All the calculations described here were performed using the Gaussian 09W package (Frisch et al., 2013). Recent studies have used the simulated annealing technique to find CdTe clusters’ lowest energy structures (Wang et al., 2009; Ma et al., 2012). Our previous study performed an extensive structural search for CdTe clusters using PSO algorithms as implemented in CALYPSO, evaluated the candidate clusters by DFT and MP2 theory levels. We re-used the lowest energy CdTe structures from our previous work for the sake of the present work (Imran et al., 2019). All the symmetric structures of bare and capped QDs were optimized without symmetry constraints. Vibrational frequency analysis indicated that optimized QD structures are actual minimum energy structures.

All the calculations were performed using hybrid functional B3LYP (Becke, 1993) with basis sets of Los Alamos double-ζ effective core potential (Lanl2dz) (Hay and Wadt, 1985a; Hay and Wadt, 1985b; Wadt et al., 1985) in the gas phase as implemented in the Gaussian 09W package. Earlier studies had found the B3LYP/Lanl2dz level of theory to be a practical approach in terms of accuracy and efficiency when used to study CdTe and CdSe bare and capped QDs (Kuznetsov et al., 2012; Lim et al., 2012; Kuznetsov and Beratan, 2014). However, utilizing the B3LYP functional may underestimate the HOMO-LUMO gaps and excited-state energy, which may be corrected by using range-separated functionals, as shown in previous studies (Salzner and Aydin, 2011; Kurban et al., 2019; Muz and Kurban, 2020). In small-sized QDs, all the cadmium atoms are exposed to the surface and potentially coordinated with ligands. We also varied the number of ligands attached to QDs to explore the effect of ligand density on the structural and electronic properties of QDs. Theoretical studies were simulated in toluene solvent (dielectric constant ε = 2.2706). The ligand-binding energies (BE) were calculated with the help of the following equation: BE = [ E ( Cd n Te n L n ) - ( E ( Cd n Te n ) + nE ( L ) ) ] / n Where E(Cd_nTe_nL_n) is the energy of capped QD, E(Cd_nTe_n) is the energy of bare QD, and E(L) is the energy of the capping agent. Time-dependent DFT calculations were performed using the B3LYP/Lanl2dz approach both in the gas and implicit solvent to study the electronic transitions of both bare and capped QDs. Calculated spectra were plotted with the help of Gabedit 2.5.0 (Allouche, 2011) to determine λ _max/E _max from plots. Molecular structures and orbitals were visualized using Molden 5.8 (Schaftenaar and Noordik, 2000) and GaussView, respectively.

Figure 2 shows the minimum energy structures of bare Cd₆Te₆, Cd₈Te₈, and Cd₉Te₉ QDs in the gas phase and their Frontier molecular orbitals. Table 2 shows calculated HOMO/LUMO energies, HOMO-LUMO gaps, E _max, and λ _max.

Cd₆Te₆ (C_3v symmetry) structure shows that it consists of stacks of Cd₃Te₃ rings of hexagonal shape with a Cd-Te bond distance of 2.87 Å inside the hexagonal rings Cd-Te bond distance between the two layers is 3.045 Å.

Cd-Te bond lengths in Cd₈Te₈ (S₄ symmetry) are calculated to be 2.856–3.002 Å in distorted six Cd₂Te₂ rhombi and four Cd₃Te₃ hexagonal rings.

Cd₉Te₉ (D_3h symmetry) consists of three interconnected Cd₃Te₃ hexagonal rings, and Cd-Te bond lengths in upper and lower hexagonal layers are 2.85 Å, while in the middle layer, Cd-Te bond lengths expand to 2.994 Å. The interlayer Cd-Te bond lengths are calculated to be 3.163 Å which is greater than the interlayer bond length of Cd₆Te₆ QD.

Geometry optimization with implicit solvent (toluene) and gas-phase gave similar geometries for all QDs. However, the amount of NBO charges on Cd and Te atoms increased by adding implicit solvent (toluene) during calculations.

