Article pubs.acs.org/JPCA
Reaction Mechanism and Product Branching Ratios of the CH + C3H8 Reaction: A Theoretical Study Joao Marcelo Ribeiro and Alexander M. Mebel* Department of Chemistry and Biochemistry, Florida International University, Miami, Florida 33199, United States ABSTRACT: The C4H9 potential energy surface accessed by the reaction of methylidyne radical, CH (X2Π), with propane, C3H8, including possible intermediates, transition states and dissociation products, has been studied by ab initio and density functional calculations at the CCSD(T)/CBS//B3LYP/6-311G(d,p) level of theory. The computed relative energies and molecular parameters were utilized to calculate collision-energy-dependent unimolecular rate constants at the zero-pressure limit for isomerization and dissociation channels of the C4H9 adducts formed in the entrance reaction channels. The rate constants were used to evaluate the product branching ratios in the CH + C3H8 reaction under single-collision conditions. The results show that the reaction can produce mostly ethene (C2H4) + ethyl radical (C2H5) and propene (C3H6) + methyl radical (CH3), and up to 14% of various butene isomers (C4H8) + H. The product branching ratios are sensitive to the initial reaction adduct (a butyl radical, C4H9) formed in the entrance channels via barrierless insertion of the CH radical into the terminal and middle C−H bonds of propane or, possibly, into the single C−C bonds. A more definite answer on relative contributions of various available CH insertion channels can be obtained through ab initio quasiclassical trajectory calculations, which are proposed for the future. The results allowed us to conclude that the CH + C3H8 reaction does not result in major amounts in the direct growth of the carbon-skeleton to four-carbon C4H8 products via the CH-for-H exchange because C−C bond cleavages in C4H9 radicals are generally more preferable than C−H bond cleavages.
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INTRODUCTION Elucidation of chemical reactions driving the growth of hydrocarbon molecules in Titan’s atmosphere has attracted numerous experimental and theoretical investigations due to possible similarities of Titan’s atmospheric processes with those that took place in the atmosphere of primordial Earth. With the photoirradiation of methane, which comprises 1.5−5% of Titan’s atmosphere,1 reactive radical species such as CH3, CH2, and CH are formed,2 thus “kick-starting” the formation of longer carbon skeletons. Despite comprising about 7% of the Lyman-α photodissociation products,3 the ground-state CH radical (X2Π) is the most reactive, being able to react with both closed-shell species as well as open-shell species, thus making it important in the chemical evolution of Titan’s atmosphere. Also, Pluto’s atmosphere is believed to be abundant in methane and hence is expected to have an effective hydrocarbon chemistry, whose detailed growth processes are largely unknown.4,5 Lara et al.6 concluded that Pluto’s atmosphere presents a rich reservoir of complex hydrocarbons but there are many major uncertainties in Pluto’s atmospheric models, which makes it necessary to investigate the growth of hydrocarbons in Pluto’s atmosphere from the “bottom up” starting with reactions of the simplest and most important radical growth species, methylidyne (CH), with the main atmospheric hydrocarbon constituent (C1−methane) via smaller hydrocarbons (C2) to more complex systems (C3). Although there are still issues to be resolved in the investigation of the reactions between the CH radical (X2Π) with C1 and C2 hydrocarbons, numerous experimental and © 2014 American Chemical Society
theoretical studies of differing levels of emphasis and scope have been performed on these systems.7−20 The reactions between CH (X2Π) and C3 hydrocarbons have been studied in much less detail, however, despite the fact that propane (C3H8) exists in greater amounts than ethene with its abundance in Titan’s atmosphere being within 1 order of magnitude of that for ethyne.21 C3H8 reactions with other chemical species are believed to be important in driving forward the growth of carbon molecules on Titan. For instance, the reactions with C2H and C4H have been studied experimentally at low temperatures and their overall rate constants have been determined.22−24 Meanwhile, the literature on the CH (X2Π) reaction with C3H8 is scarce, as only a room temperature experiment measuring its overall rate constant and branching ratios of various products has been reported.25 In this article by Loison et al., a partial theoretical investigation was included to provide a comparison with the experimental H atom branching ratio; however, no details of the reaction potential energy surface (PES) were given. Our work in the present paper seeks to expand this initial investigation by describing in detail all of the relevant portions of the C4H9 PES needed to determine the unimolecular reaction rate constants for isomerization and Special Issue: International Conference on Theoretical and High Performance Computational Chemistry Symposium Received: February 28, 2014 Revised: May 21, 2014 Published: May 22, 2014 9080
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Figure 1. Potential energy diagram of the CH + C3H8 reaction calculated at the CCSD(T)/CBS//B3LYP/6-311G(d,p) + ZPE(B3LYP/6311G(d,p)) level of theory. Relative energies of various species are shown in kcal/mol.
performed for single-collision conditions relevant to very low pressures of the upper Titan’s atmosphere or Pluto’s atmosphere and for comparison with future crossed molecular beam experiments. The relevant RRKM equation from which we extract the rate constant at a given internal energy, E, is the following:
decomposition of various butyl radicals and product branching ratios in the CH (X2Π) + C3H8 reaction.
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CALCULATION METHODS The geometries of reactants, transition states, and isomers were optimized using the Gaussian 09 software.26 The B3LYP hybrid density functional method27,28 was used with the 6-311G(d,p) basis set.29 Because B3LYP is known, however, to sometimes underestimate reaction barriers, geometries that did not converge were further investigated at the QCISD level using the 6-311G (d,p) basis set as well. The QCISD structures included in this investigation are two transition states describing H-loss from a CH3 group (namely, TSh and TSl) and the rotational barrier for interconverting trans- and cis-2butyl radical isomers (TSm). Lastly, the cis-2-butyl radical was also found only using QCISD. To characterize the nature of the stationary points, harmonic frequencies of all optimized structures were calculated. These also yielded zero-point energy corrections (ZPE) for all species. All harmonic frequencies were calculated at the B3LYP level except for the four structures described above, whose frequencies were calculated at the QCISD level. The QCISD level ZPE were scaled with the use of the factor 0.9812.30 To refine the energies of all B3LYP and QCISD minima and transition states, the Molpro 2010 package was used.31 This refinement was achieved through a three-point complete basis set extrapolation32 using Dunning’s cc-pVnZ basis sets (in particular, cc-pVDZ, cc-pVTZ, and cc-pVQZ)33 at the CCSD(T) level.34 Rice−Ramsperger−Kassel−Marcus (RRKM)35 theory was used to calculate the relevant unimolecular rate constants for isomerization and dissociation of C4H9 radicals, which can be produced in the CH + C3H8 reactions. The calculations were
k(E) =
σW ‡(E − E‡) hρ(E)
where σ is the degeneracy of the reaction path, h is Planck’s constant, W‡(E − E‡) is the total number of states for the transition state and ρ(E) represents the density of states of the energized reactants. The internal energy E was taken as a sum of the energy of chemical activation in the CH + C3H8 reaction and a collision energy, assuming that a dominant fraction of the latter is converted to the internal vibrational energy. The calculated harmonic frequencies were used to determine the total numbers and densities of states. Product branching ratios were evaluated by solving first-order kinetic equations for unimolecular reactions within the steady-state approximation, according to the kinetics schemes based on the ab initio potential energy diagrams.
