Probing computational methodologies in predicting mid-infrared spectra for large polycyclic aromatic hydrocarbons

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MNRAS 513, 3663–3681 (2022) https://doi.org/10.1093/mnras/stac976

Advance Access publication 2022 April 20

Probing computational methodologies in predicting mid-infrared spectra

for large polycyclic aromatic hydrocarbons

B. Kerkeni,

1 , 2 , 3 ‹I. Garc

ıa-Bernete,

1 ‹D. Rigopoulou,

1 ‹D. P. Tew,

4 P. F. Roche

1 and D. C. Clary

Department of Physics, University of Oxford, Oxford OX1 3RH, UK

ISAMM, Universit

e de la Manouba, La Manouba 2010, Tunisia

epartement de Physique, LPMC, Facult

e des Sciences de Tunis, Universit

e de Tunis el Manar, Tunis 2092, Tunisia

Department of Chemistry, University of Oxford, Oxford OX1 3QZ, UK

Accepted 2022 April 4. Received 2022 April 4; in original form 2021 May 6

A B S T R A C T

We extend the prediction of vibrational spectra to large sized polycyclic aromatic hydrocarbon (PAH) molecules comprising up

to ∼1500 carbon atoms by e v aluating the efﬁciency of several computational chemistry methodologies. We employ classical

mechanics methods (Amber and Gaff) with impro v ed atomic point charges, semi-empirical (PM3, and density functional tight

binding), and density functional theory (B3LYP) and conduct global optimizations and frequency calculations in order to

investigate the impact of PAH size on the vibrational band positions. We primarily focus on the following mid-infrared emission

bands 3.3, 6.2, 7.7, 8.6, 11.3, 12.7, and 17.0 μm. We dev eloped a general Frequenc y Scaling Function ( FSF ) to shift the

bands and to provide a systematic comparison versus the three methods for each PAH. We ﬁrst validate this procedure on

IR scaled spectra from the NASA Ames PAH Database, and extend it to new large PAHs. We show that when the FSF is

applied to the Amber and Gaff IR spectra, an agreement between the normal mode peak positions with those inferred from the

B3LYP/4-31G model chemistry is achieved. As calculations become time intensive for large sized molecules N

c > 450, this

proposed methodology has advantages. The FSF has enabled extending the investigations to large PAHs where we clearly see

the emergence of the 17.0 μm feature, and the weakening of the 3.3 μm one. We ﬁnally investigate the trends in the 3.3 μm/17.0

μm PAH band ratio as a function of PAH size and its response following the exposure to ﬁelds of varying radiation intensities.

Key words: astrochemistry – methods: numerical –ISM: molecules – galaxies: ISM – infrared: ISM.

1 INTRODUCTION

The investigation of polycyclic aromatic hydrocarbons (PAHs) prop-

erties is rele v ant in se veral dif ferent research ﬁelds. In particular, they

have been extensively invoked in combustion chemistry (Richter &

Howard 2000 ) as they play an important role in atmospheric pollution

and present toxic functions. In astronomy, PAHs are detected (Tielens

2011 ) in a variety of space environs via their spectral ﬁngerprints.

Observations with the Infrared Space Observatory ( ISO ) and the

Spitzer have shown since the mid-90s, among them fullerenes have

also been directly identiﬁed (Herbst 2006 ). PAHs can be considered

as ﬁnite graphene sheets passi v ated with hydrogen atoms to form

either catacondensed PAHs with all of their carbon atoms situated

in one or a maximum of two molecular constitutive rings, or

pericondensed PAHs with some of the carbon atoms situated in

more than two molecular constitutive rings. They play an important

role and are an ubiquitous component of organic matter in space.

