Polyaromatic Hydrocarbons with an Imperfect Aromatic System as Catalysts of Interstellar H 2Formation D avid P. Jelenac Anita Schneikerab Attila Tajtic G abor Magyarfalvib and

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Polyaromatic Hydrocarbons with an Imperfect Aromatic System as

Catalysts of Interstellar H2Formation

D´avid P. Jelenﬁa,c, Anita Schneikera,b, Attila Tajtic, G´abor Magyarfalvib, and

Gy¨orgy Tarczayb,d

aELTE E¨otv¨os Lor´and University, Hevesy Gy¨orgy PhD School of Chemistry P. O. Box 32,

H-1518, Budapest 112, Hungary; bELTE – E¨otv¨os Lor´and University, Institute of Chemistry,

Laboratory of Molecular Spectroscopy, PO Box 32, Budapest H–1518, Hungary; cELTE -

E¨otv¨os Lor´and University, Institute of Chemistry, Laboratory of Theoretical Chemistry, P.

O. Box 32, H-1518, Budapest 112, Hungary; dMTA-ELTE Lend¨ulet Laboratory

Astrochemistry Research Group, P. O. Box 32, H-1518, Budapest 112, Hungary

ARTICLE HISTORY

Compiled October 25, 2022

ABSTRACT

Although H2is the simplest and the most abundant molecule in the Universe, its

formation in the interstellar medium, especially in the photodissociation regions is

far from being fully understood. According to suggestions, the formation of H2is

catalyzed by polyaromatic hydrocarbons (PAHs) on the surface of interstellar grains.

In the present study we have investigated the catalytic eﬀect of small PAHs with

an imperfect aromatic system. Quantum chemical computations were performed for

the H-atom-abstraction and H-atom-addition reactions of benzene, cyclopentadiene,

cycloheptatriene, indene, and 1H-phenalene. Heights of reaction barriers and tunnel-

ing reaction rate constants were computed with density functional theory using the

MPWB1K functional. For each molecule, the reaction path and the rate constants

were determined at 50 K using ring-polymer instanton theory, and the temperature

dependence of the rate constants was investigated for cyclopentadiene and cyclo-

heptatriene. The computational results reveal that defects in the aromatic system

compared to benzene can increase the rate of the catalytic H2formation at 50 K.

KEYWORDS

H atom tunneling, instanton theory, astrochemistry, polyaromatic hydrocarbons,

interstellar H2formation, photodissociation regions

1. Introduction

Since H2is the simplest and the most abundant molecule of the interstellar medium

(ISM), the understanding its formation in detail is in the center of interest. A lot of

questions related to this issue have arisen over the years, many of which are still not

fully answered. Except for the very dense regions (e.g. stellar atmospheres, planetary

nebulas), H2cannot form in the gas-phase of the ISM by three-body collisions due to

the low particle density. The radiative association mechanism is not eﬀective either due

to the fact that the H2molecule has no dipole moment, and thus the reaction energy

cannot be dissipated resulting in the H atoms colliding without reaction [1–23].

It was ﬁrst suggested by Salpeter and co-workers [24, 25], and it is now well accepted

in astrochemistry that H2can form on the surface or in the ice layer of interstellar

arXiv:2210.12379v1 [astro-ph.GA] 22 Oct 2022

grains. There are two basic surface reaction mechanisms: the Langmuir-Hinshelwood

mechanism and the Eley-Rideal mechanism [2, 3]. In the case of the former one, both

H atoms are bound to the surface and at least one of them must be mobile. The

problem with this mechanism is that it can only be eﬀective in a certain temperature

range (e.g. in the diﬀuse interstellar medium) because at very low temperatures the

diﬀusion rate of H atoms in the ice is too low, whereas at higher temperatures the H

atoms cannot stay on the surface long enough for an eﬃcient H2formation. In the case

of the Eley-Rideal mechanism one H atom is bound on the surface and then a gaseous

H atom collides and reacts with this atom. This mechanism requires a relatively high

concentration of H atoms. Therefore, considering simple physisorption, it cannot be

considered as a main interstellar H2formation mechanism either, especially above 20 K

where the residence time of the H atoms is too short.

There are several complex solid-phase reaction mechanisms that might explain the

formation rate of interstellar H2[1–3]. The residence time of H atoms near the surface

can be increased by capturing them in the pores of amorphous carbon or silicate grains.

Another possibility is that H atoms are bound on carbon grains at a low temperature,

and a sudden increase of the temperature (for example due to a supernova explosion)

can lead to explosive recombination of H atoms in a runaway event. A third mechanism

involves the chemisorption of H atoms on the surface of interstellar grains.

