Chemical Physics Letters 595–596 (2014) 13–19

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Chemical Physics Letters

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The reaction of the benzene cation with acetylenes for the growthof PAHs in the interstellar medium

http://dx.doi.org/10.1016/j.cplett.2014.01.0400009-2614/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author.E-mail address: dahbia.talb@univ-montp2.fr (D. Talbi).

Pierre Ghesquière a, Dahbia Talbi a,⇑, Amir Karton b

a Laboratoire Univers et Particules Montpellier, UMR5299-CNRS-Université de Montpellier II, 34095 Montpellier Cedex 05, Franceb School of Chemistry and Biochemistry, The University of Western Australia, M310, 35 Stirling Hwy, Crawley 6009, Australia

a r t i c l e i n f o a b s t r a c t

Article history:Received 31 October 2013In final form 24 January 2014Available online 31 January 2014

We investigated the formation of the naphthalene cation from the successive addition of two acetyleneson the benzene cation. A DFT approach was used for that purpose. The entry channel corresponding to theaddition of the acetylenes is the energetically highest part of the entire reaction pathway. It was recalcu-lated using the ab initio W1-F12 and G4 thermochemical protocols. At these levels, the energetically high-est point in the entry channel is shown to be just below the energy of the free reactants. This Letter showsthat the formation of the naphthalene cation from benzene and acetylenes should proceed in space.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Benzene has been detected both in the upper atmosphere ofJupiter, Saturn and Titan [1,2] and outside of our solar systemtoward the carbon-rich protoplanetary nebulae CRL 618 [3], a cir-cumstellar envelope. Acetylene is known to be abundant in thecold interstellar medium (ISM) [4]. Neutral and charged polycyclicaromatic hydrocarbons (PAHs) are commonly assumed to be pres-ent in the same ISM. If the evidence for their presence is quitestrong, arising from the 3.3, 6.2, 7.7, 8.6, 11.3 lm set of bandsknown as the unidentified infrared emission bands (UIRs) [5] andcoming from a wide variety of astronomical sources [6], the chem-istry leading to their formation is still a matter of debate.

Under terrestrial conditions, benzene and PAHs are known toform in hydrocarbon flames. Following this suggestion Bauschli-cher et al. [7,8], using the hybrid B3LYP density functional theory(DFT) functional [9], have studied the growth of the benzene cationby the addition of two acetylenes molecules following a Bittner–Howard-like mechanism i.e. a mechanism where the second acet-ylene adds to the first before reacting with the existing ring to forman additional ring. In their first Letter, Bauschlicher et al. [7], havefound a route that would allow for the formation of the naphtha-lene cation through a barrierless reaction pathway. However, intheir second Letter [8], using a larger basis set, they have foundlow barriers on the reaction pathway, which prevent the reactionfrom occurring in the cold space environments of the ISM.

In the present Letter we are reinvestigating the mechanismconsidered in Bauschlicher et al. [7,8], however without

dehydrogenating the benzene cation in the first step of the reac-tion. This Letter completes our previous one [10] where we consid-ered the formation of the naphthalene cation from benzene(neutral or ionized) reacting respectively with the C4Hþ3 cationand C2H radicals in the cold interstellar medium (10–100 K). ThisLetter extends our search on efficient pathways for the growth ofPAHs in media where they are observed in abundance but whereno excess energy is available (i.e. for reaction pathways that areexothermic, with reaction barriers below the free reactantenergies).

2. Computational methods

The geometries on the potential energy profile for the succes-sive addition of two C2H2 molecules to C6Hþ6 have been optimizedusing two exchange–correlation DFT functionals: the hybrid gener-alized gradient approximation (GGA) B3LYP functional [9], and thehybrid-meta GGA M06-2X functional [11]. Three basis sets wereused in conjunctions with these DFT procedures: (i) the Pople-styletriple-zeta-valence basis set with one d-type polarization function6-311G(d,p); (ii) the double-zeta-valence basis set with two d-typeand one f-type polarization functions 6-31G(2df,p); and (iii) thecombination of the standard correlation–consistent cc-pVTZ basissets [12] on hydrogens, the aug-cc-pVTZ basis sets [13] on carbons(denoted by A’VTZ). Harmonic vibrational analyses have been per-formed at the same levels of theory to confirm each stationarypoint as either an equilibrium structure (i.e., all real frequencies)or a transition structure (TS) (i.e., with one imaginary frequency).Zero-point vibrational energy (ZPVE) corrections have been ob-tained from such calculations as one-half the sum of the harmonicfrequencies, and have been scaled using literature scaling factors

14 P. Ghesquière et al. / Chemical Physics Letters 595–596 (2014) 13–19

[14–16] a standard procedure to account for anharmonic effectsand imperfections of the theoretical models. The connectivities ofthe transition structures were confirmed by performing intrinsicreaction coordinate (IRC) calculations at the B3LYP/6-311G(d,p)level of theory [17]. The optimized geometries for all the speciesconsidered in the present Letter are given in Tables S3–S5 of theSupporting Information.

