Theoretical Study of Isomerization and Dissociation Transition States

ARTICLE pubs.acs.org/JPCA

Theoretical Study of Isomerization and Dissociation Transition States of C3H5O Radical Isomers: Ab Initio Characterization of the Critical Points and Statistical Transition-State Theory Modeling of the Dynamics Benjamin FitzPatrick* Department of Chemistry, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455, United States

bS Supporting Information ABSTRACT: I use coupled-cluster theory and a modest basis set, aug-cc-pVDZ, to calculate structures and harmonic vibrational frequencies of local minima and transition states on the C3H5O potential energy surface. Accurate energies are computed using explicitly correlated coupledcluster methods and a large basis set, cc-pVQZ-F12, to approach the one-particle basis set limit. My computations characterize eight additional stable radical structures on the global potential energy surface for this system. Additionally, this study encompasses many more isomerization and dissociation pathways, both between previously known intermediates and ones first characterized here. Analysis of the transition states and statistical transition-state theory results shows that energetically small barriers connect many of the alkenol and epoxide intermediates to the straight-chain alkoxy isomers, leading to significant branching to these alkoxy radical intermediates. Facile isomerization to these alkoxy intermediates is significant because the barrier heights leading to H þ acrolein and HCO þ C2H4 product channels are energetically accessible even at low vibrational energies. The low dissociation barrier heights and loose transition states of these pathways result in unimolecular dissociation as opposed to isomerization to a different C3H5O intermediate.

1. INTRODUCTION The C3H5O global potential energy surface (PES) exhibits a menagerie of structural isomer intermediates including etheric, enolic, and cyclic geometries. C3H5O is small enough that highlevel electronic structure calculations are feasible. Thus, the C3H5O PES provides an excellent system for benchmarking electronic structure methods. Similar to single-point energies, the structures1 and harmonic vibrational frequencies2 of intermediates and transition-state structures can vary greatly with the level of theory. C3H5O is also small enough to assess the dynamics using statistical transition-state theory (TST), variational TST, and quasiclassical trajectory simulations (although on-the-fly dynamics would not be feasible). The first two make use of the ab initio barrier heights and vibrational frequencies, and comparisons between the two methods detail the efficacy of statistical TST at properly describing loose transition states. Trajectory calculations supplement the two other dynamics methods by assessing the role of nonstatistical effects by highlighting any isomerization or dissociation pathways that are not characterized by the stationary points. The majority of the past studies focused on small parts of the C3H5O PES, and the calculations employed relatively low-levels of electronic structure theory. Choi et al.3 provide the most comprehensive characterization of the C3H5O PES to date using O(3P) þ allyl as the reference point. O(3P) addition to one of the terminal carbon atoms yields an alkoxy intermediate, INT1, or the oxygen atom can bridge the center and one terminal carbon atom, thereby creating an epoxide intermediate, INT2. Choi also presented an alternative view of the C3H5O PES by studying the r 2011 American Chemical Society

reaction of OH radicals with the three C3H4 isomers, allene, methylacetylene, and cyclopropene, that lead to enolic structures. The minima and transition states were calculated using CBS-QB3, a composite method based on B3LYP geometries and harmonic vibrational frequencies, from Choi’s work. More recently, Krylov and co-workers4 applied coupled cluster methods to characterize the ground state and lowest excited states of INT1. Another composite method, G3//B3LYP, was utilized by Butler et al.5 to extend Choi’s work on the hydroxyl-containing isomers. Two different ring-opening mechanisms of the epoxide in INT2 were characterized by Pasto6 and Radom et al.7 using QCISD(T)/6-31G* and CBS-RAD levels of theory, respectively. The first mechanism, which has a lower energetic barrier, involves ring-opening via fission of the bond between the center carbon atom and the oxygen atom resulting in an alkoxy radical, INT1. The C-C bond cleaves in the second mechanism to form a radical having an ether linkage. Radom et al.8 also studied INT1 and several of its C-C and C-H bond fission transition states using the CBS-RAD method. Last, Sun et al.9 approached the C3H5O PES by starting with the reaction of C2H3 þ H2CO. These reactants lead to many direct abstraction pathways that are not present in the other works and one new intermediate. Two composite methods, G3//B3LYP and CBS-QB3, were used to calculate all of their stationary points.

Received: September 9, 2010 Revised: January 21, 2011 Published: February 15, 2011 1701

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This work extends the knowledge gathered previously by characterizing eight new intermediates on the global PES in addition to the previously reported stationary points, using higher-level ab initio theory. The higher-accuracy calculations, augmented number of minima and transition states, and application of statistical transition-state theory help unravel the dynamics of the C3H5O system. The application of statistical TST to the C3H5O PES provides branching ratio comparisons to the experimental work.10 A complete characterization of all stationary points on the global PES would require a rigorous stationarypoint search method, such as the one developed by Ohno and Maeda,11-14 and would reveal any stationary points missed in this and previous works.

