Cd

Article pubs.acs.org/JPCC

Structural and Electronic Properties of Bare and Capped CdnSen/CdnTen Nanoparticles (n = 6, 9)

Aleksey E. Kuznetsov,*,† D. Balamurugan,†,∥ Spiros S. Skourtis,‡ and David N. Beratan†,§ †

Department of Chemistry, Duke University, Durham, North Carolina 27708, United States Department of Physics, University of Cyprus, Nicosia, Cyprus § Department of Chemistry, Biochemistry & Physics, Duke University, Durham, North Carolina 27708, United States ‡

S Supporting Information *

ABSTRACT: Relationships between structures and properties (energy gaps, vertical ionization potentials (IPv), vertical electron affinities (EAv), and ligand binding energies) in small capped CdSe/CdTe nanoparticles (NPs) are poorly understood. We have performed the first systematic density functional theory (DFT) (B3LYP/Lanl2dz) study of the structural (geometries and ligand binding energies) and electronic (HOMO/LUMO energy gaps, IPsv, and EAsv) properties of CdnSen/CdnTen NPs (n = 6, 9), both bare and capped with NH3, SCH3, and OPH3 ligands. NH3 and OPH3 ligands cause HOMO/LUMO energy destabilization in capped NPs, more pronounced for the LUMOs than for the HOMOs. Orbital destabilization drastically reduces both the IPv and EAv of the NPs compared with the bare species. For SCH3-capped Cd6X6 NPs, formation of expanded structures was found to be preferable to crystal-like structures. SCH3 groups cause destabilization of the HOMOs of the capped NPs and stabilization of their LUMOs, which indicates a reduction of the IPv of the capped NPs compared with the bare species. For the Cd9X9 NPs, similar trends in stabilization/destabilization of frontier orbitals were observed in comparison with the capped Cd6X6 species. Also, pinning of the HOMO energies was observed for the NH3- and SCH3-capped NPs as a function of a NP size.

1. INTRODUCTION Nanoclusters of bulk semiconductor materials1 (quantum dots) have useful properties2 that can be tuned by changing the particle size, shape, and surface bound ligands.2,3 Despite intensive interest, theoretical studies of NP electronic properties, optical properties, and surface chemistry (capping) are limited to small CdnSen/CdnTen NPs (diameter ≤ 2 nm, n ≤ 33). We lack an understanding of the structural and electronic changes that occur in small NPs upon capping by different kinds of ligands (of different chemistries and binding modes). Understanding the electronic structure of bare and capped NPs, and knowing the ways how to control their electronic structure, is very important for practical applications; armed by this knowledge, we would be able to tune redox, optical, and electrontransfer properties of capped NPs (vide infra). Driven by the lack of knowledge regarding structure− property relationships in small capped NPs, we performed DFT (B3LYP/Lanl2dz) studies of the structural and electronic properties of both bare and capped CdnSen/CdnTen nanoparticles (n = 6, 9). We explored the effects of the ligands coordinated to the NPs via amino, thio, and phosphine oxide groups, on the stabilization/destabilization of NP HOMO and LUMO energies, and on the HOMO/LUMO energy linked quantities: vertical ionization potentials and electron affinities. We also extended this study to long-chain thio-coordinated ligands with alkyl or carboxyl groups. Effects of the solvent on structures and electronic properties of NPs were investigated as © 2012 American Chemical Society

well. For OPH3- and SCH3-capped NPs, changes in both ligand structure (proton transfer either to the NP atoms or to the other ligands) and in the underlying NP structure (bridge formation between NP atoms, breakage of Cd−Se/Cd−Te bonds, and opening of the original NP (breakage of the stack of two Cd3X3 rings)) were observed. Both NH3- and OPH3groups were found to destabilize the HOMO and LUMO energies in capped NPs, the effect was more pronounced for the LUMOs than for the HOMOs. SCH3 groups were found to destabilize capped NP HOMOs and to stabilize their LUMOs, which significantly decreases the HOMO−LUMO gaps and reduces the IPv of the capped NPs compared with the bare species. Larger nanoparticles (Cd9X9) were found to undergo significant distortions upon capping by all ligands studied. Similar trends in stabilization/destabilization of the frontier orbitals were observed in comparison with the capped Cd6X6 species. Cd6X6 capping by the SCH2CH3 and SCH2CH2CO2H ligands results in opening of the nanoparticles due to the Cd−X bond breaking (for X = Se, Te), Cd−S−X bridge formation (only for X = Se), and coordination of carboxyl oxygens to Cd (only for X = Se). The Cd6Te6 NP was found to be more stable when bound with ligands containing a larger number of carbon atoms in the chain; the absence of Cd−S−X bridge formation Received: November 14, 2011 Revised: January 26, 2012 Published: February 1, 2012 6817