In order to obtain reliable reaction energies and barrier heightsfor the entry channel part of the reaction pathway, single point cal-culations have been carried out at the CCSD(T)/6-311++G(d,p) levelof theory (coupled cluster with singles, doubles, and quasipertur-bative triple excitations) using the B3LYP/6-311G(d,p) optimizedgeometries. These reaction energies and barrier heights have alsobeen calculated using the GAUSSIAN-4 (G4) thermochemical protocol[15] and 6-31G(2df,p) geometries. All the geometry optimizations,frequency calculations, G4 and CCSD(T)/6-311++G(d,p) calculationswere performed using the GAUSSIAN 09 program suite [18].

The G4 protocol is widely used for the calculation of accuratethermochemical and kinetic properties. Specifically, G4 obtainsmean absolute deviations (MADs) from reliable experimentalthermochemical data below the threshold of ‘chemical accuracy’(arbitrarily defined as 1 kcal/mol) [19]. For example, for the 454experimental thermochemical determinations of the G3/05 testset (including heats of formation, ionization energies, and electronaffinities), G4 attain a MAD of 0.83 kcal/mol [15]. For the computa-tion of barrier heights, G4 also offers generally good performance.For example, it gives a MAD of 0.58 kcal/mol when evaluatedagainst the 24 barrier heights in the DBH24/08 database (which in-cludes barriers for heavy-atom transfer, nucleophilic substitution,and hydrogen-transfer reactions) [20]. Similarly, for the set of 76barrier heights in the ‘hydrogen-transfer barrier heights’ (HTBH),and ‘non-hydrogen-transfer barrier heights’ (NHTBH) datasets[21,22], G4 attain a MAD of 0.71 kcal/mol [23].

In addition, high-level ab initio calculations have been carriedout using the W1-F12 thermochemical protocol with the Molpro2012.1 program suite [24]. W1-F12 theory [25] represents a lay-ered extrapolation to the relativistic, all-electron CCSD(T) basis-set-limit energy, and can achieve ‘sub-chemical accuracy’ (i.e., itis associated with a MAD from accurate atomization energies of0.32 kcal/mol, vide infra) for molecules whose wave functions aredominated by dynamical correlation [25,26]. W1-F12 combinesexplicitly-correlated F12 methods [27,28] with extrapolation tech-niques in order to approximate the CCSD(T) basis-set-limit energy.Due to the drastically accelerated basis-set convergence of the F12methods [29,30], W1-F12 is superior to the original W1 method[16] not only in terms of performance but also in terms of compu-tational cost [25].

The computational protocol of the W1-F12 method has beenspecified and rationalized in detail in Ref. [25]. In brief, the geom-etries and harmonic frequencies have been obtained at the B3LYP/A’VTZ level of theory, and ZPVE corrections have been obtainedfrom such calculations and scaled by 0.985. The Hartree–Fock com-ponent is extrapolated from the VDZ-F12 and VTZ-F12 basis sets,using the E(L) = E1 + A/La two-point extrapolation formula, witha = 5 (where VnZ-F12 denotes the cc-pVnZ-F12 basis sets of Peter-son et al. [28], which were specifically developed for explicitly cor-related calculations). Note that the complementary auxiliary basissingles (CABSs) correction is included in the SCF energy [31–33].The valence CCSD-F12 correlation energy is extrapolated fromthe same basis sets, using the same two-point extrapolation for-mula but with a = 3.67. In all of the explicitly-correlated coupledcluster calculations the diagonal, fixed-amplitude 3C(FIX) ansatz[28,30,34,35] and the CCSD-F12b approximation are employed[31,36]. The (T) valence correlation energy is obtained in the sameway as in the original W1 theory, i.e., extrapolated from the A’VDZand A’VTZ basis sets using the above two-point extrapolation