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RESULTS AND DISCUSSION A small portion of the C4H9+ PES that was relevant to the C2H3+ + C2H6 reaction has been mapped in the past.36 Here we deal with the neutral surface, and Figure 1 illustrates the potential energy diagram of the channels relevant to the CH + C3H8 reaction. From the previous experimental and theoretical studies of CH reactions with C1 and C2 hydrocarbons,7−20,25 it is known that the methylidyne radical can insert into C−H bonds or add to double and triple C−C bonds, with all these processes being barrierless and hence occurring very fast (with 9081
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rate constants in the range of 10−10 cm3 molecule−1 s−1 close to the collision kinetics limit) even at temperatures as low as 23 K; the CH + C3H8 reaction rate constant has been measured to be similarly high at 300 K.25 A barrierless insertion of CH into a single C−C bond was also considered as a possible entrance reaction channel, but Galland et al.20 suggested that such insertion for the C2H6 reaction may be sterically hindered and later, on these grounds, was ruled out by Loison et al.25 for CH reactions with larger alkanes. Nevertheless, here we do not exclude this possibility, at least in principle, and hence for our reacting system we consider three initial bimolecular entrance channels, namely, CH insertion into a C−C single bond (C−C insertion) leading to the trans-2-butyl radical, CH insertion into a terminal carbon−hydrogen single bond (terminal C−H insertion) leading to the 1-butyl radical and CH insertion into a middle carbon−hydrogen bond (middle C−H insertion) leading to the isobutyl radical. No transition states were found for any of these three entrance channel, suggesting that all of them are barrierless. To confirm this, we have mapped the minimum energy path for both C−H insertion channels and, as is illustrated by Figures 2 and 3, these channels are indeed Figure 3. Minimal energy profile for barrierless terminal C−H insertion by the methylidyne radical calculated at the B3LYP/6311G(d,p) level of theory. The surface shown in the bottom panel was produced to model a smooth and continuous H-migration from terminal carbon of propane to the methylidyne carbon.
bottom panels combined show the barrierless insertion paths of CH into CH bonds of the CH2 (Figure 2) or CH3 (Figure 3) groups of propane. As for the case of C−C insertion, we were not able to identify a descending minimal energy pathway, as the paths leading to the insertion into a CC bond intermingle with C−H insertion paths. This issue requires further investigation and the relative importance of the different C− C and C−H insertions can in principle be evaluated using ab initio calculations of quasiclassical trajectories in the entrance channels, but these time-consuming dynamics calculations are beyond the scope of the present study. Here we assume that all three channels including the C−C insertion can contribute and defer further discussion on the effect of their relative contributions on the product branching ratios until the latter stages of the article. The C−C insertion adduct, the trans-2-butyl radical, appears to be the thermodynamically favored adduct. The terminal C− H insertion produces the 1-butyl radical and is thermodynamically least favorable, whereas the central C−H insertion gives the isobutyl radical, which is less stable than trans-2-butyl but more stable than 1-butyl. Nevertheless, all three initial adducts reside in a narrow energy range between −99.4 and −96.7 kcal/ mol relative to the initial reactants. All optimized transitionstate structures are shown in Figure 4. The trans-2-butyl radical can isomerize to the 1-butyl radical through a 1,2-H shift (via TSa) or through a 2,4-H shift (via TSb), although the barrier associated with the latter H-shift is ∼1 kcal/mol higher. The trans-2-butyl radical adduct can also isomerize to the isobutyl radical through a 2,3-CH3 shift (via TSc) but the corresponding barrier is greater than its H-shift barriers by ∼20 kcal/mol. There is a small rotational barrier (TSm) that separates the trans- and cis 2-butyl radicals. As for the 1-butyl radical, there does not exist a direct connection for its rearrangement to the isobutyl radical and, in fact, it cannot isomerize to any other low-energy species except the trans-2-butyl radical. Finally, through a 1,2-H shift (via TSd) the isobutyl radical can form
Figure 2. Minimal energy profile for barrierless middle C−H insertion by the methylidyne radical calculated at the B3LYP/6-311G(d,p) level of theory. Although not included, the curve shows a large discontinuity after 2.20 Å due to the sudden geometrical rearrangement stemming from “complete” H-migration. The surface shown in the bottom panel was produced to model a smooth and continuous H-migration from the middle carbon of propane to the methylidyne carbon.
proved to be barrierless. The top panel on each figure shows the minimal energy profile as a function of the CC distance between the carbon atom of CH and the attacked carbon of C3H8. One can see that the energy steadily declines as the CC distance decreases from 3.0 to 2.3 Å. In the interval of CC = 2.1−1.9 Å, the attacked CH bond breaks and its hydrogen atom essentially migrates from a CH2 or CH3 group of propane to the carbon atom of the CH radical. A monotonous energy descent during this process is illustrated in the lower panels of Figures 2 and 3, where the energy is shown as a function of two internal coordinates, the CC distance and the CH distance of the bond in propane, which is being cleaved. The top and 9082
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Figure 4. Optimized transition-state structures. Critical bond lengths are shown in Ångstroms.
the most stable C4H9 isomer, the tert-butyl radical, and this occurs with the lowest isomerization barrier of 36.0 kcal/mol. Comparison of the calculated energies for the adducts with experimental data37,38 is shown in Table 1, where available, showing that the smallest absolute deviation of 1.1 kcal/mol is for the trans-2-butyl radical and the highest absolute deviation of 2.4 kcal/mol is for the tert-butyl radical. The unimolecular rate constants for the isomerization reactions are included in Table 2 at both 0 and 1 kcal/mol collision energies, which are relevant to the temperature range 0−335 K. This temperature range covers the reaction conditions from those typical for the interstellar medium to planetary atmospheres (Pluto and Titan) to ambient conditions. Just about all of the rate constants reflect what is to be expected from the energetics of the PES in Figure 1, showing that rotation takes place much quicker than all the different H-shifts and that CH3 migration is much slower than the all H-shifts. The fact that tert-butyl radical isomerization to the isobutyl radical is comparable in rate to its “forward” reaction can in large part be attributed to the highly symmetric nature of the tert-butyl radical as a reacting species. The PES shows that, in general, the H-loss channels are both kinetically and thermodynamically unfavorable relative to their
Table 1. Relative Energies of Various Reaction Intermediates and Products Calculated at the CCSD(T)/CBS//B3LYP/6311G(d,p) + ZPE(B3LYP/6-311G(d,p)) Level of Theory and from Experimental Thermochemical Data, All in kcal/ mol species
ΔEcalc
ΔEexp
2-butyl radical 1-butyl radical isobutyl radical tert-butyl radical propene (C3H6) + CH3 ethene (C2H4) + C2H5 1-butene + H trans-2-butene + H cis-2-butene + H isobutene + H n-propyl + CH2(3B1) isopropyl + CH2(3B1)
−99.4 −96.7 −98.0 −103.1 −77.1 −75.2 −64.6 −67.4 −66.2 −68.6 0.4 −2.6
−100.5 N/A −100.2a −105.5a −77.3b −76.1b −65.1b −67.5b −66.7b −69.2b −0.5a −2.7a
absolute deviation a
1.1 2.2 2.4 0.2 0.9 0.5 0.1 0.5 0.6 0.9 0.1
a
Computed from room temperature enthalpies of formation from ref 37. bComputed from 0 K enthalpies of formation from ref 38.