dx.doi.org/10.1021/jp2109187 | J. Phys. Chem. C 2012, 116, 6817−6830

The Journal of Physical Chemistry C

Article

those modes (without symmetry constraints) were performed. The geometries of the capped NPs were optimized without any symmetry constraints, and the structures obtained were again assessed using vibrational frequency analysis, as above. We studied both low-spin and high-spin states (singlet/triplet for NH3- and OPH3-capped NPs and doublet/quadruplet for SCH3capped NPs), and we performed global minimum energy searches. Calculations were performed using the Los Alamos double-ζ effective core potential (Lanl2dz),16 with the associated basis sets and with the hybrid B3LYP functional.17 The B3LYP/ Lanl2dz approach implemented in Gaussian03 was shown by Tretiak and co-workers to provide a useful compromise between efficiency and accuracy in studies of CdSe clusters.18a For comparison, we also performed calculations at the HF/Lanl2dz level (see Supporting Information). Very recently, Kilina and co-workers showed the importance of using an augmented basis set with polarization functions to model the structures of capped NPs with Cd33Se33 NP as a model.18b This approach, with the available Gaussian03/Gaussian09 basis sets (with polarization functions), caused both our bare and NH3-capped NPs to collapse upon geometry optimization, producing structures with unphysically short Cd−X/Cd−L bond lengths. With solvent effects taken into account, we also optimized the geometries of all the capped NPs at the B3LYP/Lanl2dz level of theory using the self-consistent reaction field IEF-PCM method19 (UA0 model, with the electrostatic scaling factor α20 set to 1.5), with water and toluene as solvents (dielectric constants ε = 78.39 and 2.379, respectively). Below, we discuss gas phase energies ΔE (without zero-point corrections) calculated at the B3LYP/ Lanl2dz levels (see Supporting Information). The IPv/EAv values were obtained using energies of systems with N and N −1/N + 1 electrons, calculated using geometries of the N-electron systems. The ligand binding energies, BE, were calculated using the following formula: BE = [E(CdnXnLn) − (E(CdnXn) + nE(L))]/ n, where E(CdnXnLn), (E(CdnXn), and E(L) are energies of a capped NP, bare NP, and ligand, respectively, calculated at the same level. Throughout the article, negative values for BE mean that ligands are bound to the NPs. Molecular orbitals and structures were visualized using Molekel 5.4.0.821 and Molden,22 respectively.

and coordination of carboxyl oxygens to Cd is explained by smaller charges at Cd and Te compared to the capped CdnSen species. Interestingly, our studies of the small NPs capped with relatively short-chain ligands also reproduced the staggered type II band alignment reported by Waldeck and co-workers in their fluorescence quenching studies of electron transfer in aggregates of capped CdSe/CdTe NPs of unspecified stoichiometry.2a The NPs studied by Waldeck and co-workers were capped with the following long-chain ligands: 3mercaptopropionic 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,Ntrimethyl-2-aminoethanechloride chloride. In the experimental scheme,2a both the conduction band and the valence band of the MPA-capped CdTe NPs are energetically higher than the corresponding band positions of the DEA-capped CdSe. In our study, however, the HOMOs/LUMOs of CdTe NPs were found to be higher in energy than the corresponding MOs of CdSe NPs for several NP pairs (vide infra). These findings establish links between theoretical and experimental studies of capped NPs. We also observed partial energy pinning of the HOMOs of the NH3- and SCH3-capped species in the gas phase. In an experimental study, the Fermi level pinning of the HOMO (or the filled states) of CdSe NPs on a dithiol-covered Au electrode was reported by Naaman and co-workers.2b In their study, a relatively weak size dependence of the HOMO energy was measured for NPs larger than 2.8 nm. The HOMO pinning was explained by interactions between the NP HOMO and the states of the substrate (Au electrode) coated with dithiol (thiol:Au states, or interfacial states). Also, recently Naaman and co-workers observed near pinning of the CdSe NP LUMO relative to the conduction band of the TiO2 electrode, which was explained by strong NP−electrode interactions.2k Thus, the HOMO pinning mechanisms are different in the theoretical studies of small isolated NPs and experimental studies of larger NPs in contact with substrates. The manuscript is organized as follows: the next section reviews previous theoretical studies of the structural and electronic properties of small bare and capped CdnSen/CdnTen NPs (diameter ≤ 2 nm, n ≤ 33); the third section describes our computational approach; the fourth section discusses our results for both bare and capped CdnXn (X = Se/Te, n = 6, 9) NPs; the final section provides conclusions and perspectives.

