular reaction channels (1)–(6) of the CH₂FCHFO radical.

III.2.B. Thermal rate constants.. In contrast to the microscopic rate constants, the macroscopically measurable thermal rate constants [k(T, P)] for various reaction channels of CH₂XCHFO (X = H, F) are not independent of each other. At low pressures the competition favors the faster channels more than that expected from the ratios of the microcanonical rates because they empty the lower energy levels of the reactant, and the collisional energy transfer cannot fill up the higher levels where the slower channels could compete more efficiently. The determination of k(T, P) requires the solution to the master equation. The UNIMOL program package is suitable for the evaluation of k(T, P).¹⁴

To study the temperature dependence of the rate constants, we performed multi-channel (up to six) rate calculations in the range 250–700 K with 760 Torr of N₂ as bath gas. The ab initio data (Tables 1 and 2), including moments of inertia and vibrational frequencies of the reactants and various transition states and the barrier heights for channels (1)–(6), were employed. The effective collision frequency between the reactant and the bath gas was calculated by Troe's weak-collision approximations.²² Since the Lennard-Jones potential parameters (i.e., well depth ε and diameter σ) for both CH₃CHFO–N₂ and CH₂FCHFO–N₂ are not available in the literature, the estimated data, ε = 200 K and σ = 5.0 Å, were used in the fall-off calculations.

During the calculations, we found that the thermal rate constants for channels (2)–(6) are much smaller than that for channel (1) (by more than three orders of magnitude), so only the rate constants for channel (1) might be kinetically measurable. After correcting for quantum tunneling using the Wigner method,²³ the rate constants for channel (1) were fitted to the following Arrhenius expressions in the temperature range 250–700 K and at 760 Torr of N₂:

The corresponding high-pressure limits of the unimolecular rate constants for channel (1) were also calculated and fitted to the Arrhenius expressions as follows:

For comparison, at T = 296 K and P = 700 Torr, the value of k₁ for the C–C bond rupture of CH₂FCHFO was calculated to be about 200×10⁴ s⁻¹, which agrees with the experimental lower limit⁶ of 6×10⁴ s⁻¹.

Fig. 4 shows the fall-off curves of the rate constants at 300 K for channel (1). Evidently, the decomposition rate of CH₂FCHFO is about three orders of magnitude higher than that of CH₃CHFO over the whole pressure range considered. This is caused by the fact that the fluorination of β-carbon weakens the CC bond and leads to a decrease in the energy barrier. The rate constant approaches the high-pressure limit near 10⁵ Torr for both CH₃CHFO and CH₂FCHFO.

Fig. 4 Fall-off curves of the rate constants at 300 K for reaction channel (1): CH₂XCHFO (X = H, F)→CH₂X+CHFO.

It is useful to estimate the lifetimes of the CH₂XCHFO (X = H, F) radicals in the atmosphere, even though this kind of estimation is rather simplistic. In view of the lower atmospheric temperatures and pressures of interest, the rates for channel (1) are expected to be in the fall-off regime. Being somewhat arbitrary, at T = 230 K and P = 100 Torr, the like ly lifetimes of the thermalized CH₃CHFO and CH₂FCHFO radicals are only 70 ms and 80 μs, respectively. Although the lifetime of CH₃CHFO may exceed that of CH₂FCHFO, it is still very short compared with that for any other process likely to remove CH₂FCHFO in the atmosphere.

IV. Conclusion

We have reported unimolecular reaction pathways and energetics of two important atmospheric alkoxyl radicals, CH₃CHFO and CH₂FCHFO. Three kinds of mechanisms, namely bond scission, elimination of HF and isomerization, were revealed. The rate constants were evaluated using the multi-channel RRKM theory. The rupture of the C–C bond dominates the decomposition of CH₃CHFO and CH₂FCHFO. The major products are CH₃ (or CH₂F) and CHFO. The other reaction channels are negligible. Both CH₃CHFO and CH₂FCHFO are expected to have relatively short lifetimes in the atmosphere.

