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Kinetics and Mechanism of the Reaction of Fluorine Atoms with Pentafluoropropionic Acid E. S. Vasiliev,† V. D. Knyazev,‡ G. V. Karpov,† and I. I. Morozov*,† †

Semenov Institute of Chemical Physics RAS, 4 Kosygin St., 119991 Moscow, Russia Research Center for Chemical Kinetics, Department of Chemistry, The Catholic University of America, Washington, D.C. 20064, United States

‡

S Supporting Information *

ABSTRACT: The kinetics of the reaction between fluorine atoms and pentafluoropropionic acid has been studied experimentally at T = 262−343 K. The overall reaction rate constant decreases with temperature: k1(T) = 6.1 × 10−13 exp(+1166 K)/T) cm3 molecule−1 s−1. The potential energy surface of the reaction has been studied using quantum chemistry. The results were used in transition state theory calculations of the temperature dependences of the rate constants of the two channels of the reaction. The abstraction channel ultimately producing HF, C2F5, and CO2 is dominant at the experimental temperatures; the addition−elimination channel producing C2F5 and CF(O)OH becomes important above 1000 K.

1. INTRODUCTION Perfluorinated carboxylic acids (PFCAs) are substances of significant environmental interest and concern. Over the past decade, PFCAs such as perfluorooctanesulfonic and perfluorooctanoic acids have been found in various environments on Earth; in particular, they are present in rain and snow in industrialized countries, as well as in wildlife.1 In a recent study of rainwater samples collected from two cities in Japan, several short-chain PFCAs were found, with the largest contributions being those of the trifluoroacetic (TFA) and pentafluoropropionic (PFPrA) acids, in the amounts 75.9 and 10.3 ng L−1, respectively.2 In China, analysis of dewatered waste sewage sludges collected from the Yangtze river delta areas found a series of PFCAs.3 In most samples, TFA and PFPrA were predominant, with concentrations in the ranges 107−562 and 4.41−395 ng g−1, respectively. These two acids accounted for 12%−93% and 0.7%−61% of the total PFCAs concentrations. The sources of PFCAs in the Earth’s environment are not wellknown. The global industrial emissions of total PFCAs from direct and indirect sources are estimated to be 3200−7300 tonnes.4 Estimates demonstrate that the majority of PFCAs released are due to fluoropolymer manufacture and use.4 Very little is known about the kinetics of the reactions with the participation of PFPrA. In 1982, the kinetics of the formation of PFPrA in the thermal decomposition of the ethyl ether of PFPrA was studied by Blake and Shraydeh.5 More recently, Andersen et al.6 obtained an upper limit for the rate constant of the reaction of PFPrA with the chlorine atoms (k ≤ 1 × 10−17 cm3 molecule−1 s−1) at 296 K and Hurley et al.7 determined the room temperature rate constant of the reaction of PFPrA with the OH radical ((1.69 ± 0.22) 10−13 cm3 molecule−1 s−1). Atmospheric lifetimes of PFPrA with respect to reaction with OH radicals were estimated to be approximately 130 days. Reaction with OH radicals is a minor atmospheric fate of PFPrA. The major atmospheric © XXXX American Chemical Society

removal mechanism is believed to be wet and dry deposition, which probably occurs on a time scale of the order of 10 days. In the current study, we report the results of our experimental and computational study of the kinetics and mechanism of the reaction of PFPrA with fluorine atoms: F + C2F5C(O)OH → HF + C2F5C(O)O• → HF + C2F5• + CO2 •

→ C2F5CF(O )OH →

C2F5•

+ CF(O)OH

(1a) (1b)

The study focused on the temperature dependence of the rate constant of reaction 1 in the 262−343 K temperature range. The relative rates technique based on mass spectrometric detection of the reactants was used. The potential energy surface of reaction 1 was studied using quantum chemistry and the competition between the two channels 1a and 1b was analyzed. Extrapolation of the rate constants of the reaction channel 1a to temperatures outside the experimental range and prediction of the rate constants of channel 1b as a function of temperature were performed using transition state theory modeling.