2. COMPUTATIONAL METHODS This study includes multiple levels of ab initio theory to provide comparisons between calculated geometries, harmonic frequencies, and single point energies. Preliminary geometry optimization, harmonic frequency, and intrinsic reaction coordinate (IRC) calculations were performed using UB3LYP/aug-ccpVDZ within the Gaussian 03 package15 because density functional calculations are economical and are the starting point for many widely used composite methods, such as G3//B3LYP16 and CBS-QB3.17 These composite methods are tested using thermodynamic quantities, and B3LYP geometries are known to be accurate at minima, making them a good choice. However, transition-state (TS) calculations have shown that B3LYP significantly overestimates dissociating bond lengths when compared to MP2 or QCISD.1 While the harmonic frequencies can be scaled to account for systematic deficiencies of a given method, there is no systematic correction for geometrical parameters. The end result of using B3LYP geometries and MP2, MP4, QCISD(T), or CCSD(T) corrections is that the corrections are calculated at a geometry corresponding to a point in the product channel and not at the transition state. Figure 1 displays a comparison between B3LYP, G3//B3LYP, and CCSD barrier heights of three pathways connected to the INT1 isomer. Comparing the B3LYP and CCSD results, top and bottom frames of Figure 1, shows that the relative ordering of the barrier heights is similar except that B3LYP predicts energetically identical barrier heights for the H þ acrolein and C2H3 þ formaldehyde channels, while CCSD predicts the H þ acrolein barrier is lower by about 1 kcal/mol. This difference disappears once the G3 corrections are applied to the B3LYP geometry, but a new discrepancy is introduced (the isomerization barrier height of the trans conformer is now 1 kcal/mol higher than the H þ acrolein barrier height). Given the above problems with composite methods based upon B3LYP geometries, it was necessary to calculate the geometries and harmonic frequencies using a higher level of theory to get accurate estimates of the barrier heights. Coupled cluster was selected because it can handle the inherently multireference nature of transition states better than MP2 or B3LYP,18,19 and its associated diagnostics20-24 provide a means for identifying problematic geometries. The geometry optimization/harmonic frequency calculation was the most computationally demanding step, and UCCSD/aug-cc-pVDZ provides a suitable balance between accuracy and speed because of the analytic gradients in Gaussian 03. The T1 and D1 diagnostics were used to make sure that the coupled-cluster equations did not break down, especially at any of the transition states. The

Figure 1. The B3LYP (top), G3//B3LYP (middle), and CCSD (bottom) barrier heights of the two energetically lowest dissociation pathways, H þ acrolein (shown in red) and C2H3 þ H2CO (in green) and the INT4 isomerization pathway (in magenta). All geometry optimizations utilized the same basis set, aug-cc-pVDZ. The zero of energy is taken to be trans-INT1, and all barrier heights are zero-point corrected.

quality of these geometries and harmonic frequencies was verified by performing similar calculations using UCCSD(T)/ aug-cc-pVNZ (N = D or T), based on an ROHF reference, in MOLPRO 2008.125-27 The resulting barrier heights, calculated using single-point energies extrapolated to the complete basis set limit as detailed below, were negligibly different, with the largest deviation being less than 0.2 kcal/mol. Similar to the negligible errors in the geometries, UCCSD provides excellent harmonic vibrational frequencies that are on par with, and sometimes better than, UCCSD(T) frequencies.28 Each zero-point vibrational energy (ZPE) was scaled by 0.98 in accord with the work of Radom et al.29 Having obtained accurate geometries and harmonic frequencies, the next step corrects the largest remaining deficiencies in the energies, inclusion of limited dynamic electron correlation and use of an incomplete one-particle basis. The method described below will be referred to hereafter as the complete basis set (CBS) coupled-cluster method. The recent maturation of explicitly correlated methods, such as UCCSD(T)-F12B30 used in this work, simplifies complete basis set calculations immensely by providing energies near to the CBS limit. Hence, the multiple large-basis-set calculations required for CBS extrapolations are replaced by a single calculation utilizing a large basis set. Each single-point calculation, performed using MOLPRO 2008.1, consisted of a restricted, open-shell Hartree-Fock (ROHF) computation, followed by a frozen-core UCCSD(T)-F12B 1702

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Figure 2. Possible products stemming from dissociation of C3H5O. All geometries were calculated using UCCSD/aug-cc-pVDZ, and they are ordered according to molecular weight.

calculation; both used the cc-pVQZ-F12 basis set.31 The ROHF energies, with complete auxiliary basis set (CABS) correction, are intermediate between ROHF calculations using aug-ccpV5Z and aug-cc-pV6Z. The singles and doubles correlation energies average about 10 mH (millihartrees) below those of UCCSD/aug-cc-pV5Z calculations. Neither the ROHF nor the UCCSD-F12B energies were extrapolated because these were already extremely close to the complete basis set limit. However, the perturbative triples contribution in the UCCSD(T)-F12 implementation in MOLPRO does not include any explicit F12 terms, rendering it necessary to perform an extrapolation of the (T) contributions. The extrapolation method of Schwenke32 and UCCSD(T)/aug-cc-pVNZ (N = D and T) single-point calculations were used to derive the perturbative triples contribution at the CBS limit. This extrapolation method was selected because it only requires two points, making application to multiple points on a PES straightforward. The extrapolated (T) values were, on average, 0.1 mH lower in energy than the triples contributions of the UCCSD(T)-F12B calculations. It should be noted that the latter was scaled using the ratio of the MP2-F12 and MP2 correlation energies. Further corrections involving corevalence correlation and relativistic effects were not calculated because they have similar magnitudes but opposite signs, leading to near cancellation.33 All geometries, unscaled harmonic frequencies, and energies are provided in the Supporting Information. Finally, all transition states exhibiting irregular T1/D1 diagnostics were probed for low-lying electronically excited states using state-averaged multiconfiguration self-consistent field (SA-MCSCF) theory in MOLPRO 2008.134,35 and the aug-cc-pVDZ basis set. A progression of active spaces was used to ensure that the resulting ground and electronically excitedstate energies were not strongly coupled to the choice of active space. The smallest active space consisted of seven electrons in seven orbitals, while the largest places 11 electrons in 11 orbitals.

