Influence of the Local Polyaromatic Structure on the Thermochemistry and

Kinetics of Hydrogen-Abstraction Reactions by a Methyl Radical

Karen Hemelsoet, *,†,‡ Veronique Van Speybroeck,† Damian Moran,‡ Leo Radom,‡,¶

Guy B. Marin§ and Michel Waroquier*,†

Center for Molecular Modeling, Ghent University, Proeftuinstraat 86, B-9000 Ghent, Belgium,

Laboratorium voor Petrochemische Techniek, Ghent University, Krijgslaan 281-S5, B-9000 Ghent,

Belgium, School of Chemistry, University of Sydney, NSW 2006, Australia, and ARC Centre of

Excellence in Free Radical Chemistry and Biotechnology

Thermodynamic and kinetic properties of hydrogen abstraction reactions from different sites at polyaromatic hydrocarbons (PAHs) by the methyl radical are investigated. The reaction enthalpy (298 K), barrier (0 K), activation energy and pre-exponential factor (700–1100 K) are calculated by means of density functional theory (DFT). More precisely, B3-LYP/6-311G(d,p) geometries, followed by BMK/6-311+G(3df,2p) single-point energy calculations are used.Based on reaction enthalpies, a classification of the different PAH sites is proposed, indicating the effect of the local polyaromatic environment on the reactivity. The reaction barriers at 0 Kelvin show that abstraction at congested sites is more difficult. The kinetic parameters and rate constants for the series of linear acenes demonstrate that abstraction is more difficult at the central rings. When the entire test set of PAHs is taken into account, it is overall seen that abstraction at smaller clusters is seen to be preferred.

*To whom correspondence should be addressed. E-mail: karen.hemelsoet@UGent.be, michel.waroquier@UGent.be†Center for Molecular Modeling§Laboratorium voor Petrochemische Techniek‡University of Sydney¶ARC Centre of Excellence in Free Radical Chemistry and Biotechnology

1

1. Introduction

Polycyclic aromatic hydrocarbons (PAHs) are among the most studied organic molecules

in modern chemistry.1,2 They play a key role in a large number of different areas as they are both

naturally occurring and anthropogenic. PAHs are the largest known class of chemical

carcinogens and mutagens.3,4,5 They are present in atmospheric aerosols and many celestial

objects such as meteorites, planetary nebulae, reflection nebulae and active galaxies,6,7,8 and

recent work reported on spectroscopic evidence of the existence of PAHs in interstellar space.9

Their importance in the formation process of hollow-cage fullerenes is also known.10 In addition,

they are key intermediate products in soot formation and coal conversion processes. 11,12,13,14 They

can arise from incomplete combustion of organic matter and as side products in a steamthermal

cracking unit used in the petrochemicalleum industry for the production of light olefines such as

ethylene and propylene. Within this view, a quantitative understanding of the formation of PAH

molecules is essential for an efficient design of clean and practical combustion devices such as

engines and incinerators and for a maximal run length of thermal crackingsteam cracking units.

PAHs can grow by means of a radical reaction network. The model beginning with a

phenyl radical, proposed by Frenklach et al.,Error: Reference source not found currently seems to

be the most favourable synthetic route. This model proposes a sequential addition of acetylene

molecules to the phenyl radical to form mainly planar, naphthalene-like PAHs consisting of

(substituted) six-membered rings. More recently, Vereecken et al.15 have studied the growth of

PAHs incorporating five-membered rings, which can also act as possible intermediates for the

formation of nonplanar systems, including fullerenes. In all PAH growth processes, various

classes of elementary reactions such as hydrogen abstraction, addition, cyclization and

dehydrogenation reactions can be distinguished and lead to the formation of a surface consisting

2

of conjugated rings.Error: Reference source not found,16 To model these potentially complex

reaction processes, calculations on some of the contributing elementary reactions are advisable,

as they provide the opportunity to obtain the required levels of insight and understanding for

model genesis.17,18,19,20,21,22,23 The initial step which allows formation of radical surface species are

hydrogen abstraction reactions by means of gas phase precursors, such as methyl and hydrogen

radicals.Error: Reference source not found,24,25,26 In an earlier paper, we performed an elaborate

level-of-theory study on the hydrogen abstraction reaction at benzene by a methyl radical, as this

reaction represents a fundamental point of comparison for radical-mediated hydrogen

abstractions from the benzenoid components of PAHs.Error: Reference source not found We

found that virtually all theoretical procedures are suitable for geometry optimization. However,

for the reaction enthalpy the W1, G3-RAD and URCCSD(T) level give best agreement with

experiment. For the reaction barriers at 0 Kelvin, the URCCSD(T) and low-cost BMK method

provide values in close agreement with the benchmark value. Overall, the G3-RAD composite

procedure, the URCCSD(T), and the cost-effective DFT methods BMK, BB1K and MPW1K

were found to give the best results for calculating the thermochemistry and kinetics of hydrogen

abstraction by the methyl radical from benzene.

Earlier studies reported on the characteristics and reactivity of aryl radicals derived from

PAHs. Unfortunately, theoretical studies of these radicals have been scarce, most probably

because of the very poor description –caused by large spin-contamination problems- of the

phenyl radical at the UHF level of theory.27 Based on electron spin resonance studies and

analysis of their spectra, in combination with theoretical calculations, Kasai et al. showed that all

aryl radicals are σ-radicals, as the unpaired electron was found to occupy the essentially non-

bonding σ-orbital corresponding to the broken bond.28 Also using semi-empirical calculations,

and by examining the bond dissociation energy (BDE) it was found that the strength of the aryl-H

3

bond is essentially independent of molecular size, but dependent on the neighbouring geometry

of the C-H bond and a classification into three types of aryl radicals was reported.29,30 Aihara et

al. used a PM3 approach in combination with a ROHF procedure, and showed that the C-H BDE

values are fairly constant for their test set.31 DFT calculations performed by Cioslowski et al.

using the BLYP functional give theoretical evidence that the hydrogen in a H-abstraction reaction

is preferentially removed from congested regions of the parent hydrocarbons, indicating that the

site specificity of the hydrogen abstraction is almost entirely governed by steric factors.32

The main goal of the current work is to examine the influence of the local polyaromatic

environment on the reactivity and kinetics of hydrogen abstraction reactions by a methyl radical.

