Understanding the Gas Phase Chemistry of Alkanes with First

Article pubs.acs.org/jced

Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Understanding the Gas Phase Chemistry of Alkanes with FirstPrinciples Calculations Jonathan William Estes, Mudit Dixit, and Giannis Mpourmpakis* Department of Chemical Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States S Supporting Information *

ABSTRACT: Alkyl radicals are key intermediates in multiple industrially important reactions, including the dehydrogenation of alkanes. Because of their diverse chemistry, alkyl radicals form various products via a number of competing reactions in the gas phase. Using Density Functional Theory (DFT) and accurate ab initio electronic structure calculations (CBS-QB3), we investigated the thermodynamics and kinetics of gas phase alkyl radical reactions. Specifically, we investigated the hydrogen abstraction, radical recombination, and alkene formation reactions of light alkyl radicals (C1−C8). We show that the hydrogen abstraction Gibbs energies are correlated with the relative Gibbs energies of the corresponding radicals. On the basis of the reaction energy calculations, we identified that the competition between radical recombination reactions and alkene formation reactions is governed by the stability of the alkene products, with the alkene formation being preferred when more substituted alkenes are formed. It was found that the radical recombination is preferred over alkene formation at 298 K, but at high temperatures (773 K) alkene formation becomes highly preferred. Importantly, owing to the competition of different reactions, we demonstrate a systematic methodology to select a computational method to investigate the complex chemistry of alkyl radicals. Overall, this study provides a rich database of reaction energies involving alkyl radicals and identifies their thermodynamic preference that can aid in the design of more efficient processes for the chemical conversion of alkanes.

1. INTRODUCTION Alkenes are important building blocks for the production of a wide range of valuable chemicals and plastics.1,2 However, their cost is steadily increasing due to their high demand in chemical industry and low abundance in common hydrocarbon resources. A promising route to produce alkenes is through the catalytic dehydrogenation of alkanes.1,3 Alkanes are major constituents of natural gas and petroleum. Because of their inherent chemical inertness, the methods for conversion of alkanes to higher value commodity chemicals require energyintensive conditions, such as high temperatures.1,4 The dehydrogenation of alkanes to alkenes is often coupled with the formation of alkyl radicals.5 Using electron paramagnetic resonance (EPR) spectroscopy, Driscoll et al. found that methyl radicals were released in the gas phase when methane was passed over MgO at high temperatures.6 In a recent study, Latimer et al. demonstrated that C−H activation of methane proceeds through a methyl radical intermediate on a wide range of catalysts.7 Subsequently, it was established that C−H activation of methane can proceed via a radical or a surface-stabilized mechanism (nonradical formation) on metal oxides.8−10 Alkyl radicals are important intermediates in various industrial processes such as the dehydrogenation of alkanes, oxidative coupling, thermal cracking of methane, and Fischer− Tropsch synthesis;11−14 however, they are unstable and react rapidly.15 © XXXX American Chemical Society

Alkyl radicals produced in industrial processes, these oddelectron “reactive intermediates”, undergo different reactions in the gas phase to produce various stable molecules.16 There are three main classes of gas-phase reactions known to occur involving alkyl radicals:16 (i) hydrogen abstraction (Figure 1a), (ii) radical recombination (Figure 1b), and (iii) alkene formation (Figure 1c). The hydrogen abstraction reaction involves the abstraction of hydrogen radical by another radical. The radical recombination reaction leads to the formation of higher alkanes by the combination of two alkyl radicals, and the alkene formation reaction yields an alkene via hydrogen abstraction from an alkyl radical by another radical. Alkyl radicals formed in the gas phase over the course of alkane dehydrogenation reactions at high temperatures can undergo numerous side reactions. Hence, it is of great importance to probe the reaction energetics of various gasphase reactions of alkyl radicals. Such knowledge can aid in improving the optimization of industrial processes and increase selectivity to high-value chemicals (e.g., olefins). In this study, using a combination of Density Functional Theory (DFT) and high-accuracy ab initio calculations, we Special Issue: Emerging Investigators Received: November 13, 2017 Accepted: January 22, 2018

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DOI: 10.1021/acs.jced.7b00992 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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(within 1 kcal/mol energy). Reactions of alkyl radicals with C2−C8 species were also studied and the Gibbs energy barriers were calculated for hydrogen abstraction and alkene formation reactions.

