Influence of dopants Cu, Ga, In, Hg on the electronic structure of Cd_nS_n (n = 6, 15) clusters – a DFT study

Abstract

The influence of doping metal ions on the structural, electronic and optical properties of Cd_n−yX_yS_n (n = 6, 15; y = 1, 2, 4) clusters is systematically studied using DFT and TD-DFT studies. Among the dopants, Cu²⁺ and In²⁺ slightly distort the structure of Cd_nS_n clusters, though they have a strong bonding interaction with S²⁻ however; another two dopants Ga²⁺ and Hg²⁺ significantly distort the cluster's structure. Molecular composition analysis reveals the dopants not only contribute to the optically active states, but also to the surface or trap states. The HOMO–LUMO gap is significantly reduced for Cu²⁺, Ga²⁺, and In²⁺ dopants. However, for Hg²⁺ the gap is meagerly affected. In large clusters, Cd₁₅S₁₅, the polarizability values decrease on doping, though individual dopants show a nonlinear pattern. The absorption spectra of doped CdS clusters are generally red shifted though a few Ga and In clusters exhibit a blue shift due to the Burstein–Moss effect.

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1. Introduction

Carrier doping of either excess electrons or holes in semiconductor nanocrystals (NCs)¹ effectively alters their structural, electronic, optical and magnetic properties.^2–9 For example, transition metals (TM²⁺) and group III elements were doped to precisely tune the optical window of II–VI materials for the improvement of optoelectronic^10–18 and photovoltaic devices.^2,19,20 Though doping does provide several advantages, it is demonstrated²¹ that quenching of luminescence at higher impurity concentration is a roadblock for multiple exciton generation (MEG),^17,22 which is not well understood so far. Recently, a higher doping rate was achieved in NCs than in the bulk,²³ simultaneously with self-purification making the dopants diffuses to the surface or near the surface region, consequently leading to quenching of luminescence. Though self-purification⁸ makes the doping difficult, it is critical because it increases the stability of NCs. Besides, the dopants location in NCs^24–27 such as substitutional²⁸ or interstitial²⁹ is expected to play a vital role in tuning the band gap of NCs. In general, the difficulty of impurity doping in NCs² is the autoionization by which the charge carriers occupy the energy levels of host materials, hence a deeper understanding is required on their influence on the band gap of NCs and should shed light on tuning their properties to design the high-efficiency photovoltaic devices.

Cadmium sulfide is a novel material to study the effect of quantum confinement on electronic and optical properties of semiconductor nanomaterials. Besides, cadmium sulfide (CdS) is the most suitable photovoltaic material among group II–VI, whose direct optical gap (2.5 eV) is easily redshifted³⁰ on doping the optically active transition metals³¹ (TM²⁺) such as Cu²⁺, Hg²⁺ and group III elements Ga²⁺, In²⁺. This kind of doping is believed to improve the performance of CdS in solar cell application.²⁸ Among these substitutional doping, Cu in CdS NCs provides p-type conductivity,³² and band gap tunability as a function of the size of the host materials.^33,34 Besides Cu doped CdS nanoparticles (NPs) produces unusual orange-red emission due to the carrier relaxation from the excitonic states to T₂ level.³¹ Further, Cu and In doped CdS QD based solar cells have shown to increase the efficiency from 0.71 to 1.28%.¹⁹ In the case of Cu²⁺ and Hg²⁺ surface doped CdS QDs luminescence quenching occurs since the dopants create the midgap states which act as main trap centers and consequently become a roadblock for carrier recombination.³⁵ Besides, the incorporation of group III element gallium with its valence 4p orbitals does not affect the wurtzite structure of II–VI materials and is found to efficiently change the electronic and optical properties of NCs due to its influence on the growth kinetics at near room temperature.³⁶ On the other hand, Ga²⁺ ion doping provides separation of photo-generated carriers by widening the valence band of CdS NCs, eventually, the Ga-doped CdS NCs exhibit the photocatalytic activity and stability for the application of solar cells.²⁹

The electronic structure of nanoclusters is a fundamental interest because it gives the pavement for their optical properties through intra and interband excitonic relaxations. Therefore, the structural and the electronic properties of Cd_nS_n (n = 1–8) clusters have been studied by using DFT methods.³⁷ It established that the lower impurity concentration has an insignificant impact on the band gap of QDs,³⁸ and also the presence of impurity on the surface of a QD due to its large surface to volume ratio can drastically change the band gap. Therefore, a theoretical understanding of the dopant's interaction in doped CdS clusters especially the dopant at the surface may shed light in improving the optical properties for the desired photovoltaic applications.