We will therefore compute optimized geometries, reaction enthalpies at 298 K (∆H298), barriers at

0 Kelvin (∆E‡0), activation energies (Ea), pre-exponential factors (A) and rate constants (k(T))

within a relevant temperature interval (700-1100 K). By studying the variations of the activation

energy and pre-exponential factor in terms of the polyaromatic structure, we want to gain insight

into which sites are preferred for the initial formation of surface radicals in a polyaromatic

network.

2. Theoretical Procedures

All calculations were performed using the Gaussian 0333 software package.

Geometries were optimized at the B3-LYP34 level of theory, in conjunction with the

triple–zeta 6-311G basis set augmented with single first d and p polarization functions.35

Frequencies were computed at the same level of theory as the geometry optimization to provide

zero-point vibrational energies (ZPVEs) and to confirm the nature of the stationary points. As

mentioned earlier, a previous study on the reference hydrogen abstraction reaction at benzene

4

showed the limited influence of the level of theory on the geometry optimization.Error:

Reference source not found Other studies on similar radical reactions also reported that the B3-

LYP method gives a reliable and quantitatively good description of geometries.36,37 A scaling

factor of 0.9806 was used to the ZPVE and a scaling factor of 0.9989 was applied to the thermal

correction of the enthalpy.38 The use of scaling factors provides a means for accounting for

systematic deviations between measured and computed frequency-dependent properties and is an

important consideration for an accurate description of reaction kinetics and

thermochemistry.Error: Reference source not found,39,40

Single-point energy calculations were performed using the BMK functional in

conjunction with the large 6-311+G(3df,2p) basis set. The BMK functional was recently

developed by Boese and Martin and is accurate in the 2 kcal mol-1 range for transition state

barriers.41 They found that BMK actually outperforms B3-LYP for most properties (geometries,

enthalpies, barriers, etc) and that it is competitive with the best currently available functionals for

equilibrium energetics. This good performance appears to hinge on the combination of a high

percentage of Hartree-Fock exchange (42%) with terms dependent on the kinetic energy density,

resulting in a “back-correction” for excessive HF exchange in systems where that would be

undesirable. The BMK functional was also found to be a method of choice in our level-of-theory

study on the reference reaction at benzene, as it is an accurate and yet affordable computational

method for the systems of considerably large size, studied in this work.Error: Reference source

not found A recent study on trends in R-X BDE also reported on the good performance of the

BMK functional, providing very reasonable predictions when compared with high-level

composite procedures.42

We applied transition state theory (TST)43 to calculate the rate constants k(T),44 including

Eckart45 tunneling correction factors. The Eckart method is a simple procedure that only needs to

5

consider the reaction stationary points and is therefore compatible with TST, although the method

is often found to overestimate the tunneling contribution, especially at very low temperature.46

The link with the macroscopic quantities found in the Arrhenius rate law is made by a linear fit to

a set of k(T) values calculated for a range of temperatures. One refinement in our theoretical

treatment comes from the observation that the transition structures (TSs) of the hydrogen

abstraction reactions have a very-low-frequency vibration, corresponding to internal rotation of

the incoming methyl group about the forming bond. The standard Harmonic Oscillator (HO)

model is known to be inappropriate for such modes and other approximations, such as the Free

Rotor (FR)Error: Reference source not found,47 and Hindered Rotor (HR)48,49 model, will

therefore be used. The choice for a particular description depends on the height of the rotational

potential barrier and the temperature. In a recent study on radical-addition reactions, we

demonstrated the importance of correctly describing hindered internal rotations in order to obtain

reliable partition functions.Error: Reference source not found,50 Summarizing, in this paper, a

mixed harmonic oscillator/free rotor (HO/FR) or mixed harmonic oscillator/hindered rotor

(HO/HR) model, in which all the internal motions -except for the methyl torsion in the TS- are

approximated as independent harmonic oscillators, will be used.

3. Results and Discussion

Hydrogen abstraction reactions from PAHs by an approaching methyl radical are studied,

leading to the formation of a variety of aryl radicals and methane. A schematic representation of

the investigated reactions is depicted in Figure 1. All studied PAH molecules are depicted in

Figure 2 and the hydrogen atoms which are considered for abstraction are numbered. The largest

systems consist of a combination of 7 six-membered aromatic rings. The entire test set of PAHs

6

can be divided into two sub-categories, with on one hand the series of linear acenes, consisting of

benzene (B), naphthalene (N), anthracene (A), tetracene (T) and pentacene (P). On the other

hand, the non-linear structures, consisting of phenanthrene (Ph), benzo[c]phenanthrene (BP),

dibenzo[c,g]phenanthrene (DBP), benz[a]anthracene (BA), dibenz[a,j]anthracene (DBA),

coronene (C), benzo[a]napht[2,1-j]anthracene (BNA), benzo[a]phenanthr[2,1-j]anthracene

(BPA), pyrene (PYR), perylene (PER) and benzo[ghi]perylene (BPER), are considered.

