Mechanistic and Kinetic Investigations on the Thermal Unimolecular

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Mechanistic and Kinetic Investigations on the Thermal Unimolecular Reaction of Heptafluoroisobutyronitrile Xiaojuan Yu, Hua Hou, and Baoshan Wang J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b07189 • Publication Date (Web): 06 Sep 2018 Downloaded from http://pubs.acs.org on September 8, 2018

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The Journal of Physical Chemistry

Mechanistic and Kinetic Investigations on the Thermal Unimolecular Reaction of Heptafluoroisobutyronitrile

Xiaojuan Yu, Hua Hou, Baoshan Wang*

College of Chemistry and Molecular Sciences, Wuhan University, Wuhan, 430072, People's Republic of China

*Corresponding authors. E-mail: [email protected]

ACS Paragon Plus Environment

The Journal of Physical Chemistry 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

ABSTRACT Heptafluoroisobutyronitrile (C4) has been utilized as a dielectric compound to replace sulfur hexafluoride for the sake of environmental concern. Energetic profiles of the potential energy surface for the unimolecular reaction of C4 were calculated using density functional theory (M06-2X), quadratic complete basis set (CBS-QB3), Gaussian-4, multireference Rayleigh-Schrodinger perturbation theory (RS2, RS2C), and state-averaged multiconfiguration self-consistent-field (SA-MCSCF) ab initio methods. Among thirty-eight production channels, the most energetically accessible reaction path is the three-centered rearrangement of cyanide to isocyanide. The C-CF3 bond appears to be the weakest bond in C4(X1A') and the symmetry-breaking C-CF3 bond cleavage undergoes to form the ground-state CF3(X2A1) and CF3CFCN (X2A") radicals. All the possible isomerization pathways involving F- and CF3-migration together with the concerted elimination and stepwise decomposition routes were revealed for C4 and i-C4. Various isomers and potential toxic byproducts including FCN, CF3CN, C2F5CN, CF2=CFCF3, CF2=CFCN, CF4, C2F6, and alkyne compounds have been identified for the first time. Master equation analysis has been carried out to obtain the temperature- and pressure-dependent thermal rate constants. Theoretical kinetics for the loss of C4 due to pyrolysis is in good agreement with the temperature-ramped flow-tube experiment. The present theoretical work provides new insights on the thermal stability and chemical reactivity of C4. Moreover, i-C4 and C2F6 are proposed to be the potential characteristic gas molecules to monitor the insulation breakdown of C4 in the electric equipments.


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I. Introduction Sulfur hexafluoride (SF6) is the most important dielectric gas in high voltage applications including power transmission lines and substations because it boasts many remarkable properties such as its high dielectric strength (~ 2.5 times that of air) and excellent arc quenching capability.1 SF6 is usually compressed at pressures of 0.4 - 0.8 MPa in the excessive sizes of the electric equipments, about 80% of the SF6 worldwide production has been used for insulation gas.2,3 Unfortunately, SF6 suffers from a significant disadvantage, that is, an aggravating agent for the greenhouse gas effect.4 The global warming potential (GWP) for time horizons of 100 year of SF6 is 23500 times great than that of CO2 because of its strong radiative effect and extremely long atmospheric lifetime (~3200 years).5 Therefore, an alternative to SF6 is highly desirable.6,7 Development of replacements for SF6 is very challenging due to the numerous stringent demanding combinations of performance, safety, and environmental properties. An improvement in one property often leads to deleterious effect in another property. After decades of research,8-10 heptafluoroisobutyronitrile (i-C3F7CN, in abbr., C4), which holds the right balance of properties to function as an SF6 alternative, appears to be a breakthrough.2,11 It has a dielectric strength about 2 times that of SF6, high thermal transfer capability, low toxicity, and more importantly, moderate GWP (~2400), which is only one tenth of that of SF6. The only deficiency of C4 is its boiling point of −4.7°C, which is too high to remain gaseous over the expected operating temperatures typically down to at least −30°C. However, such a



defect could be cured readily by mixing either CO2 or N2. Recently, the dielectric properties of C4 are attracting more and more attentions for insulation in various high voltage industrial applications.12,13 The C4-containing gaseous insulators have been subjected to considerable industrial tests. In contrast, only the atmospheric sink relevant to GWP of C4 was investigated from chemical point of view. Kinetics and mechanisms of the reactions with OH radicals, with chlorine atoms, and with ozone have been studied experimentally and theoretically.14-16 Besides the atmospheric degradation of C4, unimolecular reaction of C4 is of fundamental importance as well to characterize its thermal stability, which is crucial for the insulation capability after discharge interruption. Moreover, identification of the initial fragments after corona, spark, or arc-induced decomposition of C4 is particularly important in understanding how the various byproducts are produced. A great deal can be learned from post-discharge gas analyses and the dependence of the so-called characteristic gas on the temperature profiles. As well-established in the use of SF6 insulation,17-20 the nature and extent of insulation defects could be evaluated in situ elaborately by the nascent fragments and their kinetic evolution, which is invaluable for daily diagnostic and on-line maintenance. To date, the only experimental study on the pyrolysis of C4 was performed preliminarily by Kieffel and Owens.12,21 Thermal decomposition of C4 through a tube furnace was monitored with temperatures increasing to a maximum of approximately 1273 K. It was found that C4 can be chemically stable up to a temperature of about 1000 K without measurable loss. Above 1000 K, various degradation products, e.g.,


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HF, COF2, CF3CN, C2F6, etc., which strongly depend on the bath gases (e.g., N2, air, and CO2), have been detected using Fourier Transform Infrared (FTIR) spectroscopy and gas chromatography mass spectrometry (GC-MS). However, the nascent fragments from C4 could not be identified. In addition, even the dry N2 was employed as the bath gas, a large amount of CO and HF molecules have been detected. Apparently, neither mechanism nor kinetic data of the unimolecular decomposition of C4 could be deduced unambiguously from the experiments due to the severe impurities such as air or water vapor contamination introduced during sample handling. This work is aimed at revealing the detailed mechanisms of the thermal unimolecular reaction of C4 using various high-level ab initio quantum chemistry methods. It is worth noting that the arcing of C4 will involve high energy electrons and excited state molecules, leading to different pathways than considered here through various secondary reactions. All possible production routes have been examined and the corresponding rate coefficients have been calculated from first-principles as functions of temperature and pressure. The present work provides solid theoretical insights into the nascent products of the pyrolysis of C4 and will be helpful to develop chemical kinetic models for the C4 discharge decomposition in the electric equipments.