3. RESULTS 3.1. Possible C3H5O Dissociation Products. Before delving into the heart of the PES, it is instructive to look at the products formed from the unimolecular dissociation of C3H5O radicals. Biradicals such as carbenes are not considered, with the exception of ground-state atomic oxygen, because they tend to lie much higher in energy than nonradical isomers.3,36 Figure 2 displays the products grouped by mass so that all isomers will be in close proximity. A large portion, 13 out of 35 multiatom products, involves H-loss channels, and the remaining 22 products result from C-C or C-O bond fission. Although the importance of any pathway on the PES is largely governed by the height of its associated transition state, evaluation of the energetics of each product set yields a zeroth-order description of the PES. The energy of a given product-set asymptote provides a strict lower bound to the barrier heights of channels leading to that product set. Table 1 lists each product set according to its energy relative to the energy of the cis conformer of INT1, where the oxygen atom adds to one of the terminal carbon atoms in the allyl radical. This zero of energy, cis INT1, is used because it is a key intermediate in the O(3P) þ allyl PES and its energy is a median point leading to most of the intermediates lying near or below 0 kcal/mol and nearly all of the barrier heights and product asymptotes having energies above 0 kcal/mol. Having the energy origin fixed to one particular point also facilitates comparison of barrier heights belonging to different intermediates. Of the 28 product pairs, only three are lower in energy than c-INT1 with C2H5 þ CO being the most exoergic at -23.1 kcal/mol. Of the H-loss channels, acrolein and methylketene are the most stable with product asymptotes near 10 kcal/ mol, whereas the remaining C3H4O isomers are 20-70 kcal/mol higher in energy. The H þ propynol and H þ propadienol product pairs were not evaluated in previous studies. They lie about 40 kcal/mol above c-INT1, which makes them accessible provided their associated barrier heights do not exhibit a significant barrier beyond the endoergicity. Two other previously 1703



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Table 1. Ground-State Energies of Each Product Set Calculated Using the CBS Coupled-Cluster Methoda product set C3H5O f

H þ 2-methyloxirene

77.3

CH3 þ formethylene O(3P) þ allyl

76.5 75.2

CH3 þ oxirene

73.8

H þ 2-oxabicyclobutane

68.7

H þ 1-cyclopropenol

54.9

H þ methoxyacetylene

53.7

H þ 2-cyclopropenol

52.8

OH þ cyclopropene

51.9

H þ 2-methyleneoxirane H þ 1-propynol

42.5 40.8

H þ t-2-propynol

40.5

H þ 2H-oxete

40.1

H þ c-2-propynol

38.9

H þ t-propadienol

37.9

H þ c-propadienol

36.1

OCH3 þ acetylene

33.5

H þ cyclopropanone CH3 þ ethynol

32.2 31.6

OH þ allene

29.5

OH þ methylacetylene

28.1

H2COH þ acetylene

24.2

C2H3 þ formaldehyde

18.2

H þ c-acrolein

13.2

H þ methylketene

12.1

H þ t-acrolein CH3 þ ketene HCO þ C2H4 a

energy (kcal/mol)

C2H5 þ CO

11.1 -1.7 -2.6 -23.1

All energies are relative to cis INT1 and are in kcal/mol. Cis/trans conformers are designated by a c/t prefix, respectively.

neglected channels correspond to the production of acetylene and CH3O or H2COH, with the latter being nearly 10 kcal/mol more favorable at 24.2 kcal/mol. Finally, it should be noted that most, but not all, product asymptotes lie below that of O(3P) þ allyl, meaning that studies reacting these two species create intermediates with sufficient internal energy to access all but two product channels (all of the high-lying product channels are likely to be barrierless). 3.2. Stationary Points of the C3H5O Global Potential Energy Surface. The prior work3,5-9,37 on the C3H5O potential energy surface encompassed 15 intermediates, and the current work extends this number to 23. In addition to a larger number of intermediates, many new isomerization pathways between previously known intermediates and product dissociation channels are characterized below. The complexity of the C3H5O PES necessitates parsing it into more manageable pieces, which is accomplished by presenting the intermediates, and all associated reaction pathways, in groups according to the general molecular structure (e.g., epoxide, ether, etc.). Figure 3 displays all of the intermediates and connections between any two intermediates characterized by a first-order saddle point. Figure 3 also shows there are too many transition states between many of the intermediates to create a naming scheme with connected

Figure 3. Connectivity of the intermediates of the O(3P) þ allyl PES described by first-order saddle points. The bold lines correspond to pathways not previously characterized in other works. Similarly, bold intermediate names are first reported here. All intermediates were checked to ensure there were no imaginary frequencies. Similarly, the transition states were analyzed to confirm the presence of only one imaginary frequency, and IRC calculations certified each transition state connected the expected intermediates/products.

intermediates labeled by adjacent integers. Naming of the intermediates continued from those designated by Choi and coworkers, and each new intermediate was numbered in the approximate order in which it was found. The naming of INT4B is an anomaly that arose because it was initially characterized while looking for alternate pathways between INT4 and INT5.37 In addition, many of the intermediates have multiple conformers that are adequately described by cis/trans, corresponding to c/t in the figures, orientation of the heavy-atom backbone. However, almost all intermediates containing a hydroxyl group have at least four conformers, and in these cases two cis/trans designations are used. The first remains the same as in the simpler case, and the second describes the orientation of the hydrogen atom in the hydroxyl group relative to the two carbon atoms adjacent to the oxygen atom. For example, INT7 in Figure 3 is the cis-trans conformer. The cis designation stems from the alignment of the oxygen atom and terminal carbon atom while looking down the C-C bond between the two internal carbon atoms. The trans classification involves looking down the O-C bond, and the hydroxyl hydrogen atom is positioned approximately 180° from the middle carbon atom. Unless otherwise noted, all structures belong to the C1 point group. The diversity in Figure 3 is shown by the variety of structural isomers. There are 15 chain-like intermediates and 8 involving ring structures. Of the acyclic structures, six possess hydroxyl groups, four are etheric radicals, and the remaining intermediates are a mix of aldehydes, ketones, and alkoxy radicals. INT11, one of the etheric intermediates, is listed in Figure 3, but its geometry is excluded from the analysis because it is situated 30 kcal/mol above the next highest intermediate.3 It is not surprising INT11 is energetically unfavorable due to its triradical nature. Similar multiformity is present in the cyclic adducts, which include three epoxides, two four-center cyclic ethers, and various cyclopropane derivatives. Labeling of the carbon atoms will help when 1704