Their contribution is invoked in a broad spectrum of astronomical

observations that range from the ultraviolet to the far-infrared and

co v er a wide variety of astronomical objects ranging from meteorites

and other Solar System bodies to the diffuse interstellar medium,



E-mail: boutheina.k erk eni@ph ysics.ox.ac.uk (BK); ismael.g arciabernete

@physics.ox.ac.uk (IGB); dimitra.rigopoulou@physics.ox.ac.uk (DR)

in the local Milky Way and in external galaxies. Strong emission

features dominate the mid-infrared (MIR) spectra of our own Galaxy,

galaxies in the local Universe as well as distant galaxies exhibiting

an o v erall similar spectral proﬁle among different sources (Li 2020 ).

Distinct emission peaks at 3.3, 6.2, 7.7, 8.6, 11.3, 12.7, and 17.0

μm appear with weaker and blended features distributed in the 3–

20 μm region. The 6–9 μm region, in particular, contains three

well-known major features: a band at 6.2 μm, a large complex

of multiple o v erlapping bands at approximately 7.7 μm, and a

band at 8.6 μm. Decomposition of the 7.7 μm complex using

either Gaussians or Lorentzians identiﬁed several sub-components

with the dominant ones centred around 7.6 and 7.8 μm (Bregman

et al. 1989 ; Cohen et al. 1989 ; Verstraete et al. 2001 ; Kerckho v en

2002 ; Peeters et al. 2002 ). These features are generally attributed to

infrared (IR) ﬂuorescence of PAH molecules pumped by UV photons

followed by internal conversion and emission through a ﬂuorescence

cascade.

IR spectra of PAHs have been the subject of several observational,

experimental and modelling studies over the last decades e.g. (Van

Dishoeck 2004 ; Herbst 2006 ; Salama 2008 ; Tielens 2008 ; Cami et al.

2010 ; Candian & Sarre 2015 ; Buragohain et al. 2020 ; Li 2020 ; and

references therein), in order to identify rele v ant molecular structures

and characterize their physical and chemical conditions in various

astrophysical environments such as interstellar and circumstellar,

galactic and extra-galactic, and in the early Universe.

Published by Oxford University Press on behalf of Royal Astronomical Society

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3664 B. Kerkeni et al.

MNRAS 513, 3663–3681 (2022)

To date, the interpretation of sev eral observ ed PAH features is

still poorly understood, and the carriers are tentatively assigned

either to hydrogenated PAHs (Schutte, Tielens & Allamandola 1992 ;

Bernstein, Sandford & Allamandola 1996 ), or to PAHs with aliphatic

side groups (Kondo et al. 2012 ; Buragohain et al. 2020 ), nitrogenated

PAHs (Bauschlicher et al. 2018 ), and with metal comple x es (Simon &

Joblin 2009 ). Other authors have considered side groups attached

to PAHs such as polyphenyls (Talbi & Chandler 2012 ), vinyl

groups, Boron-nitrogen coronene and boron-phosphorous coronene

(Maurya et al. 2012 ). Other theoretical modelling of vibrational and

electronic absorption spectra (de Abreu & Lopez-Castillo 2012 ) were

explored with halogen atoms like ﬂuorine, chlorine, bromine and

iodine (Gardner & Wright 2011 ), and protonated PAHs (Bahou,

Wu & Lee 2012 ). Triplet spin states in the case of dehydrogenation

states of PAHs were investigated experimentally and computationally

(Pauzat & Ellinger 2001 ; Galu

e & Oomens 2012 ).

In some astrophysical objects PAHs are believed to account for

about 20 per cent of carbon, and can grow to immense sizes including

hundreds of atoms (Allain, Leach & Sedlmayr 1996 ; Tielens 2005 ;

Allamandola 2011 ), due to their resistance to strong UV ﬂux in

nearby star-forming regions. Presently, the detection (Cami et al.

