Influence of adsorption of gold and silver nanoclusters on structural, electronic, and nonlinear optical properties of pentacene-5,12-dione: a DFT study

The present study deals with the investigation of the change in the hyperpolarizability of Pentacene-2,5-dione (PD) on the introduction of the gold (Au) and silver (Ag) nanoclusters using the density functional theory (DFT). The involvement of the nanoclusters induces the intramolecular interactions, which is confirmed by the electrostatic potential plot and Mulliken charge distribution. The process of adsorption of metal clusters on the surface of PD is investigated by absorption spectra and the Raman spectra analysis. The global reactivity parameters validate a hike in the reactivity of the PD after the adsorption of Ag3 and Au3 nanoclusters. The study reported extraordinary enhancement in the hyperpolarizability of the metal nanoclusters adsorbed complexes. The high value of hyperpolarizability for PD-Ag3 (184.22 × 10−30esu) and PD-Au3 (2057.26 × 10−30esu) validates their applications in highly efficient NLO devices. The statistical calculation of radiative lifetime and light-harvesting efficiency reveals that probe PD can fruitfully contribute to the development of photo luminescent material and photosensitizer dye in dye-synthesized solar cells.


Introduction
Aromatic hydrocarbon is a well-known category of reactive compounds having sigma bonds and delocalized π electrons between the carbon atoms (Omidi and Dadsetani 2016). These consist of multiple benzene rings clubbed together forming polycyclic hydrocarbons. Such molecules have considerable interest among theoretical and experimental researchers due to their versatile structure and high reactivity. Many studies have been reported to work on nonlinear optical (NLO) activity of different classes of aromatic hydrocarbons like anthracenes (Yanxin et al. 2021), quinacridone (Khan et al. 2019), naphthalene (Alyar 2013), pyrene (Khan et al. 2022), benzopyrenes (Jayakrishnan et al. 2016), benzo-anthracene (Gott 1971), ovalene (Aryanpour et al. 2014), triphenylene (Gowda et al. 2019), chrysene (Tsague et al. 2022) and many more. The mentioned studies, thus, account for the high chemical reactivity of polycyclic hydrocarbons. Pentacene, on the other hand, is one of the classes of polycyclic aromatic hydrocarbons consisting of five linearly clubbed benzene rings (Chou and Cheng 2004). Pentacene and its derivatives have a number of applications in the development of organic thin-film transistors, organic NLO materials, solar cells, organic light-emitting diodes (OLEDs), etc. (Lee et al. 2003). Many studies have presented wide usage of Pentacene in the field of photovoltaics (Sadowski 2012;Srivastava and Tripathi 2022). Due to having high mobility, the derivatives of Pentacene are also used as p-type organic semiconductors (Kymissis et al. 2002). All the reported studies account for the high reactivity and applicability of the Pentacene and its derivatives in different branches of physical science. The major use of Pentacene and its derivatives was seen in the growth of the thin films (Ruiz et al. 2004). A study on Pentacene based radio frequency circuits has been reported (Baude et al. 2003). Pentacene and its compounds were also found to be used in the development of organic metal oxide semiconductor fieldeffect transistors (Kitamura and Arakawa 2008).
However, the adsorption of the organic compounds over the metal clusters has been of considerable interest to the researcher's community as the introduction of the metal nanoclusters has reportedly given immense enhancement to the electro-optical and chemical properties of the organic compounds (Amy et al. 2005). Atomic or molecular doping is also streaming field of material science that had led to advancement in technology (Tahmasebi et al. 2016;Zhu and Zhao 2022;Zhang et al. 2021;Li et al. 2022). Moreover, adsorbed and doped materials are proven more favourable in energy generating and storage applications like batteries and solar cells applications Wu et al. 2021;Tong et al. 2016;Mu et al. 2021;Zhang et al. 2022). Various studies have been reported for Pentacene from time to time. One such study targeting the enhanced hyperpolarizability of the Quinacridone after the adsorption of gold and silver nanoclusters has been reported and the results were highly appreciable (Felscia et al. 2018a). The study based on the adsorption studies of benzene, aniline and naphthylamine on reduced graphene oxides was also reported using experiments and theoretical density functional theory (DFT) (Yu et al. 2016). The development of photovoltaic cells with Pentacene adsorbed with fullerene (C 60 ) had been reported to improve the power efficiency of the cell by enhancing the short circuit current density (Pan and Rothberg 2007). The bonding between the gold and carbon atoms of Pentacene has been established using DFT and shed their applications in the second-order NLO applications (Yang et al. 2007). Studies with the substitution of gold atoms to Pentacene making complex Au 2 C 22 H 14 have also been reported to present the NLO responses of the complexes (Sun et al. 2009). NLO materials from alkali metal doped boron nitride cages are designed by many researchers (Maria et al. 2016(Maria et al. , 2017Munsif et al. 2018;Maria and Iqbal 2016a).
