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Double-Layered Composite Methods Extrapolating to Complete Basis-Set Limit for the Systems Involving More Than Ten Heavy Atoms: Application to the Reaction of Heptafluoroisobutyronitrile with Hydroxyl Radical Xiaojuan Yu, Hua Hou, and Baoshan Wang J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b08844 • Publication Date (Web): 09 Nov 2017 Downloaded from http://pubs.acs.org on November 10, 2017

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The Journal of Physical Chemistry

Double-Layered Composite Methods Extrapolating to Complete Basis-Set Limit for the Systems Involving More Than Ten Heavy Atoms: Application to the Reaction of Heptafluoroisobutyronitrile with Hydroxyl Radical

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]; [email protected]

ACS Paragon Plus Environment


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Abstract Two versions of the double-layered composite methods, including the restricted open-shell model chemistry based on the complete basis set quadratic mode (DL-ROCBS-Q) and the extrapolated CBS limit of electronic energy on the basis of the coupled cluster with single, double, and noniterative triple excitations with the hierarchical sequence of the correlation-consistent basis sets (DL-RCCSD(T)/CBS), were developed to calculate the energetic reaction routes for the systems involving thirteen/fourteen heavy atoms with good balance between efficiency and accuracy. Both models have been employed to investigate the oxidation reactions of heptafluoroisobutyronitrile [(CF3)2CFCN] with hydroxyl radical. The (CF3)2CFCN + OH reaction is dominated by the C-O addition/elimination routes as bifurcated into trans- and cis-conformations. Although the formation of isocyanic acid or hydrogen fluoride is highly exothermic, the major nascent product was predicted to be the less exoergic cyanic acid. Preference of the product channels could be tuned by the single water molecule in the presence of the H2O-HO complex. The production of amide compound was found to be the most significant route accompanying with the OH-regeneration. Moreover, the OH radical could be an efficient catalyst for the hydrolysis of (CF3)2CFCN. Implication of the current theoretical results in the chemistry of (CF3)2CFCN for both atmospheric sink and potential dielectric replacement gas was discussed.


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1. Introduction Sulfur hexafluoride (SF6) has been widely used as dielectric insulator in high-voltage transformers, transmission lines, and circuit breakers or switchgear for more than fifty years due to its strong electronegativity.1 However, SF6 has some undesirable properties. For instance, because it is an efficient infrared absorber and cannot be rapidly removed from the earth's atmosphere due to its chemical inertness, SF6 is the most potent greenhouse gas to date in view of its global warming potential (GWP) as high as 22800 with respect to CO2 over a hundred years time horizon.2 Designing the replacement gas superior to SF6 on this aspect is highly desirable.3 Among numerous alternative gases such as octafluorocyclobutane (c-C4F8),4 trifluoroiodomethane (CF3I),5 perfluorinated ketones (C5F10O, C6F12O)6 and so on, heptafluoroisobutyronitrile, i.e., (CF3)2CFCN or i-C3F7CN, has attracted considerable attention recently, which principally accounts for its high dielectric strength (2.2 that of SF6) and good arc-interruption properties.7 The mixture of (CF3)2CFCN for 4~10% of the volume with CO2 as the balance has been synthesized as the g3 gas for industrial applications. The dielectric and thermal properties of the mixture are sufficiently close to those of SF6 to allow keeping similar design and technology for the high-voltage switchgear using this alternative. Moreover, the GWP per mass unit of the g3 gas is reduced by about 98% in comparison with SF6 to typical values in the order of 300~500 because the fast degradation of (CF3)2CFCN in atmosphere. The atmospheric chemistry of (CF3)2CFCN, including reactions with OH radicals, with chlorine atoms, and with ozone, has been investigated extensively by Andersen



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and coworkers in the FTIR/smog chamber experiments.8 The main sink for (CF3)2CFCN was suggested to be the reaction with OH radicals. Using CF3CF2H and CH4 as the reference compounds, the rate coefficient was measured to be (1.45±0.25) × 10-15 cm3molecule-1s-1 at 296±2 K in 700 Torr total pressure of air and N2. Moreover, the oxidation mechanism of (CF3)2CFCN by OH and O2 was calculated on the basis of the density functional M06-2X/aug-cc-pVTZ level of theory. It was reported that the atmospheric lifetime of (CF3)2CFCN is dominant by the formation of NO, COF2, and the OH-recycling. Besides the potential environmental impact at room temperature, knowledge of the OH-induced chemistry of (CF3)2CFCN in cold climatic conditions (ca. -50oC) and at temperatures well above ambient (ca. 2000oC) is warranted to access the performance of (CF3)2CFCN under normal discharge or arc operation conditions in electrical equipments. In addition, the OH radicals are expected to form strong hydrogen bonds with water and the binary H2O-HO complex has an abundance of 5.5 × 104 /cm3 in lower atmosphere.9 In addition, the hydrated OH radical complex could exist in the electric insulators because water vapor is usually the most abundant impurity due to preparation or unavoidable leakage. Therefore, the water molecules are speculated to have a significant effect on reactivity of the constituent monomers. Temperature and pressure-dependent kinetics for the (CF3)2CFCN+OH reaction are unknown yet. Transition state theory can be utilized to predict such information on the basis of the high-level ab initio calculations on the potential energy surface for the aforementioned reactions. However, for the systems with more than ten heavy atoms,


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electron correlation theories such as the coupled cluster with single, double, and noniterative triple excitations [CCSD(T)] with extrapolation techniques to the complete basis set (CBS) limit, which is often regarded as the gold standard in quantum chemistry,10 are too prohibitively expensive to be affordable. Although the use of ab initio composite methods, e.g., G(n),11 W(n),12 CBS(n),13 and ccCA,14 can provide reliable results for varied molecular systems to within "chemical accuracy", they are still generally limited to systems containing no more than roughly ten non-hydrogen atoms.15 Therefore, ab initio calculation of the high-quality potential energy surfaces for the (CF3)2CFCN+OH/H2O reactions is the crucial challenge in order to make a priori predictions on the kinetic behavior. Motivated by the earlier works of Morokuma [IMOMO(G2MS)],16 Wilson (ONIOM-ccCA),17 and Li (ONIOM-G3B3),18 two new versions of the multilayer composite methodologies, namely, the restricted open-shell model chemistry based on the complete basis set quadratic mode (DL-ROCBS-Q) and the extrapolated CBS limit of electronic energy on the basis of CCSD(T) with the hierarchical sequence of the correlation-consistent basis sets [DL-RCCSD(T)/CBS], have been established in this work by taking advantage of the additive effects of a series of computationally expedient ab initio calculations. In view of the structural and reactive characteristics of (CF3)2CFCN, the molecular system is divided into two layers and each layer is described with a different level of theory. Through extrapolation, both ONIOM approaches effectively approximate the results of the entire system at the highest level of theory. The mechanisms for the OH-induced oxidation of (CF3)2CFCN were



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revealed in details by means of the DL-ROCBS-Q and DL-RCCSD(T)/CBS calculations. The energetic reaction routes were then employed to calculate the rate coefficients as a function of temperature and pressure. The present theoretical study provides new insights on the reaction of (CF3)2CFCN with the gaseous and hydrated OH radicals, which is helpful for the large-scale production and industrial use of the compound as dielectric gas to replace SF6. The computational methods are introduced briefly in Section 2; The technical procedures for the new DL-ROCBS-Q and DL-RCCSD(T)/CBS methodologies are detailed in Section 3.1; The method calibration or validation is discussed in Section 3.2; The microscopic mechanisms for the (CF3)2CFCN+OH reaction have been summarized in Sections 3.3, and followed by the kinetic simulations in Section 3.4; The role of water molecule in the title reaction is discussed in Section 3.5; Some concluding remarks are given in Section 4.

