Oxidation of Polycyclic Aromatic Hydrocarbons: Evidence of Similarities in Thermochemical Properties and Reaction Paths

ABSTRACT This work elaborates similarities of thermochemical properties and oxidation kinetics among several polycyclic aromatic hydrocarbons. The systems considered are benzene (A1), naphthalene (A2), phenanthrene (A3), pyrene (A4), and the larger ones, benzo[ghi]perylene (A6) and coronene (A7). For each system, thermochemical properties, bond energies and oxidation kinetics are calculated and compared. Interpretation of the results revealed strong similarities and redundancies in behavior among these systems. The results imply that reactions are not dependent on the size of the molecules and, therefore, reaction paths and kinetic barriers determined with high-level calculations for small molecules can be used as estimates in the investigation of larger aromatic hydrocarbons to avoid expensive calculation efforts.


Introduction
In the frame of reducing the emission of particulate matter (PM), several measures have been taken (The European Parliament and the Council of the European Union 2007) and priorities have been given to reduction strategies.Intensive research has been reported in developing particulate filters (PF) for trapping soot particles present in the exhaust gases of internal combustion engines and minimizing PM emission from vehicles (Bhardwaj et al. 2014;Fang and Lance 2004).For continuous regeneration of PFs by oxidation of deposited soot with residual oxygen, the knowledge of soot oxidation reactions is crucial (Huang and Vander Wal 2016;Pawlyta, Rouzaud, and Duber 2015;Vander Wal and Tomasek 2003).Soot oxidation kinetics form the basis of the development of PFs and control of PM emissions.This work investigates the attack of molecular oxygen on five aromatic hydrocarbons of different size and possible reactions following the primary attack.The study identifies and compares structures, thermochemical properties, bond energies and reaction kinetics of the different systems and elaborates similarities among these.Based on the detailed studies of the benzene (A1) (Sebbar, Bockhorn, and Bozzelli 2008b;Tokmakov et al. 2005) and naphthalene (A2) oxidation (Sebbar, Trimis and Bockhorn 2022, in revision;Mebel, Landera, and Kaiser 2017), this work proceeds to phenanthrene (A3) with three rings, pyrene with four rings (A4), and the larger ones, with six and seven rings, benzo[ghi]perylene (A6) and coronene (A7), respectively.We note that A2, A4 and A7 exhibit a zig-zag structure while A3 and A6 have an armchair structure.
The objective is to employ small aromatic hydrocarbons as model molecules for higher polycyclic aromatic hydrocarbons and to develop mechanisms for the oxidation process and reaction kinetics of soot.For all species considered in this study, oxidation is supposed to occur through hydrogen abstraction resulting in a PAH radical.For the present study, our attention has been focused on the radicals illustrated in Figure 1, which describes the hypothetical reaction sequence for the oxidation of coronene and justifies the chosen radicals.Nevertheless, this assumption is partly verified by literature data that show, e.g. that the oxidation of pyrene radical (A4•) leads to the chosen phenanthrene radical (A3•) (Raj et al. 2013;Raj, da Silva, and Chung 2012) and phenanthrene can be formed from naphthalene (A2) as reported by Kislov, Mebel, and Lin (2002).Due to its symmetrical structure, coronene (A7) reveals that all external carbons connected to a hydrogen are identical, resulting in the same type of radical site.
The oxidation of the considered species results in a radical site easily attacked by O 2 to form a peroxide A X OO• (A X = A1, A2, A3, A4, A6, A7).Bond energies and enthalpies of formation of the involved species in these systems are calculated.Reaction pathways resulting from possible subsequent reactions of these peroxides as well as the associated energy barriers are identified and reported.Results concerning A1 are already reported in a previous study (Sebbar, Bockhorn, and Bozzelli 2008b).

Quantum chemistry calculations
Thermochemical properties of the species involved in the Ax• + O 2 systems are determined using the Gaussian 16 (Gaussian 16, Revision C.01 et al. 2016;Gaussian.com)program suite using DFT methods: M06 (Zhao andTruhlar 2008, 2011), the newly developed APFD (Austin et al. 2012) and the B3LYP (Becke 1993;Lee, Yang, and Parr 1988;Montgomery, Ocherski, and Petersson 1994).The APFD method is chosen because it has shown a higher accuracy than B3LYP or M06.This is probably due to the developed function to avoid the spurious long-range attractive or repulsive interactions that are found in most density functional theory (DFT) models.The chosen basis for all methods is 6-311 G(d,p).Transition states structures were identified by their single imaginary frequency, whose mode of vibration connects the reactant and the product.Frequencies and moments of inertia from the optimized APFD/6-311 G(d,p) structures were used to calculate the contributions to entropy and heat capacity on the basis of formulas from statistical mechanics and by use of the SMCPS code (Sheng 2002).Torsional frequencies are not included in the contributions to entropy and heat capacities; instead, they are calculated separately on each internal rotor analysis.Hindered internal rotor contributions to entropy and heat capacities are determined using the Rotator program (Lay et al. 1996).All data for these entropies and heat capacities are available in the supplementary material.

