Hydrogen Shifts in Aryl Radicals and Diradicals: The Role of m

Dec 11, 2017 - (1-4) Dramatic skeletal rearrangements of PAHs, probed by flash vacuum pyrolysis (FVP) experiments, have been proposed to involve numer...
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Cite This: J. Org. Chem. 2018, 83, 314−322

Hydrogen Shifts in Aryl Radicals and Diradicals: The Role of m‑Benzynes Simon Luo,† Ariel J. Kuhn,† Ioannina Castano,† Claire Castro,† and William L. Karney*,†,‡ †

Department of Chemistry and ‡Department of Environmental Science, University of San Francisco, 2130 Fulton Street, San Francisco, California 94117, United States S Supporting Information *

ABSTRACT: Density functional and coupled cluster results are presented for hydrogen shifts in radicals derived from polycyclic aromatic hydrocarbons (PAHs) and for rearrangement mechanisms for several phenylenes. RCCSD(T)/ccpVDZ//UBLYP/cc-pVDZ free energy barriers for 1,4-H shifts at 298 K are consistently predicted to be ca. 25 kcal/mol, whereas barriers for 1,5- and 1,6-shifts range from 6 to 28 kcal/mol. The barriers correlate reasonably well with the distance from the radical center to the shifting hydrogen in the reactant. Proposed mechanisms (via diradical intermediates) of known rearrangements of linear [3]phenylene, benzo[b]biphenylene, and angular [4]phenylene have BD(T)/cc-pVDZ//(U)BLYP/ccpVDZ computed barriers of 74−82 kcal/mol, consistent with pyrolysis temperatures of 900 to 1100 °C. Hydrogen shift reactions in most of the aryl diradicals arising from phenylenes produce m-benzyne intermediates which, despite being 8−15 kcal/mol more stable than other diradicals involved in the pathways, do not significantly lower the computed overall free energies of activation.

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INTRODUCTION Polycyclic aromatic hydrocarbons (PAHs) play key roles in diverse areas, including materials, combustion, and environmental pollution.1−4 Dramatic skeletal rearrangements of PAHs, probed by flash vacuum pyrolysis (FVP) experiments, have been proposed to involve numerous types of mechanistic steps and reactive intermediates such as carbenes, radicals, and diradicals.5,6 One reaction type central to PAH chemistry is the intramolecular hydrogen shift in PAH radicals.7,8 Such shifts are exemplified by the 1,4-H shift in 2dehydrobiphenyl (1, Scheme 1), but can occur in diradicals as well as in radicals.

in more rigid PAH radicals and a low barrier of 9.3 kcal/mol for the 1,5-H shift in benzo[c]phenanthrene (2, Scheme 2).11 Scheme 2

The low activation energy for 2 presumably arises from two favorable geometric factors: the short distance between the radical center and the hydrogen, and the absence of steric interactions that cause twisting in the skeleton (as in 1).11 Sordo and Dannenberg reported similarly small computed activation energies of 8−10 kcal/mol for 1,5-H shifts in radicals derived from benzophenone, diaryl ethers, and diaryl thioethers;10 the computations are consistent with experimental results on the same systems.10,12,13 Beyond the importance of hydrogen shifts in radicals, such processes can also occur in diradicals produced by pyrolysis of metastable PAH precursors containing strained rings. Of particular interest here are hydrogen shifts resulting from pyrolysis of biphenylene-derived systems, including the conversion of linear [3]phenylene (3)14 to angular [3]phenylene (4), 15,16 the rearrangement of benzo[b]biphenylene (5)17 to fluoranthene (6),18,19 and the rearrange-

Scheme 1

Noteworthy experiments in this area include the isolation of 1- and 2-phenylbiphenylene from pyrolysis of 1,6diphenylhexa-3-ene-1,5-diyne,9 1,5-hydrogen shifts in diarylketones and related systems,10 and the use of hydrogen shifts in aryl radicals to synthesize bowl-shaped PAHs and fullerenes.8 To date, mechanistic support for experimental observations in this area comes mainly from computational studies, most of which employed relatively low levels of theory. Some key findings are summarized here. Prior computational results on hydrogen shifts in aryl radicals include a barrier of 23.6 kcal/mol for the 1,4-shift in 1 at the UBLYP/6-311G** level.11 Cioslowski and coworkers also computed barriers of 29−34 kcal/mol for the 1,4-H shift © 2017 American Chemical Society

