molecular mechanisms in the pyrolysis of unsaturated chlorinated hydrocarbons: formation of benzene...

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Article

Molecular Mechanisms in the Pyrolysis ofUnsaturated Chlorinated Hydrocarbons: Formation

of Benzene Rings Part I - Quantum Chemical StudiesGrant J. McIntosh, and Douglas Keith Russell

J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp3120379 • Publication Date (Web): 18 Apr 2013

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Molecular Mechanisms in the Pyrolysis of Unsaturated Chlo-rinated Hydrocarbons: Formation of Benzene Rings Part I - Quantum Chemical Studies

Grant J. McIntosh* and Douglas K. Russell

Department of Chemistry, University of Auckland, Private Bag 92019, Auckland, New Zealand

ABSTRACT: Analogues of important aromatic growth mechanisms in hydrocarbon pyrolysis and combustion systems are ex-tended to chlorinated systems. We consider the addition of C2Cl2 to both C4Cl3 and C4Cl5 radicals at the M06-2X/6-311+G(3df,3p)//B3LYP/6-31G(d) level of theory, and demonstrate that these reaction systems have much in common with those of non-chlorinated species. In particular, we find that these radicals appear to lead preferentially to fulvenes, and not the observed aromatic products, as is found in non-chlorinated systems. We have therefore also considered non-radical C4/C2 channels by way of Diels-Alder cyclization of C4Cl4/C2Cl2 and C4H2Cl2/C2HCl pairs to describe aromatic formation. Whilst the latter pair readily leads to the formation of partially chlorinated benzenes, the fully chlorinated congeners are sterically prohibited from ring-closing directly; this leads to a series of novel rearrangement processes which predict the formation of hexachloro-1,5-diene-3-yne, in addi-tion to hexachlorobenzene, in good agreement with experiment. This suggests, for the first time, that facile non-radical routes to aromatic formation are operative in partially and fully chlorinated pyrolysis and combustion systems.

KEYWORDS Hexachlorobenzene; Density Functional Theory; Chlorocarbon Growth; Acetylene Addition; Dichloroeth-

ylene; Trichloroethylene; Thermal Degradation.

INTRODUCTION

Incomplete combustion of chlorinated hydrocarbons and plastics in limited oxygen can lead to a number of toxicologi-cally and environmentally hazardous biproducts such as poly-chlorinated dibenzodioxins (PCDDs) and dibenzofurans (PCDFs).1 Both classes of compounds are bioaccumulative and toxic, and are known teratogens, mutagens, and probable carcinogens. These species are typically believed to be formed from the smaller (chlorinated)-polycyclic aromatic hydrocarbons [(Cl)-PAHs], which are also formed in oxygen-free environments, and many of which exhibit similar toxico-logical hazards as the PCDDs and PCDFs themselves. The discharge of these by-products has lead to the Cl-PAH con-tamination of a number of environmental and biological sam-ples2-12

Benzene production is widely acknowledged as the rate lim-iting step in the formation of soots and PAHs, and this is ex-pected to hold similarly in chlorinated systems; thus, the im-portance of the phenyl ring cannot be understated. The earli-est mechanisms proposed for non-chlorinated systems typical-ly focused on reaction between C4 and C2 species;13-18 several distinct methods of reaction have been hypothesized. Early studies dismissed Diels-Alder addition18 of acetylene to buta-diene and vinylacetylene as they predicted rates of benzene formation three orders of magnitude too low. Vinyl radical addition to 1,3-butadiene was ostensibly far more successful; however, the model originally developed by Kinney and Crowley,19 involving the addition of 1,3-butadienyl radicals to acetylene, is generally the currently accepted mechanism. The analogous reaction with C4H3 radicals has also been consid-ered.

The chemistry of acetylene addition is not particularly straightforward. Miller and Melius20 noted that C4H5 and C4H3 radicals adopt two distinct forms, denoted n- and i-isomers as in Figure 1. The i-isomer is resonantly stabilized, leading to three distinct pathways addition pathways. Consequently, the dominant pathway to growth is complicated by the distribution of n- and i-isomers and the relative reactivity of each.

Estimating accurate thermochemistry of these radicals is clearly of paramount importance. A great deal of computa-tional work has accumulated and suggests that the resonance stabilized i-C4H5 isomers are 23.3-63.6 kJ mol-1 more stable than the n-isomer;21-24 similarly, i-C4H3 isomers are found to be 27.6-50.2 kJ mol-1 more stable than n-C4H3.

24-27 This led to the conclusion that far lower abundances of n-isomers should be observed in flames, which has recently been substantiated with molecular-beam mass spectrometry experiments.28

However, addition to n-isomers requires less energy. The recent CCSD(T)/CBS//B3LYP/6-311G** explorations by Mebel and Landera29 of C4H3/C2H2 reactions suggest barriers29 of 15.1, 33.5, and 54.4 kJ mol-1 for addition to n- C4H3, and the interior and terminal carbons of i-C4H3 respectively, in good agreement with barriers quoted in other theoretical works (although these earlier studies did not locate transition states for the addition of C2H2 to the terminal carbon of C4H3).

30,31 Similar studies with C4H5 radicals find analogous results.32

This suggests that C4 radicals are not responsible for ben-zene formation, as both i-isomers lend themselves much more readily to the formation of C6H6 isomer fulvene, rather than the observed product benzene; further, the n-C4H3/C2H2

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Figure 1. C2H2 addition chemistry of n- (left) and i- (right) iso-mers of C4H3 and C4H5 showing the roles of resonance structures.

isomer also possesses a slightly lower barrier with respect to five-membered, rather than six-membered, ring cyclization processes.29-31 It was suggested, however, that the C6H5-fulvene-like isomer formed may ring open and re-close to form phenyl radicals in an energetically favorable reaction; this is consistent with later computational studies.29-31 On the other hand, computational and modeling studies strongly sug-gest i-C4H5 + C2H2 yields fulvene (+ H) as the major product over the temperature range of 500 – 2500 K.32

To address the poor description of aromatic product for-mation, non-radical processes have more recently been recon-sidered to a limited extent. In particular, non-radical cycliza-tion routes are found to be essentially the exclusive pathway to benzene during moderate temperature (400 – 500 °C) co-pyrolyses of vinylacetylene with acetylene; benzene forms as the sole C6H6 isomer under such conditions. 33 The activation energy determined for this reaction, 125.9 ± 5.4 kJ mol-1, is similar to computational estimates of barriers to Diels-Alder cyclization of C4H4 with acetylene.34,35 Similarly, recent kinet-ic modeling works also suggest that Diels-Alder cycloaddition of C4H4/C2H2 may be an effective route to benzene formation.36-38 This class of reactions represents a viable al-ternative to the radical C4/C2-based processes in hydrocarbon systems.20,39,40

Very little work concerning chlorinated systems has been undertaken, with only the heats of formation of chlorinated n-C4H3 congeners being addressed explicitly;41 however, esti-mates of the thermochemistry of important reactions were made for the early kinetic modeling attempts.42,43 These mod-els suggest that perchlorinated n-isomers are significantly higher in energy than i-isomers.42-44 Consequently, chlorinated i-isomers, which presumably would also lead to non-aromatic products upon extension of mechanisms from non-chlorinated

systems, should dominate; however, these early studies did not explicitly consider the reaction of chlorinated i-C4 radical iso-mers with chloroacetylenes. Further, both n-C4Cl5 and n-C4Cl3 adducts with C2Cl2 were assumed to simply cyclize bar-rierlessly to yield aromatic species only. Clearly, explicit study of the chlorinated analogues of C4H3 and C4H5 chemistry is necessary. Furthermore, no chlorinated analogues of non-radical processes appear to have been studied.