In the present work, we study theoretically the effect of dopants localized at the surface of the electronic structure of Cd_n−yX_yS_n (X= Cu²⁺, Ga²⁺, In²⁺, Hg²⁺) (n = 6, 15) clusters using DFT and TD-DFT methods. For this small spherical Cd_nS_n (n = 6, 15) clusters were considered in its wurtzite structure³⁹ widely used to study the properties of bare CdS.^40,41 The Cd_nS_n (n = 6, 15) clusters alone are considered here for this study because not only they are the smallest representative models that contain all the atoms on the surface, but also from the chemical point of view, the unrelaxed Cd₆S₆ cluster has an equal number of chemically more active 2-coordinated atoms while the unrelaxed Cd₁₅S₁₅ cluster has the mixture of 2- and 3-coordinated atoms on its surface. Moreover, these unsaturated atoms are greatly stabilized while relaxing and therefore justifies that these models are suitable enough to visualize the effects of dopants by their interaction with the surface atoms. The number of dopants is introduced as y = 1, 2 for n = 6 and 1, 2 and 4 for n = 15 at the surface of Cd_nXS_n clusters respectively. The number of dopants in the case of a cluster with n = 6 is restricted to y = 1, 2 is because further increase distorts the structure, however, for n = 15 it is varied as 1, 2 and 4. The Cd_n−yX_yS_n clusters were initially optimized to their lowest energy configuration at B3LYP/LANL2DZ/6-31+G(d) level taking into account both spin and multiplicity.

2. Computational details

All the electronic structures of undoped and X= Cu²⁺, Ga²⁺, In²⁺, Hg²⁺ doped CdS clusters were optimized using Gaussian09 software package.⁴² The initial Cd_nS_n(n = 6, 15) clusters were constructed synonymous to wurtzite structure with a spherical shape. As our study concentrates on the influence of the dopants at the surface of doped clusters, it is necessary to consider the most stable geometrical structures in its relaxed form. Cd_nS_n (n = 6, 15) clusters^43,44 with D_3d symmetry formed by the stacking of Cd₃S₃ rings exhibit the greater stability among several other conformers. Moreover, these structures have shown to be the best models to study the structural, electronic and optical properties of CdX (X = S, Se) nanoparticles.^43,44

The substitutional doping is modeled by replacing the surface Cd²⁺ ions using the above-mentioned dopant atoms in Cd₆S₆ and Cd₁₅S₁₅ clusters. Further, the number of dopants is increased as y = 1, 2 and 4 at the surface of Cd_n−yX_yS_n clusters. The geometry optimization was carried out in the DFT formalism with a B3LYP⁴⁵ exchange-correlation functional which is widely employed for the electronic structure calculations of II–VI materials⁴⁶ because it predicts more realistic energy gaps^47,48 due to the addition of 25% of HF exchange functional, whereas the GGA or LDA functionals underestimate the optical gaps and long-range coulombic interactions.^49–52 The combination of Los Alamos double-ζ effective core potential (LANL2DZ)^53–55 and 6-31+G* basis sets were used for Cd, Cu, Ga, In, Hg and S atoms to provide the best description of lone pairs in S and to predict precisely the interactions with cadmium. Besides, the calculated bond distances are consistent with the reported results.^43,44 The vibrational frequency calculations performed at the same level of theory, confirmed the structures are without imaginary frequencies. The absorption spectra were obtained by the TD-DFT at the same level of theory. The electronic properties such as the dopant binding energy, the HOMO–LUMO gap, density of states (DOS) spectra, MO composition and the spectral density for absorption were calculated. The natural atomic charges and spin densities were calculated by performing the Natural Bond Orbital (NBO) analysis using the NBO 3.1 software.⁵⁶

The dopant's binding energy (E_b) is calculated as

E_b = (E_undoped + mE_dopant) − (E_doped + mE_Cd) (1)

where E_undoped and E_doped refer to the energy of the undoped and doped cluster, respectively, and E_Cd and E_dopant refer to the ground-state energies of the Cd and dopant atoms in a vacuum.

The mean polarizability is calculated using the trace of the polarizability matrix

〈α〉 = 1/3tr(α_ij) = (α_xx + α_yy + α_zz)/3 (2)

3. Results and discussion

3.1. Structure of Cd_nS_n (n = 6, 15) pristine/Cu²⁺, Ga²⁺, In²⁺, Hg²⁺ doped clusters

The optimized geometrical structures of all the considered Cd_nS_n (n = 6, 15) clusters doped with Cu²⁺, Ga²⁺, In²⁺ and Hg²⁺ ions at the surface are shown in Fig. 1, 2, S1 and S2† respectively. The structural change in the clusters due to doping is denoted by the changes in bond length and angle. The pristine Cd₆S₆ cluster with wurtzite structure is formed through the stacking of two Cd₃S₃ rings through sp² hybridization. The presence of lone pairs in S²⁻ significantly facilitates the strong intralayer Cd–S bond length and angle ∠(S–Cd–S) larger than ∠(Cd–S–Cd) by relaxing outward along the Cd₃S₃ ring, while it is found to restrict the interlayer Cd–S bonds between two Cd₃S₃ rings and hence two different Cd–S bonds have formed in the Cd₆S₆ clusters.