2. Computational Methods Geometries of reactant, transition states (TS), isomers (IM), and products



involved in the unimolecular reaction of C4 were optimized using the density functional theory M06-2X with Dunning's augmented correlation consistent triple-ξ aug-cc-pVTZ (abbr. AVTZ) basis set.22,23 Vibrational frequencies were calculated at the same level of theory to obtain the zero-point energy corrections (ZPE) without scaling. Number of imaginary frequency (NIMG) of the stationary point was employed to characterize the minimum (NIMG=0) or the transition state (NIMG=1). Normal vibrational mode of the imaginary frequency or the intrinsic reaction coordinates (IRC)24 were computed to verify that the transition state connects to the correct reactant and product. In addition, dependence of the geometrical parameters on the basis set has been examined by using the more flexible aug-cc-pVQZ (AVQZ) basis set to ensure convergence. The single-point energies for stationary points were calculated using two types of ab initio model chemistries, namely, the complete basis set quadratic mode (CBS-QB3)25 and the Gaussian-4 theory26 but on the basis of the M06-2X/AVTZ optimized geometrical parameters, viz.: E(CBS-QB3) = EMP2+∆ECBS+ ∆EMP4+ ∆ECCSD(T)+ ∆ECBS-int+ ∆Eemp Here, EMP2 is the MP2 energy calculated with the 6-311+G(3d2f,2df,2p) basis set, ∆ECBS is the extrapolated second-order pair correlation energy to the CBS limit, ∆EMP4 = EMP4SDQ/6-31+G(d(f),p) - EMP2/6-31+G(d(f),p), and ∆ECCSD(T) = ECCSD(T)/6-31+G(d') EMP4SDQ/6-31+G(d'). ∆ECBS-int and ∆Eemp correspond to the empirical interference correction to the pair energies and the higher-order correlation energies, respectively. E(G4) = EMP4/6-31G(d) +∆EMP4a+∆EMP4b+∆ECC+∆EG3LargeXP+∆EHF+∆ESO+EHLC


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Here, ∆EMP4a = EMP4/6-31+G(d) - EMP4/6-31(d), ∆EMP4b = EMP4/6-31G(2df,p) - EMP4/6-31G(d), ∆ECC = ECCSD(T)/6-31G(d) - EMP4/6-31G(d), and ∆EG3LargeXP = EMP2(full)/G3LargeXP - EMP2/6-31G(2df,p) EMP2/6-31+G(d) + EMP2/6-31G(d). ∆EHF and ∆ESO are the correction to Hartree-Fock energy limit and the spin-orbital correction, respectively. EHLC represents the empirical high-level energy correction from the numbers of valence electrons. It has been demonstrated that these the composite methods performs very well for both thermochemistry and barrier heights.27-29For instance, both CBS-QB3 and Gaussian-4 methods shows good accuracy for the calculations of bond-making/breaking reaction barriers with a mean deviation of 0.06 kcal/mol and 0.71 kcal/mol for 44 and 76 barrier heights, respectively.28,29 For the primary reaction paths, the multireference second-order Rayleigh-Schrodinger perturbation theory (RS2)30 with an active space of 12 electrons in 12 orbitals, namely, (12e,12o) as illustrated in Figure 1, has been employed to check the potential multiconfiguration effect on the energetics. It is noted that the (12e,12o) active space includes the bonding σ, π, and anti-bonding π* orbitals, which were selected rigorously via orbital rotations according to the criterion that the associated bonds (e.g., all the C-C bonds, the central C-F bond, and the π bonds of C≡N) are crucial to the unimolecular decomposition or isomerization of C4 of our interest. In view of as many as 41 closed-shell orbitals for the C4 molecule, an internally contracted version of RS2, namely, RS2C, has to be used. A level-shift parameter of 0.25 was introduced to avoid intruder state problems.31 The RS2C calculations were carried out with the hierarchical sequence of the correlation consistent basis sets including AVnZ (n = D, T), while the typical RS2C/AVTZ



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calculation involves 552 contracted basis functions and 3.8×108 contracted configuration state functions. It is worth noting that a few bond cleavage decomposition routes without the definitive barriers warrant special consideration. Partial optimizations were performed to obtain the minimum energy reaction paths at the M06-2X/AVTZ level of theory. However, serious spin contamination occurs along the bond-breaking coordinates, resulting from the internal instability of the restricted or unrestricted M06-2X wavefunctions apparently due to the multiconfiguration character near the product asymptote. In order to account for the possible singlet-triplet crossing involved inherently in the bond breaking paths, the energetic reaction routes were calculated using the state-averaged multiconfiguration self-consistent-field (SA-MCSCF)32,33 with the aforementioned (12e,12o) active space and the AVDZ basis set. All ab initio calculations were carried out with the Gaussian09 programs34 and the Molpro2012.1 suite of programs.35 Thermal rate constants at the high-pressure limit (k∞) for the reversible C4 ↔ i-C4 isomerization were computed using the ab initio rovibrational parameters and energetics on the basis of the statistical Rice-Ramsperger-Kassel-Marcus (RRKM) theory and transition state theory (TST), viz.,36,37 k ∞ (T ) =