Figure 4. Minima and transition states of INT1 (top) and INT4 (bottom). If a stationary point has two numbers associated with it, the upper one corresponds to the cis conformer and the lower to the trans conformer. Similarly, a depiction of the transition-state structure is given for each conformer. The barrier height from INT4 to INT15 could not be found, but mapping the UCCSD/aug-cc-pVDZ energy as the fourmembered ring forms estimates a value of 55 kcal/mol.

discussing any of the isomerization routes, but the above diversity makes any general rules impossible. However, guidelines for linear intermediates lacking an ether linkage cover a large portion and are as follows. C1 refers to the carbon atom bonded to the oxygen atom, C2 is the carbon atom bonded to C1, and C3 is the carbon atom at the far end of the chain from oxygen. Labeling of carbon atoms in the more ambiguous cases will be discussed as needed. 3.3. Stationary Points of Straight-Chain Alkoxy Intermediates. INT1 arises from addition of ground-state atomic oxygen to either terminal carbon atom of the allyl radical. It is the lone alkoxy radical intermediate having the bulk of the radical electron density residing on the oxygen atom. The elongated C-O bond length reflects the alkoxy character with a value of 1.387 Å as compared to INT4, INT4B, and INT5 whose C-O bond lengths are clustered between 1.19, and 1.25 Å signifying carbonyl character. An additional consequence of the alkoxy character present in INT1 is that it lies 20-30 kcal/mol higher in energy than conformers possessing a carbonyl group, and this places INT1 energetically near to the epoxide intermediates, which have considerable ring strain. The cis conformer possesses Cs symmetry, but the oxygen atom in the trans conformer is about 50° out of the plane defined by the carbon atoms, rendering it C1. Figure 4 shows the two conformers of INT1 and the transition states leading from INT1. The energetically lowest pathway corresponds to isomerization of the trans conformer to INT2, which is defined by reduction of the O-C-C angle to form an epoxide ring.

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However, INT2 does not have any dissociation pathways exhibiting barrier heights comparable to the isomerization of INT1 to INT4 or dissociation of INT1 to form H þ acrolein or C2H3 þ formaldehyde. Hence, INT1 radicals with vibrational energies in excess of 7 kcal/mol may isomerize to INT2, but the only route to a product channel is through the INT1 well, and those INT1 radicals having more than 17 kcal/mol of vibrational energy will leave via one of its other pathways. This will be discussed more completely in section 3.4. The isomerization transition state leading from INT1 to INT4 is the next lowest barrier height at about 17 kcal/mol, which is surprising given that H-atom migration pathways are generally in the 20-40 kcal/mol range.3 However, the reverse barrier for isomerization of INT4 to INT1 falls in the above range, suggesting that the relatively low barrier leading to INT4 is due to INT1 lying more than 20 kcal/mol above the other intermediates having a similar structure. On the basis of geometrical concerns, it should be possible to effect a 1,3hydride shift involving the hydrogen atom lying in the plane formed by the carbon atoms, but all searches for this transition state were unsuccessful. The next two lowest barrier heights leading from INT1 are dissociation pathways. The lower pathway results in H-atom loss and the formation of acrolein, which was the major product detected in the first detailed experimental study of the reaction of allyl radicals and O(3P).38 The slightly higher transition state involves C-C bond cleavage to yield C2H3 þ formaldehyde. Both are loose transition states, evidenced by the congruence between the structure at the transition state and those of the final products. The barrier heights of H-atom migration pathways to form alkenol moieties range from 21 to 37 kcal/mol. The energetically lowest barrier height leads to INT7, involves a C1-O hydride shift, and lies energetically between those of the H þ acrolein and C2H3 þ formaldehyde pathways. The barrier of the C3-O hydride shift to form INT22 is 2-3 kcal/mol higher than the transition state to INT7, whereas the C2-O hydride shift has a considerably higher barrier at 36.5 kcal/mol. Interestingly, the formation of a ring-strained isomer, INT16, has a lower barrier height than that to INT6. INT4 has a few features similar to INT1 even though it is about 20 kcal/mol more stable; the cis conformer has Cs symmetry but the trans conformer has C1 symmetry, and they have a few dissociation barrier heights that are energetically near, or even below, the isomerization pathways. The lowest barrier height, aside from the barrierless route to INT3, corresponds to C1-C2 bond fission that yields HCO þ ethene. The barrier is approximately 25 kcal/mol above the bottom of the INT4 well, whereas the other dissociation pathway, to H þ acrolein, is 37 kcal/mol above INT4. Of the isomerization barriers, the one to INT4B is the lowest and is only 5-7 kcal/mol higher than the barrier to HCO þ ethene, as shown in the bottom frame of Figure 4. Hence, significant branching to INT4B is possible based on the relative barrier heights, but this closeness is diminished because the INT4fINT4B transition state is much tighter than the one from INT4 to HCO þ ethene. The next two lowest isomerization barrier heights, corresponding to INT5 and INT1, reside at >34 kcal/mol above INT4. The transition state leading to INT7 is the highest hydride shift barrier height, which is expected because the unpaired electron is localized on C3 and not the oxygen atom. However, significant electron density resides in the C1-O π* orbital and promotes the hydride shift from C2 to the oxygen 1705



Figure 5. Minima and transition states of the INT4B (top) and INT5 (bottom) isomers.

atom. The highest isomerization pathway, leading to INT15, was elusive. The energy was calculated with UCCSD and SAMCSCF while systematically decreasing the O-C4 distance. The former provides an estimate of the barrier height, and the latter showed that this part of the PES has a low-lying electronically excited state that is only a few kcal/mol above the ground state. INT4B was omitted from Choi’s initial assessment of the PES, and it was shown, but not discussed, by Xie et al.9 Unlike INT1 and INT4, both conformers of INT4B belong to the Cs point group, and INT4B does not have any energetically low-lying transition states (see Figure 5). As for the latter point, most of the INT4B transition states are 4-20 kcal/mol above cis INT1, making them some of the lowest on the C3H5O global PES, but INT4B is one of the most stable conformers at approximately 30 kcal/mol. Hence, the lowest barrier, the O-C3 hydride shift to form INT7, is nearly 35 kcal/mol above the bottom of the well. This low barrier between INT4B and INT7 behaves similarly to the one between INT1 and INT2 because the dissociation barrier heights of the former pair are situated at 15-20 kcal/mol, meaning all INT4B radicals isomerizing to INT7 are most likely to return to INT4B and isomerize or dissociate via a different pathway. Isomerization channels from INT4B to INT4 and