Fig. 1 The optimized structures of the pristine Cd₆S₆ and doped Cd_6−yX_yS₆ (X = Cu²⁺, Ga²⁺) clusters. The significantly distorted bond lengths (in Å) are denoted in navy and bond angles (in °) are in dark red. Cd atoms are in blue, S in dark yellow, Cu in reddish orange, Ga in olive green.

Fig. 2 The optimized structures of the pristine Cd₁₅S₁₅ and Cd_15−yX_yS₁₅ (X = Cu²⁺, Ga²⁺; y = 1, 2, 4) clusters. The significantly distorted bond lengths (in Å) are denoted in navy and bond angles (in °) are in dark red. Cd atoms are in blue, S in dark yellow, Cu in reddish orange, Ga in olive green.

Among considered dopants, Cu²⁺ has the smallest ionic radii while In²⁺ has slightly larger than Cd²⁺ however, these two dopants are found to distort the Cd₆S₆ clusters trivially through X–S bonding on both intra and interlayers, despite the hindrances from the lone pairs of S²⁻ and the nearest interlayer Cd–S bonds. Further, both the dopants contract the nearest interlayer Cd–S bonds significantly. The bond angle ∠(S–In–S) in the Cd₅InS₆ cluster is greatly reduced but for Cu²⁺ the change is only trivial.

However, as the number of dopants is increased, the intra-layer X–S (X = Cu²⁺, In²⁺) bonds are slightly distorted with a corresponding marginal increase in the ∠(S–Cu–S), while ∠(S–In–S) remains unaltered. In the case of Ga²⁺ dopants, the Ga–S moiety binds weakly with its nearest neighbors on both the layers, however, all the nearest Cd–S bonds remain strongly contracted. The presence of filled 3d orbitals and the valence 4p orbitals are the reason for the non-bonded interaction of Ga²⁺. Unlike other dopants, Ga²⁺ breaks the Cd–S bond and highly distorts the cluster as the number of dopants increases. For Hg²⁺ doped Cd₅HgS₆ cluster, the elongation of Cd–S bond lengths and angle ∠(S–Cd–S) is in the proximity of the dopant due to the larger ionic radius of Hg²⁺ which significantly pushes S²⁻ outward. Consequently, for Cd₄Hg₂S₆ cluster, both the dopants considerably influence the nearest interlayer Cd–S bond and remain unbound. Moreover, for y = 2, both the dopants still have similar interactions and the only variation is on the intralayer with uneven Hg–S bond lengths.

For the pristine Cd₁₅S₁₅ cluster, the Cd₃S₃ rings at the a₂, a₃, and a₄ layers are stacked through sp³ hybridization and therefore Cd–S bond lengths are only reduced as we move towards the middle of the cluster. The bond angle ∠(S–Cd–S) at a₁ and a₅ layers are significantly increased while for the other layers it is significantly reduced when compared to the Cd₆S₆ cluster. The Cu²⁺ substitutional doping (y = 1, 2 and 4) was performed at all the possible positions on the surface of the Cd₁₅S₁₅ cluster and the lowest energy structures are alone considered here. Among the possible doping positions, Cu²⁺ energetically prefers the a₁ layer. Unlike small size clusters (y = 1), here the Cu²⁺ dopant at the a₂ or a₃ layer distorts slightly the CdS structure at a lower concentration. However, at y = 4 (Cd₁₁Cu₄S₁₅) the bonding between layers having 3- and 4-coordinated Cd²⁺ sites breaks due to doping of Cu²⁺. This is may be due to the unequal charge distribution between 3- and 4-coordinated Cd²⁺ sites. In the same way, Ga²⁺ prefers the a₁ layer energetically to be lower. As the number of Ga²⁺ increases, the structure is highly distorted with the breaking of Cd–S bond on the entire surface.

Interlayers Hg²⁺ through has larger ionic radii does not significantly distort the structure as its number increases. However, for In²⁺ dopant with y = 2, at the a₂ layer greatly distorts the structure through the shortening of In–S bonds and breaking of Cd–S bonds. Further, when In²⁺ number is increased to y = 4, the interlayer In–Cd bond is formed by the breaking of Cd–S bond at a₁ layer followed by the contraction of the remaining Cd–S bonds. From the results, it is worthy to note that the dopant's position on the surface plays a key role on the geometries of doped CdS clusters, particularly at larger sizes.