formula with a = 3.22. The CCSD inner-shell contribution is calcu-lated with the core-valence weighted correlation–consistent aug’-cc-pwCVTZ basis set of Peterson and Dunning [37], whilst the (T)inner-shell contribution is calculated with the cc-pwCVTZ(no f)basis set (where cc-pwCVTZ(no f) indicates the cc-pwCVTZ basisset without the f functions). The scalar relativistic contribution(in the second-order Douglas–Kroll–Hess approximation) [38] isobtained as the difference between non-relativistic CCSD(T)/A’VDZ and relativistic CCSD(T)/A’VDZ-DK calculations [39]. Theatomic spin–orbit coupling terms are taken from the experimentalfine structure, and the diagonal Born–Oppenheimer corrections(DBOCs) are calculated at the HF/A’VTZ level of theory.

W1-F12 theory shows excellent performance for systemscontaining first-row elements (and H). Specifically, for the 97first-row systems in the W4-11 dataset [26], W1-F12 attains aMAD of 0.13 kcal/mol from all-electron, relativistic CCSD(T) refer-ence atomization energies at the infinite-basis-set limit. Whenconsidering reference atomization energies at the full-configura-tion-interaction (FCI) basis-set limit, a MAD of 0.32 kcal/mol is ob-tained. Essentially this is equivalent to evaluating the performanceof the W1-F12 procedure against experimental reference values.

Since W1-F12 theory represents a layered extrapolation to theCCSD(T) basis-set-limit energy, it is of interest to estimate whetherthe contributions from post-CCSD(T) excitations are likely to besignificant for the systems considered in the present Letter. Thepercentage of the total atomization energy accounted for by paren-thetical connected triple excitations, %TAEe[(T)], has been shown tobe a reliable energy-based diagnostic indicating the importance ofnondynamical correlation effects [40,41]. It has been suggestedthat %TAEe[(T)] < 2% indicates systems that are dominated bydynamical correlation, while 2% < %TAEe[(T)] < 5% indicates sys-tems that include mild non-dynamical correlation. Table S2 ofthe Supporting Information gathers the %TAEe[(T)] values for theequilibrium and transition structures located on the first part ofthe entry channel. The %TAEe[(T)] values for all the structures spana narrow range of 2.1–2.4%. For example, for aromatic systems thatare associated with similar %TAEe[(T)] values (such as benzene,pyridine, and furan), post-CCSD(T) contributions to the atomiza-tion energy range from 0.25 to 1 kcal/mol [42,43]. Nevertheless,it should be pointed out that post-CCSD(T) contributions to reac-tion energies should be smaller than for atomization reactions.Thus, the %TAEe[(T)] values suggest that our W1-F12 energiesshould be close to the full configuration interaction (FCI) basis-set limit.

To summarize, the following levels of theory have been consid-ered in the present Letter: W1-F12, G4, CCSD(T)/6-311++G(d,p)//B3LYP/6-311G(d,p), B3LYP/6-311G(d,p)//B3LYP/6-311G(d,p) andM06-2X/6-311G(d,p)//M06-2X/6-311G(d,p). In all cases energieshave been corrected adding scaled ZPVE.

3. Results and discussion

3.1. Benchmark G4 and W1-F12 reaction energies and barrier heightsfor the entry channel

Before proceeding to a detailed discussion of the G4 andW1-F12 results, it is of interest to compare our G4 and W1-F12ionization potential (IP) for benzene at 0 K with the best knownexperimental value of 213.165 kcal/mol from the Active Thermo-chemical Tables (ATcT, version Alpha 1.110 of the Core (Argonne)Thermochemical Network) database of Ruscic et al. [44–46]. Withboth the G4 and W1-F12 procedures we obtain essentially thesame IP value of 213.69 kcal/mol. This value is in good agreementwith the ATcT value (i.e. it is 0.52 kcal/mol higher thanexperiment). Some of this discrepancy is liable to come from the

Table 1relative energies (DH0 K, kcal/mol) for the stationary points of the entry channelcalculated at the B3LYP/6-311G(d,p)//B3LYP/6-311G(d,p): B3LYP, M06-2X/6-311G(d,p)//M06-2X/6-311G(d,p): M06-2X, CCSD(T)/6-311++G(d,p)//B3LYP/6-311G(d,p):CCSD(T), G4 and W1-F12 levels of theory. Energies are corrected adding scaled ZPVEas indicated in the text. At the B3LYP and M06-2X levels, relative energies arecalculated using an energy for the benzene cation with respect to benzene, adjustedto the IP experimental value. The C–C bond distances linking the acetylene to thebenzene moiety optimized at the B3LYP/6-311G(d,p) and M06-2X/6-311G(d,p) levelsare given in Å.