2010 ) of C

60 moti v ated us to wards performing computations for

large molecules. These ﬁndings moti v ate researchers to elucidate the

underlying formation mechanisms as both large aromatic systems

and a small aromatic molecule have been identiﬁed by astronomical

observations in combination with laboratory spectroscopy (Campbell

et al. 2015 ; Cernicharo et al. 2001 ; McGuire et al. 2018 ). In their

study of the two reﬂection nebulae NGC 7023 and ρOphiucus-

SR3, (e.g. Rapacioli, Joblin & Boissel 2005 ) showed that PAH

molecules are produced by the decomposition of small carbonaceous

grains inside molecular clouds, these grains being interpreted as PAH

clusters. A minimal size of 400 carbon atoms per cluster was inferred

from the analysis of astronomical observations (Tielens 2008 ). We

therefore extended the computational investigations to PAHs larger

than what is currently available in the literature. Employing a pool of

Quantum Chemical (QC) methods, we provide an inventory of MIR

spectra rele v ant from small to large PAHs, which are believed to be

ubiquitous in the spectra of galaxies near and far. We are mainly

interested in the investigation of band strengths ratios.

As the y e xhibit delocalization of the πelectrons and polarization

effects related to their extended electronic conjugation coupled with

their planar structures, PAHs are challenging systems for density

functional theory (DFT), particularly when their size increases.

Some authors (Savarese et al. 2020 ) carried out investigations of

spin density in seven open-shell PAH systems by testing a range

of different density functional approximations, they showed that

performances follow a systematic impro v ement in going from semi-

local to hybrid functionals.

The calculated MIR spectra need to be scaled in order to ac-

count for the limitations in the level of theory and the missing

anharmonicities in the computations. In their paper (Bauschlicher

et al. 2018 ), introduced version 3.20 of the NASA Ames PAH IR

Spectroscopic Database

1 (PAHdb). In the current PAHdb database

version (Boersma et al. 2014 ; Bauschlicher et al. 2018 ; Mattioda et al.

2020 ) the spectra are divided into three ranges: (i) C-H stretching

bands ( > 2500 cm

−1

; < 4 μm), (ii) bands between 2500. and

1111.1 cm

−1 (i.e. between 4 and 9 μm), and (iii) bands between

1111.1 and 0. cm

−1

(i.e. > 9 μm); for each region a speciﬁc scale

factor (0.9595, 0.9523, and 0.9563, respectively) is used to multiply

ht tp://www.astrochemist ry.org/pahdb/

the harmonic fundamentals. The computed IR spectra employing

the B3LYP/4-31G model chemistry of thousands of PAHs species

(including ionic species) with a number of carbons ( N

< 400) have

been included in the PAHdb.

On the computational side, not only the prediction of vibrational

spectra is subjected to multiplicative scaling factors to bring the

computed normal modes to the experimental ones, but also the

band strengths have to be scaled accordingly. As an example,

Bauschlicher & Langhoff ( 1997 ) reported a factor of 2 difference to

experimental values in the computed B3LYP/4-31G band intensities

pertaining to the CH stretching modes in neutral PAHs. Other

investigations, like the one by Yang et al. ( 2017 ), have scaled the

B3LYP intensities of the 3.3 μm feature of some methylated PAHs to

more sophisticated MP2/ 6-311 + G(3df,3pd) ones. Given the fact that

each computational method yields speciﬁc band intensities, and that

investigation of astronomical PAH band strengths ratios is mainly

insensitive to a selected computational method (e.g. Peeters et al.

2017 ), in this paper we only focus on the scaling of the predicted

band positions obtained by the different computational chemistry

methodologies we use.

Apart from DFT, there are very few calculations of vibrational

spectroscop y with w av efunction methods. F or e xample optimized

geometries and infrared spectra were computed (Aiga 2012 ) for

oligoacenes such as naphthalene, anthracene, naphtacene, and pen-

tacene, PAHs, and perylene, phenanthrene, and picene using the re-

stricted active space self-consistent ﬁeld method. As their electronic

ground states have an open-shell singlet multiradical character, the

calculations were based on the multiconﬁguration wave functions

instead. The author reported good agreement for the IR spectra

with experiments, after scaling all vibrations by a 0.9 factor. These

wavefunction based methods are only affordable for the small

sized molecules, consequently DFT has emerged as an alternative

methodology for computing the electronic structure of moderate size

systems.

