A DFT study of the chemical and optical properties of 7-atom Ag–X [X = Li, Na] nanoalloys for potential applications in opto-electronics and catalysis

Abstract

In this paper, Ag atoms are substituted by X (Li, Na) atoms to form Ag_mX_(7−m) clusters to explore their electronic, chemical and optical properties in the framework of density functional theory (DFT). The clusters are geometrically optimized without imposing symmetry and later, vibrational analysis is carried out to test the stability of the optimized structures. The calculation of ionization potential and electron affinity asserted that the Li and Na doped bimetallic clusters (especially, Ag₄Li₃ and Ag₃Li₄) are very stable in the neutral state, but their anions are expected to be very reactive. The calculated absorption spectra of the Ag_mX_7−m clusters have revealed that the doping of Li and Na has made the absorption band wider with regards to undoped Ag₇ clusters. Therefore, this work suggests that Li and Na doping (especially, Ag₄X₃, Ag₃X₄ and Ag₂X₅ clusters) will result in improvement of the absorption band in the 1–5 eV range, which is the prime absorption band for opto-electronic devices such as solar cells.

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1. Introduction

Bimetallic nanoclusters, which are the aggregation of two types of metal atoms of nanoparticle size, have been utilized as key components in many catalytic, optical and magnetic devices. They have been subject to the interest of both theoretical and experimental researchers for their distinct physical and chemical properties.¹ Presently, there is an growing interest in bimetallic nanoparticles, compared to monometallic nanoparticles because bimetallization can offer space for improvement in optical, catalytic and magnetic performance over the original pure mono-metal nanoparticles and can create new properties. Also, molecular tuning of these bimetallic nanoclusters may give rise to novel properties which are not realized in bulk or, monometallic nanoparticles.^2,3 The properties of these bimetallic nanoclusters are not solely size-dependent, rather the chemical composition and molecular arrangement significantly affect their specific structural,^4–7 electronic,^5,7 optical^4,8 and magnetic properties⁹ which has led to a technological interest in catalysis^10,11 and also in the application and development of new nano-devices for electronics.^2,12

Among the hundreds of bimetallic nanoalloys explored till date, Ag–X [X = Li, Na] nanoalloys are of special interest because of the special chemical and optical feature of both silver and alkali metals nanoparticles. In research history of nanomaterials, silver is the most commonly used materials due to their comparatively low optical losses in the visible and near-infrared (NIR) region. For example, the usages of silver have been demonstrated as negative refractive index material, hyperlens,¹³ superlens¹⁴ and optical transmission.¹⁵ However, when the nano-fabrication is concerned, silver degrades comparatively quickly and the thickness threshold for uniform continuous films is around 12–13 nm, which is a major barrier for transformation optic (TO) and several other micro and nano-devices.^16,17 In addition, silver's dependency on the roughness of the surface with regards to optical losses has also reduced its viability in applications.¹⁸ Apart from the technical disadvantages mentioned so far, the main demerits of silver is their relatively high prices and limitation in resources, which eventually render them unsuitable for commercial applications. On the other hand, amongst the nanometals reported to date for their plasmonic potential, lithium, sodium and potassium have shown to possess the highest absorption efficiency (Q_abs), coupled with very low inter-band transition losses at optical frequencies.^19,20 Of particular merit, these transition losses have been noted to be comparable or surpass that of silver and gold. This is coupled with the additional advantage of exhibiting the strongest free-electron-like-behavior, which result in very prominent surface plasmon resonance (SPR) in visible-UV range.¹⁸ The only drawback that had been restricting alkali metals to be used extensively in nanotechnology is their extreme reactive nature towards air and water. Therefore, alloy containing silver and alkali metals will allow us to use the excellent plasmonic properties of alkali metals, whereas silver atoms can work as the screening to capping the alkali metals to restrict their chemically reactive nature. Hence it is expected that this Ag–X nanoalloy can be an excellent improvement over the bare silver nanoparticles.