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from tert-butyl radical. The barrier heights for these two channels are 34.6 kcal/mol (TSj) and 36.1 kcal/mol (TSl), respectively. The relative energies of all products have also been compared to experimental data, as can be seen in Table 1, and the agreement is better than that of adducts as the largest absolute deviation, for ethene + ethyl radical, is below 1 kcal/ mol. Table 2 shows the unimolecular rate constants for these different product formation channels at collision energies of 0 and 1 kcal/mol. Absent from the above discussion (and calculations) are the direct H-abstraction channels leading to either isopropyl radical + methylene or n-propyl radical + methylene. These reactions are slightly exothermic or nearly isoergic in nature and in principle might be relevant in the interstellar medium and under Titan or Pluto atmospheric conditions and also in combustion. For instance, the isopropyl radical + methylene products together are 2.6 kcal/mol lower in energy than the reactants, whereas the n-propyl radical + methylene are 0.4 kcal/mol higher in energy than CH + C3H8. However, a careful search of direct H-abstraction transition states has failed; a transition state for either of these reactions could not be located as different starting geometries tended to lead to dissociated reactants or toward the insertion reaction channel. This result can be attributed to the fact that the insertion channels are much more favorable energetically and, hence, no pathways to the direct H-abstraction products going from the reactants via a first-order saddle point exist; when a CH radical approaches propane, it tends to insert into CH or CC bonds rather than to abstract a hydrogen atom. The formal H abstraction products, isopropyl + methylene and n-propyl + methylene, can be formed by cleavage of a CH2 group from isobutyl and 1-butyl radicals, respectively. However, these dissociation channels are much less favorable as compared to H, CH3, and C2H5 eliminations from these radicals and therefore are not anticipated to be competitive. Tables 3 and 4 contain the product branching ratios for CH + C3H8 at 0 and 1 kcal/mol collision energies, the 0 kcal/mol collision energy being relevant to Titan and Pluto atmospheric conditions and the 1 kcal/mol collision energy being included to aid comparison to the room temperature experiment discussed in ref 25. In both tables columns two through four are the percentages of products formed should all CH + C3H8 reacting systems proceed exclusively along the one entrance channel indicated. Columns five and six, meanwhile, average the product yields of the different entrance channels, giving equal weight to all single bonds available for CH radical to insert into (two C−C, six terminal C−H, and two central C− H), but differ in that column five assumes that the C−C insertion is viable whereas column six assumes that the C−C insertion does not contribute. In all cases the formation of carbon chains smaller than four carbons in length (via a C−C bond cleavage in the C4H9 radicals) will dominate over the
Table 2. Energy-Dependent Unimolecular Rate Constants Calculated Using RRKM Theory under Single-Collision Conditions at Collision Energis of 0 and 1 kcal/mol k (s−1), 0 kcal/mol
reaction trans-2-butyl radical → 1-butyl radical 1-butyl radical → trans-2-butyl radical trans-2-butyl radical → isobutyl radical isobutyl radical → trans-2-butyl radical trans-2-butyl radical → cis-2-butyl radical cis-2-butyl radical → trans-2-butyl radical isobutyl radical → tert-butyl radical tert-butyl radical → isobutyl radical trans-2-butyl radical → propene + CH3 trans-2-butyl radical → 1-butene + H trans-2-butyl radical → trans-2-butene +H 1-butyl radical → ethene + C2H5 1-butyl radical → 1-butene + H isobutyl radical → propene + CH3 isobutyl radical → isobutene + H tert-butyl radical → isobutene + H cis-2-butyl radical → cis-2-butene + H
1.11 2.55 6.39 5.25 1.56
× × × × ×
k (s−1), 1 kcal/mol
109 109 105 106 1012
1.22 2.76 7.53 6.17 1.56
2.59 × 1012
× × × × ×
109 109 105 106 1012
2.59 × 1012
2.02 2.88 4.52 6.21 9.81
× × × × ×
109 109 1010 109 109
2.17 3.12 4.81 6.73 1.06
× × × × ×
109 109 1010 109 1010
1.45 1.28 1.01 4.93 6.61 1.57
× × × × × ×
1011 1010 1011 109 1010 1010
1.55 1.40 1.09 5.32 7.12 1.70
× × × × × ×
1011 1010 1011 109 1010 1010
methyl/ethyl-loss counterparts. The formation of propene and methyl radical can occur via two low barrier CH3-loss channels, one resulting from the chain trans-2-butyl radical (via TSe) and another from the branched isobutyl radical (via TSf). The barrier heights for both CH3-loss channels are approximately equal, 31.2 and 31.5 kcal/mol. Through the breaking of its middle C−C single bond the 1-butyl radical can lead to the formation of ethene and ethyl radical, a channel that proceeds through TSg and with the associated barrier height of 30.2 kcal/mol. Due to the fact that the 1-butyl radical is a terminal radical, it has one possible H-loss channel leading to the formation of 1-butene and H atom although the barrier that must be overcome along this reaction path is 36.4 kcal/mol (TSi). The trans-2-butyl radical, however, because of its internal radical location, can proceed along two possible H-loss channels, terminal H-loss and internal H-loss. Terminal Hloss proceeds through the transition structure TSh with a barrier height of 37.1 kcal/mol and also leads to 1-butene and H atom. Internal H-loss, which is the kinetically favored trans-2butyl radical H-loss channel, proceeds through TSn with its barrier being 34.9 kcal/mol and leads to the trans-2-butene and H atom products. The formation of cis-2-butene and H atom proceeds through a slightly higher barrier of 35.6 kcal/mol (TSo) and is thermodynamically unfavorable by 1 kcal/mol relative to its trans counterpart. Finally, the formation of the most stable H-loss products, isobutene and H atom, can take place via two channels, H-loss from isobutyl radical and H-loss
Table 3. Product Branching Ratios Calculated at Zero Collision Energy products
C−C insertion
terminal C−H insertion
mid C−H insertion
net (including C−C insertion)
net (excluding C−C insertion)
propene + methyl radical ethene + ethyl radical 1-butene + H trans-2-butene + H cis-2-butene + H isobutene + H
63.03 1.40 8.78 13.68 13.11 0.00
1.00 90.47 8.10 0.22 0.21 0.00
93.64 0.00 0.00 0.00 0.00 6.36
31.93 54.56 6.62 2.87 2.75 1.27
24.15 67.85 6.08 0.17 0.16 1.59
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Table 4. Product Branching Ratios Calculated at the Collision Energy of 1 kcal/mol products
C−C insertion
terminal C−H insertion
mid C−H insertion
net (including C−C insertion)
net (excluding C−C insertion)
propene + methyl radical ethene + ethyl radical 1-butene + H trans-2-butene + H cis-2-butene + H isobutene + H
62.63 1.43 8.89 13.80 13.25 0.00
1.01 90.28 8.27 0.22 0.22 0.00
93.64 0.00 0.00 0.00 0.00 6.36
31.87 54.45 6.74 2.89 2.78 1.27
24.17 67.71 6.20 0.17 0.17 1.58
growth of the carbon skeleton via the CH-for-H exchange does not take place in major amounts because four-carbon hydrocarbon products (various C4H8 butene isomers) that are formed are likely to comprise only between 8% and 14% of the total products. Both three-carbon (propene C3H6 along with the methyl radical CH3) and two-carbon hydrocarbons (ethene plus ethyl radical) will dominate the product formation, making up over 86% of products. The reaction outcome appears to be sensitive to the branching of the reaction flux in the entrance channels where barrierless insertions of CH into terminal and mid C−H bonds are expected to compete with each other and possibly with the C− C insertion.