σ h

∞

∞

× ∑ (2 J + 1) ∫ G TS ( E , J )e − E / kBT dE J =0

0

∞

∑ (2 J + 1)∫ J =0

∞

ρ R ( E , J )e− E / k T dE B

0

where h and kB is Planck's constant and Boltzmann's constant, respectively. T is the reaction temperature, σ=1 is the reaction path degeneracy. The microcanonical rate coefficients were calculated using at the energy/angular momentum (E/J) resolved


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level with the K-active model in the scheme of rigid rotor harmonic oscillator (RRHO) approximation for all the species.38 GTS and ρR correspond to the sums of rovibrational state for TS1 and density of rovibrational states for C4, respectively, which are both calculated using a conventional direct count method with a grain size of 100 cm-1. Tunneling correction was considered using the asymmetrical Eckart model for simplicity.39 On the basis of the ab initio energetic reaction routes, thermal rate constants for the title reaction were calculated from first-principles for a wide range of temperatures (500 - 3000 K) using the energy grained master equation (EGME), as implemented in the MESMER program.40 Collisional energy transfer and isoenergetic interconversion between species was described with a set of coupled differential equations, viz., dp = Mp dt

where p is the population vector and M is the matrix that determines grain population evolution with a width of 100 cm-1. Collisional energy transfer was considered using an exponential down model with the appropriate Lennard-Jones parameters. The average downward energy transfer parameter 〈∆E〉down is fixed to be 200 cm-1 for all the isomers for simplicity. For the current unimolecular reaction with high barriers, it was found that the thermal rate constant is insensitive to the value of 〈∆E〉down. The changes of the temperature and pressure-dependent rate constants are less than 5% even if the value of 〈∆E〉down was arbitrarily set to 2000 cm-1. Moreover, the influence of the bath gas (e.g., N2 or CO2, which is the widely used buffer gas for dielectric medium) on the rate constants was found to be marginal as well in the pressure range



1-10 atm of our interest. The RRHO approximation was employed for all the tight transition states. For the barrierless dissociation channels such as the C-CF3 bond fission, the sum of states has been derived by taking the inverse Laplace transform (ILT) of the computed high pressure association rate coefficient. Within our formulation of the EGME, all the products were represented using the infinite sink approximation while the isomers were treated as intermediates, i.e., reversible isomerization and may undergo relaxation via collisions with the bath gas. Vibrational frequencies and rotational constants in the EGME calculation are given in the Supporting Information. It is worthwhile noting that numerical difficulty arises for the present reaction with many deep wells especially at low temperatures. Even using the high-precision quad-double (QD) arithmetic, which supports approximately 64 decimal digits, the EGME can only be solved correctly in the range 500 - 3000 K.

3. Results and Discussion Optimized geometries of all the important stationary points relevant to the unimolecular reaction of C4 are shown in Figures 2. The M06-2X/AVTZ optimized geometrical parameters are almost identical to those obtained at the M06-2X/AVQZ level, confirming the good structural convergence on the basis sets. On the basis of the M06-2X/AVTZ geometries, the computed relative energies at various levels of theory are summarized in Tables 1 together with the ZPE corrections for reference. The C4 molecule has a Cs symmetry, in which the two CF3 moieties lie symmetrically aside the FCCN bisection plane. It is interesting to note that the strong


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electron-withdrawing functional groups, i.e., CN and CF3, appear to be attractive to each other because the two π bonding orbitals of CN (Figure 1) is slight bent toward CF3. Meanwhile, the C-CN bond is roughly 0.1 Å shorter than the C-CF3 bond. Many isomerization and dissociation mechanisms exist for C4, leading to various complex isomers, molecules, and radical fragments, as illustrated by the energetic profiles in Figures 3 and will be discussed as follows.

3.1 Cyanide-Isocyanide Rearrangement Isomerization of acetonitrile to methyl isocyanide is a prototypical homogeneous unimolecular reaction that has been extensively studied with various experimental and computational approaches. The corresponding C4 isomerization to heptafluoro isobutyl isocyanide (abbr. i-C4) takes place via transition state TS1. The breaking CC bond and the making CN bond is a concerted process by rotating the CN moiety in nearly perpendicular to the molecular plane. The adiabatic barrier height for TS1 was calculated to be 62.7 kcal/mol at the CBS-QB3 level, which in good agreement with the Gaussian-4 result (62.5 kcal/mol). The T1 diagnostic value in the coupled cluster [i.e., CCSD(T)] calculations for either CBS-QB3 or Gaussian-4 was found to be 0.016, which is close to the critical value ~0.02 for the problematic single-reference wavefunction,41 showing that barrier height could be slightly overestimated by the single-determinant approaches such as CBS-QB3 and Gaussian-4. Note that the GB1 diagnostic calculated with the AVTZ basis set and the %TAE[T] diagnostic at the CCSD(T)/6-31+G(d') level for TS1 are 1.7 kcal/mol and 2.7%, respectively,



indicating a negligible or mild nondynamical correction.42 In fact, the RS2C method does predict lower barriers by 1~2 kcal/mol. Using the extrapolated (AVDZ→AVTZ) RS2 energies, the best estimated barrier height for TS1 is 59.6 kcal/mol. The barrier height for the CH3CN → CH3NC reaction was calculated to be 64.4 kcal/mol at the CBS-QB3 level, which is 1.7 kcal/mol higher than that for TS1. Apparently, the perfluoro-substitution tends to enhance the CN-rearrangement reactivity despite the heptafluoroisobutyl group is much larger that the methyl group in volume. As could be seen in Table 1, all three ab initio methods (CBS-QB3, Gaussian-4, and RS2C) predict the same thermochemistry for the isomer i-C4, that is, the formation of i-C4 is endothermic by 16.3 kcal/mol. It is noted that the energy of CH3NC is lower than that of CH3CN by 23.7 kcal/mol at the CBS-QB3 level. Therefore, the isomer i-C4 appears to be more stable than CH3NC due to the extra stability gained from the electron-withdrawing perfluorinated substitutes. As shown in Figure 2, the isomer i-C4 has Cs symmetry whereas the C-NC bond distance is shortened significantly to 1.402 Å, in comparison with 1.472 Å for the C-CN bond in C4. Theoretical high-pressure limiting rate constants for the reversible C4 ↔ i-C4 isomerization are shown in Figure 4 as a function of temperature in the range 300 3000 K. The tunneling correction for the isomerization rate constant was calculated to be 1.24 at 300 K and becomes negligible as the temperatures increase above 500 K. It is evident that the isomerization reaction is slower than the reverse reaction by at least one order of magnitude. Once i-C4 is formed, it would prefer to transform back to