From the computational point of view of IR spectra inves-

tigations, several procedures can be followed, among them are

the widely used static quantum chemical calculations, Molecular

Dynamics (MD) simulations, temperature-dependent schemes, and

Monte Carlo (MC) methods. In order to better understand spectra

obtained with either gas-phase or matrix-isolation experiments,

theoretical anharmonic static spectra were computed to explain

combination-bands and resonances in the C-H stretching region

for naphthalene, anthracene, and tetracene (Mackie et al. 2015 ;

Lemmens et al. 2019 ). Other models looked at the variation of

band positions with temperature to extract linear slopes and quantify

empirically the impact of anharmonicities (Joblin et al. 1995 ).

Some theoretical investigations by Mulas et al. ( 2006 ) included

rotational and anharmonic band structure in their MC model of

the photophysics of naphthalene and anthracene. Anharmonic IR

spectra of highly vibrationally excited pyrene were computed (Chen

et al. 2018 ) using VPT2 (Mackie et al. 2015 ) and the Wang–Landau

method in order to account for temperature effects. More recently,

Chakraborty et al. ( 2021 ) studied theoretically by means of DFT-

GVPT2 and also density functional tight binding (DFTB) combined

with MD simulations the effects of temperature and anharmonicity

in highly excited vibrational states of pyrene. The centroid and

ring-polymer molecular dynamics techniques have been employed

(Calvo, Parneix & Van-Oanh 2010 ) to naphthalene, pyrene, and

coronene. There are also methods combining Tight-binding (TB)

potentials in MD calculations of the electronic energy and wave

functions at any particular conﬁguration of the system. For example,

TB MD and consideration of anharmonicity of the potential energy

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Predicting MIR spectra for large PAHs 3665

MNRAS 513, 3663–3681 (2022)

surface were used to produce absorption spectrum for naphthalene

from a Fourier Transform of the dipole autocorrelation function and

were found to be in good agreement with the experimental spectrum

in low-temperature rare gas matrices (Van-Oanh et al. 2012 ). Effects

of temperature and anharmonicity were investigated simultaneously

in molecular dynamics studies of coronene and circumcoronene

employing a PM3 electronic potential energy surface (Chen 2019 ).

So far, dynamical calculation of vibrational spectra with classical

nuclei has been reported for various gas-phase systems (Greathouse,

Cygan & Simmons 2006 ; Schultheis et al. 2008 ) using parameterized

potential energy surfaces in most cases, but also, more recently,

surfaces based on an explicit description of the electronic structure

(Margl, Schwarz & Blochl 1994 ; Gaigeot, Martinez & Vuilleumier

2007 ; Estacio & Cabral 2008 ). Research about extending these

theoretical methodologies to account for anhamonicities to large

PAHs currently constitutes a challenge as the calculations become

time intensive.

In this paper, we hav e inv estigated the MIR spectral characteristics

of a series of PAHs with straight edges (apart from C

, C

606

706

, and C

1498

108

) and containing an even number of carbons

using semi-empirical methods, PM3 and DFTB (Spiegelman et al.

2020 ), classical force ﬁeld (FF) parameters from Amber and Gaff

(Wang et al. 2004 ), and DFT (only for N

< 450). Rele v ant PAHs span

sizes comprising six carbons to 1498 carbons and have symmetries

ranging from D

6 h to C

. Speciﬁcally we consider a pool of 21

molecules { N

= 6, 10, 14, 16, 24, 52, 54,102, 190, 294, 384,

450, 506, 600, 606, 706, 806, 846, 902, 998, 1498 } . The IR spectra

computed with B3LYP/4-31G and scaled with three factors for the

set from N

= { 10, 14, 16, 24, 52, 54,102, 190, 294, 384 } are

already reported in the PAHdb and will serve to validate our more

approximate methodologies. The choice of the shapes and sizes of

the remainder of the PAH molecules is completely arbitrary and only

serves to span a wide range of large PAHs.