2. Computational Methods Geometries of the reactants, intermediates (M), transition states (TS), and products involved in the (CF3)2CFCN+OH reaction were optimized using the unrestricted UM06-2X density functional theory (DFT)19 with Dunning's augmented correlation consistent triple-ξ aug-cc-pVTZ (abbr. AVTZ) basis set.20 Vibrational frequency analysis was carried out at the same level of theory to determine the zero-point energy (ZPE) and to characterize the nature of the stationary point. Minimum has all real frequencies and transition sate has only one imaginary


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frequency. Normal mode of the imaginary frequency and the intrinsic reaction coordinate (IRC)21 confirms that the transition state connects to the designated reactants, intermediates, and products. For the open-shell species in doublets, the expectation values of 〈S2〉 of the UM06-2X/AVTZ wavefunctions are always in the range 0.75-0.79, which deviate slightly from the corrected value of 0.75. To examine the possible influence of the spin contamination on the geometrical parameters, the restricted open-shell scheme of DFT, namely, ROM06-2X/AVTZ, was employed to optimize the corresponding structures of the species along the energetically most favorable reaction routes. Furthermore, the quadruple-ξ aug-cc-pVQZ (abbr. AVQZ) basis set has been utilized for the key species to ensure the convergence of the geometrical parameters. To improve the accuracy of the doublet potential energy surface, the single-point energies for stationary points were calculated using various high-quality ab initio methods on the basis of the (U,RO)M06-2X/AVTZ optimized geometrical parameters. All the ab initio calculations involved in this work were carried out with the Gaussian09 programs22 and the Molpro suite of programs.23

3. Results and Discussion 3.1 Theoretical Aspects For the sake of computational efficiency, two new versions of the two-layered composite methodologies have been established. The two CF3 groups of (CF3)2CFCN were divided into the low-layer model to be treated always with the low-level



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M06-2X method to obtain the energy ELL. The remaining bulk of the CFCN structures, which is the key chemically-important layer, together with OH or H2O-HO molecules were set to be the high-layer model and were calculated using various high-level ab initio methods to obtain the energy EHH. The link atoms, i.e., hydrogen, were introduced to mimic the corresponding CC covalent bonds of the real system. As a result, the total energy is defined as E(DL) = EHH + ERL - ELL

(Eq. 1)

where ERL represents the energy of the entire (real) system calculated using the low-level M06-2X method. Firstly, the two-layered restricted open-shell model chemistry based on the complete basis set quadratic mode, namely, DL-ROCBS-Q, was proposed. In contrast to the full version of ROCBS-Q,24 the most expensive calculation at the ROCCSD(T)/6-31+G(d') level in the DL-ROCBS-Q method can be performed only on the high-layer subsystem. The M06-2X/6-31+G(d') calculations for the real system and the low-layer model are not mandatory because both energies are cancelled out automatically in the composite protocol. Likewise, the ROMP4SDQ/CBSB4 calculation is required only for the high-layer model as well. However, the extrapolation of the second-order pair correlation energies to the CBS limit (∆ERCBS(2)) has been calculated at the ROMP2/CBSB3 levels of theory, which is the same as that in the full version of ROCBS-Q. Therefore, only three single-point calculations are essential to obtain the DL-ROCBS-Q total energy, viz., E (DL-ROCBS-Q) = (EHROCCSD(T) - EHMP4SDQ)/6-31+G(d')


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+ (EHMP4SDQ - EHMP2)/CBSB4 + (ERROMP2+∆ERCBS(2)+∆ERCBS-int + ∆ERemp)/CBSB3

(Eq. 2)

where EHMP4SDQ and EHMP2 are deduced simultaneously by default in the EHROCCSD(T) and EHMP4SDQ calculations, respectively. It is worth noting that the empirical correction (∆Eemp) to the higher-order correlation energy and the interference correction (∆ECBS-int) to the higher-order perturbation theory for near degeneracies are both adopted straightforwardly according to the original version of ROCBS-Q. Secondly,

the

extrapolated

CBS

limit

of

electronic

energy,

namely,

DL-RCCSD(T)/CBS, was obtained on the basis of the RCCSD(T) calculations with the hierarchical sequence of the correlation-consistent basis sets, e.g., AVnZ (n = D, T, Q, 5, 6). Separated extrapolation of the Hartree-Fock (EHF) and correlation energy (∆Ecorr) to the CBS limit was done because the convergence of ∆Ecorr with respect to the size of the atomic basis set is slower than that of EHF. The HF CBS limit (EHF-CBS) was obtained by extrapolation using25 2

E HF ( n ) = E HF −CBS + Ae− ( n−1) + Be − ( n −1) (n = 2,3,4 or 3,4,5)

(Eq. 3)

where n refers to the cardinal number of the AVnZ basis set. On the other hand, the explicit calculation of EHF with the larger V6Z basis set has been done to obtain the reliable estimate of the basis set limit, as suggested by Halkier and coworkers.26 Various empirical power forms of the extrapolation functions have been considered to calculate the correlation energy limit (∆Ecorr-CBS), including27-31 ∆Ecorr-CBS(HKKN) = ∆Ecorr(n) + a/n3 (n=2,3,4)

(Eq. 4)

∆Ecorr-CBS(HL) = [3.53∆Ecorr(3) - 2.53∆Ecorr(2)] / (3.53 - 2.53)

(Eq. 5)



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∆Ecorr-CBS(Bkw) = [32.49∆Ecorr(3) - 22.49∆Ecorr(2)] / (32.49 - 22.49)

(Eq. 6)

∆Ecorr-CBS(VP) =

[2.903∆Ecorr(3) - 2.133∆Ecorr(2)] / (2.903 - 2.133)

(Eq. 7)

[33∆Ecorr(3) - 2.0913∆Ecorr(2)] / (33 - 2.0913)

(Eq. 8)

∆Ecorr-CBS(OAN) =

It is worth noting that the low-level M06-2X energies on both the low-layer model and the real system should not be extrapolated in view of the empirical nature of the M06-2X method. In fact, the DFT energy does not exhibit the correct asymptotic behavior to the basis set convergence (vide infra). Therefore, the contribution of the environmental effect from the low-layer model has been taken account as a correction to the final DL-RCCSD(T)/CBS energy, namely, E[DL-RCCSD(T)/CBS] = EHHF-CBS + ∆EHcorr-CBS + (ERDFT - ELDFT)

(Eq. 9)

Evidently, the RCCSD(T)/AVnZ energies, which are the most extensive calculations for the current system, are required only for the high-layer models rather than for the entire system of the computational forbiddance.