Thus, literature has a feast of kinds of studies reporting the NLO activity of Pentacene complexes with other metal atoms or clusters. One such derivative of pentacene namely Pentacene-2,5-dione (PD) has been considered for the present study. The study aims to establish the intensified NLO activity of the PD molecule after the adsorption of the silver (Ag 3 ) and gold (Au 3 ) metal nanoclusters. As the initial nucleation stage of silver and gold nanoparticle is the formation of the trimers (Ag 3 and Au 3 ) Felscia et al. 2019a) and numerous researches reporting adsorption studies of Ag 3 nanocluster has been accounted in the literature with tremendous rise in the NLO activities (Otaibi et al. 2022;Shakerzadeh et al. 2022). Thus, it is considered for the present study as the nanocluster. The chemical reactivity of the probe PD, PD-Ag 3 , and PD-Au 3 complexes was established by molecular electrostatic potential (MEP) surface and frontier molecular orbital (FMO) parameters. Vibrational spectra also presented the adsorption site of the nanoclusters over the surface of the PD molecule and highlights the description of the adsorption. The intramolecular charge transfer (ICT) was also identified between the metal nanocluster and the PD molecule.

Computational methods
Hartree-Fock is an ab-initio method with good accuracy in calculating nonlinear optical response. However, all the "pure" functionals have a fraction of HF non-local exchange energy replacing a similar fraction from the DFT local exchange energy. DFT on the other hand is known to be less time taking and more precise. Thus, DFT was preferred for all the ground state and excited state quantum chemical calculations. The geometry optimization of probe PD, PD-Ag 3 , and PD-Au 3 was performed using B3LYP/6-311-G(++d,p), and B3PW91/ LANL2DZ (Los Alamos National Laboratory double zeta) level of theory in Gaussian 09 program (Frisch 2010). The B3LYP/6-311-G(++d,p) is large basis set used for the ground state and excited state calculations of organic compounds whereas B3PW91/LANL2DZ basis set is considered more accurate for quantum mechanical calculations of metal clusters and numerous studies have been reported to establish the metal-to-molecule interaction using the same pair of functions (Cramer and Truhlar 2009;Tekarli et al. 2009;Felscia et al. 2019b). All the calculations of the PD molecule are done with singlet state. The availability of the unpaired electrons imparts to the doublet state. For PD-Ag 3 and PD-Au 3 , the calculations are done in doublet state. This might be due to the availability of the unpaired electrons in Ag and Au atoms. The ground state optimization were carried out till threshold values of maximum force as 0.00045, RMS force 0.0003, maximum displacement 0.0018 and RMS displacement 0.0012 without any additional information sets. For TD-SCF calculations, convergence on RMS density matrix was at 1.00 × 10 -8 , convergence on maximum density matrix was at 1.00 × 10 -6 . The basis set superposition error (BSSE) was computed for the PD-Ag 3 and PD-Au 3 by B3PW91/LANL2DZ with counterpoise = 2 procedure (Boys and Bernardi 1970). The empirical dispersion term for the PD-Ag 3 and PD-Au 3 using "Dispersion energy = Grimme GD3" procedure for B3PW91/LANL2DZ set of functions for getting the better understanding of the interactions between the molecule and the nanoclusters (Grimme et al. 2010). The natural bond orbital (NBO) analysis was also performed for PD-Ag 3 , and PD-Au 3 for the prediction of the intramolecular interactions (Weinhold and Landis 2005). The chemical reactivity of the probe PD, PD-Ag 3 , and PD-Au 3 was established using MEP surface and global reactivity parameters. Different reactivity parameters like bandgap (ΔE), ionization potential (IP), electron affinity (EA), chemical potential (CP), electronegativity (χ), are calculated with the help of Koopman's equations given below (Gritsenko and Baerends 2009;Yadav et al. 2021;Ojo et al. 2020;Akinyele et al. 2022): The vibrational spectra was computed for the identification of the adsorption site of metal nanoclusters on PD. The Raman intensity was calculated for high frequency modes using expression: where I is Raman intensity of the vibrational mode, f is a constant with value 10 -12 , ν o has value 9398.5 cm −1 . ν i and S i is the vibrational wavenumber and Raman activity of selected mode respectively. h is Planck constant with value 4.1357 × 10 −15 eV K −1 , c is speed of light having value 3 × 10 8 m/s, K is Boltzmann constant with value 8.6173 × 10 -5 eV K −1 , and T is temperature 293.5 K.