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reproduce C4. In comparison with the CH3NC→ CH3CN reaction,43 the i-C4 → C4 conversion is less efficient due to the enhanced stability of i-C4 as mentioned above. However, the contribution of i-C4 is only marginal at normal temperatures. Theoretical equilibrium constants for the C4 → i-C4 reaction have been calculated as well (Figure 4), indicating that the yield of i-C4 is still less than 6% even under partial discharge or even arc conditions (e.g., T ~ 2000 - 3000 K). It appears that the isomerization of C4 to i-C4 at high temperatures might not affect the insulation performance of C4 even though the dielectric strength of i-C4 is slightly weaker than that of C4. On the other side, i-C4 could be a potent characteristic gas molecule to monitor the abnormal temperature change due to discharge breakdown of C4. Since the i-C4 isomer has not been experimentally known yet, the infrared spectrum of i-C4 was simulated by means of the anharmonic rovibrational analysis at the M06-2X/AVTZ level and is illustrated in Figure 5. The theoretical IR spectrum of C4 is in good agreement with the experimental spectrum.14 The strongest IR bands for C4 around 1300 cm-1 correspond to CF3-C-CF3 deform and stretch, while the stretch vibrational mode of the CN triple bond at 2380 cm-1 is nearly unobservable. In contrast, the N≡C bond stretch in i-C4 is red-shifted to 2197 cm-1 and its IR activity is enhanced considerably. Therefore, such a characteristic IR band could be utilized to determine the content of i-C4 impurity in C4 sample for practical use.

3.2 Bond Cleavage Mechanisms Three bond-cleavage product channels are available to C4, including C-CF3, C-F,



and C-CN bond breaking to form CF3 + CF3CFCN, F+(CF3)2CCN, and CN + (CF3)2CF, respectively. These product channels are highly endothermic (Table 1 and Figure 3), although the relative energies exhibit strong dependence upon the theoretical methods. The difference between the CBS-QB3 and RS2C energies could be as large as 6~9 kcal/mol. Such a phenomenon could be related to the inherent multireference nature of the radical products. For example, CN is one of the well-known problematic radical with strong multiconfigurational effect, as indicated by its large T1 diagnostic value of 0.051. The simple C-F bond cleavage at one of the CF3 groups of C4 to make CF2(CF3)CFCN is endothermic by 126.0 kcal/mol calculated at the CBS-QB3 level and thus is negligible. It is worth noting that the production of CF3 and CF3CFCN radicals from C4 is a typical symmetry-forbidden path because the ground states of the products CF3(X2A1) and CF3CFCN(X2A") can only correlate to the A" electronic state in either singlet or triplet. Therefore, symmetry breaking has to be involved in the process of the C-CF3 bond cleavage. The energetic reaction path for the C-CF3 decomposition of C4 was computed along the C-C distances with a stepsize of 0.1 Å while the rest of geometrical parameters were optimized. As illustrated in Figure 6, while the regular RM06-2X method leads to the wrong decomposition asymptote due to the instability of the restricted wavefunction, the unrestrticted UM06-2X/AVTZ calculation does show that the energies increase monotonically from C4(X1A') to the asymptote of CF3(X2A1) + CF3CFCN(X2A"). However, it was found that the UM06-2X wavefunction is seriously contaminated starting from the C-CF3 bond distance 2.45 Å,


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as indicated by the spin expectation values 〈S2〉 up to 1.02 (Figure 6). The correct 〈S2〉 should be always zero for the singlet state of our interest. In the consideration of the ineluctable overlap between singlet and triplet paths especially in regions near the dissociation asymptote, the reaction path for the C-CF3 bond dissociation was calculated using the state-averaged MCSCF method (Figure 6). The energy of the triplet C4 is considerably higher than that of the ground-state C4. Moreover, a small barrier exists on the triplet surface. Clearly, the singlet-triplet mixing becomes more and more significant as the C-CF3 bond is stretched to the product asymptote, where the singlet and triplet surfaces are essentially degenerated. Energetic profiles for the C-F and C-CN bond dissociation paths are shown in Figure 7. In contrast to the CF3(X2A1) + CF3CFCN(X2A") asymptote, both F(X2P) + (CF3)2CCN(X2B) and CN(X2Σ+) + (CF3)2CF(X2A') are symmetry-allowed product channels for the ground-state C4 decomposition. The energies increase monotonically with the breaking C-CN bond, whereas an apparent saddle point exists along the C-F dissociation path around the C-F distance of 2.8 Å. The state-averaged MCSCF calculation on the reaction path revealed that such an artifact in the single-reference UM06-2X calculation originates indeed on the seam of crossing from singlet-triplet conical interaction (see the insert plot in Figure 7). The CBS-QB3 reaction heat at 0 K (∆rHo) for the CF3+CF3CFCN channel is 84.1 kcal/mol, which is nearly 4 kcal/mol higher than that the Gaussian-4 result. This is the one of the cases where RS2C/AVTZ gives a much lower reaction enthalpy: 4 kcal/mol lower than Gaussian-4 and 9 kcal/mol lower than CBS-QB3. Additionally, it appears