Throughout the article, the following nomenclature will be used: PAH(number hydrogen) refers

to the abstraction reaction of hydrogen atom (number hydrogen) from a specific PAH.

3.1. Geometries.

The geometries of the reactants, products and TSs were optimized at the B3-LYP/6-

311G(d,p) level of theory. First of all, we note that all product radicals are of the σ-type, with the

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A key geometrical feature is the planarity of the reactant and product species. Most

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9

approximately 18 degrees. The BNA and BPA structures can furthermore be regarded as a

combination of two smaller PAH structures, more specifically Ph and BP, in case of BNA and Ph

and DBP, in case of BPA. The deviation from planarity is mainly situated into the BP- and DBP-

part, respectively, and a similar dihedral angle of 18 degrees is found in these substructures. The

non-planarity is to a large extent removed when the aryl radicals BP(1), BNA(1) and BNA(2)

(see Figure 2) are formed due to the abstraction of a hydrogen atom. In the case of the DBP(1)

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10

and consequently also the BPA(2) and BPA(3) radicals, the deviation from planarity for the

twisted plane where the hydrogen is abstracted, is largely reduced, as indicated by a dihedral

angle of 7.6 degrees in the DBP(1) structure. Other important geometrical features of the

reactants and products are bond distances and angles at the specific site of abstraction. The

perturbations due to the removal of a hydrogen atom involve a widening of the bond angle at the

ipso carbon by about 6 degrees and the accompanying shortening of the adjacent C-C bonds by

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11

ca. 0.02 Å. This was also noted earlier by Cioslowski et al.,Error: Reference source not found

for a test set of 10 PAHs containing up to a maximum of 5 six-membered rings.

For the involved TSs, the forming (d1) and breaking (d2) bond lengths are, as well as the

out-of-plane angle (γ) of the approaching methyl radical, salient geometrical features. These

parameters are illustrated in Figure 1 and the computed results are given in Table 1. It is seen

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which is consistent with a “late” (in the Hammond sense) TS and in accordance with the reaction

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12

endothermicity. Exceptions are found for DBA(1), BNA(2) and BPA(2), where the d2 bond

length is a little bit shorter than the d1 bond length (average difference approximately 0.02 Å).

This behaviour can be traced back to the more folded structure of the involved TSs, as is

illustrated in Figure 4. It is also seen that for abstraction reactions of some specific hydrogen

atoms located at the more congested sites of the PAHs, the approaching methyl radical is forced

to follow an out-of-plane pathway. For these TSs, the out-of-plane angle γ is larger than 10

degrees, with a minimum value of 12.2 degrees (for PER(1)) and a maximum value of 34.3

degrees (for BNA(2)). These large values of γ are basically due to steric hindrance between the

incoming methyl radical and closely positioned hydrogen atoms, in combination with the non-

planarity of the PAH reactant.

3.2. Reaction Enthalpies and Barriers.

∆H298 and ∆E‡0 values for the reactions between the different PAHs and methyl radical

were calculated using the BMK/6-311+G(3df,2p)//B3-LYP/6-311G(d,p) level of theory, using

scaled ZPVEs and thermal corrections.51 The results are given in Tables 2 and 3.

3.2.1. Reaction enthalpies. Inspection of the results in Table 2 shows that the reaction

enthalpies lie within a broad range between -1.83 and 34.27 kJ mol-1. The studied hydrogen

abstraction reactions are all endothermic, with the exception of the BNA(2) reaction, which is

slightly exothermic.

In a previous study, we carefully investigated the bond dissociation enthalpies at 298 K

(BDE) for an extended set of hydrocarbons, and their corresponding ethynylic, arylic, vinylic,

alkylic, propargylic, benzylic and allylic radicals.52 In this study, all possible aryl radicals of

50[?] Van Cauter, K.; Van Speybroeck, V.; Vansteenkiste, P.; Reyniers, M. F.; Waroquier, M.

ChemPhysChem. 2006, 7, 131.

13

PAHs were classified into a limited set of groups, each characterized by a given reactivity. As

the BDE value actually is a measure of the reaction enthalpy of the studied hydrogen abstraction

reactions by a methyl radical, we refer to this study for a more detailed comprehension of this

topic. Summarizing, based on BDE values or reaction enthalpies, the calculated values segregate

into six groups with different reactivity, and which can be related to the local structure of the

specific site, as is illustrated in Figure S1 of the Supporting Information. An average value of the

computed ∆H298 results for a specific site X (<∆H298>X) can be defined. In order of decreasing

reaction enthalpies, we distinguish B-like sites (<∆H298>B = 32.02 kJ mol-1), Ph-like sites

(<∆H298>Ph = 24.96 kJ mol-1), DBP-like sites (<∆H298>DBP = 18.43 kJ mol-1), BPA-like sites

(<∆H298>BPA = 12.11 kJ mol-1), BP-like sites (<∆H298>BP = 4.46 kJ mol-1) and BNA-like sites

(<∆H298>BNA = -1.83 kJ mol-1). In Figure 2 the hydrogen atoms belonging to a specific category

are indicated using different symbols. It is concluded that the reaction enthalpies of abstraction at

the more congested sites correspond to smaller enthalpy values, due to a release of steric

hindrance upon creation of a radical. Cioslowski et al. reported earlier that the increased stability

of systems with the radical center located at congested sites of a PAH structure, can be traced

back to a geometrical stabilizing effect as hydrogen shift reactions are more easily facilitated.53