The electronic properties such as doping energy (E_b), HOMO–LUMO gap (E_g), spin density (ρ_X) and natural atomic charge (q_X) of dopants are calculated for the pristine Cd_nS_n (n = 6, 15) clusters and are compared with their doped structures in Tables 1 and S1† respectively. For the pristine Cd_nS_n (n = 6, 15) clusters, it is noted that as the cluster size increases, the HOMO–LUMO gap decreases while the cluster shows the greater stability by the strong binding energy due to the significant increase in the atomic interactions particularly, between interlayer in the middle of the cluster by sp³ hybridization with decreasing Cd–S interlayer bond lengths. The calculated dopant binding energy (E_b) is the measure of the stability of the doped cluster and therefore, the increase in the binding energy of dopants on increasing their concentration show that the cluster's structures have the lower stability. It is worthy to note that the Hg²⁺ doped clusters are greatly stabilized upon doping and on increasing its concentration. Conversely, the Ga and In doped clusters are more destabilized by the introduction of dopants and the cluster's stability is also highly affected by their concentration increase. However, for the Cu doped clusters, it is clear that the stability of the cluster is not significantly affected due to the lower concentration. Except for Cu²⁺ in Cd_15−yCu_yS₁₅ clusters, the trend in the HOMO–LUMO gap is found to be decreased for all the clusters upon doping.

Table 1 Dopant's binding energy (E_b), HOMO–LUMO gap (E_g), natural atomic charge (q_X) and spin density (ρ_X) of dopants for the pristine Cd₆S₆ and doped Cd_6−yX_yS₆ clusters. The spin multiplicity 2S + 1 is shown in parentheses

System	Eb [eV]	Eg [eV]	qX [a.u.]	ρX
Cd6S6 (1)	—	3.34	—	—
Cu (2)	0.92	1.82	0.42	0.07
Cu2 (3)	2.03	1.74	0.40	0.08
Ga (2)	1.53	1.49	0.96	0.18
Ga2 (3)	2.61	0.78	1.02	0.16
In (2)	1.39	1.70	1.10	0.22
In2 (3)	2.66	1.27	1.10	0.20
Hg (1)	−1.29	3.11	0.98	0
Hg2 (1)	−2.55	3.05	0.96	0

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For Cd₁₃Cu₂S₁₅ clusters, it is noted that the position of the dopant plays an important role in determining its optical properties and it has an experimental evidence that Cu dopant exhibits dual color emission.³¹ The variation between the binding energy and HOMO–LUMO gap as a function of different dopants is shown in Fig. 3. Except for Hg²⁺, for all other dopants, an inverse correlation is found between binding energies and the HOMO–LUMO gaps. From the dopant spin density values, it is worth to note that the spin densities are highly delocalized for Cu²⁺ towards the outer layers while for the Ga²⁺ and In²⁺ dopants the spin density is localized in the middle layer. From the natural atomic charges, the unequal charge accumulation at individual dopants such as Cu²⁺, Ga²⁺, and In²⁺ demonstrate that the dopant's interaction with the cluster varies as the number of dopants increases and thus the impedes cluster. On the other hand, the charges of individual Hg²⁺ dopants remain unaltered and therefore, its cluster stability is further increased upon doping.

Fig. 3 The variation between the binding energy and HOMO–LUMO gap of pristine and doped Cd_nXS_n (n = 6, 15) clusters as a function of dopants at different concentration y = 1, 2 and 4.

3.2. Density of states (DOS) analysis

The calculated total and partial density of states (TDOS and PDOS) spectra of the considered pristine Cd_nS_n (n = 6, 15) and doped Cd_6−yX_yS₆ (y = 1, 2) clusters are plotted in Fig. 4 and S3.† In order to capture the influence of dopants on the energy gap of clusters due to their significant atomic orbitals (AOs) contribution to the formation of the frontier molecular orbitals (FMOs), in the PDOS spectra, the mid-gap between the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO) is set to zero. For the pristine Cd_nS_n clusters, the HOMO is dominated by the 3p AOs of sulfur and the LUMO is mainly due to the Cd 6s AOs and are separated by the energy gaps of 3.34 and 3.11 eV respectively.

Fig. 4 The calculated total (TDOS) and partial (PDOS) density of states for the considered pristine Cd_nS_n (n = 6, 15) and doped Cd_6−yX_yS₆ (X = Cu, Ga, and y = 1, 2) clusters. The positive and negative amplitudes represent the spin up and spin down states of the doped clusters respectively. The midgap is set to zero.