formation of butenes + H, as can be expected from the H-loss barrier heights described by the PES. For instance, the terminal C−H insertion should result in the preferable formation of ethene + ethyl radical, whereas the mid C−H insertion and the C−C insertion (to a lesser extent) favor the formation of propene + methyl radical. The inclusion of the C−C insertion in the product branching ratio calculations does cause the Hloss channels (carbon-skeleton growth channels) to factor in at close to double their overall branching ratio as opposed to when it is not included, driving down formation of propene and methyl radical as well as ethene and ethyl radical by a combined amount of about 6%. This inclusion results in the H-loss products making up 13.51% of the products at 0 kcal/mol collision energy and 13.68% of the products at 1 kcal/mol collision energy. The exclusion of the C−C insertion channel causes the H-loss to have a diminished role in product formation, driving the H-loss products to make up only 8.00% of products at 0 kcal/mol collision energy and 8.12% at 1 kcal/ mol collision energy. It is possible that steric hindrance of C−C insertion might reduce the rate of formation of bimolecular C− C insertion adducts while not necessarily excluding them completely from participation, in which case the H-loss product branching ratio is likely to fall between the ranges described above when the proper weights are assigned to the channels. The experimental value of the H-loss product branching ratio is 19 ± 7%, however, so that inclusion of C−C insertion into calculations makes the H atom production fall within the experimental result. Loison et al.25 attributed the fact that the experimental H atom yield is higher than their theoretical value computed with exclusion of the C−C insertions to secondary prompt decomposition of the C2 H 5 product at their experimental condition. Alternatively, we can see that the experimental H atom yield can be explained if the C−C insertion is included. A more definite answer on the relative contributions of various available CH insertion channels can be obtained through ab initio quasiclassical trajectory calculations, which are planned for the future. Experimentally, it would be useful to carry out this reaction in crossed molecular beams under single-collision conditions where only primary reaction products can be observed and thus the elementary reaction outcome could be further elucidated and compared with the theoretical branching ratios.
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AUTHOR INFORMATION
Corresponding Author
*A. M. Mebel: e-mail, mebela@fiu.edu; telephone, +1-305-3481945. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported in part by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Sciences of U.S. Department of Energy (Grant No. DE-FG02-04ER15570).
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REFERENCES
(1) Raulin, F.; Brasse, C.; Poch, O.; Coll, P. Prebiotic-like Chemistry on Titan. Chem. Soc. Rev. 2012, 41, 5380−5393. (2) Atreya, S. K.; Adams, E. Y.; Niemann, H. B.; Demick-Montelara, J. E.; Owen, T. C.; Fulchignoni, M.; Ferri, F.; Wilson, E. H. Titan’s Methane Cycle. Planet. Space Sci. 2006, 54, 1177−1187. (3) Gans, B.; Boye-Peronne, S.; Broquier, M.; Delsaut, M.; Douin, S.; Fellows, C. E.; Halvick, P.; Loison, J.; Lucchese, R. R.; Gauyacq, D. Photolysis of Methane Revisited at 121.6 nm and at 118.2 nm: Quantum Yields of the Primary Products, Measured by Mass Spectrometry. Phys. Chem. Chem. Phys. 2011, 13, 8140−8152. (4) Krasnopolsky, V. A. Middle Ultraviolet Spectroscopy of Pluto and Charon. Icarus 2001, 153, 277−284. Krasnopolsky, V. A. Titan’s Photochemical Model: Further Update, Oxygen Species, and Comparison with Triton and Pluto. Planet. Space Sci. 2012, 73, 318−326. (5) Krasnopolsky, V. A.; Cruikshank, D. P. Photochemistry of Pluto’s Atmosphere and Ionosphere near Perihelion. J. Geophys. Res.: Planets 1999, 104, 21979−21996. (6) Lara, L. M.; Ip, W. H.; Rodrigo, R. Photochemical Models of Pluto’s Atmosphere. Icarus 1997, 130, 16−35. (7) Canosa, A.; Sims, I. R.; Travers, D.; Smith, I. W. M.; Rowe, B. R. Reactions of the Methylidine Radical with CH4, C2H2, C2H4, C2H6, and But-1-ene Studied between 23 and 295 K with a CRESU Apparatus. Astron. Astrophys. 1997, 323, 644−651. (8) Maksyutenko, P.; Zhang, F.; Gu, X.; Kaiser, R. I. A Crossed Molecular Beam Study on the Reaction of Methylidyne Radicals
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CONCLUSIONS The C4H9 potential energy surface accessed via the reaction of methylidene radical with propane, including possible intermediates, transition states, and dissociation products, was studied by ab initio and density functional calculations. Unimolecular rate constants for the isomerization and dissociation channels of the C4H9 adducts formed in the entrance reaction were calculated under single-collision conditions (zero-pressure limit) and were used to evaluate the product branching ratios. The results show that the direct 9085
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[CH(X2Π)] with Acetylene [C2H2(X1Σg+)] − Competing C3H2 + H and C3H + H2 Channels. Phys. Chem. Chem. Phys. 2011, 13, 240−252. (9) Zhang, F.; Maksyutenko, P.; Kaiser, R. I. Chemical Dynamics of the CH(X2Π)+C2H4(X1A1g), CH(X2Π) +C2D4(X1A1g) and CD(X2Π) +C2H4(X1A1g) Reactions Studied under Single Collision Conditions. Phys. Chem. Chem. Phys. 2012, 14, 529−537. (10) Goulay, F.; Trevitt, A. J.; Meloni, G.; Selby, T. M.; Osborn, D. L.; Taatjes, C. A.; Vereecken, L.; Leone, S. R. Cyclic Versus Linear Isomers Produced by Reaction of the Methylidyne Radical (CH) with Small Unsaturated Hydrocarbons. J. Am. Chem. Soc. 2009, 131, 993− 1001. (11) Wang, Z.-X.; Huang, M.-B.; Liu, R.-Z. Theoretical Study on the Insertion Reaction of CH (X2Π) with CH4. Can. J. Chem. 1997, 75, 996−1001. (12) Wang, Z.-X.; Huang, M.-B. Insertions of Methylidyne and Silylidyne into Methane and Silane. J. Chem. Soc., Faraday Trans. 1998, 94, 635−640. (13) Fleurat-Lessard, P.; Rayez, J.-C.; Bergeat, A.; Loison, J.