3. RESULTS AND DISCUSSION 3.1. Stability of Alkanes, Radicals, and Alkenes. The investigation of relative stability of alkanes is important to probe the gas phase reaction preference of alkyl radicals at high temperatures. We studied the relative (total) Gibbs energy difference of a series of alkanes with varying carbon atoms (Cn). These data, which are presented in Table S1, show that more substituted alkanes are more stable than the less substituted alkanes. For instance, for the normal alkanes of C5 series (Table S1), the relative energy follows the trend: Pentane, 12 > Isopentane, 11 > and Neopentane, 10. The increase in the stability of alkanes with alkyl substitution corroborates with previous experimental20 and theoretical21−23 studies, which suggested that the substituted alkanes are more stable than their respective chain isomers. For cyclic alkanes, for the series with three to six carbon atoms (C3−C6), the unsubstituted cycloalkane is the most stable isomer. However, for the series of higher alkanes (C7− C8), the isomers with six membered cyclic structures are most stable (methylcyclohexane, 40, and 1,4-dimethylcyclohexane, 64, Table S1). The stability of six-member cyclic structures can be attributed to their lower ring strain (Table S2) compared to the other cycloalkanes.24 The higher stability of substituted chain alkanes compared to the straight chain nonsubstituted alkanes suggest that the more substituted alkanes are more likely to be observed during gas phase oligomerization reactions (radical recombination reactions). In addition to the stability of substituted alkanes, we investigated the relative Gibbs energy of alkenes. Alkenes follow a similar stability pattern to alkanes with respect to the degree of substitution (Table S3). However, the location of the double bond (terminal or nonterminal) has an impact on the stability of alkenes. For instance, terminal unsubstituted alkenes are less stable than the nonterminal substituted ones. The higher stability of substituted alkenes compared to the unsubstituted counterparts arises from the higher degree of hyperconjugation. This can be seen in the isomers of hexene, 95 and 104, (Table S3), 1-hexene, (ΔGrel = 23.6 kJ/mol) for which the one with the terminal double bond is the least stable, whereas, the nonterminal (substituted) symmetrical alkene (2,3-dimethylbut-1-ene, 104, ΔGrel = 0.0 kJ/mol,) is the most stable isomer. These results show that the symmetrical structural configuration (substitution) around the double bond increases the stability of the molecule. In general, our results (Table S3) indicate that alkenes with more substituted double bonds are more stable, in line with early experiments, which showed that the substituted alkenes are more stable than the unsubstituted alkenes.25 Finally, regarding the stability of alkyl radicals, we found that it increases with the degree of substitution of the radical center. In general, the tertiary radical sites were found to be more stable than the secondary radicals. For instance, in the C5 series of radicals (Table S4), tertiary isopentyl radical, 265, is the most stable radical (ΔGrel = 0.0 kJ/mol), followed by the secondary isopentyl radical, 266 (ΔGrel = 7.3 kJ/mol), and the primary neopentyl radical being the least stable out of these three radicals (ΔGrel = 13.9 kJ/mol). These results are in accordance with well-established experimental findings which

Figure 1. (a) Hydrogen abstraction reaction between methyl radical and propane to form secondary propyl radical and methane; (b) radical recombination reaction of two secondary propyl radicals to form 2,3-dimethylbutane; and (c) propene (alkene) formation from propyl and methyl radicals.

investigated the gas phase reactions of potential radicals formed during alkane dehydrogenation, by analyzing the formation thermodynamics of different species (alkanes, alkenes, and radicals). Importantly, we demonstrate thermodynamic energy relationships as a function of hydrocarbon substitution, and we unravel key kinetic barriers for the reactions of interest.

