Structural and Electronic Properties of Bare and Capped Cd33Se33

Article pubs.acs.org/JPCC

Structural and Electronic Properties of Bare and Capped Cd33Se33 and Cd33Te33 Quantum Dots Aleksey E. Kuznetsov*,† and David N. Beratan Departments of Chemistry, Biochemistry and Physics, Duke University, Durham, North Carolina 27708, United States S Supporting Information *

ABSTRACT: We performed comparative DFT (B3LYP/ Lanl2dz) studies of the structural and electronic properties of bare and NH3-, SCH3-, and OPH3-capped Cd33Se33 and Cd33Te33 quantum dots (QDs). The capping groups were chosen as simple models for capping ligands used broadly in experiments. We explored the effects of the capping ligands, coordinated to the QDs via N, S, and O atoms, on the stabilization/destabilization of the QD HOMO and LUMO energies, and on the HOMO/LUMO energy related quantities: vertical ionization potentials and electron affinities. The effects of solvents commonly used in experimental studies of capped QDs (water, toluene, and acetonitrile) on QD structures and electronic properties were investigated as well. Analysis of the bare and capped QD frontier orbital composition was performed using the projected density of states approach. We also studied Cd33Se33 and Cd33Te33 QDs capped with N(CH3)3 and SCH2CO2H ligands.

1. INTRODUCTION Nanoclusters of bulk semiconductor materials1 (“quantum dots”, QDs) have useful properties2 that are tuned by varying the QD size, shape, and capping ligands.2−17 Despite intensive theoretical studies of electronic properties, optical properties, and surface chemistry (capping) of experimentally relevant “large” CdnSen and CdnTen QDs (d ≥ 1.3 nm, n ≥ 33),18−40 comparative studies of these QDs are still absent. We lack an understanding of the structural and electronic changes that occur in large QDs upon capping by different kinds of ligands that bind to the QD surface via N, S, or P atoms. Understanding the electronic structure of bare and capped large QDs, and knowing how to control their electronic structure, is very important for practical applications. With this knowledge, we may be able to tune the redox, optical, and electron-transfer properties of capped QDs (vide inf ra). Also, comparison of structures and electronic properties of CdnSen and CdnTen QDs with the same size (n) and capping ligand type are of great interest due to applications of their assemblies in photovoltaic devices.2,3,12 A review of prior structural and electronic property theoretical studies for bare and capped CdnSen and CdnTen QDs (d ≥ 2 nm, n ≥ 33)18−40 is provided in Table S1 in the Supporting Information. Driven by the need to develop structure−property relationships for the mediumsized capped QDs CdnXn (n = 33, X = Se and Te), we performed comparative DFT (B3LYP/Lanl2dz) studies of the structural and electronic properties of bare and capped Cd33Se33 and Cd33Te33 quantum dots. We explored the effects of the ligands coordinated to the QDs via N (NH3 group), S (SCH3 group), and O (OPH 3 group) atoms on the stabilization/destabilization of the QD HOMO and LUMO © 2014 American Chemical Society

energies, and on HOMO/LUMO energy linked quantities: vertical ionization potentials and electron affinities. Effects of the solvent on the structures and electronic properties of QDs were examined as well. NH3, SCH3, and OPH3 ligands serve as simple models for longer-chain capping groups. Importantly, no theoretical studies of Cd33Se33 and Cd33Te33 QDs capped with experimentally relevant S-containing ligands (vide inf ra) have been performed. Further motivation for our current theoretical study comes from reports of Waldeck and co-workers on fluorescence quenching by electron transfer in aggregates of capped CdSe and CdTe QDs of unspecified stoichiometry.2 The QDs studies of Waldeck and co-workers employed QDs capped with various long-chain ligands: 3-mercaptopropionic acid (MPA), trioctylphosphine oxide, N,N,N-trimethyl(11mercapto-undecyl)-ammonium chloride, N,N-dimethyl-2-aminoethanethiol hydrochloride (DEA), N,N,N-trimethyl-1-dodecylammonium chloride, and N,N,N-trimethyl-2-aminoethanechloride chloride. We compared the predicted structures and electronic properties of both bare and capped Cd33Se33 and Cd33Te33 quantum dots, in the gas phase and with implicit solvent effects included. We studied Cd33Se33 and Cd33Te33 QDs capped with larger N(CH3)3 and SCH2CO2H ligands and performed comparisons of their structures and electronic properties as well. The manuscript is organized as follows: the next section describes our computational approach; the third section discusses our results for both bare and capped CdnXn (X = Received: January 23, 2013 Revised: February 21, 2014 Published: March 4, 2014 7094

dx.doi.org/10.1021/jp4007747 | J. Phys. Chem. C 2014, 118, 7094−7109

The Journal of Physical Chemistry C

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Se/Te, n = 33) QDs; the final section provides conclusions and perspectives.

containing ligands was shown to provide robust and reliable results (see, for example, refs 2, 3, 5, 6, and 14) but other experimental studies (see, e.g., ref 13) showed that currently available ligand-exchange procedures starting with trioctylphosphine-capped QDs often lead to poor stability of the colloids in water. Thus, below we discuss both the gas-phase electronic energies (E) (without zero point corrections) calculated at the B3LYP/Lanl2dz levels and results obtained with implicit solvent effects from toluene and acetonitrile included, and results obtained with water as a solvent are provided in the Supporting Information. The IPv/EAv values were obtained from the energies of systems with N and N ± 1 electrons, calculated using geometries of the N-electron systems. The IPad/EAad values were computed from the energies of the systems with N and N ± 1 electrons, calculated using optimized geometries of the N ± 1 electron species. The ligand-binding energies (BE) were calculated as BE = [E(CdnXnLn) − (E(CdnXn) + nE(L))]/n, where E(CdnXnLn), E(CdnXn), and E(L) are energies of a capped QD, bare QD, and ligand, respectively, calculated at the same level, both in the gas phase and with implicit solvent included. Throughout the paper, negative BE values refer to ligands that are bound to the QDs. In order to estimate the contributions of specific atoms to the HOMO and LUMO of the QDs, we performed calculations of total densities of states (DOS) and fragment densities of states (projected densities of states, PDOS), using the keywords “Fragment” and “Population” as implemented in the Gaussian 09 program. For the fragment densities of states calculations, the QDs were “split” into the fragments corresponding to Cd, Se/Te, and ligands. To further address the difference between effects on DOS of the neutral SCH3 and charged SCH3− ligands, we performed the gas-phase geometry optimization (using the same approach as above) for the charged [Cd33Se33(SCH3)9]9‑ species, calculated its total and projected densities of states and made comparisons with the neutral Cd33Se33(SCH3)9 and Cd33Se33(SCH3)21 species (see below). The electronic structure of multiply charged anionic species should be considered with caution, but we did not want to introduce extra effects on the anion electronic structure by using countercations or solvent effects. We also wanted to avoid the disruption of the QD core structure when capped with a larger number of SCH3− anions, because we observed the opening and disruption of the QD core for smaller CdSe QDs, Cd 6 Se 6 and Cd 9 Se 9 , fully capped with SCH 3 − . The [Cd 33Se 33 (SCH3 )9 ]9‑ PDOS plots are provided in the Supporting Information (Figure S7). Molecular orbitals and structures were visualized using Molden software.61

2. COMPUTATIONAL APPROACH The calculations described here were performed using the Gaussian 09 program.41 The geometries of the bare QDs were optimized beginning with structures in C1 symmetry without symmetry constraints. The resulting structures were assessed using vibrational frequency analysis to probe whether or not the QD structures represent true minimum-energy geometries. If imaginary frequencies were found, further optimizations along those normal coordinates (without symmetry constraints) were performed. The geometries of the capped QDs (in C1 symmetry as well) were optimized without symmetry constraints, and the structures obtained were once again assessed with vibrational frequency analysis, as above. We studied both low-spin and high-spin states (singlet and triplet for NH3-, N(CH3)3- and OPH3-capped QDs and doublet and quadruplet for SCH3- and SCH2CO2H-capped QDs), and we performed global minimum energy searches. Calculations were performed using the Los Alamos double-ζ effective core potential (Lanl2dz),42−44 with the associated basis sets, and with the hybrid B3LYP functional.45−47 The B3LYP/Lanl2dz approach implemented in Gaussian 03 was shown by Tretiak and co-workers to provide a useful compromise between efficiency and accuracy in studies of CdSe clusters.48 Recently, Kilina and co-workers showed the importance of using an augmented basis set with polarization functions to model capped QD structures, using Cd33Se33 as a model.49 We found earlier that employing the same approach, using augmented Gaussian 03/Gaussian 09 basis sets with polarization functions, caused our bare and NH3-capped QDs to collapse upon geometry optimization, producing structures with unphysically short Cd−X and Cd−L bond lengths (L = ligand).50 It is well established that electronic structure calculations using the GGA or LDA functionals tend to severely underestimate HOMO/ LUMO energy gaps.19,51−54 However, the hybrid functionals, such as B3LYP including a portion of the exact HF exchange, are routinely used to partially remedy the above problem and provide calculated energy gaps very close to experimental data.54 In order to explore the effect of different functionals on the HOMO/LUMO energy gaps, we performed single-point electronic structure calculations of the bare, NH3-, SCH3-, and OPH3-capped QDs using the LSDA functional,55,56 two GGA functionals (PBE57 and PW9157), and the hybrid functional PBE0.58 We also performed time-dependent DFT calculations of the optical gap values for the bare, NH3-, SCH3-, and OPH3capped QDs using the TDB3LYP approach. All of these calculations were performed with gas-phase B3LYP/Lanl2dz optimized geometries, using the Lanl2dz effective core potential42−44 with the associated basis sets. Results of these calculations are presented in Table S5 in the Supporting Information. With implicit solvent effects taken into account, we also optimized the geometries for all of the bare and capped QDs at the B3LYP/Lanl2dz level of theory using the selfconsistent reaction field IEF-PCM method59 (the UFF default model used in the Gaussian 09 package, with the electrostatic scaling factor α60 set to 1.5), with water, toluene, and acetonitrile as solvents (dielectric constants ε = 78.3553, 2.2706, and 35.688, respectively). However, there are some ambiguities related to the choice of water as a solvent in simulations: in some experimental studies the use of aqueous solutions of CdSe and CdTe QDs capped with N-, S-, or P-