Current efforts to characterize and study interstellar PAHs rely

heavily on theoretically predicted infrared (IR) spectra. The aim

behind testing several methodologies is to be able to compute MIR

spectra for large PAH molecules by reducing the computational

cost. In this paper we only focus on scaling band positions and

do not consider band strengths scalings. Even though we consider

lo wer le vel computational methods for describing intramolecular

interactions, we endea v our to reproduce the experimental bond

lengths and infrared normal modes. This raises the questions about

the validity and extension of semi-empirical and FFs parameter

sets in producing accurate normal modes positions. Addressing the

questions related to shifting band positions is at the very heart of the

present paper, where the MIR spectra of 21 PAHs are analysed at

dif ferent le vels of theory. Anharmonic calculations are not applicable

to large species and therefore are out of the scope of the present

work.

The validation of the computed spectra for the small PAHs employ-

ing more approximated methods and comparison to DFT served as a

benchmark for the large PAH’s IR-spectra band positions prediction.

In Section 2 we discuss the different theoretical methodologies

employed to describe the geometrical parameters and the infrared

spectra of these systems. Section 3 shows the major results obtained

with DFT, semi-empirical, and FF methods, and the procedure for

ﬁtting the scale factor functions to shift band positions for any PAH

size. The resulting ﬁtting function developed for each QC method

can be applied to shift any PAH molecule MIR spectra even outside

the pre-selected set that served for the ﬁtting. Shifted infrared spectra

for PAHs are presented, and astrophysical implications are discussed

in Section 4 . The main conclusions are gathered in Section 5 .

Figure 1. Structures of PAH molecules studied in this work. The number of

carbons in the PAH molecules is given by N

= { 6, 10, 14, 16, 24, 52, 54,102,

190, 294, 384, 450, 506, 600, 606, 706, 806, 846, 902, 998, 1498 } .

2 METHODOLOGY

Because of computational limitations, the whole set of PAH

molecules cannot be studied with the same method with either DFT or

PM3. Therefore, in the present work, we employ DFT for N

= { 6,

10, 14, 16, 24, 52, 54,102, 190, 294, 384, 450 } , semi-empirical

methods PM3 for N

= { 6, 10, 14, 16, 24, 52, 54,102, 190, 294,

384, 450, 506, 600, 606, 706, 806 } , DFTBA for N

= { 6, 10, 14,

16, 24, 450, 600, 606, 706, 806, 846, 902, 998 } , and FF classical

molecular mechanics (MM; Amber and Gaff) for N

= { 6, 10, 14,

16, 24, 52, 54,102, 190, 294, 384, 450, 506, 600, 606, 706, 806,

846, 902, 998, 1498 } to compute infrared spectra. We perform a

comparison between the spectra obtained from the different methods

for the av ailable N

c v alues. All three types of calculations have

been performed with GAUSSIAN 16 (Frisch et al. 2016 ) software to

search for global optimizations to be sure that we have local minima,

and compute harmonic vibrational spectra. Within each method,

we computed the electronic energy and electric dipole moment,

and their second and ﬁrst deri v ati ves respecti vely at the optimized

geometries.

Computationally, it is challenging to extend and adapt clev-

erly the current methods and accurately study large molecules

( N

c > 450) of different chemical composition, and predict their

spectroscopic ﬁngerprints. Ho we ver, if this challenge is met, it

will enable us for the ﬁrst time to reach sizable PAH molecules

and will aid in the interpretation of observed MIR spectra of a

wide range of astronomical sources irrespective of their typical

physical conditions (ionization, VUV, cosmic radiation, etc). For

those PAHs with N

> 450, whose simulation becomes exceedingly

e xpensiv e when using methods like DFT due to their intrinsic

cubic scaling, we e v aluate the performance of more approximate

methodologies, including PM3 (Stewart 1989 ), DFTB (Porezag

et al. 1995 ; Seifert, Porezag & Frauenheim 1996 ; Elstner et al.