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INT5 are 6-10 kcal/mol higher in energy than the one leading to INT7, but they have small dissociation barriers, which make it likely that any INT4B radicals isomerizing to INT4 or INT5 will exit one of their product channels before isomerizing again. The other isomerization pathways are considerably higher in energy and are unlikely to appreciably influence the unimolecular reaction dynamics of INT4B. The primary interest in INT4B is as one of the radical intermediates en route to the C2H5 þ CO product channel (via INT5), the most exothermic product channel of the O(3P) þ allyl reaction. However, the large isomerization barrier between INT4 and INT4B renders this channel unimportant as compared to the direct dissociation of INT4 to HCO þ C2H4. While INT4B has a myriad of isomerization pathways, it only exhibits two dissociation pathways, and both involve H-atom loss. The barrier height corresponding to H þ acrolein is about 35 kcal/mol above INT4B. The barrier height of the trans conformer is lower than that of the cis, in accord with the H þ acrolein channels belonging to other intermediates such as INT1, INT4, and INT7. The other dissociation pathway, H þ methylketene, is 2-4 kcal/mol higher than the dissociation barrier of H þ acrolein, and there is a negligible difference between the barrier height associated with each conformer. INT5 is the most stable conformer on the C3H5O global PES, and the respective energies of the cis and trans conformers are 31.7 and 31.2 kcal/mol below that of cis INT1. INT5 also has the only route to the most exothermic product set, C2H5 þ CO, whose transition state dominates the dynamics of INT5 radicals having at least 15 kcal/mol of vibrational energy because it is 27 kcal/mol below the next-lowest barrier height (see Figure 5). The remaining transition states, both isomerization and dissociation, have energies between 10-17 kcal/mol, making them relatively low-lying with respect to the rest of the PES. One note about the H þ methylketene transition state is that a scan of the dihedral angle interconverting cis/trans conformers is nearly flat, making it likely both INT5 conformers access the same transition-state geometry. 3.4. Stationary Points of Epoxide Intermediates. INT2 is formed from the addition of O(3P) between a terminal and the center carbon atoms to give a bridged structure. It is the most stable of the epoxide conformers, but only by 3-4 kcal/mol. Figure 6 displays the transition states leading from INT2. The isomerization routes to INT1 and INT12 have low barrier heights, 5.2 and 13.0 kcal/mol, respectively. However, the barrier heights of the other two isomerization pathways, leading to the other epoxide conformers, are about 50 kcal/mol above INT2, which is not surprising given that the epoxide ring prevents the heavy-atom backbone from contorting significantly to facilitate hydride transfer. Additionally, the lone dissociation barrier height of INT2 is over 30 kcal/mol above the isomerization barrier height to INT12. The result of these energetically high-lying transition states is that dissociation of INT2 will be negligible because all of the INT2 radicals will isomerize to INT1 or INT12. However, the latter has relatively high isomerization and dissociation barriers, which will lead to much of the INT12 isomerizing back to INT2. The only epoxide intermediate with multiple conformers is INT10, and Figure 6 shows both conformers. The H atom on C1 is on the same side as the H atom on C2 in the more energetically stable conformer, INT10-2. The interconversion barrier (4.8 kcal/ mol calculated using G3//B3LYP) between the two conformers is relatively large when compared to cis/trans isomerization barriers 1706



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Figure 6. Conformers and transition states of INT2 (top) and INT10 (bottom). The two conformers of INT10 are distinguished by the position of the hydrogen atom bonded to the C1 carbon atom. The INT10fINT4B barrier exhibits a large D1 diagnostic, 0.147 (most minima and transition states have values less than 0.1), which indicates there is a small region of the molecule that is not well described by the coupled cluster equations. However, the value of the T1 diagnostic is only slightly elevated at 0.040 (most stationary points have values less than 0.030), and the ratio of the T1 to the D1 diagnostic is 0.27, which is in line with the values calculated at other stationary points. The latter indicates that the coupled-cluster wave function does not have any large variations in the orbital rotation parameters, which would definitely suggest a breakdown of the method at this stationary point.

of INT1 and similar intermediates. However, this barrier is still small as compared to the energetically lowest barrier, which leads from INT10 to trans INT4B and is approximately 14 kcal/mol above the INT10 conformers. The remaining channels, H-atom migration to the other epoxide intermediates and oxirene þ CH3, will contribute negligibly to the INT10 dynamics because they are more than 30 kcal/mol above the INT4B isomerization barrier. 3.5. Stationary Points of Enolic Intermediates. Hydroxylcontaining isomers comprise a significant fraction of the C3H5O isomers, and INT6 is the first of these, shown in Figure 7; it corresponds to addition of OH to one of the terminal carbon atoms of allene. The oxygen atom sits in the plane of the carbon atoms in the c-c and c-t conformers, but only the c-t conformer has Cs symmetry because the hydroxyl hydrogen atom in the c-c conformer is 63° out of the plane formed by the heavy atoms. In contrast to the c-c and c-t conformers, the oxygen atom in the trans backbone is 60° out of the plane created by the carbon atoms. The nonplanarity present in the trans

Figure 7. Transition states and conformers of INT6 (top) and INT7 (bottom); the conformers are first grouped by the orientation of the heavy-atom backbone, and the second grouping is based on the orientation of the hydroxyl H atom.