2. COMPUTATIONAL METHODS All the DFT and high-level electronic structure calculations were performed using the Gaussian 09 package.17 All stationary points were confirmed by analyzing vibrational frequencies. The thermochemistry has been studied at room temperature (T = 298.15 K) and standard atmospheric pressure (P = 1 atm). A large data set of 184 alkanes, 262 alkyl radicals, and 183 alkenes with carbon atom number 1−8 (C1−C8) were studied using the M06-2X/6-311+G(d,p) level of DFT. A selected data set of 45 alkanes, 149 alkyl radicals, and 93 alkenes were further studied with the high-level, complete basis set ab initio method, CBSQB3.18 We have accounted for doublet spin states for alkyl radicals and singlets for the alkanes and alkenes. The total Gibbs energies of chain alkanes were referenced to the corresponding values of the most stable species of the respective Cn series (Table S1). To compute the relative Gibbs energy (ΔGrel) of radicals, the lowest energy radical of the respective Cn series was considered as a reference. For cyclic alkanes, all relative Gibbs energies were computed with reference to the Gibbs energy of the most stable cyclic molecules in the corresponding series of alkanes. For alkenes, (E)-geometric isomers (low energy) were selected to compute their relative Gibbs energy and reaction energy. To confirm that the considered structures are the lowest energy conformers, we performed a GMMX (molecular mechanics force field) conformer search on 20 selected alkanes, alkenes, and alkyl radicals through the random rotor search using the Avogadro visualization program.19 Low energy structures predicted by the conformer search were then fully optimized using DFT (M062X) calculations. We note that in all cases the initially considered structures (built using Gaussview) were slightly lower in energy compared to the corresponding conformers generated by Avogadro, except for one instance, where the conformer generated by Avogadro was found to be isoenergetic B



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Figure 2. Hydrogen abstraction Gibbs energies of alkanes (via methyl radical) using (a) M06-2X (full data set), (b) M06-2X (selected data set), and (c) CBS-QB3 method on the same data of panel b. Cn indicates the alkane series. C8 (Full) is the full data set of C8 alkanes. Gibbs energies for the hydrogen abstraction reaction (in kJ/mol) of C8 series of alkanes are given in Table S5. Symbols: black dash, primary radical; cyan circle, secondary radical; red diamond, tertiary radical.

Table 1. Reaction Enthalpies (kJ/mol) of Simple Reactions Obtained Using the Computational Methods M06-2X and CBS-QB3 and Corresponding Experimental Values reaction •

CH2CH3 → CH2CH2 + H CH3CH3 → CH2CH3 + H• CH3CH2CH2 → CH3CHCH2 + H• CH3CHCH3 → CH2CHCH3 + H• CH3CH2CH3 → CH2CH2CH3 + H• CH3CH2CH2CH3 → CH2CH2CH2CH3 + H• CH3CH2CH2CH3 → CH3CHCH2CH3 + H• CH3C(CH3)2 → CH2C(CH3)2 + H CH2CH3 → CH2• + CH3• • CH2CH2CH3 → CH2CH2 + CH3• • CH2CH2CH2CH3 → CH2CH2 + •CH2CH3 CH3CH(CH3)2 → •CH3 + •CH2CHCH3 CH3CHCH2CH3 → •CH3 + •CH2CHCH3 a

experimentala

reaction enthalpy M06-2X

reaction enthalpy CBS-QB3

151.63 421.20 138.28 148.54 423.08 424.92 413.00 152.25 413.46 98.24 90.66 96.19 97.19

154.43 417.35 139.19 154.02 420.24 419.72 407.61 153.23 407.92 104.77 99.84 99.50 105.22

148.32 425.48 134.11 148.57 428.46 427.88 415.13 148.47 419.52 95.23 92.23 92.84 97.90

Experimental values obtained from ref 31.