The NLO activity of the probe and metal nanoclusters adsorbed complexes was developed by polar frequency calculations. The tensor components were obtained for computing total isotropic polarizability (α total ), and anisotropy of polarizability (Δα) and first order hyperpolarizability (β total ) using finite field theory approach (Yadav et al. 2021). These parameters are computed using following expression: where α xx , α yy , and, α zz are the tensor components of polarizability and β xxx , β yyy , and β zzz are the tensor components of hyperpolarizability.

Structure and charge analysis
PD has planar geometry with C1 point group symmetry due to which the dipole moment vectors of the atoms cancel each other (Kirtman et al. 1998). The 2O and 1O attached to the opposite sides give rise to a low magnitude of the dipole moment of 0.0002 Debye for the PD molecule. After the adsorption of Ag 3 and Au 3 nanoclusters, a rise in the dipole moment of the adsorbed complexes was observed due to their unsymmetrical structures. The value of dipole moment for PD-Ag 3 and PD-Au 3 was observed as 8.71 Debye and 3.96 Debye respectively. The high value of dipole moment was probably due to the larger differences between electronegativities of the donor and acceptor moieties present in the complexes (Lakhera et al. 2021;Rana et al. 2016;Yang et al. 2022;Wu et al. 2022;. The rise in the dipole moment shows the enhanced chemical reactivity of the adsorbed complexes. The parameters obtained after the structure optimization of the PD adsorbed with Ag 2 , Ag 4 , Au 2 , and Au 4 better supported our selection of the trimer for the present study. The dipole moment for the optimized geometries of PD-Ag 2 , PD-Ag 4 , PD-Au 2 , and PD-Au 4 were calculated as 2.17, 4.17, 3.7, and 2.5 Debye respectively. The values of the dipole moment were comparatively lower than the value of dipole moment of PD-Ag 3 and PD-Au 3 . The optimized geometries of the probe PD, and PD after adsorption of Ag 3 and Au 3 nanoclusters are illustrated in Fig. 1. The calculated empirical dispersion value of PD-Ag 3 is -33.711 kcal/mol and the calculated empirical dispersion value of PD-Au 3 is -32.014 kcal/mol. The comparison of these energy shows the higher empirical correction was added to the PD-Ag 3 and PD-Au 3 was quite stable than former. To get the better validation of the interaction between the molecule and the nanocluster, the interaction energy was computed using the following expression (Gordon and Jensen 1996): where E int is the interaction energy between the PD and nanocluster (Ag 3 and Au 3 ), E complex is the energy of the complex PD-Ag 3 and PD-Au 3 , E component is the energy of the components of complex (say PD and Ag 3 , Au 3). The computed values of interaction energies of PD-Ag 3 and PD-Au 3 are − 13.74 kcal/mol and − 18.19 kcal/mol respectively. The more negative interaction energy is corresponding to the more stable complex. That means PD-Au 3 is higher than PD-Ag 3. The BSSE energy of PD-Ag 3 was 0.00261 kcal/mol and PD-Au 3 was 0.00372 kcal/mol. The bond lengths of the PD, PD-Ag 3 , and PD-Au 3 are mentioned in SD 1. The bond length of 1O=13C and 2O=14C of the carbonyl group in PD has lower bond lengths than the C=C bonds associated with the PD molecule. The C-H bonds have lower bond lengths showing the stability of the C-H bonds. The shorter the bond length, the lower will be the chances of bond dissociation, and the longer the bond, the higher will be the chances of easy dissociating of the bond (Lakhera et al. 2022a). The bond dissociation will give rise to the charge cloud resulting in ICT. Similarly, the bond angles (SD 2) had a large variation in magnitudes between the C-H bonds and C=O bonds. High magnitudes of the bond angles lead to easier bond dissociation. After the adsorption of the metal clusters on the surface of the PD molecule, there seems a rise in the bond length of the C=O bonds of the carbonyl group. The larger bond are weaker and need less energy to dissociate and thus, they can easily be dissociated with very low amount of energy. This shows the inverse proportionality