Roaming Radical Pathways for the Decomposition of Alkanes

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Roaming Radical Pathways for the Decomposition of Alkanes Lawrence B. Harding* and Stephen J. Klippenstein Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439 w This paper contains enhanced objects available on the Internet at http://pubs.acs.org/JPCL. n

ABSTRACT CASPT2 calculations predict the existence of roaming radical pathways for the decomposition of propane, n-butane, isobutane and neopentane. The roaming radical paths lead to the formation of an alkane and an alkene instead of the expected radical products. The predicted barriers for the roaming radical paths lie ∼1 kcal/mol below the corresponding radical asymptotes. SECTION Kinetics, Spectroscopy

Werner.14 The MOLPRO program package15-17 was used for all electronic structure calculations. For propane, higher-level calculations were done to test the accuracy of the (2E,2O)-CASPT2 results. In these calculations, the size of the active space and the size of the basis sets were both expanded. Two larger active spaces were tested. A (4E,4O) active space was chosen in which σ,σ* orbitals for both CC bonds were included, and a (6E,6O) active space in which σ,σ* orbitals for the CH bond being broken were also included. Finally, multireference configuration interaction calculations, CASþ1þ2, using the same three sets of active spaces were also carried out as a further check of the accuracy of the CASPT2 calculations. These calculations included the Davidson correction (þQC) for higher-order excitations. The relative energies for the stationary points on the propane surface from all of these calculations are summarized in Table 1. All of the energies are remarkably insensitive to the size of the active space. The energy of the propane minimum relative to CH3 þ C2H5 does change by 2-3 kcal/mol depending on the level of theory used, with the larger basis sets and the CI calculations giving the larger bond energies. The energy of the saddle point, again relative to CH3 þ C2H5, is insensitive to the size of the basis set and active space. The CI calculations yield barriers 0.3-0.5 kcal/mol higher than the CASPT2 calculations. We do note a small but consistent trend; the difference between the CASPT2 and CASþ1þ2 saddle point energies decreases as the size of the active space increases, with the larger changes occurring in the CI energies. From these results, we conclude that the (2E,2O)-CASPT2/aug-cc-pvdz calculations yield reasonably accurate barrier heights, and we use this method to characterize the reaction paths for the larger molecules. The structure of the roaming saddle point for propane is shown in Figure 1 along with several points along the associated IRC. An animation of this IRC is available (see Figure 1).

I

t is commonly assumed that alkanes thermally decompose by carbon-carbon bond cleavage, resulting in the formation of alkyl radicals.1-4 Another possibility is a “roaming radical” mechanism.5-7 The existence of a roaming methyl radical mechanism in the photodissociation of acetaldehyde8,9 is now well-established. The recent observation of a roaming methyl radical mechanism in the thermal decomposition of acetaldehyde10,11 suggests that similar mechanisms should be considered in the thermal decomposition of alkanes and other compounds. A roaming methyl radical mechanism for the decomposition of propane might be written as follows CH3 CH2 CH3 f ½CH3 3 3 3 CH2 CH3 f ½CH3 3 3 3 CH3 CH2 ð1Þ f CH4 þ CH2 CH2 Here, the reaction starts with the elongation of one of the CC bonds (the weakest bonds) followed by a reorientation of the two nascent radical fragments to allow a disproportionation reaction in which the nascent methyl radical abstracts a hydrogen atom from the nascent ethyl radical to yield methane plus ethylene as the final products. In this Letter we present theoretical evidence that such pathways do indeed exist, having barriers slightly below the corresponding radical asymptotes. The majority of electronic structure calculations are multireference, second-order perturbation theory, CASPT2. This level of theory has been demonstrated to yield accurate predictions for the roaming radical paths in both formaldehyde and acetaldehyde.12 In particular, we employ a twoelectron, two-orbital (2E,2O) active space consisting of the two nearly singly occupied radical orbitals of the nascent radicals. For the reactant alkane, this active space correlates with a CC σ,σ* pair and with a π,π* pair in the alkene product. Saddle points for the roaming radical mechanisms were located and verified by following the intrinsic reaction coordinates (IRC) to both reactants and products. The CASPT2 calculations employ the Dunning13 aug-cc-pvdz, aug-cc-pvtz, and aug-cc-pvqz basis sets and the formalism of Celani and

r 2010 American Chemical Society

Received Date: August 16, 2010 Accepted Date: September 15, 2010 Published on Web Date: September 24, 2010

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DOI: 10.1021/jz101160u |J. Phys. Chem. Lett. 2010, 1, 3016–3020

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Figure 1. Structures for several points along the CASPT2/aug-cc-pvdz IRC for the roaming radical dissociation of propane. The middle structure corresponds to the saddle point.