0-Dimensional simulation calculations
Time dependent concentrations profiles of species evolved in the different systems for a homogeneous, isobaric and isothermal reacting mixture are calculated.For the simulation, the SENKIN flame program of the CHEMKIN package (Kee et al. 2000) is used.With the help of THERMFIT (Sheng 2002), the calculated thermodynamics properties (available in the supplementary material) are converted into the NASA polynomial format as required by SENKIN.The kinetic parameters are calculated for the different systems and channels using ThermKin (Sheng 2002) which calculates the forward rate constants, k(T) on the basis of the canonical transition state theory (CTST).

Enthalpy of formationΔ f H 0 298
Standard enthalpies of formation are obtained from DFT calculations (B3LYP, M06, APFD) for all compounds involved in the investigated systems.Following the primary attack of O 2 , six subsequent channels are plausible for the A X OO• peroxides.The reaction paths comprise important exothermic chain branching reactions and the formation of unsaturated oxygenated hydrocarbon intermediates.If not available from literature, thermochemical properties of stable species as well as radicals and transition state structures are estimated and listed in Tables 1,2,3,4,5.Optimized geometries, frequencies and moments of inertia of all species and transition state structures resulting from the APFD/6-311 G(d,p) calculations are used in the estimation of the thermodynamic properties.
Tables 1 to 5 also list the calculated energies of the transition state TSA required for the abstraction of a hydrogen from A X to the radical A X • + OOH.Addition of O 2 through the transition state TSB result in a peroxy radical A X OO•.The thermochemical properties of the species resulting from subsequent reactions of the A X OO• peroxy radicals are also calculated and listed in Tables 1 to 5. The structures of the formed species are illustrated in the potential diagrams in section 4. All calculated barriers and enthalpies are in good agreement among the applied calculation methods.Values obtained by the new developed APFD-DFT method are recommended and highlighted in bold in the Tables.
The first subsequent reaction is the bond formation of the terminal oxygen of the A X OO• peroxy radical and the adjacent carbon atom (TS1 -Channel-1) forming A X •YC2O2 radicals.Channel-2 is the ipso addition of the terminal oxygen.The oxygen attacks the carbon atom connected with the peroxy group (TS2) through formation of a threemembered ring (COO), resulting in A X •YCO2 radicals.In channel-3 (TS3) the A X OO• peroxy radical undergoes an O -O bond dissociation to A X O• + O.A new class of reactions , where the oxygen radical attacks the carbon of the adjacent ring (TS4) via formation of a five-membered/six-membered ring (CCCOO/CCCCOO), results in the formation of A X •YC3O2/A X •YC4O2 radicals.Hydrogen abstractions forced by the oxygen radical can take place on each of the neighboring sides of the peroxy site (TS5a and TS5b) resulting in two hydroxyl radicals A X •OOH.A detailed description of these reactions along with the structure of the species are illustrated in section 4.1 and Figures 4 to 8.