3. RESULTS AND DISCUSSION 3.1. Structural and Electronic Properties of Bare Cd33X33 (X = Se, Te) Quantum Dots. Gas-phase optimized global-minimum singlet structures of bare Cd33X33 (X = Se, Te) (C1 symmetry) and their frontier orbitals are shown in Figure 1. The bare Cd33X33 QD HOMO/LUMO energy gaps, calculated in the gas phase and with implicit solvent, appear in Table 1 (the bare Cd33X33 QD HOMO/LUMO energies are given in Table S2 of the Supporting Information). The HOMO/LUMO energy gaps for capped QDs and the ionization potentials and electron affinity values calculated for the bare and capped species are given in Tables 1 and 2, respectively (for the full set of the bare QD total energies and HOMO/LUMO energies calculated in the gas phase and with solvent effects taken into account, see Table S2. The five highest energy filled molecular 7095



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Table 1. Bare and Capped Cd33Se33 and Cd33Te33 QDs Calculated at B3LYP/Lanl2dz Levelb species, state Cd33Se33, 1A

Cd33Te33, 1A

Cd33Se33(NH3)21, 1A

Figure 1. Calculated structures of Cd33X33 (X = Se, Te) quantum dots (represented by the Cd33Se33 QD structure), along with the Cd33X33 singlet−triplet energy gaps and plots of their frontier orbitals. Atoms are represented as follows: Cd by large yellow spheres and X by small red spheres. Also, HOMO/LUMO gap energy values, in eV, for both QDs are given.

Cd33Te33(NH3)21, 1A

Cd33Se33(SCH3)21, 2A

orbitals and five lowest-energy empty molecular orbitals of the bare QDs are shown in Figure S1). Triplet state structures were computed to be very high in energy compared to the ground state singlet species for Cd33Se33 and Cd33Te33, by 43.1 and 41.8 kcal/mol, respectively. These values are close to the singlet−triplet differences calculated for smaller species in our previous study, 43.2/38.7 kcal/mol for Cd6Se6 and Cd6Te6 and 44.1/27.6 kcal/mol for Cd9Se9 and Cd9Te9.50 To study solvent effects on the HOMO/LUMO energy gaps, we performed both single-point calculations with implicit solvent based on gas-phase optimized QD geometries and full geometry optimization in the presence of continuum solvent. Comparison of the calculated HOMO/LUMO energy gaps for Cd33Se33 and Cd33Te33 shows the gaps to be very similar, both in the gas phase and with implicit effects from water, toluene, and acetonitrile (see Tables 1 and S2). Generally, including implicit solvent effects destabilizes both the filled and empty MOs of the bare QDs, destabilizing the empty orbitals to a greater extent (see Table S2). Implicit solvent effects increase the HOMO/LUMO energy gaps compared to the gas-phase calculated values (Table S2) and move the energy gaps closer to the experimental optical gap values, 2.96 eV (from UV−vis absorption spectroscopy in water solutions for Cys-capped Cd33Se33 and Cd34Se34 QDs)5,6 and 2.99 eV (found by UV−vis absorption spectroscopy in toluene solutions for Cd33Se33 and Cd34Se34 QDs).7 However, the calculated HOMO/LUMO energy gaps are likely to better model the ionization potential/ electron affinity data than UV−vis absorption spectroscopy data, so caution should be used when comparing computed energy gaps. Including implicit solvent effects in the singlepoint energy calculations with the gas-phase optimized QD geometries gives larger HOMO/LUMO gaps than are found with the solvent-optimized structures (Table S2). Implicit acetonitrile causes more significant HOMO/LUMO destabilization than toluene. Optical bulk bandgap values of CdSe and CdTe are 1.8462 and 1.4463 eV, respectively. Thus, the question could be raised as to why the Cd33Se33 QD has a HOMO/LUMO gap very close to that of the Cd33Te33 QD, both in the gas phase and with implicit solvent effects (see Tables 1 and S2). However, if we look at the HOMO/LUMO energy gap values calculated on the B3LYP/Lanl2dz optimized geometries employing other

Cd33Te33(SCH3)21, 2A

Cd33Se33(OPH3)21, 1A

Cd33Te33(OPH3)21, 1A

gap, eVa Cd33X33 2.50 (gas phase) 2.59 (toluene) 2.73 (acetonitrile) 2.52 (gas phase) 2.59 (toluene) 2.67 (acetonitrile) Cd33X33(NH3)21 2.45 (gas phase) 2.54 (toluene) 2.71 (acetonitrile) 2.46 (gas phase) 2.55(toluene) 2.70 (acetonitrile) Cd33X33(SCH3)21 α: 1.27 β: 1.44 (gas phase) α: 1.32 β: 1.44 (toluene) α: 1.32 β: 1.29 (acetonitrile) α: 1.02 β: 0.94 (gas phase) α: 0.98 β: 1.02 (toluene) α: 1.09 β: 1.12 (acetonitrile) Cd33X33(OPH3)21 2.53 (gas phase) 2.63 (toluene) 2.74 (acetonitrile) 2.66 (gas phase) 2.44 (toluene) 2.66 (acetonitrile)

BE/L, kcal/mola −

−

−19.2 −18.8 −18.3 −17.6 −17.5 −17.3

−18.7 −17.6 −16.3 −21.1 −20.5 −19.5 −7.6 −6.7 −5.6 −4.5 −4.1 −3.7

a

Results are given in the following order: gas phase, C6H5CH3, CH3CN. bFor each QD, the global minimum spin state is provided. Ligand binding energies in kcal/mol and HOMO/LUMO energy gaps in eV are given as calculated in the gas phase and with implicit solvent effects from C6H5CH3 and CH3CN.

density-functional theory approaches (see the Computational Approach), we will find that the situations are different: with the TDB3LYP/Lanl2dz approach, the Cd33Se33 optical gap is now larger than the Cd33Te33 optical gap, 2.65 eV vs 2.42 eV (see Table S5), in agreement with the bulk optical bandgap trend. The hybrid PBE0 functional again gives similar HOMO/ LUMO gap values for both QDs, which may be considered as an overestimate compared with the B3LYP calculated HOMO/ LUMO gap values and with the TDB3LYP optical gap values. And both the LSDA and two GGA functionals strongly underestimate the HOMO/LUMO gap values and, moreover, tend to make the Cd33Se33 HOMO/LUMO gap value smaller than that for the Cd33Te33 QD (Table S5). Generally, one should use care when comparing the calculated HOMO/LUMO energy gaps which are just differences between the LUMO and HOMO energies with the optical bandgap values; the timedependent approach is more appropriate for estimating optical gaps. 7096