I0 I1 T1-2 I2 I3 T3-4 I4

DH0 K

B3LYP 0.0 �11.2 �6.20 �6.20 �9.00 �4.70 �42.7M06-2X 0.0 �8.70 �6.00 �5.80 �11.6 �5.00 �45.1CCSD(T) 0.0 �3.80 �0.80 �1.70 �5.80 +1.60 �38.9G4 0.0 �5.75 �2.28 �2.81 �8.35 �1.76 �41.7W1-F12 0.0 �4.84 �2.07 �1.56 – – –

DistancesC–C B3LYP – 2.83 1.93 1.71 3.55 2.37 1.46C–C M06-2X – 2.76 2.01 1.74 3.32 2.26 1.46

P. Ghesquière et al. / Chemical Physics Letters 595–596 (2014) 13–19 15

approximations in the scaled harmonic ZPVEs involved in thesethermochemical protocols and from the complete neglect ofpost-CCSD(T) contributions [41].

The energy profile for the entry channel of the successive addi-tion of two C2H2 molecules to C6Hþ6 has been investigated using thehigh-level composite G4 and W1-F12 thermochemical protocols[15,25]. The G4 and W1-F12 potential energy surfaces (DH0 K) forthe entry channel are shown in Figure 1. Energies are given relativeto the free reactants (2 C2H2 and C6Hþ6 ). Let us begin with the po-tential energy surface (PES) obtained at the G4 level. The additionof the first acetylene proceeds via the formation of a long-rangecomplex (I1). This entry channel complex involves p–p interac-tions between the C6Hþ6 and the C2H2 species and is more stablethan the free reactants by 5.75 kcal/mol. The transition structure(T1-2) for the formation of the second intermediate lies2.28 kcal/mol below the starting reactants. Thus, at the G4 levelthe reaction barrier for the C2H2 þ C6Hþ6 ! C8Hþ8 reaction is3.47 kcal/mol. The second reaction intermediate (I2) is more stablethan the free reactants by 2.81 kcal/mol. This I2 reaction interme-diate can form a long-range complex with another C2H2 molecule,resulting in a reaction intermediate (I3) that is more stable thanthe starting reactants by 8.35 kcal/mol. The subsequent transitionstructure (T3-4) for binding of the second acetylene lies1.76 kcal/mol below the free reactants. The resulting reactionintermediate (I4) in which the acetylene is covalently bonded tothe C8Hþ8 moiety is very stable and is lower in energy than the freereactants by as much as 41.7 kcal/mol.

For the species that involve up to 8 carbon atoms (namely, I1,T1-2 and I2) we were able to obtain enthalpies at 0 K (DH0 K) bymeans of the computationally more expensive W1-F12 procedure.Figure 1 and Table 1 shows the good agreement between the G4and W1-F12 results (the deviations being within �1 kcal/mol)[25,26,47,48]. Specifically, relative to the W1-F12 results, the G4energies for the intermediates (I1 and I2) are lower by 0.91 and1.25 kcal/mol, respectively. The G4 and W1-F12 energies for theT1-2 transition structure are in excellent agreement with eachother, namely the G4 energy (–2.28 kcal/mol, relative to the freereactants) is lower by just 0.21 kcal/mol than the W1-F12 energy(�2.07 kcal/mol).

We have also calculated the PES for the entry channel at theCCSD(T)/6-311++G(d,p)//B3LYP/6-311G(d,p) level of theory. Theseresults are summarized in Table 1. The CCSD(T)/6-311++G(d,p)

Figure 1. The entrance channel of the lowest energy path (DH0 K, kcal/mol) for the succeF12 (in between brackets) levels of theory. Atomic color scheme: local minima structurethe references to color in this figure legend, the reader is referred to the web version of

energies are systematically higher than the G4 energies by nontriv-ial amounts ranging from 1.1 (I2) up to 3.3 (T3-4) kcal/mol.Furthermore, the T3-4 transition structure is higher in energy by1.6 kcal/mol than the free reactants. Thus, at the CCSD(T)/6-311++G(d,p) level of theory the entry channel pathway has anoverall reaction barrier (DHz0 K) of + 1.6 kcal/mol and should notproceed at very low temperatures according to classical transitionstate theory. This indicates that the CCSD(T)/6-311++G(d,p) level oftheory should be applied with caution when modeling reactionsthat involve polycyclic aromatic hydrocarbons.

