# Adsorption of Silver Clusters on Naphthalene: Theoretical Insights into Structural, Energetic, Electronic, and Infrared Properties

Rahma Dahmani, Camille Alauzet, Gabriella Di Genova, Fernand Spiegelman, Aude Simon

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Rahma Dahmani, Camille Alauzet, Gabriella Di Genova, Fernand Spiegelman, Aude Simon. Adsorption of Silver Clusters on Naphthalene: Theoretical Insights into Structural, Energetic, Electronic, and Infrared Properties. Journal of Physical Chemistry A, 2025, 129 (17), pp.3829-3843. 10.1021/acs.jpca.5c00436. hal-05042263

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Adsorption of Silver Clusters on Naphthalene:
Theoretical Insights into Structural, Energetical,
Electronic and Infrared properties

Rahma Dahmani,† Camille Alauzet,† Gabriella Di Genova,†,‡ Fernand

Spiegelman,† and Aude Simon*,†

†Laboratoire de Chimie et Physique Quantiques (LCPQ), FeRMI Institute, UMR5626
Université de Toulouse [UT3 Paul Sabatier] & CNRS, 118 Route de Narbonne, 31062
Toulouse, France

‡Current affiliation: Dipartimento di Chimica, Biologia e Biotecnologie, Università degli
Studi di Perugia, 06123 Perugia, Italy.

E-mail: aude.simon@irsamc.ups-tlse.fr

Phone: +33 5 61 55 60 33

Abstract

In the present study we carry out a comprehensive investigation of the structural,
bonding and infrared spectral properties of the low-energy complexes of silver clusters
Ag<sub>n</sub> (n=1-8) adsorbed on naphthalene C<sub>10</sub>H<sub>8</sub> (Nap). The structural properties are
obtained through a systematic multi-method global optimization scheme. The poten-
tial energy surfaces of the complexes are first explored at the Density Functional based
Tight Binding level of theory *via* extensive Monte-Carlo Parallel Tempering simulations
complemented by gradient-driven quenching, thus providing a pre-screened sample of
low energy structural conformations. The most stable isomers are then re-optimized
at the Density Functional Theory level using a functional that includes dispersion,
namely B3LYP-D3BJ. The properties of the global minima are analysed at the latter
level. Unsurprisingly, the structures of Ag<sub>n</sub> adsorbat within the most stable complexes
are close to those of the bare clusters. Regarding 2D Ag<sub>n</sub> structures (n=2-6), those
with Ag<sub>n</sub> perpendicular to the Nap plane are found to be the most stable for n=2-4
while parallel conformations are preferred for n=5,6. The significant role of dispersion
interactions on the stabilities of these complexes is shown. The study of the influence
of Ag<sub>n</sub> adsorption on the evolution of the HOMO-LUMO band gaps and vertical ion-
ization potentials (VIPs) shows that the odd-even alternation of the adsorbat cluster
electronic properties is maintained and that the VIP decreases with size. Finally, the
influence of the adsorption of Ag<sub>n</sub> on the infrared properties of Nap is analysed: small
shifts are observed as well as the appearance of new bands due to symmetry reduction.
The essential novelty consists in relative intensity changes reflecting charge transfer
(though not dominant) from Nap to Ag<sub>n</sub>. Our study globally shows that Nap-Ag<sub>n</sub>
interactions lead to a modulation of the electronic and vibrational properties of Ag<sub>n</sub>
and Nap. This could be of interest for structural diagnosis and reactivity. Perspec-
tives concerning the use of the present structural search methodology for more complex
hybrid metal-organic systems in various applications fields are suggested.

# 1 Introduction

Hybrid organic-inorganic materials, and more specifically noble metal clusters (NMCs) linked
to organic ligand, play an increasingly important role in a wide variety of fields owing to
their present and future promising applications in catalysis, electronics, optics and biology.
For instance and non exhaustively, they have been extensively used as catalysts in vari-
ous chemical reactions,¹⁻⁵ to develop electroluminescent (EL)⁶ and semiconductor⁷ devices,
light-Emitting materials (LEDs),⁸ biosensing material, or in biomedicine applications,⁹⁻¹²
nanophysics and nanotechnology.¹³ A number of textbooks have reviewed various funda-
mental aspects and applications.¹⁴⁻¹⁶ Liganded noble metal clusters have been particularly investigated and one may refer to the book by Bonacic-Koutecky and Antoine¹⁷.

In all cases, the organic-inorganic interface plays a key role in the properties of materials. Understanding their behaviour at the molecular level is crucial to improve the efficiencies of the processes and is important to provide a guideline for the rational design of new hybrid materials. A family of hybrid metal-organic systems which has been the object of a variety of experimental and computational studies is that of metal nanoparticles or clusters in interaction with polycyclic aromatic hydrocarbons (PAHs), motivated by tuning and enhancing the electronic, optical and catalytic properties that graphene, or more generally carbon nanoparticles (known as Cdots), and metal clusters possess separately.¹⁸⁻²⁶

Metals are indeed used as interfaces between graphene and conventional electronics. It is therefore crucial to understand metal-graphene interactions in order to fully optimise the potential of nano-electronics and nanodevices.²⁷ In this context, Granatier et al.¹⁸ investigated the binding between Ag, Au and Pd to benzene, coronene $C_{24}H_{12}$, and graphene using post Hartree-Fock methods (MP2 and CCSD(T)) and density functional theory (M06-2X, DFT-D3, PBE and vdW-DF). They showed that the nature of the binding is different for the three metals: while silver essentially interacts through dispersion (van der Waals) forces, the binding in the case of Pd has a covalent character while in the case of Au, the binding is a combination of charge transfer, dispersion and relativistic effects. They also showed that DFT with empirical corrections to describe van der Waals interactions tends to overestimate the metal-aromatic bonding in some cases. Granatier et al.¹⁹ extended this work to the study of the interaction of the dimer and tetramer of Ag, Au and Pd to coronene, validating the results of MP2 calculations using CCSD(T) reference benchmark. They showed that the binding energy increases linearly with the number of metal atoms (up to the tetramer) and that the stability of metal clusters is maximum for Pd with dative bond involved, followed by Au, and is minimum for Ag with charge transfer and dispersion interactions involved in the two latter cases. Jadoon et al.²² conducted a comprehensive study of the interaction be-
tween silver clusters $Ag_n$ (n=1-10) and large PAHs, e.g. coronene and dodecabenzocoronene. Local optimizations using the M06-2X functional and the LANL2DZ effective core potential were performed, and interaction energies, bond nature, ionization potentials and electron affinities as a function of cluster size were determined. They observed in particular that the 2D-3D transition for $Ag_n$ occurred at n=7. Their calculations showed that the hollow-top interaction site is favored with respect to bridge-top and head-top binding sites over the coronene lattice. All the above-mentioned studies show that silver-PAH interactions are weak.<sup>18,19,22</sup> In order to increase this interaction energy, functionalizing Cdots surfaces was considered. For instance, DFT studies by Robein et al.<sup>25</sup> show that the presence of an epoxy group allows to anchor silver clusters (n=1-3) and that charge transfer and orbital overlap occur between O and Ag atoms.