of bond length with the stability of the bond. Or it can be considered that the bonds between the nanoclusters i.e., Au and Ag atoms in their respective nanoclusters are bonded with larger bonds. Thus, the bonds will get easily dissociated and give free electron pairs. This highlights the participation of nanoclusters in inducing the intramolecular interactions . The optimization parameters suggest that there is a possibility of ICT between the PD and the metal nano-  the intramolecular interactions between these two parts of PD. After the introduction of Ag 3 and Au 3 nanoclusters, the involvement of the Ag and Au atoms in the intramolecular interactions was observed. The charge distribution of PD-Ag 3 and PD-Au 3 complex was distributed in ranges ± 0.669 e and ± 0.806 e respectively. The Ag atoms 37Ag (0.182 e), 38Ag (0.034 e), and 39Ag (0.064 e) contribute to the positive charge indicating the participation of the Ag 3 nanocluster as a donor moiety. The Au 3 atoms 37Au (0.154 e), 38Au (− 0.143 e), and 39Au (− 0.13 e) impart positive as well as negative to the overall charge distribution of the complex. The variation of the charges between the Au atoms and carbon and oxygen atoms of the carbonyl groups shows the intramolecular interactions between the Au 3 nanocluster and the carbonyl groups. Thus, the charge distribution highlights the enhanced intramolecular interactions in PD molecules after the adsorption of the Ag 3 and Au 3 nanoclusters.

MEP surface analysis
MEP surface is used to illustrate the ICT of molecules. These surfaces are used to locate the areas with electron excess and electron deficiency of the molecule which are responsible for inducing ICT within the molecule (Oyeneyin et al. 2022). There are five colors that a MEP surface constitutes and they are in a sequence from negative to positive nature as red < yellow < green < light blue < dark blue. The moieties over which the surface is of red color are highly negative or electronegative in nature whereas the dark blue surface indicates the positive or electropositive moieties. Green color indicates the neutral part of the molecule or the region that doesn't participate in the intramolecular interactions. Yellow is slightly electronegative whereas sky blue is slightly electropositive in nature. The moieties with donor properties are known as positive regions and are indicated by blue color while the acceptor moieties are called negative and are indicated by red color (Lakhera et al. 2022a). The potential range of the MEP surface is indicated by the color band at the top of  Fig. 2a validates the positive nature of C-H bonds of the benzene rings and the negative nature of 1O=13C and 2O=14C bonds of the carbonyl group. The electrostatic potential range for probe PD is ± 5.004 × 10 -2 electrons/Å 3 . The hydrogen atoms are highly electropositive and oxygen atoms are highly electronegative. The MEP map identifies the transportation of heavily accumulated charge from the C-H bonds towards the C=O bonds of the carbonyl groups. Adsorption of Ag and Au nanoclusters over the PD molecule induces a redistribution of electron density. The involvement of the Ag and Au nanoclusters in ICT within the PD-Ag 3 and PD-Au 3 complexes was identified by the MEP map of PD-Ag 3 and PD-Au 3 shown in Fig. 2b, c respectively. It is observed that the blue region over the C-H bonds of the PD molecule is shifted over the Ag 3 nanocluster after the adsorption of the Ag 3 nanocluster. Thus, the Ag 3 nanocluster acts as a donor part of the PD-Ag 3 complex, and ICT is seen to act from Ag 3 towards the carbonyl groups. This supports the results analyzed from Mulliken charge variation. A similar kind of ICT is seen in the PD-Au 3 complex where the charge cloud dislocated from the Au 3 nanocluster to carbonyl groups. The availability of the donor and acceptor moieties within the PD, PD-Ag 3 , and PD-Au 3 validates the enhanced ICT within the PD molecule after the introduction of the Ag 3 and Au 3 metal nanoclusters. This shows the high chemical reactivity of PD, PD-Ag 3 , and PD-Au 3 as mentioned by structural parameters.