1998 ; Frauenheim et al. 2000 , 2002 ; Oliveira et al. 2009 ), and the

Amber and Gaff FF parameters (Wang et al. 2004 ), for which we

adapted the charges to be able to reproduce the dipole moment

accurately. Unless noted otherwise, the IR-spectra are computed

for geometries that are optimized at the respective level of the-

ory.

Fig. 1 shows the molecules studied in this work. Some of them

= { 10, 14, 16, 24, 52, 54,102, 190, 294, 384 } are chosen because

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3666 B. Kerkeni et al.

MNRAS 513, 3663–3681 (2022)

their computed gas-phase IR spectra are available in the PAHdb

database (Bauschlicher et al. 2018 ). Therefore, they are used as a

reference to validate the accuracy of the more approximate methods.

2.1 DFT calculations

DFT approximations to the functionals (Hohenberg & Kohn 1964 )

allow the study of PAH systems with efﬁcient computational time

for molecules comprising a few hundred atoms. In the routinely used

K ohn–Sham (KS) approach (K ohn & Sham 1965 ), the electronic

problem is solved by minimizing the energy, which only depends

on the electronic density, for a system of ﬁctitious non-interacting

electrons with the same electronic density and energy as the real

system. Technically, this is a self-consistent mean ﬁeld approach

whose ﬁnal energy is the same as for the fully correlated system. The

structures were fully optimized and the harmonic (for N

= 6, 10, 14,

16, 24, 52, 54, 102, 190, 294, and 384) frequencies were computed

using DFT.

The B3LYP hybrid density functional (Becke 1993 ; Stephens et al.

1994 ) has been e xtensiv ely used by Bauschlicher et al. ( 2018 ) as it

provides MIR spectra in better agreement with experiments regarding

band positions than the cheaper BP86 functional.

Some publications have noted slightly different biases for the

low and high harmonic frequencies (Scott & Radom 1996 ; Halls,

Velkovski & Schlegel 2001 ; Yoshida et al. 2002 ; Sinha et al. 2004 ). A

few have recommended scaling low and high harmonic frequencies

separately (Halls et al. 2001 ; Sinha et al. 2004 ; Laury, Carlson &

Wilson 2012 ). The B3LYP/4-31G computed and scaled harmonic

frequencies by Bauschlicher & Langhoff ( 1997 ) have been reported

to be in agreement with the matrix isolation experiments (Langhoff

1996 ) of PAH’s MIR fundamental frequencies.

Pech, Joblin & Boissel ( 2002 ) and Mulas et al. ( 2006 ) found that

the MIR scale factor was reasonable for the far-infrared bands as well.

A far-infrared study of neutral coronene, ovalene, and dicoronylene

(Mattioda et al. 2009 ) also showed that the MIR scale factor of

0.958 can be applied to the far-infrared spectral region as it brings

the computed B3LYP/4-31G harmonic frequencies into excellent

agreement with the experimental far-infrared frequencies. The same

scale f actor w as used by Boersma et al. ( 2010 ) to bring the computed

bands positions in the 15–20 μm range for 13 large molecules into

the best agreement with experiment.

Ho we ver, it has to be mentioned that using the B3LYP method

with even better basis sets, results (Yang et al. 2017 ) in larger

computed intensities (by ∼30 per cent ) compared to experimental

ﬁndings. Whereas in Bauschlicher & Langhoff ( 1997 ) it was reported

that a factor 2 o v erestimation of the computed B3LYP/4-31G band

intensities pertaining to the CH stretching modes in neutral PAH

systems is to be expected.

In light of past computations by Pavlyuchko, Vasilyev & Gribov

( 2012 ) who reported that MP2/6-311G(3df,3pd) IR intensities of

benzene and toluene would match experimental results, other authors

(Yang et al. 2017 ) have scaled the computed B3LYP/6-31G(d) band

intensities of methylated PAHs and their cations in the case of the

3.3 μm aromatic C −H stretch and the 3.4 μm aliphatic one by

performing accurate MP2/6-311 + G(3df,3pd) calculations.