Due to their unique electronic properties, silver-graphene quantum dots are promising electrochemical sensors. For instance, experimental studies show that silver-modified carbon-substrates can be used for the detection of Cd through electro chemical processes.<sup>28,29</sup> This motivated computational studies of the adsorption of a Cd atom on silver clusters adsorbed on coronene with or without the presence of an epoxy function,<sup>26</sup> demonstrating that the adsorbed Cd on the silver cluster is stabilized by charge transfer from Cd to the substrate correlated with orbital overlap. Silver nanoparticles based graphene composites have also been experimentally investigated for non enzymatic electrochemical sensing of glucose and $H_2O_2$.<sup>30</sup> This motivated the comprehensive study by Jadoon et al.<sup>24</sup> of the interaction of coronene decorated by $Ag_6$ with glucose and $H_2O_2$. These computational studies conducted at the DFT level (M06-2X functional) validate the sensing properties of the $Ag_6$-coronene system. Interestingly, Ag doping-induced vacancies defects have also been considered in order to modify the electronic structure of graphene and hence its sensing properties. For instance, the DFT studies by Benchallal et al.<sup>20</sup> show that doping graphene nanoribbons with $Agn$ (n=1-3) increases their stabilities and induces different electronic behaviors following the number of Ag-doping atoms.
Regarding smaller systems, the interaction of Ag<sub>3</sub> with benzene, naphthalene C<sub>10</sub>H<sub>8</sub>, anthracene C<sub>14</sub>H<sub>10</sub> and pyrene C<sub>16</sub>H<sub>10</sub> was investigated by means of spectroscopic experimental studies complemented with DFT and Time-dependent DFT calculations (B3PW91 functional and LANL2DZ basis set).<sup>31-34</sup> In the case of anthracene and pyrene, the interaction is revealed by a redshift of the UV-visible spectra with respect to that of bare PAH. Raman spectroscopy also reveals a downshift of the ring breathing modes, in agreement with computed vibrational spectra.<sup>33,34</sup> This was also observed in the case of naphthalene.<sup>32</sup> Interestingly, the adsorption of Ag<sub>3</sub> on pyrene also leads to enhanced non linear optical properties. All these studies show that the adsorption of Ag<sub>3</sub> on small PAHs leads to a significant reduction of the HOMO-LUMO gap of the PAH, involving weak charge transfer from the PAH to the silver trimer. These findings highlight the potential use of complexes of small PAHs with Ag<sub>3</sub> as electroactive molecular systems.

Finally, one may mention that in the gas phase context, PAHs have sustained a lot of interest in the astrophysicists' and astrochemists' community since the mid-eighties when they were proposed to be the carriers of the Aromatic Infrared Bands (AIBs).<sup>35,36</sup> It is only very recently that specific PAH molecules were detected in the giant molecular cloud TMC-1, i.e. isomers of cyanonaphthalene and cyanopyrene.<sup>37,38</sup> The role of metals in the formation of PAHs in astrophysical environments is a current key question in astrochemistry, motivating ex Experimental and theoretical studies. In this respect, Bérard et al.<sup>39</sup> provided a strong experimental evidence on the impact of the presence of silver atoms and clusters on carbon dust composition, also suggesting its catalytic role in hydrocarbon molecular growth. Indeed, the IR analysis of plasma samples with and without the presence of Ag has revealed the appearance of hydrocarbon population in the Ag-containing sample especially in the 2800-3000 cm<sup>-1</sup> (-CH<sub>3</sub>, -CH<sub>2</sub>) and 1500-1800 cm<sup>-1</sup> (C=C) spectral regions. Furthermore, they confirmed the presence of small PAHs, and naphthalene in particular. A similar study in absence of Ag did not provide evidence for the presence of hydrocarbons, confirming the key role of silver atoms or clusters in PAH formation. These gas phase experiments
were complemented with DFT calculations using the ωB97-XD functional for small silver-
hydrocarbon complexes. Reaction mechanisms leading to the formation of the nucleation
seed Ag<sub>n</sub>-C<sub>2</sub>H were proposed. Before being detected, PAHs are likely to be complexed with
silver atoms and clusters. Silver-PAH clusters are then expected to be the last intermediates
of the catalytic cycle leading to the formation of small PAHs from small carbon precursors,
which motivated this comprehensive study. As detection in gas phase experiments is often
made by mass spectrometry, it is also important to determine the ionization energies of the
systems. Infrared spectroscopy is also a powerful tool to evidence the interaction of PAHs
with metal<sup>40-43</sup> with results of potential astrophysical interest.

In this context, the present work aims at providing a contribution to the understanding
of the PAH-metal interaction and is dedicated to a comprehensive investigation of silver
cluster interacting with the smallest PAH molecule, namely naphthalene (hereafter short-
ened as Nap). DFTB was shown to reproduce satisfactorily the structural and electronic
properties of isolated gas phase silver and gold clusters over a wide size scale from the dimer
to the bulk.<sup>44,45</sup> It also provides a good description of organic compounds<sup>46,47</sup> and in par-
ticular PAHs.<sup>48</sup> It can moreover be complemented by phenomenological account of pairwise
dispersion forces. The present study is therefore based on global optimization structural ap-
proach within a multi-method scheme, involving extensive parallel tempering Monte Carlo
simulations (PTMC) run at the density functional tight-binding (DFTB) level of theory.
This global PES exploration is complemented by quenches via gradient-driven structural
optimization at the density functional (DFT) level, which provides a variety of low energy
isomers in competition. Single point MP2 benchmark calculations are also achieved occa-
sionally for comparison, complementing the final DFT results. For the sake of completeness,
the work considers silver clusters in the size range n=1-8 and several properties, namely
stabilities, electronic properties (HOMO-LUMO gaps), ionization potentials and infrared
spectra are determined. The methodology is detailed in Section 2. The results are reported
and discussed in Section 3.