-C. Reaction of Methylidyne CH(X2Π) Radical with CH4 and H2S: Overall Rate Constant and Absolute Atomic Hydrogen Production. Chem. Phys. 2002, 279, 87−99. (14) Taatjes, C. A.; Klippenstein, S. J. Kinetic Isotope Effects and Variable Reaction Coordinates in Barrierless Recombination Reactions. J. Phys. Chem. A 2001, 105, 8567−8578. (15) Guadagnini, R.; Schatz, G. C.; Walch, S. P. Ab Initio and RRKM Studies of the Reactions of C, CH, and 1CH2 with Acetylene. J. Phys. Chem. A 1998, 102, 5857−5866. (16) Vereecken, L.; Pierloot, K.; Peeters, J. B3LYP-DFT Characterization of the Potential Energy Surface of the CH(X2Π)+C2H2 Reaction. J. Chem. Phys. 1998, 108, 1068−1080. (17) Nguyen, T. L.; Mebel, A. M.; Lin, S. H.; Kaiser, R. I. Product Branching Ratios of the C(3P) + C2H3(2A′) and CH(2Π) + C2H2(1Σg+) Reactions and Photodissociation of H2CCCH(2B1) at 193 and 242 nm: An Ab Initio/RRKM Study. J. Phys. Chem. A 2001, 105, 11549−11559. (18) Vereecken, L.; Peeters, J. Detailed Microvariational RRKM Master Equation Analysis of the Product Distribution of the C2H2 + CH(X2Π) Reaction over Extended Temperature and Pressure Ranges. J. Phys. Chem. A 1999, 103, 5523−5533. (19) Thiesemann, H.; Clifford, E. P.; Taatjes, C. A.; Klippenstein, S. J. Temperature Dependence and Deuterium Kinetic Isotope Effects in the CH (CD) + C2H4 (C2D4) Reaction between 295 and 726 K. J. Phys. Chem. A 2001, 105, 5393−5401. (20) Galland, N.; Caralp, F.; Hannachi, Y.; Bergeat, A.; Loison, J.-C. Experimental and Theoretical Studies of the Methylidyne CH(X2Π) Radical Reaction with Ethane (C2H6): Overall Rate Constant and Product Channels. J. Phys. Chem. A 2003, 107, 5419−5426. (21) Coustenis, A.; Jennings, D. E.; Nixon, C. A.; Achterberg, R. K.; Lavvas, P.; Vinatier, S.; Teanby, N. A.; Bjoraker, G. L.; Carlson, R. C.; Piani, L.; et al. Titan Trace Gaseous Composition from CIRS at the End of the Cassini−Huygens Prime Mission. Icarus 2010, 207, 461− 476. (22) Hoobler, R. J.; Opansky, B. J.; Leone, S. R. Low-Temperature Rate Coefficients for Reactions of Ethynyl Radical (C2H) with Propane, Isobutane, n-Butane, and Neopentane. J. Phys. Chem. A 1997, 101, 1338−1342. (23) Murphy, J. E.; Vakhtin, A. B.; Leone, S. R. Laboratory Kinetics of C2H Radical Reactions with Ethane, Propane, and n-Butane at T = 96−296 K: Implications for Titan. Icarus 2003, 163, 175−181. (24) Berteloite, C.; Le Picard, S. D.; Balucani, N.; Canosa, A.; Sims, I. R. Low Temperature Rate Coefficients for Reactions of the butadiynyl radical, C4H, with Various Hydrocarbons. Part I: Reactions with Alkanes (CH4, C2H6, C3H8, C4H10). Phys. Chem. Chem. Phys. 2010, 12, 3666−3676. (25) Loison, J.; Bergeat, A.; Caralp, F.; Hannachi, Y. Rate Constants and H Atom Branching Ratios of the Gas-Phase Reactions of Methylidyne CH(X2Π) Radical with a Series of Alkanes. J. Phys. Chem. A 2006, 110, 13500−13506.
(26) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, Revision B.01; Gaussian, Inc.: Wallingford, CT, 2010. (27) Becke, A. D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 1993, 98, 5648−5652. (28) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785−789. (29) Krishnan, R.; Frisch, M.; Pople, J. A. Contribution of Triple Substitutions to the Electron Correlation Energy in Fourth Order Perturbation Theory. J. Chem. Phys. 1980, 72, 4244−4245. (30) Merrick, J. P.; Moran, D.; Radom, L. An Evaluation of Harmonic Vibrational Frequency Scale Factors. J. Phys. Chem. A 2007, 111, 11683−11700. (31) Werner, H.-J.; Knowles, P. J.; Kinizia, G.; Manby, F. R.; Schutz, M. MOLPRO, version 2010.1, a package of ab initio programs, 2010. (32) Peterson, K. A.; Dunning, T. H. Intrinsic Errors in Several ab Initio Methods: The Dissociation Energy of N2. J. Phys. Chem. 1995, 99, 3898−3901. (33) Dunning, T. H. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007−1023. (34) Purvis, G. D.; Bartlett, R. J. A Full Coupled-Cluster Singles and Doubles Model: The Inclusion of Disconnected Triples. J. Chem. Phys. 1982, 76, 1910−1918. (35) Eyring, H.; Lin, S. H.; Lin, S. M. Basic Chemical Kinetics; Wiley: New York, 1980. (36) Campomanes, P.; Suarez, D.; Sordo, T. L. Theoretical Study of the Ion−Molecule Reaction of the Vinyl Cation with Ethane. J. Phys. Chem. A 1999, 103, 5996−6002. (37) NIST Chemistry WebBook, NIST Standard Reference Database Number 69; http://webbook.nist.gov/chemistry/. (38) Ruscic, B. Updated Active Thermochemical Tables (ATcT) values based on ver. 1.110 of the Thermochemical Network (2012); available at ATcT.anl.gov.
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Reaction Mechanism and Product Branching Ratios of the CH + C3H8 Reaction: A Theoretical Study Joao Marcelo Ribeiro and Alexander M. Mebel* Department of Chemistry and Biochemistry, Florida International University, Miami, Florida 33199, United States ABSTRACT: The C4H9 potential energy surface accessed by the reaction of methylidyne radical, CH (X2Π), with propane, C3H8, including possible intermediates, transition states and dissociation products, has been studied by ab initio and density functional calculations at the CCSD(T)/CBS//B3LYP/6-311G(d,p) level of theory. The computed relative energies and molecular parameters were utilized to calculate collision-energy-dependent unimolecular rate constants at the zero-pressure limit for isomerization and dissociation channels of the C4H9 adducts formed in the entrance reaction channels. The rate constants were used to evaluate the product branching ratios in the CH + C3H8 reaction under single-collision conditions. The results show that the reaction can produce mostly ethene (C2H4) + ethyl radical (C2H5) and propene (C3H6) + methyl radical (CH3), and up to 14% of various butene isomers (C4H8) + H. The product branching ratios are sensitive to the initial reaction adduct (a butyl radical, C4H9) formed in the entrance channels via barrierless insertion of the CH radical into the terminal and middle C−H bonds of propane or, possibly, into the single C−C bonds. A more definite answer on relative contributions of various available CH insertion channels can be obtained through ab initio quasiclassical trajectory calculations, which are proposed for the future. The results allowed us to conclude that the CH + C3H8 reaction does not result in major amounts in the direct growth of the carbon-skeleton to four-carbon C4H8 products via the CH-for-H exchange because C−C bond cleavages in C4H9 radicals are generally more preferable than C−H bond cleavages.