that the energies strongly depend on the basis sets in view of the unexpected large difference between RS2C/AVDZ and RS2C/AVTZ calculations. Although the RS2C method includes the multireference effect, it might not be good enough to recover the dynamic electron correlation of importance to the reaction. Note that the T1 diagnostic of C4, CF3, and CF3CFCN is 0.014, 0.017, and 0.019, respectively, as indicative of the general reliability of the single-reference wavefunction. In order to assess the quality of the theoretical reaction heat, the state-of-the-art explicitly-correlated coupled cluster calculations, namely, CCSD(T)-F12,44 have been carried out with the VTZ-F12 basis set.45 Note that the F12 scheme is capable of yielding results close to the basis-set limit. The calculated ∆rHo for the CF3+CF3CFCN channel is 82.1 kcal/mol, which happens to be the average of CBS-QB3 and Gaussian-4, supporting the relative reliability of the latter two composite models. The abnormally low energies at the RS2C level might be ascribed to the incompleteness of the dynamical electron correlation or the active space or the inherent size-inconsistency. For the F and CN production channels, the CCSD(T)-F12 calculated ∆rHo are 97.5 kcal/mol and 109.3 kcal/mol, respectively. Even though it is difficult to improve further the accuracy of the energetics from first-principles due to the prohibitively large size of the molecules of our interest, we can safely conclude that the C-CF3 bond is the weakest bond in C4 and the formation of CF3 and CF3CFCN radicals should be the predominant thermal decomposition path for the barrierless bond-breaking reactions of C4. Neither F nor CN radical could be competitive. Detailed knowledge of the rate constants for the CF3 + CF3CFCN association


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together with the reverse dissociation is warranted to access its impact on the C4 stability. Conventional transition state theory is apparently inappropriate because the location of the transition state is not fixed for the barrierless processes. Therefore, the variable reaction coordinate transition state theory (VRC-TST) has been employed on the basis of the potential energy surface.46 The C-CF3 bonding interaction was evaluated using the SA-MCSCF/AVDZ energetic profile on the singlet state (Figure 6) by means of interpolation along the reaction coordinate. The interaction potentials orthogonal to the reaction coordinate were built by summing the pairwise Lennard-Jones(12-6) non-bonding potentials with the well depths (ε = 35.6, 25.9, and 36.7 cm-1) and the distance parameters (σ = 3.35, 3.31, and 2.83 Å) for C, N, and F atoms, respectively.47 Moreover, a potential anisotropy form assuming a bonding potential with the exponent of two in the angular dependence function, which is cylindrically symmetric with respect to each fragment, has been considered in this work. Number and density of states were calculated variationally using the flexible transition state theory with Monte-Carlo integration at the E/J resolved level. Bimolecular association rate constants at the high-pressure limit for the CF3 + CF3CFCN reaction are shown in Figure 8. As expected, the association rate constants exhibit negative temperature dependence and can be expressed by the modified Arrhenius form as follows (in the unit of cm3molecule-1s-1),

ka∞ (T ) = (6.56 ± 0.11) × 10 −11 (T 298 )

− (0.912 ± 0.02)

where the activation energy is set to zero, i.e., the association was assumed barrierless. The correlation coefficient (R2) for the non-linear fit is 0.992. Unimolecular



decomposition rate constants for the reverse C4 → CF3 + CF3CFCN reaction were calculated using the detailed equilibrium. It should be noted that the bimolecular association rate constants are less sensitive to the bond energy of C-CF3 because the loose nature of the bottleneck which always occurs near the dissociation asymptote in the temperature range of our interest. However, the unimolecular rate constants depend strongly on the reaction heat of the CF3 + CF3CFCN channel. For the sake of consistency, the unimolecular rate constants of the C-CF3 decomposition of C4 have been estimated using the CBS-QB3 energies. Note that the rate constants should be taken with caution to be the lower-limits because the dissociation energy decreases more or less at CCSD(T)-F12, Gaussian-4, and RS2C levels of theory. As shown in Figure 8, the C4→i-C4 rearrangement is faster than the C-CF3 bond cleavage at temperatures below 600 K. After temperatures increases to above 1000 K, the decomposition of C4 into CF3 radicals becomes dominant. Experimentally, it has been found the pyrolysis of C4 around 1000 K always produces C2F6,21 which can be formed via recombination of the two CF3 radicals.48-50 It is worth noting that the GWP of C2F6 is 11100,5 which is much higher than that of C4. It is interesting to note that the isomer i-C4 involves the bond fission channels analogous to C4. Moreover, the formation of CF3 radical via the barrierless C-CF3 bond breaking mechanism is the most energetically preferable decomposition path with an endothermicity of 88.0 kcal/mol at the CBS-QB3 level, which is about 4 kcal/mol higher than that of C4. The C-NC bond breaking of i-C4 produce the same fragments as C4. The C-NC bond energy in i-C4 was calculated to be 95.3 kcal/mol at


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the CBS-QB3 level in comparison with the C-CN bond energy of 111.6 kcal/mol in C4, implying that the C-NC bond has been slightly weakened with respect to the C-CN bond. Nevertheless, the C-F bond is enhanced and it becomes the strongest bond in i-C4 in view of the dissociation energy of 104.1 kcal/mol. Besides the barrierless bond-breaking mechanism, many isomerization and direct elimination channels of C4 are open successively at evaluated temperatures. Most of these reaction routes involve tight transition states and significant barriers, which were supposed to be unimportant to the unimolecular reaction of C4. However, the experimental study did detect the complicated products from the decomposition of C4 after arc interruption, for instance, (CF3)2C=CF2, CF2=CFCN, CF3CN, C2F5CN, etc.,12 which cannot be attributed readily to either CN rearrangement or simple bond cleavage mechanism. The C-F bond fission of the CF3CFCN fragment undergoes barrierlessly to generate CF2=CFCN with an endothermicity of 70.6 kcal/mol at the CBS-QB3 level. As a result, atomic F and CF3 radicals floating around with C4, i-C4, and CF2=CFCN to make a large potential set of secondary reactions, which might account for the experimentally observed products at the arcing condition. In addition, non-thermal chemistry in the arc can play an important role during arcing. Such an exploration is outside the scope of the present work and will be detailed separately. For completeness, all the possible high-energy channels for the pyrolysis of C4 were explored as follows.