In order to exploring the chemical and optical properties of the Ag–X nanoalloys, we have picked up the decahedral shape for its special chemical and optical features. Decahedral is a special one being the intermediate building blocks for rods and wire shaped nanoparticles.²¹ Moreover, their remarkable optical properties has made decahedral silver nanoparticle a popular commercial product (such as SCIVENTION's 35–120 nm sized decahedral silver) for the opto-electronic, catalytic and biological applications.^21,22 In our current work we have used the 7-atoms decahedral Ag₇ structures with D_5h symmetry as the quantum model, which is a reported global minimum geometry for 7 atoms silver, lithium and sodium as well.^23,24 Later silver atoms have been replaced by the X atoms to form Ag_mX_(7−m) nanoalloys. In our previous work^25,26 the electronic, chemical and optical properties of Ag–X [X = Li, Na, K] nanoalloys were explored in the framework of density functional theory (DFT). In that work, single X atom was added by replacing an silver atom from the 13-atoms decahedral silver cluster; hence only 12 : 1 ratio for Ag : X was checked. In contrary, in our current work all the mixing ratios in between Ag : X = 6 : 1 to Ag : X = 1 : 6 are explored to find out the best fit alloying ratio. Apart from our previous reports, several articles on photoionization spectroscopy of metal dimers including Ag–Li,^27,28 Ag–Na,²⁹ Ag–K³⁰ have been published till date but to our knowledge this is the first report on very small Ag–X bimetallic clusters of less than 1 nm diameter size, where a wide range of mixing ratios have been reported.

In this paper, a systematic investigation of electronic and optical properties of doped neutral clusters of Ag_mX_(7−m) is explored against its potential for opto-electronic and catalytic applications. For this purpose, m = 1–6 Ag atom has been replaced by an alkali metal atom (X = Li, Na) to form Ag_mX_(7−m) bimetallic clusters. Using these geometrically optimized structures, DFT based calculations of binding energy, HOMO–LUMO gap; vertical ionization potential (VIP) and vertical electron affinity (VEA) are carried out to characterize the stability and chemical inertness of the doped bimetallic clusters. TDDFT calculation has been carried out to predict the optical spectra of the clusters, which is then followed by the partial density of states (PDOS) calculations.

In the following section, a brief description of the computational method will be provided. Then, the structural and electronic properties will be presented, followed by optical spectrum and PDOS of the clusters.

2. Computational method

In this study, the investigation of geometrical and energetic stabilities and optical properties of the doped Ag_mX_(7−m) bimetallic structures are investigated using the density functional spin-polarized calculations using DMol3 Accelrys Inc. code.^31,32 All geometrical structures of the neutral clusters are optimized without imposing any symmetry or geometry constrains. Calculations have been performed using the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional.³³ The Kohn–Sham equation was expanded in a double numeric quality basis set (DNP) with polarization functions. The valence configurations of Ag, Li and Na are 4d¹⁰5s¹, 1s²2s¹ and 2p⁶3s¹, respectively; hence the multiplicity is 2 for all the neutral Ag_mX_7−m clusters. To consider the relativistic effect, the semi-core pseudo-potentials³⁴ are used for the treatment of the core electrons of the doped clusters. The orbital cut off range and Fermi smearing were selected as 5.0 Å and 0.001 Ha respectively. The self-consistent-field (SCF) procedures were performed with a convergence criterion of 10⁻⁶ a.u. The energy, maximum force and maximum displacement convergence were set as 10⁻⁶ Ha, 0.002 Ha Å⁻¹ and 0.005 Å respectively. The ALDA kernal exchange co-relation method was employed with TDDFT for calculating the optical excitation spectra.³⁵ The absorption spectra presented in the figures below give the oscillator strength as a function of the excitation energy, together with a curve obtained by Lorentzian broadening.