In the gas phase, HOMO-LUMO gaps of Cd6Te6, Cd8Te8, and Cd9Te9 QDs revealed that all the QDs were semiconductor-like (Table 1). The calculated HOMO-LUMO gaps are 3.05, 3.09, and 2.76 eV for Cd₆Te₆, Cd₈Te₈, and Cd₉Te₉ QDs. Generally, an increase in the size of QDs decreases HOMO-LUMO gaps, but in the present study, HOMO-LUMO gaps of Cd₉Te₉ QD are less than Cd₆Te₆ QD while Cd₈Te₈ QD shows a higher HOMO-LUMO gap than the other two species. We attribute this observation to different structural motifs of each size of QD. Cd₆Te₆ and Cd₉Te₉ are similar to wurtzite structures with six atoms in a ring, whereas Cd₈Te₈ is somewhat similar to zinc-blende structures. Probably this structural difference is the reason behind the unexpected higher bandgap of Cd₈Te₈.

Table 2 presents TD-DFT calculations of excitation energies (E _max) and absorption wavelengths (λ _max) of excited states with maximum oscillator strength. The calculated excitation energies (E _max) of bare QDs in the gas phase are close to the HOMO-LUMO gaps of the same QDs and consistent with the previous computational report (Lim et al., 2012). The inclusion of toluene solvent in calculations slightly increased the excitation energies. A blue shift in the absorption maxima caused by the solvent is an interesting observation. One may find few previously published studies on solvents’ effect on the absorption spectrum of CdSe clusters reporting a blue shift occurrence (Xu et al., 2010a; Xu et al., 2010b; Lim et al., 2012). In our research, we have observed a similar blue shift occurrence in the case of CdTe clusters.

IP_v and EA_v values are considered to be an index of stability of QDs. It is energetically not favorable for QDs with large IP_v and EA_v values to be activated toward a chemical reaction. Hence, QDs with large IP_v and EA_v values can be considered more stable. Calculated IP_v/IP_ad values and EA_v/EA_ad values are given in Table 3. It is observed that IP_v/IP_ad values decrease with an increase in the size of bare QDs, while EAv/EAad values increase gradually with an increase in the size of bare QDs.

We capped CdTe QDs with aromatic thiol-radical ligands: TP (C₆H₅S-), MBT (CH₃OC₆H₄S-), MBN (CNC₆H₄S-), and MBA (COOHC₆H₄S-), (see Figure 1). The aromatic ligands were coordinated to the QDs via sulfur, which significantly changed the geometries of bare QDs after geometry relaxation. We explored different numbers of capping ligands and different modes of ligands’ coordination with QD.

Cd₆Te₆L₆ and Cd₆Te₆L₄ (L = TP, MBT, MBN, and MBA) species gave stable and physically acceptable geometry after geometry relaxation. For both Cd₆Te₆L₆ and Cd₆Te₆L₄ species, different geometries arose from bare QD because of Cd-Te bond breakage and Cd-S-Te bridge formation in the form of a 5-membered ring. However, the overall structural motif remained intact, containing interconnected two hexagonal (6-membered rings) layers (see Figure 3 and Supplementary Figure S1). Closed structural configurations were observed after optimization of Cd₆Te₆L₆ and Cd₆Te₆L₄ species, and these results are different from previous works of Kuznetsov et al. (2012), Lim et al. (2012), where they had capped Cd₆Te₆ with small-sized ligands and observed open structures after geometry relaxation.

The capping of Cd₈Te₈ QDs (with S₄ point group) by all four aromatic ligands led to a slight opening of the bare QD structure due to Cd-Te bond breakage, Cd-S-Cd bridge formation with 4-membered rings, Cd-S-Te bridge formation with 5-membered rings, and formation of one 8-membered ring. We explored the geometries of two Cd₈Te₈L₈ and Cd₈Te₈L₄ species and found that ligands caused a slight opening of the bare QD structure in both cases. On a relative scale, the coordination of eight ligands caused a larger opening than four ligands (see Figure 4 and Supplementary Figure S2).