Received: October 27, 2017 Published: December 11, 2017 314

DOI: 10.1021/acs.joc.7b02724 J. Org. Chem. 2018, 83, 314−322

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The Journal of Organic Chemistry ment of angular [4]phenylene (7)20 to biphenylene dimer (8),21,22 as shown in Scheme 3. The strain due to the four-

geometries. The RCCSD(T) method minimizes spin contamination that can arise in UCCSD(T) calculations.30 For reactions involving diradicals (i.e., systems with closed-shell starting points), single point energies were computed using the Brueckner doubles method, BD(T),33 with the cc-pVDZ basis set at the (U)BLYP geometries. The BD(T) method is known to give good results for diradicals in which the two radical sites interact weakly or not at all.34 In addition, the validity of BD(T) calculations on the m-benzyne intermediates of interest here was confirmed by a combination of RCCSD(T) and CASPT235 calculations on biphenylene (19) and singlet and triplet 2,6-didehydrobiphenyl (21). Details are provided in the Supporting Information. BLYP and BD(T) calculations were performed using Gaussian 09, 36 and RCCSD(T) calculations were carried out with MOLPRO.37,38 CASPT2 calculations were done with Molcas 8.0.39 Structures were visualized with MacMolPlt,40 and vibrational modes and orbitals were viewed using Molden.41

Scheme 3

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RESULTS AND DISCUSSION Monoradical Model Systems. We first describe results on monoradicals in an attempt to clarify the most important factors affecting barrier height. The systems in Schemes 4, 5, and 6 represent 1,4-, 1,5-, and 1,6-H shifts, respectively, and Scheme 4 membered rings23 makes the starting materials susceptible to C−C bond cleavage, producing aryl diradicals. The mechanisms proposed for these cases involve hydrogen shifts over chains of four, five, or six carbons, along with m-benzyne intermediates. Whereas the structure, thermochemistry, and spectroscopy of m-benzyne have been studied extensively,24−26 little work has been done on hydrogen abstraction reactions involving m-benzynes. Given the paucity of high-level computational and experimental mechanistic studies on these systems, we investigated hydrogen shift reactions in PAH radicals and diradicals using more sophisticated levels of theory. Here we report density functional and coupled cluster calculations aimed at elucidating the mechanisms and activation energies for the reactions in Scheme 3 and numerous monoradical model systems, and we address the following questions: (1) How does barrier height for hydrogen shifts in aryl radicals depend on chain length and C−H distance in the cyclic transition state? (2) How does the presence of a second nearby radical site affect the barrier height for hydrogen shifts? Does the presence of a m-benzyne intermediate affect the overall barrier? (3) Are the computed mechanisms and barrier heights for the reactions in Scheme 3 consistent with experimental observations such as the pyrolysis temperatures employed?

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COMPUTATIONAL METHODS

Geometries of all stationary points were optimized at the (U)BLYP/ cc-pVDZ level of theory.27−29 The UBLYP method was chosen because it has been shown to perform well for m-benzyne, compared to CCSD(T) results.24 UBLYP/cc-pVDZ vibrational analyses were also performed for all stationary points to verify whether they were minima or transition states, and to obtain zero-point energies and thermal corrections to the free energy. Wave functions of singlet diradicals and adjacent transition states were tested for stability to confirm that lower-energy wave functions could not be found at the optimized geometries. For monoradicals, single point energies were computed using restricted open-shell coupled cluster theory, RCCSD(T),30−32 with the cc-pVDZ basis set, at the UBLYP 315

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Scheme 6

within each category span a range of chain lengths and C•−H distances. Figure 1 depicts UBLYP/cc-pVDZ optimized structures of representative minima and transition states. The RCCSD(T)/cc-pVDZ//UBLYP/cc-pVDZ computed free energies of activation at 298 K for the 1,4-H shifts in Scheme 4 are all remarkably similar: 24.5−25.8 kcal/mol. In the phenylbiphenylene radicals 11a and 11c, the barrier is only about 1 kcal/mol lower than in 1, regardless of which hydrogen shifts. This suggests that the fused four-membered ring exerts little influence on the reaction. In all the systems in Scheme 4, the C•−H distances in the transition state are in the range 1.375−1.395 Å compared to ca. 2.60 Å in the reactants. Radical 10a is an exception (C•−H = 2.83 Å) due to steric interactions between hydrogens. Nevertheless, significant inter-ring bending in transition state TS10a (as reflected in the CCC angles in Figure 1) largely relieves the steric interactions between hydrogens. For all systems in Scheme 4, the coupled cluster barriers are ca. 5−6 kcal/mol higher than those obtained with BLYP. In contrast to the relative consistency of barrier heights for 1,4-shifts, the free energies of activation for the 1,5-shifts shown in Scheme 5 span a large range, with RCCSD(T) values from ca. 10 kcal/mol for benzo[c]phenanthrene (2) to ca. 28 kcal/mol for phenylbenzopentalene 12c. In this series, lower barriers correlate roughly with shorter distances between the radical center and the transferring hydrogen: 2.07 Å in 2, 2.38 Å in 10c, 2.51 Å in 12a, and 3.07 Å in 12c. The representative geometries in Figure 1 show C•−H