Therefore, this study (hereafter referred to as Paper I) will primarily focus on ab initio studies of important C4/C2 growth pathways in chlorinated systems, using the chemistry of non-chlorinated species as a prototype. These calculations will be used to supplement a combined experimental/kinetic modeling work in a companion paper (hereafter referred to as Paper II). Paper II details unique product distributions in perchlorinated systems in which we observe considerable quantities of the linear species hexachloro-1,5-diene-3-yne alongside hexachlo-robenzene. The latter work will also justify the neglect of chlorinated C3 dimerization routes (a strongly supported alter-native aromatic formation pathway in hydrocarbon systems).

THEORETICAL METHODOLOGY

The geometries of all stationary points were located with ei-ther the Spartan 0845 or Gaussian 09 suites.46 We have chosen the B3LYP hybrid functional47,48 within the DFT framework utilizing 6-31G(d) basis sets for all geometry optimizations as this functional has been shown to yield good geometries for a number of compounds, particularly in spin contaminated sys-tems. Refinement of energies has been achieved with a varie-ty of single point energies, obtained with the Gaussian soft-ware suite; all energies are subjected to Zero Point Energy (ZPE) corrections scaled by the empirical factor of 0.9806.49

MP2/6-31+G(d) single point energies (SPEs) have been used for selected calculations; in addition to utilizing default spin settings, we have also used the restricted-open (RO) framework as unrestricted methods for open-shell species have been found to be very badly spin-contaminated.50-52 Quadratic configuration interaction and coupled cluster methods, both with single and double excitations and perturbative corrections for triple excitations (QCISD(T) and CCSD(T)) have also been utilized. Due to computational expense, only relatively small basis sets, 6-31G(d), have been used. These values were also used to perform calculations with the highly accurate G2MS method:53,54

E(G2MS) = E[CCSD(T)/6-31G(d)] + E{MP2/6-311+G(2df,2p)] - E{MP2/6-31G(d)] + HLCG2MS + ZPE

HCLG2MS is an empirically determined high-level correction factor, which is usually deemed negligibly small.

Due to the expense of these SPE calculations, the M06-2X hybrid functional (recently developed by Truhlar et al.55 and recommended for barrier heights and reaction kinetics, amongst other applications) has also been utilized extensively. For basis sets, a survey of the gas-phase enthalpies of isomeri-zation of a number of hydrocarbons (including thermodynam-ics associated with chlorinated hydrocarbons) has shown that M06-2X/6-311+G(3df,3p) SPE calculations are of comparable accuracy to expensive high level methods such as CBS-QB3 and G4MP2.56 Consequently, all energies reported in this

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work are M06-2X/6-311+G(3df,3p)//B3LYP/6-31G(d) SPEs, with ZPE corrections, unless stated otherwise.

RESULTS AND DISCUSSION

A. Benchmarking Calculations

As it appears that this study represents the first full theoreti-cal description of the elementary radical reactions of chlorin-ated C4H3 and C4H5 species, or vinylacetylene/acetylene mo-lecular additions, benchmarking is of the utmost importance. This is particularly necessary as the sizes of the systems in-volved rule out the use of the highest levels of theory. Several classes of reaction of likely importance are explored; C-C cleavage in heavily-chlorinated structures, Diels-Alder cy-cloaddition, and H- and Cl-shifts. Our prototype examples are listed below.

C2Cl6 → 2CCl3 (a)

(b)

(c)

(d)

The energy barriers (and, for reaction (a), the spin expecta-tion values) are given in Table 1. Reference values, experi-mental data when available or high-level ab initio values oth-erwise, are also included. The high-level QCISD(T), CCSD(T), and G2MS calculations all perform very well (par-ticularly the G2MS level) as anticipated; however, these calcu-lations are not feasible for C6Cl6 isomers (they will, however, be sparingly used for C6H3Cl3 clusters). This largely restricts post-HF calculations to MP2 or DFT frameworks; however, incomplete or semi-empirical treatments of electron correla-tion can render these prone to error. MP2 values are in the poorest agreement with experimental and high-level calcula-tions; however, the application of the RO-framework provides values that are in far better agreement. This appears to be the result of severe perturbations in the MP2 values by even a modest degree of spin contamination. The B3LYP values are similarly in very good agreement with the reference data; the exception is the C-C bond cleavage of C2Cl6 (reaction (a)). DFT has been shown to perform quite poorly with the C-C and C-Cl bond dissociations in chlorinated ethanes;50 the underes-timates in reaction enthalpy have been traced to an over-estimate of repulsive forces involving Cl, most likely the result of the well-known inability of DFT to adequately describe dispersion interactions.57,58 However, the more recent M062X functional of Zhao and Truhlar55 does not appear susceptible to this error and performs very well for all benchmarking cal-culations. The results of this functional appear to agree most closely with the reference data and therefore represent our highest practical level of theory. While M06-2X values are reported throughout this work, B3LYP and ROMP2 based

Table 1. Energy barriers/kJ mol-1

and, for reaction (a),

spin expectation values <S2> for CCl3 radicals, of reactions

relevant to chlorobenzene formation. All values are SPE

calculations based on DFT/B3LYP/6-31G(d) geometries

and are inclusive of scaled ZPE corrections.

Reaction: (a) (b) (c) (d)

DFT/B3LYP/6-31+G(d)

215.6

<0.754>

112.8 184.4 234.8

M062X/6-311+G(3df,3p)

304.5

<na>

93.7 184.6 244.6

MP2/6-31+G(d)

319.9

<0.767>

86.8 205.0 272.0

ROMP2/6-31G(d)

302.6

<na>

103.6 187.3 230.2

QCISD(T)/6-31G(d)

274.4

<0.767>

114.6 194.7 246.8

CCSD(T)/6-31G(d)

274.8

<0.767>

114.7 195.0 247.9

G2MS 304.0

<na>

99.1 174.4 232.9

Ref.† 293±15

<0.75>

100.8±

12

188.3 241.3

†Experimental reference energy for reaction (a) from refer-ences 50-52; for reaction (b) from references 59,60: theoretical barriers for reactions (c) and (d) from calculations performed at the QCISD(T)/6-311+G(d,p)//MP2/6-31G* level of theory by Riehl et. al.61

energies are also recorded in the supporting information for all processes considered for comparison sake, and will be re-ferred to on occasion throughout this study.

B. C4Cl3 + C2Cl2

The reaction of C4Cl3 radicals with C2Cl2 is now considered in detail. The M06-2X/6-311+G(3df,3p)//B3LYP/6-31G(d) PES is depicted in Figure 2. We consider only a Cl-abstraction step as the sole initiation reaction; while unimolec-ular bond cleavage is possible, such processes are generally found to initiate the Cl radical pool, but do not explicitly con-tribute significantly to the decomposition of C4Cl4. As is nor-mally the case for bond dissociation reactions, a genuine tran-sition state for loss of Cl from C4Cl4 at the DFT/B3LYP/6-31G(d) level of theory could not be located, with the leaving Cl moving to unrealistically long distances from the remaining C4Cl3 fragment during the course of the optimization. Thus the endothermicity of the reaction serves as a sufficient esti-mate of the energy barrier.