4. RESULTS AND DISCUSSION a. Bare Cd6X6 and Cd9X9 (X = Se, Te) Nanoparticles. Calculated structures of bare Cd6X6/Cd9X9 (X = Se, Te) species, along with their bond lengths and Mulliken charges, are shown in Figure 1a. Their HOMO/LUMO energies and HOMO−LUMO gaps calculated in the gas phase at the B3LYP/Lanl2dz level appear in Tables 2 and 3, along with relevant data for capped NPs (for the full set of HOMO/ LUMO energies and HOMO−LUMO gaps calculated in the gas phase and with solvent effects taken into account at the B3LYP/Lanl2dz and HF/Lanl2dz levels, see Tables S4 and S5, Supporting Information). Figure 1a shows that the Cd6X6/ Cd9X9 species are formed by stacks of Cd3X3 hexagonal rings. In the wurtzite structure, the nearest-neighbor Cd−Se distances are 2.631 and 2.635 Å;24 in bulk CdTe, the nearest-neighbor Cd−Te distance is 2.81 Å.23 The bond distances between the two layers in Cd6X6 are significantly longer than those within the Cd3X3 rings, by 0.164/0.165 Å for X = Se/Te, respectively (Figure 1a). Interestingly, this difference is not influenced by species X. The D3h Cd9X9 species are composed of three hexagonal layers, and the Cd−X bond lengths differ significantly in the middle and outer layers: the middle layer

2. BACKGROUND Table 1 summarizes the notable previous theoretical results regarding the structural and electronic properties of small bare and capped CdnSen/CdnTen NPs (diameter ≤ 2 nm, n ≤ 33) (see Supporting Information, section 1, for further details). 3. COMPUTATIONAL APPROACH The calculations described here were performed using the Gaussian03 program.15 The aims of our calculations were to explore the effects of capping groups on the structural relaxations and electronic properties of NPs, and also to analyze solvent effects on the NP structures and electronic properties. Thus, the geometries of the bare NPs were optimized beginning with symmetric structures. The resulting structures were assessed using vibrational frequency analysis to probe whether or not the NPs are true minimum energy structures. When imaginary frequencies were found, further optimizations along 6818


6819

CdnSen, n = 3, 4, 6, 97a CdnTen, n = 3, 4, 6, 98a

SCH2CH2COOH, SCH2CH2−N(CH3)2, SCH2CH2NH2, SCH2CH2(OH), SCH2CH(NH2)−COOH, SCH2CH(OH)− CH2(OH), SCH2COOH

(CH3)3PO, CH3(OH)2PO3− PO, CH3COOH, (CH3)3N

(CH3)3PO

(CdSe)n, n = 6, 15, 175

(CdSe)n, n = 15, 336

NH3, NH2CH3, N(CH3)3, CH3COOH, HCOOH, H2O, P(CH3)3, OP(CH3)3, OP(OH)2CH3

ligands

(CdSe)n, n = 1−374

NP; size, n; ref

NP structures, electronic properties, and spectra; effects of solvents and ligands

ligand binding to NP (0001), (0001−), (011−0), and (112−0) facets

effects of ligands and oxidation on the NP structure and spectra

effects of solvents and ligands on the structure, stabilities, and spectra of selected NPs

what studied

B3LYP/Lanl2dz; TDB3LYP/Lanl2dz

DFT plane-wave implementation, with LDA and PBE functional

B3LYP/Lanl2dz and TDDFT

structure enumeration with Monte Carlo basin hopping method and DFT geometry optimization

approach used

systems studied

(i) CdnSen NPs with n = 3, 6, and 9 are composed of Cd3Se3 rings (similar to wurtzite), Cd3Se3, (Cd3Se3)2, and (Cd3Se3)3; Cd4Se4 has the structure composed of two tetrahedrons, Cd4 and Se4, similar to zinc blend (ii) calculated Raman spectra NPs have the first intense peak around 150−175 cm−1, closer to 150 cm−1 for (Cd3Se3)2 and (Cd3Se3)3, and closer to 175 cm−1 for Cd3Se3 and Cd4Se4 (iii) ligand effects in the aqueous phase on the spectra are studied in the following series of species: Se−Cd−SCH2CH2COOH, Se−Cd−SCH2− CH2N(CH3)2, Se−Cd−SCH2CH2NH2, Se−Cd−SCH2−CH2(OH), Se− Cd−SCH2CH(NH2)COOH, Se−Cd−SH2CH(OH)CH2(OH), and Se− Cd−SCH2COOH (no studies of completely or partially capped clusters performed);the ligands weaken the Se−Cd bond; both solvent and ligands cause the blue shift of absorption peaks

(i) LDA BEs follow the order Cd15Se15, CH3(OH)2PO(0001−)Cd > (CH3)3PO(0001−)−Cd > (CH3)3N(0001)Se > (CH3)3N(0001−)Cd > CH3COOH(0001−)Cd > (CH3)3PO(0001)Se = CH3(OH)2PO(0001)Se > CH3COOH(0001)Se; Cd33Se33, CH3(OH)2PO(01−10)Cd/Se > (CH3)3PO(112−0)Cd/Se > CH3(OH)2PO(112−0)Cd/Se > (CH3)3PO− (01−10)Cd/Se > CH3(OH)2PO(0001−)Cd > (CH3)3PO(0001−)Cd > CH3(OH)2PO(0001)Se > (CH3)3PO(0001)Se. (ii) binding always occurs between the double bound oxygens in the PO/COOH groups and Cd atoms on the NP surface