show that the stability of radicals increases with the increase in the degree of alkyl substitution.26 3.2. Identifying a Suitable DFT Method for Radical Reactions. Extensive benchmarking of different DFT functionals suggested that M06-2X functional outperforms several other functionals for treating alkyl radicals.27 Consequently, we applied this method to calculate the hydrogen abstraction reactions of alkanes as shown in Figure 2a. Interestingly, we found that the radical abstraction Gibbs energies using M06-2X functional show significant spreading between primary,

secondary, and tertiary radicals (Figure 2a,b). However, based on the relative stability of different radicals, it is expected that the radical abstraction energies should follow a general trend relative to the degree of substitution of the radical center: primary < secondary < tertiary (in absolute values, favoring the formation of tertiary radicals). The accurate calculations of thermochemical quantities demand high-level quantum mechanical calculations which can account for electron correlation. However, such multireference methods (e.g., Configuration Interaction, CI) have a C



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significant computational cost. Alternatively, methods such as CBS-QB3, explicitly designed for thermochemical calculations, are shown to reach a similar chemical accuracy at a lower computational cost.18,28 Indeed, the mean absolute deviation for the CBS-QB3 method on the G2/97 set (contains 302 entries of experimentally well-established molecular properties such as enthalpies of formation, ionization potentials, electron affinities, etc.) was found to be ∼1 kcal/mol.29 Therefore, we employed the CBS-QB3 method on a selected data set of alkanes (alkenes and radicals) and on the full C8 series (C8 (Full), Figure 2c). The selected data set was created by including different primary, secondary, and tertiary structures with high and low relative energies in each series of alkanes. The selected alkanes (and radicals) and corresponding Gibbs energies are presented in Table S6. We noticed that the spreading of hydrogen abstraction Gibbs energies between primary secondary and tertiary radicals is significantly reduced at the CBS-QB3 level of theory (Figure 2c). It is important to note that both the M06-2X and CBS-QB3 methods show similar general trends in hydrogen abstraction energies within the same class of radicals (i.e., primary, secondary, and tertiary). In Figure S1 we compare the hydrogen abstraction Gibbs energies calculated with CBSQB3 and M06-2X methods for the C8 series of radicals. The difference in the values of hydrogen abstraction Gibbs energies obtained using the M06-2X functional and corresponding CBSQB3 values can be as large as 12 kJ/mol (Figure S1 and Table S5). The reaction Gibbs energies obtained using the CBS-QB3 method generally show a trend with the degree of substitution of corresponding product radicals: tertiary radical > secondary radical > primary radical (in absolute energy trends). To analyze the complex radical reactions with similar structures (and thus, with very low energy differences), high accuracy is desired. Therefore, to examine the accuracy of the adopted methods, we compared our results with available experimental data for simple reactions. Table 1 shows the experimental and calculated reaction enthalpies. It is clear from the table that the results obtained using both the M06-2X and CBS-QB3 methods are in agreement with the experimental data. However, the mean absolute error (MAE) for the M06-2X method (4.62 kJ/mol) was found to be slightly higher than the CBS-QB3 method (3.13 kJ/mol). Previous studies demonstrated that the difference in the alkane C−H bond dissociation energies (BDE) involved in the radical formation reaction gives a good estimate of the radical formation enthalpy.30 Therefore, to further assess the accuracy of our computational methods, we compared the calculated radical formation enthalpy with the experimental C−H BDE (relative to methane). Figure 3 shows a parity plot between the radical formation enthalpy and the experimental BDE (referenced to methane BDE) with the corresponding values being presented in Table S7. It can be noticed that the radical formation enthalpies obtained using the CBS-QB3 method are in better agreement with the experimental bond dissociation energies (relative), and show slightly lower MAE (4.6 kJ/mol) than the M06-2X method (6.8 kJ/mol). These results suggest that both the M06-2X and CBSQB3 methods offer good accuracy, but the CBS-QB3 outperforms the M06-2X for this class of reactions. 3.3. Reactions of Alkyl Radicals. First, we investigated the hydrogen abstraction reaction (by methyl radical) of different alkanes to yield methane and the corresponding radicals, using the M06-2X functional (Figure 2a). As previously discussed,