The theoretically obtained values for the reaction enthalpies for H-abstraction at different

sites of the PAH’s could easily be differentiated in distinct classes. In earlier works a similar

classification has been proposed on basis of other properties. For example in ref. 23 the different

sites have been differentiated based on geometrical parameters of the reactants. It is worth

investigating in how far the various classifications coincide with each other. In both models the

local environment plays a crucial role. In ref. 23 the number of intermediate carbon atoms

between the specific hydrogen for abstraction and adjacent hydrogen atoms was the

determiningative factorparameter. In this study a smaller test set of PAHs (B, N, A, Ph, BP and

14

DBP) was considered. A distinction could be made between B-, N-, A-, Ph-, BP- and DBP-like

sites. The similarity with the classification obtained on basis of reaction enthalpies is large. The

most striking discrepancy is that the reaction enthalpies are not able to discriminate between the

B-, N- or A-sites. Another discrepancy is found for the DBA(1) site which is, based on

thermodynamical considerations, characterized as a DBP-site. However this can not be detected

on ground of geometrical features. Very probably this diverse behavior is coincidental. In

principle the latter site can be regarded as a combination of two Ph sites. Referring to the

discussion held in reference Error: Reference source not found, the stabilization energy (defined

as SEPAHx = <∆H298>x - <∆H298>B) of the DBA site, calculated using the BMK/6-

311+G(3df,2p)//B3-LYP/6-311G(d,p) level of theory, amounts to 12.97 kJ mol-1. This is

approximately twice the value found for the Ph site (SEPh = 7.05 kJ mol-1). It is rather a

coincidence that the stabilization energy of a DBP site amounts to 13.59 kJ mol -1, as on

geometrical grounds there is manifestly no relation between the DBA(1) and DBP(1) sites. The

classification proposed in the current paper, based on the reaction enthalpies and using a large

test set of PAHs, provides a more fundamental description of the reactivity of the local

environment and is therefore preferred.

3.2.2. Reaction Barriers. The calculated reaction barriers at 0 Kelvin are given in Table

3 and shown in Figure 5 where they are grouped according to the previously introduced

classification. The obtained barriers are relatively high and lie between 70.79 and 89.17 kJ mol-1,

with an average value of 74.16 kJ mol-1 (Table 3). Within a given class such as the B-sites, Ph-

sites, DBP-sites and BP-sites the variations are rather limited, indicating that the reactivity

classification based on the reaction enthalpies is roughly followed by the reaction barriers at 0

Kelvin. In other words for most of the studied hydrogen abstraction reactions, steric, electronic

effects in the TS are not dominant in the sense that they reverse the reactivity pattern of the

15

PAHs. It is however clear that for some sites large discrepancies are noticed with respect to the

reference value, i.e. the abstraction at benzene corresponding to a value of 71.79 kJ mol -1. The

optimized geometries of the corresponding TSs are depicted in Figure 4. The first noticeable

deviation is found for DBA(1) with a barrier of 89.17 kJ/mol. Following the discussion given in

previous section, the characterization of the DBA(1) site as a DBP-like site is rather a

coincidence. Consequently and not surprisingly, the trend in the kinetic result does not follow the

reaction enthalpies or bond dissociation enthalpies. Additionally, the approaching methyl radical

encounters large steric hindrance effects in the TS and also contributes to the increase of the

reaction barrier at 0 Kelvin. Inspection of the various reaction barriers in Figure 5 5

teacheslearns that a group of three ∆E‡0 values is also deviatingbroken away from the general

trend. They correspond with the BA(2), BNA(2) and BPA(2) abstraction reactions. The barriers

amount to 82.88, 80.74 and 82.18 kJ mol-1, respectively. The optimized structures of the

corresponding TSs reveal that the geometrical features for the active part of the involved PAH

surface are very similar, as seen in Figure 4, and also here the approaching methyl radical

encounters steric hindrance caused by other hydrogen atoms, explaining why the ∆E‡0 values are

higher. Inspection of Table 1 indicates a more direct link between the calculated high barriers

and their geometrical origin. More precisely, the out-of-plane angle of the approaching methyl

radical is seen to be very high: calculated values of γ amount to 33.0, 18.7, 34.3 and 31.2 degrees,

for DBA(1), BA(2), BNA(2) and BPA(2), respectively.

Summarizing, the ∆E‡0 values corresponding to abstraction reactions at the heavily

congested sites of the PAHs, e.g. the BNA- and BPA-like site, are higher compared to the

reference value found at benzene. The abstraction at B-like sites is preferred in terms of the

reaction barrier at 0 Kelvin, although the formed aryl radicals are somewhat less stable as

indicated by the reaction enthalpies.

16

3.3. Kinetic Parameters and Rate Constants.

Rate constants k(T), the corresponding activation energies Ea and pre-exponential factors

A for the reactions between the different PAHs and methyl radical were calculated using the

BMK/6-311+G(3df,2p)//B3-LYP/6-311G(d,p) level of theory in the temperature interval of 700

to 1100 Kelvin, which is relevant for the thermal crackingsteam cracking and coke formation

process. In the calculations two refinements are taken into consideration: the effect of tunneling

corrections on one hand and a correct description of the low-lying vibrational rotation of the

methyl group in the transition structures on the other. An overview of all computed kinetic

parameters can be found in Table S3 of the Supporting Information.

In this work, the Eckart tunneling contributions amount to an average downward shift of

4.5 kJ mol-1 for the activation energy, whereas the pre-exponential factor is only modestly

influenced, indicated by an average decrease with a factor of 1.3 as shown by the ratio A without

tunneling/A with tunneling.