(i) ligand removal produces surface reconstruction (ii) (CdSe)6 and (CdSe)17 (only three-coordinate surface atoms) have large bandgaps (3.14 and 2.66 eV, respectively) (iii) (CdSe)15 (12 two-coordinate surface atoms) has narrow bandgap (1.89 eV) (iv) capping produces notable blueshifts in the NP adsorption spectra: bandgaps are 4.03, 2.73, and 2.54 eV for the capped (CdSe)6, (CdSe)15, and (CdSe)17, respectively (v) (CdSe)6 and (CdSe)17: an additional O-atom inserts into the surface Cd−Se bond, with minor NP distortion (vi) oxidized (CdSe)15 undergoes significant reconstructions. (vii) NP oxidation results in the appearance of an absorption peak close to 700 nm for all NPs.

(i) bare NPs with n = 9, 12, 16, 18, 21, 24, 28, 32, 33, 35, and 36 have high relative stability (magic clusters) (ii) ligand binding energies (BEs) follow the order NH3 (Cd6Se6) > OP(OH)2CH3 (Cd12Se12) > H2O (Cd6Se6) > NH2CH3 (Cd6Se6) > CH3COOH (Cd12Se12) > HCOOH (Cd12Se12) > OP(CH3)3 (Cd6Se6) > N(CH3)3 (Cd6Se6) > P(CH3)3 (Cd6Se6)

main results/conclusions

Table 1. Summary of the Prior Theoretical Studies of the Structural and Electronic Properties of Small Bare and Capped CdnSen/CdnTen NPs (Diameter ≤ 2 nm, n ≤ 33)

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6820

H2CO, CH3COOH, NH3, CH3NH2

CdnSen, n = 13, 19, 33, 6611

CH3COOH, CH3COO−

SCH3−

Cd6Se6−[SCH3]−10b

Cd33Se3313

hydrogens, Cys, and Cys− Cys dimer

CdnSen, n = 3, 6, 10, 1310a

H-atoms

(CH3)3PO, C6H13(OH)2PO

CdnSen, n = 6, 15, 33, 459

CdnTen, n = 1−6, 12, 15, 33, 3412

ligands

NP; size, n; ref

Table 1. continued

binding of CH3COOH/ CH3COO− to Cd33Se33 NPs: modeling the interactions of Ru− polypyridine complexes with CdSe NPs

structural and electronic properties of CdTe NPs

structural, electronic, and optical properties of a series of CdSe NPs protected by various ligands

ground state and low-lying excited states of the Cd6Se6−[SCH3]− complex

peptide binding and hydrogen passivation effects on the NP geometries and excitation spectra

structures and electronic and optical properties of bare and capped NPs

what studied

B3LYP/Lanl2dz

molecular dynamics and PBE geometry optimization

LDA Vosko−Wilk− Nusair (VWN) functional, with [DZ +TZP] basis set; TDPW91

PBE0/[Lanl2dzdp +631+G**]; TDPBE/ [Lanl2dz +6-311+ +G**]

B3LYP/[Lanl2dz +6-311+ +G**]; TDB3LYP/ [Lanl2dz +6-311+ +G**]

DFT plane-wave implementation, with LDA

approach used

systems studied

(i) for the CH3COO− group, the coupling to two Cd atoms via a bridging mode is the energetically most favorable mode of attachment for all nonequivalent NP surface sites; the attachment of the protonated carboxylic acid is thermodynamically significantly less favorable

(i) H-passivation increased the stability of individual NPs (ii) the self-healing phenomenon observed previously for CdSe NP9 was observed as well.

(i) ligands play a crucial role in stabilizing the NP structure in a bulk-like geometry and strongly affect the NP optical gap (ii) structural relaxations and capping by carboxylate ligands are necessary for a proper design of the model NPs. (iii) for the NPs capped with both formates and hydrogens, increasing the cluster size results in a red shift of the spectra and an increase in the absorption intensity (iv) the best agreement between the calculated and the experimental spectra is found for the clusters capped only with the formate−hydrogen combination.