2. EXPERIMENTAL STUDY AND RESULTS The experimental setup and methodology of relative rates kinetic experiments have been described in detail before;8 thus, only a brief description is given here. The experiments were performed in a thermostated discharge flow reactor, 50 cm long and 2.3 cm i.d., coupled to a molecular beam electron impact quadrupole mass spectrometer. Fluorine atoms were produced in a high-frequency discharge in a F2/He mixture in a side arm Received: March 25, 2014 Revised: May 8, 2014

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more, it becomes difficult to find the optimal experimental conditions and even more difficult to vary the extent of reaction ratios while still staying in the good signal-to-noise ratio range. And finally, the third requirement is that the rate constant of the reference reaction has to be known at the temperature of interest. The reference reaction selected for use in the current study is that of fluorine atoms with gaseous nitric acid:

of the reactor located 40 cm upstream from the mass spectrometer sampling inlet. The discharge zone contained an alumina insert to minimize production of oxygen atoms (due to the reaction of fluorine with the wall) in the discharge. The central inlet of the reactor (1.7 cm i.d., 20 cm upstream from the mass spectrometer sampling inlet) was used to supply flows of the reactants, C2F5C(O)OH and the reference compound, HNO3, diluted in the carrier gas, helium, in varying concentrations. A typical flow velocity inside the reactor was 1.6 m s−1, and the reactor pressure was 0.80 Torr. The concentrations of the reactants and products in the reactor detection zone were monitored using a molecular beam mass spectrometer. The molecular beam was formed by the nozzle and a skimmer; a modulating chopper was located between the skimmer and the electron impact ion source. Electron impact energies of 12−100 eV were used. The following gases were used: helium (99.996%), pentafluoropropionic acid (97%, Fluka), and fluorine (99.9%, 5% mixture in helium, Merck AG). Standard relative rate procedures were employed. Mixtures of PFPrA and the reference compound (HNO3) in varying concentrations diluted in the excess of helium carrier gas were supplied through the central injector. The extent of depletion of PFPrA relative to that of the reference compound (REF) was monitored and rate constant ratios, k1/kREF, were determined using the following equation: k1 kREF

=

ln([PFPrA]0 /[PFPrA]) ln([REF]0 /[REF])

F + HNO3 → products

(2)

The room temperature kinetics of this reaction has been studied experimentally by four groups,10−13 with reasonable agreement on the value of the rate constant (2.1−2.7) × 10−11 cm3 molecule−1 s−1. The temperature dependence of the k4 has been determined by Wine et al.12 in the temperature range of 260−373 K. The values of the rate constant decrease with increasing temperature in the 260−320 K range but stay independent of temperature above 330 K. The authors of ref 12 attributed this complex temperature dependence to changing relative importance of two channels of reaction 2, with abstraction of an H atom dominating at low temperatures and substitution channel(s) being more important at higher temperatures. The expected products of all possible channels of reaction 2 include HF, NO3, OH, FNO2, FNO, and HO2. None of these compounds interfere with mass spectrometric monitoring of the concentration of PFPrA at m/z = 45. In the experiments performed in the current work, the concentration of HNO3 was monitored using the molecular ion at m/z = 63, where neither PFPrA nor products of reaction 1 provide any contribution. An example of the results of the relative rates experiment is presented in Figure 1 (T = 323 K). The obtained value of k1/k2

(I)

The mass spectrum of PFPrA has the base peak at m/z = 45 (attributed to the C(O)OH+ ion). The molecular ion peak at m/z = 164 is very weak, less than 2% relative to the base peak. The spectrum is in qualitative, if not quantitative agreement with the database spectrum obtained from the NIST Mass Spectral database.9 A comparison between these mass spectra is provided in the Supporting Information. Because of the weakness of the molecular ion peak, it was not possible to use it for monitoring the concentration of PFPrA. Instead, the m/z = 45 base peak was used for this purpose. The products of the reaction channel 1a (HF + C2F5 + CO2) cannot provide any contribution to this mass. The products of the other possible channel of reaction 1, channel 1b, potentially, can contribute to the m/z = 45 peak. However, as is shown below, the branching fraction of channel 1b is negligible under the conditions of the experiments performed in the current study. Therefore, the observed mass peak at m/z = 45 can be fully attributed to PFPrA only. The choice of the reference compounds to be used in kinetics measurements is guided by three considerations. First, both the reference compound and the products of its reaction with atomic fluorine should have mass spectra that do not interfere with the mass peak used for the detection of PFPrA. Second, rate constant of the reaction between F atoms and the reference compound should be reasonably close in value to that of the reaction under study, reaction 1. If the second requirement is not satisfied, then the accuracy of the relative rate measurement suffers. Ideally, the most favorable signal-tonoise ratio is obtained under the conditions where both the [PFPrA]0/[PFPrA] and the [REF]0/[REF] ratios significantly differ from unity but are not too large, roughly in the 1.2−10 range. If the rate constants of the reference reaction and that of the reaction under study differ by an order of magnitude or

Figure 1. Dependence of the extent of depletion of PFPrA relative to that of the reference compound (REF) obtained in experiments at 323 K. The ratio of the rate constants k1/kREF was obtained from the slope of the fitted straight line (eq I).