3.2 Method Validation In order to calibrate the accuracy of the two-layered DL-ROCBS-Q composite methodology on the calculations of the high-quality potential energy surface for the (CF3)2CFCN+OH reaction, the full version of ROCBS-Q, reliable but expensive, has been used to calculate the energies of a total of 73 stationary points. The data are collected in Tables 1-3 and are illustrated in Figure 1 for comparison. Apparently, the DL-ROCBS-Q energies are in good agreement with the ROCBS-Q reference data in the range from -50 kcal/mol to 80 kcal/mol, especially for the intermediates and


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transition states of the most importance to the title reaction. The mean absolute deviation (MAD) for all the 73 energies is 1.2 kcal/mol. Moreover, the DL-ROCBS-Q method shows good performance even for the species in which the low-layered CF3 groups indeed participate in the reaction directly rather than the irrelevant spectators. The reasons for such a success are two-folds: first, the low-level energies in the DL-ROCBS-Q protocol have been cancelled out due to the additive effect; second, the higher-order corrections to the pair correlation energies have been evaluated using the full-size system. Meanwhile, the computational efficiency has been improved significantly. It takes about 72 hours of CPU time to perform one full-size ROCBS-Q calculation using Gaussian09 with our AMD-Opteron computers but the DL-ROCBS-Q calculation completes in only 15~30 minutes, showing roughly two orders of magnitude acceleration. In comparison with the ONIOM-G3B3 composite method, our DL-ROCBS-Q method outperforms by two advantages: (1) using the RCCSD(T)/6-31+G(d') rather than the subset of coupled cluster QCISD(T)/6-31G(d) level of theory; (2) using the full-size empirical correction to the higher-order correlation energy rather than only for the high-layer subsystem. In comparison with the ONIOM-ccCA method, the present DL-ROCBS-Q method is much more efficient because of making use of smaller basis sets in the expensive RCCSD(T) calculations. On the other hand, a few corrections in the ONIOM-ccCA method such as scalar relativistic effect and core-valence effect have not been considered in the DL-ROCBS-Q method since the DL-ROCBS-Q method is designed specifically for the large (C, N, O, F, S,



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halogen)-containing molecules. To access the empirical nature of the composite ROCBS-Q energy, the RCCSD(T)/CBS calculation appears to be essential. The only affordable full-size RCCSD(T) calculation for the (CF3)2CFCN+OH reaction is to use the double-ξ VDZ basis set. More flexible basis sets would involve too many atomic orbital (AO) functions (e.g., 621 for VTZ and 1086 for VQZ) to be done for the present 103-electron system. Fortunately, as shown in Figure 2, it was found that the two-layered ONIOM(RCCSD(T):M06-2X/VDZ) energies are in good agreement with the full-size RCCSD(T)/VDZ reference energies. The MAD is only 0.8 kcal/mol for all the 73 energies covering the wide energy range -50 ~ 80 kcal/mol. In addition, the two-layered ONIOM scheme is even capable of treating the CF3-reacting species, although a few high-energy stationary points (ca. > 50 kcal/mol), which are of little importance in the title reaction, do show some deviations. The encouraging good performance of the two-layered ONIOM method, especially for the energetically accessible regions of the potential energy surface of the (CF3)2CFCN+OH reaction, indicates that the use of M06-2X method to simulate the layered core/environment system is an appropriate approximation. Therefore, the DL-RCCSD(T) calculations were carried out by extrapolating to the CBS limit with the AVnZ (n=D, T, Q) basis sets, namely, E[DL-RCCSD(T)/CBS] = EHHF-CBS(D→T→Q) + ∆EHcorr-CBS(OAN) + (ERM06-2X/AVQZ - ELM06-2X/AVQZ) The

(Eq. 10)

DL-RCCSD(T)/CBS energies are in reasonable agreement with the


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DL-ROCBS-Q data (Tables 1-3). The general consistence between two sets of energies obtained by the totally different protocols suggests that the ab initio energies should be reliable enough for further use. It is worth noting that a few highly endothermic

radical

product

channels

are

exceptions.

For

example,

the

DL-RCCSD(T)/CBS energies for the two CF3 production channels deviate significantly from the DL-ROCBS-Q data. Such a deficiency results from the fact that the CF3 radical fragments have been only treated as the low-layer by the low-level theory in the DL-RCCSD(T)/CBS calculation. For the sake of kinetic simulation, the barrier heights obtained at DL-RCCSD(T)/CBS and DL-ROCBS-Q levels for the critical transition states deserves further analysis. For instance, the barrier heights for (t,c)TS1, which are the most important transition states for the title reaction, does exhibit the difference of 0.2~0.4 kcal/mol between DL-RCCSD(T)/CBS and DL-ROCBS-Q levels (Table 1). The possible source for the uncertainty of the DL-RCCSD(T)/CBS energy has been explored and the respective contributions from EHHF-CBS, ∆EHcorr-CBS, and (ERDFT ELDFT) are detailed in Table 4. Apparently, the HF/CBS energy shows little dependence on the basis sets used in the extrapolation. Moreover, the extrapolated HF/CBS energy is nearly identical to the single-point energy at the HF/V6Z level, indicating that the current estimate to the CBS limit should be reliable as suggested by Halkier and coworkers.26 Similarly, the correlation energy at the RCCSD(T) level is insensitive to the extrapolation schemes either since the deviation for HKKN, OAN, HL, Bkw, and VP extrapolations is less than 0.1 kcal/mol. For completeness, the



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correlation energy correction has been evaluated at the RCCSD(T)/AVQZ level for tTS1. It turns out that the barrier height for tTS1 can be further lowered by 0.1 kcal/mol in comparison with that at the RCCSD(T)/AVTZ level. However, the CBS limit is almost identical for either (D,T) or (T,Q) HKKN extrapolation. As mentioned above, the corrections from (ERDFT - ELDFT) do not show systematic convergence from level to level so that the DFT energies should not be extrapolated straightforwardly to the CBS limit. Note that the barrier height for tTS1 could be lowered by about 0.2 kcal/mol if the AVDZ or AVTZ basis set used in the M06-2X calculation for the low-layer model system, leading the DL-RCCSD(T)/CBS barrier height be exactly the same as the DL-ROCBS-Q result. Because the restricted open-shell HF wavefunction was used as reference in both CCSD(T) and MPn calculations, the relative energies are free of spin contamination but might be deprecated by the potent multireference character of the electron-correlation wavefunction. Apparently, neither complete active space SCF nor multireference configuration interaction calculation is affordable for the present system. Therefore, both the T1 diagnostic values and the largest doubles amplitudes T2 of the CCSD wavefunction have been examined for all the species to examine the effect of multireference wavefunction.32 The result is shown in Figure 3. It is evident that the T1 and T2 values for most species are smaller than 0.03 and 1.0, respectively, except for the F-migration transition states (e.g., tTS14, cTS7, and cTS10), the SN2-type transition states (e.g., TS2d and TS3d), and the CN radical. As a result, the corresponding barrier heights and the thermodynamics of the CN production channel


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could be overestimated. Fortunately, the energetic reaction routes involving these problematic stationary points are unimportant to the (CF3)2CFCN+OH reaction and thus negligible.