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INTRODUCTION Elucidation of chemical reactions driving the growth of hydrocarbon molecules in Titan’s atmosphere has attracted numerous experimental and theoretical investigations due to possible similarities of Titan’s atmospheric processes with those that took place in the atmosphere of primordial Earth. With the photoirradiation of methane, which comprises 1.5−5% of Titan’s atmosphere,1 reactive radical species such as CH3, CH2, and CH are formed,2 thus “kick-starting” the formation of longer carbon skeletons. Despite comprising about 7% of the Lyman-α photodissociation products,3 the ground-state CH radical (X2Π) is the most reactive, being able to react with both closed-shell species as well as open-shell species, thus making it important in the chemical evolution of Titan’s atmosphere. Also, Pluto’s atmosphere is believed to be abundant in methane and hence is expected to have an effective hydrocarbon chemistry, whose detailed growth processes are largely unknown.4,5 Lara et al.6 concluded that Pluto’s atmosphere presents a rich reservoir of complex hydrocarbons but there are many major uncertainties in Pluto’s atmospheric models, which makes it necessary to investigate the growth of hydrocarbons in Pluto’s atmosphere from the “bottom up” starting with reactions of the simplest and most important radical growth species, methylidyne (CH), with the main atmospheric hydrocarbon constituent (C1−methane) via smaller hydrocarbons (C2) to more complex systems (C3). Although there are still issues to be resolved in the investigation of the reactions between the CH radical (X2Π) with C1 and C2 hydrocarbons, numerous experimental and © 2014 American Chemical Society
theoretical studies of differing levels of emphasis and scope have been performed on these systems.7−20 The reactions between CH (X2Π) and C3 hydrocarbons have been studied in much less detail, however, despite the fact that propane (C3H8) exists in greater amounts than ethene with its abundance in Titan’s atmosphere being within 1 order of magnitude of that for ethyne.21 C3H8 reactions with other chemical species are believed to be important in driving forward the growth of carbon molecules on Titan. For instance, the reactions with C2H and C4H have been studied experimentally at low temperatures and their overall rate constants have been determined.22−24 Meanwhile, the literature on the CH (X2Π) reaction with C3H8 is scarce, as only a room temperature experiment measuring its overall rate constant and branching ratios of various products has been reported.25 In this article by Loison et al., a partial theoretical investigation was included to provide a comparison with the experimental H atom branching ratio; however, no details of the reaction potential energy surface (PES) were given. Our work in the present paper seeks to expand this initial investigation by describing in detail all of the relevant portions of the C4H9 PES needed to determine the unimolecular reaction rate constants for isomerization and Special Issue: International Conference on Theoretical and High Performance Computational Chemistry Symposium Received: February 28, 2014 Revised: May 21, 2014 Published: May 22, 2014 9080
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Figure 1. Potential energy diagram of the CH + C3H8 reaction calculated at the CCSD(T)/CBS//B3LYP/6-311G(d,p) + ZPE(B3LYP/6311G(d,p)) level of theory. Relative energies of various species are shown in kcal/mol.
performed for single-collision conditions relevant to very low pressures of the upper Titan’s atmosphere or Pluto’s atmosphere and for comparison with future crossed molecular beam experiments. The relevant RRKM equation from which we extract the rate constant at a given internal energy, E, is the following:
decomposition of various butyl radicals and product branching ratios in the CH (X2Π) + C3H8 reaction.
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CALCULATION METHODS The geometries of reactants, transition states, and isomers were optimized using the Gaussian 09 software.26 The B3LYP hybrid density functional method27,28 was used with the 6-311G(d,p) basis set.29 Because B3LYP is known, however, to sometimes underestimate reaction barriers, geometries that did not converge were further investigated at the QCISD level using the 6-311G (d,p) basis set as well. The QCISD structures included in this investigation are two transition states describing H-loss from a CH3 group (namely, TSh and TSl) and the rotational barrier for interconverting trans- and cis-2butyl radical isomers (TSm). Lastly, the cis-2-butyl radical was also found only using QCISD. To characterize the nature of the stationary points, harmonic frequencies of all optimized structures were calculated. These also yielded zero-point energy corrections (ZPE) for all species. All harmonic frequencies were calculated at the B3LYP level except for the four structures described above, whose frequencies were calculated at the QCISD level. The QCISD level ZPE were scaled with the use of the factor 0.9812.30 To refine the energies of all B3LYP and QCISD minima and transition states, the Molpro 2010 package was used.31 This refinement was achieved through a three-point complete basis set extrapolation32 using Dunning’s cc-pVnZ basis sets (in particular, cc-pVDZ, cc-pVTZ, and cc-pVQZ)33 at the CCSD(T) level.34 Rice−Ramsperger−Kassel−Marcus (RRKM)35 theory was used to calculate the relevant unimolecular rate constants for isomerization and dissociation of C4H9 radicals, which can be produced in the CH + C3H8 reactions. The calculations were
k(E) =
σW ‡(E − E‡) hρ(E)
where σ is the degeneracy of the reaction path, h is Planck’s constant, W‡(E − E‡) is the total number of states for the transition state and ρ(E) represents the density of states of the energized reactants. The internal energy E was taken as a sum of the energy of chemical activation in the CH + C3H8 reaction and a collision energy, assuming that a dominant fraction of the latter is converted to the internal vibrational energy. The calculated harmonic frequencies were used to determine the total numbers and densities of states. Product branching ratios were evaluated by solving first-order kinetic equations for unimolecular reactions within the steady-state approximation, according to the kinetics schemes based on the ab initio potential energy diagrams.
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RESULTS AND DISCUSSION A small portion of the C4H9+ PES that was relevant to the C2H3+ + C2H6 reaction has been mapped in the past.36 Here we deal with the neutral surface, and Figure 1 illustrates the potential energy diagram of the channels relevant to the CH + C3H8 reaction. From the previous experimental and theoretical studies of CH reactions with C1 and C2 hydrocarbons,7−20,25 it is known that the methylidyne radical can insert into C−H bonds or add to double and triple C−C bonds, with all these processes being barrierless and hence occurring very fast (with 9081
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rate constants in the range of 10−10 cm3 molecule−1 s−1 close to the collision kinetics limit) even at temperatures as low as 23 K; the CH + C3H8 reaction rate constant has been measured to be similarly high at 300 K.25 A barrierless insertion of CH into a single C−C bond was also considered as a possible entrance reaction channel, but Galland et al.20 suggested that such insertion for the C2H6 reaction may be sterically hindered and later, on these grounds, was ruled out by Loison et al.25 for CH reactions with larger alkanes. Nevertheless, here we do not exclude this possibility, at least in principle, and hence for our reacting system we consider three initial bimolecular entrance channels, namely, CH insertion into a C−C single bond (C−C insertion) leading to the trans-2-butyl radical, CH insertion into a terminal carbon−hydrogen single bond (terminal C−H insertion) leading to the 1-butyl radical and CH insertion into a middle carbon−hydrogen bond (middle C−H insertion) leading to the isobutyl radical. No transition states were found for any of these three entrance channel, suggesting that all of them are barrierless. To confirm this, we have mapped the minimum energy path for both C−H insertion channels and, as is illustrated by Figures 2 and 3, these channels are indeed Figure 3. Minimal energy profile for barrierless terminal C−H insertion by the methylidyne radical calculated at the B3LYP/6311G(d,p) level of theory. The surface shown in the bottom panel was produced to model a smooth and continuous H-migration from terminal carbon of propane to the methylidyne carbon.