In order to establish a correct description of the low-lying vibrational mode corresponding

to the rotation of the methyl group about the forming/breaking bond in the TSs, rotational

potentials were computed. For the B-like sites, the barrier height of the rotational potential was

found to be very small, more precisely 0.1 kJ mol-1 or less. On this basis, the free rotor model

was found appropriate to describe the methyl rotation and a mixed harmonic oscillator/free rotor

(HO/FR) model was used for the calculation of kinetic properties. For the other sites (Ph-, BP-,

DBP-, BNA- and BPA-like sites) the barriers were found to be higher and a maximum value of

approximately 5 kJ mol-1 was obtained for DBA(1). A 1-dimensional hindered rotor model was

chosen to model the internal rotation so a mixed harmonic oscillator/hindered rotor (HO/HR)

model was used for the calculation of kinetic properties at non-B-like sites. The influence of

17

internal rotations for the investigated hydrogen abstraction reactions is non-negligible. The

activation energy is lowered by about 3.3 kJ mol-1 whereas the pre-exponential factor decreases

with a factor of 5.6. The overall influence on the rate constant k(T) amounts to a factor

(=kmixed/kHO) of 0.59, 0.54 and 0.49 at 700, 900 and 1100 K, respectively. The origin of this large

shift is due to the presence of the small rotating methyl group, which is characterized by a low

moment of inertia. Moreover, the potentials are relatively low activated. The corresponding

frequencies νm are tabulated in Tables 4 and 5. It is found that for the series of linear acenes

(Table 4), resulting νm values lie in the range between 4.2 and 56.1 cm -1. The low values for νm

result in overestimations of the HO partition function for the methyl rotation. The abstraction at

the non-B-sites show a larger value for the frequency, a maximum value of 147.3 cm-1 is found

for the abstraction at DBA(1) (Table 5). Moreover an extra symmetry number of 3 is taken into

account in the HR model. Both previous factors contribute to the reduction of the partition

function in the HR model.

3.3.1. Linear Acenes. For the series of linear acenes, it was shown in section 3.2.1 that

all hydrogen atoms can be classified as B-like types. The mixed HO/FR model was therefore

used for the computation of the rate constants k(T). In Figure 6 (a), the rate constants for the

hydrogen abstractions at N, A, T and P are depicted, and the abstraction at the B molecule serves

as a reference. Table 4 gives the rate constants at 700, 900 and 1100 K together with the derived

kinetic parameters. The abstraction at the benzene molecule is the fastest. Abstractions of a

hydrogen atom located at a central ring (more precisely A(1), T(1), P(1) and P(2)) are the

slowest, i.e. approximately three times slower than abstraction at benzene. Based on the k(T)

values, abstraction reactions at non-central rings are preferred. This trend is supported by both

kinetic parameters: the activation energy is approximately 3 kJ mol-1 lower whereas the pre-

exponential factor is 1.7 times higher.

18

Another interesting aspect is the convergent behavior of the kinetic parameters and rate

constants with increasing PAH size. Comparison of the kinetic parameters E a and A for the

abstraction reactions at B(1), N(1), A(1), T(1) and P(1) shows a convergent behavior for both

parameters. The region of convergence starts with the anthracene molecule, this is also seen in

Figure 6(a). It is thus sufficient to take into account three six-membered rings in order to model

the kinetics of the linear acenes.

3.3.2. Non-linear PAHs. In Table 5, calculated rate constants at different temperatures

and the kinetic parameters Ea and A are given for the abstraction reactions at the non-linear PAHs

and Figure 6 (b) depicts the ratio of the rate constant at the characteristic sites X with respect to

the rate constant at benzene in the relevant temperature range. Inspection of the results obtained

for the different categories Ph(1), BP(1), DBP(1), BNA(2) and BPA(2) reveals that abstraction at

the smaller PAHs is preferred, as the calculated k(T) values are higher at all temperatures.

Further investigation of the results obtained for the abstraction at these non-B-like sites shows

that the variation seen in the kinetic parameters is also larger than previously observed in the

series of linear acenes. The Ea values lie in a range 80.93–96.67 kJ mol-1 and the A values vary

between 5.30 x 105 and 1.01 x 107 m3 mol-1 s-1. It is immediately clear that the differences found

for the series of more congested PAHs are more substantial than those found in previous section

3.2.1 for the series of linear acenes. The kinetic parameters corresponding to the 6 different

categories based on reaction enthalpies are depicted in Figure 7. The pre-exponential factors

clearly support the conclusion that the abstraction at the smaller clusters is preferred. The

decrease of the calculated A values with increasing molecular size is due to the presence of low-

lying global skeletal motions, which become more and more important and prominent in the

larger molecules. For the activation energy values corresponding to the Ph(1), BP(1) and DBP(1)

reactions, a modest decrease is observed when the PAH size is increased; however the differences

19

are rather limited. In addition, the Ea values for the very congested sites BNA(2) and BPA(2) are

substantially higher. Overall it is concluded that, based on kinetic parameters, abstraction at the

small PAH molecules is preferred.

Detailed inspection of the results in Table 5 also shows that even within a specific PAH,

abstraction at B-like sites is always preferred over abstraction at a more congested site. For

instance, when the calculated rate constants at 900 K of the Ph molecule are inspected, it is seen

that abstraction at the Ph-like site (Ph(1)) is more difficult compared with the abstractions at the

B-like sites (Ph(i), i=2,..,5), as indicated by an average factor of 2.3 between the specific rate

constants.

20

4. Conclusions

In this work, hydrogen abstraction reactions at an extended set of polyaromatic hydrocarbons

(PAHs) by an approaching methyl radical have been studied by means of DFT calculations.

Large systems, containing up to 7 six-membered rings, have been tested. The influence of the

polyaromatic environment on thermodynamic and kinetic properties has been investigated More

precisely, B3-LYP/6-311G(d,p) geometries and subsequent BMK/6-311+G(3df,2p) single-point

energy calculations have been used, leading to the following conclusions.