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atoms were ca. -(0.92−1.06)/(0.74−0.89)e for Cd33Se33 and Cd33Te33, respectively (see Table S4). 3.2. Structural and Electronic Properties of Capped Cd33X33 Quantum Dots. 3.2.1. NH3-Capped QDs. Gas-phase optimized minimum-energy singlet structures of NH3-capped CdX (X = Se, Te) species and their frontier orbitals appear in Figure 2, and the computed energy gaps are given in Table 1. For the NH3-capped Cd33X33 species, triplet states were again calculated to be very high in energy for both Se and Te, although slightly lower than computed for the bare QDs, by 39.9 and 38.5 kcal/mol, respectively. These values are relatively close to the singlet−triplet energy differences calculated for the smaller NH3-capped species in our earlier study, 54.0/71.3 kcal/mol for Cd6Se6 and Cd6Te6 and 51.5/46.7 kcal/mol for Cd9Se9 and Cd9Te9 QDs.50 Increasing the QD size thus produces a slight decrease in the calculated singlet−triplet energy gaps. Analysis of the NH 3 -capped QDs shows that the Cd33Se33(NH3)21 geometry is slightly different from that of Cd33Te33(NH3)21 (Figure 3). The calculated H−Se/H−Te bond lengths in the gas-phase optimized structures are in the range 2.57−2.77/2.72−3.07 Å, suggesting the possibility of hydrogen bond formation between X atoms and NH3 ligands. Hydrogen bonds should be somewhat weaker in Cd33Te33(NH3)21 than in the Cd33Se33(NH3)21 QD due to the slightly smaller negative natural bonding orbitals (NBO) charges on Te vs Se atoms in the bare QD (see above). This possible interaction of the NH3-groups with X atoms via hydrogen bonds, and the resulting QD core distortion, resembles distortions of the NH3-capped Cd9X9 species found in our earlier study50 (see also Figure S6 in the Supporting Information). To further explore the possibility of hydrogen bond formation between X atoms of the QD core and amine ligands, we performed geometry optimizations of the Cd33Se33 QD with three different NH2-containing ligands: C4H8NH2, C5H11NH2, and C6H13NH2. In the cases of C4H8NH2 and C6H13NH2, three ligands were bound to the QD. In the case of C5H11NH2, two ligands were bound to the QD core, and optimizations for all the ligands studied were performed both in the gas phase and with implicit effects from water and toluene taken into account. We found that for all three ligands lengths studied, both in the gas phase and with implicit solvent effects included, ligands did not tend to form hydrogen bonds with the QD X atoms. The shortest distance between the amino hydrogens and the QD atoms (Se) was found to be about 3.15 Å, which is too long for any significant hydrogen bonding. Therefore, we conclude that, for amine ligands with long alkyl chains, where many conformations for the ligands are possible, hydrogen bond formation with the QD X atoms is unlikely. In the case of small NH3-ligands, however, the situation is different, because the ligands are restricted in their movements during geometry optimizations, and thus some hydrogen bond formation may occur. NBO charge analysis of the NH3-capped QDs indicates that the positive Cd charges in the Cd33Se33(NH3)21 QD remain almost the same, (0.85−1.13)e vs (0.87−1.02)e in the bare Cd33Se33 QD (see Table S4), and the same is true for negative charges on the Se atoms (Table S4). Significant negative charge accumulates on the N atoms of NH 3 -groups in Cd33Se33(NH3)21, about −(1.17−1.21)e on each N, and the hydrogens bear positive charges of ca. (0.40−0.44)e. In Cd33Te33(NH3)21, the positive charge range on the Cd atoms differs slightly from that found in bare Cd33Te33, (0.68−1.00)e

Table 2. Calculated Ionization Potentials (IP) and Electron Affinities (EA) of the CdnSen and CdnTen Species Capped by NH3, SCH3, and OPH3 Groups, Vertical (IPv and EAv) and Adiabatic (IPad and EAad) Values (B3LYP/Lanl2dz Level of Theory) species Cd33Se33, 1A

Cd33Te33, 1A

Cd33Se33(NH3)21, 1A

Cd33Se33(SCH3)21, 1A

Cd33Te33(SCH3)21, 1A

Cd33Se33(OPH3)21, 1A

Cd33Te33(OPH3)21, 1A

IPv/IPad, eVa Cd33X33 7.25/6.93 (gas phase) 6.54/6.22 (toluene) 6.04/5.66 (acetonitrile) 6.82/6.57 (gas phase) 6.20/5.94 (toluene) 5.75/5.44 (acetonitrile) Cd33X33(NH3)21 6.31/4.91 (gas phase) 4.87/4.55 (toluene) 4.78/4.40 (acetonitrile) Cd33Te33(NH3)21, 1A 5.04/4.69 (gas phase) 4.65/4.45 (toluene) 4.53/4.33 (acetonitrile) Cd33X33(SCH3)21 6.68/4.96 (gas phase) 6.28/6.08 (toluene) 6.00/4.78 (acetonitrile) 6.32/4.55 (gas phase) 5.93/4.16 (toluene) 5.67/4.94 (acetonitrile) Cd33X33(OPH3)21 5.77/3.79 (gas phase) 5.59/5.27 (toluene) 5.77/3.79 (acetonitrile) 5.52/5.03 (gas phase) 5.52/5.03 (toluene) 5.52/5.03 (acetonitrile)

EAv/EAad, eVa 3.13/3.20 3.32/3.38 3.33/3.36 2.86/3.13 3.07/3.16 3.12/3.18

(gas phase) (toluene) (acetonitrile) (gas phase) (toluene) (acetonitrile)

1.11/1.20 (gas phase) 1.64/1.20 (toluene) 2.03/1.98 (acetonitrile) 1.01/1.51 (gas phase) 1.50/1.53 (toluene) 1.85/2.27 (acetonitrile) 3.99/6.02 4.40/6.54 4.71/5.58 3.98/4.74 4.36/5.05 4.64/5.47


1.83/3.97 2.33/2.91 2.73/3.42 1.75/4.08 2.17/2.36 2.48/3.19


a Results are given in the following order: gas phase, C6H5CH3, and CH3CN.

Further analysis of the bare QD electronic properties indicates that the LUMOs of the bare QDs are dominated by surface Cd and X orbitals, with larger contributions from the Cd atoms (see MO plots in Figure 1 and PDOS plots in Figure 2), and the HOMOs of both bare QDs are dominated by the X (X = Se or Te) contributions, with some contributions from the Cd atoms in the Cd33Te33 case (Figure 2). The HOMO is more spatially localized and the LUMO is more delocalized over the entire QD surface (see Figure 1). Analysis of the calculated IP and EA values (Table 2) shows a decrease in both vertical and adiabatic IP/EA values for Cd33Te33 compared with Cd33Se33. The energy decrease is explained by the Cd33Te33 HOMO/ LUMO destabilization compared to the case for the Cd33Se33 QD. The vertical IP/EA value decrease is larger than the decrease in the adiabatic IP/EA values (see Table 2). Inclusion of acetonitrile solvent effect causes a significant decrease in the calculated IPv/IPad values, by 1.2−1.3 eV for the Cd33Se33 QD and by 1.08−1.15 eV for the Cd33Te33 QD (Table 2). Toluene solvation decreases the calculated IPv/IPad values by ca. 0.7 eV for Cd33Se33 and by ca. 0.6 eV for Cd33Te33. The implicit solvent effects on the calculated EAv/EAad values are much less pronounced (see Tables 2 and S3). NBO charges on Cd atoms were calculated to be ca. (0.87−1.02)/(0.71−0.84)e and on X 7097



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Figure 2. Density of states (DOS) near the HOMO/LUMO gap for the bare Cd33Se33 (a) and Cd33Te33 (b) quantum dots calculated using the B3LYP/Lanl2dz method. The black dotted line shows the total DOS, the brown line shows the projected density of states (PDOS) calculated for the Cd atoms, and the blue line shows the PDOS calculated for the Se/Te atoms. The energy of the molecular orbitals, in eV, given on the x-axis was kept unscaled.

for NH3 binding to CdnSen species, which show a steady decrease of the ligand binding energies with the cluster size: −18.0 kcal/mol, Cd6Se6 in S6 symmetry; −16.0 kcal/mol, Cd9Se9 in C3h symmetry; −14.1 kcal/mol, Cd12Se12 in S6 symmetry; −13.5 kcal/mol, Cd15Se15 in C3h symmetry; −13.2 kcal/mol, Cd16Se16 in Td symmetry; −13.0 kcal/mol, Cd18Se18 in C3h symmetry; −12.6 kcal/mol, Cd21Se21 in C3h symmetry; and −14.8 kcal/mol, Cd24Se24 in S6 symmetry. The observed discrepancy is likely explained by differences in the approaches used (B3LYP/Lanl2dz in our analysis vs B3LYP/[VDZ-SD+631G(d)] in the studies of Nguyen et al.18). Our BE results are relatively close to those of Stener and co-workers,21 −16.5/− 17.8/−18.8 kcal/mol (PW91 functional with a DZ basis set for Cd and Se and TZP basis sets for N and H, as implemented in the ADF code21), and −24.6/−25.9/−29.5 (VWN functional with DZ basis sets for Cd and Se and TZP basis sets for N and H21), for Cd33Se33 QD capped with 21/12/9 NH3 ligands, respectively. Comparison of the calculated HOMO/LUMO energy gaps for the NH3-capped Cd33X33 species shows that the counterion X (X = Se/Te) has a weak influence on these values, as in the case of the bare QDs (see Tables 1 and S2). Comparison of the NH3-capped QDs optical energy gaps and HOMO/LUMO energy gaps (see Table S5) shows a trend similar to that found in the case of the bare QDs (see above): both hybrid functionals, B3LYP and PBE0, give essentially the same HOMO/LUMO energy gap values, but the Cd33Se33(NH3)21 optical gap is again larger than the Cd33Te33(NH3)21 optical gap value; the LSDA and GGA functionals again give smaller HOMO/LUMO gaps for the capped Cd33Se33 QD (Tables S4 and S5). The LUMOs of both Cd33Se33(NH3)21 and Cd33Te33(NH3)21 have dominant contributions from the QD core Cd and X atoms, as seen from the results of the DOS and PDOS calculations, Figure 4. The HOMOs of both capped QDs have dominant contributions from the X atoms (Figure

Figure 3. Calculated structures of NH3-capped Cd33X33 (X = Se, Te) quantum dots, their singlet−triplet energy gaps, and plots of their frontier orbitals. Atoms are represented as follows: Cd by large yellow spheres, Se by red spheres, Te by large light gray spheres, H by small yellow spheres, and N by blue spheres. HOMO/LUMO gap energies are in eV.