# 2 Computational methods

## 2.1 PES exploration and electronic structure methods

Global PES explorations were first conducted using an algorithm based on Parallel Tempering Monte Carlo (PTMC) simulations$^{49,50}$ with the electronic structure described at the Self-Consistent-Charge DFTB (SCC-DFTB) level of theory$^{51}$ as implemented in the deMonNano code.$^{52}$ In order to insure a correct description of the geometries, we used the SCC-DFTB parameters specifically determined for carbonaceous systems interacting with silver atoms and clusters.$^{53}$ This DFTB parametrization involves two-body repulsive terms determined from accurate ab initio Multi Reference Configuration Interaction type calculations of atomic pairs and hence a description of dispersion interactions. Concerning the optimization algorithm, for each stoichiometry, several PTMC simulations of 100 000 steps each were conducted, starting from different initial configurations. In the PTMC simulations, the intramolecular vibrational modes of naphthalene were maintained frozen. A range of 30 temperatures uniformly distributed between 40 and 3000 K following a geometric sequence were used. Exchanges between all temperatures were allowed. In order to prevent from evaporation, a repulsive wall with radius $50 a_0$ centered at the center of mass of the system was applied.$^{54}$ The 600 lowest energy structures resulting from all the PTMC simulations for a given stoichiometry were locally optimized at the SCC-DFTB level using the quenching procedure developed by Dontot et al.$^{55}$ where redundant structures are eliminated using geometric and energetic criteria. As a result of the PTMC/DFTB simulations and quench procedures, we could identify different structural families (groups of clusters with similar structures and energies). The most stable clusters of the most stable families were finally used as starting geometries for further DFT local optimization.
The description of weakly bonded systems is quite challenging for DFT methods and the results may depend on the choice of the exchange-correlation functional. In order to accurately describe relatively weak interactions between Nap and silver clusters, we tested the following DFT functionals: B3LYP<sup>56</sup>,<sup>57</sup> PBE0,<sup>58</sup> LC-wPBE,<sup>59</sup> M06-2X<sup>60</sup> and ωB97XD.<sup>61</sup> In order to describe dispersion forces,<sup>62</sup> we added to B3LYP Grimme's dispersion correction D3 with Becke and the Johnson (BJ) damping function.<sup>63</sup> This functional was recently used to study the interaction of H<sub>2</sub> molecules with Cu-doped and Cu-decorated coronene.<sup>23</sup> From our benchmark studies (see Section 3.1), we chose the latter functional, quoted hereafter as B3LYP-D3BJ. In the present study we used the Stuttgart relativistic effective core potential for Ag, where the 28 core electrons are described with a pseudo-potential and the 19 valence 4s<sup>2</sup>4p<sup>6</sup>4d<sup>10</sup>5s<sup>1</sup> electrons are explicit with the related valence [6s,5p,3d] basis set.<sup>64</sup> A cc-pVTZ basis set was used for C and H atoms. All DFT calculations were performed using the Gaussian16 suite of programs.<sup>65</sup>

## 2.2 Properties

The stabilities of the lowest energy isomers of Nap-Ag<sub>n</sub> (n=1-8) were determined through the calculations of their interaction energy (IE) with respect to dissociation into Nap and Ag<sub>n</sub>.

$$IE = E_{Nap-Agn} - (E_{Nap} + E_{Agn})$$

E<sub>Nap-Agn</sub> is the total energy of Nap-Ag<sub>n</sub> at the equilibrium geometry, E<sub>Nap</sub> and E<sub>Agn</sub> are the energies of Nap and Ag<sub>n</sub> respectively at the equilibrium geometry of the system. Basis set superposition errors (BSSE) were estimated using the counterpoise correction scheme of Boys and Bernardi.<sup>66</sup> The electronic properties were investigated through the calculations of the frontier molecular orbitals (highest occupied molecular orbital HOMO, and lowest unoccupied molecular orbital LUMO) and the determination of the vertical ionization potentials
(VIPs) subtracting the energy of neutral cluster to the one of the ionized form at the geometry of the neutral. The infrared (IR) characteristic features were also investigated via the determination of the vibrational spectra in the double-harmonic approximation. In all reported IR spectra, the computed wavenumbers were scaled using different scaling factors per energy range, based on the comparison between the computed spectrum of naphthalene (this work) with the experimental spectrum in the IR spectra NASA database.⁶⁷⁻⁶⁹ Scaling factors of 0.980, 0.988 and 0.965 in the 0-1000, 1000-2000 and 2000-3500 cm⁻¹ region, respectively, were obtained. All reported spectra result from the convolution of the discrete spectra by a Lorentzian profile (with a full width at half maximum corresponding to a temperature of 10 K).

# 3 Results and discussion

## 3.1 Benchmark

### 3.1.1 Nap-Ag: DFT benchmark and bond analysis

The adsorption site of a single Ag atom on Nap is very sensitive to the applied quantum chemical method as a consequence of the flatness of the PES. Performing local optimization from the same starting point geometry indeed led to different minima depending on the functional (see Figure S1). Three possible adsorption sites were identified, leading to three isomers, 1.a, 1.b and 1.c as reported in Figure 1. In isomer 1.a, Ag is located on top of the central C-C bond (top-bridge isomer #1), in 1.b on top of an external C-C bond (top-bridge isomer #2), and in 1.c on top of an aromatic ring (top-hollow isomer). Isomer 1.a was found to be the most stable one with both B3LYP-D3BJ and ωB97XD functionals (see Table S1). Isomers 1.b and 1.c were the next most stable, located 1.34 and 1.70 kcal.mol⁻¹ above 1.a, respectively. This ordering was confirmed by single-point MP2 calculations. The MP2 single point calculations resulted in energy differences that were quite close to the B3LYP-D3BJ
results (Table S1). Interestingly, Granatier et al.<sup>19</sup> considered three types of isomers for Ag-coronene depending on the interaction site of Ag with the central ring of coronene, i.e. top, bridge and hollow sites. The three types of isomers were found degenerate within 0.3 kcal.mol<sup>-1</sup>, the most stable situation being dependent on the method, i.e. MP2, DFT-D3 and M06-2X. The larger energy difference between the Nap-Ag isomers is then due to finite-size effects.

<figure><img src="image_2.png" /><figcaption>Figure 1: Local minima found for Nap-Ag. The reported geometries are those obtained with the B3LYP-D3BJ functional.</figcaption></figure>

Regarding the energetics, the B3LYP-D3BJ interaction energy of isomer 1.a was found at -0.27 eV (6.3 kcal.mol<sup>-1</sup>) and -0.26 eV (6.1 kcal.mol<sup>-1</sup>) without and with BSSE, respectively. Single point MP2 calculations provide weaker IEs of -0.19 eV (4.4 kcal.mol<sup>-1</sup>) and -0.11 eV (2.5 kcal.mol<sup>-1</sup>), without and with BSSE, respectively. These values fall in between the extrapolated interaction energy values of Ag-benzene and Ag-coronene determined by Granatier et al.<sup>18</sup> using the MP2, DFT-D3 and M06-2X functionals. The presently determined IEs for Nap-Ag are however more similar to the IEs extrapolated by Granatier et al.<sup>18</sup> for Ag-coronene. For instance, the coronene-Ag extrapolated IE for the top-bridge position was found to be -4.0 kcal.mol<sup>-1</sup> using the Douglas-Kroll relativistic MP2 hamiltonian, -5.8 kcal.mol<sup>-1</sup> using the DFT-D3 functional and -6.3 kcal.mol<sup>-1</sup> using M06-2X. The difference between B3LYP-D3BJ and MP2 values was quite expected given the previous studies by Granatier et al.<sup>18,19</sup>. MP2 results are however expected to be more dependent on the basis
set. Actually, a higher level reference would be CCSD(T) calculations which are expensive
in terms of time and memory.

As we also aim at describing Nap-Ag<sub>n</sub> IR spectra, and due to the lack of experimental data
on Nap-Ag<sub>n</sub> (neutral complex), we compared the harmonic IR spectra obtained from selected
DFT functionals to an experimental Infrared Photodissociation spectra (IRPD) of [Nap-Ag]<sup>+</sup>
published by Savoca et al.<sup>40</sup> where they reported the first experimental mid-infrared spectra
of [Ag-PAH]<sup>+</sup> (PAH = naphthalene and azulene) recorded in the range of (550-1650 cm<sup>-1</sup>).
The optimization of the cationic complex [Nap-Ag]<sup>+</sup>, reported in Figure S2 in the Support-
ing Information, reveals the same spectral signatures for the low-energy structure using the
tested DFT functionals as in the experiment. The description of the lowest energy structure
is less delicate than in the neutral case as stabilising polarisation interactions are present in
the cationic case. As can be seen in Figure S3, the peak positions of the out-of-plane CH
bending mode computed at 833 cm<sup>-1</sup> and of the in plane CH bend combined with the CC
stretch computed at 1391 cm<sup>-1</sup> at B3LYP-D3BJ level of theory have the best agreement with
the experimental values.