distances for TS10c (1.340 and 1.346 Å) and TS12a (1.343 and 1.393 Å) generally shorter than those for the 1,4-shift transition states. The barriers for 2 and 10c are fairly similar despite the 41° torsional angle between the rings in 10c, presumably because sterics decrease dramatically in the Cs-symmetric transition state when the phenyl ring leans toward the shifting hydrogen. The differing angles on the two sides of the phenylbenzopentalene (see 12a in Figure 1) result in large differences in the C•−H distance in the two conformations 12a (2.509 Å) and 12c (3.073 Å), giving rise to a 13 kcal/ mol difference in activation energies. As with the 1,5-shifts, the computed barriers for the 1,6-H shifts shown in Scheme 6 span a large range, and particular 316

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Figure 1. UBLYP/cc-pVDZ optimized structures of representative minima and transition states for 1,4-, 1,5-, and 1,6-H shifts in PAH radicals. Selected distances (Å) and CCC angles (deg) are shown, including some H---H distances for relevant steric interactions.

cases exhibit extremely low activation energies. The RCCSD(T) calculation on TS14 was beyond our capabilities, so only a DFT energy is available for that system. Except for 13a, all barriers in Scheme 6 are lower than those for the 1,4-shifts in Scheme 4. Of all the radicals considered in this study, the lowest H-shift barriers were computed for the hypothetical systems 17a and 18 (ca. 6 kcal/mol). Indeed, those radicals are predicted to have the shortest C•−H distances (ca. 1.94 Å), even shorter than that in 2 (2.07 Å) As suggested above, a reasonable correlation exists between the computed barriers and the distance between the radical center and the shifting hydrogen in the starting material. Figure 2 depicts the relationship for the RCCSD(T) results. The seeming outlier at r(C•−H) = 2.799 Å and ΔG⧧ = 12.1 kcal/mol corresponds to the 1,6-shift in radical 16b (Scheme 6), in which the large distance is due to strong twisting of the phenyl ring. This system is able to achieve small C−H distances in the transition state TS16 (1.319 and 1.336 Å) without significant changes in inter-ring CCC angles, whereas larger changes in those angles in other systems are responsible for a substantial part of the barrier. For example, distorting the inter-ring CCC angles in biphenyl to those required in TS1 (110°) costs 7.2 kcal/mol at the CCSD(T)/ cc-pVDZ//BLYP/cc-pVDZ level. Diradical-Based Mechanisms. The energetics discussed above for radical systems serve as a reference point for considering hydrogen shifts in diradicals. For such diradical reactions, a key issue is whether a similar C•−H distance correlation dominates, or if the presence and specific location of a second radical site exerts an influence. The ca. 55 kcal/ mol of strain in biphenylene (19, Figure 3)23 renders the cyclobutane C−C bonds easily cleaved and thus makes biphenylene derivatives convenient precursors for aryl

Figure 2. Plot of RCCSD(T) computed free energies of activation (298 K, kcal/mol) vs distance from radical center to the shifting hydrogen atom for radical systems in Schemes 4−6. Green = 1,4shifts; red = 1,5-shifts; blue = 1,6-shifts.

diradicals and subsequent lower-energy rearrangement products.15,18,21 Biphenylene itself can be considered a prototype for systems involving ring cleavage, where the resulting diradical can undergo two sequential H-shifts followed by ring closure. In some systems (including 19) the first H-shift produces a m-benzyne42 intermediate. Figure 3 depicts energetic results for the degenerate rearrangement of biphenylene. The m-benzyne intermediate 21 is computed to be 13−14 kcal/mol more stable than the initially formed diradical 20. This energy difference compares reasonably well with the biradical stabilization energy (BSE) in the parent m317