Figure 3. Comparison between calculated reaction enthalpies of hydrogen abstraction (at M06-2X and CBS-QB3 levels of theory) and experimental (relative) C−H bond dissociation energies (BDE). The corresponding values are presented in Table S7.

due to the very small differences in the reaction Gibbs energies of structurally similar alkanes, significant spreading between the reaction Gibbs energies of primary, secondary, and tertiary alkanes was observed. Therefore, the hydrogen abstraction reaction was investigated for alkanes of C8 series (full series) with the CBS-QB3 method (Figure 4), and the corresponding

Figure 4. Gibbs reaction energies of hydrogen abstraction of C8 series of alkanes using the CBS-QB3 method vs relative energies of the corresponding radicals. The corresponding Gibbs energy values are reported in Table S8.

values are reported in Table S8. We choose the C8 series to study the radical reactions because the alkanes of this series have hydrogen atoms with different degrees of substitution (primary, secondary, and tertiary) and various structurally distinct alkanes can be studied within this series. We distributed the alkanes (and radicals) of the C8 series in different structural classes, such as dimethylhexanes, methylheptanes, trimethylpentanes, etc., based on their degree of substitution. Subsequently, we calculated the hydrogen abstraction reaction Gibbs energies of these alkanes by abstracting the hydrogen atoms from primary, secondary, and tertiary carbon atoms to yield methane and the corresponding radicals. A good correlation between the relative radical Gibbs energies and hydrogen abstraction Gibbs energies was identified within each class of alkanes (Figure 4). The lowest quality of correlation between the hydrogen abstraction Gibbs energy and relative radical Gibbs energy was noted for dimethyl hexanes, because D



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of the high structural heterogeneity among the molecules of this class. Importantly, within each alkane class, the absolute hydrogen abstraction Gibbs energy was found to increase (more exothermic) with increasing degree of substitution of the corresponding radical center (i.e., primary radical < secondary radical < tertiary radical). It was noted that the degree of alkyl substitution of nonreacting carbon atoms also influences the hydrogen abstraction energy. For instance, the lowest absolute hydrogen abstraction energies (less exothermic) were found for neooctane, which has no tertiary carbon atom (has a quaternary carbon), and the highest absolute hydrogen abstraction energies (most exothermic) were found for 2,2,3-trimethylpentane, which has three tertiary carbon atoms. This effect can be attributed to the higher stabilization of alkanes with a high degree of alkyl substitution. These results indicate that the hydrogen abstraction Gibbs energy depends on both the nature of product radical and the structural class of the alkane. Figure 5

Figure 6. Gibbs reaction energies of alkene formation vs radical recombination of C1−C4 and C7−C8 alkyl radicals using the CBS-QB3 method. The corresponding energy values are given in Tables S10− S12.