backbone of INT6 gives rise to three conformers instead of the usual two seen in other hydroxyl-containing intermediates. However, two of these conformers, trans-cis and trans-cis2, are isoenergetic, and the energy barrier for interconversion is negligibly small. Given the small OH torsional barrier, it is not surprising that the trans-cis2 conformer does not have any distinct transition states leading to other intermediates or dissociation products. In addition to being barrierless, the OH þ allene product channel is the lowest energetically at approximately 27 kcal/mol above INT6. All of the OH-loss pathways exhibited imaginary frequencies less than 200 cm-1 at the UB3LYP/aug-cc-pVDZ level of theory in addition to two vibrational frequencies below 100 cm-1. Some pathways predicted as barrierless by coupled-cluster 1707


The Journal of Physical Chemistry A calculations have small barriers when calculated at the B3LYP level of theory. Hence, the nearly barrierless B3LYP transition states mentioned above posit that the OH-loss dissociation pathways should be regarded as barrierless. The other dissociation transition states are approximately 10-15 kcal/mol higher in energy, thereby making them unlikely contributors to the dynamics of INT6 radicals. The INT6 isomerization barrier heights also lie higher in energy, ranging from 33 to 49 kcal/mol above INT6, when compared to the OH þ allene product asymptote. An interesting feature in Figure 7 is the variability in the C1-C2 hydride shift barrier height proceeding to INT7. The transition states corresponding to the c-x conformers are about 10 kcal/ mol lower than their t-x counterparts. Looking at the transitionstate structures, it is evident that the heavy atoms lie in the same plane. Hence, the t-x conformers must reorient the heavy atoms to lie in the same plane to complete H-atom migration, whereas the c-x conformers already have the heavy atoms in a planar arrangement. All conformers of INT7 belong to the Cs point group, and they are approximately 20 kcal/mol lower in energy than the other OH-containing intermediates. Delocalization of the unpaired electron across the entire heavy-atom framework accounts for the added stability of INT7. As Figure 7 shows, INT7 has an enormous number of isomerization and dissociation pathways. The lowest barrier height is the O-C3 H-atom shift yielding INT4B, and all other barrier heights are at least 15 kcal/mol higher in energy. The three next lowest transition states are clustered about 45 kcal/mol above INT7 and correspond to a loose dissociation leading to H þ acrolein and two tight isomerization pathways leading to INT1 and INT9. In the former transition state, the hydroxyl hydrogen atom swings out of the symmetry plane as the O-H distance increases, thereby destroying the Cs symmetry present in INT7. Each of the H þ acrolein transition-state structures, presented in the lower frame of Figure 7, possesses an enantiomer having an identical barrier height. Of the INT1 and INT9 pathways, only the transition state leading to INT1 leads to dissociation products because INT9 is a cyclopropene derivative whose other transition states lie much higher in energy than the energy required for isomerization back to INT7. INT8 is similar to INT7 in that all of its conformers belong to the Cs point group, and it is similar to INT6 because it has a barrierless OH-loss channel. This OH-loss channel results in methylketene as the cofragment, which is about 1.5 kcal/mol lower in energy than the OH þ allene product asymptote of INT6. The next lowest barrier height, corresponding to isomerization to INT4B, is relatively similar in energy, at 33 kcal/mol above INT8. The isomerization barrier heights to other alkenol radical intermediates, INT7 and INT17, are 7-10 kcal/mol above the O-C2 hydride shift leading to INT4B. The H-loss barrier heights are close in energy to those of the INT7 and INT17 isomerization pathways. INT17 is the only linear, hydroxyl-containing C3H5O isomer possessing only two conformers. Figure 8 shows that the heavyatom backbone can take on cis or trans configurations, whereas the hydroxyl H atom is always trans (as defined previously in section 3.2). The radical electron is localized in an sp2 hybridized orbital on C1, and the interaction of this unpaired electron with the lone pair on the oxygen atom prevents the hydroxyl H atom from forming stable cis conformers. All of the INT17 transition states have barriers in excess of 30 kcal/mol, which will isolate INT17 from the rest of the C3H5O PES. It is likely that the

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Figure 8. Transition states and conformers of INT8 (top), INT17 (middle), and INT22 (bottom); the conformers are first grouped by the orientation of the heavy-atom backbone, and the second grouping is based on the orientation of the hydroxyl H atom. INT17 is the exception to this rule because it only has two conformers corresponding to the orientation of the heavy-atom backbone.

INT17 dynamics will be largely determined by tunneling through the H-atom migration barriers to INT4B, INT7, and INT8. Any INT17 radicals exhibiting more than 35 kcal/mol of vibrational energy will undergo isomerization to INT4B because its barrier height is at least 6 kcal/mol lower than the other barriers. All of the conformers of INT22 have C1 symmetry except for the cis-trans conformer, which belongs to the Cs point group. H-atom migration from the oxygen atom to C3 defines the energetically lowest pathway, which has a barrier of 19 kcal/mol and results in the formation of INT1 radicals. The next lowest barrier is the transition state leading to the H2COH þ acetylene product channel. Even though this dissociation barrier height is 1708



Figure 9. Conformers of INT12 (top), INT13 (middle), and INT14 (bottom) and their associated reaction pathways. The cis/trans conformers are defined by the orientation of the heavy-atom backbone. The T1 and D1 diagnostics of the acetylene þ OCH3 transition state are higher than average, with values of 0.032 and 0.132, respectively.