w An animation of this IRC is available. n

Table 1. Energies of the Propane Minimum and the Saddle Point for Roaming Radical Decompositiona basis set method

aug-cc-pvdz

aug-cc-pvtz

aug-cc-pvqz

Propane (2E,2O)-CASPT2

-91.2

-92.2

-92.6

(4E,4O)-CASPT2 (6E,6O)-CASPT2

-91.1 -90.9

-92.3 -92.0

-92.7 -92.4

(2E,2O)-CASþ1þ2þQC

-91.7

-93.6

-94.2


-91.8

-93.7

-94.3


-91.8

-93.7

-94.2

Roaming Saddle Point (2E,2O)-CASPT2

-1.42

-1.21

-1.10

(4E,4O)-CASPT2

-1.41

-1.20

-1.10

(6E,6O)-CASPT2

-1.37

-1.16

-1.06

(2E,2O)-CASþ1þ2þQC (4E,4O)-CASþ1þ2þQC

-0.99 -1.01

-0.74 -0.76

-0.62 -0.64


-1.07

-0.82

-0.70

Figure 2. Plot of the energy (open circles) and GVB orbital overlap (filled circles) along the reaction path for roaming radical dissociation of propane.

All energies are in kcal/mol and are relative to the CH3 þ C2H5 radical asymptote. All calculations employ the (2E,2O)-CASPT2/aug-ccpvdz geometries. a

At the saddle point, the carbon-carbon bond distance for the breaking bond is 3.9 Å, while the carbon-hydrogen distance for the new CH bond is 2.5 Å. Both of these are more than twice the equilibrium values. An unusual aspect of this reaction path is that the roaming methyl fragment undergoes an inversion during the course of the reaction. The reverse reaction, addition of a CH bond of methane across the π bond of ethylene, appears to be a 2 þ 2 pericyclic addition and therefore might be expected to be Woodward-Hoffmann-forbidden.18-20 However, the inversion of the methyl radical fragment makes this an allowed path. This can be confirmed with an orbital phase continuity principle (OPCP) analysis.21,22 To do this, we first transform the two active natural orbitals from the CASSCF calculation into singly occupied, overlapping generalized valence bond23-25 (GVB) orbitals and then calculate the GVB orbital overlap at each point along the reaction path. A plot of the GVB orbital overlap is shown in Figure 2, from which it can be seen that the overlap remains nonzero along the entire path, confirming that this is an orbital-phase-allowed path. Also shown in Figure 2 is the energy along this IRC. Unlike IRC


Figure 3. Comparison of optimal MEP (filled circles) and constrained MEP (open circles). The Me-m-CH2 angle is taken as the distinguished coordinate (m is the midpoint of the ethyl CC bond). The internal coordinates of the fragment are kept rigid, a Cs symmetry constraint is imposed, and the m to methyl carbon distance is fixed at 3.8 Å.

energy profiles for typical tight transition states, which tend to be fairly sharply peaked, the energy profile for this roaming radical reaction has a broad plateau shape. To better understand the amount that the barrier is lowered by allowing the methyl fragment to invert, we calculate two constrained minimum energy paths (MEPs). The energies

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Figure 4. Structures for several points along the CASPT2/aug-cc-pvdz IRC for the Woodward-Hoffmann-allowed roaming radical dissociation of neopentane, path (a). The saddle point geometry is indicated by SP.


Figure 5. Structures for several points along the CASPT2/aug-cc-pvdz IRC for the Woodward-Hoffmann-forbidden roaming radical dissociation of neopentane, path (b). The saddle point geometry is indicated by SP.


Table 2. (2E,2O)-CASPT2 Energies of the Saddle Points for Roaming Radical Decompositions of Propane, Isobutene, And Neopentanea aug-cc-pvdz

the barriers on the OPT and 90° paths are 0.09 and 0.01, respectively. In Table 2, we summarize the energies of the roaming saddle points relative to the respective radical asymptotes for propane, isobutane, and neopentane. For neopentane, two distinct pathways are found. In one, (a), the roaming methyl fragment inverts, whereas in the second, (b), the methyl does not invert. Snapshots of geometries along these two paths are shown in Figures 4 and 5, and animations are available. In path (a), between the reactant and the saddle point, one can see that the methyl fragment rotates ∼180° around one of its CH bonds (the CH bond pointing toward the upper left), resulting in the inversion of the methyl fragment. An OPCP analysis confirms that path (a) is an orbital-phase-allowed path, whereas for path (b), the GVB orbital overlap changes sign upon going from reactants to products, indicating an orbital-phase-forbidden reaction. A plot of the orbital overlap for path (b) is shown in Figure 6. The most surprising result is that the forbidden path is predicted to have a slightly lower barrier than the allowed path. Apparently for larger radicals, long-range dispersion forces, which do not depend on orbital

aug-cc-pvtz

propane

-1.4(-0.7)

-1.2(-0.5)

isobutane

-1.8 (-1.3)

-1.5(-1.0)

neopentane path a (allowed)

-0.7(-0.6)

-0.6(-0.5)

neopentane path b (forbidden)

-1.6(-1.2)