Based on calculated reaction enthalpies six different categories, corresponding to

benzene-, phenanthrene-, benzophenanthrene-, dibenzophenanthrene-, benzonaphtanthracene-

and benzophenanthranthracene-like sites are distinguished. The congested sites correspond to

lower reaction enthalpy values mainly indicating the release of steric hindrance upon creation of

the radical. The reaction barriers at 0 Kelvin on the other hand show that abstraction at benzene-

like sites is preferred over abstraction at the more congested sites.

21

Rate constants, activation energies and pre-exponential factors, calculated in the

temperature interval 700-1100 K, support the observation that abstraction at the benzene-like

sites is preferred for the initial formation of radical species. For the series of linear acenes the

kinetic parameters are found to vary modestly, whereas for the entire test set, larger variations

are observed. For the calculation of the rate constants two refinements are taken into account,

more specifically Eckart tunneling corrections are included and a correct description of the

rotation of the incoming methyl group about the breaking/forming bond in the transition

structure. The latter effect reduces the rate constant by about 1.87 (at a relevant temperature of

900 K) and is non-negligible. The tunneling corrections particularly contribute to a shift of the

activation barriers by approximately 4.5 kJ mol-1. Overall, combination of both effects results in

an average downward shift of 7.8 kJ mol-1 for the activation energies and a reduction by

approximately a factor of 7.4 for the pre-exponential factors.

Acknowledgement. KH wishes to thank Professor Leo Radom and members of his research

group for their kind hospitality during her stay at the University of Sydney in January–May 2005,

where this work originated. DM thanks the University of Sydney for a Sesqui Postdoctoral

Fellowship. VVS and MW thank the Fund for Scientific Research - Flanders, the Research Board

of Ghent University. LR thanks the Australian Research Council for a Discovery Grant, and

funding from the ARC Centre of Excellence in Free Radical Chemistry and Biotechnology, and

gratefully acknowledges generous allocations of computing time from the Australian Partnership

for Advanced Computing, the Australian National University Supercomputing Facility and the

Australian Centre for Advanced Computing and Communication. Finally, we thank Professor

Jan Martin for making the BMK functional available for our use.

22

Supporting Information Available: Reaction enthalpies at 298 K (Figure S1). Spin

densities of all product radicals (Table S1 and Figure S2), total energies, zero-point vibrational

energies, and thermal corrections (Table S2), effect of model used to correctly describe the low-

lying vibrational rotation of the methyl group in the transition structures and effect of Eckart

tunneling corrections on activation energies and pre-exponential factors (Table S3). This

material is available free of charge via the Internet at http://pubs.acs.org.

23

TABLE 1: Calculated Forming d1 and Breaking d2 Bond Lengths (in Å) and Out-of-

Plane Angle γ (in degrees) in the Transition Structures for Hydrogen Abstraction from

PAHs by Methyl Radical a

PAH(hydrogen) d1 d2 γ PAH(hydrogen) d1 d2 γ

B(1) 1.307 1.379 0.1 DBP(1) 1.322 1.362 17.8

N(1) 1.308 1.381 0.0 DBP(2) 1.305 1.379 1.0

N(2) 1.305 1.380 0.0 DBP(3) 1.304 1.381 2.7

A(1) 1.313 1.385 0.0 DBP(4) 1.309 1.380 2.8

A(2) 1.308 1.381 0.0 DBP(5) 1.306 1.383 5.0

A(3) 1.306 1.379 0.0 DBP(6) 1.308 1.380 0.9

T(1) 1.312 1.385 0.3 DBP(7) 1.306 1.383 4.2

T(2) 1.308 1.380 0.0 BA(1) 1.322 1.373 0.2

T(3) 1.306 1.379 0.0 BA(2) 1.333 1.368 18.7

P(1) 1.314 1.382 0.0 BA(3) 1.308 1.381 0.4

P(2) 1.313 1.383 0.0 DBA(1) 1.355 1.343 33.0

P(3) 1.308 1.380 0.0 DBA(2) 1.323 1.371 0.0

P(4) 1.306 1.379 0.0 DBA(3) 1.305 1.380 0.1

Ph(1) 1.323 1.373 0.2 BNA(1) 1.332 1.354 22.6

Ph(2) 1.305 1.380 0.0 BNA(2) 1.361 1.331 34.3

Ph(3) 1.304 1.382 0.0 BNA(3) 1.322 1.371 17.2

Ph(4) 1.308 1.382 0.0 BPA(1) 1.318 1.373 14.4

Ph(5) 1.308 1.381 0.0 BPA(2) 1.355 1.338 31.2

BP(1) 1.333 1.352 21.8 BPA(3) 1.323 1.361 21.5

24

BP(2) 1.306 1.378 2.5 C(1) 1.307 1.382 0.0

BP(3) 1.303 1.382 2.9 PYR(1) 1.305 1.384 0.0

BP(4) 1.309 1.380 2.1 PYR(2) 1.305 1.380 0.0

BP(5) 1.306 1.383 3.5 PYR(3) 1.308 1.381 0.0

BP(6) 1.308 1.381 2.2 PER(1) 1.322 1.370 12.2

BPER(1) 1.321 1.374 0.0

a Calculated using the BMK/6-311+G(3df,2p)//B3-LYP/6-311G(d,p) level of theory, see Figure 1

for definitions of γ, d1 and d2.