= 1.25 ± 0.04, combined with the value of k2(323 K) = (2.07 ± 0.31) × 10−11 cm3 molecule−1 s−1 obtained from the Arrhenius expression and quoted 15% absolute uncertainty of ref 12, results in the rate constant of reaction 1 k1(323 K) = (2.58 ± 0.47) × 10−11 cm3 molecule−1 s−1. Experiments were performed at temperatures below and above ambient, T = 262−343 K. The results are presented in Figure 2 and in Table 1. Two sets of error bars are given for the data points on the Arrhenius plot. The smaller, wider-cap error bars represent the uncertainties of the current experimental relative-rates study (2σ). The larger, narrow-cap error bars show the overall uncertainties of k1 determinations, which include the 15% uncertainties for the rate constants of the reference reaction 2 reported by Wine et al.12 As can be seen B

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F + CF3C(O)OH → HF + CF3C(O)O• → HF + CF3• + CO2

(3a)

→ CF3CF(O•)OH → CF3• + CF(O)OH

(3b)

In our earlier study17 of reaction 3, we used the CCSD(T)18,19 method for single-point energy calculations. Reaction 1 involves more heavy atoms, and thus the use of CCSD(T) method is problematic. Therefore, the method of isodesmic reactions and the RESLIR(CCSD(T)BH&HLYP/ aug-cc-pVDZ)20 method based on the application of the formalism of isodesmic reactions to transitions states were used for evaluating the energies of the PES minima and saddle points, respectively. The CCSD(T) level energies obtained in ref 17 were used in these calculations. The Gaussian 09 program21 was employed in all potential energy surface (PES) calculations. The version of the BH&HLYP functional implemented in Gaussian 09 was used, which, as described in the Gaussian manual, is different from that of ref 14. Energy values quoted in the text henceforth are given as X/Y, where the first value is obtained in isodesmic/ RESLIR and the second−in BH&HLYP calculations and include vibrational zero point energies unless stated otherwise. The results of the PES study are summarized in Table 2 and Figure 3, and the detailed information is given in the Supporting Information. The mechanism of reaction 1 involves two different reaction paths. Acidic hydrogen atom abstraction initiates the reaction path 1a, and addition of the fluorine atom to the carbon atom of the carbonyl group is the initial step of the other path 1b. The reaction path of channel 1a has a weakly bound CF3CF2C(O)OH···F complex on the reactants side (−21.7/− 17.8 kJ mol−1, denoted vdW1 in Figure 3), followed by an energy barrier. Both the BH&HLYP and the RESLIR calculations give energies of the barrier that are below the energy of the reactants. However, the barrier is substantial at the BH&HLYP level (12.8 kJ mol−1 relative to the complex and −5.0 kJ mol−1 relative to the reactants, TS1 in Figure 3) but practically disappears at the RESLIR(CCSD(T)) level (8.4 kJ mol−1 relative to the complex without ZPE but −3.0 kJ mol−1 when ZPE is included). The products of channel 1a, HF + CF3CF2C(O)O, also form a weakly bound complex, −15.3/16.0 kJ mol−1 relative to the separated products (vdW2 in Figure 3). Reaction channel 1a can be expected to be followed by a rapid decomposition of the CF3CF2C(O)O radical to C2F5 + CO2; the energy barrier to this decomposition is only 0.2/ 18.4 kJ mol−1:

Figure 2. Experimental (circles and solid line Arrhenius fit) and the calculated (dashed line) k1(T) dependences. Smaller error bars are 2σ; larger error bars also include the uncertainties in the value of the reference reaction rate constant.

from the plot, k1 shows noticeable negative temperature dependence, which can be expressed with the following equation: k1(T ) = (6.1 ± 4.5) × 10−13 exp( +(1166 ± 219 K)/T ) (II) cm 3 molecule−1 s−1 Here, the quoted uncertainties of the preexponential factor and the activation energy are given as the standard error of the fit and bear no physical meaning. Statistical experimental errors in the experiment shown in Figure 1 are significantly lower than the typical values for the other temperatures due to temporal instability of MS signal. The experiment at 323 K was carried out at relatively high MS signal stability. Thus, 12 measurements were enough. At the other temperatures, the MS signal stability was worse markedly. Due to this, the noticeable dispersion of experimental points was compensated by an increase of measurements to be made from 12 to approximately 20. The relative consumption of reagents is rather limited, but it is quite reasonable for our experiments. The lines have been constrained through the origin in all plots. Otherwise, the gradient difference was ∼20%.