In order to get insights into the Nap-Ag bond, the molecular orbitals (MOs) were ana-
lyzed (see Figure S4). As can be seen in Figure S4, stabilising interactions are insured by the
donation from the π MOs of naphthalene to the d orbitals of silver (HOMO-8, HOMO-10
and HOMO-13). However, antibonding orbitals are also found (HOMO-2 and HOMO-3).
Globally, a small electron transfer is observed from naphthalene to Ag (Mulliken/Natural
charge of -0.065/-0.008 on Ag). The analysis of the contribution of dispersion interactions
(see Table S2) reveals that dispersion forces contribute to the stability of Nap-Ag complex:
the Grimme-dispersion term (D3BJ) contributes for -7.7 kcal.mol<sup>-1</sup> at equilibrium. This
contribution from dispersion forces is expected to increase with increasing cluster size up to
a limit, especially in the case of planar parallel conformations.
Further check of the adequacy of the B3LYP-D3BJ functional will be discussed below in
the Results section when analysing the computed properties.

3.1.2 Silver clusters (Ag$_n$)

Although the B3LYP-D3BJ functional is expected to provide satisfactory results for organic
molecules and organic molecular clusters, the description of silver clusters with such func-
tional had to be verified. A large number of quantum chemical studies on silver clusters
were performed and their PES, energetic and electronic properties are now well known (see
review⁷⁰ and references therein). In the present work, the initial geometries were taken from
Chen et al.⁷¹ and correspond to the most stable geometries of the *n* = 2 – 8 Ag*n* clusters.
Their B3LYP-D3BJ optimized geometries are reported in the first row of Figure 2 and their
corresponding cohesion energies per atom are shown in Figure 3, alongside additional DFT
and wavefunction type calculation results for comparison. As illustrated in this figure, the
B3LYP-D3BJ functional shows excellent agreement with other functionals and provides en-
ergy values that are closer to CCSD(T) results as compared to the B3LYP functional alone.
In terms of structures, the B3LYP-D3BJ functional provides bond lengths consistent with
B3LYP⁷¹ and PBE values⁷² (Table S3). Although it was only checked for n=2, B3LYP-D3BJ
bond lengths tend to be slightly overestimated with respect to experimental measurements
(+0.064 Å,⁷³) and CCSD(T) calculations.⁷¹

In conclusion of the present subsection, the B3LYP-D3BJ functional appears as an ade-
quate choice to study structures, energetics and IR features of Nap-Ag<sub>n</sub> (n=2-8) complexes.
<figure><img src="image_3.png" /><figcaption>Figure 2: Geometries of Agn (n=2-8) clusters optimized at the DFT/ B3LYP-D3BJ level of theory. The geometries in the first row were optimized using structures of ref⁷¹ as starting points. Geometries in lower rows were obtained starting from Agn parts in PTMC/DFTB simulations of the complex as described in Section 3.2.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Figure 3: Cohesion energy per atom of Ag<sub>n</sub> (n=2-8) clusters: present B3LYP-D3BJ, TPSS,<sup>74</sup> PBE,<sup>72</sup> M06<sup>71</sup>, B97<sup>71</sup>, PW91,<sup>71</sup> B3LYP,<sup>71</sup> CCSD(T)<sup>71</sup> and CI.<sup>75</sup></figcaption></figure>

## 3.2 General features of the Nap-Ag<sub>n</sub> PES exploration

As specified in Section 2 the PES of Nap-Ag<sub>n</sub> (n=1-8) was first explored using PTMC/DFTB simulations followed by a quench procedure. As shown in Alauzet et al.<sup>53</sup>, the DFTB method with the appropriate parameterization scheme is expected to provide satisfactory geometries but preliminary studies<sup>53</sup> revealed a trend to underestimate the interaction energies.

As expected, DFTB calculations yielded a high density of low-energy isomers after local optimization: numerous stable geometries were found in a narrow energy range, even for small silver clusters, differing by the relative position of the silver cluster with respect to the naphthalene plane, fingerprinting the flatness of the PES (see Figure S5). For all complexes, the most stable one corresponds to the whole silver cluster interacting with naphthalene. Higher energy structures characterized by silver atoms interacting with two different faces of Nap were found (see for instance Figure S6 illustrating the dimer case where the structure
with the two separated silver atoms is found 1.72 eV higher in energy than the most stable
one at the DFT level). When increasing the size of the systems, families of isomers where the
silver clusters adopt different shapes compete (see for instance Figure S7 where four distinct
isomers are found within 0.20 eV for n=8 at the DFT level).

In the following subsections, we focus on the most stable structures of Nap-Ag<sub>n</sub> (n=1-8)
retrieved from the DFTB quench procedure and optimized at the DFT level.

<figure><img src="image_5.png" /><figcaption>Figure 4: Equilibrium geometries of the most stable Nap-Ag<sub>n</sub> complexes (n = 1-8), identified at the DFTB/PTMC process and finally optimized using DFT calculations with the B3LYP-D3BJ functional.</figcaption></figure>

**3.3 Structural and energetic properties**

The lowest energy isomers of Nap-Ag<sub>n</sub> (n=1-8) obtained at the B3LYP-D3BJ level of theory
are reported in Figure 4. For all stoichiometries, the geometries of the silver cluster in these
complexes are very close to the most stable structures of the bare silver clusters. Only slight
distortions are observed with small variations of Ag-Ag bond lengths upon complexation
(see Table S3).