3.3 Fluorine Migration Mechanisms



The seven fluorine atoms in C4 can be classified into two types, namely, one on the central carbon and six belong to the CF3 group. The most feasible F-migration path involves the fluorine atom on the central carbon and undergoes via a three-center transition state TS2 (Figure 2), leading to the isomer IM1. The migrating F atom is approaching to the C atom of the CN group and simultaneously the terminal N atom is bonding to the central C site. Note that the structure with the linear CCN geometry does not exist on the singlet surface. IM1 exhibits a highly strained three-member-ring geometry but it is relatively stable in view of the reaction heat ∆rHo = 29.5 kcal/mol with respect to C4. The adiabatic barrier height for TS2 is not

only higher than that for TS1 by 30.7 kcal/mol but also well above the CF3+CF3CFCN asymptote. As could be seen in Table 1, the CBS-QB3 energy for TS2 is identical to the RS2C/AVTZ energy even though the T1 diagnostic from the CCSD(T) calculation in CBS-QB3 is 0.035. The good performance of CBS-QB3 appears to be the systematic error cancelation. The F atom on the central carbon can migrate to the terminal N atom via transition state TS3 to form IM2. Although TS3 is a four-member-ring structure, its energy is about 10 kcal/mol higher than that of the three-centered TS2. Moreover, the isomer IM2 is considerably higher than IM1 in energy. Strong electronegativitiy of the F atom is capable of altering the valence-bonding feature of C4 to some extent. The fluorine atoms on the CF3 groups can also be transferred to the nearby CN group, forming FCN and CF3CF=CF2 via TS4 or IM3 via TS5. As shown in Figure 2, TS4 is a concerted 4-center elimination transition state. At the M06-2X/AVTZ level,


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TS4 is even lower than TS2 by 7.5 kcal/mol. However, the energy of TS4 tends to be slightly higher than that of TS2 using the high-level calculations. Therefore, the direct formation of FCN and CF3CF=CF2 (hexfluoropropene) could be a competitive pathway. Once again, the five-centered TS5 is about 35 kcal/mol higher in energy that the four-centered TS4. Moreover, IM3 is a highly unstable isomer in view of its energy of as high as 95.4 kcal/mol above C4, leading this F→N migration energetic route being negligible. The concerted loss of molecular F2 to form CF2=C(CF3)CN or CF3CF(CF)CN or cyclic (CF2)2CFCN is highly endothermic by 127.7, 196.1, and 169.4 kcal/mol, respectively, at the CBS-QB3 level and thus these product channels are ruled out.

3.4 Trifluoromethyl Migration Mechanisms Analogous to the atomic F, the CF3 moiety can be shifted around as a whole in C4. One of the CF3 groups migrates from the central C atom to the C atom of CN via TS6 to form IM4. The geometry of TS6 exhibits a late barrier character, which is similar to that of TS2 except the reacting CF3 group (Figure 2). The energy of IM4 is nearly identical to that of IM1, in accordance with the same cyclic three-member-ring CCN structures for both isomers. It is interesting to note that the energy of TS6 is about 3 kcal/mol higher than that of TS2 at the M06-2X/AVTZ, CBS-QB3, and Gaussian-4 levels. However, the RS2C method predicts the reverse order for the energies of TS2 and TS6. At the RS2C/AVTZ level, TS6 is roughly 5 kcal/mol below TS2 in energy. The T1 diagnostic of 0.048 for TS6 indicates problems with the single reference



theoretical methods. The 4-centered CF3 migration occurs via TS7, which is about 24 kcal/mol higher than the 3-centered TS6. In addition, the energy of TS7 is higher than that of TS3 by 15.7 kcal/mol. The geometry of TS7 is significantly different from that of TS3 (Figure 2), although both structures correspond to the 4-centered transformation pathways. The CCN bond angle in TS7 is bent to 72.1 degrees with respect to the nearly linear CCN geometry, in comparison with 135.3 degrees in TS3. On the other hand, the isomer IM5 resulting from TS7 appears to be more stable in energy than IM2. Besides isomerization, a few direct elimination routes involving CF3 have been revealed. TS8, TS9, and TS10 correspond to the 3-centered transition states for CF4, CF3CN, and C2F6 elimination paths, respectively. Although the fluorinated alkanes are very stable, the accompanying products are high-energy perfluorocarbene radicals, leading the direct production of CF4, CF3CN, and C2F6 being thermodynamically unfavorable in view of the respective endothermicities up to 90 kcal/mol. TS11 exhibits an alternative reaction path to form CF4 and CF2=CFCN via a four-centered transition state. The energy of TS11 is only 2 kcal/mol higher than that of TS8 but the formation of CF4+CF2=CFCN is endothermic by only 24.6 kcal/mol. TS12 is the transition state for the 3-centered C2F5CN elimination path. The barrier height is 120.8 kcal/mol and the formation of C2F5CN+CF2 is endothermic by 60.8 kcal/mol. Although the above direct elimination pathways involve considerable barriers, they might be capable of contributing to the unimolecular decomposition of C4 under specific conditions, for instance, extremely high temperatures. It is worth noting that


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CF3CN, C2F5CN, and CF2=CFCN (perfluoroacrylonitrile) have been identified experimentally as the primary products of arced C4.12 Toxic byproducts due to the decomposition of C4 are great concerns for the safety issue. Besides the primary reactions mentioned above, the consecutive reaction pathways starting from various isomers of C4 have been summarized in the Supporting Information (Note S1). Three highly toxic species, i.e., FCN, CF3CN, and perfluoroalkyne [CF3C≡C-N(CF3)F] have been identified theoretically, but all these reactions have to surmount significant barriers to form the final products.