Assuming that once a C4/C2 adduct is formed it is largely converted to products (rather than dissociating) the first step taken by each reaction pair is of particular importance in de-termining the extent to which possible C4Cl3 routes contribute to growth. While the energy barrier associated with the addi-tion of C2Cl2 units to the C4 moiety is important, we will first examine the instantaneous concentration of the C4 species

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Figure 2. PES of the reaction of C4Cl3 isomers with C2Cl2; all energies (in kJ mol-1 and calculated at the M06-2X/6-311+G(3df,3p)//B3LYP/6-31G(d) level of theory, and are inclusive of ZPE corrections) are relative to C4Cl4 + C2Cl2 (+Cl) and include the energy of the Cl2 product.

which is also very influential in determining the rate of the C4Cl3/C2Cl2 reaction. With instantaneous concentrations of C4Cl3 in mind, we note that for radical species such as C4Cl3 (and, indeed, C4Cl5) both the barriers associated with for-mation and the energy of unimolecular decomposition via Cl-loss are vitally important, as the latter may represent a major sink for radical species. As a consequence, we have treated both the initial Cl-driven Cl abstraction from C4Cl4 and de-composition of the resulting C4Cl3 radicals to dichlorodiacety-lene and a Cl atom with several additional levels of theory. All values are given in Table 2, in which we also include the energy barriers employed in previous modeling works.42,43 For further reference, we have computed the barrier to C2Cl3 radi-cal decomposition, and also included data both used in previ-ous kinetic models42,43 and determined experimentally.62

In our previous work,63,64 we have argued that as the meas-ured barrier to C2Cl3 decomposition is significantly lower than the values used in previous kinetic models (which found that trichlorovinyl radicals were important chain carriers), this should result in considerably lower C2Cl3 yields. This in turn should have profound implications on the predicted mecha-nism; in fact, we found that the revised C2Cl3 rates rendered radical channels far too slow to dominate growth (we read-dress this point in Paper II). In light of the importance of these processes, and the fact that similar approximation methods employed in assessing the C2Cl3 decomposition energy were

extended to C4Cl3 radicals in previous kinetic studies, we have employed several high-level SPEs to supplement our M06-2X values, particularly in light of the absence of experimental data. As Table 2 shows, our M06-2X values are in good agreement with the highly accurate CBS-QB3 method; signifi-cantly, these values are also in good agreement with the exper-imental energy for C2Cl3 decomposition. For all unimolecular radical decomposition reactions, high-level quantum chemical values are significantly lower than the barriers employed in the kinetic models of Taylor et al.;42,43 similarly, the barriers to the initial abstraction reaction producing C2Cl3 and C4Cl3 radi-cals are higher than employed in previous kinetic modeling works.42,43 Both results suggest that C4Cl3 radical concentra-tions are likely to be significantly lower than previously thought, casting doubt on the roles of these species in hydro-carbon growth. Further, both the values presented in Table 2 and the results of the preceding section suggest that M06-2X/6-311+G(3df,3p) SPEs are sufficiently accurate for our purposes.

Drawing parallels with high-temperature hydrocarbon sys-tems, C4Cl3 radicals may adopt two distinct isomers, both of which lead to unique chemical pathways. The relative ther-modynamics of these species are particularly important in describing the product distribution in the C4Cl3/C2Cl2 reaction system, and therefore these too have been considered in detail,

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for the formation of C4Cl3 radicals by Cl-initiated Cl-abstraction from C4Cl4, and Cl loss

energies from both C4Cl3 radicals and C2Cl3. All values are SPE calculations based on DFT/B3LYP/6-31G(d) geometries

and are inclusive of scaled ZPE corrections.

Reaction B3LYP/6-31+G(d)

M06-2X/6-311+G(3df,3p)

UB3LYP/6-311G(2d,d,p)

CCSD(T)/6-31+G(d')

CBS-QB3

Prev. kinet-ic work42,43

Expt62

C4Cl4 + Cl → i-C4Cl3 + Cl2

83.7 97.6 66.7 160.3 103.6 56.0

C4Cl4 + Cl → n-C4Cl3 + Cl2

137.2 133.7 120.6 185.0 139.2 121.4

i-C4Cl3 → C4Cl2 + Cl 130.7 123.9 127.3 107.1 127.8 203.7

n-C4Cl3 → C4Cl2 + Cl 77.2 87.9 73.3 82.4 92.2 138.0

C2Cl3 → C2Cl2 + Cl 92.8 90.4 91.1 77.1 93.2 137.2 109.8 ± 6.7

and we have calculated the energy of the i- and n-C4Cl3 rad-icals by a number of single-point methods to assess the relia-bility of our results. These are shown in Table 3. Clearly, all methods but the DFT approaches are plagued by spin contam-ination (the expected value of <S2> for a doublet state is 0.75). MP2/6-31G(d) SPE values were also computed (yielding 440.2 and 445.5 kJ mol-1 for the n- and i-isomers respectively) and are very poor, even predicting the anticipated relative en-ergies of the two radicals incorrectly. (The expected ordering is justified by the resonance-stabilizing effect of delocalized spin density across two carbons in the i-isomer – see Figure 3 – as is found in non-chlorinated species). This, and the poor performance during benchmarking trials, has led us to dismiss the MP2 data for chlorinated radicals. MP4(SDTQ) estimates predict a very small difference in the energies of these iso-mers, also unlikely to be realistic as i-C4Cl3 is resonance stabi-lized; CCSD(T) gives a larger energy separation of the two isomers, although it is still unclear whether they reproduce absolute energy barriers correctly. They are, however, close to ROMP2/6-31G(d) estimates, which are not spin contaminated; as an aside, the latter values reaffirm that the DFT/B3LYP/6-31+G(d) approach underestimates these C-Cl bond cleavage barriers (although this effect is somewhat minimized due to the low numbers of Cl atoms present). The results suggest that the best absolute values at reasonable computational expense are via either the ROMP2 or M06-2X approaches; B3LYP does, however, appear to calculate relative energies well.

The PES for the reactions of both of these isomers with C2Cl2 are depicted in Figure 4. The energies shown are from the M06-2X/6-311+G(3df,3p)//B3LYP/6-31G(d) level. All stationary points have also been considered with the B3LYP functional at the ROMP2 level of theory for comparison, and these energies are given in the supporting information. How-ever, there is generally little deviation from the M06-2X pre-dictions. Considering C2Cl2 addition pathways, the lower energy i-isomer 1A is likely to be more significant than the n-isomer 9A in determining the product ratio. The transition states for addition of C2Cl2 to the 1- and 3-carbons of i-C4Cl3, TS2A and TS3A respectively, and to the unique radical site of n-C4Cl3, TS10A, all show low energy barriers (~10-50 kJ mol-

1), as expected by analogy with non- chlorinated systems. The resonance stabilized i-C4Cl3 is found to be the less reactive. The C≡C bond lengths of the attacking C2Cl2 unit are all very close to its DFT/B3LYP/6-31G(d) C2Cl2 equilibrium bond length of 1.206 Å, and the new C-C bond is clearly non-

bonding at 2.3-2.4 Å, consistent with very early transition states.

Considering the addition of C2Cl2 to i-C4Cl3 first, it can be seen that addition to the interior carbon atom via TS3 is signif-icantly easier (by 18.2 kJ mol-1, according to M06-2X calcula-tions) than addition to the terminal carbon; similarly, the re-sulting adduct is more stable. The addition barriers (27.8 and 46.0 kJ mol-1, respectively) are also similar to barriers in non-chlorinated systems.29 The previous modeling results of Tay-lor et al. do not consider C2Cl2 addition to i-C4Cl3, presuming that these species are less reactive due to resonance stabiliza-tion.42,43 Instead, these radicals were presumed to be simply a source of n-C4Cl3 which was hypothesized to carry growth to the expected aromatic product.


and spin expectation

values <S2> for the formation of C4Cl3 radicals via Cl-loss

from C4Cl4. All values are SPE calculations based on

DFT/B3LYP/6-31G(d) geometries and are inclusive of

scaled ZPE corrections. All calculations utilize 6-31G(d)

basis sets except B3LYP+ and which employ a 6-31+G(d),

and M06-2X a 6-311+G(3df,3p), basis set.