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degenerate “phenyl walk” rearrangement in 19 (which would be detectable with isotopic labeling) is 78 kcal/mol.45 Figure 4 shows the UBLYP/cc-pVDZ optimized structures of some representative intermediates and transition states for systems proceeding via diradicals. The computed distances between the dehydro-carbons in m-benzyne intermediates, e.g. 1.98 Å in 21 and 1.95 Å in 30b, are similar to the value of 2.02 Å computed by Winkler and Sander for the parent mbenzyne.24 The energetics in Figure 3 above exemplify some general trends regarding relative energies obtained with the UBLYP and BD(T) methods. For m-benzyne analogues such as 21, BD(T) energies are 3−5 kcal/mol higher than those from UBLYP relative to the starting biphenylene. On the other hand, BD(T) relative energies of non-m-benzyne diradicals are slightly lower than those from UBLYP. Transition states for hydrogen shift reactions are predicted to be 7−10 kcal/ mol higher in energy with BD(T) than those with UBLYP. The significant differences between the two methods, especially for transition states, underscore the importance of using high-level methods for energetics in these systems. Whereas the sequence shown for biphenylene (19) is degenerate, the analogous process for linear [3]phenylene (3) is not; it produces angular [3]phenylene (4), which is ca. 2 kcal/mol more stable. The presumed mechanism, shown in Figure 5, involves, like that of biphenylene, only 1,4-H shifts.15 The first diradical intermediate can lead to two different m-benzyne intermediates. In general, the m-benzyne intermediates are predicted to be from 8 to 15 kcal/mol lower in energy than the non-m-benzyne intermediates involved in the rearrangements of phenylenes. In addition, diradical 23b, with the m-benzyne in a phenyl ring, is 5−6 kcal/mol more stable than 23a, with the m-benzyne in a biphenylene moiety, because the perturbed CCC bond angles in the m-benzyne subunit of 23a increase strain at the fusion with the four-membered ring. Consistent with this, the •C− C• distance in 23a (2.103 Å) is significantly longer than that in 23b (1.977 Å). The second radical site in 22 does not seem to impact the barrier for the first (exergonic) H-shift. However, when the diradical is a m-benzyne, the ΔG⧧ for the subsequent H-shift is ca. 8−15 kcal/mol higher than for the analogous monoradical. Despite the difference in stability of the two possible m-benzyne intermediates, the overall activation free energies for the two pathways are within 1 kcal/mol of each other, at ca. 80 kcal/mol (only slightly higher than that for biphenylene). Moreover, all the H-shift transition states for this system have relative free energies in the narrow range 78.3−80.3 kcal/mol. The thermal rearrangement of benzo[b]biphenylene (5) to fluoranthene (6), studied experimentally by Scott,18 exhibits similarities to and differences from the reaction of linear [3]phenylene. The proposed mechanism and energetics are shown in Figure 6. The overall transformation can be broken into two stages: (1) conversion of benzo[b]biphenylene (5) into benzo[a]biphenylene (28) and (2) conversion of 28 to fluoranthene (6). Each stage has a branching point leading to two possible diradical intermediates, which then converge in the subsequent step. The first stage (5 to 28) involves only 1,4-H shifts, with H-shift free energy barriers of 24−26 kcal/ mol leading to a m-benzyne and 36−39 kcal/mol leading away from a m-benzyne. Both paths are computed to have very similar overall barriers of 82−83 kcal/mol at 298 K (Table 1).

Figure 3. Computed mechanism and energetics for ring opening of biphenylene (19) and subsequent hydrogen shifts and ring closure. Asterisks indicate positions of isotopic labels in a hypothetical labeling experiment. Free energies of activation are given for each step under the arrow relative to the starting material for that step. All energies are at 298 K in kcal/mol.

benzyne, which can be estimated using the isodesmic reaction in eq 1. Using experimental enthalpies of formation,25,43,44 the energy change for eq 1 is −20 kcal/mol.