alkene formation (points close to parity line show competition between the two reactions). A clear preference for radical recombination was noted over alkene formation (dehydrogenation). This preference for radical recombination was more pronounced for the radicals which form alkenes with a low degree of substitution (low stability) of the corresponding double bond. In most of the structural classes, two distinct clusters of alkene formation energies can be noticed (Figure 6) depending on the degree of substitution of reactant radical and the degree of substitution of the carbon bound to the abstracting hydrogen atoms. For instance, for the production of terminal disubstituted alkenes, the reactant radicals can be either primary or tertiary. The absolute alkene formation energies of the primary radicals of this class are higher (more exothermic) than that of the corresponding tertiary radicals (highlighted with yellow circles, Figure 6). This is because the production of alkenes (of this class) from primary radicals requires hydrogen abstraction from tertiary carbons, whereas the tertiary radicals require hydrogen abstraction from primary carbon. The competition between the radical recombination and alkene formation is pronounced (low Gibbs energy difference between the corresponding reactions) for the radicals which yield alkenes with a high degree of substitution (trisubstituted and tetra-substituted alkenes, blue and black circles, Figure 6). One exception for this general trend was noted for the radical which yields less-substituted alkene and shows preference for alkene formation (primary 3,3-dimethylpentyl radical, Figure 6). This exception could be attributed to the destabilization of the alkane (product formed by recombination) due to the steric effects of gem-dimethyl groups. Interestingly, only one cluster of alkene formation energies of a specific class of radicals was observed (orange circles, Figure 6), which forms disubstituted (nonterminal) alkenes, because the degree of substitution of both the reactant radicals and abstracting hydrogen is the same (secondary). These results demonstrate that the preference for alkene formation and radical recombination is determined by the degree of alkyl substitution of reactant radicals (relative stabilities) and alkene products. We summarize the thermodynamic analysis of the different reactions in Table 2. Notably, all the considered reactions are thermodynamically favorable, demonstrating the reactive nature of alkyl radicals. The similar Gibbs energy magnitude for radical recombination and alkene formation of radicals with a high

Figure 5. Gibbs reaction energy of alkene formation of C8 radical series vs relative energy of the corresponding radicals using CBS-QB3 method. The respective Gibbs energy values are tabulated in Table S9.

shows the reaction Gibbs energies of alkene formation (of the radicals of C8 series), plotted against the corresponding radical Gibbs energies (relative), and the respective values are tabulated in Table S9. It can be noticed that the reaction Gibbs energies of alkene formation are significantly more exothermic compared to the corresponding alkane hydrogen abstraction reaction energies (Figure 4). In general, the reaction Gibbs energy of alkene formation becomes more exothermic (negative) with increasing relative radical Gibbs energy. However, for this reaction, no clear trend was noted within different structural classes of alkenes. Radical recombination and alkene formation are competing reactions. Therefore, to understand the thermodynamic preference of radical recombination vs alkene formation, we investigated both of these reactions for small (C1−C4) and medium-sized (C7−C8) radicals with the CBS-QB3 level of theory (the corresponding values are given in Tables S10− S12). First, we categorized the radicals based on the substitution degree of the alkene products, such as di-, tri-, terta-substituted alkenes, as well as terminal and nonterminal alkenes. Subsequently, we plotted the alkene formation Gibbs energy against the recombination reaction Gibbs energy of the corresponding radical. Figure 6 shows a parity plot of alkene formation Gibbs energy vs the Gibbs energy of the corresponding radical recombination reaction. Points below the parity line show a preference for radical recombination, whereas points above the parity line show a preference for E



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3.4. Kinetics of Hydrogen Abstraction and Alkene Formation. To investigate the kinetics of hydrogen abstraction and alkene formation reaction, we identified the transition states (TS) and computed the reaction barriers of these reactions on different carbon atoms of 2,3-dimethylhexane using the M06-2X DFT functional. The selection of 2,3dimethylhexane to study the kinetics was based on the availability of the different nature of hydrogen atoms (bound to carbons of different substitution). Figure 7 shows the Gibbs energy profiles of alkene formation and hydrogen abstraction reaction through the abstraction of hydrogens (by methyl radical) bound to primary, secondary, and tertiary carbon atoms. It was noted that the hydrogen abstraction Gibbs energies become more exothermic (negative) with increasing degree of substitution of product radical center, whereas, the reaction barriers decrease, demonstrating a Bronsted−Evans− Polanyi (BEP)-type of relationship.32−34 Specifically, the absolute reaction Gibbs energies of hydrogen abstraction follow the trend as primary radical (−16.07 kJ/mol, Figure 7a) < secondary radical (−26.96 kJ/mol, Figure 7b) < tertiary radical (−38.48 kJ/mol, Figure 7c) and the hydrogen abstraction barriers follow an inverse trend as primary radical (73.8 kJ/mol, Figure 7a) > secondary radical (63.07 kJ/mol, Figure 7b) > tertiary radical (49.4 kJ/mol, Figure 7c). For the alkene formation reaction, similar trends were noted. The