In the case of the smallest clusters (n=2-5), the two lowest energy isomers differ by the
relative orientation of the silver cluster with respect to the PAH (Nap) plane. For n=2-4,
the most stable complexes correspond to a conformation where the plane of the silver cluster
is quasi orthogonal to the naphthalene plane. In the case n=2, conformer 2.a with one silver
atom pointing towards the naphthalene plane, is more stable by 0.11 eV than conformer 2.b
with the silver dimer parallel to the naphthalene plane. In the presence of naphthalene, the
Ag-Ag bond length decreases slightly by 0.0074 Å (2.5904 Å) in complex 2.a and increases
slightly by +0.0026 Å (2.6004 Å) in complex 2.b. In terms of charge transfer, the total
charge transfer is similar for the two complexes, with electron donation from naphthalene to
silver resulting in a total Mulliken charge of -0.12 on Ag<sub>2</sub> (Natural charge analysis: -0.034)
for complex 2.a and of -0.11 for complex 2.b. The charge distribution is however different. In
complex 2.a, the silver atom close to the naphthalene plane is positively charged (Mulliken
charge: +0.48, natural electron configuration: 5s( 0.91)4d( 9.95)5p( 0.08)) while the remote
one is negatively charged (-0.60, natural electron configuration: 5s( 1.10)4d( 9.98)5p( 0.01)).
In conformer 2.b, the charge is similar on both silver atoms (-0.054, 5s( 0.99)4d( 9.99)5p(
0.03)). The anisotropy of the charge distribution in 2.a enhances its electrostatic stabilisa-
tion. Oppositely, dispersion is stronger in 2.b with +0.19 eV (or 4.34 kcal.mol<sup>-1</sup>) difference
in the total dispersion energy. In the case n=3, the most stable isomer is similar to the one
obtained by Rekha et al.<sup>32</sup> with the silver trimer quasi orthogonal to the Nap plane. The
closest silver atom to the Nap plane points towards the middle of an external C-C bond. As
in the case of the silver dimer, this atom is positively charged with its 5s orbital depleted in
favor of the 5p (+0.45, 5s( 0.71)4d( 9.94)5p( 0.32)5d( 0.01)) while the Mulliken charges on
the two other atoms are -0.33 and -0.24 with natural electron configurations of 5s( 0.99)4d(
9.98)5p( 0.05) and 5s( 1.00)4d( 9.98)5p( 0.06) respectively. No complex with the Ag<sub>3</sub> plane
parallel to Nap was found, which is probably due to strong repulsive interactions.
In the case of n=4, the most stable isomer 4.a corresponds to the silver tetramer interacting with naphthalene with one Ag atom preferentially that has a positive Mulliken charge of +0.61. For the atoms more distant from naphthalene, the atomic charges decrease to 0.02, and then to -0.38 and -0.43, leading to a total Mulliken charge of -0.17 (Natural charge analysis: -0.08). In the case of isomer 4.b, the silver tetramer is not planar anymore with two atoms closer to Nap with a Mulliken charge of -0.14 for each of them, and two other atoms slightly further. This provides a total Mulliken charge of -0.22. Electron transfer is then more important in isomer 4.b. Locally, electrostatic interactions do not appear to have a stabilizing effect as the Ag atoms closer to the Nap plane own a negative charge. In isomer 4.b, stability is favored by dispersion interaction, namely +0.25 eV (5.9 kcal.mol⁻¹) in isomer 4.b vs isomer 4.a.

Contrary to the clusters with fewer atoms (n=2,3,4), the lowest energy structure for n=5 consists of a planar pentamer now parallel to the Nap plane. Furthermore (contrary to isomer 4.b), Ag₅ remains keeps a strictly planar structure as in the gas phase. In isomer 5.b, 0.13 eV higher than isomer 5.a, the Ag₅ plane is perpendicular to the Nap plane. Stabilisation due to dispersion interactions prevails contrary to n=2-4. It is also so for n=6 where the lowest energy isomer 6.a is similar to the n=5 case. At this stoichiometry, there starts to be a competition between 2D and 3D structures for the silver. The lowest energy isomer with a 3D structure for Ag₆, characterized by a five-(member ring with an atom on the top, was found 0.14 eV higher in energy.

For n=7, the most stable structures correspond to the 3D structure of bare Agn interacting preferentially with three atoms that tend to carry locally a positive charge. The planar Ag₇ isomer interacting with naphthalene (7.c) is found 0.43 eV above 7.a while another 3D isomer 7.b, having two silver atoms preferentially interacting with Nap, lies 0.16 eV above 7.a. In the case of n=8, only geometries with silver clusters adopting 3D structures were
found (see Figure 4). However, for *n* = 8, the most stable geometry of Ag₈ (isomer 8.a in Figure 2) does not yield the most stable interaction with naphthalene and is correlated with complex 8.c of Figure 4, 0.12 eV higher in energy than complex 8.a. Instead, the subsequent Ag₈ 8.b isomer, quasi energetic with 8.a (see Figure 2), leads to the most stable Nap-Ag₈ complex 8.a. Isomers 8.b and 8.d result from the interaction of the Ag₈ cluster 8.c with naphthalene but in different relative orientations. These isomers are 0.08 eV and 0.20 eV less stable than 8.a, respectively.

It is interesting to compare the structures obtained in this work with those obtained for coronene-Ag<sub>n</sub> (n=2-8) by Jadoon et al.<sup>22</sup> using the M06-2X funcional and the LAN2DZ potential. The structures are similar for n=2, 7 and 8 but differences are found for n=3-6. In coronene-Ag<sub>3</sub>, the silver trimer loses its triangular shape and interacts with coronene via two silver atoms in the most stable structure. In coronene-Ag<sub>4</sub>, the most stable structure is analog to conformer 4.b while the second low lying one is similar to 4.a. In coronene-Ag<sub>5</sub>, the most stable structure is similar to 5.b but Ag<sub>5</sub> interacts with coronene through two silver atoms. The structure similar to 5.a is found 3.39 kcal.mol<sup>-1</sup> above. Finally, the most stable isomer of coronene-Ag<sub>6</sub> is similar to 6.a but two other isomers are found below the isomer similar to 6.b. It would be interesting to know whether the differences come from the functional, a different exploration of the PES or whether they are only due to the size differences of the PAH.
3.4 Global minima: Interaction energies and charge analysis

<figure><img src="image_6.png" /><figcaption>Figure 5: (a) Interaction energy IE (including BSSE correction) of the most stable Nap-Ag$_n$ (n=1-8) complexes at B3LYP-D3BJ level of theory. n.a labels the lowest energy isomer, and n.b the lowest next ones. (b) Interaction energy IE with and without BSSE correction of the lowest energy isomers n.a at MP2 and B3LYP-D3BJ levels of theory. Data related to this figure can be found in Table S4.</figcaption></figure>
Figure 5 (a) presents the BSSE corrected IEs of Nap-Ag<sub>n</sub> at B3LYP-D3BJ level of theory as a function of silver cluster size. IE values range between -0.26 and -0.76 eV from n=1 to n=8. Interestingly, for n =6 and after BSSE correction, complex 6.b becomes more stable than complex 6.a with a larger interactions energy (more negative values) by 0.09 eV. In the other cases, from n=1 to n=4, the interaction energy increases with cluster size. This is generally consistent with the decrease of equilibrium distances between the nearest Ag-C atoms found to be 3.17, 2.68, 2.51 and 2.59 Å for the most stable structures of Nap-Ag, Nap-Ag<sub>2</sub>, Nap-Ag<sub>3</sub> and Nap-Ag<sub>4</sub>, respectively. Starting from n=4, the value of |IE| fluctuates between larger values for even n and smaller values for odd n with however a global increase as the minimum |IE| is found for n=8 (IE = -0.76 eV) and the smallest |IE| for odd n is found for n=5 with IE = -0.64 eV and n=3 with IE = -0.65 eV.

It is interesting to analyse the contribution of dispersion to the Nap-Ag<sub>n</sub> interaction for the most stable complexes (see Table S2). As expected, the global trend is that the contribution of E<sub>disp</sub> increases with Ag<sub>n</sub> size. A transition (increase by 8.6 kcal.mol<sup>-1</sup>) is observed at n=5. It corresponds to the first case where the Ag<sub>n</sub> plane interacts with the π cloud of naphthalene. The dispersion energy is the largest for n=6 (-22.5 kcal.mol<sup>-1</sup>) that corresponds to the largest 2D cluster whose plane interacts with the π cloud of Nap. For n=7,8 (3D clusters), E<sub>disp</sub> is found at -18.7 and -19.9 kcal.mol<sup>-1</sup> respectively.