3. Structural and energetic stability

The first aspect of investigation is to ensure the geometric and energetic stability of the Ag–X clusters. For the quantum model, a 7-atom decahedron cluster with D_5h symmetry was selected, where silver atoms from Ag₇ was replaced to form Ag_mX_7−m bimetallic clusters. The variations are shown in Fig. 1. The decahedron with D_5h symmetry has been identified as the lowest-energy structure for Ag₇, Li₇ and Na₇ by other researchers. For alloys, we have only considered the decahedron structure, without any symmetry constraints, because we are interested in characterizing the changes in electronic, chemical, optical properties when Ag atoms are substituted by Li or Na atoms. Thus, the scope addressing the energy considerations specific to substitutions to the Ag atoms in the decahedral geometry. Fig. 1 and 2 shows all the doping positions and lowest energy isomers for 7 atoms Ag_mX_7−m nanoclusters along with their respective binding energies (BE). Ag₇, Li₇ and Na₇ clusters have the geometrical global minima with D_5h symmetry with binding energies of 9.61 eV, 6.41 eV and 4.46 eV respectively which is in accordance with the previous reports.^23–26 Among the same doped numbered groups, the structures with highest binding energies, i.e. panels b, d, j, p, s, and v in Fig. 1 and panels b, d, j, n, s and v in Fig. 2, are selected for further electronic, chemical and optical properties' calculations. It was instructive for us at this stage, to conduct confirmation of the stability for the pure and doped clusters through harmonic vibrational frequency calculations. For this procedure, the stability of the clusters was confirmed by the absence of imaginary frequencies. The lowest and highest vibrational frequencies of the clusters are charted in Table 1.

Fig. 1 Lowest-energy structures for 7-atoms Ag_mLi_7−m clusters. Point group symmetry and binding energy are given. Li and Ag atoms are in red and green respectively.

Fig. 2 Lowest-energy structures for 7-atoms Ag_mNa_7−m clusters. Point group symmetry and binding energy are given. Na and Ag atoms are in red and green respectively.

Table 1 Lowest and highest vibrational frequencies of the Ag_mX_7−m nanoclusters

Compound	Lowest vibrational frequency cm^−1	Highest vibrational frequency cm^−1	Compound	Lowest vibrational frequency cm^−1	Highest vibrational frequency cm^−1
Ag7	40.41	158.24	Ag7	40.41	158.24
Ag6Li1	26.67	334.64	Ag6Na1	29.03	156.53
Ag5Li2	29.13	351.05	Ag5Na2	23.42	182.25
Ag4Li3	39.37	346.62	Ag4Na3	45.20	186.80
Ag3Li4	44.76	327.05	Ag3Na4	41.03	169.52
Ag2Li5	63.65	332.56	Ag2Na5	45.90	163.90
Ag1Li6	83.70	350.81	Ag1Na6	47.85	155.89
Li7	60.58	313.52	Na7	33.87	176.62

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4. Electronic and chemical properties

After discussing the geometrical structure and stability of the doped clusters in the previous section, now we focus our attention towards the electronic structure of these doped clusters and for that Tables 2 and 3 are compiled with binding energy (BE), ionization potential (IP), electron affinity (EA) and HOMO–LUMO gaps of the entire Ag_mX_7−m nanoclusters. In times of calculating IP and EA, the ionized clusters are of same geometry of the neutral clusters; hence the IP and EA of the clusters are actually vertical ionization potential and vertical electron affinity. At this point, before moving towards their electronic and chemical properties, let's first make sure that our functional basis sets have calculated the data perfectly. From the data provided in Tables 2 and 3, it is evident that Ag₇ is showing binding energy, VIP, VEA and HOMO–LUMO gap of 9.61, 6.43, 1.34 and 0.34 eV respectively, which is a fine match with previous reports.^24,36–38 Similarly, the electronic and chemical parameters of Li and Na charted in the table are found to be agreed with the previous reports.^39–42

Table 2 Binding energy (BE), vertical ionization potential (VIP), vertical electron affinity (VEA) and HOMO–LUMO gaps of Ag_mLi_7−m clusters. All values are in eV

Compounds	Binding energy	Vertical ionization potential	Vertical electron affinity	HOMO–LUMO gap
Ag7	9.61	6.43	1.34	0.34
Ag6Li1	10.00	6.23	1.13	0.34
Ag5Li2	10.17	5.94	1.05	0.35
Ag4Li3	10.22	5.93	0.79	0.45
Ag3Li4	9.96	5.79	0.30	0.82
Ag2Li5	8.84	4.72	0.23	0.53
Ag1Li6	7.64	4.53	0.18	0.56
Li7	6.41	4.36	0.16	0.58

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Table 3 Binding energy (BE), vertical ionization potential (VIP), vertical electron affinity (VEA) and HOMO–LUMO gaps of Ag_mNa_7−m clusters. All values are in eV