(i) red shift in the (Cd6Se6)[SCH3]− spectra compared to the bare Cd6Se6 is caused by ligand−NP orbital interaction (ii) binding of multiple NH3 to Cd6Se6 causes blue shift of the Cd6Se6·6NH3 excitation spectra compared to Cd6Se6

(i) peptide binding causes the blue shift of the electronic excitation spectra of nonpassivated NPs but red shifts spectra of H-passivated NPs. (ii) important structural feature of the CdnSenH2n−Cys and CdnSenH2n−Cys−Cys systems is the four-membered O−Cd−H-Cd ring

(i) surface reconstructions are remarkably similar for both bare and capped NPs (ii) surface relaxations of the bare NPs increase an optical gap (self-healing of the surface electronic structure), although a midgap state is also observed

(iv) very similar results regarding structures, optical properties, and effects of ligands and solvent obtained for the CdnTen species

main results/conclusions

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In the Cd6Te6 NP, the intralayer Cd−Te bond lengths are close to the average Cd−Te distance of ca. 2.85 Å reported for the H-passivated Cd6Te6 species by Bhattacharya and Kshirsagar,12 but the interlayer Cd−Te bond distances are significantly larger (Figure 1a). For Cd6X6 vs Cd9X9, the average intralayer bond distance increases by 0.759 Å for X = Se and by 0.046 Å for X = Te; however, the average interlayer bond lengths remain almost unchanged for X = Se, 2.861 compared to 2.865 Å, and they increase by 0.048 Å, from 3.043 to 3.091 Å, for X = Te. From the Cd6X6 to Cd9X9, the Cd3X3 layer becomes more planar, although the chair conformation is retained. Cd−X−Cd−X dihedral angles decrease from 26.060/34.848° (Cd6Se6/ Cd6Te6) to 18.194/23.715° (Cd9Se9/Cd9Te9). The ionic and covalent radii increase in going from Se to Te, whereas the electronegativity and ionization energies decrease. Interestingly, geometry optimization with solvent effects included gives very similar geometries, with slightly larger deviations for the Cd9X9 species. This is explained by the relatively low polarity of the solvents used in our calculations, along with the net neutrality of the species studied. Results of Mulliken analysis (Figure 1a) show that charge transfer from Cd to X is more pronounced for X = Se, which is expected based on higher Se electronegativity compared to Te. Interestingly, in the Cd9X9 species, the Mulliken charges on Cd and X in the middle layer are noticeably higher than on the Cd and X atoms of the outer layers, both for X = Se and Te (Figure 1a). Charges on the outer layer Cd/X atoms in the bare Cd9X9 species are close to those in the bare Cd6X6 species. DFT calculated gas phase HOMO−LUMO gaps of Cd6X6 indicate that the NPs are semiconductor-like. The HOMO− LUMO gaps are on the scale of eV, 3.15/3.05 eV for X = Se/Te, and Cd9X9, 2.91/2.76 eV for X = Se/Te (Tables 2 and 3),

Figure 1. (a) Calculated Cd6X6 (top) and Cd9X9 (bottom) structures (X = Se, Te), their bond distances (CdnSen/CdnTen, in Å), and Mulliken charges (in red); (b) HOMOs and LUMOs of Cd6X6 (left) and Cd9X9 (right) exemplified by the CdnSen species. Cd atoms are shown in yellow; Se/Te atoms are shown in red.

is noticeably expanded, with the Cd−X bond lengths elongated by 0.153/0.145 Å for X = Se/Te, respectively. The average interlayer bond distances in Cd9X9 are significantly longer than within the outer Cd3X3 rings, by 0.179/0.240 Å for X = Se/Te, respectively, and elongated by 0.026/0.095 Å for X = Se/Te, respectively, compared with those of the middle layer (Figure 1a). The calculated structural parameters are in excellent agreement with the theoretical results obtained by Cui and co-workers,7,8 who used the same theoretical approach (C3v rather than D3d symmetries of Cd6X6 were analyzed).7,8

Table 2. Cd6Se6/Cd6Te6 Species Calculated at the B3LYP/Lanl2dz Level of Theory (Gas Phase) species (symmetry and state)

−0.23822/−0.12261 [−6.48/−3.34] −0.16767/−0.02320 [−4.56/−0.63] −0.20446/−0.14294 [−5.56/−3.89] −0.21032/−0.13577a [−5.72/−3.69]a −0.16864/−0.03384 [−4.59/−0.92]

Cd6Se6 (C3v 1A1) Cd6Se6(NH3)6 (C1 1A) Cd6Se6(SCH3)6 (C1 1A) Cd6Se6(OPH3)6 (C1 1A)

−0.22624/−0.11404 [−6.16/−3.10] −0.16627/−0.02304 [−4.52/−0.63] −0.20313/−0.14334 [−5.53/−3.90] −0.21421/−0.13474a [−5.83/−3.67]a −0.15892/−0.03033 [−4.32/−0.83]

Cd6Te6 (C3v 1A1) Cd6Te6(NH3)6 (C1 1A) Cd6Te6(SCH3)6 (C1 1A) Cd6Te6(OPH3)6 (C1 1A) a

E(HOMO/LUMO) (A.U.) [eV]

gap (eV) Cd6Se6 3.14 3.93 1.67 2.03a 3.67 Cd6Te6 3.06 3.89 1.63 2.16a 3.50

R(Cd−X), intra/interlayer (Å)

Rav(Cd−L) (Å)

BEav/L (kcal/mol)

2.700/2.864, 2.865 2.730−2.733/2.872−2.878 2.643−3.064/2.847−3.508 2.619−2.978a 2.716−2.808/2.832−2.975

2.403 2.659 2.613a 2.273

−21.9 −24.2 −24.6a −26.5

2.878/3.043 2.907−2.914/3.056−3.068 2.812−3.265/3.020−3.806 2.839−3.715a 2.894−2.985/3.009−3.170

2.412 2.664 2.622a 2.282

−20.2 −25.7 −26.5a −23.6

Open structure, see Figure 2.