Similarly, Cd₉Te₉ QD (with D_3h point group) was also capped with the aromatic thiol-radical ligands, which led to significant changes in QD’s structure compared to its bare lowest energy structure (see Figure 5 and Supplementary Figure S3). Optimized structures of Cd₉Te₉L₉ species showed open structures with a hexagonal ring at the center while above and lowered layer opened up to stabilize the structure. It resulted in Cd-Te bond breakage, Cd-S-Cd bridge formation with 4-membered rings, and Cd-S-Te bridge formation with 5-membered rings. However, in the case of Cd₉Te₉L₄ species with a smaller number of capping ligands attached to QDs, the closed-shell configuration of Cd₉Te₉ QDs remained intact with the slight opening of the QDs structures. These changes in the structure of capped Cd₉Te₉ QDs also arise from the formation of multiple Cd-S-Te bridges in 5-membered ring configuration and breakage of Cd-Te bonds. These findings are consistent with the previous works of Kuznetsov et al. (2012), Lim et al. (2012).

We performed NBO charge analysis to explore the distribution of charges on QDs after capping with aromatic ligands. Cd atoms in all Cd₆Te₆L₆ species displayed positive charges that range from 0.71e to 0.85e. While positive charges on Cd atoms in bare Cd₆Te₆ QDs were 0.76e. There was an increase in the positive charge on Cd atoms in all capped QDs. The ranges of negative charges on Te atoms in capped Cd₆Te₆L₆ species were from −0.11e to −0.77e, close to −0.76e charge on Te atoms in bare Cd₆Te₆ QD.

In Cd₈Te₈L₈ species, the positive charges on the Cd atoms were also higher than bare Cd₈Te₈ QD. The positive charges on Cd atoms in ligated Cd₈Te₈L₈ species were in the range of 0.64e to 0.94e. Compared to bare Cd₈Te₈ QD, there was no significant negative charge change on Te atoms in ligated Cd₈Te₈L₈ species. However, those Te atoms which formed a bridge configuration of Cd-S-Te in capped Cd₈Te₈L₈ species displayed low negative charges.

In bare Cd₉Te₉ QD, the range of positive charges on Cd atoms and negative charges on Te atoms were (0.71–0.79)e and -(0.72–0.85)e, respectively. The range of positive charges on Cd atoms in Cd₉Te₉L₉ species was 0.74e to 0.91e. The negative charges on the Te atom in ligated Cd₉Te₉L₉ species varied from −0.05e to −0.87e. Both positive and negative charge distribution in capped Cd₉Te₉L₉ species varied tremendously. A significant negative charge accumulates on the oxygen of the methoxy group of MBT, the nitrogen of the nitrile group of MBN, and oxygens of the carboxyl group of MBA.

At the CdTe-ligand interface, the charge interchange between the ligand and the QD produces a dipole layer that could influence the oxidation potential of QDs. The extent of charge transfer between the ligand and the QDs determines the strength of the dipole layer. Adsorption of ligands to the QDs causes a change in the net charge of the capping ligands. Table 4 presents the total net change in the NBO charge of capping ligands and the net change in the NBO charge per ligand for all capped QDs. A negative value of net charge transfer by ligands indicates that ligands withdraw electron density from the QDs. The net NBO charge change is in the following order: Cd_nTe_n(MBA)_n > Cd_nTe_n(MBN)_n > Cd_nTe_n(TP)_n > Cd_nTe_n(MBT)_n for each value of n.