3. POTENTIAL ENERGY SURFACE AND TRANSITION STATE THEORY MODEL OF REACTION 1 The potential energy surface (PES) of reaction 1 was studied using quantum chemistry. Molecular structures were optimized using the density functional BH&HLYP14,15 method with the aug-cc-pVDZ16 basis set and vibrational frequencies were calculated for all PES stationary points using the same technique. The reaction PES and mechanism are very similar to those of the reaction of fluorine atoms with trifluoroacetic acid, as described below.

C2F5C(O)O• → C2F5• + CO2

(4)

Table 1. Conditions and Results of the Experiments To Determine k1 T/K

[PFPrA]a

[REF]a

[F]a

262 278 293 323 343

0.9−4.2 2.3−7.3 0.7−2.3 1.2−5.9 1.7−5.1

2.2−16.1 3.8−7.7 1.4−28 9.5−15.9 3.6−12

1.4−8.6 2.4−4.4 0.9−9.4 3.9−6.5 2.3−5.2

k1/kREFb

kREFc

± ± ± ± ±

2.76 2.53 2.35 2.07 2.0

2.19 1.33 1.34 1.25 0.88

0.18 0.09 0.11 0.04 0.07

k1d 6.06 3.37 3.10 2.58 1.77

± ± ± ± ±

0.50 0.24 0.30 0.07 0.13

(±1.41) (±0.75) (±0.77) (±0.46) (±0.40)

In units of 1012 molecules cm−3. HNO3 was used as the reference compound. bThe error limits are given as standard error of the fit. cIn units of 10−11 cm3 molecule−1 s−1. dIn units of 10−11 cm3 molecule−1 s−1. Error limits given without parentheses are derived from the uncertainties in k1/kREF. Error limits given in parentheses include the uncertainties in the rate constant of the reference reaction as a systematic contribution.32 a

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Table 2. Energies of Reactants, Products, and Stationary Points on the PES of Reaction 1 Obtained in Quantum Chemical Calculationsa method species CF3CF2C(O)OH···F complex (vdW1) CF3CF2C(O)O···H···F (TS1) CF3CF2C(O)O···HF complex (vdW2) HF + CF3CF2C(O)O HF + CF3CF2···C(O)O (TS3) HF + CF3CF2 + C(O)O CF3CF2C(···F)(O)OH (TS2) CF3CF2CF(O)OH CF3CF2···CF(O)OH (TS4) CF3CF2 + CF(O)OH

b

isodesmic/RESLIRc

BH&HLYP

Channel 1a −17.8 −5.0 −84.5 −68.5 −50.1 −169.4 Channel 1b 23.0 −81.8 −41.6 −123.7

−21.7 −24.8 −96.3 −81.0 −80.8 −186.7

modelingd

−10.2

9.8 −80.8 −55.7 −120.0

Energy values are given in kJ mol−1 relative to F + CF3CF2C(O)OH and include zero-point vibrational energy (ZPE). bOptimized in BH&HLYP/ aug-cc-pVDZ calculations. cApplication of the methods of isodesmic reactions/RESLIR20 to reaction 1 is equivalent to obtaining the energies of PES stationary points by using the high-level (CCSD(T)/aug-cc-pVDZ) energies for the cognate PES features of reaction 3 and correcting them by the differences between the energies obtained at the lower computational level (BH&HLYP/aug-cc-pVDZ). For example, E(CF3CF2C(O)O···H···F) = E(CF3C(O)O···H···F,CCSD(T)) + E(CF3CF2C(O)O···H···F,BH&HLYP) − E(CF3C(O)O···H···F,BH&HLYP), where E is the ZPE-corrected energy relative to the reactants. dResults of the fitting of the experimental data with the RRKM model. a