Table 3. Cd9Se9/Cd9Te9 Species Calculated at the B3LYP/Lanl2dz Level of Theory (Gas Phase) species (symmetry and state) Cd9Se9(D3h 1A1′) Cd9Se9(NH3)9 (C1 1A) Cd9Se9(SCH3)9 (C1 2A) Cd9Se9(OPH3)9 (C1 1A) Cd9Te9 (D3h 1A1′) Cd9Te9(NH3)9 (C1 1A) Cd9Te9(SCH3)9 (C1 4A) Cd9Te9(OPH3)9 (C1 1A)

E(HOMO/LUMO) (A.U.) [eV]

gap (eV)

Cd9Se9 −0.23146/ −0.12449 [−6.30/−3.39] 2.91 −0.16748/−0.03258 [−4.56/−0.89] 3.67 α, −0.20567/−0.16226; β, −0.20542/−0.18024 [α, −5.60/−4.42; β, −5.59/−4.90] α, 1.18; β, 0.69 −0.17841/−0.04850 [−4.85/−1.32] 3.54 Cd9Te9 −0.21873/−0.11713 [−5.95/−3.19] 2.76 −0.16274/−0.03507 [−4.43/−0.95] 3.48 α, −0.21342/−0.10987; β, −0.22088/−0.17006 [α, −5.81/−2.99; β, −6.01/−4.63] α, 2.82; β, 1.38 −0.17403/−0.05928 [−4.74/−1.61] 3.12 6821

Rav(Cd−L) (Å)

BEav/L (kcal/mol)

2.389 2.663 2.267

−21.1 −22.3 −30.8

2.400 2.659 2.239

−20.5 −24.2 −33.2



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consistent with experimental data.25 Optical bulk bandgap values of CdSe and CdTe are 1.8426 and 1.4427 eV, respectively. The HOMO−LUMO gap of 3.15 eV for the Cd6Se6 NP is in excellent agreement with the bandgap of 3.14 eV calculated by Inerbaev et al.5 using the same B3LYP/Lanl2dz approach. Increasing the number of atoms and changing from Se to Te decreases the HOMO−LUMO gaps. This is in line with previous theoretical studies performed for Cd6Se6/Cd15Se15/ Cd 17 Se 17 , 5 Cd 13 S 16 H 12 6+ , Cd 13 Se 16 H 12 6+, Cd 13 Te 16 H 12 6+ , Cd17Se28H242+, Cd17Se28H242+, and Cd17Te28H242+,14 for Hpassivated CdnTen (n = 1−6) and nonpassivated CdnTen (n = 12, 15, 33, 34) NPs.23 Our results are in agreement with the observations obtained in the combined experimental/theoretical studies of the oleic acid stabilized CdTe QDs with a size range 2.4−4.7 nm27 and bare CdnSen clusters (n = 3, 6, 13, 16).24 Also, our computed data agree with the results of the following experimental studies: (i) the quantized growth study of CdTe QDs in the presence of hexadecylamine, hexylphosphonic acid, and trioctylphosphine oxide above 200 °C monitored by in situ UV−vis absorption spectroscopy;28a (ii) UV−vis absorption/ photoluminescence spectroscopy characterization of thiolcapped CdTe NPs up to 6.0 nm in diameter;28b and (iii) UV−vis absorption/photoluminescence spectroscopy characterization of capped CdTe, CdSe, and CdS nanocrystals up to 8 nm in size.28c As expected, the Hartree−Fock approach overestimates the HOMO−LUMO energy differences of the species studied, giving values of 7.98/7.40 eV for Cd6Se6/ Cd6Te6 and 7.95/7.27 eV for Cd9Se9/Cd9Te9 (Tables S4 and S5, Supporting Information), which are too large compared with the optical gap experimental value of 3.14 eV reported by Jose et al. in their study of bare CdnSen clusters (n = 3, 6, 13, 16).24