25

TABLE 2: Reaction Enthalpies (ΔH298) for the Hydrogen Abstraction Reactions at various

sites of the PAHs (kJ mol–1), calculated using the BMK/6-311+G(3df,2p)//B3-LYP/6-

311G(d,p) level of theory

hydrogen number

PAH 1 2 3 4 5 6 7

B 30.63  

N 32.07 30.85  

A 34.25 31.94 30.82  

T 34.27 31.60 30.40  

P 33.96 33.84 31.46 29.91  

   

Ph 24.71 31.09 32.19 32.12 31.69  

BP 4.91 30.24 32.13 31.64 32.74 32.04  

DBP 19.34 31.01 32.04 31.90 33.03 31.76 33.13

BA 24.49 26.79 32.23  

DBA 19.05 23.61 31.23  

C 34.03  

BNA 4.00 -1.83 24.51  

BPA 26.01 12.11 16.90  

PYR 33.74 30.81 31.76  

PER 23.66  

BPER 25.94            

26

TABLE 3: Barriers (ΔE‡0) for the Hydrogen Abstraction Reactions at various sites of the

PAHs (kJ mol–1), calculated using the BMK/6-311+G(3df,2p)//B3-LYP/6-311G(d,p) level of

theory

hydrogen number

PAH 1 2 3 4 5 6 7

B 71.79  

N 72.68 71.75  

A 74.76 72.60 71.29  

T 74.57 72.06 70.97  

P 74.37 74.15 71.51 70.79  

   

Ph 76.46 71.55 71.97 72.44 72.16  

BP 75.22 71.57 72.24 72.77 73.09 72.55  

DBP 74.06 71.89 73.01 73.31 73.67 72.52 73.84

BA 76.91 82.88 72.84  

DBA 89.17 76.19 71.29  

C 73.16  

BNA 72.76 80.74 76.55  

BPA 77.56 82.18 73.46  

PYR 73.33 71.50 71.86  

PER 76.95  

BPER 76.81            

27

TABLE 4: Frequency corresponding with the methyl rotation (νm in cm-1), Calculated Rate

Constants at Various Temperatures (k700, k900, k1100 in m3 mol-1 s-1), Activation Energies (Ea

in kJ mol–1) and Pre-Exponential Factors (A in m3 mol-1 s-1), calculated using the BMK/6-

311+G(3df,2p)//B3-LYP/6-311G(d,p) level of theorya

PAH(hydrogen) νm k700 k900 k1100 Ea A

B(1) 4.2 2.55 x 101 5.12 x 102 3.97 x 103 80.90 2.62 x 107

N(1) 52.8 1.45 x 101 2.99 x 102 2.36 x 103 81.63 1.69 x 107

N(2) 12.1 1.74 x 101 3.53 x 102 2.76 x 103 81.13 1.86 x 107

A(1) 14.4 7.36 x 100 1.64 x 102 1.35 x 103 83.57 1.20 x 107

A(2) 50.6 1.34 x 101 2.76 x 102 2.18 x 103 81.58 1.55 x 107

A(3) 23.5 1.99 x 101 3.96 x 102 3.05 x 103 80.66 1.96 x 107

T(1) 28.6 7.62 x 100 1.68 x 102 1.39 x 103 83.38 1.20 x 107

T(2) 56.1 1.78 x 101 3.62 x 102 2.83 x 103 81.23 1.94 x 107

T(3) 21.0 2.15 x 101 4.25 x 102 3.26 x 103 80.43 2.04 x 107

P(1) 19.1 7.73 x 100 1.70 x 102 1.40 x 103 83.37 1.21 x 107

P(2) 33.3 8.02 x 100 1.75 x 102 1.43 x 103 83.04 1.19 x 107

P(3) 32.6 1.71 x 101 3.41 x 102 2.64 x 103 80.75 1.71 x 107

P(4) 21.1 2.19 x 101 4.29 x 102 3.27 x 103 80.26 2.02 x 107

aCalculated using the mixed HO/FR model and including Eckart tunneling corrections.

28

TABLE 5: Frequency corresponding with the methyl rotation (νm in cm-1), Calculated Rate

Constants at Various Temperatures (k700, k900, k1100 in m3 mol-1 s-1), Activation Energies (Ea

in kJ mol–1) and Pre-Exponential Factors (A in m3 mol-1 s-1), calculated using the BMK/6-