3.3 The (CF3)2CFCN+OH Reaction Sixteen products channels were explored in which four channels are exothermic, including the formation of HF, HNCO, HOCN, and CF3OH. A total of 15 intermediates (e.g., tM1~tM5, cM1~cM5, tM1n~tM3n, cM1n~cM2n) and 39 transition states (e.g., tTS1~tTS13, cTS1~cTS10, tTS1n~tTS5n, cTS1n~cTS3n, TS1~TS8) have been located on the potential energy surface of the (CF3)2CFCN+OH reaction. Three kinds of mechanisms have been revealed for the (CF3)2CFCN+OH reaction, namely, C-O addition/elimination, N-O addition/elimination, and concerted displacement routes, as illustrated in Figures 4, 5, and 6, respectively. Due to the unique structure of (CF3)2CFCN, the reaction routes for both C-O and N-O association mechanisms bifurcate into trans and cis conformational pathways depending on the orientation of the OH radical towards the CN group. The geometries of the species involved in the trans and cis C-O association/elimination mechanisms are shown in Figures 7 and 8, respectively. The geometries of the species involved in the N-O addition/elimination and the concerted mechanisms are shown in Figure 9. It is evident that the geometrical parameters for all the species have been well converged with the basis sets in view of the critical bond distances and angles. The UM06-2X/AVTZ optimized geometries are almost identical to the data obtained by



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means of the larger AVQZ basis set. Therefore, in the following discussion, the UM06-2X/AVTZ optimized geometrical parameters and the DL-ROCBS-Q calculated energies will be used unless stated otherwise.

3.3.1 The C-O Addition/Elimination Mechanism The structure of (CF3)2CFCN has Cs symmetry and the terminal N atom is slightly bent towards the two CF3 groups. The OH radical can approach to the middle C atom of the C-C≡N moiety from either the opposite side (trans) or the same side (cis) with respect to the CF3 groups. Therefore, the C-O association path is bifurcated via tTS1 or cTS1, leading to tM1 and cM1, respectively, as illustrated in Figure 4. Energetically, the trans C-O addition is more favorable than the cis addition because the energy of tTS1 is 0.8 kcal/mol lower than that of cTS1. The inter-conversion between tM1 and cM1 may occur rapidly via a marginal barrier TS-iso by an internal rotation around the CC single bond. The forming CO distances in tTS1 (Figure 7) and cTS1 (Figure 8) are nearly the same, i.e., 1.96 Å, which is about 0.6 Å longer than the equilibrium CO bond length in the intermediates tM1 and cM1. Meanwhile, the C≡N triple bond is stretched slightly. Therefore, both tTS1 and cTS1 appear to be the early barriers, in accordance with the high exothermicity in forming tM1 and cM1. Note that the OH radical does not lie in the symmetric plane of (CF3)2CFCN, instead, the O atom of OH is outside the FCCN plane by 54° and 30° for tTS1 and cTS1, respectively. In addition, the H atom of OH prefers to align along the C≡N bond rather than to form intramolecular hydrogen bond with either F atom or CF3 groups. In fact, the intramolecular H...F bonding in tM2 and cM2 does not provide any


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additional stability in comparison with tM1 and cM1. Interestingly, the intramolecular H...F bonding appears to play a role to some extent in the subsequent CC bond cleavage reaction to produce (CF3)2CF radical and HOCN. For instance, the breaking CC bond distances in tTS2 and tTS4 (Figure 7) are identical but the barrier height for tTS4, which has an intramolecular hydrogen bond, is about 1 kcal/mol lower than that for tTS2. The similar energetic pathways occur for cTS2 and cTS4. The production of HOCN is exothermic by 5.2 kcal/mol. Moreover, the CC bond fission barriers tTS2, tTS4, cTS2, and cTS4 are all lower than the C-O addition barriers (tTS1 and cTS1). It is conceivable that the formation of HOCN is the predominant product channel in the (CF3)2CFCN+OH reaction. Besides the CC bond cleavage, H-shift from O to the terminal N atom may take place via tTS5 or cTS5 to form tM4 or cM4, respectively (Figures 7 and 8). Due to the strains inside the four-member-ring geometries of tTS5 and cTS5, the corresponding barriers lie above those for tTS1 and cTS1 by 2.9 kcal/mol and 1.3 kcal/mol, respectively. Subsequent CC bond cleavage of tM4 and cM4 undergoes via tTS6 and cTS6, leading to HNCO, which is an isomer of HOCN and more stable. The production of HNCO is more exothermic by 25 kcal/mol than the HOCN channel. Additionally, both tTS6 and cTS6 are the lowest barriers ever found for the title reaction. Consequently, the formation of HNCO could be feasible in the (CF3)2CFCN+OH reaction. Besides HOCN and HNCO, the HF elimination, which is the most exothermic product channel in the (CF3)2CFCN+OH reaction, has been found to start from tM2



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via tTS7. The transition state tTS7 exhibits a five-member-ring geometry together with a cyclic CNC structure (Figure 7). The HF elimination is accompanied by the simultaneous CC bond breaking and N-migration, forming HF and (CF3)2C=N-C=O. The energy of tTS7 is fairly high, indicative of the negligible role of HF production in the title reaction (Figure 4). For completeness, the F-shift reaction routes starting from the initial C-O adducts tM1 and cM1 to produce alkenes [e.g., CF2=CFCF3] or ketene [e.g., (CF3)2C=C=O] were examined via transition states tTS8-tTS14 and cTS7-cTS10. In view of the energetic routes as summarized in Figure 4, it is evident that neither alkenes nor ketene production is feasible at all and thus these highly endothermic product channels could be ruled out safely.

3.3.2 The N-O Addition/Elimination Mechanism In comparison with the complicated C-O association mechanism, the N-O addition/elimination routes (Figure 5) appear to be straightforward. The OH radical is attacking the terminal N atom of (CF3)2CCN bifurcately via tTS1n and cTS1n. Geometrically (Figure 9), both tTS1n and cTS1n are reactant-like, in view of the significantly long N-O distances with respect to those in the adducts tM1n and cM1n. However, the energetic profiles for the trans or cis N-O association are fairly flat. For example, the energy of tTS1n is only 0.7 kcal/mol higher than that of tM1n. After ZPE correction, tTS1n even lies below tM1n (Figure 5). Therefore, the N-O association might not involve the well-defined barriers due to the significant endothermicity to form the adducts. Furthermore, the intramolecular F...H bonding, as


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exists in tTS2n, tM2n, cTS2n, and cM2n, does not affect the basic feature of the N-O addition. The CC bond fission of the N-O adducts generates HONC, which is an unstable isomer of HOCN. Partial optimization along the breaking CC bond demonstrates that the energies increase monotonically to the highly endothermic final products. The only stable stationary point in the N-O addition mechanism is tM3n. However, the barriers before tM3n, i.e., the cyclic H-shift transition state tTS4n, and after tM3n, i.e., the cyclic HF-elimination transition state tTS5n are both as high as 60 kcal/mol, excluding any importance of these reaction routes.

3.3.3 The Concerted Displacement Mechanism As expected, the direct displacement routes in the (CF3)2CFCN+OH reaction involve significantly barriers (Figure 6). Although these reaction paths do not play any role in the title reaction, the geometries of the transition states appear to be interesting, as shown in Figure 9. While TS1d-TS5d shows the typical transition state structures for the SN2-like pathways, TS6d and TS7d exhibit the different displacement structures, that is, the approaching OH and the leaving F or CF3 group are in the same side rather than the opposite side of the substrates. Although the geometry of TS8d seems to be analogous to that of TS7d, TS8d is not a displacement transition state, instead, it leads to CF3OH by the concerted CC bond breaking and CO bond forming. In comparison with the direct SN2 pathway to form CF3OH via TS1d, the barrier height for the concerted CF3OH formation is lowered by about 17 kcal/mol. Certainly, the formation of CF3OH in the title reaction should be negligible in view of



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the barrier of TS8d, even though it is a highly exothermic product channel.