compared to (0.71−0.84)e, which is also true for negative charges on the Te atoms, which increase somewhat to −(0.82− 0.97)e compared to −(0.74−0.89)e in bare Cd33Te33. The ligand binding energies were computed to be slightly higher for Cd33Se33(NH3)21 than for Cd33Te33(NH3)21, both in the gas phase and with implicit solvent effects included, see Table 1. The calculated values agree with our previous findings for NH3-capped Cd6X6 and Cd9X9 QDs,50 with the gas-phase calculated binding energies −21.9/-20.2 kcal/mol for the capped Cd6X6 and −21.1/−20.5 kcal/mol for the capped Cd9X9 QDs, respectively. Our calculated binding energies for the capped Cd33Se33 QD differ from results of Nguyen et al.18 7098



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Figure 4. Density of states (DOS) near the HOMO/LUMO gaps for the NH3-capped Cd33Se33 (a) and Cd33Te33 (b) quantum dots calculated using the B3LYP/Lanl2dz method. The black dotted line shows the total DOS, the brown line shows the PDOS calculated for the Cd atoms, the blue line shows the PDOS calculated for the Se/Te atoms, and the red line shows the PDOS calculated for the NH3 ligands. The energy of the molecular orbitals, in eV, given on the x-axis was kept unscaled.

Figure S8) and thus ligands HOMOs interact with deeply located Cd states of bare QDs causing their significant destabilization (see Figure 2 and 4) which brings about the overall occupied MOs destabilization of the NH3-capped QDs. Smaller destabilization of the Cd33Te33 HOMO can be explained by the Cd33Te33 Cd states being higher in energy compared to the Cd33Se33 Cd states (Figure 2a,b). The QD LUMOs, which have dominating X contributions (X = Se, Te), are much closer in energy to the ligand LUMOs and thus should be less destabilized compared to the QD HOMOs. There are noticeable differences between larger and smaller NH3-capped QDs, too: the EAv values of the NH3-capped Cd6X6 and Cd9X9 QDs were computed to be negative (or very close to zero) compared with the EAv values for bare small QDs, which is not the case for the capped Cd33Se33 and Cd33Te33 species. The gas-phase computed IPv values are computed to increase in the series Cd9Se9(NH3)9 (5.68 eV) < Cd6Se6(NH3)6 (5.81 eV) < Cd33Se33(NH3)21 (6.31 eV) and to decrease in the series Cd 6 Te 6 (NH 3 ) 6 (5.69 eV) > Cd9Te9(NH3)9 (5.66 eV) > Cd33Te33(NH3)21 (5.04 eV). To study solvent effects on the HOMO/LUMO energy gaps in greater detail, we performed both single-point calculations with implicit solvent effects included using the gas-phase optimized QD geometries, and geometry optimization with implicit solvent effects included. Inclusion of implicit solvent effects was shown to stabilize both filled and empty MOs of the capped QDs (see Table S2). The smaller implicit solvent stabilization of the empty MOs increases the solvent-calculated HOMO/LUMO energy gaps compared to the gas-phase values. Inclusion of solvent effects drastically lowers the computed IPv values and, to a lesser extent, lowers the computed IPad and increases computed EAv/EAad values (see Tables 2 and S3). 3.2.2. SCH3-Capped QDs. Figure 5a shows gas-phase optimized doublet structures of Cd33Se33(SCH3)21 and Cd33Te33(SCH3)21 QDs; their filled and empty frontier orbitals are shown in Figure 5b. No prior theoretical studies of Cd33Se33

4). The contributions of the ligand MOs (mostly N atom atomic orbitals (AOs)) appear only at very low MO energies (not shown at the PDOS plots, Figure 4) or at high MO energies (red lines at positive MO energy values at Figure 4, parts a and b). The capped QD HOMOs are localized on the QD surface and the LUMOs are “smeared” over the whole QD surface (see Figure 3). This is similar to the case of the bare QDs (see above, Figure 1) and agrees with our previous theoretical findings for the NH3-capped Cd6X6 and Cd9X9 species.50 Analysis of the calculated IP and EA values (Table 2) indicates that again both vertical and adiabatic IP/EA values for capped Cd33Te33 are lower compared with the same values for the capped Cd33Se33 species, as in the case of bare QDs (see above). Further, NH3 capping leads to a significant decrease of both vertical and adiabatic IP/EA values compared with the bare species (see Tables 2 and S3). Comparison with our previous study50 finds similarities in behavior of the larger QD and the smaller QD vertical IPs and EAs: NH3-capping of Cd6X6 and Cd9X9 drastically reduces both the vertical QD IPs and EAs compared to the bare species. Understanding of this effect can be obtained from the analysis of the MO interactions between the QD and the ligands, similar to that employed in our previous study.50 In Figure S8, we provide a qualitative molecular orbital diagram showing the interactions between the frontier MOs of the Cd6Se6 QD and six NH3 ligands. This diagram is used for simplicity, but it helps to understand the effects of the NH3-ligands on both the vertical and adiabatic IP/ EA values: NH3-ligands destabilize both the HOMOs and LUMOs in capped QDs (see Figure S8). However, in comparison with the smaller QDs,50 the destabilization effect is more pronounced for the HOMOs instead of the LUMOs: NH3 destabilizes the HOMO/LUMO by 2.13/2.07 eV for Cd33Se33 and by 1.94/1.88 eV for Cd33Te33 (see Table S1). Stronger HOMO destabilization can be explained by the fact that the ligands coordinate to Cd via their lone pairs (see 7099



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(β-spin) in Cd33Se33(SCH3)21 and from 0.60e (α-spin) to 0.99e (β-spin) in Cd33Te33(SCH3)21. Large amounts of unpaired spin density located on S and Se/Te in the doublet Cd33Se33(SCH3)21 and Cd33Te33(SCH3)21 species cause significant spin-contamination (see Table S2), similar to the previous findings for the SCH3-capped Cd9Se9 and Cd9Te9 QDs.50 NBO charge analysis shows that the SCH3-capping does not change the charges on the Cd atoms significantly (they were computed to be ca. (0.91−1.08)/(0.68−0.97)e for Cd33Se33(SCH3)21 and Cd33Te33(SCH3)21, respectively, see Table S4) and somewhat changes the negative charges on the X atoms, to −(0.41−1.06)/(0.15−0.90)e for Cd33Se33(SCH3)21 and Cd33Te33(SCH3)21, respectively, compared to the charges calculated for bare QDs (see Table S4). Charges on the S atoms vary broadly, from −0.02e to −0.50e for Cd 33 Se 33 (SCH 3 ) 21 and from −0.04e to −0.50e for Cd33Te33(SCH3)21. Significant negative charge was calculated to be on the C atoms, ca. −0.70e for Cd33Se33(SCH3)21 and for Cd33Te33(SCH3)21 (see Table S4). Space electron charge distributions of the Cd33Se33(SCH3)21 and Cd33Te33(SCH3)21 frontier orbitals (see Figure 5b) differ significantly from those found for the bare and NH3-capped QDs (Figures 1 and 3, respectively). For the SCH3-capped Cd33X33 QDs, both filled and empty MOs are more localized in space compared with those of the bare and NH3-capped QDs. Analysis of the calculated PDOS values for the Cd33Se33(SCH3)21 QD (Figure 6) shows that both the α- and β-LUMOs of the QD have significant contributions from both the ligand MOs, dominated by the S-AOs contributions, and from the Se-AOs, which is also found for the α-HOMO of the QD (cf. Figure 6, parts a and b). The β-HOMO of the QD, however, has very large Se-AOs contributions, and the small Cd-localized AOs appear far from the frontier MO energies. Comparison of the calculated PDOS for the Cd33Se33(SCH3)21 and Cd33Te33(SCH3)21 QDs (cf. Figures 6 and 7) shows noticeable composition similarities of the α-HOMOs/LUMOs (Figures 6a and 7a) and β-LUMOs (Figures 6b and 7b) of the both QDs but significant differences in the composition of their β-HOMOs: the Cd33Te33(SCH3)21 β-HOMO is composed mostly of the ligands’ MOs compared to the dominant Se-AOs contributions to the β-HOMO of the Cd33Se33(SCH3)21 QD. The Cd33Te33(SCH3)21 α-HOMO also has some small Cd-AOs contributions. The features of the frontier orbitals for the SCH3-capped QDs make them very different from their NH3-capped counterparts (cf. Figures 4 and 6, 7). To show the effect of the ligand concentration on the capped electronic QD structure, similar to theoretical studies performed by Kilina and co-workers for the Cd33Se33 QDs capped with NH2Me and OPMe3,28,29 in Figure 8 we provide calculated DOS plots for the Cd33Se33 QD capped with 9 SCH3 ligands. Similar to the Cd33Se33 QD capped with 21 SCH3 ligands the quadruplet spin state of the partially SCH3-capped QD was found to be essentially degenerate in energy with the ground-state doublet state, and for the sake of simplicity we study the doublet state here. Comparison of the PDOS for fully and partially capped Cd33Se33 QDs (Figures 6 and 8, respectively) shows that: (i) both α- and β-HOMOs/LUMOs of the partially capped QD have similar composition, with significant Se and ligand contributions for the HOMOs and contributions only from Se for the LUMOs (see Figure 8); (ii) both α- and β-LUMOs of the partially capped QD have no ligand contributions compared with strong ligand contributions for the fully capped