Compounds	Binding energy	Vertical ionization potential	Vertical electron affinity	HOMO–LUMO gap
Ag7	9.61	6.43	1.34	0.34
Ag6Na1	9.39	5.39	1.29	0.32
Ag5Na2	8.79	5.37	1.11	0.36
Ag4Na3	8.58	4.83	0.81	0.48
Ag3Na4	7.89	4.28	0.48	0.46
Ag2Na5	6.87	4.16	0.43	0.41
Ag1Na6	5.68	4.02	0.36	0.34
Na7	4.46	3.39	0.31	0.31

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As a first step towards the confirmation of the electronic stability of the nanoclusters, the average binding energy per atom is calculated in the following way, where E refers to the energy of the attached cluster and X = Li and Na.

BE (Ag_mX_7−m) = mE (Ag) + (7 − m)E (X) − E (Ag_mX_7−m)

From the data presented in Table 2, it is evident that the Ag_xLi_7−x clusters maintain an interesting pattern of binding energies. With respect to Ag₇ cluster, the binding energy increases with the addition of Li into the system. More interestingly, it keeps increasing with the number of Li atoms doped into the system and reaches to its highest value with Ag₄Li₃ by maintaining the following pattern: Ag₇ < Ag₆Li₁ < Ag₅Li₂ < Ag₄Li₃. From the next alloy, i.e. from Ag₃Li₄ to Li₇, decrementing pattern is observed with Li clusters having the lowest binding energy amongst all the nanoclusters. The gap in the Pauling electronegativity of Ag (1.93) and Li (0.98) can explain this result. The large gap of electronegativity between Ag and Li have most probably created some ionic bonding and this ionic bonding gets stronger with equal number of atoms from both of Ag and Li. Hence, the binding energies of all the clusters in between Ag₆Li₁ to Ag₃Li₄ are higher with respect to Ag₇, while the highest binding energy is observed in Ag₄Li₃.

On the contrary, very opposite feature is observed in Na-doped clusters, where the binding energy followed a decreasing graph from Ag₆Na₁ to Ag₁Na₆. Moreover, all the doped clusters have lower binding energy than Ag₇. As like as Li-doped clusters, the Ag–Na alloys were also expected to follow a similar pattern. But the atomic size of Ag and Na has played the key role here. The atomic radii of Ag (165 pm) and Li (167 pm) are very close; hence doping Li atoms by replacing Ag atoms doesn't harm the geometrical harmony. But the atomic radii of Na (190 pm) is quite higher than Ag; therefore doping far bigger Na atoms by replacing Ag seriously dispatch the geometry of the Ag–Na alloys which is liable for their low binding energies.

Subsequently, our attention is then focused towards the VIP and VEA values, which are key parameters needed in the analysis of the chemical nature of small clusters. Given our knowledge that a higher value of IP specifies a deeper HOMO energy level, which in turn signifying that the structures with large value of IP are expected to be chemically more stable or, exhibiting lesser chemical reactivity. On the contrary, higher value of EA indicates a more solid binding between the cluster and an electron. Thus, low EA and IP values imply more chemically reactive nature of the clusters. Here, from the data provided in Tables 2 and 3, it is clear that IP and EA follow a declining trend from Ag₇ to Ag₁X₆ clusters. It is well known that in the periodic table, the ionization energy decreases from top to bottom and increases from left to right. Thus, both of Li and Na possess lower EA and IP with respect to Ag; hence addition of alkali atoms into Ag will make the alloy' IP and EA lower than the pure one. Thus, the alloyed clusters have lower IP and EA compared to the pure Ag clusters, which in turn implies that the Ag–X alloyed clusters are chemically more reactive than the Ag clusters. In addition, it needs to be mentioned that the vertical electron affinity of Ag_mLi_7−m follows a declining trend with increasing m, while the HOMO–LUMO gap is found to be increase with m (Table 2). The variations are monotonic, and reflect the differences between Ag and Li. The VEA of Ag₇ and Li₇ are 1.34 and 0.16 eV respectively, thus the decrease in VEA with increasing m is expected. Similar comments can be made for Na. At the atomic level, the EA of alkali atoms is about half that of silver. As a matter of fact, the EA given in Table 2 is the VEA, i.e. the anion is calculated at the geometry of the neutral specie, so a low vertical EA cannot be considered as an indicator of a low stability of the anion.