3.4 Kinetic Analysis On the basis of the potential energy surface for the (CF3)2CFCN+OH reaction calculated at the DL-ROCBS-Q and DL-ROCCSD(T)/CBS levels of theory, the dominant reaction mechanism could be integrated as follows,

where "*" indicates the energy-rich intermediates and [M] means the bath gas for collisional deactivation. In addition, the trans and cis reaction routes are internally connected by TSiso. It is worth noting that two weakly bound pre-reactive complexes (e.g., tRC and cRC in Supporting Information, Figure S1) were located at the M06-2X/AVTZ level of theory. However, the Gibbs free energy calculation shows that both complexes cannot be formed spontaneously until the temperature decreases below 100 K. Since only the temperature range 200-2000 K is of our interest, these pre-reactive complexes are ruled out in the kinetic analysis for simplicity. The geometries of the stationary points in the dominant reaction mechanism were re-optimized at the restricted open-shell ROM06-2X/AVTZ level of theory to eliminate the possible inherent uncertainty in the unrestricted UM06-2X data subject to spin contamination. The geometrical parameters are compared in Figures 7 and 8. Overall, the reacting bonds tend to be shortened at the ROM06-2X/AVTZ level


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especially for the most important transition state (t,c)TS1. The forming CO bond is about 0.05 Å shorter than that at the UM06-2X/AVTZ level. As a result, the DL-ROCBS-Q calculated barrier heights for (t,c)TS1 using the ROM06-2X/AVTZ geometries are lowered by 0.1~0.2 kcal/mol. The rate coefficients for the (CF3)2CFCN+OH reaction were calculated using the multichannel transition state/RRKM theory with the rigid-rotor harmonic-oscillator (RRHO) approximation, as detailed elsewhere.33 Because all the barriers are tight transition states, the variational effect of the minimum energy path has not been considered temporarily. In order to compare with the experimental rate coefficient at 296 K in the presence of 700 Torr of N2, the kinetic calculation was carried out using the same bath gas and the same pressure as a function of temperatures in the range 200-2000 K. The collisional energy transfer parameter between intermediates and bath gas was estimated to be 100 cm-1 in the standard exponential-down model. Preliminary calculations show that the rate coefficient is indeed near to high-pressure limit in 700 Torr total pressure of N2. Therefore, the uncertainty in the energy transfer parameter is negligible at present. Mater equation was solved at the energy/angular momentum (E/J) resolved level. Note that the tunneling correction was considered using the Eckart model.34 The calculated rate coefficients in the range T = 200 - 2000 K are shown in Figure 10. Theoretical rate coefficient at 296 K was calculated to be 0.66 × 10-15 cm3molecule-1s-1, which is smaller than the experimental value, i.e., (1.45±0.25) × 10-15 cm3molecule-1s-1,8 by a factor of 2.2. The apparent disagreement between



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experiment and theory could be understood in view of the uncertainty in the barrier heights along the reaction routes. In fact, if the barrier heights for the C-O association were lowered arbitrarily by 0.5 kcal/mol, the theoretical rate coefficient could be in good agreement with the experimental value, although it is unlikely that the current high-level ab initio energies would involve such a large uncertainty. Instead of the energetic factor, in the consideration of the unique structure of (CF3)2CFCN, it is suggested that some harmonic vibrations should better be replaced by the hindered rotors. It is well-known that the hindered rotor can play critical roles in the rate calculations.35,36 For instance, the torsion normal mode of the CF3 group is indeed the internal rotation around the CC bond. Therefore, the normal vibrational modes corresponding to internal rotations for all the species involved in the above reaction mechanism were identified by solving the vibrational problem for the constrained system in the redundant internal coordinates. The atomic composition of the rotating groups was determined automatically by means of the constrained Wilson-G matrix without any user’s intervention or expertise,37 as implemented in the Gaussian09 program. Such a scheme has been demonstrated to perform well in the calculation of partition functions for a wide range of temperatures. The sum of states of the one-dimensional hindered rotors were calculated using the simple cosine function, i.e., V = V0 × cos(n×ϕ). The internal rotation barrier height V0 is proportional to the square of the vibrational frequency ν and to the reduced moment of inertia Ir, namely, V0 = 8π2ν2Ir/m2, m is the multiplicity of the rotations. The rate coefficient for the (CF3)2CFCN+OH reaction was re-calculated using the one-dimensional hindered


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rotor approximation with the parameters as listed in the Supporting Information (see Table S1), and the results are illustrated in Figure 10 for comparison. Without using any adjustable parameters for energies, it is encouraging that the agreement between theory and experiment is excellent at 296 K, indicating the importance of the hindered rotors for the title reaction. The yield of HOCN molecule was monitored as a function of temperatures at 700 Torr. At ambient temperature and below, the yield of HOCN is less than 10%, whereas the collisional deactivation of the (t,c)M1 intermediates dominates the nascent products (Figure 10). As a result, in the presence of oxygen, the secondary reactions of (t,c)M1 with O2 might take place under typical atmospheric conditions, initializing the OH-recycling mechanisms. However, as the temperature increases to 500 K and above, the production of HOCN starts to be dominant. Therefore, at typical discharge environment inside the dielectric insulators, it is expected that the HOCN molecules could be the one of the major discharge decomposition products of (CF3)2CFCN, which might cause corrosion of the naked metal devices. Note that in the whole range of temperatures of our concern, neither HNCO nor HF has any observable yield (e.g., Φ < 0.001). For practical use, the high-pressure limit rate coefficients were calculated as well and have been fitted to the following expression, viz., k∞(T/K) = 7.61 × 10-14 (T/298)1.23 e-1196/T cm3molecule-1s-1

3.5 The Role of Water Molecules


(Eq. 11)


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In order to clarify the potential importance of water molecule in the (CF3)2CFCN+OH reaction, the most energetically feasible HOCN and HNCO production channels involved in the water-mediated C-O association mechanism were considered in details. Profile of the potential energy surface for the corresponding water-catalyzed reaction routes is shown in Figure 11. Apparently, the reaction routes remains being bifurcated by trans and cis conformations. The geometries of the stationary points are shown in Figure 12. The relative energies with respect to the asymptote of (CF3)2CFCN with the H2O-HO complex at the DL-ROCBS-Q and DL-RCCSD(T)/CBS levels of theory are summarized in Table 5. The reaction of (CF3)2CFCN with the H2O-HO complex undergoes by the formation of two hydrogen-bond complexes, that is, (t,c)RC in Figure 12. Both complexes have floppy cyclic geometries in which the H2O molecule acts as proton donor to the terminal N atom and proton acceptor to the H atom of the OH radical. Interestingly, the O atom of OH radical tends to interact with the F atom and CF3 group in the trans conformer so that the O atom lies above the middle of the CC single bond rather than the CN triple bond. As a result, the cis complex is more stable than the trans complex even though the hydrogen bonds are even shorter in the later. Subsequently, the formation of (t,c)M1w intermediates occurs via (t,c)TS1w. The reacting C-O bonds in (t,c)TS1w become slightly shorter by 0.02 Å than those in the dry association paths. Because of the water-mediated cyclic tighter structures, the barriers for (t,c)TS1w are reduced by about 2 kcal/mol. As a result, the water-mediated C-O association becomes nearly barrierless, that is, the energies of