Figure 5. (a) Calculated structures of the SCH3-capped Cd33X33 (X = Se, Te) quantum dots along with their gas-phase doublet-quadruplet energy gap values and (b) plots of their frontier orbitals. Atoms are represented as follows: Cd by large yellow spheres, Se by small red spheres, Te by large light gray spheres, H by small yellow spheres, S by orange spheres, and C by small orange spheres. HOMO/LUMO energy gap values are in eV.

and Cd33Te33 QDs capped with experimentally significant Scontaining ligands (see, for example, ref 2) were previously reported. Similar to previous findings for the SCH3-capped C9X9 (X = Se, Te) QDs,50 the quadruplet spin states of the SCH3-capped larger QDs were found to be essentially degenerate in energy with the ground-state doublet states (see Figure 5a and Table S2) (cf. with −0.007/−0.01 kcal/mol in the gas phase for Cd9Se9 and Cd9Te9, respectively50). For simplicity, we examine the doublet states here. SCH3-capping causes significant distortions of the Cd33X33 QD, with Cd-X bond breakage, rearrangements, and Cd−S−Se/Te and Cd− S−Cd bridge formation (see Figure 5a), similar to the previous theoretical findings for smaller Cd6X6 and Cd9X9 QDs.50 The ligand binding energies were calculated to be slightly larger for Cd33Te33(SCH3)21 than for Cd33Se33(SCH3)21 (see Tables 1 and S2). In the doublet state, sulfurs of the Cd33Se33(SCH3)21 and Cd33Te33(SCH3)21 QDs have significant amounts of unpaired spin-density (from 0.77e (α-spin) to 0.75e (β-spin) in the doublet Cd33Se33(SCH3)21 and from 0.74e (α-spin) to 0.66e (β-spin) in the doublet Cd33Te33(SCH3)21), based on Mulliken spin-density analysis. Some Se/Te atoms carry even larger amounts of unpaired spin-density, from 1.00e (α-spin) to 0.98e 7100



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Figure 6. Density of states (DOS) near the HOMO/LUMO gaps for the Cd33Se33 QD capped with 21 SCH3-ligands, α- (a) and β-MOs (b), calculated using the B3LYP/Lanl2dz method. The black dotted line presents the total DOS, the brown line shows the PDOS calculated for the Cd atoms, the blue line shows the PDOS calculated for the Se/Te atoms, and the red line shows the PDOS calculated for the SCH3 ligands. The energy of molecular orbitals, in eV, given on the x-axis was kept unscaled.

Figure 7. Density of states (DOS) near the HOMO/LUMO gaps for the Cd33Te33 QD capped with 21 SCH3-ligands, α- (a) and β-MOs (b), calculated using the B3LYP/Lanl2dz method. The black dotted line presents the total DOS, the brown line shows the PDOS calculated for the Cd atoms, the blue line shows the PDOS calculated for the Se/Te atoms, and the red line shows the PDOS calculated for the SCH3 ligands. The energy of molecular orbitals, in eV, given on the x-axis was kept unscaled.

QD (see Figures 6 and 8); (iii) for both partially and fully capped QDs, there are no Cd contributions in both HOMOs and LUMOs. Thus, the increase of the capping ligand concentration causes noticeable changes in the capped QD electronic structure leading to different surface states of the capped QDs and different HOMO/LUMO gaps, too (see Figures 6 and 8). These results are in line with the findings of Kilina and co-workers for other ligand types.28−30

It is also of interest to explore how capping of the QD with the charged thiolate ligands, SCH3−, will affect the capped QD electronic structure. We performed DOS calculations for the completely optimized charged [Cd33Se33(SCH3)9]9‑ QD, as described in the Computational Approach. We understand that the electronic structure of multiply charged anionic species should be considered with caution, but we did not want to introduce extra effects on the anion electronic structure by 7101



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Figure 8. Density of states (DOS) near the HOMO/LUMO gaps for the Cd33Se33 QD capped with 9 SCH3-ligands, α- (a) and β-MOs (b), calculated using the B3LYP/Lanl2dz method. The black dotted line presents the total DOS, the brown line shows the PDOS calculated for the Cd atoms, the blue line shows the PDOS calculated for the Se atoms, and the red line shows the PDOS calculated for the SCH3 ligands. The energy of molecular orbitals, in eV, given on the x-axis was kept unscaled.

As described above, NH3-groups can coordinate to Cd only by their lone pairs, whereas SCH3-groups apparently can interact with Cd and Se/Te via their lone pairs and also via their unpaired electrons. Sulfur in the SCH3-ligand has an unpaired electron in its 3p-orbital. It is apparently favorable for the doubly occupied QD HOMO to interact with the singly occupied β−LUMOs of the SCH3-ligands, which has strongly pronounced d-character (Figure S9). This interaction somewhat destabilizes the HOMO of the capped QDs. The QD LUMOs can interact favorably with the α−LUMOs of the ligands, apparently with some contributions from the β− LUMOs as well, which strongly stabilizes the LUMOs of the capped species (see Figure S9). Both vertical and adiabatic IP and EA values calculated for the SCH3-capped Cd33Te33 QDs are generally lower compared to the calculated vertical and adiabatic IP values for the SCH3capped Cd33Se33 species (see Tables 2 and S3), similar to the above results for bare and NH3-capped species. SCH3-capping generally reduces both vertical and adiabatic IPs compared with bare species (see Tables 2 and S3), but the computed EAv/EAad values are higher for the SCH3-capped species compared to the bare QDs. This is consistent with our previous findings for the smaller SCH3-capped QDs50 and is attributed to HOMO destabilization and LUMO stabilization in the SCH3-capped QDs. Inclusion of implicit solvent effects does not change the calculated HOMO/LUMO energy gaps significantly compared to the gas-phase values computed for Cd33Se33(SCH3)21 and Cd33Te33(SCH3)21 (see Tables 1 and S2). The effect for more polar solvent CH3CN is slightly more pronounced than the effect for C6H5CH3. Inclusion of implicit solvent effects lowers the computed IPv/EAv values for the SCH3-capped QDs, but the influence on the IPad/EAad values is more complicated (see Tables 2 and S3). Comparison with our previous study50 shows

introducing countercation or solvent effects. We also wanted to avoid disrupting the QD core when capped with a larger number of SCH3− anions, because we observed the opening and breaking of the QD core for smaller CdSe QDs, Cd6Se6 and Cd9Se9, fully capped with SCH3−. Close consideration of the [Cd33Se33(SCH3)9]9‑ DOS plots (see Figure S7) shows their striking similarity to the DOS of the bare Cd33Se33 QD (cf. Figure 2a): large HOMO/LUMO gap, the HOMO dominated by the Se contributions, the LUMO dominated by Cd contributions, and the very small total DOS of the unoccupied MOs compared to the occupied MOs. This implies that the negatively charged thiolate ligands should not affect the electronic structure of the capped QD significantly. The SCH 3 -groups somewhat destabilize the Cd 33 X 33 HOMOs (see Table S2), by 0.39/0.36 eV for the α/βHOMOs of capped Cd33Se33 and by 0.42/0.42 eV for the α/βHOMOs of capped Cd33Te33. The ligands more significantly stabilize the Cd33X33 LUMOs by 0.85/0.70 eV for the α/βHOMOs of Cd33Se33(SCH3)21 and by 1.08/1.16 eV for the α/ β-HOMOs of Cd33Te33(SCH3)21 (see Table S2) (cf. with 0.70/ 0.71 eV for α/β-HOMOs of Cd9Se9 and by 0.15/0.01 eV for α/ β-HOMOs of Cd9Te9, and with 1.03/1.52 eV for α/β-HOMOs of capped Cd9Se9 and by 0.89/1.44 eV for α/β-HOMOs of capped Cd9Te950). The HOMO destabilization and LUMO stabilization leads to a drastic decrease of the HOMO/LUMO gaps, by 1.23/1.06 eV for the α/β-gaps of Cd33Se33(SCH3)21 and by 1.50/1.58 eV for the α/β-gaps of Cd33Te33(SCH3)21 (Tables 1 and S2). These effects are more significant for the Cd33Se33 species, in contrast with previous theoretical results found for the SCH3-capped Cd9Se9 and Cd9Te9 species.50 Again, analysis similar to the case of smaller capped QDs50 is helpful here (see Figure S9). The HOMOs of the SCH3-capped QDs have dominant contributions from sulfur 3p-orbitals of the capping group with some minor contributions from QD atoms. 7102