Table 2. Alkyl Radicals, Thermodynamic Preference and Comparison of Different Reactions ofGibbs Energy ΔG range reaction

reactant

hydrogen abstraction

alkane-A + methyl radical radical A + methyl radical radical A + radical B

radical recombination alkene formation

thermodynamic preference

CBS-Q3 (kJ/mol)

radical-A + methane

slightly favorable

−13 to −60

alkane

highly favorable

−290 to −325

alkene

highly favorable

−270 to −315

product

degree of alkyl substitution suggest that both these reactions compete in these radicals. In general, the radicals with a low degree of alkyl substitution show preference for radical fomation. It should be noted that the results presented in Figure 6 (and Table 2) are obtained at 298 K. We note that the relative preference for alkene formation versus radical recombination (competing reactions) can change at high temperature. Our calculations showed that at 500 °C the alkene formation becomes highly preferred over radical recombination (Figure S2), due to entropic contributions.

Figure 7. Gibbs energy profiles of hydrogen abstraction (at M06-2X level) on a (a) primary, (b) secondary, and (c) tertiary carbon. Gibbs energy profile of alkene formation reaction on (d) primary, (e) secondary, and (f) tertiary carbon. F



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absolute reaction Gibbs energies increase with the degree of substitution of the carbon (except for the tertiary carbon) atom bound to the reacting hydrogen atom: secondary carbon (−281.47 kJ/mol, Figure 7d) > tertiary carbon (−272.95 kJ/ mol, Figure 7f) > primary carbon (−268.8 kJ/mol, Figure 7e). An anomalous behavior due to the tertiary carbon center was noted and can be attributed to the steric effects of the tertiary substituents. The barriers for alkene formation decrease with the degree of substitution of corresponding carbon atoms. Specifically, the highest barrier was found for the reaction involving the hydrogen atom bound to the primary carbon (71 kJ/mol, Figure 7d), followed by the hydrogen bound to secondary carbon (61.3 kJ/mol, Figure 7e), and the lowest barrier was found for the reaction involving the hydrogen atom bound to the tertiary carbon (48.4 kJ/mol, Figure 7f). We note that for our model system, the Gibbs energy barriers for hydrogen abstraction and alkene formation are found to be low and in a similar energy range (48−75 kJ/mol). To determine the accessibility (under dehydrogenation conditions) of the computed barriers, we employed Eyring’s equation (from transition state theory) to compute the rate constant (turnover frequency): k=

kBT −Ea / RT e h

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Mudit Dixit: 0000-0001-9456-7806 Giannis Mpourmpakis: 0000-0002-3063-0607 Author Contributions

G.M. and M.D. designed the research and supervised the work. J.W.E. performed all the theoretical calculations. Funding

The Donors of the American Chemical Society Petroleum Research Fund (ACS-PRF, 56989-DNI5) are acknowledged for support of this research. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank the Center for Research Computing (CRC) at the University of Pittsburgh for computational support.