Natural bond orbital (NBO) analysis
NBO analyses were performed to describe the intramolecular/intermolecular electronic interactions (Lakhera et al. 2022b). The charge delocalization of donor NBO towards acceptor NBO give rise to the higher degree of conjugation leading to the stability of the complex. The second order perturbation approach was used for computing the stabilization energy (E(2)) corresponding to each donor (i) and acceptor (j) atom. The E(2) corresponding to the delocalization of each i → j were calculated using the expression: where F(i,j) are the Fock matrix element between i and j NBO orbitals, E j and E i are the energies of the acceptor and donor NBOs. The interactions with higher values of E(2)for PD-Ag 3 and PD-Au 3 are listed in Table 1. In case of PD-Ag 3 , second order perturbation theory analysis of NBO, higher values of E(2) were obtained for interactions of 37Ag with the atoms of PD molecule. This shows the participation of atom 37Ag in charge dislocation. The maximum value of stabilization energy was observed for the interaction between 21C and 37Ag. On the other hand, the interaction between the 21C and 37Au has the maximum value of stabilization energy of 6.74 kcal/mol for PD-Au 3 . Thus, higher value of stabilization was observed for PD-Au 3 which shows the higher intramolecular charge transfer between donor and acceptor moieties of PD-Au 3 as compared to PD-Ag 3.

Molecular orbital analysis
The FMO parameters are derived from the energies corresponding to the highest occupied and lowest unoccupied molecular orbitals (HOMO-LUMO). These parameters are computed to confirm the chemical reactivity of the molecules ). All the computed FMO parameters are listed in Table 2. The energy gap or band gap (ΔE) is the virtue  (Lakhera et al. 2022c). It is seen that the ΔE for probe PD was 2.14 eV but a decrease in the ΔE was observed when the metal nanoclusters are adsorbed by the PD molecule. Thus, the low value of ΔE for PD-Ag 3 (2.01 eV) and PD-Au 3 (1.02 eV) shows that the electrons of PD can easily jump up to the higher energy state when combined with metal nanoclusters. However, the value of ΔE for PD-Au 3 is lower than that of PD-Ag 3. The lower bandgap has a greater probability of the free charge transiting to higher energy states. This shows that the PD-Au 3 might have larger absorbance than PD-Ag 3. The ionization potential (IP) of a molecule should be low to remove the electrons easily from the outermost shell of the donor atoms. PD-Au 3 (4.91 eV) has the lowest value of IP than the probe PD (5.75 eV) and PD-Ag 3 (5.23 eV). The high value of electron affinity (EA) shows the greater tendency of the atoms to gain electrons. The EA is highest for PD-Au 3 (3.89 eV). The chemical potential (CP) shows the high tendency of the molecules to undergo charge transfer and molecules having a high value of CP are highly reactive. PD, PD-Ag 3 and PD-Au 3 have the value of CP mutually close showing the high chemical reactivity of the three title molecules. The high value of electronegativity (χ) for PD-Ag 3 as compared to PD-Ag 3 shows how easily Au 3 adsorbed complex attracts the shared electrons. The distribution of the HOMO-LUMO surface over the title molecules is illustrated in Fig. 3a-c. The red surface indicates the positive and the green surface indicates the negative phases in molecular orbital wave function. The HOMO-LUMO surface is uniformly distributed over the geometry of PD. Larger positive and negative surfaces over the metal nanoclusters in HOMO are shifted over the benzene rings in LUMO. This shifting of surfaces shows that ICT exists from nanoclusters to PD molecules as stated by structural analysis. The chemical reactivity of PD undergoes enhancement as the Ag 3 and Au 3 metal nanoclusters get adsorbed to the surface of the PD molecule. Thus, the analysis of the FMO parameters shows that the introduction of Ag 3 and Au 3 nanoclusters to PD intensifies its chemical reactivity.