The 4d orbitals of Cd reside at −13 eV in the valence band and they do not contribute to the HOMO because of being completely filled AO, while the empty 5p and 6p AOs are distributed over the higher energy regions of the conduction band. The similar trend has also been observed for Cd₁₅S₁₅ clusters and the calculated results are consistent with the previous results.^44,57 The PDOS spectra of Cu, Ga, and In, Hg doped Cd_15−yX_yS₁₅ (y = 1, 2, 4) clusters are shown in Fig. 5 and S4† respectively. For the Cu doped clusters, the HOMO is apparently shifted towards the Fermi level by the β (spin down) MOs and significantly contributed by both 3d and 3p AOs of Cu and S respectively rather than α (spin up) MOs even at the lower concentration of Cu dopant. This gives the energy gaps of 1.82 eV and 1.55 eV for Cd₅CuS₆ and Cd₁₄CuS₁₅ clusters respectively. Thus, the energy gap is largely reduced to 1.81 and 1.55 eV for Cd₅CuS₆ and Cu₁₄CuS₁₅ clusters respectively. As the Cu²⁺ concentration increases the trend in the PDOS spectra is greatly altered by the larger shift in LUMO which is made up of 6s AOs of Cd for Cd₄Cu₂S₆ cluster.

Fig. 5 The calculated total (TDOS) and partial (PDOS) density of states for the doped Cd_15−yX_yS₁₅ (X = Cu, Ga, and y = 1, 2, 4) clusters. The positive and negative amplitudes represent the spin up and spin down states of the doped clusters respectively. The midgap is set to zero.

For the Ga-doped clusters, the HOMO of Cd₅GaS₆ and LUMO of Cd₁₄GaS₁₅ clusters are greatly influenced by the contribution of the α (spin up) MOs formed by the 5s AOs of Ga (or 6s AOs of In) and 6s AOs of Cd at lower concentration respectively. At a higher Ga concentration, the HOMO is highly altered with the energy gap 1.34 eV due to the contribution of 5s AOs of Ga in Cd₁₁Ga₄S₁₅ cluster. The In-doped clusters show the reduced energy gap due to the strong shift in HOMO by the contribution of 5s AOs to the α (spin up) MOs at a lower concentration. While the LUMO is greatly altered by the contribution of 6s AOs of both In and Cd of Cd₄In₂S₆ cluster. Nevertheless, in the case of Cd₁₁In₄S₁₅ cluster, both the HOMO and LUMO give the energy gap of 1.33 eV due to the strong influence of dopant's interaction. Further, in the case of Hg-doped clusters, the energy gap is notably altered only by the shift of the LUMO while the HOMO remains unaltered by the presence of Hg dopants. Here the LUMO is significantly dominated by the 7s AOs of Hg. With increasing Hg concentration, the energy gap reduces gradually due to the increasing amplitudes of 7s AOs. Conclusively, from the PDOS spectra, it is worthy to note that the dopant influence on the frontier MOs leads to the change in the energy gap of doped clusters.

3.3. Molecular orbital compositional analysis

Fig. 6 presents the composition of MOs by their constituent's AOs and their energy levels near HOMO and LUMO for both Cd₆S₆ and Cd₁₅S₁₅ clusters. Therein the green arrow shows the TDDFT calculated optical gap, for the singlet excitation between the occupied and virtual MOs due to the absorption of photons. The MO composition shows that the occupied MOs such as H−7, H−8 of Cd₆S₆ and H−6 of Cd₁₅S₁₅ clusters respectively, are degenerate, optically active, with the highest oscillator strength and are dominated by the p AOs of S atoms, while the LUMOs are substantially contributed by s AOs of Cd atoms. The energy gap between H−7, H−8, and LUMO or H−6 and LUMO corresponds to the optical gap of the clusters and varies with the cluster's size. Moreover, from the analysis, we observe that the unsaturated charges at the surface of Cd²⁺ and S²⁻ ions largely produce degenerate and optically inactive surface states with a large optical gap.

Fig. 6 The energy levels of MOs near HOMO and LUMO of both Cd₆S₆ and Cd₁₅S₁₅ clusters along with their MO composition by the constituent's AOs are indicated by dark blue for Cd²⁺ and yellow for S²⁻ ions. The green arrows represent the singlet transitions calculated using TD-DFT.

The influence of Cu²⁺ on the MOs of both Cd_6−yCu_yS₆ and Cd_15−yCu_ySe₁₅ clusters is shown in Fig. 7. In general, Cu²⁺ possess a high spin density because of five up (↑) spins and four down (↓) spins in its 3d orbitals. Therefore, obviously, the influence of 3d orbitals of Cu²⁺ could be higher and more significant even at lower impurity concentrations. For Cd₅CuS₆ cluster, the optically active states are found in both alpha and beta MOs, however, the beta MOs dominate optically active states than alpha MOs in larger clusters. As Cu²⁺ concentration increases, the density of surface states in alpha MOs also increases. In contrast, beta MOs show a greater shift of optically active states towards Fermi level due to down spin. For a smaller size cluster, the contribution of Cu²⁺ ions is towards optically active HOMO and no surface states were formed at y = 2. However, at y = 4, Cu²⁺ ions significantly dominate over the AOs contribution of Cd²⁺, and leads to more surface states in beta MOs, as the cluster size increases. Moreover, Cu²⁺ dopant's influence on the MOs varies with cluster size.