Formation of peroxy radicals A X OO•
Following the H-abstraction from a stable compound A X , a stabilized peroxy radical A X OO• is formed via O 2 addition onto the radical site of A X •. Figure 2 illustrates the A X • + O 2 reactions for the different systems leading to the peroxide radical A X OO•.For comparison, the phenyl radical system reported in a previous study (Sebbar, Bockhorn, and Bozzelli 2008b) is also illustrated.As expected, the oxygen addition on the radical of each system takes place with a similar excess of energy varying between 45 and 50 kcal mol −1 .We note that the formation of the first series of peroxides, A1OO•, A2OO•, A4OO• and A7OO• releases approximately the same energy near 50 kcal mol −1 , while that of the formation of A3OO• and A6OO• is slightly lower at ca. 46 kcal mol −1 .
Examination of the geometries reveals that the O 2 addition to the species A1•, A2•, A4• and A7• occurs at zigzag-carbon atoms while at both A3• and A6•, O 2 is added to armchair carbon atoms.Addition of O 2 to the radical site is slightly hindered by this armchair edge, which may explain the ~ 4 kcal mol −1 difference in the released energy.To prove this assumption, calculations have been performed for the second isomer of A3•, see Figure 3. Figure 3 compares the O 2 addition to the two isomers of the A3• radical.A3•-a has an armchair structure of the carbon atoms while A3•-b exhibits a zig-zag configuration.Calculation of the energy released during O 2 addition shows 45.7 kcal mol −1 for the armchair configuration and 50.9 kcal mol −1 for the zig-zag structure which is comparable with the energy released during A1OO•, A2OO•, A4OO• and A7OO• formation.This confirms the impact of the structure on the released energies.The results further suggest that small systems may serve for estimations of kinetic parameters for larger systems, see also discussion in ref (Sebbar, Bockhorn, and Bozzelli 2008a).

Bond energy calculations
Bond energies in the peroxy radicals A X OO• and the corresponding hydroperoxydes A X OOH have been calculated.Table 6 lists the bond energies of Ax -OO• and AxO -O• in the different peroxy radicals and A X -OOH, A X O -OH and A X OO -H in the corresponding hydroperoxides.The calculations reveal that the Ax -OO• bond energies are about 50 kcal mol −1 except for A3• and A6•, where the bond energies are lower by about 4 kcal mol −1 (see discussion in section 2 above).The O -O• bond energies in the A X OO• radicals are in the range of 33 to 39 kcal mol −1 .The phenyl system exhibits the highest bond energy of 38.8 kcal mol −1 probably due to the lack of adjacent rings affecting the resonance energies.The • have a slightly lower one (~2.kcal mol −1 ).It is still important to notice that the deviations are in the order 3 to 4 kcal mol −1 only and can be also caused partly by calculation uncertainties.Similar bond energies of 87 to 89 kcal mol −1 for the A1-OOH, A2-OOH, A4-OOH, and A7-OOH bonds have been calculated.As for the peroxy radicals, the bond energies for A3-OOH and A6-OOH are both weaker by some 5 kcal mol −1 compared to the others.This confirms the impact of the armchair geometry and the radical site location on the strength of the bonds.Except for A1•, the O -OH bonds are in the order of 21 kcal mol −1 .The ROO -H bond energies for the different systems are similar in all cases.As expected, we point out that, the armchair/zig-zag geometries have no impact on O -O•, O -OH and ROO -H bond energies.

Reaction pathways for each system
Similarly to the oxidation of A2• (Sebbar, Trimis and Bockhorn 2022, in revision), the different systems A X • (x = 3, 4, 6, 7) considered in this work undergo barrierless O 2 addition forming a chemically activated peroxy radical [A X OO•] # , see e.g (Kislov et al. 2015;Raj, da Silva, and Chung 2012;Sebbar et al. 2019;Sebbar, Bockhorn, and Bozzelli 2008b, 2011, 2014).The excess of energy released during O 2 addition allows subsequent reactions of the activated [A X OO•] # with energy barriers lower than the energy of the entrance channel A X • + O 2 .For the systems  4 illustrates the subsequent reactions reported in the detailed study of A2• (Sebbar, Bockhorn and Bozzelli in revision).It has been elaborated that the activated peroxy radical formed during addition of O 2 reacts further through six reactions.The study reveals the dominance of channel-2 (TS2) with the ipso addition of the oxygen radical.For the other aromatic hydrocarbons considered in this study, the analogous pathways have been evaluated.Figure 5 illustrates the potential diagram of the radical resulting from phenanthrene oxidation.Formation and subsequent reactions of A3OO• occur similarly to A2• via the analogous six reaction paths.Kislov et al. (Kislov et al. 2015) have investigated and reported the final products of the O -O dissociation from A1OO• and A2OO• to phenoxy and naphthoxy radical products.They report that the general trends in the oxidation kinetics of phenyl and naphthyl radicals are similar, which support the results of this work.Channel-4 (TS4) for the addition of the oxygen atom on the carbon atom of the non-adjacent ring may however, be different.Due to the armchair structure of A3OO• a six membered ring is formed, which is more stable than the corresponding radical resulting from A2•. Figures 6 to 8 illustrate the oxidation of A4•, A6• and A7• through the same set of oxidation reactions.We focus on the fact that, except A1 and A7, all molecules considered in this study, have different radical isomers.The choice of these particular radicals is based on the plausible intermediates resulting from the decomposition of the coronene radical.We note that A4• and A7• are very similar to A2•, while A6• is similar to the A3•.Indeed, examination of the intermediate species resulting from the attack of the terminal oxygen in the peroxy radical on the carbon situated in the non-adjacent ring (channel-4 -TS4) shows a loose six-membered ring for A3• and A6•.For these two systems, the attack of the oxygen on the adjacent ring is facilitated by the well of the armchair structure.
Formation of a reactive ortho-hydroperoxy-radical A X •OOH-alpha occurs via TS5-alpha by abstraction of the hydrogen adjacent to the peroxy group of the AxOO• radical.Another reaction sequence involves the abstraction of a hydrogen from the adjacent ring (TS5-beta) forming a second hydroperoxide radical A X •OOH-beta.The calculations show that for all systems the energy of TS5-beta is lower than that of TS5-alpha.This can be explained by the six-membered ring transition state structure involved in TS5-beta versus the slightly more strained five-membered ring in TS5-alpha.For all channels and all systems, the calculated energy barriers are below the energy of the entrance channel and accessible for the chemically activated peroxy radicals.