-0.9(-0.5)

a All energies are in kcal/mol and are relative to the corresponding CH3 þ R radical asymptote. The numbers in parentheses include the harmonic zero point. All calculations employ (2E,2O)-CASPT2/aug-ccpvdz geometries.

of these two paths are plotted in Figure 3. In one, labeled OPT, the methyl is allowed to invert, while in the other, labeled 90°, the plane of the methyl fragment is kept perpendicular to the line connecting the methyl carbon and the midpoint of the ethyl CC bond. The perpendicular geometry is close to optimal at both ends of the path but results in a ∼0.5 kcal/mol increase in the barrier. The GVB orbital overlaps at


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Table 3. Relative Energies of the Saddle Points for Roaming Radical Decompositions of n-Butane and the C3H7 þ CH3 Radical Asymptotea method

aug-cc-pvdz

aug-cc-pvtz

aug-cc-pvqz -1.2(-0.6)

n-butane f C2H6 þ C2H4

CASPT2

-1.6(-1.1)

-1.3(-0.8)

n-butane f C3H6 þ CH4

CASPT2

-1.1(-0.8)

-0.2(0.0)

C3H7 þ CH3

CASPT2

þ1.0(þ0.7)

þ1.6(1.3)

þ1.7(1.4)

C3H7 þ CH3

CCSD(T)

þ1.0(þ0.8)

þ1.7(1.4)

þ1.8(1.6)

All energies are in kcal/mol and are relative to the C2H5 þ C2H5 asymptote. The numbers in parentheses include the harmonic zero point. All calculations employ (2E,2O)-CASPT2/aug-cc-pvdz geometries. a

The major conclusions from this study can be summarized as follows: (1) For alkanes larger than ethane, roaming radical decomposition paths exist with barriers ∼1 kcal/mol below the lowest bond cleavage paths. (2) These pathways can be thought of as frustrated bond cleavages, in which two nascent radical fragments begin to separate but, before the separation is complete, the radical fragments reorient or “roam” in such a way as to allow access to a barrierless, highly exothermic radical-radical disproportionation path. (3) For alkanes, we find two kinds of roaming radical paths, Woodward-Hoffmann-allowed and WoodwardHoffmann-forbidden. In the allowed paths, one of the roaming radicals undergoes an inversion along the IRC. In the forbidden paths, neither radical fragment undergoes an inversion. For small hydrocarbons, C3 and C4, the Woodward-Hoffmann-allowed paths appear to be the energetically preferred (and probably only) paths. For larger hydrocarbons, C5 and higher, the increased importance of long-range dispersion forces in the saddle point region results in a decreased preference for the Woodward-Hoffmann-allowed paths. (4) The use of RRKM theory to calculate the rates for these unimolecular decompositions is complicated by the fact that the saddle points lie on broad, fairly flat energy plateaus. Variational effects are expected to be very important. Also, anharmonic effects for the very low-frequency modes associated with motions of the two radical fragments with respect to each other are expected to be large. Work is progressing in this laboratory to address both of these issues within the framework of statistical rate theory.

Figure 6. Plot of the energy (open circles) and GVB orbital overlap (filled circles) along reaction path (b) for roaming radical dissociation of neopentane.

overlaps, become more important relative to covalent interactions, which do depend on orbital overlaps. In Table 3, we summarize results for two roaming radical paths for the decomposition of n-butane. CH3 CH2 CH2 CH3 f ½CH3 CH2 3 3 3 CH2 CH3 f C2 H6 þ C2 H4 ð2Þ CH3 CH2 CH2 CH3 f ½CH3 3 3 3 CH2 CH2 CH3 f CH4 þ C3 H6 ð3Þ We note there is a slight inconsistency in these calculations owing to the use of a (2E,2O) active space. For the calculations associated with the 2C2H5 asymptote and its roaming saddle point, the two active orbitals are the σ,σ* pair for the central CC bond. For the calculations associated with the CH3 þ C3H7 asymptote and its roaming saddle point, the two active orbitals are the σ,σ* pair for one of the end CC bonds. This turns out to be a negligible inconsistency, as evidenced by the fact that the relative energies of these two asymptotes calculated with CASPT2 and CCSD(T) are in very good agreement. The 2C2H5 asymptote is lower than the CH3 þ C3H7 asymptote, and as one might expect, the roaming saddle point associated with the 2C2H5 asymptote is lower than that associated with the CH3 þ C3H7 asymptote. Both reaction paths involve an inversion of one of the radical centers, in line with the Woodward-Hoffmann arguments discussed above. Interestingly, the saddle point associated with the CH3 þ C3H7 asymptote is ∼0.5 kcal/mol more stable with respect to it is own CH3 þ C3H7 asymptote than the 2C2H5 saddle point is with respect to the 2C2H5 asymptote.


AUTHOR INFORMATION Corresponding Author: *To whom correspondence should be addressed.

ACKNOWLEDGMENT This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, under Contract No. DE-AC02-06CH11357.

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Roaming Radical Pathways for the Decomposition of Alkanes

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