BH&HLYP/aug-cc-pvdz calculations were used. The energy of the transition state for the reaction channel 1a were adjusted to reproduce the experimental k1(T) dependence, as described below. Transition state theory22 calculations were performed for the addition−decomposition channel 1b, using the RESLIR(CCSD(T)) level energy barrier height. For the channel 1a, modeling was performed under the assumption that TS1 represents the dynamic bottleneck of the reaction. The assumption is reasonable, as it can be expected that most of the trajectories sampling the coordinate space of the CF3CF2C(O)OH···F complex and having energies above that of the reactants proceed back to F + CF3CF2C(O)OH through a very “loose” transition state with high density of states and only a small fraction passes through the “tight” PES saddle point (TS1) and leads to the HF + CF3CF2C(O)O products. Rate constant values were calculated using the equation

Figure 3. Potential energy surface of reaction 1 obtained in quantum chemical calculations (see text and Table 2). Solid lines: RESLIR(CCSD(T)/aug-cc-pdz//BH&HLYP/aug-cc-pdz) energies. Dashed lines: BH&HLYP/aug-cc-pdz energies. The dotted line indicates the recommended fitted value of the TS1 energy barrier obtained in modeling of the experimental data.

k(T ) =

‡ ‡ (T ) Q inact (T ) Q trans

Q F(T ) Q CF CF C(O)OH(T ) 3

Addition to the carbon atom of the carbonyl bond channel has a barrier of 9.8/23.0 kJ mol−1 (TS2 in Figure 3). Addition to the carbonyl oxygen atom does not occur: a relaxed PES scan with varying O−F distance demonstrated the absence of a potential energy minimum with the fluorine atom bonded to oxygen. The CF3CF2CF(O)OH adduct formed in the initial step of channel 1b is highly vibrationally excited (91/105 kJ mol−1) and is expected to decompose to C2F5 + CF(O)OH via a 25.1/40.2 kJ mol−1 barrier (TS4 in Figure 3). The experimental temperatures of the current study are limited to the 262−343 K range, where the barrierless reaction channel 1a is expected to dominate. In an attempt to provide means for an extrapolation of the experimental k1(T) dependence to temperatures outside the experimental range, and to estimate the contribution of the reaction channel 1b to the overall reaction, an RRKM/transition state theory model of reaction 1 was created in the current work. Molecular structure and vibrational frequencies of involved species obtained in the

×

∫E

∞ 0

2

⎛ E − E0 ⎞ W ‡(E − E1) exp⎜ − ⎟ dE kBT ⎠ ⎝

(III)

where Q‡trans(T) and Q‡inact(T) are the partition functions of the translational and the overall 2-dimensional (inactive) rotational degrees of freedom of the transition state, QF(T) and QCF3CF2C(O)OH(T) are the partition functions of the F and CF3CF2C(O)OH reactants, W‡(E − E1) is the sum-of-states function of the active23−25 degrees of freedom of the transition state, E0 and E1 are the energies of the reactants and the transition state, respectively (E0 > E1), and kB is the Boltzmann constant. Equation III was obtained in ref 26 by simplification of a formula derived by Mozurkewich and Benson27 (eq 12 of ref 27) for reactions proceeding over shallow potential energy wells. The simplification resulted from the above-mentioned assumption of predominant dissociation of the weakly bound adduct complexes back to the reactants and from an approximate treatment of the effects of angular momentum D

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mol−1) is closer to the value obtained in the BH&HLYP rather than in the RESLIR(CCSD(T)) calculations. It is, however, also strongly dependent on the values of vibrational frequencies of the transition state TS1. For example, if these frequencies were to be modified in transition state theory calculations to better match the slope of the experimental k1(T) dependence on the Arrhenius plot in Figure 2, the fitted barrier would likely change noticeably. Such a computational exercise was performed in the study17 of reaction 3, which resulted in a decrease of the fitted energy barrier by −7.2 kJ mol−1. Thus, the results of the modeling cannot be interpreted as indicating a better performance of one of the two quantum chemistry methods over the other in evaluating energy barriers of this type. In the absence of any experimental data on the rate of the addition−decomposition pathway of reaction 1 (channel 1b), we recommend using the temperature dependence of eq V on the basis of the quantum chemistry study performed in this work and transition state theory calculations. As mentioned above, the addition−decomposition channel results in the formation of the C2F5 + CF(O)OH products. The contribution of this channel becomes comparable to that of the abstraction channel 1a only at high temperatures, above 1000 K. At these temperatures, CF(O)OH will decompose to HF + CO2. The energy barrier for CF(O)OH decomposition has been reported in two quantum chemical studies: 133.l kJ mol−1 was obtained by Ljubić and Sabljić30 in CASPT2/cc-pVTZ//CASSCF/ccpVTZ calculations, whereas Uchimaru et al.31 obtained the value of 138.5 kJ mol−1 at the CCSD(T)/cc-pVTZ//MP2/ccpVQZ level. The results of these two groups are consistent with each other. A rough estimation of the rate constant with a low preexponential factor of 1012 s−1 and the activation energy of 138.5 kJ mol−1 results in the value of 6 × 104 s−1 at 1000 K. Thus, both channels of reaction 1 will ultimately lead to the same set of final products: HF + C2F5 + CO2.