311+G(3df,2p)//B3-LYP/6-311G(d,p) level of theorya

PAH(hydrogen) νm k700 k900 k1100 Ea A

Ph(1) 92.8 2.91 x 100 6.76 x 101 5.78 x 102 84.82 5.85 x 106

Ph(2) 9.3 8.62 x 100 1.73 x 102 1.34 x 103 80.85 8.78 x 106

Ph(3) 21.6 8.43 x 100 1.72 x 102 1.35 x 103 81.29 9.27 x 106

Ph(4) 53.6 6.39 x 100 1.30 x 102 1.01 x 103 81.18 6.89 x 106

Ph(5) 59.2 7.87 x 100 1.59 x 102 1.24 x 103 81.07 8.32 x 106

BP(1) 97.6 1.10 x 100 2.41 x 101 1.99 x 102 83.33 1.71 x 106

BP(2) 35.0 4.63 x 100 9.30 x 101 7.21 x 102 80.88 4.74 x 106

BP(3) 21.5 4.20 x 100 8.68 x 101 6.85 x 102 81.63 4.90 x 106

BP(4) 65.4 3.30 x 100 6.81 x 101 5.38 x 102 81.62 3.84 x 106

BP(5) 52.5 3.29 x 100 6.92 x 101 5.54 x 102 82.16 4.20 x 106

BP(6) 52.2 3.77 x 100 7.77 x 101 6.13 x 102 81.62 4.38 x 106

DBP(1) 84.4 9.96 x 10-1 2.14 x 101 1.74 x 102 82.80 1.41 x 106

DBP(2) 24.2 4.31 x 100 8.77 x 101 6.87 x 102 81.28 4.72 x 106

DBP(3) 12.3 3.48 x 100 7.40 x 101 5.96 x 102 82.42 4.64 x 106

DBP(4) 58.2 2.79 x 100 5.86 x 101 4.69 x 102 82.13 3.54 x 106

DBP(5) 49.3 2.78 x 100 5.97 x 101 4.84 x 102 82.68 3.88 x 106

DBP(6) 58.8 3.37 x 100 6.92 x 101 5.44 x 102 81.45 3.81 x 106

29

DBP(7) 50.3 2.72 x 100 5.90 x 101 4.80 x 102 82.87 3.93 x 106

BA(1) 104.2 1.92 x 100 4.61 x 101 4.02 x 102 85.62 4.44 x 106

BA(2) 102.6 1.51 x 10-1 4.53 x 100 4.57 x 101 91.61 9.71 x 105

BA(3) 52.7 3.69 x 100 7.68 x 101 6.10 x 102 81.87 4.48 x 106

DBA(1) 147.3 4.84 x 10-2 1.76 x 100 2.02 x 101 96.67 7.44 x 105

DBA(2) 124.5 3.79 x 100 8.65 x 101 7.32 x 102 84.36 7.03 x 106

DBA(3) 5.9 9.51 x 100 1.90 x 102 1.47 x 103 80.75 9.54 x 106

BNA(1) 87.7 1.19 x 100 2.38 x 101 1.86 x 102 80.93 1.23 x 106

BNA(2) 120.1 1.42 x 10-1 3.77 x 100 3.53 x 101 88.45 5.30 x 105

BNA(3) 68.6 5.43 x 10-1 1.27 x 101 1.09 x 102 84.92 1.11 x 106

BPA(1) 95.5 4.59 x 10-1 1.12 x 101 9.83 x 101 86.00 1.13 x 106

BPA(2) 142.6 1.09 x 10-1 3.09 x 100 3.00 x 101 89.99 5.33 x 105

BPA(3) 89.4 1.30 x 100 2.72 x 101 2.18 x 102 82.14 1.64 x 106

C(1) 41.1 3.63 x 101 7.70 x 102 6.18 x 103 82.34 4.77 x 107

PYR(1) 38.2 1.25 x 101 2.66 x 102 2.15 x 103 82.46 1.68 x 107

PYR(2) 10.4 1.84 x 101 3.71 x 102 2.89 x 103 80.99 1.92 x 107

PYR(3) 57.5 1.68 x 101 3.37 x 102 2.61 x 103 80.83 1.71 x 107

PER(1) 97.5 2.24 x 100 5.31 x 101 4.60 x 102 85.35 4.93 x 106

BPER(1) 98.4 4.71 x 100 1.11 x 102 9.59 x 102 85.21 1.01 x 107

aCalculated using the mixed HO/FR or HO/HR model and including Eckart tunneling corrections.

30

Figure 1. Hydrogen abstraction from PAH by the methyl radical to form an aryl radical with

methane. The forming bond length (d1), breaking bond length (d2), and out-of-plane angle (γ) of

the transition structure are highlighted.

31

Figure 2. Structures of all studied PAHs. The sites where hydrogen abstraction is considered are

numbered. The sites are labelled according to their site-selectivity obtained using the reaction

enthalpy (● for B-sites, ■ for Ph-sites, ▼ for BP-sites, ▲ for DBP-sites, for BNA-sites and

for BPA-sites).

32

Figure 3. Optimized geometries, calculated using the B3-LYP/6-311G(d,p) level of theory, of

non-planar reactants BP, DBP, BNA and BPA. The dihedral angles, characterizing the non-

planarity, are given.

33

Figure 4. Optimized geometries, calculated using the B3-LYP/6-311G(d,p) level of theory, of

transition state structures BA(2), DBA(1), BNA(2) and BPA(2).

34

Figure 5. Reaction barriers at 0 Kelvin (∆E‡0) for the Hydrogen Abstraction Reactions at various

sites of the PAHs (kJ mol–1), calculated using the BMK/6-311+G(3df,2p)//B3-LYP/6-311G(d,p)

level of theory and scaled ZPVE corrections.

35

Figure 6. Ratio of calculated rate constants kX(T)/kB(T)a for the Hydrogen Abstraction Reactions at the possible sites of (a) linear

PAHs (kJ mol–1) and (b) non-linear PAHs, within the temperature range 700-1100 K.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

700 750 800 850 900 950 1000 1050 1100

N(2)N(1)

A(1)

A(2)

A(3)T(3)P(4)

P(3)T(2)

P(2)P(1)T(1)

T (K)

k X/k B

(a)

k X/k B

700 750 800 850 900 950 1000 1050 1100T (K)0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16Ph(1)

BP(1)

BPA(2)BNA(2)

DBP(1)

(b)

a Calculated using the BMK/6-311+G(3df,2p)//B3-LYP/6-311G(d,p) level of theory, in the mixed HO/FR or HO/HR level (see text)

and including Eckart tunneling corrections.

36

Figure 7. Activation Energies (Ea, kJ mol–1) and Pre-Exponential Factors (A, m3 mol-1 s-1),

calculated using the BMK/6-311+G(3df,2p)//B3-LYP/6-311G(d,p) level of theory for all specific

PAH sites.

37

51[?] The component absolute energies, ZPVEs and thermal corrections are presented in Table

S2 of the Supporting Information.

52[?] Van Speybroeck, V.; Marin, G. B.; Waroquier, M. ChemPhysChem. 2006, submitted.

53[?] Cioslowski, J.; Liu, G.; Moncrieff, D. J. Org. Chem. 1996, 61, 4111.

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