Energy barriers
Table 7 lists for each system the energy barriers in the different reaction channels.The energy barriers required for the hydrogen abstraction by O 2 (TSA) are in all cases similar around 65 to 70 kcal mol −1 .We note that the barriers for species with a symmetrical structure (A1•, A2•, A7•) are slightly higher.The energy released during oxygen addition is around 50 kcal mol −1 as discussed in section 2. The energy barriers leading to TS1 are identical for A1•, A2•, A6• and A7•.In all cases, channel 2 (TS2) requires the lowest energy and is consequently the most dominant pathway.Channel 4 exhibits the same energy barrier for A2•, A4• and A7• at ca. 32 kcal mol −1 , while for A3• and A6•, the barrier is approximately 10 kcal mol −1 lower.This is again due to the armchair structure, where TS4 exhibits a loose six-membered ring compared with a more strained five-membered ring in A2•, A4• and A7•.As expected, the energy barrier for channel 5a is similar for all systems since the structure of the species has no impact on TS5a.On the other hand, the energy barriers for channel 5b exhibit the same differences as the ones for channels 4. The energy barrier for A3• and A6• are ~ 22 kcal mol −1 , which is slightly lower than for the other systems.This is due to the formation of a loose sevenmembered cyclic transition state structure.This result is comparable with the transition state   structure of the 2-butanone-4-yl, CH 3 C(=O)CH 2 CH 2 • conversion to the CH 2 •C(=O)CH 2 CH 2 (OOH) radical (Sebbar et al. 2019) involving also a seven-membered ring structure with an energy barrier of some 23 kcal mol −1 .Raj, da Silva, and Chung (2012) report the oxidation of pyrenyl (A4•) calculated at B3LYP/6-311++G(d,p)//HF/6-311 G(d,p) level.It appears that phenanthrenyl is one of the main product of pyrenyl.The energy barriers (in kcal mol −1 ) reported by the authors are 40.7 (channel-1), 21.8 (channel-2) and 29.0 (channel-3).These results (channels 1, 2 and 3) agree with those presented in this work.Channels 4, 5a and 5b are not investigated Ref. (Raj, da Silva, and Chung (2012).
Singh et al (Singh, Mebel, and Frenklach 2015).also report and energy barrier of 27.5 kcal mol −1 (at G3 (MP2,CC) level) for the elimination of an oxygen atom from the pyrenylperoxy radical (A4OO•), that is 3 kcal mol −1 lower than the calculated value in this work.Zhou et al. (2012) have investigated the oxidation of naphthyl (A2•) and reported two main channels, the ipso addition and the oxygen atom elimination.The energy barrier for the ipso addition channel (TS2 in this work) is found to be 20.7 kcal mol −1 (at G3 level) which is in excellent agreement with our calculated value at 20.9 kcal mol −1 .The transition state barrier for O -O bond dissociation reported by the authors is at 29.1 kcal mol −1 at B3LYP/6-311 G** level and 28.9 kcal mol −1 at G3 level which is ca. 2 kcal mol −1 lower than our calculations.
In recent work of Morozov et al. (2021) have revisited the phenoxy radical + O recombination and reported 24.3 kcal mol −1 for the ipso addition (TS2) which support our value at 24.2 kcal mol −1 .