3.5 Master Equation Calculations Based on the CBS-QB3 energies, the calculated overall rate constants for the C4 decomposition at 1, 5, and 10 atm of CO2 (e.g., the pressures commonly used in electric equipments) are shown in Figure 9 and documented in Table 2. For practical use, the rate constants were expressed by least-square fit to the modified Arrhenius forms (units: s-1),

k (T , P = 1atm ) = (6.17 ± 1.69) × 1025 (T 298 )

− (12.8 ±1.6)

k (T , P = 5atm ) = (4.71 ± 1.60) × 1024 (T 298 )

− (11.1±1.8)

k (T , P = 10atm ) = (1.26 ± 0.37) × 10 24 (T 298 )

e − ( 44604 ±1840) / T

( R 2 = 0.997)

e− (43800 ± 2008) / T

( R 2 = 0.997)

− (10.3±1.8)

e− (43358± 2064) / T

( R 2 = 0.997)

Theoretical calculations demonstrate that the formation of CF3 radical fragment is the only observable product channel over the whole temperature range of our interest. The experimentally observed C2F6 molecules are likely due to the recombination of the CF3 radicals. Apparently, C2F6 could be a potent characteristic gas molecule to monitor the discharge breakdown of C4. CF3CN was also detected experimentally but



with much lower concentration than C2F6. Theoretically, the contributions from i-C4 and other stable products such as CF3CN are always less than 1%. In fact, except for C2F6, other gaseous species observed in the FTIR experiments are elusive because of the impurities in the C4 sample as indicated by the coproduction of CO and HF.12,21 To our best knowledge, there is no experimental measurement on the rate constants of the C4 unimolecular reaction to date. Therefore, the unambiguous conclusion could not be drawn rigorously about the present kinetics from first principles due to the unpredictable uncertainties in the CBS-QB3 energies. Although the more accurate protocols such as HEAT has been successfully used in the study of unimolecular reaction of acetonitrile,43 application of the similar method to the current C4 molecule containing 12 heavy atoms is unaffordable yet. In order to assess the reliability of our theoretical kinetic data, we attempted to simulate the concentration curves obtained from the tube furnace experiment by Kieffel and Owens.12,21 With the total pressure of 1.4 atm, the dilute C4 gas mixtures were heated with temperatures increasing 10 K per minute to about 1273 K. According to the gas flow rate in the reaction tube, the effective residence time of C4 within the tube was estimated to be around 100 milliseconds. Therefore, the quasi-equilibrium appears to exist for the C4 decomposition inside the tube furnace. The temporal species profiles of C4 were obtained straightforwardly from the EGME calculations. Consequently, the temperature-dependent concentration curve for the loss of C4 can be constructed by taking the yield of C4 at the reaction time of 0.1 seconds, and then compared with the experimental observations in Figure 10. It is evident that the purely theoretical results


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are in excellent agreement with the experimental data, supporting appropriate quality of the present a priori predictions on both mechanisms and kinetics of the unimolecular reaction of C4.

4. Conclusions Energetic profiles of the potential energy surface for the unimolecular reaction of heptafluoro-iso-butyronitrile have been calculated using various ab initio quantum methods including DFT (M06-2X), CBS-QB3, Gaussian-4, RS2, SA-MCSCF, and CCSD(T)-F12 methods. The most energetically accessible reaction path is the 3-center rearrangement of cyanide to isocyanide. The isomer i-C4 gains extra stability due to the electron-withdrawing substitutes and thus its energy is only 16.3 kcal/mol higher than that of cyanide, in comparison with the 24.7 kcal/mol energy difference between acetonirtrile and methyl isocyanide. The C-CF3 bond is the weakest bond in both cyanide and isocyanide. The simple C-CF3 bond cleavage of C4 produces the ground-state CF3(X2A1)) and CF3CFCN (X2A") radicals via symmetry breaking pathway. No transition state exists for the bond fission although the singlet-triplet interaction is significant near the dissociation asymptote. All the possible isomerization pathways of C4 and i-C4 were revealed involving F- and CF3-migration, together with the concerted elimination and stepwise decomposition routes, forming various isomers and potential toxic byproducts including FCN, CF3CN, C2F5CN, CF2=CFCF3, CF2=CFCN, CF4, C2F6, and alkyne. Regardless F or CF3, the three-center reactions involving the highly-strained structures appear to be



energetically more feasible than the four or five-center processes. Rate constants at the high-pressure limit for the C4 → i-C4 reaction and the C4 → CF3 + CF3CFCN reaction, together with the reverse reactions, were calculated using RRKM theory and variational transition state theory, respectively. Once i-C4 is formed, it would prefer to transfer back to reproduce C4. The yield of i-C4 is generally less than 6% even under arc conditions. The C4 → i-C4 rearrangement could be competitive with the C-CF3 bond dissociation at temperatures below 600 K. However, at temperatures above 1000 K, formation of the CF3 radicals becomes the dominant product channel. Master equation analysis on the overall thermal rate constants at 1-10 atm pressure demonstrates that the decomposition of C4 produce exclusively the CF3 radicals, which can recombine to form C2F6. Theoretical kinetics for the loss of C4 are in good agreement with the experimental observation. It was proposed that i-C4 and C2F6 could serve as the characteristic molecules to monitor the insulation breakdown of C4 in electric equipments.

■ ASSOCIATED CONTENT Supporting Information A note for the high-energy consecutive secondary reaction mechanisms, tables for Cartesian coordinates, vibrational frequencies, rotational constants, and the absolute energies, figures for geometries of the product molecules.

■ AUTHOR INFORMATION


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Corresponding Authors *B. Wang, E-mail: [email protected]

Notes The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS This work was supported by the National Key Research and Development Program of China (No. 2017YFB0902500).