Inclusion of solvent effects does not change the gaps significantly: generally, the HOMO−LUMO gap increases slightly in the series gas phase → toluene → water. However, Cd9X9 does not follow this sequence (see Tables 3 and S5 (Supporting Information): its HOMO−LUMO gap remains the same, 2.91 eV, in the gas phase and with toluene used as a solvent in the calculations. The Cd9X9 HOMO−LUMO gap increases to 2.97 eV when the geometry optimization is performed with water as a solvent in the calculations. This, apparently, can be explained by significant Mulliken charges on the middle layer Cd/X atoms in the Cd9X9 structures (see Figure 1a); the middle layer Cd/X atoms contribute to the Cd9X9 HOMOs/LUMOs (see Figure 1b), and interaction of the charges on those atoms with polar water molecules can result in the HOMO/LUMO destabilization, which changes the HOMO/LUMO gaps in a different way than in the Cd6X6 case. The HOMOs of both Cd6X6 and Cd9X9 clusters are predominantly composed of Cd 4d-orbitals and Se/Te 4p-orbitals (see Figure 1b), whereas the LUMOs have contributions from Cd 5s- (mostly), 5p- and Se/Te 4p-orbitals. b. Capped Cd6X6 (X = Se, Te) Nanoparticles. The computed Cd6X6L6 structures (X = Se, Te; L = NH3, SCH3, OPH3) are shown in Figure 2, and their frontier orbitals appear in Figure 3. Figure 2a,e shows that both NH3 and OPH3 groups perturb the Cd6X6 structures but not significantly. Both NH3 and OPH3 groups cause elongation of intralayer Cd−Se/Te bond lengths: in Cd6Se6(NH3)6 by 0.030 to 0.033 Å, in Cd6Te6(NH3)6 by 0.029 to 0.036 Å, in Cd6Se6(OPH3)6 by 0.016 to 0.108 Å, and in Cd6Te6(OPH3)6 by 0.016 to 0.107, respectively (cf. Figures 1 and 2). OPH3-caused elongations cover a broader range than with the NH3 systems. However,

Figure 2. Calculated capped structures (X = Se, Te): Cd6X6(NH3)6 (a), Cd6X6(SCH3)6 (b), open Cd6Se6(SCH3)6 (c), open Cd6Te6(SCH3)6 (d), Cd6X6(OPH3)6 (e). Bond distances (in Å) are shown in black, and Mulliken charges are shown in red. Atoms are represented as follows: Cd by large yellow spheres, X/Se by red spheres, Te by large light gray spheres, H by small yellow spheres, N by blue spheres, S by orange spheres, C by small dark orange spheres, O by purple spheres, and P by small light gray spheres. 6822



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Cd6Se6(OPH3)6 compared to the uncapped species, see Figure 2a,c) and significant accumulation of negative charge on Se/Te centers (from −0.42e to −0.62e in Cd6Se6(NH3)6 and from −0.42e to (0.65−0.69)e in Cd6Se6(OPH3)6 compared to the uncapped species). Both NH3 and OPH3 ligands destabilized the HOMOs and LUMOs in capped NPs (see Figure 4a,b). The effect was more pronounced for the LUMOs: NH3 destabilizes the HOMO/ LUMO by 1.92/2.71 eV for Cd6Se6 and by 1.63/2.48 eV for Cd6Te6; OPH3 destabilizes the HOMO/LUMO by 1.89/ 2.42 eV for Cd6Se6 and by 1.83/2.28 eV for Cd6Te6. Stronger LUMO destabilization is explained by larger overlap between the NP LUMO (and, possibly, higher-lying NP MOs), having more pronounced s-character (Figure 4a,b), and the ligand LUMO, having strong s-character in the NH3 case and greater p-character in the OPH3 case (Figure 4a,b). Very large energy gaps between the NP and ligand LUMOs, 0.22059 A.U. (6.0 eV) for NH3 and 0.12649 A.U. (3.44 eV) for OPH3, result in stronger Cd6Se6L6 LUMO destabilization for both NH3 and OPH3 groups. A smaller energy difference between the NP and OPH3 LUMOs compared to the NH3 case explains the smaller Cd6Se6(OPH3)6 LUMO destabilization (see above). The smaller HOMO destabilization energy compared to the LUMO is explained by the fact that the ligands coordinate to Cd via their lone pairs, and both the Cd and the coordinated ligands do not contribute much to the capped NP HOMOs (see Figure 4a,b). However, the Cd and the coordinated ligand contributions to the capped NP LUMO are much more pronounced. Small ligand contributions to the capped NP HOMOs also help to explain weak effects of both NH3 and OPH3 binding on the capped NPs geometries (see above). The stronger LUMO destabilization relative to the HOMO in the capped NPs, in turn, drastically increases the HOMO−LUMO gaps of the capped NPs, by 0.78/0.85 eV for Cd6Se6(NH3)6/Cd6Te6(NH3)6 and by 0.52/0.45 eV for Cd6Se6(OPH3)6/Cd6Te6(OPH3)6. This trend agrees with the results of Inerbaev et al.5 for the trimethylphosphine oxide capped Cd6Se6 NPs. Generally, the effect of the OPH3 group on the increase of the HOMO−LUMO gaps of the capped NPs is less pronounced. Also, NH3- and OPH3-capping drastically reduces both the vertical IP and EA of the NPs compared with the bare species (see Table 4). Interestingly, the EAv of both NH3- and of OPH3-capped NPs become negative compared with the EAv of bare NPs (Table 4), which is attributed to strong LUMO destabilization in the capped NPs. The influence of ligands on NP frontier orbitals is quite different for the SCH3 groups compared to the other capping species (Figure 2b−d). First, SCH3 tends to form Cd−S−Se/ Te bridges (Figure 2b), and second, for both SCH3-capped Cd6Se6 and Cd6Te6 NPs, the ligated species form open rather than the closed structures derived from the original Cd6X6 species (Figure 2c,d). The open structure was found to be more stable than the closed one by 2.5/5.2 kcal/mol in the gas phase for Cd6Se6(SCH3)6/Cd6Te6(SCH3)6. Interestingly, the open structure has only one Cd−S−X bridge vs three bridges in the closed species, and the open species also has Cd−Cd bonds (Figure 2c,d). Intra- and interlayer Cd−X bond distances in the closed structures were found to change as follows (compared to the bare Cd6X6 species): in Cd6Se6(SCH3)6 by −0.057 to 1.064 Å and by −0.017 (nonbridged Cd−X) to 0.644 Å (S-bridged Cd−X) Å; in Cd6Te6(SCH3)6 by −0.066 to 0.387 Å and by −0.023 (nonbridged Cd−X) to 0.763 (S-bridged Cd−X) Å. In the open structures, Cd−X bond distances were found to range from 2.619 to 2.978 Å in Cd6Se6(SCH3)6 vs 2.700/2.864,2.865 Å