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(t,c)TS1w are almost identical to that of the initial reactants. Decomposition of (t,c)M1w adducts takes place via (t,c)TS2w to form HOCN. Because the water molecule does not participate into such C-C bond fission processes, the barrier heights for the C-C decomposition pathways remain to be 30 kcal/mol. In contrast, the HNCO production mechanism has been changed dramatically due to the single water molecule. As can be seen in Figure 12, the transition states (t,c)TS3w for proton migration from O to N exhibit six-member-ring structures, in comparison with the four-member-ring structures of (t,c)TS5 in the non-catalytic mechanism (see Figures 7 and 8). Consequently, the barrier heights for proton transfer are lowered by up to 14 kcal/mol due to the water catalysis. The energies of (t,c)TS3w become about 5 kcal/mol lower than those of (t,c)TS2w, that is, the proton-transfer pathway to form (t,c)M2w intermediates becomes even more preferable than the CC bond cleavage route. However, the subsequent CC bond breaking of (t,c)M2w to produce HNCO still involves significant barriers, namely, the rate-determining transition state (t,c)TS4w (Figure 11). Therefore, the formation of HNCO in the water-mediated mechanism should be still a minor product channel with respect to HOCN. It is worth noting that a new decomposition pathway for the (t,c)M2w intermediates has been found. The hydrogen atom, being a spectator during the proton transfer in (t,c)TS3w, is shifted consecutively to the terminal N atom via (t,c)TS5w (Figure 12) to form amide (CF3)2CFC(O)NH2 and simultaneously the OH radical is regenerated. Interestingly, the barrier heights for these two H-shift routes, namely, (t,c)TS3w and (t,c)TS5w, are nearly identical. Therefore, the formation of amide and



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the regeneration of OH is the predominant product channel in the water-mediated reaction of (CF3)2CFCN with OH. In contrast to the well-known OH/O2-initialized OH-recycling mechanism,38,39 for the first time, it is discovered that the water molecule could be an active substrate or bridge for the OH recycling. Moreover, preliminary calculations show that such a mechanism exists in all the analogous reactions of nitriles with OH radicals. Adding more water molecules in the gas phase can promote the efficiency of the OH-recycling mechanism further by lowering the corresponding barriers. However, a different mechanism might be resulted in the presence of a continuum solvent dielectric environment. Since only the gaseous degradation of (CF3)2CFCN is of our concern in the present work, aqueous decomposition of (CF3)2CFCN in solution will be reported separately. Meanwhile, it is noted that amide is indeed the final product of hydrolysis of (CF3)2CFCN. The transition state for the (CF3)2CFCN+H2O reaction is shown in the Supporting Information (Figure S2). The barrier height was calculated to be as high as 49 kcal/mol. Even in the consideration of (H2O)2 and OH(H2O)-involved hydrolysis, the barrier heights are still as high as 19.0 kcal/mol and 26.0 kcal/mol, respectively. Therefore, the water-mediated (CF3)2CFCN+OH association/elimination reaction actually provides an efficient alternative mechanism for the hydrolysis of (CF3)2CFCN. In short, in the presence water humidity, no matter oxidation or hydrolysis of (CF3)2CFCN will generate the amide compound exclusively via the OH-recycling mechanism.


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4. Conclusions Calculation of the high-level potential energy surfaces to the so-called "chemical accuracy "(≤1 kcal/mol from experiment or better) for the molecular systems with more than thirteen heavy atoms is theoretically challenging. Two versions of the double-layered complete basis set model chemistries, namely, DL-ROCBS-Q and DL-RCCSD(T)/CBS, have been developed in this work and applied to calculate the microscopic mechanisms for the oxidation reaction of (CF3)2CFCN with OH radicals. The reliability of the ab initio structures and energies has been verified not only by the general consistence of the two sets of 73 energetic data in the range -50 ~ 80 kcal/mol but also by the good agreement between theoretical and experimental rate coefficients. In addition, even though the CF3 groups were treated as environmental low-layer model, the two DL composite models are capable of working for the CF3-reacting energetic routes as well. The (CF3)2CFCN+OH reaction is dominated by the bifurcated trans and cis C-O addition/elimination mechanisms. Neither N-O association nor concerted displacement could be competitive. It is confirmed that the production of HOCN is predominant, although the formation of HNCO or HF is more exothermic. In the presence of a water molecule, the oxidation pathways of (CF3)2CFCN by the hydrated H2O-HO complex have been changed dramatically. Instead of HOCN or HNCO, the novel OH-regeneration mechanism accompanying with the formation of amide compound has been revealed to be dominant due to the water catalysis on the consecutive proton migration. It is suggested that the OH



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radical is a recyclable oxidant for the atmospheric degradation of (CF3)2CFCN even in the absence of oxygen. Meanwhile, the water-mediated association/elimination reaction is indeed a short cut for the hydrolysis of nitriles.

■ ASSOCIATED CONTENT Supporting Information Gibbs free energy as a function of temperature for the pre-reactive complexes tRC and cRC (Figure S1), geometries and barrier heights of the transition states involved in the hydrolysis reactions of (CF3)2CFCN (Figure S2), vibrational frequencies and the reduced moments of inertia of the hindered rotors for the species involved in the dominant mechanisms (Table S1), and Cartesian coordinates of the stationary points for the reaction of (CF3)2CFCN+OH/H2O reaction optimized at the UM06-2X/Aug-cc-pVTZ level of theory (Table S2).

■ AUTHOR INFORMATION Corresponding Authors *B. Wang, E-mail: [email protected]; H. Hou, E-mail: [email protected] Notes The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS This work was supported by the National Key Research and Development


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Program of China (No. 2017YFB0902500) and partially by the NSF of China (No. 21273166, 21573165).

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(30) Varandas, A. J. C.; Pansini, F. N. N. Narrowing the Error in Electron Correlation Calculations by Basis set Re-hierarchization and Use of the Unified Singlet and Triplet Electron-pair Extrapolation Scheme: Application to a Test Set of 106 Systems. J. Chem. Phys. 2014, 141, 224113. (31) Okoshi, M.; Atsumi, T.; Nakai, H. Revisiting the Extrapolation of Correlation Energies to Complete Basis Set Limit. J. Comput. Chem. 2015, 36, 1075-1082. (32) Lee, T. J.; Taylor, P. R. A Diagnostic for Determining the Quality of Single-reference Electron Correlation Methods. Int. J. Quantum Chem. 1989, S23, 199-207. (33) Hou, H.; Li, A.; Hu, H.; Li, Y.; Li. H.; Wang, B. Mechanistic and Kinetic Study of the CH3CO+O2 Reaction. J. Chem. Phys. 2005, 122, 224304. (34) Johnston, H. S.; Heicklen, J. Tunneling Corrections for Unsymmetrical Eckart Potential Energy Barriers. J. Phys. Chem. 1962, 66, 532-533. (35) Song, X.; Zugner, G. L.; Farkas, M.; Illes, A.; Sarzynski, D.; Rozgonyi, T.; Wang, B.; Dobe, S. Experimental and Theoretical Study on the OH-Reaction Kinetics and Photochemistry of Acetyl Fluoride (CH3C(O)F, an Atmospheric Degradation Intermediate of HFC-161(C2H5F). J. Phys. Chem. A 2015, 119, 7753-7765. (36) Carr, S. A.; Still, T. J.; Blitz, M. A.; Eskola, A. J.; Pilling, M. J.; Seakins, P. W.; Shannon, R. J.; Wang, B.; Robertson, S. H. Experimental and Theoretical Study of the Kinetics and Mechanism of the Reaction of OH Radicals with Dimethyl Ether. J. Phys. Chem. A 2013, 117, 11142-11154. (37) Ayala, P.; Schlegel, H. Identification and Treatment of Internal Rotation in