B3LYP+ M06-2X ROMP2

E[n-C4Cl3]; S2 332.5; 0.75 378.0; 0.77 369.1

E[i-C4Cl3 ] ]; S2 279.0; 0.76 341.9; 0.79 328.5

MP4(SDTQ) CCSD(T) G2MS

E[n-C4Cl3] ]; S2 409.1; 1.28 347.5; 1.28 382.7

E[i-C4Cl3 ] ]; S2 401.9; 1.49 322.3; 1.49 359.1

Figure 3. Spin density maps of (left) i- and (right) n-C4Cl3 radi-cals.

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The examination of spin-density maps shows that the initial adducts 2A and 3A both possess radical sites localized exclu-sively on the β-carbon of the incoming acetylene moiety, which is thus a site for further reaction. The LUMO maps of these radicals show largely networks of π-bonding and anti-bonding orbitals. As these networks cover all carbon atoms, 2A may undergo either 5- or 6-membered ring cyclization, via TS7A or TS5A respectively; further, the Cl on the 3-carbon has a vacant p-orbital allowing for a Cl migration to form the pentachlorinated 1-dichloromethylene-4,4,5-trichloro-4-penten-2-ynyl radical, 4A, through TS4A. Fulvene cyclization is the easiest process available, by 70-80 kJ mol-1, to 2A. Un-fortunately, there is little agreement considering the relative importance of the competing processes (TS4A or TS5A) when we compare M06-2X values to the data tabulated in the sup-porting information, although it is very clear that neither pro-cess will contribute appreciably.

3A, although possessing a similar network of orbitals, can-not easily be converted into any experimentally observed structure other than fulvene without a number of high energy rearrangement steps. Electronically, there should be little bar-rier to this cyclization, as evidenced by the unoccupied p-orbital on the 4-carbon of the i-C4Cl3 moiety when examining the LUMO. All levels of theory considered (see, also, the supporting information) indicate a relatively low barrier to fulvene cyclization of ~30-60 kJ mol-1. Again, we note that there are no comparable processes in previous modeling works as i-isomers, by virtue of their stability, were presumed unim-portant in direct C6-product formation channels.

We now consider the second bimolecular addition channel via n-C4Cl3, 9A. TS10A leads to the C2Cl2 addition product 10A. The energy, relative to the zero of energy, of the addi-tion product is comparable to the other C2Cl2 addition process-es; however, the higher energy of 9A means that the actual addition barrier is considerably lower (11.0 kJ mol-1, com-pared with ~30-50 kJ mol-1) than those associated with the i-isomer. Again, this barrier is similar to that found in non-chlorinated systems.29 This also agrees reasonably well with the value employed by Taylor et al.42 of 21.0 kJ mol-1 for chlo-rinated species. This adduct, 10A, will also rapidly cyclize; the spin density and α-LUMO maps suggest small electronic barriers as the unpaired spin resides solely on the C2Cl2-moiety β-carbon, and unfilled orbitals span the carbon centers involved in 5- and 6-membered ring closure. In fact, all levels of theory that we have considered suggest fulvene cyclization occurs barrierlessly, or with an extremely low barrier (5.9 kJ mol-1 at the M06-2X level, compared to 10-20 kJ mol-1 in non-chlorinated systems),29,30,65 via TS12A; however, phe-nyl formation via TS11A requires at least 100 kJ mol-1. We conclude, therefore, that n-isomers also lead far more easily to fulvene, rather than benzene or linear structures. The previous chlorinated phenyl radical growth mechanisms employed a considerably different model from that determined here; ful-vene-like structures were ignored, and the aromatic cyclization channel was assumed to be barrierless.

Thus, we find that i-C4Cl3 is thermodynamically favored, and undoubtedly plays the major role in product formation, as in non-chlorinated systems. Acetylene addition to either the terminal or interior carbon of i-C4Cl3 should lead almost ex-clusively to fulvene. Although addition to the interior carbon

was not considered in their study of i-C4H3 + C2H2, the for-mation of fulvene structures in non-chlorinated systems was also found by Walch.30 As we noted for the n-C4Cl3/C2Cl2 system, the product may undergo one of two cyclization pro-cesses leading to either fulvene- or benzene-related radicals. While the former is considerable more favorable in chlorinated systems, in non-chlorinated systems one finds that while ful-vene-like cyclization is still a lower barrier processes, phenyl cyclization is anticipated to be only 15 kJ mol-1 higher;30 this barrier is supported by more recent studies.29,65 Thus reaction is not as markedly in favor of fulvene cyclization; this differ-ence is presumably a consequence of the steric hindrance pre-sented by chlorine. Walch included an isomerization step analogous to TS13A, which should allow for the more rapidly formed analog of 6A to isomerize to a 12A structure that may then ring-open, and then easy re-cyclization to thermodynami-cally favored phenyl radicals, thus redeeming C4H3 as a poten-tial candidate in benzene formation. However, such processes are unlikely on the C6Cl5 PES, given the far greater energy disparity between the two transition states TS11A and TS12A; thus C4Cl3 radicals should lead predominantly to fulvene iso-mers at all but the highest temperatures which can drive a thermodynamic distribution of isomers.

B. C4Cl5 + C2Cl2

This system has much in common with that discussed above. Consequently, we have not considered the stationary points with levels higher than M06-2X/6-311+G(3df,3p). The M06-2X/6-311+G(3df,3p)//B3LYP/6-31G(d) PES depicting the possible reactions in the C4Cl5/C2Cl2 system is given in Figure 4. The C4Cl5 radical could conceivably be formed ei-ther by Cl addition to C4Cl4 or Cl loss from C4Cl6, or the less likely C2Cl2 + C2Cl3. The C4Cl5 radical possesses n- and i- isomers, with the latter of lower energy as a result of reso-nance stabilization. M06-2X, B3LYP and ROMP2 (see sup-porting information) approaches agree reasonably closely for most processes other than that of initial formation; however, as discussed in the previous section, the M06-2X data agrees well with very high level calculations for similar processes.

Formation of the initial radical (taken here to be Cl loss from C4Cl6) is again barrierless, and leads to a thermodynamic distribution of the two isomers 1B and 10B. The C4Cl6 mole-cule itself is known to possess a twisted structure,66 unlike the planar trans-form adopted by its fully hydrogenated conge-ner.67 Our own DFT/B3LYP/6-31+G(d) studies corroborate this, finding the twisted form some 73 kJ mol-1 (MP2/6-31+G(d) gives 89 kJ mol-1) lower than the planar form, lend-ing support to the conclusions drawn from these calculations. The i-isomer of C4Cl5, 1B, adopts an almost Cs structure, while the n-isomer 10B resembles C4Cl6 – this observation suggests that Cl-Cl steric interactions leads to non-planarity of the par-ent. Spin density maps again reveal extensive delocalization in the i-isomer, whereas spin density is localized on the terminal carbon in the n-isomer, as is found in non-chlorinated species. The barriers that we find to i- and n-C4Cl5 radical formation are 96.7 and 135.4 kJ mol-1 respectively, compared to 63.6 and 104.8 kJ mol-1 respectively employed in previous modeling work.42,43 Consequently, our values suggest a considerably smaller radical pool than previous results.

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Figure 4. PES of the reaction of C4Cl5 isomers with C2Cl2; all energies (in kJ mol-1 and calculated at the M06-2X/6-

311+G(3df,3p)//B3LYP/6-31G(d) level of theory, inclusive of ZPE corrections) are relative to C4Cl4 + C2Cl2 (+Cl) and include the energy of the Cl2 product.