As expected, as can be seen in Figure 5 (b), BSSE effects are small at the DFT level. Single point MP2 calculations using the B3LYP-D3BJ optimized geometries were achieved, motivated by the studies by Granatier et al.<sup>18,19</sup>. MP2 interaction energies without BSSE corrections were found to be stronger than B3LYP-D3BJ interaction energies, except for n=1 and n=5 to lesser extent. Unsurprisingly, BSSE effects on MP2 results are significant and corrected MP2 interaction energies are weaker than B3LYP-D3BJ ionization energies. However, globally, the evolution of MP2 interaction energies as a function of silver cluster size
is similar as the DFT one. However, starting from n=5, we no longer observe the fluctuations
found at the DFT level and the increase of |IE| from n=5 to 8 tends to be more pronounced
at the MP2 level. Obtaining accurate IE values would require the use of more reliable post
Hartree-Fock method such as CCSD(T) in a large basis set, which currently appears quite
out-of-reach for these systems.

We now consider charge transfer. Our findings, based on either natural charges (based
on Population Analysis (NPA)) or Mulliken charge data (see Table S9 in the supplemen-
tary information), reveal that the Ag clusters acquire a weak however non negligible net
charge upon adsorption (see Figure 6). This could be expected as the electron affinity of
naphthalene<sup>76</sup> is lower than that of Ag<sub>n</sub> (n=1-8).<sup>77</sup> While electron transfer (ET) is relatively
small (natural charge ranging from -0.03 for n=2 to -0.14 for n=8), it nevertheless induces
attractive electrostatic forces between naphthalene and the silver clusters. Natural and Mul-
liken charges have the same evolution, but the former are systematically smaller than the
latter. Moreover, as cluster size increases, the extent of ET also increases, highlighting the
significant influence of cluster size on electron transfer. This is particularly important as
it can lead to the formation of silver nanoparticles (AgNPs) through aggregation processes
that become energetically favorable once sufficient electrons are transferred.<sup>78</sup>

**3.5 Ionization potentials and frontier molecular orbitals**

We examine in this section the evolution of the VIPs and the frontier molecular orbitals as
a function of size.

We first re-examine the validity of the DFT B3LYP-D3BJ functional and basis sets em-
ployed in this work in concern with the determination of VIPs on isolated Agn clusters since
experimental data<sup>79</sup> are available. As shown in Figure 7, we globally obtain a somewhat
better agreement between B3LYP-D3BJ results and experimental data than with ωB97XD.
The magnitude of the discrepancy depends on the stoichiometry. For n=1,2,7 and 8 the
variation between experimental and calculated values is in the range of 0.3 - 0.5 eV and for
<figure><img src="image_7.png" /><figcaption>Figure 6: Evolution of Mulliken and natural charges on Agₙ in Nap-Agₙ complexes as a function of size.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 7: Experimental and computed vertical ionization potential (VIP) of Agₙ with B3LYP-D3BJ and ωB97XD functionals. The data can be found in Table S5.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Figure 8: Computed Vertical ionization potential (VIP) of Nap-Ag<sub>n</sub> at B3LYP-D3BJ level of theory. The data can be found in Table S6.</figcaption></figure>

n= 3,4,5 and 6 it becomes ≤ 0.1 eV. Regarding the VIP value of naphthalene, it was found at 7.93 eV with B3LYP-D3BJ although the experimental value is 8.12 eV<sup>80</sup> , which indicates an underestimation of ~ 0.19 eV. However, as can be seen in Figure S8, the HOMO orbital is mainly developed on the silver cluster, which makes the benchmark on silver cluster for Nap-Ag<sub>n</sub> complexes more relevant.

The size evolution of the VIPs of both Agn and Nap-Agn is reported in Figure 8. The
evolution is similar for the two systems consistently with the weak (van der Waals) inter-
action between Nap and Agn. The odd-even alternance is maintained upon complexation.
Adsorption on naphthalene leads to a systematic decrease of the VIP with respect to bare
Agn by about 0.5 eV except a larger decrease of 1.14 eV for n=1, reflecting the partial ET
from Nap to Agn. As a consequence, the ability of the complex to undergo donation processes
within other chemical environments is likely to be enhanced. The present results suggest
that the most reactive system as an electron donor is found for n=3 with a VIP decrease
from 6.20 eV for Ag₃ to 5.30 eV for [Nap-Ag₃], closely followed by n=7 (VIP decrease from
6.04 to 5.46 eV.

Following Koopmans’ theorem, the evolution of the VIPs can be rationalized by the evolution
of the HOMO orbitals, which are indeed destabilised upon adsorption. The size evolution of
the energies of both HOMO and LUMO orbitals is shown in Figure 9 while their shapes are
reported in Figure S8 of the SI. As can be seen in Figure 9, both HOMO and LUMO are
destabilised in the complex with respect to the case of isolated clusters Ag*n*. It confirms that
Nap-Ag*n* is expected to be a better electron donor than Ag*n*. The gap is hardly modified
upon complexation (see the values of the gaps in Table S8): the systems with the smaller
gaps, expected to be the most reactive in terms of electron donor-acceptor, are those for odd
values of n. Among those, the HOMO-LUMO evolution confirms that [Nap-Ag₃] is the best
electron donor while [Nap-Ag₅] is expected to be the best electron acceptor.

As can be seen in Figure S8, all HOMO and LUMO orbitals in the complex are mostly
located on Ag*n* except in a few cases as for n=2,8 for which the LUMO orbitals are mostly
developed on naphthalene. Promoting an electron from the HOMO to the LUMO for these
stoichiometries would clearly lead to a charge-transfer excited complex. To lesser extent, for
n=3,4, the LUMO orbital results from a combination between the LUMO orbital of Ag*n* and
the LUMO orbital of naphthalene. In these complexes, some specific Ag atoms of the clusters
are closer to the Nap plane. Interestingly, the frontier orbitals for n=3 found in this work are
different from those determined by Rekha and coworkers who found them developed on both
naphthalene and silver clusters.³² Their HOMO orbital correspond to the HOMO-2 orbital
with our methodology. In their work, they used the B3PW91 functional with a different
ECP and smaller basis set (LANL2DZ).
<figure><img src="image_10.png" /><figcaption>Figure 9: Energies (in eV) of the frontier molecular orbitals of Nap-Ag<sub>n</sub> complexes and Ag<sub>n</sub> clusters (with n=1-8) at B3LYP-D3BJ level of theory. The values are reported in Table S7.</figcaption></figure>

Considering the VIP of naphthalene as the reference value, our study shows that its interaction with Ag<sub>n</sub> (n=1-8) leads to a decrease of its VIP by 0.86 eV (n=2) down to 2.63 eV (n=3). In the DFT study by Jadoon et al.<sup>22</sup> using the M06-2X functional, they show that the adsorption of Ag<sub>n</sub> (n=1-10) on dodecabenzocoronene (DBC) also leads to a decrease of its VIP by 0.89 eV (n=2) to 1.92 eV (n=10). Globally, the VIP values of DBC-Ag<sub>n</sub> (n=1-8) clusters are found between 4.35 and 5.23 eV.<sup>22</sup> They are thus lower than that of Nap-Ag<sub>n</sub> lying between 5.30 and 7.07 eV (this work). This can be understood as DBC possesses a lower VIP (6.12 eV from the calculations by Jadoon et al.<sup>22</sup>) than Nap. Besides, while the odd-even alternance of the Ag<sub>n</sub> VIP is preserved in the case of Nap-Ag<sub>n</sub>, it is not rigorously the case for DBC. It seems therefore that although the interaction with Nap appears to only perturb the electronic properties of Ag<sub>n</sub>, the interaction with a larger PAH with a lower
VIP induces more drastic changes. In a more general view, playing on the shape, size and chemical functions of the PAHs is expected to offer a variety of possibilities to tune the electronic properties of the PAH-Ag$_n$ systems.