10 kcal/mol above the isomerization barrier height to INT1, it may still contribute to the INT22 dynamics. In contrast to the isomerization route to INT1 that can only proceed via the cis-cis conformer, all INT22 conformers can access the H2COH þ acetylene transition states independently, thereby giving this route an effective statistical factor of 4 relative to isomerization to INT1. Additionally, branching to the acetylene þ H2COH product channel is elevated because the dissociation channel transition states are loose as compared to the INT1 transition state. 3.6. Stationary Points of Etheric Intermediates. INT12 is the first of three C3H5O isomers containing an ether linkage and is more stable than the other two by 8-17 kcal/mol. INT12 is connected to INT2 via a relatively small, 16.9 kcal/mol, transition state shown in Figure 9. The isomerization proceeds via a ring-opening mechanism alternate to the one discussed in connection with INT1; in this case, the carbon-carbon bond in the epoxide ring breaks, resulting in isomerization of INT2 to INT12. The next lowest transition state leading from INT12 is an H-atom migration from C3 to C1 (in the ether structures, C1 is

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the isolated terminal carbon atom), and it is 13 kcal/mol above the INT2 isomerization barrier. INT12 has one product channel, leading to C2H3 þ H2CO, which is about 34 kcal/mol above the bottom of the well. The next lowest pathway leads to a fourmembered ring, INT15, and the highest barrier from INT12 is associated with the second H-atom migration pathway (this time from C2 to C1) that yields INT13. INT13 differs from the other two ether isomers in that it does not have any isomerization pathways with small barrier heights (see Figure 9). The energetically lowest transition state leads to the ketene þ CH3 product channel via the cis conformer of INT13. The trans conformer of INT13 accesses a second-order saddle point during the C1-O bond cleavage, but the looseness of this transition state results in a difference of less than 2 kcal/mol with respect to the first-order saddle point associated with the cis conformer. The three isomerization pathways have barriers greater than 30 kcal/mol above the INT13 well (and >17 kcal/ mol above the ketene þ CH3 barrier), thereby making their contributions to the INT13 dynamics vanishingly small. INT14, pictured in Figure 9, has the highest energy isomers of any C3H5O radicals studied in this work at approximately 15 kcal/mol above the INT1 isomers. In starting 15 kcal/mol above INT1, INT14 radicals having insufficient vibrational energy to surmount the lowest barrier, isomerization to INT12, but could still dissociate by first tunneling through the H-atom migration barrier to INT12, followed by isomerization to INT2. The next lowest barrier height corresponds to the acetylene þ OCH3 product channel. The only other intermediate possessing an acetylene product channel is one of the hydroxyl isomers, INT22. The INT14 acetylene product channel is not likely to contribute significantly to the overall product branching of the O(3P) þ allyl reaction because its barrier height is 10 kcal/mol higher than that of INT22 and INT14 is removed from INT1 by several isomerization steps. 3.7. Stationary Points of Three-Membered Ring Intermediates. INT3 is an alkoxy radical, analogous to INT1, which is reflected in the C-O bond length of 1.304 Å. The isomerization of INT3 to INT4, shown in Figure 10, does not exhibit a barrier using the CBS coupled-cluster method. However, G3// B3LYP and UCCSD/aug-cc-pVDZ calculations predict 0.8 and 0.5 kcal/mol isomerization barrier heights, respectively, which illustrates that the presence of this barrier is independent of the method and is caused by an incomplete one-particle basis. The disappearance of the INT3 to INT4 barrier with larger basis set agrees with Choi’s findings using CBS-QB3.3 Even if a small barrier exists between INT3 and INT4, the remaining INT3 barrier heights are at least 40 kcal/mol higher in energy, and all INT3 radicals will isomerize to INT4. INT9 is a cyclopropene derivative in which OH adds to either one of the carbon atoms involved in the double bond. The single small-barrier pathway, shown in Figure 10, is about 11 kcal/mol above INT9 and leads to the t-c and t-t conformers of INT7. Hydride transfer routes involving two carbon atoms in the ring have much higher barrier heights than the other isomerization pathways, which is similar to H-atom migration transition states between the epoxide conformers. In both cases, the ring structure cannot adjust significantly to facilitate the hydride shift. This fact is evidenced by the difference in barrier heights between the routes to INT3 and INT18. The barrier height of the former is 10 kcal/mol lower than that of the latter. In terms of structural rearrangement, the O-C1-C2 angle decreases by 25° in going from INT9 to the transition state connecting to INT3. 1709



Figure 10. Minima and transition states of INT3 (top) and INT9 (bottom).

Figure 11. INT15 and INT16 minima and their associated transition states.

3.8. Stationary Points of Four-Membered Ring Intermediates. Figure 11 depicts the portion of the C3H5O PES describ-

ing the four-membered ring isomers, INT15 and INT16. Although it is apparent that INT15 belongs to the C1 point group, assigning the point group symmetry to INT16 is more difficult because it nearly has C2v symmetry. The hydrogen atom on the carbon atom geminal to the CH2 groups is 25° out of the plane formed by the heavy atoms, which lowers the symmetry to Cs. The lowest energetic pathways of both C3H5O isomers are ring-opening isomerizations. INT15 has a second such pathway, to INT4, but it is 20 kcal/mol higher than the barrier to INT12, and it has a low-lying excited state. The next lowest barrier heights correspond to the 2H-oxete channel from H-atom loss,

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Figure 12. Energetics of the INT18 (top), INT19 and INT21 (middle), and INT20 (bottom) radicals and their transition states. The INT20fINT19 transition state exhibits large T1 and D1 diagnostic values of 0.060 and 0.254, respectively. The combination of these elevated diagnostic values and a smaller-than-average ratio of 0.24 means that coupled cluster does not provide a reasonable description of this saddle point, and its accuracy should be viewed with caution.

which should contribute to the dynamics because these pathways are much looser than any of the ring-opening transition states. H þ 2H-oxete formed from the dissociation of INT15 is barrierless, but the INT16 analogue has a small barrier beyond the endoergicity. The H-atom migration barrier height is 50 kcal/mol above the INT15 minimum, which makes isomerization between INT15 and INT16 unlikely because it is >7 kcal/mol above the next-highest barrier and it is a tight transition state. 3.9. Stationary Points of the Remaining C3H5O Intermediates. Unlike the previous groups of intermediates, the final four C3H5O isomers do not share structure similarities. However, Figure 12 demonstrates they constitute a part of the potential energy surface in which interconversion barrier heights between INT18-INT21 are relatively small, but isomerization to other intermediates is prohibited by significantly larger barrier heights. Dissociation of INT19 to methyl þ ketene is the only pathway having a low energetic barrier. It is 40 kcal/mol above the INT19 well, but it is 5-15 kcal/mol lower than the interconversion barrier heights. Hence, methyl þ ketene is expected to be the major product pair resulting from C3H5O radicals born on this part of the PES. To approach this from a slightly different perspective, collisions between OH and allene that undergo addition/elimination will likely result in methyl þ ketene production. One isomerization pathway of note belongs to the 1710



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branching fraction to HCO þ C2H4 slightly in the lower-energy regime. Calculations beginning with INT4 produced the expected results, almost complete branching to HCO þ C2H4, so these results were not included in Figure 13. Similarly, INT4B was omitted because branching from INT7 to INT4B is significant and a plot of the INT7 branching describes both. The branching ratios are discussed thoroughly in section 4.