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symmetry; −17.0 kcal/mol, OP(OH)2CH3 bound to Cd12Se12 in S6 symmetry. Our calculated binding energies (BE) differ significantly from the local-density approximation values of Puzder et al. for phosphine oxide derivatives bound to Cd15Se15 ((CH3)3PO, −24.4; CH3(OH)2PO, −25.8) and to Cd33Se33 ((CH3)3PO, −19.6; (CH3)3PO, −28.4; CH3(OH)2PO, −25.6; CH3(OH)2PO, −33.4; CH3(OH)2PO, −29.1, all in kcal/ mol).20 Our calculated OPH3 BE values also differ from results of Tretiak and co-workers28,29,33 for the OPMe3 binding to Cd33Se33 species: −(5.3−31.6) kcal/mol13 or −(18.7−30.4) kcal/mol,33 which is explained by the different ligand models and the different theoretical approaches used in the two studies. More generally, the OPH3-binding energies are difficult to interpret because of the (numerous) H-transfer processes occurring upon structural relaxations that change the chemistry of the ligands. More detailed studies of OPH3 and related ligands binding to CdSe and CdTe QDs should be the subject of future investigations. NBO charge analysis shows that, in the Cd33Se33(OPH3)21 QD, the calculated positive charges on the Cd atoms are generally slightly larger than the calculated charges on the Cd atoms in Cd33Te33(OPH3)21, (0.82−1.19)e vs (0.64−1.08)e. The calculated negative charges on the Se atoms of Cd33Se33(OPH3)21 are also larger than the charges on the Te atoms of Cd33Te33(OPH3)21, −(0.56−1.08)e vs −(0.33− 0.92)e. In both capped QDs, significant positive charges are computed to accumulate on the P atoms, (0.16−1.14)e/(0.59− 1.19)e in Cd33Se33(OPH3)21 and Cd33Te33(OPH3)21, respectively, along with large negative charges computed to accumulate on the O atoms, more than −1e for both Cd33Se33(OPH3)21 and Cd33Te33(OPH3)21 (see Table S4). Comparison with the bare QDs shows that the Cd charge range remains essentially the same for the Cd33Se33(OPH3)21 QD and becomes more broadly distributed for the Cd33Te33(OPH3)21 QD (see Table S4). The X charge ranges become significantly broader for both Cd33Se33(OPH3)21 and Cd33Te33(OPH3)21 compared with the bare Cd33X33 (see Table S4). The Cd33Se33(OPH3)21 and Cd33Te33(OPH3)21 HOMOs are dominated by AOs of the QD core Se/Te atoms (see Figure 10). The LUMOs of the capped QDs have some contributions from Cd-AOs, smaller contributions from Se/Te-AOs, and some contributions from ligand MOs (Figure 10). HOMOs of both capped QDs are spatially localized and LUMOs are more delocalized over the QD surfaces (see Figure 9). The composition and spatial distribution of the frontier MOs of the large capped QDs resemble those found previously in our study of OPH3-capped Cd6X6 and Cd9X9 species.50 Comparison of the calculated HOMO/LUMO energy gaps for the OPH3-capped Cd33X33 species, both in the gas phase and with implicit solvent effects included, shows the gaps to be more significantly influenced by the X atoms compared to the NH3capped QDs (see Tables 1 and S2). The HOMO/LUMO gap comparison performed with different DFT functionals (see Table S5) shows some differences compared with the Cd33X33 and Cd33X33(NH3)21 QDs. The TDB3LYP approach gives a larger optical gap for the Cd33Se33(OPH3)21 QD, the same as for the Cd33X33 and Cd33X33(NH3)21, while the B3LYP and PBE0 approaches give results opposite of each other, in disagreement with the data obtained for Cd33X33 and Cd33X33(NH3)21. The functional comparison for the Cd33X33(OPH3)21 QD HOMO/LUMO energy gap values again shows that different DFT approaches

similarities with the smaller QD case: Cd6X6(SCH3)6 and Cd9Te9(SCH3)9 species have lower vertical IPs and all of the SCH3-capped smaller QDs have higher EAv values compared with the bare species as well. As found for the NH3-capped QDs, the gas-phase computed IPv values decrease in the series Cd9Se9(SCH3)9 (7.95 eV) > Cd6Se6(SCNH3)6 (7.19 eV) > Cd33Se33(SCH3)21 (6.68 eV), and the gas-phase computed IPv values decrease from smaller to larger SCH3-capped CdnTen species: Cd6Te6(SCH3)6 (6.94 eV) > Cd9Te9(SCH3)9 (6.78 eV) > Cd33Te33(SCNH3)21 (6.32 eV). 3.2.3. OPH3−Capped QDs. Cd33X33 capping by the OPH3 ligands causes significant QD core distortions, similar to those seen in our previous theoretical study of the OPH3-capped Cd9X9 QDs.50 In these structures, numerous proton transfers occur either to X atoms or O atoms of the OPH3-groups (Figure 9). Triplet structures were calculated to be surprisingly

Figure 9. Calculated structures of the OPH3-capped Cd33X33 (X = Se, Te) quantum dots, along with their gas-phase singlet−triplet energy gap values, and plots of their frontier orbitals. Atoms are represented as follows: Cd by large yellow spheres, Se by small red spheres, Te by large light gray spheres, H by small yellow spheres, O by purple spheres, and P by small light gray spheres. HOMO/LUMO gap energy values, in eV, are provided for both QDs as well.

low in energy compared to the ground-state singlet species for both X = Se and Te, by 0.1 and 6.5 kcal/mol, respectively, compared to 49.8/42.6 kcal/mol and 46.7/48.1 kcal/mol for the OPH3-capped Cd6Se6 and Cd6Te6 and Cd9Se9 and Cd9Te9 QDs, respectively.50 Increasing the QD size significantly decreases the calculated singlet−triplet gaps in this case. The exact answer to the question of why the singlet−triplet energy gap becomes so small in the OPH3-capped QDs will be the subject of follow-up studies. The ligand binding energies were calculated to be much lower for the OPH3-capped Cd33X33 species compared to the previously computed values for the smaller OPH3-capped QDs: −7.6 kcal/mol for Cd33Se33(OPH3)21 and −4.5 kcal/mol for Cd33Te33(OPH3)21 (calculated in the gas phase, see Tables 1 and S2) vs −26.5/-23.6 kcal/mol for Cd6Se6(OPH3)6 and Cd6Se6(OPH3)6 and −30.8/−33.2 kcal/mol for Cd9Se9(OPH3)9 and Cd9Se9(OPH3)9 (gas-phase calculated values).50 Our theoretically observed trend of the OPH3 binding energy decreasing with increasing QD size is consistent with results of Nguyen et al.18 for OPH3-derived ligand binding energies: −14.1 kcal/mol, OP(CH3)3 bound to Cd6Se6 in S6 symmetry; −9.7 kcal/mol, OP(CH3)3 bound to Cd12Se12 in S6 7103



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Figure 10. Density of states (DOS) near the HOMO/LUMO gaps for the OPH3-capped Cd33Se33 (a) and Cd33Te33 (b) quantum dots calculated using the B3LYP/Lanl2dz method. The black dotted line shows the total DOS, the brown line shows the PDOS calculated for the Cd atoms, the blue line shows the PDOS calculated for the Se/Te atoms, and the red line shows the PDOS calculated for the OPH3 ligands. The energy of molecular orbitals, in eV, given on the x-axis was kept unscaled.

unchanged. In the case of Cd33Se33(OPH3)21, inclusion of implicit solvent effects does not influence the calculated IPad values. The computed EAv values increase with both solvents, while the EAad values decrease with both solvents. In comparison with our previous study,50 the gas-phase computed IPv values follow different sequences for CdnSen and CdnTen. For CdnSen, Cd9Se9(OPH3)9 (5.95 eV) > Cd6Se6(OPH3)6 (5.82 eV) > Cd33Se33(OPH3)21 (5.77 eV), but for CdnTen, Cd9Te9(OPH3)9 (5.84 eV) > Cd33Te33(OPH3)21 (5.52 eV) > Cd6Te6(OPH3)6 (5.45 eV). 3.2.4. Cd33X33 QDs Capped with Larger Ligands, N(CH3)3 and SCH2CO2H. To understand the effects of larger ligands on the Cd33X33 QD geometries and electronic structure, we studied species capped with N(CH3)3 and SCH2CO2H ligands (Figure 11 and Table 1; for more details regarding Cd33X33 capped with N(CH3)3 and SCH2CO2H ligands, see the Supporting Information). The most important features of Cd33Se33 and Cd33Te33 capped with N(CH3)3 and SCH2CO2H groups are now summarized. (1) Capping with N(CH3)3 does not cause significant distortions of the QD core (Figure 11a), and this result is similar to that found with NH3 ligands (see above). Capping with SCH2CO2H groups results in strong QD core geometric distortions. These distortions are accompanied by Cd−O−Cd and Cd−S−Cd bridging, hydrogen bonding between ligands, formation of 5-member Cd−O−C−C−S rings similar to 5- and 6-member rings found in our previous studies for the Cd6X6 QDs capped by SCH2CH2CO2H groups50 and for the CdnXn (n = 3, 4, 6, 9; X = Se, Te) QD capped with SCH2CO2H, SCH2CH2CO2H, and SCH2CH2NH2 groups.64 Even abstraction of SCH2CO2H ligands from Cd along with the ligand coupling via S−S-bond formation and hydrogen bond network formation can occur (Figure 11b, Cd33Se33(SCH2CO2H)21 species). (2) NMe3-capping changes the capped QD HOMO energies very little compared with capping by NH3 groups (see Table S2) but destabilizes the capped QD LUMOs to a greater extent compared with NH3-