Calculated ligand binding energies are given in Table 5. The ligand-binding energies of all ligated QDs decrease in the following order: Cd_nTe_n(MBA)_n > Cd_nTe_n(MBN)_n > Cd_nTe_n(TP)_n > Cd_nTe_n(MBT)_n for each value of n. A possible explanation of this sequence of ligand binding energies can be the HOMOs, and LUMOs stabilization, and higher IP_v and EA_v values depicted by MBA and MBN capped QDs (see Table 1, 2, and 5). On the other hand, Cd_nTe_n(MBT)_n and Cd_nTe_n(TP)_n present lower ligand binding energy due to their HOMOs destabilization and low IP_v and EA_v values. These results are also reflected in NBO charge analysis, where MBA exhibits the biggest charge change by withdrawing electrons density from the QDs. Charge analysis also reveals that oxygens of -COOH groups in Cd_nTe_n(MBA)_n possess greater charges about −(0.598–0.787)e compared to the nitrogen of -CN groups in Cd_nTe_n(MBN)_n that shows charges about −(0.308–0.363)e. This could be another reason for higher ligand binding energies of Cd_nTe_n(MBA)_n. Our calculated ligand binding energies values are close to the previous findings of Lim and co-workers (Lim et al., 2012), who calculated binding energies with the B3LYP/Lanl2dz approach in the gas phase for Cd_nSe_n/Cd_nTe_n QDs (n = 3,4,6, and 9) capped with SCH₂COOH–, SCH₂CH₂CO₂H–, and SCH₂CH₂NH₂ ligands. Our calculated values also agree with the work of Kuznetsov and co-workers (Kuznetsov et al., 2012), who studied Cd_nSe_n/Cd_nTe_n QDs (n = 6,9) capped with NH₃, SCH₃, and OPH₃ ligands in the gas phase using B3LYP/Lanl2dz approach.

Figure 6 presents the interaction of S containing ligands with Cd₆Te₆ QD frontier orbitals. The partial density of states (PDOS) plots (see Figure 7) shows the dominant contributions of sulfur 3p orbitals of the aromatic thiol-radical ligands in the HOMOs of capped Cd₆Te₆ QDs with minor contributions from QD atoms. On the other hand, the LUMOs of the capped Cd₆Te₆ QD show high contributions from both QD atoms and ligand groups: with slightly higher contributions from Te atoms (see Figure 7). The S containing ligands tend to use their lone pair and their unpaired electrons to interact with Cd and Te atoms. An unpaired electron is present in the sulfur 3p orbital of thiol-radical ligands. Seemingly, the singly occupied β-LUMOs of thiol-radical ligands favorably interact with the doubly occupied HOMO of the QD, which possesses some d-character from Cd atoms. This interaction destabilizes the HOMO of the capped QDs, as depicted in Figures 7A,B. The interaction of the LUMOs of QD with the α-LUMOs and β-LUMOs of thiol-radical ligands highly stabilizes the LUMOs of the capped QDs.

Capping with all four aromatic thiol-radical ligands stabilize the LUMOs of all QDs, while HOMOs are either stabilize or destabilize (see Tables 2 and 5). Both TP and MBT ligands destabilize HOMOs in all capped QDs. The effect is much prominent for HOMOs of MBT capped QDs: MBT destabilizes the HOMO by 8.72 eV for Cd₆Te₆, 8.68 eV for Cd₈Te_8, and 8.44 eV for Cd₉Te₉.

On the other hand, both MBN and MBA ligands tend to stabilize HOMOs of all capped QDs. MBN capped QDs show a more pronounced effect with HOMOs stabilization by 4.52 eV for Cd₆Te₆, 4.19 eV for Cd₈Te₈, and 5.82 eV for Cd₉Te₉. All the aromatic thiol-radical ligands decrease the HOMO-LUMO gap of all the capped QDs (see Tables 2 and 5) due to the interaction of frontier orbitals of ligands with frontier orbitals of QDs, as shown in Figure 8. These observations are due to the stronger stabilization of LUMOs as compared to HOMOs. A drastic decrease in the HOMO-LUMO gap is observed for capped Cd₆Te₆ QDs: 1.45 eV for Cd₆Te₆(TP)₆, 1.49 eV for Cd₆Te₆(MBT)₆, 1.16 eV for Cd₆Te₆(MBN)₆, and 1.28 eV for Cd₆Te₆(MBA)₆. While all the other capped QDs show a less pronounced decrease in the HOMO-LUMO gap. This effect of thiol-radical capping ligands is in line with the previous report, where SCH₂COOH, SCH₂CH₂CO₂H, and SCH₂CH₂NH₂ capped Cd_nSe_n/Cd_nTe_n QDs (n = 3,4,6, and 9) were studied by Lim et al. (2012).