## 3.6 Infrared spectra

The IR spectra were computed for the most stable complexes of Nap-Ag$_n$ (with n=1-8), for the corresponding Ag$_n$ clusters and for Nap. The parts of the spectrum corresponding to the modes of naphthalene are reported in Figures 10 and 11 for Nap-Ag$_n$ (n=1-8) and Nap. The 400-500 cm$^{-1}$ region (Figure 10 (a)) corresponds to the out-of-plane deformation modes of Nap ("oop def."), the 700-900 cm$^{-1}$ region (Figure 10 (b)) to the out-of-plane C-H bending modes ($\gamma_{CH}$). The 1000-2000 cm$^{-1}$ region corresponds to the CC stretch ($\nu_{CC}$) and in-plane C-H bend ($\delta_{CH}$) (Figure 11 (a)) and the 3000 cm$^{-1}$ region (Figure 11 (b)) to the resonance of the C-H stretching modes ($\nu_{CH}$). The low energy parts of the spectra ($\bar{\nu} < 300$ cm$^{-1}$) correspond to softer modes involving those of the Ag$_n$ clusters, out-of-plane deformation modes of naphthalene and relative motions of Ag$_n$ and Nap in the complexes. In many occurrences, these modes are coupled to each other. They are reported in Figure 12 for Nap-Ag$_n$ and Ag$_n$. The exact positions of the modes and intensities are reported in Table S10 in the SI.

The most important change induced by the adsorption of Ag$_n$ on the Nap modes concerns the intensity ratio $I(\gamma_{CH})/I(\nu_{CH})$ that decreases when the size of the silver cluster increases (see Figure 13). Interestingly, it is then correlated with the increase of ET from Nap to Ag$_n$ (see Figure 6). In this respect, when the size of the silver cluster increases, the $I(\gamma_{CH})/I(\nu_{CH})$ ratio becomes closer to that of cationic naphthalene [see the DFT spectrum in the PAH NASA database$^{67-69}$]. However, contrary to the spectrum of Nap$^+$, the intensities in the $\nu_{CC} + \delta_{CH}$ region remain weak.

Regarding the positions of the fundamental modes of naphthalene, only small shifts are
observed consistently with the weak interaction between Ag$_n$ and naphthalene. Focusing on the most intense bands, the $\gamma_{CH}$ band is slightly blue-shifted, the largest blue-shift being observed for n=3 (+11cm$^{-1}$). The $\nu_{CH}$ bands are also slightly blue-shifted ($\Delta\nu \le 8$ cm$^{-1}$). On the opposite, the two most intense bands in the $\nu_{CC} + \delta_{CH}$ region, found respectively at 1535 and 1625 cm$^{-1}$ in the naphthalene spectrum, are slightly red-shifted. The maximum values of the shifts for these two bands were found for n=3 and amount to -10 cm$^{-1}$ and -13 cm$^{-1}$ respectively. Satellite bands also appear at lower energy for these two bands after adsorption of naphthalene on Ag$_n$ (see Figure 11 (a)). These bands, located at 1498 cm$^{-1}$ (6.76 $\mu$m) and 1597 cm$^{-1}$ (6.26 $\mu$m) respectively, result from the activation of some modes of naphthalene upon symmetry breaking due to adsorption on Ag$_n$.

These studies allow to identify specific features due to the adsorption of Nap on Ag$_n$ that can be used, for instance, as fingerprints for the formation of Nap-Ag$_n$ $\pi$- complexes in noble gas matrices. Interestingly, in order to investigate the influence of the adsorption of a "metallic" atom or ion on the IR features of a PAH, several DFT studies were performed for systems of astrophysical interest where the "metal" is Si,⁸¹ Mg⁸² and Fe.⁸³,⁸⁴ In the case of FePAH clusters, the main effect also concerns the intensities of the bands but in the 6-10 $\mu$m region: these bands, intense in cationic PAHs and weak in neutral PAHs, respectively, lose and gain intensity upon the coordination of iron, which happens to have a general moderating effect. Small shifts also appear in the positions of the 6.2 and 11.3 $\mu$m bands for iron-coordinated PAHs versus bare PAHs.⁸³ However, to our knowledge, no systematic study has focused on the influence of the adsorption of a metallic cluster on the IR features of a PAH, and in particular of naphthalene whose cyano derivatives were recently detected in TMC-1 molecular cloud.³⁷

The symmetry breaking due to the adsorption leads to the activation of the Ag$_n$ modes in the 0-300 cm$^{-1}$ region, that couple in many occurrences either to out-of-plane deformation
modes of naphthalene (ν̄ > 100 cm⁻¹) or to modes corresponding to relative motions of Agₙ
and Nap (stretching, rotation, translation, ν̄ < 100 cm⁻¹). The soft modes however remain
of low intensity (see Figure 12). In the case of n=1, the Ag-Nap stretch is found at 57 cm⁻¹.
In the case of n=2, it is found at 97 cm⁻¹ while the most intense band is found at 206 cm⁻¹
and corresponds to a combination of out-of-plane deformation of Nap, of the Ag-Ag stretch
and of the Ag-Nap stretch. A band of similar nature is found between 170 and 180 cm⁻¹ for
all complexes studied in the present work. When the silver cluster size increases, the features
below 100 cm⁻¹, that involve Agₙ modes combined with Nap-Agₙ modes, start resembling
a continuum. From this work, we may then infer it would be of interest to experimentally
investigate Nap-Agₙ complexes, and more generally PAH-Agₙ complexes in order to reveal
Agₙ spectroscopic features or low-energy PAH deformation modes. Besides, features found
in the far-IR domain (around 55-58 µm in the Nap case) could be searched for in space
telescope surveys such as the James Web Telescope as they may reveal the presence of PAH
in interaction with metallic clusters in space. This must however be confirmed for PAHs
interacting with metallic clusters of astrophysical interest (Si, Mg, Al, Fe).
<figure><img src="image_11.png" /><figcaption>(a) Out-of-plane deformation modes of naphthalene ("oop def.")</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Figure 10: Computed IR spectra of Nap-Ag<sub>n</sub> complexes (n=0-8) in different energy regions: 300-700 cm<sup>-1</sup> (panel (a) and 700-1000 cm<sup>-1</sup> (panel (b)).</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>(a) In-plane C-C stretch ($\nu_{CC}$) and C-H bending modes ($\delta_{CH}$)</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>(b) C-H stretching modes ($\nu_{CH}$)</figcaption></figure>