Fig. 7 The energy levels of MOs near HOMO and LUMO of both Cd₆S₆ and Cd₁₅S₁₅ clusters doped with Cu²⁺ along with their composition due to the AOs are indicated by dark blue for Cd²⁺, yellow for S²⁻ and red for Cu²⁺ ions. The green arrows represent the singlet transitions calculated using TD-DFT.

The influence of low spin density dopants like Ga²⁺ and In²⁺ which arises from one up (↑) spin in their valence 4p AOs, on the MOs of Cd_nS_n clusters are plotted in Fig. S5 and S6.† Here, the alpha MOs are usually more effective than beta MOs due to up spin contribution by doping of Ga²⁺ and In²⁺. Besides the dopants, highly contribute to the drastic shift in the HOMO of alpha MOs towards Fermi level and thereby reducing the optical gap. Here no surface states were formed inside the optical gap at y = 1. This is due to the sp² hybridization of dopants with clusters. In contrast, for Ga²⁺ = 2, the optical gap is blue shifted for clusters (Cd₆S₆) and surface states are introduced within the optical gap. Further, from, the position of Ga²⁺ we surmise that dopants in the middle of cluster increase the optical gap due to Ga²⁺–Ga²⁺ interaction. However, for larger size Cd₁₅S₁₅ cluster with Ga²⁺ = 2 or 4, the energy gap is red shifted and there are no surface states. On the other hand, In²⁺ prefers only the top (a₁ layer) of the Cd₁₄InS₁₅ cluster and does not form surface states but the optical gap blue shifted when In²⁺ = 4. Finally, Fig. S7† shows the influence of impurity Hg²⁺ on the MOs of Cd_nHg_yS_n clusters which has large Z value and similar electronic configuration as of Cd²⁺. The contribution of atomic orbitals of Hg²⁺ in the surface states shifts the occupied MOs towards Fermi level and decreases the optical gap at y = 1 in the Cd₅HgS₆ cluster. As the number of Hg²⁺ dopant increases, the density of trap states becomes larger but correspondingly increases the optical gap. In the case of a Cd₁₅Hg_ySe₁₅ cluster, for y = 1 or 2, the contribution of Hg²⁺ is large in the LUMO and pushes them towards Fermi level and redshifts optical gap. However, for y = 4, surface states are formed by the significant contribution of Hg²⁺ impurities.

3.4. Polarizability

Polarizability is an important property to analyze the presence of metallic-like nature in small clusters. For the CdS clusters, the electron density is largely localized on S²⁻ along with the outward of Cd₃S₃ rings and therefore, calculating the polarizability in their doped clusters captures the significant changes in the electron density while doping. The changes in the polarizability as a function of pristine Cd_nS_n and their doped clusters are shown in Fig. 8.

Fig. 8 Polarizability of pristine Cd_nS_n (n = 6, 15) and its doped clusters as function of dopants at different concentration y = 1, 2 and 4.

On comparing pristine Cd₆S₆ and Cd₁₅S₁₅ clusters, the polarizability increases as the size of the clusters increases. It infers that the localized densities are disturbed when the number of atoms increases. Interestingly, this is obviously different from the polarizability values calculated for small Cd_nS_n (n = 2–8) clusters.⁵⁸ However, the trend in the calculated polarizability greatly differs for both the Cd₆S₆ and Cd₁₅S₁₅ clusters. For the doped Cd₆XS₆ clusters, although all the dopants increase the polarizability of Cd₆S₆, especially Ga²⁺ and In²⁺ dopants have the larger polarizability values by enhancing the localization of electron density on the nearest S²⁻ whereas Cu²⁺ and Hg²⁺ significantly destabilize the electron density of S²⁻ and hence decrease in the polarizability. In the case of Cd₁₅XS₁₅ clusters, in general, the electron density is highly delocalized by the introduction of dopants of all types. Further, in larger clusters, as the concentration of dopant increases, clusters polarizability also increases due to the large localization of the electron density. However, contrast behavior is found for Ga²⁺ that at a higher dopant concentration (at y = 4) the polarizability suddenly decreases.