conservation where the rate constant value obtained for zero angular momentum is multiplied by the ratio of the partition functions of the two-dimensional rotational (inactive) degrees of freedom of the transition state and the active molecule. The latter ratio is close to unity (0.96) in the case of reaction 1, which justifies the use of the approximation. Tunneling has no influence on the calculated rate constants because k(E) dependences with and without tunneling differ very little above the energy barrier28,29 and energies of the reactive trajectories passing from the CF3CF2C(O)OH···F complex to the products part of the PES are higher than that of the reactants and thus are always above the energy barrier. The location of the barrier for channel 1a on the energy scale is rather uncertain, as demonstrated by the divergence of the BH&HLYP and the RESLIR(CCSD(T)) results. Therefore, the optimum value was obtained in fitting the barrier height used in the computational model to the experimental k1(T) dependence. The resultant energy of the transition state is −10.2 kJ mol−1; the calculated temperature dependence is shown in Figure 2 by the dashed line. The calculated temperature dependence of the rate constant of the reaction channel 1a can be represented with the following modified Arrhenius expression: k1a = 6.14 × 10−14T −0.51 exp(970 K/T ) cm 3 molecule−1 s−1 (200−1000 K)

(IV)

The calculated dependence lies somewhat askew relative to the experimental one but still within the envelope of uncertainties of the individual rate constant determinations (Figure 2). The transition state theory calculations of the rate constants of reaction channel 1b (addition−decomposition) result in the following modified Arrhenius expression: k1b = 3.35 × 10−17T1.59 exp( −911 K/T ) cm 3 molecule−1 s−1 (200−2000 K)

■

(V)

ASSOCIATED CONTENT

S Supporting Information *

The contribution of channel 1b becomes comparable to that of channel 1a only at temperatures above 1000 K.

A supplement, including the mass spectrum of C2F5COOH obtained in the experimental study and the detailed results of the quantum chemistry study of reaction 1 (Tables 1S and 2S, Figure 1S, 10 pages). This material is available free of charge via the Internet at http://pubs.acs.org.

4. DISCUSSION The current study represents the first determination of the rate constant of reaction 1 and its temperature dependence. The negative temperature dependence is consistent with the barrierless potential energy surface of the initial approach of the fluorine atom to PFPrA and the reaction bottleneck located below the energy of the reactants on the energy scale, as inferred from the quantum chemical part of the study. The computational study of reaction 1 was performed in this work to assess possible reaction pathways and to provide means for the extrapolation of the k1(T) temperature dependence to outside the experimental temperature range. Although the model of reaction channel 1a results in the calculated k1(T) dependence that lies somewhat askew relative to the linear fit to the experimental data on the Arrhenius plot (Figure 2), the deviation between the slopes of the two lines is lower than the experimental uncertainties. The amount of scatter and the uncertainties of the experimental individual data points do not allow for a precise determination of the activation energy. The activation energy value resulting from the model (−7.3 kJ mol−1 in the experimental temperature range) is well within the 2σ range of the experimental uncertainties (−9.7 ± 3.6 kJ mol−1). The fitted energy of the transition state (−10.2 kJ

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AUTHOR INFORMATION

Corresponding Author

*I. I. Morozov: telephone, +7-495-939-7316; fax, +7-495-13783-18; e-mail, [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the Ministry of Science and Education of the Russian Federation under Agreement No. 8532 of 7 March 2012, Russian Foundation for Basic Research grant No. 13-05-00477, and Program No. 1 of the Department of Chemistry and Materials Science of RAS.

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