3.2. DFT energies for the entire reaction channel

In the previous section we have calculated the PES (DH0 K) forthe entry channel of the successive addition of two C2H2 moleculesto C6Hþ6 by means of the high-level thermochemical protocols (G4and W1-F12). We have shown that the energies of all the speciesinvolved in the entry channel are bellow the energy of the freereactants, i.e. the reaction is barrierless at 0 K. We also showed thatthe final reaction intermediate of the entry channel (I4, Figure 1) ismore stable than the free reactants by as much as 41.7 kcal/mol (atthe G4 level). Here we study the entire reaction pathway for the

ssive addition of two acetylenes to the benzene cation calculated at the G4 and W1-s are shown in gold; transition structures are shown in silver. (For interpretation ofthis article.)

16 P. Ghesquière et al. / Chemical Physics Letters 595–596 (2014) 13–19

formation of the naphthalene cation with DFT methods that have asignificantly reduced computational cost (namely, the B3LYP/6-311G(d,p) level of theory). This is a standard electronic structurecalculation for such types of reactions [7,8,10,49,50]. We show thatthe PES, after the entry channel reported Figure 2a, is highly exo-thermic. Therefore there is no need to obtain it with computation-ally expensive procedures (such as G4) in order to be sure that theentire reaction pathway is submerged relative to the free reactants.

Before proceeding to a detailed discussion of the complete PES,we note that at the B3LYP/6-311G(d,p) level our calculated ioniza-tion potential (IP) of 207.63 kcal/mol for benzene, is underesti-mated by 5.53 kcal/mol, with respect to the ATcT experimentalvalue of 213.165 kcal/mol [43–45]. Our relative energies for the

Figure 2a. The lowest energy path (DH0 K, kcal/mol) for the successive addition of two a311G(d,p) level. All energies are calculated with respect to the reactant energies for wh213.165 kcal/mol.

Figure 2b. The lowest energy path (DH0 K, kcal/mol) for the successive addition of two ac6-311G(d,p) level. All energies are calculated with respect to the reactant energies for wh213.165 kcal/mol.

entire reaction path (Figure 2a to Figure 2d) are calculated with re-spect to a B3LYP absolute energy of the benzene cation correctedfor this 5.53 kcal/mol discrepancy. The van der Waals structures lo-cated along the entrance channel have been also optimized usingthe M06-2X functional [11], considered to be suited for medium-range noncovalent interactions, using the same 6-311G(d,p) basisset. The resulting relative energies can be viewed in Table 1. Theyare calculated with respect to an energy for the benzene cation ad-justed to the experimental IP value, although we note that withthis functional the calculated IP of C6Hþ6 (212.2 kcal/mol) is closerto the experimental one. The M06-2X relative energies agree ratherwell with the B3LYP ones (Table 1). We have also reported Table 1the C–C bond distances linking the acetylene to the benzene

cetylene radicals on benzene cation: the entrance path calculated at the B3LYP/6-ich the energy of benzene cation has been adjusted to the experimental IP value of

etylene radicals on benzene cation: the intermediate path calculated at the B3LYP/ich the energy of benzene cation has been adjusted to the experimental IP value of

P. Ghesquière et al. / Chemical Physics Letters 595–596 (2014) 13–19 17

moiety. Comparing these distances at both DFT levels for the longdistance complexes (I1 and I3) and the transition structures (T1-2and T3-4) we note that they are rather close (within 0.1–0.2 Å). Forthe equilibrium structures as I2 they are as expected almost iden-tical (Figure 3).

We now compare our entrance reaction path to the one re-ported in reference [8] and corresponding to the addition of thetwo acetylenes, it is worth noting that while in reference [8] theaddition of C2H2 on a dehydrogenated benzene cation lead to aC6H5 � CCHþ2 structure, with two H atoms attached at the C termi-nal, with the consequence that the addition of the next C2H2 moi-ety involve a barrier, the addition of C2H2 on the benzene cationC6Hþ6 lead to the I2 structure (Figure 2a) on which a second C2H2

can add without a barrier allowing for the reaction to proceedfurther. Once structure I4 is formed the evolution toward thehydrogenated naphthalene cation is rather straightforward. Thecorresponding B3LYP/6-311G(d,p) energy profiles can be viewed

Figure 2d. The lowest energy path (DH0 K, kcal/mol) for the successive addition of two ac311G(d,p) level. All energies are calculated with respect to the reactant energies for wh213.165 kcal/mol.