The energy gap between the HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital) is considered as an important quantity for evaluating the kinetic and chemical stability of the clusters. A signature feature of clusters with large HOMO–LUMO gaps is their thermodynamic and chemical stability. This is because it is energetically unfavorable to add electrons to a high-lying LUMO, to extract electrons from a low-lying HOMO, and so to form the activated complex of any potential reaction.^43,44 In this point, looking at the numbers provided in Tables 2 and 3, it is apparent that Li₇ possesses better chemical stability with larger HOMO–LUMO gap compared to Ag₇ and Na₇, whereas Na₇ is chemically least stable amongst. Amongst all the Ag–X bimetallic clusters, Ag₃Li₄ retains the highest band gap with 0.82 eV; hence expected to be the most chemically stable amongst all. The probable reason behind its high band-gap is the presence of ionic bonding because of the large gap of electronegativity between Ag and Li. When we are looking the trend of HOMO–LUMO gap of the doped clusters, it is clear that the doped clusters' band gaps get higher from Ag₇ to Ag₃X₄, reaches its highest value in Ag₃Li₄ and Ag₄Na₃ and then again starts to fall down. Moreover, the band gap values are higher for Ag–Li clusters with respect to Ag–Na clusters, which is because Li₇ structures own high HOMO–LUMO gaps.

Given the current discussions on the electronic attributes of the Ag_mX_7−m clusters, it is strongly implied that the doped clusters retained excellent electronic and chemical properties. In particular, the neutral clusters with high HOMO–LUMO gaps are expected to be very reactive as cations. This is due to their lower EA values as it becomes easier to lose electrons from the orbital, given the lower LUMO values.⁴⁵ Similarly, in this work it is evident that the Ag_mX_7−m clusters exhibit high HOMO–LUMO gap with low electron affinity. Especially, Ag₃Li₄ and Ag₂Li₅ clusters possess high HOMO–LUMO gaps with very small electron affinity; hence they should be excellent potential for catalytic applications.

5. Optical spectra and partial density of states (PDOS)

The absorption spectra of doped clusters are shown in Fig. 2 and 3. The oscillator strength is provided as a function of the excitation energy. In each case, Lorentzian broadening (with a full width at half-height of 0.1 eV) is applied to exclude the oscillations from the excited electrons and in order to provide a result comparable to the experimental results. As the peak optical spectra of both of Ag and X (Li, Na) lie in between 2 and 5 eV, these optical spectra are limited up to 5 eV as well. For instance, in our calculation the primary optical peak of Ag, Li and Na are 3.74 eV, 2.75 eV and 3 eV respectively, which are fine match to the previous reports.^46–49

Fig. 3 Optical absorption spectra of Ag_mX_7−m bimetallic clusters.

The optical spectrum of Ag is characterized by an intense and narrow band centered at 3.74 eV, whereas the Li doping into Ag has yielded some interesting spectra. In the spectrum of Ag₆Li and Ag₅Li₂, the peak is slightly blue-shifted whereas the optical intensity is found to be marginally increased with respect to Ag₇. More interesting spectrum is yielded by Ag₄Li₃, where the spectra got broadened with more peaks in lower frequencies. Similar broad-spectra are found for Ag₂Li₅ and Ag₁Li₆ clusters as well. But the highest peak is blue-shifted with respect to Ag₇ for the Ag₁Li₆ cluster when this cluster offer higher light absorption intensity compared to all other Ag_mLi_7−m clusters.

As like as Li-doped clusters, Na doping has also produced interesting changes in optical spectra. The absorption peak of Ag₆Na and Ag₅Na₂ are marginally blue-shifted, when Ag₅Na₂ has offered more broadened spectrum with respect to Ag₇. The optical spectra of Ag₄Na₃, Ag₃Na₄ and Ag₂Na₅ clusters seem to be more interesting as they offer large absorption spectra with higher intensity from 2 to 5 eV, while their peaks are blue-shifted with respect to Ag₇. The spectrum of Ag₁Na₆ is similar to Na₇, while Ag₁Na₆ possesses more absorption peaks compared to Na₇. However, the sodium cluster here offers more absorption intensity.