Figure 11: Computed IR spectra of Nap-Ag<sub>n</sub> complexes (n=0-8) in different energy regions: 1000-2000 cm<sup>-1</sup> (panel (a)) and 2800-3400 cm<sup>-1</sup> (panel (b)).
<figure><img src="image_15.png" /><figcaption>Figure 12: Computed IR spectra of Nap-Ag<sub>n</sub> and of the corresponding Ag<sub>n</sub> clusters for n=2-4 (panel (a)) and n=6-8 (panel (b)) in the 0-300 cm<sup>-1</sup> region.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>Figure 13: Intensity ratio I(γCH)/I(νCH) as a function of cluster size.</figcaption></figure>

**4 Conclusion**

The PES of Nap-Ag$_n$ complexes, with n ranging from 1 to 8, were initially probed using PTMC/DFTB simulations followed by a quenching procedure with DFT. In this systematic study, an important density of stationary points and isomers were found. The structural, energetical and vibrational properties of the most stable complexes were investigated at the DFT level of theory. The B3LYP-D3BJ functional was chosen based on a benchmark on Ag$_n$ clusters and Nap-Ag complex. Unsurprisingly, the structures of Ag$_n$ within the most stable complexes are hardly deformed upon adsorption. Regarding 2D structures (n=2-6) obtained for the metal cluster on top of Nap, those with Ag$_n$ perpendicular to the Nap plane are found to be the most stable for n=2-4 while parallel conformations were found to be preferred for n=5,6, illustrating the significant role of dispersion interactions in the Nap-Ag$_n$ binding. Back electron donation from naphthalene to the silver cluster was evidenced, and shown to increase with the size of the Ag$_n$. Regarding the VIPs, we show that the odd-even alternance observed for the electronic properties of the bare silver clusters are maintained, and that the
same is true for the HOMO-LUMO gap. and that for all n values, the VIP of Nap-Ag<sub>n</sub> is
systematically lower than that of the corresponding Ag<sub>n</sub> cluster, consistently with the fact
that the HOMO is higher in energy in the complex. Nap-Ag<sub>3</sub> was identified as the best
electron donor complex and Nap-Ag<sub>5</sub> as the best electron acceptor. These findings are in
general agreement with the existing literature on similar PAH-silver compounds involving
different PAHs or cluster sizes.

Regarding the influence of the Nap-Ag*n* interaction on the IR properties related to naph-
talene, we show that the intensity ratio I(νCH)/I(γCH) decreases when n increases. This can
be correlated to an increase in electron transfer from Nap to Ag*n* with n. Small blueshifts of
the γCH and red shifts of the δCH + νCC modes are also observed. Satellite bands are found
for these modes due to the activation of modes of null intensity in naphthalene, that become
activated due to symmetry breaking. In the softer modes regions, the modes of silver clusters
become active due to symmetry breaking.

Our study globally shows that Nap-Ag*n* interactions lead to a modulation of the elec-
tronic and vibrational properties of Ag*n* and Nap that could be of interest for reactivity
control and structural diagnosis. Although Ag is not particularly of astrophysical interest
in the interstellar or circumstellar environments, the present analysis of IR features may
also provide spectroscopic trends to identify the possible interactions of PAHs with metallic
clusters in space.

As a perspective, the multi-method approach employed in this work can easily be ex-
tended to larger similar systems, either increasing the size of the PAH or the size of the
silver cluster, for which determining the global miminum remains a challenge.⁸⁵ It could also
be extended to systems chemically modified, either through doping of the metallic center
or functionalizing the carbon surface, or substituting CH groups or C atoms by O, N or Si
atoms, in order to determine trends concerned with structural features, energetical, chemical,
vibrational or electronic properties. As shown by Ambrusi et al.²⁶ in the particular case of
the functionalization by an epoxy group, such modification may improve the sensing proper-
ties of the organometallic cluster. One may also think of bimetallic noble metal systems or
of transition metal dopants. For instance, doping the silver cluster with a transition metal
atom such as Cu, Ti, Zn<sup>86</sup> or Ru<sup>87</sup> could modify the metal cluster-naphthalene interactions
and hence their electronic properties and binding with atoms and small molecules. As an
example among others, sensing properties can be improved, as well and storage ability of
small molecules such as H<sub>2</sub>.<sup>23</sup> In the astrophysical context, it would be interesting to consider
light metals such as Fe, Ti or Al which can actually be found in circumstellar or interstellar
dust. Of course, extending the chemical variability would make the structural search more
complex, and the present global search multi-method algorithm combining a computation-
ally efficient method such as DFTB still keeping the essential orbital character, and first
principle DFT, might be valuable.

Finally, beyond investigations based on structural optimization, molecular dynamics
studies would also bring valuable information concerning the rigid/flexible nature of the
structural configurations, isomerization, and more generally the influence of temperature on
various properties and in particular on the shifting or broadening of IR spectral features.

Acknowledgement

This work has been funded by the French "Agence Nationale de la Recherche" (ANR), project GROWNANO ANR-21-CE29-0001. This study has also been partially supported through the EUR grant NanoX ANR-17-EURE-0009 in the framework of the "Programme des Investissements d'Avenir". The authors thank the computing mesocenter CALMIP ("CAL cul en MIdi Pyrénées", UAR3667 of CNRS) for generous allocation of computer resources (project p17002).
**Supporting Information Available**

Figures S1 and S2 report geometries of Nap-Ag and Nap-Ag⁺ optimized with different functionals.

Figure S3 reports the experimental and computed (with different functionals) positions of the most intense vibrational modes of Nap-Ag⁺.

Figure S4 contains higher energy occupied molecular orbitals of Nap-Ag.

Figure S5 reports the energies of the different conformers organized in families of Nap-Ag₂ obtained after PTMC/DFTB and quench.

Figures S6 and S7 represent the most stable isomers of Nap-Ag₂ and Nap-Ag₈ and their relative energies at the DFTB and DFT level (B3LYP-D3BJ functional).

Figure S8 reports the frontier molecular orbitals of Nap-Agₙ and their energies computed with the B3LYP-D3BJ functional.

Table S1 contains the relative energies of conformers 1a, 1b and 1c of Nap-Ag at different levels of theory.

Table S2 contains the contribution of dispersion interactions to the Nap-Agₙ binding energies for n=1-8.

Table S3 contains Ag-Ag distances within Agₙ clusters with different functionals and Nap-Agₙ complexes with B3LYP-D3BJ.

Table S4 contains IE values of Nap-Agₙ clusters used in Figure 5.

Tables S5 and S6 contains VIP values used in Figure 7 and Figure 8.

Table S7 contains the energies of the HOMO and LUMO orbitals used in Figure 9. The gaps are reported in Table S8.

Table S9 contains the values of Mulliken and natural atomic charges on Ag atoms and clusters in Agₙ and Nap-Agₙ used to build Figure 6.

Table S10 contains the energies and intensities of the most intense modes of Nap-Agₙ (n=0-8), and of the modes of Agₙ.

The cartesian coordinates of the geometries of Nap-Agₙ (n=0-8) and Agₙ reported in Fig-
ures 1 and 3 are contained in the Zenodo database (10.5281/zenodo.14674090).

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