0-D-simulations: time dependent species concentrations for the A x •+ O 2 systems
Results for time-dependent species profiles for a homogeneous, isobaric and isothermal reacting mixture in a closed system are presented below starting with Ax• + O 2 ➔ AxOO• ➔ Products.The temperature has been set to non-flame conditions at T = 1000 K, which represents the reaction temperature for PF-regeneration.The initial mixture composition of 90 mol% O 2 and 10 mol% Ax• These simulations help to identify the crucial reaction channels developed for the chosen radicals in this study.We are aware that the interpretation of the following results performed at one temperature only shall be taken carefully.Although we do not expect any drastic change in the results, the importance of the channels may change under different conditions.Nevertheless, in the Figures below, promising results can already be seen.The mole fraction profiles of the species resulting from the subsequent reactions of the activated peroxy radicals A X OO• calculated at P = 1 atm and T = 1000K are given in Figures 9 and 10.As illustrated in Figure 9 for A2OO•, A4OO• and A7OO• the mole fraction profiles of the products formed via the ipso addition (channel 2) are markedly higher than the other compounds formed through the other channels.This is probably explained by the low energy barrier required for the ipso addition.This implies that channel 2 is by far the dominant channel in the oxidation of these peroxy radicals.The other reaction pathways play a minor role.Also, for the species presenting an armchair structure, A3OO• and A6OO• (Figure 10), channel 2 is still the dominant and most important subsequent reaction.However, due to their armchair structures, channel-5b seems to gain slightly in importance.Most likely due to the formation of a loose transition state structure formed through a seven-membered ring.
These results have an important impact concerning the study of much larger systems, since they allow focussing on the detailed investigation of the dominant channel avoiding consequently expensive calculation time.

Conclusion
This study investigates the oxidation of five PAHs by molecular oxygen.The PAHs are naphthalene A2, phenanthrene A3, pyrene A4, benzo[ghi]perylene A6 and coronene A7.Thermochemical properties (enthalpy of formation, entropy, and heat capacities) of adducts, first intermediates and transition states resulting from the A X + O 2 and A X • radical + O 2 reactions have been determined.Bond energies (A X -OOH, A X O -OH and A X OO -H) in the stable hydroperoxides and in the corresponding peroxide radicals (A X -OO• and A X O -O•) show high similarities among the systems.For all systems, the oxidation sequence by molecular oxygen follows the same process: formation of a peroxy radical A X OO• with an excess of some 45-50 kcal mol −1 , suitable for further chemical activation reactions through six paths.Examination of the energy barriers of each channel reveal similarities among A2•, A4• and A7• but a slight deviation for A3• and A6•.The differences can be explained by the armchair the structure of the last two radicals.Using SENKIN, the calculation of the time dependent mole fraction profiles of the products of the subsequent reactions following A X • + O 2 helped to identify the crucial main channels.It turns out, that in the temperature range of 1000 K channel 2 is by far the most determinant.Detailed investigation of the further reaction/dissociation of the species formed through each channel (each system) are in progress.However, it is important to point out that the identification of the most determinant channel is advantageous in the investigation of larger aromatic hydrocarbons, avoiding expensive calculation efforts for channels playing minor roles.Analogies in bond energies, well depths, types of bonds and reaction paths in these systems imply and confirm that the primary reactions are not dependent on the size of the molecule.

Table 2 .
Formation and subsequent reactions of A3OO•; enthalpies of formation Δ f H 0 298 in kcal mol −1 for radicals and transition state structuresΔH TS .

Table 3 .
Formation and subsequent reactions of A4OO•; enthalpies of formation Δ f H 0 298 in kcal mol −1 for radicals and transition state structuresΔH TS .
considered in this work, pathways for possible subsequent reactions of A X OO• have been investigated.The different pathways are plotted in Figures 4 to 8.Figure

Table 4 .
Formation and subsequent reactions of A6OO•; enthalpies of formation Δ f H 0 298 in kcal mol −1 for radicals and transition state structuresΔH TS .

Table 5 .
Formation and subsequent reactions of A7OO•; enthalpies of formation Δ f H 0 298 in kcal mol −1 for radicals and transition state structuresΔH TS .

Table 6 .
Bond energies in A X OO• and A X. OOH.

Table 7 .
Energy barriers for the different transition states relative to the energy of Ax and AxOO • , respectively.