3.5. Absorption spectra

The strongest electronic transitions with their absorption energies (Ω both in eV and in nm), maximum oscillator strength (f in a.u.) and the corresponding MOs of pure and doped Cd_nS_n (n = 6, 15) clusters calculated using TD-DFT are summarized in Table 2 and S2.† Fig. 9 shows the absorption spectra of Cd_nS_n clusters calculated using TD-DFT. The absorption of the Cd₆S₆ cluster at 3.32 eV (374 nm) is blue shifted due to the quantum confinement effect when compared with the absorption peak at 515 nm of bulk CdS. The responsible electronic transitions are from HOMO−7 and HOMO−8 to LUMO for the Cd₆S₆ cluster. On the other hand, the absorption spectra of Cd₁₅S₁₅ clusters show that an apparent decrease in the optical gap by 0.32 eV due to the redshift of 38.823 nm, as the cluster' size increases. The calculated absorption spectra have good agreement with UV-Vis spectra of a set of CdS QDs.⁵⁹ Fig. 10 shows the absorption spectra of Cu²⁺ doped at the surface of both Cd_6−yCu_yS₆ (y = 1, 2) and Cd_15−yCu_yS₁₅ (y = 1, 2 and 4) clusters calculated using TD-DFT. The calculated spectra confirm the previous results³⁸ that the impurities doped at the surface significantly influence the absorption spectra than doped at the center of the cluster.

Table 2 The calculated absorption energy (E in eV and λ in nm) and oscillator strength (f, in a.u.) of bare Cd₆Se₆ cluster doped by a variety of dopants at TD-B3LYP/Lanl2dz/6-31+G* level of theory^c

System	Absorption energy (E) [eV]	Absorption wavelength (λ) [nm]	Orbital transitions	Oscillator strength f (a.u.)
a a and b refers to alpha and beta MOs.b Values given within parenthesis are the orbital coefficient.c For information only the transitions with oscillator strength higher than 0.010 a.u. are given.
Cd6S6	3.32	374.057	H−7 → LUMO (0.55)^b	0.090
	3.32	374.00	H−8 → LUMO (0.55)	0.090
Cd5CuS6	2.80	442.108	H−2(a)^a → LUMO(a) (0.65)	0.011
			H−1(b)^a → L+1(b) (0.52)	0.011
Cd4Cu2S6	1.03	1206.196	HOMO(b) → LUMO(b) (0.77)	0.011
	1.86	668.094	H−9(b) → LUMO(b) (0.81)	0.010
Cd5GaS6	2.07	598.527	HOMO(a) → L+2(a) (0.98)	0.051
Cd4Ga2S6	2.54	487.458	H−1(a) → L+1(a) (0.41)	0.026
			H−5(b) → LUMO(b)(0.75)	0.026
Cd5InS6	1.77	700.796	HOMO(a) → LUMO(a) (0.98)	0.034
	2.47	501.233	HOMO(a) → L+2(a) (0.98)	0.034
Cd4In2S6	2.81	441.950	H−1(a) → L+1(a) (0.88)	0.042
			H−7(b) → LUMO(b)(0.28)	0.042
Cd5HgS6	2.72	455.492	H−2 → LUMO (0.70)	0.047
	3.27	379.553	H−8 → LUMO (0.48)	0.047
Cd4Hg2S6	3.20	387.938	H−5 → LUMO (0.84)	0.084

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Fig. 9 The absorption spectra of Cd_nS_n (n = 6, 15) clusters were calculated using TD-DFT.

Fig. 10 The absorption spectra of Cd_n−yCu_yS_n (n = 6, 15; y = 1, 2) clusters where y = 1, 2 were calculated using TD-DFT when the impurity is located at the surface.

On doping Cu²⁺, the energy gap of CdS clusters decreasing rapidly as the number of dopants increases at the surface. More precisely, the energy gaps for both the clusters are initially found to be decreased by 0.52 eV and 1.17 eV at y = 1, but then the energy gaps reduce abruptly to 1.14 eV and 1.93 eV for Cd₆S₆ (y = 2) and Cd₁₅S₁₅ (y = 4) clusters respectively due to the surface Cu²⁺. For Cu²⁺ dopants, the range of absorption spectra lies in the longer wavelength region between 440 and 1200 nm, is good agreement with the experimentally observed absorption spectra,³¹ however, depends on the number of dopants. Further, the substitutional doping of Cu²⁺ (at y = 1) at various possible positions on the surface of Cd₁₄CuS₁₅ clusters reveals the reason for the strong orange-red emission observed in Cu doped CdS nanoparticles.³¹ Similarly, when the number of Cu²⁺ is 2, due to the position, the absorption wavelength is significantly increased, 47.429 nm. Besides, it is worth to mention that closer dopants, more the reduction in the energy gap. Similar to Cu²⁺ dopant, the absorption spectra plotted in Fig. 11 for Ga²⁺ shows that the energy gaps of both Cd_6−yGa_yS₆ (y = 1, 2) and Cd_15−yGa_yS₁₅ (y = 1, 2 and 4) clusters decrease but gradually upon increasing the number of Ga²⁺ at the surface. However, the energy gaps are decreased by large magnitudes like 1.25 eV and 1.50 eV at y = 1, with the maximum shift in the energy gap up to 1.34 eV (926.713 nm) for y = 4 in Cd₁₁Ga₄S₁₅ clusters. Interestingly, for Cd₄Ga₂S₆ cluster alone a blue shift in the energy gap by 0.47 eV (111.069 nm) is observed. This blue shift may be because of Burstein–Moss effect wherein Fermi level shift towards the LUMOs due to the strong Ga–S interaction and the dangling bonds from the 2-coordinated Cd and Ga atoms. Besides from the spectra, it is worth to note that peaks of Ga²⁺ doped clusters lie in the range of 487 and 926 nm and are independent of cluster sizes. However, the oscillator strength is considerably larger than Cu²⁺ dopants because of Ga–S interaction substantially build the electron density upon doping.