Absorption analysis
The absorption spectra for PD, PD-Ag 3 , PD-Au 3 compounds are illustrated in Fig. 4 and the details of the transitions had been listed in SD 3. The transition S 0 → S 1 of PD occurred at wavelength 561 nm was majorly responsible for the broad absorption band of PD. The oscillator strength (f) for this transition was observed as 0.719 and the excitation energy for this mode was computed as 2.2 eV. The high value of excitation energy and the f reveals the high reactivity of the PD. It was observed that the introduction of metal nanoclusters to the PD shows a rise in the intensity of the transitions and bathochromic shift of wavelength. Broad spectra for PD-Ag 3 and PD-Au 3 were seen to range between 500 and 3000 nm. The transition S 0 → S 6 for PD-Ag 3 and PD-Au 3 occurred at wavelengths of 662 and 637 nm respectively were the crucial transition (transitions having the highest oscillator strength) for both of spectra. Higher values of oscillator strength indicate a higher possibility of the transition occurring. Therefore, it can be considered that the transition in PD-Au 3 is most likely to occur than in PD-Ag 3 . Moreover, the rise in the intensity of the absorption in PD-Au 3 also indicates the involvement of the nanocluster in the ICT. This creates a close relationship between the ICT developed by the HOMO-LUMO surface distribution in the molecular orbital analysis (Li et al. 2020;Hou et al. 2014;Chen et al. 2005). As the HOMO densities plot indicates the availability of excess electrons in PD-Au 3 , it can be said that PD-Au 3 possesses more possibility of undergoing ICT between PD and Au 3 . The absorbance shifts in the wavelength and intensity were mainly due to the interference in the hyperconjugation of the bonds. This leads to the rise in the count of partial double bonds (π bonds) giving rise to lone pair of electrons. Thus, the hyperconjugation in the metal clusters results in absorbance shifts. Moreover, the rise in conjugation is proportional to the bond lengths. This also makes a good agreement with the higher bond lengths obtained for the metal clusters in structural analysis. The higher absorbance intensity was also in accord with band gap of the complex.

Vibrational analysis
The nature of adsorption of metal nanoclusters on the surface of the PD molecule was established by computing vibrational spectra using the B3PW91/LANL2DZ basis set. The important vibrational modes and the assignments are illustrated in Fig. 5 and listed in SD 3. We have observed a rise in the intensities of different vibrational modes after the introduction of the metal nanoclusters. This rise seems to confirm the enhancement of the Fig. 4 Absorption spectra of PD, PD-Ag 3 and PD-Au 3 computed using B3PW91/LANL2DZ basis set. Insight of Fig. 4 indicates the crucial peaks of PD-Ag 3 and PD-Au 3 with their wavelength and oscillator strength chemical reactivity of the PD after adsorption of the metal nanoclusters. The low frequency modes for the vibration of metal nanoclusters (113.8 cm −1 for PD-Ag 3 and 113.8 cm −1 and 160.56 cm −1 for PD-Au 3 ) were observed showing adsorption interaction between the PD and metal nanoclusters. The out of plane bending of the geometry of PD was observed at 541.8, 549.94, 620.81, and 698.17 cm −1 . Contrastingly, the out of plane vibrations for PD-Ag 3 are observed at comparatively higher frequencies 556.9, 628.86, 697.36, 740.99, and 793.26 cm −1 . Similar rise in the frequency was observed for the out of plane vibrational modes for PD-Au 3 at 535. 59, 548.85, 629.21, 696.78, 739.27, 778.67 cm −1 . The carbonyl groups of the PD show ν CO mode at 1695.05 cm −1 . The ν CO mode for PD-Ag 3 and PD-Au 3 was identified at 1586.11 cm −1 and 1584.77 cm −1 respectively. Stretching of C=C bond of benzene ring for PD-Ag 3 (1412.14 cm −1 , and 1418.92 cm −1 ) and PD-Au 3 (1414.98 cm −1 , and 1427.09 cm −1 ) confirms the potential site for adsorption in each case.