Attack of C2Cl2 on the high spin density centers again oc-curs via an early transition state in all cases, with the C-C bond in C2Cl2 almost unchanged; however, the structure of the C4Cl5 moiety itself changes markedly. Attack on the central C site in the i-isomer via TS2B is preferred over the terminal atom via TS3B by about 16.8 kJ mol-1, resulting in a reaction about 10 times faster at estimated pyrolysis temperatures. At-tack on the less abundant n-isomer via TS11B is again the most facile addition channel, favored by 20.4 kJ mol-1. The M06-2X barriers that we have computed for TS2B, TS3B, and TS11B (31.4, 48.3, and 11.1 kJ mol-1) are considerably lower than values (48.5, 56.9, and 23.4 kJ mol-1, respectively) com-puted for analogous hydrocarbon systems,32 and the B3LYP-based values included in the supporting information.

There is little previous data concerning chlorinated systems – Taylor et al.42,43 considered only addition to the n-isomer (the i-isomer only represents a ready source for the n-isomer and is not directly influential in growth, as assumed for the C4Cl3 system) and employed a barrier of 21.0 kJ mol-1. Con-sequently, our model agrees reasonably well with the barrier included by Taylor et al.42,43 for growth reaction, although we do predict slightly slower addition reactions. However, we again predict considerably lower barriers (faster reactions) for the unimolecular decomposition of C4Cl5 radicals; we have computed 136.1 and 97.4 kJ mol-1 from i- and n-C4Cl5 respec-

tively, compared with 183.7 and 143.0 kJ mol-1 respectively employed by Taylor et al.42,43 These differences in energy suggest an increase by approximately two orders of magni-tude, at pyrolytic temperatures, in the rate of unimolecular decomposition of C4Cl5 radicals over those of earlier kinetic models. This will have a considerable impact on the instanta-neous concentrations of these species, which may in turn have profound mechanistic implications.

The models of Taylor et al.42,43 provide little detailed insight into the mechanism of product formation from these initial adducts; the models include only barrierless cyclization of the n-C4Cl5 adduct 11B to yield hexachlorobenzene. However, studies of C6H7 PESs indicate that analogous non-chlorinated species may undergo a number of possible reactions.32 H-migrations to yield linear isomers are found to be reasonably high in energy; we find Cl-migrations are similarly high in energy (TS14B). However, a fulvene-like cyclization is found to be only marginally higher in energy (by 5.1 kJ mol-1) than cyclization to benzene-based C6H7 species. We have exam-ined the analogous reactions, via TS12B and TS13B, and find that fulvene-like cyclization is, in fact, kinetically favored (by 16.2 kJ mol-1) for chlorinated species.

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Figure 5. PES of the reaction of C4Cl4 with C2Cl2; all energies (in kJ mol-1 and calculated at the M06-2X/6-

311+G(3df,3p)//B3LYP/6-31G(d) level of theory, and are inclusive of ZPE corrections) are relative to C4Cl4 + C2Cl2. See the text for further details concerning the entrance barriers.

Despite their neglect by Taylor et al.42,43 in chlorinated sys-tems, Senosiain and Miller find that, for hydrocarbons at least, the i–isomers drive growth due to their greater stability and therefore greater accumulation in flame and pyrolysis systems.32 Figure 4 demonstrates that addition to the interior carbon atom (TS2B) is, as found for both C4Cl3 and C4H5 sys-tems, both kinetically and thermodynamically favored over addition to the terminal carbon atom (yielding 3B). Further, while rearrangement from 2B to the most likely species per-chlorofulvene appears relatively facile, the 6-membered ring cyclization transition state (TS6B) required for rearrangement of 3B to an aromatic product is significantly higher in energy than dissociation back to C4Cl5 and C2Cl2. Consequently, we expect that the i-C4Cl5 radical will lead almost exclusively to perchlorofulvene, and not the expected hexachlorobenzene product. We have neglected Cl-migration processes leading to linear species as these are presumed, on the basis of results from the channel following n-C4Cl5, to be too high in energy to be competitive.

C. C4Cl4 + C2Cl2

The M06-2X/6-311+G(3df,3p)//DFT/B3LYP/6-31G(d) PES depicting the molecular addition chemistry of C4Cl4 and C2Cl2 is presented in Figure 5; energies (and additional SPE values) are presented in the supporting information. The natural start-ing point for this chemistry is the Diels-Alder addition of C2Cl2 to C4Cl4, the only molecular process that has received attention in previous work.13-15 However, all attempts to opti-mize an unambiguous Diels-Alder transition state using

DFT/B3LYP/6-31G(d) on the C6Cl6 PES failed. While a C-C bond between the two ethynyl portions formed readily, that between the acetylene unit and the double bond of C4Cl4 lengthened during optimization, resulting in the essentially linear form of TS1C shown in Figure 5. This is very similar to that formed between two chlorinated acetylene units as de-scribed in our earlier work,63,64 where stabilization of the re-sultant carbene center located on the β-carbon of the attacking C2Cl2 (or, incidentally, C2HCl) was rationalized by the elec-tron withdrawing effect of the a β-substituted Cl atom. Ulti-mately, it is this effect renders these non-radical channels fea-sible in chlorinated systems whilst non-chlorinated analogues are too high in energy to be observed. This transition state has a DFT/B3LYP/6-31+G(d) energy of 102 kJ mol-1 relative to the starting materials, somewhat lower than estimates for gen-

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uine Diels-Alder transition states in non-chlorinated systems.34,35 Given the novelty and potential importance of this step (likely to be rate-limiting), bond formation was con-sidered in greater detail.

According to the B3LYP-PES, the addition process forms a C-C single bond producing the linear adduct 1C in Figure 5. This may subsequently react through two possible routes. One leads very directly to the dominant product observed at lower temperatures, ie 1,1,2,5,6,6-hexachloro-1,5-hexadien-3-yne (2C), through a 1,3-Cl shift (TS2C, barrier 50 kJ mol-1 with B3LYP/6-31+G(d)). The second involves the formation of cyclopropenylcarbenes (3C) by analogy with the acetylene dimerization case.63 However, SPE refinements with both MP2 and the M06-2X functional suggest that intermediate 1C is higher in energy than its formation transition state TS1C. This was explored further by first computing the B3LYP/6-31G(d) intrinsic reaction coordinate (IRC) of TS1C with the Gaussian 09 software suite. 46 Following this, the SPEs, EM062X(s), of several points either side of the B3LYP transition state were re-computed at the M062X/6-311+G(3df,3p) level. There is a significant difference (18.4 kJ mol-1) between EM062X(s = 0) and the maximum energy along the M062X/6-311+G(3df,3p)//B3LYP/6-31G(d) IRC, as determined by a cubic fit to the points along the IRC. Re-fitting the energies between 1.04 ≤ s ≤ 2.0 amu½ Bohr after the addition of un-scaled B3LYP/6-31G(d) ZPE corrections at each point yields 140.6 kJ mol-1 as the best estimate of the M062X/6-311+G(3df,3p) energy of TS1C.

The transition state TS3C also appears problematic as it is intermediate in energy between the reactants and products it connects (1C and 3C, respectively). IRC-following indicates that conversion of 1C to 3C is in fact barrierless. This effec-tively shuts down the most direct perchloro-1,5-hexadien-3-yne formation channel through TS2C given the significant barrier required for the necessary Cl-migration. Similarly, a second bimolecular addition step, involving the addition of the C4Cl4 ethynyl group across the C≡C bond of C2Cl2 (via TS12C) has also been followed. While the detailed chemistry along this PES is discussed shortly, this is undoubtedly only a minor channel as it is found to be considerably higher in ener-gy than C2Cl2 addition to C4Cl4 forming 3C by ~20 kJ mol-1 which, at typical pyrolytic temperatures, slows unimolecular reactions by an order of magnitude.