In the case of the latter mechanism, a molecule can ﬁrst chemisorb an H atom

which in the second step is abstracted by another H atom, resulting in the formation

of an H2molecule and the reformation of the original catalyst molecule. Therefore,

this process can be considered as a catalytic cycle. Being a cycle, the mechanism can

also start with abstraction of a H atom, followed by an addition, resulting in the

original molecule. Starting from a closed-shell molecule regardless to the ﬁrst step

being abstraction or addition, former studies revealed that this ﬁrst step of the cycle

usually has an activation energy [4–7]. The second step is a reaction that includes a

free radical and a H atom, and it is generally a barrierless process. Consequently, the

rate-limiting process is the ﬁrst step, which can take place via H-atom tunneling at

low temperatures.

It was suggested on the basis of astronomical observations by Habart and co-workers

that the high number of polycyclic aromatic hydrocarbons (PAHs) present in the

photon-dominated regions (PDRs) may be related to the rapid formation of molecular

hydrogen in these regions. Therefore, PAHs might act as catalysts in the H2forma-

tion in PDRs [15–18]. The potential catalytic role of various PAHs has already been

investigated both experimentally and theoretically [8–12].

Based on computations, the H-atom-addition reaction of benzene [8, 9] and pyrene

[10] have a reaction barrier that is permeable for H atoms by tunneling. Moreover, the

reaction rates of these reactions are non-negligible at low temperatures in contrast to

those of the H-atom-addition reactions of graphene or graphite. In addition, experi-

ments have also proved that H atoms and H2molecules can react with benzene and

small PAHs, forming so-called superhydrogenated species [19–22]. Another experimen-

tal evidence was provided by Menella and coworkers [11], showing that coronene can

react with deuterium atoms in a D-atom-addition reaction and the resulting species

is able to react with another deuterium atom, resulting in the formation of HD or D2

and the reformation of coronene [11]. Therefore, this experiment demonstrated that

neutral PAH molecules can act as catalysts in the formation of interstellar H2.

Computations and experiments have also revealed that the carbon atoms at dif-

ferent positions in PAHs have diﬀerent reactivity, and there is a speciﬁc order of

sequences of hydrogenation of PAHs [26, 27]. It was shown that among the hydro-

genated PAH (HPAH) isomers, the most stable is the one that contains the maximum

possible number of non-hydrogenated aromatic rings [28]. Many types of defects in

aromaticity can also lower the barrier of the H atom addition. For instance, oxygen

functionalized PAHs, e.g. 6,13-pentacenequinone, has enhanced reactivity compared

to PAHs [29]. Barrales-Mart´ınez and Guti´errez-Oliva have performed computations

for H-atom-addition reactions of some N-and Si-doped coronenes. They found that

the H-atom-addition reaction onto the N atom located in the external ring position

and onto the Si atom, regardless of its position, has no activation energy. In addition,

H-atom-addition onto carbon atoms next to these heteroatoms was found to have a

lower activation energy than for the H-atom-addition reaction of coronene and the cor-

responding rate constants are also larger [23]. Miksch and co-workers investigated the-

oretically the rate of the H-atom-addition to benzene and small heterocycles, pyridine,

pyrrole, furan, thiophene, silabenzene, and phosphorene, in a wide temperature range,

from 50 to 500 K. According to their results, the H-atom-addition reaction rate onto

carbon atoms next to the heteroatoms of pyrrole or furan can be ca. 200 times faster

than that onto the carbon atoms of benzene at a temperature of 50 K. This is an indi-

cation that small heterocycles can be better catalysts than PAHs in the formation of

interstellar H2[9]. Several recent experiments on pyrrole and furan support these theo-

retical ﬁndings [30, 31]. Schneiker et al. also investigated the reaction of 1H-phenalene

with H atoms [12], ﬁnding that the H-atom-addition reaction of the phenalenyl radical

is barrierless, whereas the H-atom-abstraction reaction of 1H-phenalene has a very low

barrier permeable for H atoms by H atom tunneling even at very low temperatures

[12].

In the present work, we investigated the inﬂuence of the aromatic character on

the catalytic eﬀect of PAHs. For this, the heights of reaction barriers, the reaction

energies, and the rate constants were computed for small PAHs with diﬀerent, imper-

fect aromatic systems: cyclopentadiene, cycloheptatriene, indene, and 1H-phenalene.

Among these, cyclopentadiene and indene were recently identiﬁed in the ISM [32, 33],

while the possible formation mechanism of 1H-phenalene under conditions relevant to

the ISM was experimentally explored [34]. The results obtained for these model sys-

tems are compared to the same computational data obtained for benzene (identiﬁed

in the ISM in 2001 [35]). We also discuss how these PAH motifs can contribute to the

interstellar H2formation.