bottom panels combined show the barrierless insertion paths of CH into CH bonds of the CH2 (Figure 2) or CH3 (Figure 3) groups of propane. As for the case of C−C insertion, we were not able to identify a descending minimal energy pathway, as the paths leading to the insertion into a CC bond intermingle with C−H insertion paths. This issue requires further investigation and the relative importance of the different C− C and C−H insertions can in principle be evaluated using ab initio calculations of quasiclassical trajectories in the entrance channels, but these time-consuming dynamics calculations are beyond the scope of the present study. Here we assume that all three channels including the C−C insertion can contribute and defer further discussion on the effect of their relative contributions on the product branching ratios until the latter stages of the article. The C−C insertion adduct, the trans-2-butyl radical, appears to be the thermodynamically favored adduct. The terminal C− H insertion produces the 1-butyl radical and is thermodynamically least favorable, whereas the central C−H insertion gives the isobutyl radical, which is less stable than trans-2-butyl but more stable than 1-butyl. Nevertheless, all three initial adducts reside in a narrow energy range between −99.4 and −96.7 kcal/ mol relative to the initial reactants. All optimized transitionstate structures are shown in Figure 4. The trans-2-butyl radical can isomerize to the 1-butyl radical through a 1,2-H shift (via TSa) or through a 2,4-H shift (via TSb), although the barrier associated with the latter H-shift is ∼1 kcal/mol higher. The trans-2-butyl radical adduct can also isomerize to the isobutyl radical through a 2,3-CH3 shift (via TSc) but the corresponding barrier is greater than its H-shift barriers by ∼20 kcal/mol. There is a small rotational barrier (TSm) that separates the trans- and cis 2-butyl radicals. As for the 1-butyl radical, there does not exist a direct connection for its rearrangement to the isobutyl radical and, in fact, it cannot isomerize to any other low-energy species except the trans-2-butyl radical. Finally, through a 1,2-H shift (via TSd) the isobutyl radical can form
Figure 2. Minimal energy profile for barrierless middle C−H insertion by the methylidyne radical calculated at the B3LYP/6-311G(d,p) level of theory. Although not included, the curve shows a large discontinuity after 2.20 Å due to the sudden geometrical rearrangement stemming from “complete” H-migration. The surface shown in the bottom panel was produced to model a smooth and continuous H-migration from the middle carbon of propane to the methylidyne carbon.
proved to be barrierless. The top panel on each figure shows the minimal energy profile as a function of the CC distance between the carbon atom of CH and the attacked carbon of C3H8. One can see that the energy steadily declines as the CC distance decreases from 3.0 to 2.3 Å. In the interval of CC = 2.1−1.9 Å, the attacked CH bond breaks and its hydrogen atom essentially migrates from a CH2 or CH3 group of propane to the carbon atom of the CH radical. A monotonous energy descent during this process is illustrated in the lower panels of Figures 2 and 3, where the energy is shown as a function of two internal coordinates, the CC distance and the CH distance of the bond in propane, which is being cleaved. The top and 9082
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Figure 4. Optimized transition-state structures. Critical bond lengths are shown in Ångstroms.
the most stable C4H9 isomer, the tert-butyl radical, and this occurs with the lowest isomerization barrier of 36.0 kcal/mol. Comparison of the calculated energies for the adducts with experimental data37,38 is shown in Table 1, where available, showing that the smallest absolute deviation of 1.1 kcal/mol is for the trans-2-butyl radical and the highest absolute deviation of 2.4 kcal/mol is for the tert-butyl radical. The unimolecular rate constants for the isomerization reactions are included in Table 2 at both 0 and 1 kcal/mol collision energies, which are relevant to the temperature range 0−335 K. This temperature range covers the reaction conditions from those typical for the interstellar medium to planetary atmospheres (Pluto and Titan) to ambient conditions. Just about all of the rate constants reflect what is to be expected from the energetics of the PES in Figure 1, showing that rotation takes place much quicker than all the different H-shifts and that CH3 migration is much slower than the all H-shifts. The fact that tert-butyl radical isomerization to the isobutyl radical is comparable in rate to its “forward” reaction can in large part be attributed to the highly symmetric nature of the tert-butyl radical as a reacting species. The PES shows that, in general, the H-loss channels are both kinetically and thermodynamically unfavorable relative to their
Table 1. Relative Energies of Various Reaction Intermediates and Products Calculated at the CCSD(T)/CBS//B3LYP/6311G(d,p) + ZPE(B3LYP/6-311G(d,p)) Level of Theory and from Experimental Thermochemical Data, All in kcal/ mol species
ΔEcalc
ΔEexp
2-butyl radical 1-butyl radical isobutyl radical tert-butyl radical propene (C3H6) + CH3 ethene (C2H4) + C2H5 1-butene + H trans-2-butene + H cis-2-butene + H isobutene + H n-propyl + CH2(3B1) isopropyl + CH2(3B1)
−99.4 −96.7 −98.0 −103.1 −77.1 −75.2 −64.6 −67.4 −66.2 −68.6 0.4 −2.6
−100.5 N/A −100.2a −105.5a −77.3b −76.1b −65.1b −67.5b −66.7b −69.2b −0.5a −2.7a
absolute deviation a
1.1 2.2 2.4 0.2 0.9 0.5 0.1 0.5 0.6 0.9 0.1
a
Computed from room temperature enthalpies of formation from ref 37. bComputed from 0 K enthalpies of formation from ref 38.
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from tert-butyl radical. The barrier heights for these two channels are 34.6 kcal/mol (TSj) and 36.1 kcal/mol (TSl), respectively. The relative energies of all products have also been compared to experimental data, as can be seen in Table 1, and the agreement is better than that of adducts as the largest absolute deviation, for ethene + ethyl radical, is below 1 kcal/ mol. Table 2 shows the unimolecular rate constants for these different product formation channels at collision energies of 0 and 1 kcal/mol. Absent from the above discussion (and calculations) are the direct H-abstraction channels leading to either isopropyl radical + methylene or n-propyl radical + methylene. These reactions are slightly exothermic or nearly isoergic in nature and in principle might be relevant in the interstellar medium and under Titan or Pluto atmospheric conditions and also in combustion. For instance, the isopropyl radical + methylene products together are 2.6 kcal/mol lower in energy than the reactants, whereas the n-propyl radical + methylene are 0.4 kcal/mol higher in energy than CH + C3H8. However, a careful search of direct H-abstraction transition states has failed; a transition state for either of these reactions could not be located as different starting geometries tended to lead to dissociated reactants or toward the insertion reaction channel. This result can be attributed to the fact that the insertion channels are much more favorable energetically and, hence, no pathways to the direct H-abstraction products going from the reactants via a first-order saddle point exist; when a CH radical approaches propane, it tends to insert into CH or CC bonds rather than to abstract a hydrogen atom. The formal H abstraction products, isopropyl + methylene and n-propyl + methylene, can be formed by cleavage of a CH2 group from isobutyl and 1-butyl radicals, respectively. However, these dissociation channels are much less favorable as compared to H, CH3, and C2H5 eliminations from these radicals and therefore are not anticipated to be competitive. Tables 3 and 4 contain the product branching ratios for CH + C3H8 at 0 and 1 kcal/mol collision energies, the 0 kcal/mol collision energy being relevant to Titan and Pluto atmospheric conditions and the 1 kcal/mol collision energy being included to aid comparison to the room temperature experiment discussed in ref 25. In both tables columns two through four are the percentages of products formed should all CH + C3H8 reacting systems proceed exclusively along the one entrance channel indicated. Columns five and six, meanwhile, average the product yields of the different entrance channels, giving equal weight to all single bonds available for CH radical to insert into (two C−C, six terminal C−H, and two central C− H), but differ in that column five assumes that the C−C insertion is viable whereas column six assumes that the C−C insertion does not contribute. In all cases the formation of carbon chains smaller than four carbons in length (via a C−C bond cleavage in the C4H9 radicals) will dominate over the