for the electronic structure calculations in such systems should be used with caution. Analysis of the calculated IP and EA values (Table 2) indicates that both the vertical and adiabatic IP values for OPH3-capped Cd33Te33 are lower compared to the OPH3capped Cd33Se33 species, as is the case for bare QDs (see above), although moderately. The effect of Se vs Te on the calculated EAv/EAad values is more complicated. OPH3 capping again leads to a significant decrease in both the vertical and the adiabatic IP values compared with the bare species (Tables 2 and S3). This finding can again be explained using the same approach as above for the NH3-capped QDs. In Figure S10, we provide the qualitative diagram showing the interactions between the frontier MOs of the Cd6Se6 QD and six OPH3 ligands. OPH3-ligands destabilize both the HOMOs and LUMOs in capped QDs (see Figure S10), similar to NH3ligands. Stronger HOMO destabilization can be explained by the fact that the ligands coordinate to Cd via their lone pairs (cf. Figures S8 and S10) and thus ligands HOMOs interact with deeply located Cd states of bare QDs causing their significant destabilization which brings about the overall occupied MOs destabilization of the OPH3-capped QDs. The QD LUMOs, which have dominating X contributions (X = Se, Te), are much closer in energy to the ligand LUMOs and thus should be less destabilized compared to the QD HOMOs. Inclusion of implicit solvent effects generally stabilizes both the HOMO, and to a lesser extent, the LUMO of the capped QDs, compared with the bare species (Table S2). Acetonitrile causes more significant HOMO/LUMO stabilization compared to less polar toluene. For Cd33Se33(OPH3)21, the HOMO/ LUMO energy gaps calculated with implicit solvents are again found to be larger compared to the gas-phase calculated values. However, for Cd33Te33(OPH3)21, the gaps are about the same or smaller (Tables 1 and S2). In the case of Cd33Se33(OPH3)21, inclusion of implicit solvent lowers the IPv values and increases the IPad values (in C6H5CH3) or leaves the IPad value 7104



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the capped Cd33Se33 QD as well as in destabilization of the αHOMO and α-LUMO, β-LUMO, and β-HOMO of the capped Cd33Te33 QD compared with the SCH3-capped species (see Table S2). This causes closure of both the α- and β-HOMO/ LUMO gaps of the capped Cd33Se33 QD, opening of the αHOMO/LUMO gap of the capped Cd33Te33 QD, and drastic closure of its β-HOMO/LUMO gap. (5) The spatial distributions of the HOMO/LUMO for the SCH2CO2Hcapped Cd33Se33 and Cd33Te33 QDs resemble those of the SCH3-capped species (cf. Figures 5b and 11c). More detailed theoretical studies of the Cd33Se33 and Cd33Te33 QDs capped with larger ligands (NMe3 and SCH2CO2H) are in progress.

4. CONCLUSIONS AND OUTLOOK We performed comparative DFT (B3LYP/Lanl2dz) studies of the structure and electronic properties of bare and capped Cd33Se33 and Cd33Te33 quantum dots. The capping groups chosen are simple models for widely used capping ligands (see, for example, refs 2−16). We explored the influence of the capping ligands on the vertical ionization potentials, electron affinities, and frontier orbital energetics, and provided explanations of the capping ligand effects on these values. The effects of solvent on QD structure and electronic properties were investigated as well. We performed detailed analysis of the HOMO/LUMO compositions for the SCH3capped QDs, including NBO charge analysis and projected densities of states calculations. The motivation for this theoretical study was provided in part by studies of Waldeck and co-workers performed on aggregates of capped CdSe and CdTe QDs,2 which were capped with several different long-chain ligands. Our theoretical investigations provide useful links to experimental studies of capped QDs. The results of the current study are summarized as follows: (1) For Cd33Se33 and Cd33Te33 species, the inclusion of implicit solvent effects destabilizes both HOMOs and LUMOs of the bare QDs, LUMOs to a greater extent, thus expanding the HOMO/LUMO energy gaps for solvent calculations compared to the gas-phase results. The calculated gas-phase Cd33Se33 TD-DFT optical gap was found to be larger than the Cd33Te33 TD-DFT optical gap, in line with the experimental optical bulk bandgap values for CdSe and CdTe. However, one should be careful when comparing the calculated HOMO/LUMO energy gaps with the optical bandgap values; the time-dependent approach is expected to give more reliable results. The PDOS analysis showed that the LUMOs of the bare QDs are dominated by Cd- and Se/ Te-AOs, with larger contributions from the Cd atoms, and the HOMOs of the both bare QDs are dominated by the X (X = Se or Te) contributions, with some contributions from the Cd atoms in the Cd33Te33 case. Both vertical and adiabatic IP/EA values for the Cd33Te33 QD are decreased compared with the Cd33Se33 species, which is explained by the Cd33Te33 HOMO/LUMO destabilization compared to the Cd33Se33 QD. (2) The calculated Cd33Se33(NH3)21 structure was found to be slightly different from the Cd33Te33(NH3)21 QD structure. The calculated HOMO/LUMO energy gaps for the NH3-capped Cd33X33 species were found not to be significantly affected by the X chemistry. Comparison of the NH3-capped QDs optical energy gaps and

Figure 11. (a) Calculated structures of N(CH3)3-capped Cd33X33 (X = Se, Te) quantum dots and plots of their frontier orbitals, (b) calculated structures of SCH2CO2H-capped Cd33X33 (X = Se, Te) nanoparticles, and (c) plots of their frontier orbitals. Atoms are represented as follows: Cd by large yellow spheres, Se by small red spheres, Te by large light gray spheres, H by small yellow spheres, S by orange spheres, N by blue spheres, and C by small orange spheres. HOMO/ LUMO energy gaps are given in eV.

capping (Table S2). The larger LUMO destabilization compared with HOMO destabilization results in increasing the HOMO/LUMO energy gaps. (3) As expected, the HOMOs and LUMOs of the Cd33Se33(N(CH3)3)21 and Cd33Se33(N(CH3)3)21 resemble the spatial distribution of the HOMOs and LUMOs for the NH3-capped species (cf. Figures 3 and 11a). (4) Capping by SCH2CO2H ligands results in destabilization of the α-HOMO, β-HOMO, and α-LUMO of 7105



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HOMO/LUMO energy gaps (see Tables 4 and S5) showed a trend similar to that of the bare QDs. The LUMOs of both Cd33Se33(NH3)21 and Cd33Te33(NH3)21 were shown to have dominant contributions from the QD core Cd and X atoms, and the HOMOs of both capped QDs were shown to have dominant contributions from the X atoms. The contributions of the ligand MOs (mostly N atom localized) appear only at very low MO energies or at quite high MO energies. (3) For the SCH3-capped Cd33X33 QDs, the ligand binding energies were calculated to be slightly higher for Cd33Te33(SCH3)21 than for Cd33Se33(SCH3)21. In the ground-state doublet, Cd 3 3 Se 3 3 (SCH 3 ) 2 1 and Cd33Te33(SCH3)21 QDs sulfurs and some Se/Te atoms were computed to have significant amounts of unpaired spin density. Space electron charge distributions of the Cd33Se33(SCH3)21 and Cd33Te33(SCH3)21 frontier orbitals were found to differ significantly from those found for the bare and NH3-capped QDs. Both the α- and βLUMOs of the Cd33Se33(SCH3)21 QD were calculated to have significant contributions both from the ligand MOs and from the Se-AOs, which is also found for the αHOMO of the Cd33Se33(SCH3)21 QD. The β-HOMO of the Cd33Se33(SCH3)21 QD, on the contrary, was computed to have very large Se-AOs contributions. Comparison of the calculated PDOS for the Cd33Se33(SCH3)21 and Cd33Te33(SCH3)21 QDs showed strong composition similarities of the α-HOMOs/ LUMOs and β-LUMOs (Figures 6b and 7b) of both QDs but significant differences in the composition of their β-HOMOs. SCH3-groups were shown to generally destabilize the capped Cd33X33 HOMOs and to stabilize the capped Cd33X33 LUMOs, which leads to a drastic decrease of the calculated HOMO/LUMO energy gaps. These effects were shown to be more significant for the Cd33Se33 QD. (4) Cd33X33 capping by the OPH3 ligands was found to cause significant QD distortions, similar to those seen in our theoretical study of OPH3-capped Cd9X9 QDs.50 The ligand binding energies were calculated to be surprisingly small for the OPH3-capped Cd33X33 QDs, and more detailed analysis of this phenomenon should be the subject of follow-up studies. Comparison of the calculated HOMO/LUMO energy gaps for the OPH3capped Cd33X33 species showed them to be significantly influenced by the X atom type. Generally, inclusion of implicit solvents was found to stabilize the HOMOs and the LUMOs of the capped QDs (LUMOs to a smaller extent) compared to the bare species. The Cd33Se33(OPH3)21 and Cd33Te33(OPH3)21 HOMOs are dominated by AOs of the QD core Se/Te atoms and the LUMOs of the capped QDs have some contributions from Cd-AOs, smaller contributions from Se/Te-AOs, and some contributions from the ligand MOs as well. (5) Comparison of the PDOS for fully (21 SCH3-ligands) and partially (9 SCH3-ligands) capped Cd33Se33 QDs shows that: (i) both α- and β-HOMOs/LUMOs of the partially capped QD have similar composition, with significant Se and ligand contributions for the HOMOs and contributions only from Se for the LUMOs; (ii) both α- and β-LUMOs of the partially capped QD have no ligand contributions compared with strong ligand contributions for the fully capped QD; (iii) for both