The BD(T) free energy barrier (298 K) for 1,4-H shift from 20 to 21 is 24.4 kcal/mol (Figure 3), very similar to 25.8 kcal/mol for the biphenylyl radical (1), suggesting that the m-benzyne stability has only a small effect here on barrier. On the other hand, the subsequent step from 21 to 20′ has ΔG⧧ (298 K) of 37.9 kcal/mol due to the difficulty of losing the stabilization of the m-benzyne moiety. Such a barrier is ca. 12 kcal/mol higher than that for the analogous radical 1. While Figure 3 shows barriers for each step, Table 1 summarizes the overall free energy barriers computed for the rearrangement of 19 and other phenylenes. The computed overall free energy barrier (at 298 K) for the Table 1. BD(T)/cc-pVDZ Overall Free Energy Barriers (kcal/mol) for Diradical-Based Rearrangementsa reaction 19→19′ 3→4 5→28 28→6 5→6 7→8

path via 23a via 23b via 26a via 26b via 30a via 30b via 26b, 30b

highest TS

overall ΔG⧧ (298 K)

overall ΔG⧧ (1273 K)

TS20 TS22a TS23b TS25a TS26b TS30a TS29b TS26b

77.9 79.7 80.3 82.9 82.4 88.4 82.0 82.4

72.5 74.5 74.9 78.4 78.0 84.0 77.8 78.0

TS32

86.1

81.8

a

At (U)BLYP/cc-pVDZ geometries. 318

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Figure 4. UBLYP/cc-pVDZ optimized structures of representative intermediates and transition states for 1,4-, 1,5-, and 1,6-H shifts in diradical systems. Selected distances (Å) are shown. All species are singlets.

Figure 5. Computed mechanism and energetics for rearrangement of linear [3]phenylene (3) to angular [3]phenylene (4). Free energies of activation are given for each step under the arrow, relative to the starting material for that step. All energies are at 298 K in kcal/mol.

In contrast, the second stage must involve a 1,5-H shift as well as a 1,4-H shift. The ΔG⧧ values for the 1,4-shifts 29 → 30b and 30a → 31 are close to that of 25.6 kcal/mol for the radical model system 10a (Scheme 4). For systems consisting only of benzene or benzenoid rings (e.g., 29, 30, 31, and model systems 10a and 10c), the shorter C•−H distance for

1,5-shifts generally results in a significantly lower barrier than for 1,4-shifts. The computed C•−H distances for 1,5-H shift in precursors 29 and 30b are 2.141 and 2.374 Å, respectively. These are significantly shorter than the analogous distances for 1,4-H shift in precursors 29 (2.507 Å) and 30a (2.620 Å). However, the larger ΔG⧧ for 30b → 31 than for 29 → 30b 319

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Figure 6. Computed mechanism and energetics for rearrangement of benzo[b]biphenylene (5) to angular [3]phenylene (6) via benzo[a]biphenylene (28). Free energies of activation are given for each step under the arrow, relative to the starting material for that step. BD(T) (plain) and BLYP (italics) results are shown. All energies are at 298 K in kcal/mol.

reflects the loss of m-benzyne stabilization during 30b → 31. In addition, intermediate 30a is not a m-benzyne diradical, so both steps in that pathway do not benefit from the stabilization of a m-benzyne intermediate. As a result, the route through 30a is disfavored by 6.4 kcal/mol in terms of overall barrier (88.4 kcal/mol) relative to the path via mbenzyne diradical 30b (82.0 kcal/mol) (see Table 1). The final system of interest here, the conversion of angular [4]phenylene (7) to biphenylene dimer (8),21 involves only 1,6-H shifts. Vollhardt’s proposed mechanism, shown in Figure 7, does not involve any m-benzyne intermediate, so there is no associated stabilization. The BD(T) overall free energy barrier for the process is 86 kcal/mol, with TS32 the highest-energy transition state, only about 4−6 kcal/mol higher than that for 3 → 4 and 5 → 6 (favored pathway). Table 1 summarizes the BD(T) computed free energies of activation for the reactions 19 → 19′, 3 → 4, 5 → 6, and 7 → 8. In the present systems, it is worth noting that the highest overall barrier corresponds to 7 → 8; the ratedetermining step is a 1,6-H shift in which the C•−H distance in the reactant (32) is 3.046 Å, one of the longest such distances in this study. Except for 19 → 19′, the transformations listed in Table 1 have been observed experimentally using pyrolysis temperatures of 900−1100 °C (Scheme 3). The computed overall ΔG⧧ values at 1000 °C for the favored pathways are in the range of 74 to 82 kcal/mol. These barriers are similar to those computed for benzene ring contractions in phenylenes,46 reactions that compete with the processes studied here and are known to occur at about the same temperatures.15,21,47 Thus, the