Figure 13. Branching ratios calculated using RRKM theory and the coupled-cluster stationary points given in the previous subsections. All oscillations in the branching-ratio curves stem from too few stochastic trials in the RRKM calculations. Increasing the number of trials from 10 000 to 100 000 should remove most of these artifacts.

INT19 methyl migration that yields INT5. Any radicals traversing this route will likely dissociate before having the opportunity to isomerize back to INT19. The transition state is only 14 kcal/mol above that leading to methyl þ ketene, which makes the isomerization route mildly competitive for radicals having large amounts of vibrational energy. Additionally, radicals with very little vibrational energy may leak through to INT5 via tunneling because the INT19 and INT5 isomers lie close in energy. 3.10. RRKM Branching Ratios. Figure 13 shows the branching ratios calculated for INT1 and INT7 using Multiwell.39,40 The harmonic frequencies were used without alteration because the small correction of 0.98 produced insignificant differences when tried with only one intermediate well. H-atom tunneling was neglected in these calculations because it produced negligible differences in most of the branching ratios. However, when tunneling was included for transition states between intermediates via 1-D asymmetric Eckart barriers, it increased the

4. DISCUSSION The above subsections demonstrated the diversity present in the C3H5O PES; inclusion of only five isomers (INT1, INT2, INT4, INT4B, and INT7) provides transition states reaching all but 5 of the 22 isomers discussed in this work. The dynamics of radicals born on the C3H5O PES depend greatly upon their originating location, but some general conclusions can nonetheless be drawn. INT4 and INT5 preferentially dissociate because the barriers to their respective HCO þ C2H4 and C2H5 þ CO pathways are small as compared to isomerization pathways leading to other isomers. Hence, Figure 13 shows that dissociation of INT4 and INT5 radicals will occur before they could isomerize to another intermediate. Even though INT1, INT2, INT4B, and INT7 do not have low-barrier dissociation pathways analogous to those found in INT4 and INT5, they have low-lying isomerization barriers leading to INT4 and INT5. These isomerization barriers allow INT1, INT2, INT4B, and INT7 to act as funnels that direct C3H5O radicals toward INT4 and INT5. INT4B possesses hydride shift barriers energetically similar to INT4 as to INT5, making it the only plausible route leading to INT5 because isomerization of INT4 to INT5 is not likely given INT4’s proclivity to dissociate to the HCO þ C2H4 product channel. Thus, the bulk of the C3H5O dynamics stemming from an intermediate able to readily isomerize INT1, INT2, or INT4 will result in HCO þ C2H4. Starting intermediates having low isomerization barriers to INT4B or INT7 will result in a mixture of HCO þ C2H4 and C2H5 þ CO, as shown in Figure 13. Comparing the above branching to experimental results shows qualitative agreement. Bulk kinetics work in 2009 by Hoyermann et al.41 used laser flash photolysis to generate the O and allyl reactants and measured the branching to the stable end products of the reaction by quantitative FTIR spectroscopy at room temperature. The measured branching is 47% to H þ acrolein, 41% to H þ CO þ C2H4, 7% to H2CO þ C2H3, and 40 kcal/mol. Most of the isolated intermediates are singletons that only have energetically unfavorable isomerization barrier heights (e.g., INT6, INT8, and INT14). As such, these lone isolated intermediates do not block off any other portions of the PES by acting as a bottleneck. In contrast, INT18-INT21 form a small group where the isomerization barriers between these isomers are relatively small, but the isomerization barriers leading to intermediates on the rest of the PES are quite large. Therefore, the dynamics of INT18-INT21 radicals is relatively decoupled from the rest of the C3H5O PES, and the majority of radicals born in the INT18-INT21 wells will eventually isomerize to INT19 or INT21 and subsequently dissociate to CH3 þ ketene or OH þ allene, respectively. A survey of about 50 barrier heights on the C3H5O PES showed that the coupled-cluster method used in this work and G3//B3LYP have marked differences. The discrepancies between the coupled-cluster and G3//B3LYP isomerization barrier heights are scattered relatively uniformly about 0 kcal/mol, with most of the differences falling within (0.5 kcal/mol. The dissociation barrier heights exhibited a different trend where a large fraction of the differences were 1.5 ( 0.5 kcal/mol. Comparison of Choi’s PES3 is difficult because the conformers are not given, which can make a significant difference in barrier height for some of the transition states. Comparing the conformers in this work that yield barrier heights closest to those calculated by Choi resulted in an average difference of 1 ( 1 kcal/mol, which shows that CBS-QB3 has an accuracy similar to G3//B3LYP. The small number of data points precludes any analysis as to whether CBS-QB3 exhibits systematic discrepancies similar to those seen with G3//B3LYP.

’ ASSOCIATED CONTENT

bS

Supporting Information. Structures, harmonic vibrational frequencies, rotational constants, and extrapolated energies are given herein for all intermediates and transition states. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: benjfi[email protected].

’ ACKNOWLEDGMENT This work was supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy, under Grant No. De-FG02-92ER14305 under the supervision of my Ph.D. adviser, L. J. Butler. A special thanks is also due K. Peterson for his enlightening discussions regarding the explicitly correlated coupled cluster calculations.

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Theoretical Study of Isomerization and Dissociation Transition States

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