partially and fully capped QDs, there are no Cd contributions in both HOMOs and LUMOs. Thus, the increase of the capping ligand concentration causes noticeable changes in the capped QD electronic structure leading to different surface states of the capped QDs and different HOMO/LUMO gaps, too. These results are in line with the findings of Kilina and co-workers for other ligand types.28−30 To see how capping of the QD with the charged thiolate ligands, SCH3−, will affect the capped QD electronic structure, we performed DOS calculations for the completely optimized charged [Cd33Se33(SCH3)9]9‑ QD, as described in the Computational Approach section. Close consideration of the [Cd33Se33(SCH3)9]9‑ DOS plots (see Figure S7) shows their striking similarity to the DOS of the bare Cd33Se33 QD (cf. Figure 2a): large HOMO/LUMO gap, the HOMO dominated by the Se contributions, the LUMO dominated by Cd contributions, and the very small total DOS of the unoccupied MOs compared to the occupied MOs. This implies that the negatively charged thiolate ligands should not affect the electronic structure of the capped QD significantly. To understand the role of the ligands in the HOMO/ LUMO gaps and IP/EA changes, we employed an approach similar to the one used in our previous study of smaller capped QDs:50 diagrams showing the interactions between frontier MOs of the bare QDs and capping ligands (see Figures S8−S10), exemplified by the smaller QDs for the sake of simplicity. The HOMOs of the SCH3-capped QDs have dominating contributions from sulfur 3p-orbitals of the capping group with some minor contributions from QD atoms (see Figure S9). SCH3-groups apparently can interact with Cd and Se/Te via their lone pairs and also via their unpaired electrons. Sulfur in the SCH3-ligand has an unpaired electron in its 3p-orbital. It is apparently favorable for the doubly occupied QD HOMO to interact with the singly occupied β-LUMOs of the SCH3-ligands, which has strongly pronounced d-character (Figure S9). This interaction somewhat destabilizes the HOMO of the capped QDs. The QD LUMOs can interact favorably with the α-LUMOs of the ligands, apparently with some contributions from the β-LUMOs as well, which strongly stabilizes the LUMOs of the capped species (see Figure S9). Both NH3 and OPH3 groups can coordinate to Cd only by their lone pairs (see Figures S8 and S10), which leads to significant destabilization of the capped QD HOMOs and smaller destabilization of their LUMOs. Stronger HOMO destabilization can be explained by the fact that the ligands coordinate to Cd via their lone pairs (cf. Figures S8 and S10) and thus ligand HOMOs interact with low-energy Cd states of bare QDs causing their significant destabilization which brings about the overall occupied MOs destabilization of the OPH3capped QDs. The QD LUMOs, which have dominating X contributions (X = Se, Te), are much closer in energy to the ligand LUMOs and thus should be less destabilized compared to the QD HOMOs. (6) To understand the effects of ligand size on the Cd33X33 QD geometries and electronic structure, we studied species capped with larger N(CH3)3 and SCH2CO2H ligands and we found that: (i) capping with N(CH3)3 7106



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linked model capped Cd33Se33 and Cd33Te33 QDs and to investigate if the situation similar to the type II band alignment would occur for the QD pairs, and how the MOs alignment of the linked QDs could be tuned. Of course, it would be of great interest to determine the detailed geometries and electronic structures of linked QDs in such assemblies as well. The detailed follow-up comparative studies of the optical properties of bare and capped Cd33Se33 and Cd33Te33 QDs would be of great interest, too.

does not cause significant distortions of the QD core, which is similar to the case for NH3-capped QDs, and capping with SCH2CO2H results in very strong QD core distortion; (ii) capping by SCH2CO2H results in closure of both the α- and β-HOMO/LUMO gaps of the capped Cd33Se33 QD, opening of the α-HOMO/LUMO gap of the capped Cd33Te33 QD, and significant closure of the capped Cd33Te33 QD β-HOMO/LUMO gap (all values calculated in the gas phase). Additional theoretical studies of the Cd33Se33/Cd33Te33 QDs capped with larger ligands (NMe3 and SCH2CO2H), including detailed effects of implicit solvents on the QD geometries and electronic structures, are in progress Generally, it is important to emphasize the necessity of including (implicit) solvent effects in the bare and capped QD calculations in order to establish a proper description of the QD geometries, electronic structure, and ligand binding energies. We showed that the implicit solvents affect the QD geometries, HOMO and LUMO energies and thus the HOMO/LUMO gaps and related values, including IPs and EAs, and ligand binding (although not very significant). These observations are in line with previous theoretical QD studies by Tretiak and co-workers,33,49 where it was demonstrated that ‘a dielectric environment (solvent) has important effects and needs to be incorporated into quantum-chemical calculations for the proper description of the electronic structure and optical properties of ligated QDs.’33 However, it is important to note that the experimental studies of ionization energies of large (4.7 nm) CdSe QDs,65 ionization potentials of large (3.6 and 6.0 nm) CdSe QDs tethered to gold substrates,66 spectroscopic and redox properties of CdSe nanocrystals in solution,67 electrochemical and spectroelectrochemical responses of CdSe nanocrystals in solution,68 electrochemical behavior of thiol-capped CdTe nanocrystals in aqueous solution,69 optical properties of CdSe QDs in solution,70 size-dependent absorption cross section of CdSe nanocrystal quantum dots,71 and of the extinction coefficient per mole of nanocrystals at the first exitonic absorption peak for high-quality CdTe, CdSe, and CdS nanocrystals,72 showed that properties of interest were not usually affected by the solvent nature but rather by other factors, such as the surface ligand chemistry,65−70,74 the QD size,69,72−75 etc. This means that implicit solvents should be used with caution in capped QD theoretical studies, especially for the electronic structure. Replacement of the implicit solvents with explicit solvent molecules would probably prove more effective. Further important and interesting follow-up study of the capped CdSe and CdTe QDs is expected from research of Waldeck and co-workers on electron transfer in aggregates of capped CdSe and CdTe QDs2 capped with various long-chain ligands: 3-mercaptopropionic acid (MPA), trioctylphosphine oxide, N,N,N-trimethyl(11-mercapto-undecyl)ammonium chloride, N,N-dimethyl-2-aminoethane-thiol hydrochloride (DEA), N,N,N-trimethyl-1-dodecylammonium chloride, and N,N,N-trimethyl-2-aminoethanechloride chloride. In the experimental scheme,2 both the conduction and the valence band edges of the MPA-capped CdTe QDs were shown to lie energetically higher than the corresponding band positions of the DEA-capped CdSe (“the type II alignment”). It will be of high interest to develop a theoretical approach that would allow us to compare energies of the frontier molecular orbitals of the

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ASSOCIATED CONTENT

* Supporting Information S

Summary of the prior most important theoretical studies on the structural and electronic properties of small bare and capped CdnSen and CdnTen QDs (d ≥ 1.3 nm, n ≥ 33); CdnSen and CdnTen species calculated at B3LYP/Lanl2dz level; ionization potentials and electron affinities of the bare and capped CdnSen and CdnTen QDs calculated at the B3LYP/Lanl2dz level; NBO charges for the bare and capped QDs calculated in the gas phase at the B3LYP/Lanl2dz level of theory; HOMO/LUMO energies and energy gaps for the bare and capped QDs calculated in the gas phase using the B3LYP/Lanl2dz optimized geometry and the approaches LSDA/Lanl2dz, PBE/Lanl2dz, PW91/Lanl2dz, PBE0/Lanl2dz, and TDB3LYP/Lanl2dz; molecular orbitals (five highest occupied and five lowest unoccupied MOs) of bare and capped QDs; calculated Cd 9 X 9 L 9 structures capped by NH 3 , SCH 3 , and OPH 3 groups;50 density of states near the HOMO/LUMO gap for the anionic [Cd33Se33(SCH3)9]9‑ quantum dot calculated using the B3LYP/Lanl2dz method in the gas phase; qualitative MO diagram showing interactions between the frontier MOs of the Cd6Se6 QD and 6 NH3 ligands; qualitative MO diagram showing interactions between the frontier MOs of the Cd6Se6 QD and 6 SCH3 ligands; qualitative MO diagram showing interactions between the frontier MOs of the Cd6Se6 QD and 6 OPH3 ligands; and complete ref 41. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Telephone: 919-886-0854. Present Address †

Departamento de Quı ́mica, Universidade Federal de São Carlos, Caixa Postal 676, CEP 13565-905, São Carlos - SP − Brasil Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by DOE Grant ER 46430. We thank David Waldeck and Ron Naaman for useful discussions. REFERENCES

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Structural and Electronic Properties of Bare and Capped Cd33Se33

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