In order to correct for anharmonicities inherent to the theoretical

methodologies and computational approximations, in the present

B3LYP/4-31G calculations we use ‘off the shelf’ previously re-

ported by Bauschlicher et al. ( 2018 ) the three harmonic scale

factors to shift our B3LYP/4-31G computed spectra. Ho we ver, in

the case of PM3, Amber, Gaff, and DFTBA ones, we devise a

ﬁtting function to account for the scale factors for use in the MIR

region.

2.1.1 Harmonic frequencies

As we perform static/time-independent ab initio methods and due

to the large number of interactions/resonances in large PAHs, anhar-

monic IR spectra cannot be produced for big sized systems. There are

essentially three different types of IR peaks: fundamental, o v ertone,

and combination bands. In the harmonic approximation, the potential

energy surface is truncated, which means that it is approximated

to only second order Taylor series. It also implies approximating

the dipole moment by its Taylor expansion truncated at the ﬁrst

order. And it is the reason why only fundamental transitions, and not

combination/difference/o v ertone bands are obtained in this way.

Ignoring higher-order curvature terms in the potential energy

function leads to deviations of the vibrational spectra predictions to

those from experimental observations. Moreover, the computational

combination of method and basis set choices, and also the numerical

approximations may lead to severe quantitativ e ﬂa w in predicting

vibrational spectra.

By deﬁnition, at the harmonic level, combination bands, and

o v ertones hav e zero IR intensity. Fundamental bands have inherently

intense bands, make up most of the peaks seen in MIR spectra,

and comprise most of the diagnostically useful peaks we have seen

and will be studying for interpretation purposes. These so-called

double harmonic intensities of vibrational modes are calculated

using the ﬁrst deri v ati ve of the dipole moment with respect to a

normal coordinate, consequently, they can be method related. This

kind of calculation is therefore sensitive to the accuracy of the

electronic density and its variations, which in turn is the reason

why DFT calculations with a basis set as small as 4-31G may yield

reasonably good frequencies, modulo an empirical scaling factor, but

comparatively less good intensities.

Within the harmonic approximation, molecular vibrational energy

le vels are e venly spaced, the peak positions in an IR spectrum are

given by

ω = (1 / 2 πc)( K/ μ)

1 / 2

where ω is the wavenumber of the molecule in cm

−1

, K the force

constant, and μthe reduced mass.

After a geometrical optimization of the molecule, in the case of

the harmonic approximation, the vibrational spectrum is computed

from the diagonalization of the Hessian matrix.

2.2 Density functional TB approximations

For the large systems, starting from N

> 450 and up to N

= 1498,

with B3LYP/4-31G model chemistry we were not able to perform any

geometry optimizations due to computational limitations. Instead,

we have employed DFTB approaches which are semi-empirical

approximations to DFT. Three sets of parameters have been tested,

including DFTBA (Zheng et al. 2007 ), MIO, and 3ob.

The method

implemented in GAUSSIAN , i.e. DFTBA, is derived from a second

order Taylor series expansion of the density functional DFT total

energy expression around a reference density. DFTBA is a version

that uses analytic expressions for the matrix elements. Whereas

DFTB employs the tabulated matrix elements as in the original

implementation of Elstner and co-w ork ers (Porezag et al. 1995 ;

ht tps://dftb.org/paramet ers/download

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MNRAS513,3663–3681(2022)https://doi.org/10.1093/mnras/stac976AdvanceAccesspublication2022April20Probingcomputationalmethodologiesinpredictingmid-infraredspectraforlargepolycyclicaromatichydrocarbonsB.Kerkeni,1,2,3‹I.Garc´ıa-Bernete,1‹D.Rigopoulou,1‹D.P.Tew,4P.F.Roche1andD.C.Clary41DepartmentofPhysic...

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Probing computational methodologies in predicting mid-infrared spectra for large polycyclic aromatic hydrocarbons

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