NLO analysis
NLO materials interacting with electric field lines must have a high polarization density. When a material is kept in the homogeneous electric field, the energy possessed by the material is expanded as Taylor's series expansion where the α and β are the coefficients of the Taylor series expansion (Hutchings et al. 1992). These coefficients are correlated to NLO activity as the high value of the coefficient of high order derivatives leads to high NLO activity of the molecule. Thus, to predict the NLO activity, α total , Δα and β total are computed for the title molecules. All the computed tensor components of the α total , Δα and Vibrational spectra for the PD, PD-Ag 3 and PD-Au 3 molecule computed using B3PW91/ LANL2DZ basis set (Symmetric stretching-ν, torsional bending in plane (scissoring)-δ, twisting-τ, rocking-ρ, and wagging-ω, stretching of C-C bonds in benzene-λ) β total for PD, PD-Ag 3 , and PD-Au 3 molecules are mentioned in SD 3, and SD 4 respectively and the values of polarizability parameters are mentioned in Table 3. The value of α total is computed as 54.73 × 10 −24 esu for probe PD molecule but after the adsorption of Ag 3 and Au 3 nanoclusters, this value was increased to 129.79 × 10 -24 and 108.65 × 10 −24 esu respectively. These values are approximately twice the value of α total for probe PD molecule. The values of Δα for PD-Ag 3 (532.44 × 10 −24 esu) and PD-Au 3 (436.42 × 10 −24 esu) are higher than the Δα for PD (211.76 × 10 −24 esu). A very low value of β total for probe PD (0.000181 × 10 -30 esu) was computed but an extraordinary rise in the values of the β total was observed after the adsorption of metal nanoclusters. The values of β total for PD-Ag 3 and PD-Au 3 were observed as 184.22 × 10 −30 esu and 2057.26 × 10 −30 esu. These values are 10,117,790 and 11,427,777 times higher than the β total for probe PD. Two-level mode was also used for the validation of the NLO activity of complex. The dependency of hyperpolarizability on the dominating factors was examined by the two-level mode by using expression of hyperpolarizability (Maria and Iqbal 2016b): where Δµ is the difference between the dipole moment of ground state and crucial excited state, f is the oscillator strength of the crucial transition obtained in UV-Vis spectra. Crucial transition is the transition having the higher value of oscillator strength. ΔE is the excitation energy of the crucial transition. For both PD-Ag 3 and PD-Au 3 , S 0 → S 6 was the crucial transition with f values equal to 0.1973 and 0.374 respectively. According to two-level mode, the hyperpolarizability shares the direct proportionality to the f values, in our case f was larger for PD-Au 3 . Thus, PD-Au 3 was verified to have higher value of β total and hence high NLO activity. Validation of the findings was done by comparing the β total of PD-Ag 2 , PD-Ag 4 , PD-Au 2 , and PD-Au 4 with that of PD-Ag 3 and PD-Au 3 . The values of β total of PD-Ag 2 , and PD-Ag 4 were 481.57 × 10 −30 esu, and 149.36 × 10 −30 esu respectively. PD-Ag 3 has higher β total than PD-Ag 4 but less than that of PD-Ag 2. In case of Au nanoclusters, the values of β total for PD-Au 2 , and PD-Au 4 were 10.66 × 10 −30 esu, and 59.72 × 10 −30 esu respectively which are comparatively much lower than the PD-Au 3 . This shows that PD give promising NLO activity when adsorbed with the Au trimer. The value of β total for pure Ag 3 and Au 3 clusters were computed as 0.8 × 10 −30 esu, and 73.77 × 10 −30 esu respectively. There are some studies in the literature that had reported high NLO activity of the pure nanoclusters. But pure Ag 3 and Au 3 clusters have significantly lower NLO responses. In comparison with the generally used reference NLO material Urea (0.781 × 10 −30 esu), the value of β total for PD-Ag 3 and PD-Au 3 are 236 and 2637 times higher (Cassidy et al. 1979). Thus, this comparison is fairly enough to justify that the PD can act as an excellent NLO material when adsorbed with Ag 3 and Au 3 nanoclusters (Fig. 6).