Figure 7. Computed mechanism and energetics for rearrangement of angular [4]phenylene (7) to biphenylene dimer (8). Free energies of activation are given for each step under the arrow relative to the starting material for that step. BD(T) (plain) and BLYP (italics) results are shown. All energies are at 298 K in kcal/ mol.

overall barriers computed here are consistent with experimental results and support the diradical mechanisms proposed by Scott18 and Vollhardt.15,21 In addition, we predict that pyrolysis of isotopically labeled biphenylene (19) using temperatures slightly below those used to convert 19 to benzopentalene47 should result in scrambling of the labels. For the monoradicals, the computed 320

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(6) Necula, A.; Scott, L. T. Polycyclic Aromat. Compd. 2010, 30, 260. (7) Brooks, M. A.; Scott, L. T. J. Am. Chem. Soc. 1999, 121, 5444. (8) Peng, L.; Scott, L. T. J. Am. Chem. Soc. 2005, 127, 16518. (9) Polishchuk, A. L.; Bartlett, K. L.; Friedman, L. A.; Jones, M. J. Phys. Org. Chem. 2004, 17, 798. (10) Karady, S.; Cummins, J. M.; Dannenberg, J. J.; del Rio, E.; Dormer, P. G.; Marcune, B. F.; Reamer, R. A.; Sordo, T. L. Org. Lett. 2003, 5, 1175. (11) Cioslowski, J.; Liu, G.; Moncrieff, D. J. Org. Chem. 1996, 61, 4111. (12) Using AM1 calculations, Dannenberg concluded that barriers are insensitive to the C−H−C angle (in the transition state) in the range of 145−180°. (13) Huang, X. L.; Dannenberg, J. J. J. Org. Chem. 1991, 56, 5421. (14) Berris, B. C.; Hovakeemian, G. H.; Lai, Y. H.; Mestdagh, H.; Vollhardt, K. P. C. J. Am. Chem. Soc. 1985, 107, 5670. (15) Dosa, P. I.; Schleifenbaum, A.; Vollhardt, K. P. C. Org. Lett. 2001, 3, 1017. (16) Barton, J. W.; Walker, R. B. Tetrahedron Lett. 1978, 19, 1005. (17) Jensen, F. R.; Coleman, W. E. Tetrahedron Lett. 1959, 1, 7. (18) Preda, D. V.; Scott, L. T. Org. Lett. 2000, 2, 1489. (19) Tucker, S. H.; Whalley, M. Chem. Rev. 1952, 50, 483. (20) Schmidt-Radde, R. H.; Vollhardt, K. P. C. J. Am. Chem. Soc. 1992, 114, 9713. (21) Dosa, P. I.; Gu, Z.; Hager, D.; Karney, W. L.; Vollhardt, K. P. C. Chem. Commun. 2009, 1967. (22) Rajca, A.; Safronov, A.; Rajca, S.; Ross, C. R.; Stezowski, J. J. J. Am. Chem. Soc. 1996, 118, 7272. (23) Bachrach, S. M. J. Phys. Chem. A 2008, 112, 7750. (24) Winkler, M.; Sander, W. J. Phys. Chem. A 2001, 105, 10422. (25) Wenthold, P. G. Aust. J. Chem. 2010, 63, 1091. (26) Sander, W.; Exner, M.; Winkler, M.; Balster, A.; Hjerpe, A.; Kraka, E.; Cremer, D. J. Am. Chem. Soc. 2002, 124, 13072. (27) Becke, A. D. Phys. Rev. A: At., Mol., Opt. Phys. 1988, 38, 3098. (28) Dunning, T., Jr J. Chem. Phys. 1989, 90, 1007. (29) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37, 785. (30) Knowles, P. J.; Hampel, C.; Werner, H. J. J. Chem. Phys. 1993, 99, 5219. (31) Knowles, P. J.; Hampel, C.; Werner, H.-J. J. Chem. Phys. 2000, 112, 3106. (32) Watts, J. D.; Gauss, J.; Bartlett, R. J. J. Chem. Phys. 1993, 98, 8718. (33) Handy, N. C.; Pople, J. A.; Head-Gordon, M.; Raghavachari, K.; Trucks, G. W. Chem. Phys. Lett. 1989, 164, 185. (34) Johnson, W. T. G.; Cramer, C. J. J. Am. Chem. Soc. 2001, 123, 923. (35) Andersson, K.; Malmqvist, P. Å.; Roos, B. O. J. Chem. Phys. 1992, 96, 1218. (36) Frisch, M. J.; et al. Gaussian 09, revision D.01; Gaussian, Inc.: Wallingford, CT, 2009. (37) Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M. WIREs Comput. Mol. Sci. 2012, 2, 242. (38) Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M.; et al.http://www.molpro.net, accessed Dec. 8, 2017. (39) Aquilante, F.; De Vico, L.; Ferre, N.; Ghigo, G.; Malmqvist, P.-A.; Neogrady, P.; Pedersen, T. B.; Pitonak, M.; Reiher, M.; Roos, B. O.; Serrano-Andres, L.; Urban, M.; Veryazov, V.; Lindh, R. Molcas 8.0. J. Comput. Chem. 2010, 31, 224. (40) Bode, B. M.; Gordon, M. S. J. Mol. Graphics Modell. 1998, 16, 133. (41) Schaftenaar, G.; Noordik, J. H. J. Comput.-Aided Mol. Des. 2000, 14, 123. (42) Sander, W. Acc. Chem. Res. 1999, 32, 669. (43) Tsang, W. In Energetics of Organic Free Radicals; Simoes, J. A. M., Greenberg, A., Liebman, J. F., Eds.; Blackie Academic and Professional: London, 1996; p 22.