We digress briefly from the mechanistic details to address the energies of transition states TS3C and TS5C, relative to the preceding intermediates in greater detail. Exploring the IRC around 1C and 3C with the B3LYP functional, we find the PES is extremely flat, and that only extremely low barriers are associated with the saddle points. The observation of low-er-than-reactant transition state energies is likely due to devia-tions from the true M06-2X geometries of stationary points around this region of the PES. However, one must also con-cede that chemical intuition suggests that a 1,4-biradical such as 1C would be very susceptible to cyclization; this raises the intriguing possibility that 1C may in fact cyclize directly to 5C, with the rearrangement steps through TS3C and TS5C merely being an artifact of assumptions inherent in the B3LYP functional. The calculations required to reliably assess wheth-er the carbene 3C is a ‘true’ intermediate are prohibitively expensive for species with many

-200.2

-365.0

-207.3

-331.9

-215.7

-400

-350

-300

-250

-200

-150

En

erg

y/ k

J m

ol-1

20C + Cl

2C + Cl

13C

14C

TS14C

Figure 6. M062X/6-311+G(3df,3p)//DFT/B3LYP/6-31G(d), inclusive of ZPE corrections, for the conversion of the cyclic in-termediate 20C to perchloro-1,5-hexadien-3-yne 2C via Cl-addition and isomerization.

heavy atoms such as C6Cl6, and have not been performed here. However, the results would not affect the mechanistic implications, which is the focus of this current study. Either C4Cl4/C2Cl2 are converted to 5C by several low barrier rear-rangements, or 5C forms directly; the net mechanistic effect is essentially identical. However, as we cannot rule out these species as true intermediates (they do exist as intermediates on the B3LYP PES), they must be retained for completeness.

From the acetylene addition adduct 3C there are two possi-bilities for ring formation. All calculations (including values tabulated in the supporting information) suggest that ring for-mation across the C≡C bond of the C4 unit via TS5C to yield the vinylcyclobutadiene intermediate 5C proceeds barrierless-ly. This should outcompete Cl-migration TS4C, which ulti-mately leads to a higher energy channel through the perchlo-rovinylmethylenecyclopropene species 4C (eventually this channel is likely to favor re-formation of 3C).

The facile formation of the vinylcyclobutadiene 5C is fol-lowed by a number of routes by analogy with the C2 + C2 case;63,64 our M06-2X values, shown in Figure 5, indicate that a Cl shift to yield 20C and eventually linear products is com-petitive with conversion to a Dewar-benzene system 7C and thence to hexachlorobenzene (hCB) 11C itself, in line with our experimental observations. The M06-2X values are generally in reasonable agreement with the B3LYP values with the ex-ception of the final Cl-migration TS22C required to produce the observed product perchlorohexa-1,5-dien-3-yne (2C).

The substantial increases in energy of the Cl migration sad-dle points TS2C and TS22C severely limits the predicted yields of perchloro-1,5-hexadien-3-yne. However, it was not-ed that the intermediate 20C (perchloroethenylidenecyclobu-tene) is predicted to be surprisingly stable at all levels of theo-ry employed, and very similar in energy to perchloro-1,5-hexadien-3-yne; preliminary kinetic simulations showed that this species will accumulate in this system. This is quite simi-lar to the C6H6 family of compounds, where ethenylidenecy-clobutene is also predicted to be almost isoenergetic with 1,5-hexadien-3-yne.68 However, as both the experimental results of Earl and Titus69 and our own IR spectroscopic data64 have

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Figure 7. PES of the reaction of C4Cl4 with C2Cl2, following a second (higher energy) addition pathway; all energies (in kJ mol-1

and calculated at the M06-2X/6-311+G(3df,3p)//B3LYP/6-31G(d) level of theory, inclusive of ZPE corrections) are relative to C4Cl4 + C2Cl2.

suggested (see Paper II for further details), the non-aromatic isomer produced in the pyrolysis of heavily chlorinated sys-tems is perchloro-1,5-hexadien-3-yne; therefore, it was con-cluded that certain channels must still be missing. We have considered a number of potential non-radical alternative routes to this product; however, none appear feasible, typically fail-ing due to high Cl-migration barriers. Turning to radical-based channels instead, as it was noted that 20C may accumu-late, Cl-addition to this species was considered – see Figure 6.

The inclusion of such channels is quite reasonable when considering the global pyrolysis system as similar processes, Cl addition/loss for other stable species, already naturally arise in our final kinetic model, presented in Paper II; for example, C6Cl7 ↔ C6Cl6 + Cl processes for perchlorofulvene and hCB appear in Figure 4. Cl addition to the α-carbon of the ethylene moiety produces a vinyl unit; now sp3-hybridized between the vinyl moiety and the ring, we have assumed that the vinyl group in the resulting product may rotate freely. As a conse-quence the ring opening step that follows (at 157.6 kJ mol-1, so unlikely to be prohibitively high) may occur in the correct conformation to yield a linear C6Cl7 radical. Cl loss (or, con-versely, a barrierless Cl-abstraction forming Cl2) readily yields perchloro-1,5-hexadien-3-yne. With a view to modeling C2H2Cl2 and C2HCl3 systems (Paper II), chain radical reactions

with the parent ethylenes maintain a ready supply of Cl-atoms, and thus these processes should be fast. However, these chan-nels are perfectly valid in systems based on purely non-radical processes or where the supply of Cl atoms is limited, and one may predict that this reaction channel should be unfavorable under such conditions, predicting linear products form in low yields.

As we discussed, the initial linear adduct 1C may initiate a second rearrangement pathway, although this channel does have a considerably higher barrier and is likely to be largely negligible. The M06-2X/6-311+G(3df,3p)//B3LYP/6-31G(d) PES of these addition channels is depicted in Figure 7. Reac-tion through TS12C, already noted to be higher in energy than the barrierless competing process TS3C, yields 23C; this spe-cies is very closely related to 3C in Figure 5, but now vinyla-cetylene bridges across the acetylenic triple bond. As well as possessing a higher barrier to formation, 23C is 34.5 kJ mol-1 less stable than 3C indicating that this channel is also thermo-dynamically less favourable than competing reactions.

We have considered a number of rearrangements from 23C. TS24C and TS25C represent two different Cl-migrations; the

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Figure 8. PES of the Diels-Alder reaction of C2HCl with C4H2Cl2; all energies (in kJ mol-1 and calculated at the M06-2X/6-311+G(3df,3p)//B3LYP/6-31G(d) level of theory, and are inclusive of ZPE corrections) are relative to C4Cl4 + C2Cl2.

latter is considerably more favourable, and yields the pro-penylcyclopropene-based intermediate 25C. This is, however, almost isoenergetic with the concerted ring-opening/ring-closing process through TS26C which leads to 5C, thus re-entering the lower energy processes depicted in Figure 5. This channel, as discussed, ultimately leads to either hexachloro-benzene or hexachloro-1,5-hexadien-3-yne. For species that do continue on to 25C, Figure 7 demonstrates that a reasona-bly facile cyclization step leads to the perchlorinated bicy-clo[3.1.0]hexa-1,4-diene species 27C which in turn can ring-open via TS29C and, following several reasonably facile Cl-migrations, can eventually yield perchlorofulvene. This is the only feasible channel we could find to perchlorofulvene via non-radical processes. However, it must be noted that the key transition state, TS29C, in this channel is in competition with TS28C, a lower energy ring-opening step yielding a 6- mem-bered ring intermediate 28C; this, too, may undergo relatively facile rearrangement processes that eventually yield 10C.