Radiative and light harvesting properties
The absorption spectra were computed for the probe PD molecule to get an idea about the electronic transitions. The spectra comprised of a broad strong absorption band identified with its peak at 361 nm wavelength. The transition S 0 → S 1 occurred at the peak wavelength with f of 0.719 and excitation energy 2.20 eV. The other two transitions S 0 → S 2 and S 0 → S 3 occurred at wavelengths 246 and 246 nm respectively. The high excitation energy highlights the possibility of the π → π * and n → π * nature of the S 0 → S 1 transition. Thus, the existence of such transitions shows the ICT in the PD molecule. The absorption spectra of PD was also used to establish the radiative and light-harvesting property of the probe molecule. The radiative lifetime (τ) was computed by below given formula (Felscia et al. 2018b): where c is the speed of light and f and E are the oscillator strength and the excitation energy obtained in the absorption spectra respectively. The radiative lifetime accounts for the nature of transitions possessed by the molecules i.e., whether the molecules emit radiation during the transitions or the transitions are non-radiative. The former is called emissive transition and the latter is called non-emissive transition. However, the transitions having lifetime values larger than 10 are non-radiative. The electronic transitions for which the τ value is less than 10 are known to be radiative and these transitions eject energy in the form of photons (Poor and Flores 2014). Thus, for the PD molecule, the value of τ is computed to be 5.9 nm ~ 6 nm. The τ < 10 for PD indicates that the transition S 0 → S 1 occurred between the HOMO-LUMO of PD was radiative and shows its nature to possess photoluminescence (Bünzli et al. 2010). Thus, this establishes the potent applicability of PD molecules as an active luminescent material.
f is also used for calculating the light harvesting efficiency (LHE) for PD using the below mentioned formula (Lakhera et al. 2022d): LHE measures the efficiency of any material to increase the ability of any solar cell to convert light energy into electrical energy. Thus, the applicability of the molecule to be used as photosensitizer dye in Dye-Sensitizer Solar Cells (DSSC) is statistically explained by LHE (Mary et al. 2019). For PD, the LHE is computed to be 80.91. The adsorption of Ag 3 and Au 3 on the PD, gave a decrease in the LHE of the compounds PD-Ag 3 (27%) and PD-Au 3 (20%). This can be due to the reflective nature of the Ag and Au. These materials do not absorb light up to the extent that is required for solar cells, and therefore give a lustrous glare. Thus, PD can convert 80% of the light incident on it into electrical energy. Hence, PD synthesized dye can lead to tremendous enhancement of the efficiency of solar cells.

Conclusion
A complete study of quantum mechanical properties of PD in probe state and adsorbed with Ag 3 and Au 3 nanoclusters were reported in the paper. The adsorption sites of the nanoclusters were identified by the high Raman intensity modes in vibrational spectra. The PD was found highly chemically reactive right after the adsorption of the Ag 3 and Au 3 nanoclusters and their chemical reactivity was verified using FMO parameters. The MEP surface over the nanoclusters also validated the electropositive character of nanoclusters and established their participation in inducing the ICT within the complex structures. In particular, the DFT calculations indicate the tremendous rise in the NLO activity of the PD after the adsorption of the Ag 3 and Au 3 nanoclusters. Thus, it can be concluded that the studied complexes hold considerable NLO activity and can be recommended for the high-tech applications of efficient NLO materials. Also, the experimental design of the studied complexes will be surely generative. The low value of τ signifies the radiative emission of photons resulting in the application of PD as a potent photoluminescent molecule. Employment of PD as a photosensitizer dye was noted by its high LHE. Thus, the probe PD can better act as a photoluminescent material as well as a dye in DSSC.