Acknowledgements

The authors thank Professor R. G. Gilbert for providing a copy of the UNIMOL program package.

References

1. S. Solomon, Nature (London), 1990, 347, 6291.
2. R. Atkinson, J. Phys. Chem. Ref. Data, 1989, Monograph No. 1..
3. T. J. Wallington, M. D. Hurley, J. M. Fracheboud, J. J. Orlando, G. S. Tyndall, J. Sehested, T. E. Møgelberg and O. J. Nielsen, J. Phys. Chem., 1996, 100, 18116.
4. R. Atkinson, Atmos. Environ., Part A, 1990, 24A, 1.
5. T. J. Wallington, P. Dagaut and M. J. Kurylo, Chem. Rev., 1992, 92, 667.
6. T. J. Wallington, M. D. Hurley, J. C. Ball, T. Ellermann, O. J. Nielsen and J. Sehested, J. Phys. Chem., 1994, 98, 5435.
7. L. A. Curtiss, P. C. Redfern, B. J. Smith and L. Radom, J. Chem. Phys., 1996, 104, 5148.
8. W. Hehre, L. Radom, P. V. R. Schleyer and J. A. Pople, Ab Initio Molecular Or bital Theory, Wiley, New York, 1986..
9. C. Gonzalez and H. B. Schlegel, J. Chem. Phys., 1989, 90, 2154; C. Gonzalez and H. B. Schlegel, J. Phys. Chem., 1990, 94, 5523.
10. L. A. Curtiss, K. Raghavachari, P. C. Redfern and J. A. Pople, J. Chem. Phys., 1997, 106, 1063.
11. D. W. Rogers, F. J. McLafferty and A. V. Podosenin, J. Phys. Chem. A, 1998, 102, 1209.
12. R. G. Gilbert and S. C. Smith, Theory of Unimolecular and Recombination Reactions, Blackwell, Oxford, 1990..
13. M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. W. M. Gill, B. G. Johnson, M. A. Robb, J. R. Cheeseman, T. A. Keith, G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A. Allaham, V. G. Zakrzewski, J. V. Ortiz, J. B. Foresman, J. Cioslowski, B. B. Stefanov, A. Nanayakkara, M. Challacombe, C. Y. Peng, P. Y. Ayala, W. Chen, M. W. Wong, J. L. Andres, E. S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J. Defrees, J. Baker, J. P. Stewart, M. Head-Gordon, C. Gonzales and J. A. Pople, GAUSSIAN 94, Revision E.1, Gaussian, Pittsburgh, PA, 1995..
14. R. G. Gilbert, S. C. Smith and M. J. T. Jordan, UNIMOL Program Suite (Calculation of Fall-off Curves for Unimolecular and Recombination Reactions), Sydney University, NSW, 1993..
15. T. J. Wallington, J. J. Orlando and G. S. Tyndall, J. Phys. Chem., 1995, 99, 9437.
16. J. Shi, T. J. Wallington and E. W. Kaiser, J. Phys. Chem., 1993, 97, 6184.
17. M. M. Maricq, J. Shi, J. J. Szente, L. Rimai and E. W. Kaiser, J. Phys. Chem., 1993, 97, 9686.
18. T. J. Wallington, M. Bilde, T. E. Mogelberg, J. Sehested and O. J. Nielson, J. Phys. Chem., 1996, 100, 5751.
19. B. Wang, H. Hou and Y. Gu, J. Phys. Chem. A, 1999, 103, 2060.
20. H. Hou, B. Wang and Y. Gu, J. Phys. Chem. A, 1999, 103, 8075.
21. H. Hou, B. Wang and Y. Gu, J. Phys. Chem. A, , , in press.
22. J. Troe, J. Chem. Phys., 1977, 66, 4745.
23. J. I. Steinfeld, J. S. Francisco and W. L. Hase, Chemical Kinetics and Dynamics, Prentice Hall, Englewood Cliffs, NJ, 1989..

---