H-shift barriers of ca. 6 kcal/mol in hypothetical systems 17a and 18 suggest that, when tunneling is taken into account, these systems may effectively be nonclassical aryl radicals of the type that Cioslowski sought.11

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CONCLUSION For 1,4-, 1,5-, and 1,6-H shifts in PAH radicals, RCCSD(T)/ cc-pVDZ//UBLYP/cc-pVDZ results show a strong correlation between activation energy and C•−H distance in the reactant, in agreement with earlier work.11 Barriers for 1,5and 1,6-shifts can vary dramatically from 6 to 28 kcal/mol due to a wide range of possible C•−H distances resulting from different carbon skeletons. Most of the diradical-based mechanisms for phenylene derivatives proceed via m-benzyne intermediates, which are 8−15 kcal/mol more stable than other diradical intermediates involved. These mechanisms exhibit some H-shift steps with ΔG⧧ values similar to those for radical models, but H-shift steps beginning from m-benzyne intermediates have ΔG⧧ values 8−15 kcal/mol larger than other H-shift steps. Nevertheless, among the systems studied here, the presence of m-benzyne intermediates lowers the overall ΔG⧧ for the reactions by only a small amount. The computed overall barriers are consistent with experimental results and proposed mechanisms for the flash vacuum pyrolyses of linear [3]phenylene (3), benzo[b]biphenylene (5), and angular [4]phenylene (7).

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.joc.7b02724. Absolute energies, zero point energies, ⟨S2⟩ values, thermal corrections, and optimized Cartesian coordinates for all stationary points (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

William L. Karney: 0000-0003-0976-742X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the National Science Foundation (Grants CHE1213425 and CHE-1565793) and the University of San Francisco Faculty Development Fund for generous financial support. We are grateful to Prof. Peter Vollhardt for stimulating our interest in this area, and we thank Mitchell Santander for preliminary calculations.

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REFERENCES

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DOI: 10.1021/acs.joc.7b02724 J. Org. Chem. 2018, 83, 314−322

Article

The Journal of Organic Chemistry (44) Roux, M. V.; Temprado, M.; Chickos, J. S.; Nagano, Y. J. Phys. Chem. Ref. Data 2008, 37, 1855. (45) It is also conceivable that diradical 20 can dissociate to two obenzynes, which could then recombine to give 19 in which the isotopic labels have been scrambled. Our BLYP calculations on such a path connecting 19 and its isotopomer yield an overall barrier more than 25 kcal/mol higher than that shown in Figure 3. (46) Pastor, M. B.; Kuhn, A. J.; Nguyen, P. T.; Santander, M. V.; Castro, C.; Karney, W. L. J. Phys. Org. Chem. 2013, 26, 750. (47) Brown, R. F. C.; Choi, N.; Coulston, K. J.; Eastwood, F. W.; Wiersum, U. E.; Jenneskens, L. W. Tetrahedron Lett. 1994, 35, 4405.

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DOI: 10.1021/acs.joc.7b02724 J. Org. Chem. 2018, 83, 314−322