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Normal Mode Vibrational Analysis. J. Chem. Phys. 1998, 108, 2314−2325. (38) Hynes, A. J.; Wine, P. H. Kinetics and Mechanism of the Reaction of Hydroxyl Radicals with Acetonitrile under Atmospheric Conditions. J. Phys. Chem. 1991, 95, 1232-1240. (39) Galano, A. Mechanism of OH Radical Reactions with HCN and CH3CN: OH Regeneration in the Presence of O2. J. Phys. Chem. A 2007, 111, 5086-5091.


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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


Table 1. Zero-point energy corrections (∆ZPE) and relative energies for the species involved in the trans-conformational C-O addition/elimination reaction routes with respect to the (CF3)2CFCN+OH asymptote.a Species

∆ZPE

UM06-2X/AVTZ b

DL-RCCSD(T)/CBS

ROCBS-Q

DL-ROCBS-Q

2.2

1.9

2.0 (1.8)b

tTS1

1.5

2.4 (4.0)

tM1

4.3

-35.4 (-35.1)

-32.9

-33.1

-32.5 (-32.5)

tTS2

2.2

-6.3 (-4.9)

-2.6

-3.0

-2.3 (-2.6)

HOCN+C3F7

1.5

-12.8

-9.8

-7.7

-6.7

tTS3

3.5

-29.6 (-29.3)

-27.0

-27.4

-26.7 (-26.7)

tM2

4.2

-34.4 (-34.2)

-32.0

-32.1

-31.5 (-31.5)

tTS4

2.1

-7.9 (-6.5)

-4.8

-5.0

-4.4 (-4.8)

tTS5

0.9

6.0 (7.2)

6.6

5.2

5.5 (5.6)

tM3

3.4

-32.7 (-32.2)

-31.2

-31.2

-30.8 (-30.4)

tTS6

2.0

-12.2 (-11.1)

-7.5

-8.5

-5.2 (-4.8)

HNCO+C3F7

1.2

-37.4

-34.2

-32.6

-31.5

tTS7

2.7

16.2

19.2

14.3

14.7

HF+(CF3)2CNCO

0.9

-51.9

-49.5

-49.3

-48.7

tTS8

2.7

59.5

63.2

64.6

66.8

tM4

4.0

21.6

23.0

33.0

25.6

tTS9

2.3

57.8

58.3

62.3

60.7

CF3+CF2=CFC(NF)OH

2.4

53.9

38.5

59.3

43.8

tTS10

1.4

62.5

59.6

66.5

73.3

CF2=CFCF3+FNCOH

1.1

62.3

61.7

67.2

69.8

tTS11

0.9

64.7

62.9

67.1

64.8

tM5

4.0

20.5

20.8

24.5

23.4

tTS12

2.0

50.1

52.3

54.1

52.7

CF2=CFCF3+HNFCO

1.7

45.7

44.1

50.1

51.1

tTS13

2.4

54.8

54.8

59.4

57.0

CF3+CF2=CFC(O)NFH

2.5

51.7

39.5

57.2

53.1

tTS14

2.1

60.1

62.9

58.9

66.9

a

All energies are in kcal/mol. The data in parenthesis were calculated on the basis of the ROM06-2X/AVTZ optimized geometries.

b



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

Page 36 of 52

Table 2. Zero-point energy corrections (∆ZPE) and relative energies for the species involved in the cis-conformational C-O addition/elimination reaction routes with respect to the (CF3)2CFCN+OH asymptote.a Species TS-iso

∆ZPE 4.4

UM06-2X/AVTZ

DL-RCCSD(T)/CBS

ROCBS-Q

DL-ROCBS-Q

b

-30.3

-30.2

-29.5 (-29.4)b

-32.6 (-32.3)

cTS1

1.6

2.6 (4.2)

2.3

2.3

2.7 (2.6)

cM1

4.3

-35.5 (-35.2)

-32.7

-33.3

-32.6 (-32.6)

cTS2

2.1

-5.9 (-4.6)

-2.0

-2.5

-1.6 (-1.9)

cTS3

3.5

-30.3 (-30.0)

-27.6

-27.8

-27.1 (-27.0)

cM2

4.3

-32.7 (-32.4)

-30.0

-30.1

-29.5 (-29.5)

cTS4

2.3

-6.9 (-5.5)

-3.2

-3.4

-2.9 (-3.3)

cTS5

1.0

5.7 (7.0)

6.4

4.8

4.6 (4.7)

cM3

3.1

-32.3 (-31.9)

-30.7

-31.2

-30.7 (-30.7)

cTS6

2.2

-13.9 (-12.7)

-9.3

-10.6

-5.4 (-4.0)

cTS7

2.4

47.7

43.0

43.1

47.9

cM4

4.0

0.71

3.4

3.9

5.2

cTS8

0.9

44.5

46.8

46.7

48.0

cM5

4.2

0.08

3.0

3.6

4.6

cTS9

2.7

30.2

32.9

32.8

32.0

(CF3)2CCO+HNF

0.88

22.0

23.5

23.8

23.1

cTS10

2.2

48.6

44.4

44.3

47.5

a

All energies are in kcal/mol. The data in parenthesis were calculated on the basis of the ROM06-2X/AVTZ optimized geometries.

b


Page 37 of 52

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


Table 3. Zero-point energy corrections (∆ZPE) and relative energies for the species involved in the N-O addition/elimination and the concerted displacement reaction routes with respect to the (CF3)2CFCN+OH asymptote.a Species