Referring back to Figure 5, we see that this species readily rearranges to give hexachlorobenzene. Therefore, we con-clude that the additional rearrangement processes depicted in Figure 7, while providing the only feasible non-radical chan-nel to hexachlorofulvene, not only require a higher energy input to initiate than the competing reactions shown in Fig-

ure 5, but also tend to lead back to intermediates in this lower-energy scheme. Consequently, it appears that while both radi-cal and non-radical processes yield benzene, the only reasona-ble channel to hexachlorofulvene is via radical processes; sim-ilarly, the presence and quantities of hexachloro-1,5-hexadien-3-yne should be diagnostic for strictly non-radical reactions.

Finally, we note that if, as discussed early, TS1C actually leads directly to 5C in the PES of Figure 5, the PES of Fig-ure 7 may not be relevant. However, we again note that as very few species explore the PES of Figure 7 (due to high energies), and that those that do largely revert to 5C (and therefore to the PES of Figure 5) there would be no significant mechanistic implications if the PES of Figure 7 could not be accessed. Further, we also reiterate that our computations do suggest the existence of intermediate steps between TS1C and 5C and we must discuss these for completeness.

D. C4H2Cl2 + C2HCl

The discussion above suggests that the C4 + C2 system re-sults in a number of C6Cl6 isomers in the fully chlorinated case, in keeping with experimental observations (see Paper II).

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0

40

80

120

160

-5 -3 -1 1

E/

kJ

mo

l-1

s/ amu1/2 bohr

0

40

80

120

160

-2 -1 0 1 2

E/

kJ

mo

l-1

s/ amu1/2 bohr

Figure 9. IRC of non-Diels-Alder molecular addition of C2HCl to C4H2Cl2; all energies (in kJ mol-1 and calculated at the M06-2X/6-311+G(3df,3p)//B3LYP/6-31G(d) level of theory, inclusive of ZPE corrections) are relative to C4Cl4 + C2Cl2.

To explore the corresponding reaction pathways in partially chlorinated systems, we have selected one of the dominant C4 products of C2H2Cl2 pyrolysis observed in our earlier work, namely Z-1,2-C4H2Cl2, with the HCl elimination product C2HCl.63,64

First, reaction through linear adducts analogous those de-scribed above for the fully chlorinated case was explored, leading to very similar conclusions to those obtained for C6Cl6. Here, however, barriers to C6 cyclization are considera-bly lower than those for Cl shifts, suggesting aromatic and not linear isomers are produced; further, no low energy routes to 5-membered rings were located. Structures and energies along these reaction channels are given in the supporting infor-mation. More importantly, however, we now find that direct Diels-Alder cycloaddition is possible (see the PES in Figure 8) and exhibits (as is discussed shortly) a much lower activation energy for the rate-limiting bimolecular addition step, and therefore will be far faster than linear addition. There are two possible modes of cyclo-addition, and both have very similar activation energies; further, the barriers to the subsequent H or

2.2

2.6

3

3.4

0 1 2 3

C-C

dis

tan

ce, d

/ Å

Number of substituents

Chlorine

Fluorine

Methyl

Figure 10. Influence of Cl, F, and CH3 substitution on the Diels-Alder transition state; note there are multiple ways to arrange 1 or 2 substituents around the groups labelled X in the structure inset.

Cl shifts leading to trichlorobenzene (triCB) isomers are all very low.

The relative contributions of Diels-Alder and linear addition steps are crucial in our understanding of the overall process. Based on the M06-2X values, there is a considerable energy disparity between the two routes. Diels-Alder reactions ap-pear to have overall activation energies of ~130 kJ mol-1, which is in good agreement with barriers to cyclization in non-chlorinated systems;59,60 however, the IRCs of two distinct acetylene attack reactions via non-Diels-Alder processes, giv-en in Figure 9, suggest barriers at least 30 kJ mol-1 higher again. Given their significance, we were prompted to explore both of these processes at higher levels. We first considered the Diels-Alder processes by performing rQCISD(T)/6-31G(d) and MP4(SDTQ)/6-31G(d) SPE calculations. rQCISD(T) estimates give 125.2 kJ mol-1 for TS13D, in excellent agree-ment with M06-2X estimates, while MP4(SDTQ)/6-31G(d) predicts a slightly lower barrier of 110.8 kJ mol-1; the second Diels-Alder cyclization was not reconsidered as it is likely to be almost isoenergetic with TS13D. Similarly, the energies of transition states analogous to TS1C and TS3C found on the C6Cl6 PES were found to be 97.7 and 145.7 kJ mol-1 with rQCISD(T) calculations, and 85.1 and 152.7 kJ mol-1 with MP4(SDTQ), respectively for the reaction pair depicted at the top of Figure 9. This strongly suggests that, overall, Diels-Alder cycloaddition, with barriers of ~130 kJ mol-1, will sig-nificantly out-compete analogies of the C6Cl6 formation routes of the previous section, with overall barriers of around 160 kJ mol-1.

E. Interpretation of Novel Molecular Routes

PES searches in the preceding sections indicate that the mechanism of non-radical growth is fundamentally different in

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to the decomposition of

important C4 radicals (C4Xn →C4Xn-1 + X, X = H, Cl, n = 3,

5).

n-C4X3 i-C4X3 n-C4X5 i-C4X5

X = Cla 73.3 127.3 97.4 136.1

X = Hb 245.2

X = Hc 141.4 192.9

X = Hd 128.0 179.1

a M06-2X/6-311+G(3df,3p) level computations from this work; b Activation energy used in the kinetic model of Norinaga and Deutschmann37; c BAC-MP4 values from Miller et al.;22 d QCISD(T)/cc-pvtz//B3LYP/6-311++G(d,p) and QCISD(T)/cc-pvqz//B3LYP/6-311++G(d,p) calculations, extrapolated to an infinite basis set limit, of Klippenstein and Miller.25

C6Cl6 from the trichlorobenzenes. However, close inspec-tion demonstrates that the routes operative in C6Cl6 may be simply thought of as ‘failed’ Diels-Alder cyclizations as the result of steric hindrance presented by Cl atoms and therefore arise as a natural variation of the mechanism of formation of non-radical adducts as the degree of chlorination increases.

Figure 10 presents the C-C bond length of a number of Diels-Alder transition states optimized at the DFT/B3LYP/6-31G(d) level of theory. The bond length, d/Å, between the vinylacetylene vinyl group and the incoming acetylene is plot-ted as a function of degree of chlorination, fluorination, or methylation of the carbons in this bond. Chlorine can be seen to lengthen this bond; the extreme case is C6Cl6 where this bond is too long to form, with this failure leading naturally to the novel C6Cl6 mechanism described earlier. Varying the substituents provides further information regarding the origin of these novel processes. Equally bulky, but with far lower electronegativity, 70,71 methyl groups appear to have the same effect; fluorine (with electronic properties similar to Cl, but much smaller) leads to negligible changes in this bonding dis-tance, indicating that non-closure in highly chlorinated ana-logues is predominantly steric, rather than electronic, in origin.

DISCUSSION AND CONCLUSIONS

This work describes the first detailed ab initio study of the reaction of chloroacetylenes with chlorinated C4 species. Conventional thinking has assumed that chlorinated systems mimic non-chlorinated analogues closely; indeed, in most stages of reaction of C4Cl3 and C4Cl5 radicals with C2Cl2, this appears to be largely true.