We further explore the effect of aromatic thiol-radical ligands on vertical and adiabatic IPs and EAs of QDs in the gas phase (see Table 1 and Figure 9). Analysis of IP/EA values for bare, and capped QDs reveals that both IP_v/IP_ad values show a decrease after capping with all aromatic thiol-radical ligands. However, Cd₆Te₆(MBA)₆, Cd₉Te₉(MBN)_9, and Cd₉Te₉(MBA)₉ species exhibited an increase in IP_v/IP_ad values as compared to bare QDs. EA_v/EA_ad values increase after capping with all aromatic thiol-radical ligands as compared to bare QDs. It is worth noticing that the capping of QDs with MBT ligand causes the highest decrease in IPv values. Generally, IP_v and EA_v values are considered to be an index of stability of capped-QDs. It is energetically not favorable for QDs with large IP_v and EA_v values to be activated toward a chemical reaction. Hence QDs with large IP_v and EA_v values can be more stable toward a chemical reaction. It is observed that IP_v and EA_v values of capped-QDs decrease in the order MBA > MBN > TP > MBT, so the large IP_v and EA_v values of MBA capped QDs are associated with their higher stability.

The density of states (DOS) plots of thiol-radical ligands revealed the presence of midgap states which were not present in the parent thiol ligands. The conversion of thiol into thiol-radical by dehydrogenation generates one singly occupied 3p orbital of the sulfur, which appears as midgap states between the HOMO and LUMO states (see Supplementary Figures S5, S6). The PDOS plots of Cd₆Te₆L₆ species are presented in Figure 7 as a representative, while DOS plots of the rest of ligands and QDs (both bare and capped species) are given in the supporting information. As indicated in Figure 7, the Frontier orbitals of the capped Cd₆Te₆ QDs are mainly composed of ligands’ orbitals, which affect the electronic properties of capped QDs, especially the HOMOs and LUMOs energies of the QDs.

To probe the effect of capping on electronic transitions of QDs, we also performed a TD-DFT study. TDB3LYP/Lanl2dz calculations for bare and capped QDs are given in Tables 3 and 6. We computed excitation energies (E _max), and maximum absorption wavelengths (λ_max) for maximum intensity excited states in the gas phase and with implicit solvent (toluene).

All ligated QDs displayed a decrease in excitation energies compared to the excitation energies of their respective bare QDs. For capped QDs species, all the thiol-radical ligands altered the absorption spectra of bare Cd₆Te₆ and Cd₈Te₈ QDs by shifting the absorption peaks towards lower energy (redshift) because of the midgap states generated by 3p orbitals of sulfur, as shown in Figure 10. Aromatic ligands are known to influence the electronic and optical properties of QDs by stabilizing the LUMOs and reducing the bandgap. The delocalization of the exciton across the ligand shell is attributed to a significant redshift in the absorption spectra of capped CdTe QDs compared to bare QDs. The ligands’ Frontier orbitals coincide with the bandgap of CdTe QDs. Such a resonance situation might generate interfacial QD-ligand states, which would improve the optical properties of the QDs and perhaps open up new relaxation routes for photoexcited charge carriers, hence cause a redshift of the absorption peaks in capped QDs.

The addition of the solvent shifted the redshift toward higher wavelengths for all capped QDs except for Cd₆Te₆(TP)₆ and Cd₆Te₆(MBA)₆ QDs. It was observed that the redshift in the gas phase for capped-Cd₆Te₆ QDs decreased in the following order: TP > MBT > MBA > MBN. For capped-Cd₈Te₈ QDs, it decreased in the order: MBT ≈ MBN > MBA > TP. These results align with previous studies of similar QDs, which suggested that aromatic thiol ligands cause a redshift of the spectrum (Tan et al., 2012; Nadler and Sanz, 2015; Plata et al., 2017).