2. Computational details

In this study, the reaction channels of the H-atom-abstraction and H-atom-addition

reactions are examined with density functional theory (DFT) and instanton ring poly-

mer rate theory for small PAHs containing one saturated carbon atom. The results are

compared with the corresponding reactions of benzene to investigate the role of the aro-

matic character in the catalytic eﬀect on the hydrogen molecule formation. Goumans

and co-workers [8] investigated the hydrogenation reaction of benzene and found that

computations with the MPWB1K functional [36] and double-ζquality basis sets yield

results comparable to high-level CCSD(T)/CBS computations. Recently, Miksch and

co-workers studied the hydrogenation reactions of small heterocycles and argue for a

triple-ζquality basis set which gives slightly lower rate constants for benzene at low

temperatures than the 6-31G*(*) basis originally used by Goumans et al. Based on the

ﬁndings of these studies [8, 9], the MPWB1K functional was used with the cc-pVDZ

and cc-pVTZ basis sets in our calculations. Since the MPWB1K/6-31G*(*) and the

MPWB1K/def2-TZVP gave very similar results for benzene [9], the temperature de-

pendence of the rate constant of the H-atom-addition reaction of benzene was not

recomputed at MPWB1K/cc-pVTZ level.

For each molecule, the reaction channels were determined by transition state

searches using the Gaussian 09 program package [37], followed by the validation of

the path using intrinsic reaction coordinate (IRC) computations [38, 39].

In the case of the monocyclic molecules cyclopentadiene and cycloheptatriene,

the H-atom-additions were investigated at all unsaturated carbon atoms (C2-C3

and C2-C4 positions, respectively) and the H-atom-abstraction at the saturated one

(C1 position). For the polycyclic indene and 1H-phenalene molecules we analysed

H-atom-additions only at the unsaturated carbon atoms in the ring containing the

saturated atom (C2 and C3 positions) and H-atom-abstraction only at the saturated

carbon atoms (C1 position). The transition states and products were optimized at

the MPWB1K/cc-pVTZ and MPWB1K/cc-pVDZ levels. The barrier heights and re-

action energies were computed as the energy diﬀerence between the transition state

and the reactants and between products and reactants, respectively, with and with-

out zero-point vibration energy (ZPVE) corrections. Furthermore, the HOMA index

[40] (Harmonic Oscillator Model of Aromaticity) was calculated for each species to

characterize the aromaticity of these systems. The parameters for the HOMA index

were chosen as Ropt = 1.385 ˚

A and α= 288.85 ˚

A−2, based on MPWB1K/cc-pVDZ

calculations for benzene and cyclohexane.

At very low temperatures, classical transition state theory gives a wrong estimation

of the rate constants because below a characteristic temperature called the crossover

temperature Tc, the tunneling mechanism becomes more favorable. An approximation

to the crossover temperature is given by [41]

Tc=~ωi

2πkB

,(1)

where ωiis the absolute value of the imaginary frequency of the transition state.

The vibrational mode corresponding to this frequency determines the tunneling path.

In instanton ring polymer rate theory [42, 43], the rate constant is given by the

expression[44]

kinst =1

βP~sBN

2πβP~2

Qinst

Qreac

e−S/~,(2)

where Qreac and Qinst refer to the quantum partition functions of the reactants and

the instanton, respectively, while Sis the so-called instanton action determined us-

ing a discretized closed Feynman path (CFP) integral[45, 46]. BNis a normalization

factor and βP=β/P = (kBT P )−1, with Pbeing the number of beads used in the

calculation. The beads are diﬀerent replicas of the system from which the instanton is

constructed, usually obtained from the harmonic expansion of the transition structure

along the tunneling path [45, 46]. For a detailed introduction to instanton rate theory,

its applications and capabilities, the reader is advised to study the excellent reviews

of Litman [42] and Richardson [44, 47, 48].

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PolyaromaticHydrocarbonswithanImperfectAromaticSystemasCatalystsofInterstellarH2FormationDavidP.Jelena;c,AnitaSchneikera;b,AttilaTajtic,GaborMagyarfalvib,andGyorgyTarczayb;daELTEEotvosLorandUniversity,HevesyGyorgyPhDSchoolofChemistryP.O.Box32,H-1518,Budapest112,Hungary;bELTE{EotvosLorandU...

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Polyaromatic Hydrocarbons with an Imperfect Aromatic System as Catalysts of Interstellar H 2Formation D avid P. Jelenac Anita Schneikerab Attila Tajtic G abor Magyarfalvib and

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