Now let's move our focus towards the electronic evolution of the spectra of the doped clusters. Here, with the presence of alkali atoms these bimetallic Ag_mX_7−m clusters in the excited states lead to a quasi-continuum spectrum. In particular, for the case of Ag₇, the electronic transitions are happening as a result of excitations from the s and d orbitals. These s and d orbitals are well localized in surface silver atoms, along with its evolution as hybrid s–p orbitals in the wide areas of outer region where several atoms are involved with the system.⁵⁰ On the contrary, the absorption spectra of alkali metal clusters are explained as collective oscillation of s valence electrons and the shift of absorption energies of very small particles, compared to the larger ones explained by a spill out (extension of the electronic wave functions out of the “classical volume” of the cluster) of these s-electrons.⁵¹ Therefore, when we are doping an alkali metal into the noble metal cluster, a systematic investigation of the excitations in molecular level is quite complicated. To this end, for investigating the absorption spectrum of the clusters we have presented the partial density of states (PDOS) calculation in Fig. 4, where the PDOS of Ag₇, Ag₅Li₂, Ag₂Li₅ and Li₇ clusters shown for clarification of the clusters optical spectra.

Fig. 4 Partial density of states of (a) Ag₇, (b) Ag₅Li₂, (c) Ag₂Li₅ and (d) Li₇ clusters.

From the Fig. 4(a), it is evident that d electrons are more influential in Ag₇ cluster with its peak range from −2 to −6 eV. On the other hand, this band has got narrower as a result of doping Li into Ag. For instance, in Ag₅Li₂ the d-electrons band got thinner ranged from −3 to −6 eV. It gets even narrower with the addition of more Li atoms, as we see the band comprises from −4 to −5 eV only in the case of Ag₂Li₅ clusters. Hence, it is obvious that the d-electrons are more dominant in the silver clusters but with the addition of alkali atoms, its dominance gets weaker. On the contrary, the s–p hybridization orbitals become stronger with the addition of Li and the influence of s–p hybridization is proportional to the number of Li atoms added into the system.

6. Conclusion

In this paper, the X (Li, Na) doped Ag nanoparticles are explored as potential improvement over Ag nanoparticles for plasmonic applications. For this work, X atoms are used to substitute Ag atoms from decahedral Ag₇ structures to form Ag_mX_7−m bimetallic clusters. Later, the ground state structures, chemical and optical properties of all the doped clusters are calculated in the framework of density functional theory. One of the targeted applications for this work is catalysis and it requires the materials to be of large band gap with very low electron affinity so that their anions become very reactive. Our calculation has found that the Li and Na doped clusters; especially the Ag₄Li₃ and Ag₃Li₄ clusters own high HOMO–LUMO gaps with low EA; hence these bimetallic clusters will be an excellent potential for catalytic applications. On the contrary, the calculated absorption spectrums of the Ag_mX_7−m clusters have revealed that the doping of Li and Na has made the absorption band wider with regards to undoped Ag₇ clusters. Typically opto-electronic devices, such as solar cells absorb lights in the range of 1–5 eV. With the calculations provided above, this work is suggesting that Li and Na doping (especially, Ag₄X₃, Ag₃X₄ and Ag₂X₅ clusters) will result in improvement of absorption band in the mentioned range. Consequently, the wider band will allow the increase of photo-current as well as the overall optical absorption efficiency. Hence, these Li and Na doped bimetallic nanoparticles can significantly improve the overall efficiency of opto-electronic devices such as thin film solar cells.

Acknowledgements

The authors wish to acknowledge the University of Malaya-Ministry of Higher Education Grant UM.C/625/1/HIR/MOHE/ENG/29, University of Malaya Research Grant (UMRG) RP023B-13AET, University of Malaya Research Grant (UMRG) RP014C-13AET, and Malaysian Ministry of Science and Technology's Science Fund (06/01/03/SF0831) for the financial support. Deepest thanks also go to Professor Rene Fournier, Department of Chemistry, York University, Canada for the technical discussions and acknowledgment also to Prof. Dr Nasrudin Bin Abd Rahim and Universiti Malaya Power Energy Dedicated Advanced Centre (UMPEDAC) for the constructive support during the course of this work. The authors wish to thank Dr S. Balamurugan for his assistance in improving the text.

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