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REFERENCES

(1) Sattler, J. J.; Ruiz-Martinez, J.; Santillan-Jimenez, E.; Weckhuysen, B. M. Catalytic Dehydrogenation of Light Alkanes on Metals and Metal Oxides. Chem. Rev. 2014, 114, 10613−10653. (2) Market Study: Propylene, 2nd ed. http://www.ceresana.com/en/ market-studies/chemicals/propylene/ (September 10, 2017). (3) Cavani, F.; Trifiro, F. The Oxidative Dehydrogenation of Ethane and Propane as an Alternative Way for the Production of Light Olefins. Catal. Today 1995, 24, 307−313. (4) Coperet, C. C− H Bond Activation and Organometallic Intermediates on Isolated Metal Centers on Oxide Surfaces. Chem. Rev. 2009, 110, 656−680. (5) Lunsford, J. H. The catalytic oxidative coupling of methane. Angew. Chem., Int. Ed. Engl. 1995, 34, 970−980. (6) Driscoll, D. J.; Martir, W.; Wang, J. X.; Lunsford, J. H. Formation of Gas-Phase Methyl Radicals Over Magnesium Oxide. J. Am. Chem. Soc. 1985, 107, 58−63. (7) Latimer, A. A.; Kulkarni, A. R.; Aljama, H.; Montoya, J. H.; Yoo, J. S.; Tsai, C.; Abild-Pedersen, F.; Studt, F.; Nørskov, J. K. Understanding Trends in CH Bond Activation in Heterogeneous Catalysis. Nat. Mater. 2017, 16, 225−229. (8) Latimer, A. A.; Aljama, H.; Kakekhani, A.; Yoo, J. S.; Kulkarni, A.; Tsai, C.; Garcia-Melchor, M.; Abild-Pedersen, F.; Norskov, J. K. Mechanistic insights into heterogeneous methane activation. Phys. Chem. Chem. Phys. 2017, 19, 3575−3581. (9) Aljama, H.; Nørskov, J. K.; Abild-Pedersen, F. Theoretical Insights into Methane C−H Bond Activation on Alkaline Metal Oxides. J. Phys. Chem. C 2017, 121, 16440−16446. (10) Varghese, J. J.; Mushrif, S. H. Insights into the C−H Bond Activation on NiO Surfaces: The Role of Nickel and Oxygen Vacancies and of Low Valent Dopants on the Reactivity and Energetics. J. Phys. Chem. C 2017, 121, 17969−17981. (11) Dickens, K. A.; Stair, P. C. A study of the Adsorption of Methyl Radicals on Clean and Oxygen-Modified Ni (100). Langmuir 1998, 14, 1444−1450. (12) Baker, R.; Baldwin, R.; Walker, R. Alkene Formation in Hydrocarbon Oxidation; Elsevier: Amsterdam, 1977. (13) Toledo, J.; Armendariz, H.; Lopez-Salinas, E. Oxidative Dehydrogenation of n-butane: a Comparative Study of Thermal and Catalytic Reaction Using Fe−Zn Mixed Oxides. Catal. Lett. 2000, 66, 19−24. (14) Arutyunov, V.; Strekova, L.; Nikitin, A. Partial Oxidation of Light Alkanes as a Base of New Generation of Gas Chemical Processes. Eurasian Chem.-Technol. J. 2015, 15, 265−273.

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We note that for activation Gibbs energies (Ea) lower than 80 kJ/mol, turnover frequencies are found to be significantly higher than 1 s−1 at 500 °C. These calculations confirm that radical abstraction reactions (Ea < 80 kJ/mol) via the methyl radical are not limited by kinetics.

4. CONCLUSIONS In summary, we investigated the stability (relative Gibbs energy) of a number of alkanes, alkenes, alkyl radicals, and their corresponding gas phase reactions using electronic structure calculations. On the basis of our calculated reaction Gibbs energy, we unraveled the reaction preference of alkyl radicals based on the structure of corresponding products. Our results demonstrated that the alkene formation can be preferred over radical recombination at high temperatures, whereas radical recombination is preferred at 298 K. We identified a good correlation between the hydrogen abstraction Gibbs energies and relative Gibbs energies of alkyl radicals of a given structural class of alkanes. Moreover, we demonstrated that highly accurate computational methods are essential to probe the chemistry of alkyl radicals. Finally, the large number of chemical reaction energy data as well as the energy trends presented in this study can aid in optimizing the gas phase side reactions of different chemical processes of industrial relevance involving alkyl radicals.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00992. Relative Gibbs energies, reaction Gibbs energies, and total energies of alkanes, alkyl radical, and alkenes; hydrogen abstraction Gibbs energies of alkanes; reaction Gibbs energies of alkene formation and radical recombination reaction at 500 °C (PDF) G



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Understanding the Gas Phase Chemistry of Alkanes with First

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