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Table 1. Zero-point energies (ZPE, in kcal/mol) and relative energies (∆E, in kcal/mol, without ZPE) of all the species involved in the primary decomposition mechanisms of C4 at various levels of theory. Species i-C3F7CN (C4) TS1 i-C3F7NC (i-C4) CF3+CF3CFCN F+(CF3)2CCN CN+(CF3)2CF TS2 IM1 TS3 IM2 TS4 TS5 IM3 TS6 IM4 TS7 IM5 TS8 CF4+CF3CCN TS9 CF3CN+CF3CF TS10 C2F6+FCCN TS11 CF4+CF2=CFCN TS12 C2F5CN+CF2

ZPE 30.7 29.0 30.3 27.2 27.6 27.0 28.4 31.1 28.3 30.2 28.7 28.2 30.1 28.4 31.0 28.4 30.9 28.3 27.3 26.7 27.3 27.3 27.1 28.1 29.0 27.7 27.1

∆E

∆E

∆E

∆E

∆E

(M06-2X/AVTZ)

(CBS-QB3)

(Gaussian-4)

(RS2/AVDZ)

(RS2/AVTZ)

0.0 60.4 14.4 83.5 100.8 114.8 105.6 25.2 116.9 62.5 98.1 135.6 93.8 108.3 24.1 119.2 21.8 114.7 78.9 147.0 88.0 151.0 78.6 116.3 23.4 124.6 63.9

0.0 64.4 16.7 87.6 102.1 115.3 95.7 29.1 106.4 63.9 97.1 131.7 95.4 98.5 28.1 122.1 25.6 117.8 80.8 148.1 89.3 151.9 80.3 120.1 26.3 123.8 64.3

0.0 64.2 16.7 83.2 97.7 111.1 92.7 28.7 102.9 63.4 96.0 130.2 95.6 97.5 27.5 122.4 25.1 116.0 77.8 147.4 87.0 151.6 77.9 118.4 24.5 123.0 62.6

0.0 63.3 18.0 83.1 98.7 109.6 95.1 29.7 106.2 67.0 97.4 131.8 96.8 93.7 28.1 120.3 28.2 125.2 145.0 148.9 126.7 127.5 -

0.0 62.0 16.8 78.9 99.7 109.4 95.7 25.7 107.6 64.7 96.4 133.2 96.2 90.9 24.3 117.2 23.4 122.1 144.0 146.8 123.7 127.8 -



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Table 2. Thermal rate constants (in the unit of s-1) for the overall loss of C4 at 1-10 atm of CO2 in the temperature range 500 - 3000 K.

Temperatures / K

P = 1 atm

P = 5 atm

P = 10 atm

500

6.4E-16

6.4E-16

6.4E-16

600

2.7E-11

2.7E-11

2.7E-11

700

6.7E-8

6.7E-8

6.7E-8

800

3.7E-5

3.7E-5

3.7E-5

900

6.8E-3

7.1E-3

7.2E-3

1000

0.45

0.51

0.52

1200

1.7E2

2.5E2

2.8E2

1400

6.4E3

1.2E4

1.6E4

1600

5.5E4

1.4E5

2.0E5

1800

2.0E5

6.0E5

9.3E5

2000

4.4E5

1.5E6

2.4E6

2200

7.4E5

2.7E6

4.6E6

2400

1.1E6

4.0E6

7.0E6

2600

1.4E6

5.4E6

9.6E6

2800

1.7E6

6.7E6

1.2E7

3000

1.9E6

8.0E6

1.4E7


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Figure 1. The designated active space (12e, 12o) for C4 molecule used in the SA-MCSCF and RS2 calculations. HOMO and LUMO represents the highest occupied molecular orbital (No. 47th) and the lowest unoccupied molecular orbital (No. 48th), respectively. An isovalue of 0.05 au was employed for orbitals.



Figure 2. Optimized geometries for the species involved in the primary decomposition mechanisms of C4. Upper entries: M06-2X/AVTZ; Lower entries: M06-2X/AVQZ. Note that TS9 was optimized at the MP2/6-311G(d) level. Bond distances and angles are in Å and degrees, respectively.


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Figure 3. Energetic reaction routes for the unimolecular decomposition and isomerization of C4 at the CBS-QB3 level of theory.



Figure 4. Rate constants at the high pressure limit for the isomerization between C4 and i-C4. Black line: C4 → i-C4; Red line: i-C4 → C4; Dashed line: equilibrium constants. Thermal rate constants for the CH3NC → CH3CN reaction43 are shown in squares for comparison.


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Figure 5. Theoretical anharmonic infrared spectra of C4 (bottom) and i-C4 (top) predicted at the M06-2X/AVTZ level. The experimental spectrum of C4 (middle) is taken from ref 14 for comparison.



Figure 6. Energetic reaction paths for the C-CF3 bond cleavage of C4. Solid triangles: UM06-2X/AVTZ; Dashed line: the expectation values of S2 for the UM06-2X/AVTZ wavefunction. Open squares and circles represent the state-averaged MCSCF/AVDZ energies for singlet and triplet states, respectively.


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Figure 7. Minimum energy reaction paths for the C-F and C-CN bond cleavages of C4. Solid lines: UM06-2X/AVTZ; Dashed and dotted lines represent the state-averaged MCSCF/AVDZ energies for singlet and triplet states along the C-F bond distances, respectively. The singlet-triplet crossing near the F+(CF3)2CCN asymptote is shown in the insert plot for clarity.



Figure 8. Bimolecular recombination rate constants (squares) for the CF3+CF3CFCN → C4 reaction and the unimolecular rate constants (black line) for the reverse reaction C4 → CF3+CF3CFCN at the high pressure limit. Dashed line: least-square fit to the bimolecular rate constants (see text). Unimolecular rate constants (blue line) for the C4 → i-C4 reaction are shown for comparison.


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Figure 9. Overall rate constants for the loss of C4 at 1(black), 5(red) , and 10(green) atm of CO2 as functions of temperatures.



Figure 10. Thermal loss profile of C4 at the temperature-ramped flow-tube FTIR experiments12,21 (solid squares, scaled by the initial average concentration of [C4] = 563 ppm). Red line: theoretical predicted profile at the sampling time of 100 milliseconds.


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Mechanistic and Kinetic Investigations on the Thermal Unimolecular

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