Fig. 11 The absorption spectra of Cd_n−yGa_yS_n (n = 6, 15; y = 1, 2) clusters were calculated using TD-DFT when the impurity is located at the surface.

The absorption spectra in Fig. S8† show that the energy gaps of both Cd_6−yIn_yS₆ and Cd_15−yIn_yS₁₅clusters decrease to 1.77(9) eV (692.885 nm) upon introducing In²⁺ at the surface. However, as the number of dopants In²⁺ is increased y = 1, 2 and 4 the energy gaps of the Cd_15−yIn_yS₁₅ cluster, are decreased to 1.21 eV, 1.30 eV, and 1.67 eV as respectively. Peculiarly for Cd₄In₂S₆ cluster, there is a blue shift in the energy gap by 1.04 eV (258.846 nm). Here, the blue shift is due to the shift of the Fermi level towards HOMOs (Burstein–Moss effect). Such shift occurs because of the strong In–S interaction augmented by the accumulation of excess charges on the neighboring S²⁻ than Cd²⁺ centers. In general, from the spectra, it is worth to note that peaks of In²⁺ doped clusters lie in the range of 441 and 930 nm.

Fig. S9† shows the absorption spectra of Hg²⁺ doped at the surface of both Cd_6−yHg_yS₆ (y = 1, 2) and Cd_15−yHg_yS₁₅ (y = 1, 2 and 4) clusters calculated using TD-DFT. On doping Hg²⁺, unlike other dopants, here the energy gap of CdS clusters decreases gradually as the number of dopants is increased at the surface. Though the energy gaps are initially found to decrease by 0.6 eV and 0.09 eV at y = 1, but gets sharply reduced to 2.75 eV (450.183 nm) at y = 4 due to the larger ionic radius of Hg²⁺ and breaking of Cd–S bond in Cd₁₅Hg₄S₁₅ cluster. For Hg²⁺ dopants, the range of absorption spectra lies in the longer wavelength region between 380–455 nm. The substitutional doping of Hg²⁺ with y = 1 at various possible positions on the surface of Cd₁₄CuS₁₅ clusters does not alter the energy gap and is distinct from other dopants. Similarly, when y = 2, depending on the position of Hg²⁺, the absorption wavelength significantly varies up to 75.939 nm. This also indicates that spectra are strongly affected the when dopants are close to each other than when are away from each other.

4. Conclusions

In the present work, the influence of a variety of metal ions on the structural, electronic and optical properties of Cd_n−yX_yS_n (n = 6, 15; y = 1, 2, 4) clusters is systematically studied using DFT and TD-DFT studies. The dopants Cu²⁺, Ga²⁺, In²⁺, and Hg²⁺ are substitutional doped at the Cd_nS_n cluster's surface.

• The ionic radii of the dopants have the substantial role on the bonding interaction with Cd_nS_n clusters. Although Cu²⁺ and In²⁺ do not distort the structure at a lower concentration, they collapse the cluster like other dopants, as the number of dopants increases.

• The dopant's binding energy is found to be increased for all dopants as the concentration increases, except Hg²⁺.

• The HOMO–LUMO gap is significantly reduced for Cu²⁺, Ga²⁺, and In²⁺ dopants. However, for Hg²⁺ the gap is meagerly affected.

• Molecular composition analysis reveals that the dopant contributes not only to the optically active states but also to the surface or trap states.

• Polarizability increases with increase in the size of pristine clusters. However, on introducing dopants the polarizability increases for the Cd₆S₆ cluster but reduces for Cd₁₅S₁₅. The former behavior apparently shows the influence of the lower concentration of dopants at the surface by significantly destabilizing the electron density. However, the latter is due to the cancellation of the effective delocalization of electron density due to higher dopant concentration.

• The absorption spectra of doped CdS clusters are generally red shifted though few Ga and In clusters exhibit blue shift nature due to Burstein–Moss effect.

Acknowledgements

One of the authors Paramasivam Ganesan thanks the Department of Science and Technology, India, for the financial support provided under the DST-PURSE PROGRAMME, through No. BU/DSTPURSEPROG./APPT./22 and CMSD, University of Hyderabad, India for the computing facilities.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra15049g

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