Figure 2c. The lowest energy path (DH0 K, kcal/mol) for the successive addition of two a311G(d,p) level. All energies are calculated with respect to the reactant energies for wh213.165 kcal/mol.

Figure 2b and Figure 2c. Hydrogen migrations lead to structure I6that can close to structure I7 (Figure 2b). Thanks to the exothermi-city related to the formation of I7, it can lose a hydrogen leading toprotonated naphthalene I11 (Figure 2c). The transition structuresinvolved are far below the energy of the reactants as are all thetransition states involved between I4 and I6. The formation ofprotonated naphthalene is exothermic enough to allow for the re-moval of one more hydrogen to give the naphthalene cation(Figure 2c).

The reaction intermediate I6 can also evolve through a differentpath, as shown in Figure 2d. Hydrogen migration can transform I6–I12, followed by the closure of the cycle to form a structure with a5-membered ring attached to the six-membered ring. The resultingstructure I13 is an isomer of protonated naphthalene. The forma-tion of the 5 membered structure F0 (Figure 2d) from I13 is how-ever slightly endothermic with respect to the energy of the freereactants:+1.3 kcal/mol at the B3LYP/6–311G(d,p) level (Figure 2d).

etylene radicals on benzene cation: the alternative path calculated at the B3LYP/6-ich the energy of benzene cation has been adjusted to the experimental IP value of

cetylene radicals on benzene cation: the terminal path calculated at the B3LYP/6-ich the energy of benzene cation has been adjusted to the experimental IP value of

Figure 3. Optimized I2 structure (shown in Figure 1a) at the B3LYP/6-311G(d,p), M06-2X/6-311G(d,p) and B3LYP/A’VTZ (used in the W1-F12 calculations) levels of theory(bond lengths are given in Å and selected angles are given in degrees).

18 P. Ghesquière et al. / Chemical Physics Letters 595–596 (2014) 13–19

We have calculated this endothermicity to be 5.87 kcal/mol at theG4 level. This energy is high enough to prevent the formation ofthis isomer of naphthalene from C6Hþ6 and C2H2, in the cold inter-stellar medium where no excess energy is available. We recall herethat we have shown in a previous Letter [10], that this isomer canbe formed efficiently in the cold interstellar medium from the reac-tion of C6H6 with C4Hþ3 .

4. Conclusions

We show, by means of high-level ab initio calculations, thatthe formation of the naphthalene cation from the benzene cationand two acetylene molecules should occur in the cold interstellarmedium. All the steps are exothermic and the barriers located areall below the reactant energies. The highest point of the PES isthe TS for the addition of a second acetylene molecule to theC8Hþ8 cation (T3-4, Figure 1). At the G4 level, this TS lies1.76 kcal/mol below the energy of the starting reactants. Thus,the formation of the naphthalene cation from the benzene cationand two acetylenes should be considered in the astrochemicalnetworks related to PAHs growth. From an observational pointof view, regarding the facility with which this reaction shouldoccur we do encourage for the search of naphthalene in spaceeven though the last attempts for its detection have remainedunsuccessful.

From a methodological point of view we show that the potentialenergy surface for the entry channel obtained at the CCSD(T)/6-311++G(d,p) level of theory deviates significantly from those ob-tained at the W1-F12 and G4 levels. For example, the deviationsbetween the G4 and CCSD(T)/6-311++G(d,p) results range between1.1 and 3.3 kcal/mol. This indicates that the latter level of theoryshould be applied with caution when modeling reactions that in-volve polycyclic aromatic hydrocarbons, and that higher levels oftheory (e.g. W1-F12 or G4) must be used when chemical accuracyis required.

The next step of this Letter would be dynamical calculationsusing the presently calculated PES in order to provide theastrochemists modeling the chemistry of PAH’s in the ISM withreliable rate constants for the 10–100 K temperature domain ofinterest.

Acknowledgements

We acknowledge the French national program PCMI for itsfinancial support and the HPC resources from GENCI-[CCRT/CINES/IDRIS] (Grant 2012-[x2012085116]/grant 2013-[x2013085116]) for the computing time. We also acknowledgefunding (to AK) from the Australian Research Council (DiscoveryProject Grant: DP110102336) and the generous allocation of com-puting time from the National Computational Infrastructure (NCI)National Facility and the support of iVEC through the use of ad-vanced computing resources located at iVEC@UWA.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.cplett.2014.01.040.

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