∆ZPE

UM06-2X/AVTZ

DL-RCCSD(T)/CBS

ROCBS-Q

DL-ROCBS-Q

tTS1n

2.0

16.9

16.5

14.3

14.8

tM1n

3.8

11.7

14.0

13.5

14.1

tTS2n

1.6

21.3

20.7

18.7

19.2

tM2n

3.8

14.8

17.2

17.0

17.7

tTS3n

2.7

19.0

21.2

20.7

21.4

HONC + C3F7

0.9

45.7

49.6

51.6

52.6

tTS4n

-0.3

73.2

73.9

72.9

72.7

tM3n

3.9

-13.8

-10.9

-12.5

-11.7

HCNO + C3F7

0.3

33.9

35.5

36.5

37.6

tTS5n

-0.6

69.8

72.3

71.1

72.5

HF + (CF3)2CCNO

0.5

4.6

5.8

3.3

12.3

cTS1n

1.9

16.3

16.2

13.6

14.5

cM1n

3.8

11.7

14.5

13.7

14.5

cTS2n

1.6

20.8

20.6

18.3

19.1

cM2n

3.8

15.3

18.1

17.7

18.5

cTS3n

2.7

18.6

21.1

20.7

21.6

TS1d

0.13

79.5

82.5

81.9

81.3

TS2d

1.2

79.6

80.8

78.9

81.5

TS3d

1.5

66.7

64.5

64.9

64.7

TS4d

1.4

55.2

56.5

51.3

58.0

TS5d

0.5

65.5

60.3

59.3

67.8

TS6d

2.0

71.4

67.9

67.6

68.0

TS7d

1.4

63.9

63.5

63.3

64.0

TS8d

1.3

62.8

63.4

62.5

64.7

CF3OH+CF3CFCN

1.8

-35.6

-35.4

-31.9

-30.9

C3F7OH+CN

1.7

7.2

5.5

6.5

7.4

(CF3)2C(CN)OH+F

2.4

9.2

9.6

9.7

9.6

CF3CF(CN)OH+CF3

2.2

-15.8

-12.3

-12.6

-9.0

FOH+(CF3)2CCN

0.6

51.5

49.5

50.7

50.8

a

All energies are in 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 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 52

Table 4. RCCSD(T) electron-correlation (∆Ecorr), Hartree-Fock (∆EHF), and M06-2X (∆EM062x) energy contributions to the barrier height for tTS1 with respect to the (CF3)2CFCN+OH asymptote in the DL-RCCSD(T)/CBS energy.a AVDZ

∆Ecorr

∆EHF

∆EM062x a

AVTZ

AVQZ

HKKN

HKKN

OAN

HL

Bkw

VP

(D→T)

(T→Q)

(D→T)

(D→T)

(D→T)

(D→T)

-18.34

-18.30

-18.40

-18.44

-18.44

-18.42

-17.48

-18.09

-18.20

D→T→Q

T→Q→5

V6Z

21.12

21.20

21.17

AVDZ

AVTZ

AVQZ

AV5Z

V6Z

-0.66

-0.64

-0.48

-0.48

-0.51



Page 39 of 52

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Table 5. Zero-point energy corrections (∆ZPE) and relative energies for the species involved in the water-mediated C-O addition/elimination reaction routes with respect to (CF3)2CFCN and the H2O-OH complex asymptote.a Species

∆ZPE

UM06-2X/AVTZ

DL-RCCSD(T)/CBS

DL-ROCBS-Q

tRC

2.0

-5.1

-4.0

-3.1

tTS1w

1.9

-0.22

-0.23

0.22

tM1w

4.5

-40.9

-37.9

-37.4

tTS2w

2.2

-12.9

-8.8

-8.3

C3F7 + HOCN-H2O

1.8

-18.7

-15.4

-11.9

tTS3w

1.6

-18.1

-13.6

-13.5

tM2w

3.5

-35.2

-33.1

-32.9

tTS4w

1.6

-11.6

-6.7

-4.2

C3F7 + HNCO-H2O

1.0

-37.6

-34.6

-31.9

tTS5w

1.1

-18.0

-14.1

-12.9

C3F7C(O)NH2 + OH

2.6

-26.1

-22.8

-23.2

cRC

1.7

-5.9

-4.6

-4.3

cTS1w

1.9

-0.10

-0.40

0.59

cM1w

4.5

-41.2

-37.9

-37.6

cTS2w

2.1

-12.5

-8.1

-7.7

cTS3w

1.5

-18.4

-13.7

-13.9

cM2w

3.4

-34.7

-32.5

-32.8

cTS4w

1.5

-13.1

-8.4

-5.0

cTS5w

2.6

-17.4

-13.4

-13.3

a




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

Figure 1. The DL-ROCBS-Q energies (in kcal/mol) in comparison with those calculated using the full-version ROCBS-Q method. Solid squares: for the intermediates and transition states. Open circles: for the products. Open triangles: for the species with the reacting CF3 groups.


Page 40 of 52

Page 41 of 52

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


Figure 2. The ONIOM(RCCSD(T):M06-2X/VDZ) energies (in kcal/mol) in comparison with those calculated at the RCCSD(T)/VDZ level of theory. Solid squares: for the intermediates and transition states. Open circles: for the products. Open triangles: for the species with the reacting CF3 groups.



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

Figure 3. RCCSD/AVTZ calculated T1 diagnostic values and the largest T2 amplitudes for the species involved in the (CF3)2CFCN+OH reaction. The labeled species with T1 > 0.03 are indicated by triangles.


Page 42 of 52

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Figure 4. Energetic reaction routes for the C-O addition/elimination mechanism of the (CF3)2CFCN+OH reaction at the DL-ROCBS-Q level of theory. Solid lines: trans-conformational pathways. Dashed lines: cis-conformational pathways.



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

Figure 5. Energetic reaction routes for the N-O addition/elimination mechanism of the (CF3)2CFCN+OH reaction at the DL-ROCBS-Q level of theory. Solid lines: trans-conformational pathways. Dashed lines: cis-conformational pathways.


Page 44 of 52

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Figure 6. Energetic reaction routes for the concerted displacement mechanism of the (CF3)2CFCN+OH reaction at the DL-ROCBS-Q level of theory.



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

Figure 7. Optimized geometries of the species involved in the trans-conformational reaction routes for the C-O association mechanism of the (CF3)2CFCN+OH reaction at the UM06-2X/AVTZ (upper entries), UM06-2X/AVQZ (lower entries) and ROM06-2X/AVTZ (the third entries whenever available) levels. Bond distances are in Ångstroms. Bond angles are in degrees.


Page 46 of 52

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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


Figure 8. Optimized geometries of the species involved in the cis-conformational reaction routes for the C-O association mechanism of the (CF3)2CFCN+OH reaction at the UM06-2X/AVTZ (upper entries), UM06-2X/AVQZ (lower entries) and ROM06-2X/AVTZ (the third entries whenever available) levels. Bond distances are in Ångstroms. Bond angles are in degrees.



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

Figure

9.

Optimized

geometries

of

the

species

Page 48 of 52

involved

in

the

N-O

association/elimination and the concerted displacement mechanisms of the (CF3)2CFCN+OH

reaction

at

the

UM06-2X/AVTZ

(upper

entries)

and

UM06-2X/AVQZ (lower entries) levels. Bond distances are in Ångstroms. Bond angles are in degrees.


Page 49 of 52

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Figure 10. Calculated rate coefficients for the (CF3)2CFCN+OH reaction at 700 Torr of N2 as a function of temperatures. Red dot: experimental value in ref 8. Dashed line: RRHO approximation without hindered rotors. Solid line: RRHO approximation with hindered rotors. The yield of HOCN is illustrated by the blue line as of the right y axis.



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

Figure 11. Energetic reaction routes for the C-O addition/elimination mechanism of the (CF3)2CFCN+OH+H2O reaction at the DL-ROCBS-Q level of theory. Solid lines: trans-conformational pathways. Dashed lines: cis-conformational pathways.


Page 50 of 52

Page 51 of 52

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Figure 12. Optimized geometries of the species involved in the water-mediated C-O association

mechanism

of

the

(CF3)2CFCN+OH+H2O

reaction

at

the

UM06-2X/AVTZ level of theory. Bond distances are in Ångstroms. Bond angles are in degrees.



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

TOC Graphic


Page 52 of 52

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