Table 2. Energy-Dependent Unimolecular Rate Constants Calculated Using RRKM Theory under Single-Collision Conditions at Collision Energis of 0 and 1 kcal/mol k (s−1), 0 kcal/mol
reaction trans-2-butyl radical → 1-butyl radical 1-butyl radical → trans-2-butyl radical trans-2-butyl radical → isobutyl radical isobutyl radical → trans-2-butyl radical trans-2-butyl radical → cis-2-butyl radical cis-2-butyl radical → trans-2-butyl radical isobutyl radical → tert-butyl radical tert-butyl radical → isobutyl radical trans-2-butyl radical → propene + CH3 trans-2-butyl radical → 1-butene + H trans-2-butyl radical → trans-2-butene +H 1-butyl radical → ethene + C2H5 1-butyl radical → 1-butene + H isobutyl radical → propene + CH3 isobutyl radical → isobutene + H tert-butyl radical → isobutene + H cis-2-butyl radical → cis-2-butene + H
1.11 2.55 6.39 5.25 1.56
× × × × ×
k (s−1), 1 kcal/mol
109 109 105 106 1012
1.22 2.76 7.53 6.17 1.56
2.59 × 1012
× × × × ×
109 109 105 106 1012
2.59 × 1012
2.02 2.88 4.52 6.21 9.81
× × × × ×
109 109 1010 109 109
2.17 3.12 4.81 6.73 1.06
× × × × ×
109 109 1010 109 1010
1.45 1.28 1.01 4.93 6.61 1.57
× × × × × ×
1011 1010 1011 109 1010 1010
1.55 1.40 1.09 5.32 7.12 1.70
× × × × × ×
1011 1010 1011 109 1010 1010
methyl/ethyl-loss counterparts. The formation of propene and methyl radical can occur via two low barrier CH3-loss channels, one resulting from the chain trans-2-butyl radical (via TSe) and another from the branched isobutyl radical (via TSf). The barrier heights for both CH3-loss channels are approximately equal, 31.2 and 31.5 kcal/mol. Through the breaking of its middle C−C single bond the 1-butyl radical can lead to the formation of ethene and ethyl radical, a channel that proceeds through TSg and with the associated barrier height of 30.2 kcal/mol. Due to the fact that the 1-butyl radical is a terminal radical, it has one possible H-loss channel leading to the formation of 1-butene and H atom although the barrier that must be overcome along this reaction path is 36.4 kcal/mol (TSi). The trans-2-butyl radical, however, because of its internal radical location, can proceed along two possible H-loss channels, terminal H-loss and internal H-loss. Terminal Hloss proceeds through the transition structure TSh with a barrier height of 37.1 kcal/mol and also leads to 1-butene and H atom. Internal H-loss, which is the kinetically favored trans-2butyl radical H-loss channel, proceeds through TSn with its barrier being 34.9 kcal/mol and leads to the trans-2-butene and H atom products. The formation of cis-2-butene and H atom proceeds through a slightly higher barrier of 35.6 kcal/mol (TSo) and is thermodynamically unfavorable by 1 kcal/mol relative to its trans counterpart. Finally, the formation of the most stable H-loss products, isobutene and H atom, can take place via two channels, H-loss from isobutyl radical and H-loss
Table 3. Product Branching Ratios Calculated at Zero Collision Energy products
C−C insertion
terminal C−H insertion
mid C−H insertion
net (including C−C insertion)
net (excluding C−C insertion)
propene + methyl radical ethene + ethyl radical 1-butene + H trans-2-butene + H cis-2-butene + H isobutene + H
63.03 1.40 8.78 13.68 13.11 0.00
1.00 90.47 8.10 0.22 0.21 0.00
93.64 0.00 0.00 0.00 0.00 6.36
31.93 54.56 6.62 2.87 2.75 1.27
24.15 67.85 6.08 0.17 0.16 1.59
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Table 4. Product Branching Ratios Calculated at the Collision Energy of 1 kcal/mol products
C−C insertion
terminal C−H insertion
mid C−H insertion
net (including C−C insertion)
net (excluding C−C insertion)
propene + methyl radical ethene + ethyl radical 1-butene + H trans-2-butene + H cis-2-butene + H isobutene + H
62.63 1.43 8.89 13.80 13.25 0.00
1.01 90.28 8.27 0.22 0.22 0.00
93.64 0.00 0.00 0.00 0.00 6.36
31.87 54.45 6.74 2.89 2.78 1.27
24.17 67.71 6.20 0.17 0.17 1.58
growth of the carbon skeleton via the CH-for-H exchange does not take place in major amounts because four-carbon hydrocarbon products (various C4H8 butene isomers) that are formed are likely to comprise only between 8% and 14% of the total products. Both three-carbon (propene C3H6 along with the methyl radical CH3) and two-carbon hydrocarbons (ethene plus ethyl radical) will dominate the product formation, making up over 86% of products. The reaction outcome appears to be sensitive to the branching of the reaction flux in the entrance channels where barrierless insertions of CH into terminal and mid C−H bonds are expected to compete with each other and possibly with the C− C insertion.
formation of butenes + H, as can be expected from the H-loss barrier heights described by the PES. For instance, the terminal C−H insertion should result in the preferable formation of ethene + ethyl radical, whereas the mid C−H insertion and the C−C insertion (to a lesser extent) favor the formation of propene + methyl radical. The inclusion of the C−C insertion in the product branching ratio calculations does cause the Hloss channels (carbon-skeleton growth channels) to factor in at close to double their overall branching ratio as opposed to when it is not included, driving down formation of propene and methyl radical as well as ethene and ethyl radical by a combined amount of about 6%. This inclusion results in the H-loss products making up 13.51% of the products at 0 kcal/mol collision energy and 13.68% of the products at 1 kcal/mol collision energy. The exclusion of the C−C insertion channel causes the H-loss to have a diminished role in product formation, driving the H-loss products to make up only 8.00% of products at 0 kcal/mol collision energy and 8.12% at 1 kcal/ mol collision energy. It is possible that steric hindrance of C−C insertion might reduce the rate of formation of bimolecular C− C insertion adducts while not necessarily excluding them completely from participation, in which case the H-loss product branching ratio is likely to fall between the ranges described above when the proper weights are assigned to the channels. The experimental value of the H-loss product branching ratio is 19 ± 7%, however, so that inclusion of C−C insertion into calculations makes the H atom production fall within the experimental result. Loison et al.25 attributed the fact that the experimental H atom yield is higher than their theoretical value computed with exclusion of the C−C insertions to secondary prompt decomposition of the C2 H 5 product at their experimental condition. Alternatively, we can see that the experimental H atom yield can be explained if the C−C insertion is included. A more definite answer on the relative contributions of various available CH insertion channels can be obtained through ab initio quasiclassical trajectory calculations, which are planned for the future. Experimentally, it would be useful to carry out this reaction in crossed molecular beams under single-collision conditions where only primary reaction products can be observed and thus the elementary reaction outcome could be further elucidated and compared with the theoretical branching ratios.
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AUTHOR INFORMATION
Corresponding Author
*A. M. Mebel: e-mail, mebela@fiu.edu; telephone, +1-305-3481945. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported in part by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Sciences of U.S. Department of Energy (Grant No. DE-FG02-04ER15570).
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REFERENCES
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CONCLUSIONS The C4H9 potential energy surface accessed via the reaction of methylidene radical with propane, including possible intermediates, transition states, and dissociation products, was studied by ab initio and density functional calculations. Unimolecular rate constants for the isomerization and dissociation channels of the C4H9 adducts formed in the entrance reaction were calculated under single-collision conditions (zero-pressure limit) and were used to evaluate the product branching ratios. The results show that the direct 9085
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