In good agreement with non-chlorinated systems, both C4Cl3 and C4Cl5 may adopt the n-isomer and a lower energy resonance stabilized i-isomer, leading to three distinct modes of acetylene addition. Also in close analogy with hydrocar-bons, addition to n-isomers is favored over addition to the interior carbon of the i-isomer, which in turn is easier than addition to the terminal carbons of the i-isomer. Furthermore, barriers to addition are very similar, and subsequent rear-rangement to C6 products encounters largely similar energy changes when compared to non-chlorinated systems. One of the largest departures from direct analogues with non- chlorin-

ated systems is in the relative barriers to cyclization of the linear adduct formed between n-C4Cl3 and C2Cl2. In hydro-carbon systems (as in chlorinated systems) cyclization to ful-vene is preferred, but only slightly, relative to benzene for-mation; Walch suggested this would restore benzene for-mation routes30 (the typically observed aromatic products are not the kinetically favored products predicted by C4-radical processes) by means of fulvene ring-opening and recyclization as thermodynamically favored benzene. The C6Cl5 PES, how-ever, shows a far higher energy barrier to aromatic formation, therefore largely shutting down hexachlorobenzene through analogous ring-opening/re-closing steps. In agreement with hydrocarbon systems, radical C4 + C2Cl2 reaction pathways, at least in perchlorinated systems, predict fulvenes as the domi-nant products.

Despite agreement with hydrocarbon systems, our findings do not agree with the barriers and mechanisms underlying earlier kinetic models of growth in highly chlorinated sys-tems.42-44 Here, while n-isomers are found to be lower energy, i-isomers were assumed to be wholly unreactive, merely providing a source of n-isomers for growth; further, n-isomers were assumed to undergo cyclization to aromatic products only. Further, close scrutiny of thermodynamics also reveals important additional discrepancies. Barriers to radical for-mation were underestimated, and the energies of unimolecular decomposition of C4 radicals were overestimated relative to our extensive calculations (it must be noted that the early models necessarily employed less reliable estimation methods to obtain thermochemical data). Therefore, in addition to ne-glecting important (and arguably dominant) reactions to com-peting products, these estimates will also have led to consider-able overestimates in the instantaneous concentrations of C4 radical pools by several orders of magnitude, and therefore their rates of overall reaction. These findings cast doubts on the ability of the reaction of C4 radicals with C2Cl2 to describe growth, not only product distributions but even the rates of product formation in heavily chlorinated systems. Further, close agreement between perchlorinated and non-chlorinated systems implies this mechanism will probably be similarly problematic when applied to partially chlorinated systems.

It should be noted, too, that radical processes in chlorinated systems should be treated with considerable care. C-H bond dissociation barriers are far higher that corresponding C-Cl barriers – see, for example, Table 4 for radicals pertinent to this study. Therefore, hydrocarbon radicals are significantly more stable, and consequently accumulate in higher concentra-tions for reaction, than would be expected of chlorinated radi-cals. As such, radical reactions in general may not extend readily to chlorinated systems.

This does, of course, ignore the possible role of C3 radicals; while we again refer the reader to Paper II for a full discussion on this point, we will briefly summarize the important findings to justify our focus on non-radical routes in this study. Exper-imental studies of mixed di- and trichloroethylene (DCE and TCE, respectively) yield chlorobenzene congeners that are well-described by acetylene trimerization; doping with various C4Cl4 and C2H2 is also found to conform to C2 trimerization (or equivalently, C2 + C4 processes). Furthermore, when DCE and TCE systems are doped with dichloromethane, product yields remain in line with C2 + C4 models, and both C2 and C4 byproducts are found whilst C3 species are absent. Converse-

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ly, TCE/C4Cl6 co-pyrolyses are found to yield a very different set of C6 products from those predicted in our C2 + C4 frame-work and those observed in all other experiments, due to the decomposition of C4Cl6 into C1 and C3 species. Finally, kinet-ic modeling results show C2 + C4 processes alone adequately describe the time-dependent chemistry of TCE.

The search for alternatives therefore turned to non-radical systems for useful analogues, and Diels-Alder reactions of vinylacetylenes with acetylenes were therefore considered. Diels-Alder cyclization between C4H2Cl2 and C2HCl, a repre-sentative partially chlorinated system, demonstrates entrance barriers which are comparable to those in non-chlorinated analogues, which recent kinetic models have indicated are the dominant benzene formation pathway during acetylene pyrol-ysis.36-38 However, direct ring closure in fully chlorinated systems was not achieved (Figure 10 demonstrates that the reason is steric in origin) leading to the novel chemistry asso-ciated with a linear C4Cl4-C2Cl2 adduct explored in this work. Careful IRC searches of the M06-2X/6-311+G(3df,3p)//B3LYP/6-31G(d) PES suggest that this reac-tion has a barrier of 140.6 kJ mol-1, only marginally higher than the Diels-Alder transition state on the C6H3Cl3 PES of Figure 8 (found to be ~130 kJ mol-1, depending on the isomer). Consequently, this new pathway should possess very similar kinetic behavior to Diels-Alder cycloadditions which, as al-ready noted, have been found to be feasible.

Figure 5 and Figure 7 demonstrate that most pathways are likely to produce hexachlorovinylcyclobutadiene, 5C; this may undergo either cyclization to a hexachlorobicy-clo[2.2.0]hexa-1,5-diene species (7C) and eventually hexa-chlorobenzene, or a Cl migration to hexachloro-3-vinylidenecyclobut-1-ene (20C) and, via Cl-atom added isom-erization (see Figure 6) to hexachloro-1,5-hexadiene-3-yne, identified as an important product in TCE photolysis.69

It is also noteworthy that, while this linear adduct pathway is accessible on the C6H3Cl3 PES, it is much higher in energy than direct Diels-Alder cyclization and is therefore unlikely to be followed; hence, the appearance of non-aromatic isomers is only expected in heavily chlorinated systems, and this new mechanism arises naturally from Diels-Alder cyclization. These observations will be discussed and compared with ex-periment in greater detail in Paper II.

To conclude, explicit treatment of perchlorinated systems within the C4H3/C4H5 + C2H2 framework that dominated early literature on pyrolytic and combustion systems has shown that the chemistry is, indeed, very similar; however, these path-ways tend to predict high quantities of fulvenes, in conflict with typical observations. Extension of other successful frameworks, such as Diels-Alder cyclization between vinyla-cetylene and acetylene, leads to more success. However, in heavily chlorinated systems, simply analogy breaks down, in agreement with the observations of Detert et al.72 who noted that the chemistry of hydrocarbons may not readily extend to chlorinated systems. These new pathways have the potential, however, to describe a variety of C6 isomers and congeners in a range of partially to fully chlorinated systems, in particular, the appearance of linear products alongside hexachloroben-zene. Our subsequent paper, therefore, will present extensive experimental and kinetic modeling work comparing all of the

mechanisms discussed here, and their ability to describe our observations.

ASSOCIATED CONTENT

Supporting Information. Tables of energies of all stationary points, and their pertinent ge-ometric parameters are provided; additionally, the Cartesian coor-dinates of all structures are given. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION

Corresponding Author

* Address, School of Chemical Sciences, University of Auckland, Private Bag 92019, Auckland, New Zealand; Tel: +64 9 928 8302; E-mail: [email protected]

ACKNOWLEDGMENT

The authors thank the University of Auckland, the Marsden Fund and Lottery Science for grants towards equipment. We also grate-fully acknowledge the University of Auckland for financial sup-port of Grant McIntosh through a Guaranteed Doctoral Scholar-ship. Finally, we are also very grateful for the support provided by the Computational Chemistry Group at the School of Chemical Sciences, The University of Auckland.

ABBREVIATIONS

PAH, Polycyclic Aromatic Hydrocarbon; DCE, Dichloroethylene; TCE, Trichloroethylene; IR LPHP, Infrared Laser Powered Ho-mogeneous Pyrolysis; ZPE, Zero-Point Energy; tri(/tet/p/h)CB, tri(/tetra/penta/hexa)chlorobenzene; IRC, Intrinsic Reaction Coor-dinate

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