Figure 3. Frontier orbitals of the Cd6X6L6 species (exemplified by Cd6Se6L6) capped by NH3 groups (a), SCH3 groups (b, open structure in the bottom row), and OPH3 groups (c).

the NH3 group only causes lengthening of interlayer Cd−X bonds (by 0.008 to 0.013 Å in Cd6Se6(NH3)6 and by 0.013 to 0.025 Å in Cd6Te6(NH3)6), while the OPH3 group induces both elongation and shortening of the interlayer Cd−X bond distances: in Cd6Se6(OPH3)6, these bond distances cover a length range from 2.832 to 2.975 Å compared with 2.864/2.865 Å in bare Cd6Se6, and in Cd6Te6(OPH3)6, they cover a length range from 3.009 to 3.170 Å compared to 3.043 Å in the bare Cd6Te6. For the capped Cd6Se6 species, the calculated bond distances Rav(Cd−N), 2.403 Å, and Rav(Cd−O), 2.273 Å, are in reasonable agreement with the values found by Tretiak and coworkers29 for the Cd33Se33 NP capped with methylamine, Rav(Cd−N) = 2.43 (9 ligands) and 2.44 Å (21 ligands), and with trimethylphosphine oxide, Rav(Cd−O) = 2.35 (9 ligands) and 2.38 Å (21 ligands). Rav(Cd−N) and Rav(Cd−O) are slightly elongated when going from Cd6Se6L6 to Cd6Te6L6 (Table 2), by 0.009 Å. Calculated ligand binding energies are slightly higher for Cd6Se6L6 species, −21.9 vs −20.2 and −26.5 vs −23.6 kcal/mol for NH3 and OPH3 groups, respectively (Table 2). The Cd6X6 NPs are found to bind somewhat more strongly with phosphine oxide than with NH3. Our calculated binding energies contrast with results of Nguyen et al.4 for NH3 (−18.0, Cd6Se6), OP(OH)2CH3 (−17.0, Cd12Se12), and OP(CH3)3 (−14.1, Cd6Se6), which may be explained by differences in the approaches used (B3LYP/Lanl2dz in our calculations vs B3LYP/[VDZ-SD+6-31G(d)] in the calculations of Nguyen et al.4). Our binding energies are closer to the local density approximation values reported by Puzder et al. for phosphine oxide and ammonia derivatives bound to Cd15Se15 ((CH3)3PO, −24.4; CH3(OH)2PO, −25.8; (CH3)3N, −21.0) 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).6 We found triplet structures for both NH3- and OPH3-capped NPs to be very high in energy relative to the ground state singlet species, 54.0/71.3 and 49.8/ 42.6 kcal/mol for the NH3- and OPH3-capped Cd6Se6/Cd6Te6 species, respectively (compared with 43.2/32.3 kcal/mol for the bare Cd6Se6/Cd6Te6 species, see Table S4, Supporting Information). Mulliken analysis of the capped species shows an increase in the positive charge on the Cd atoms (from 0.42e to 0.48e in Cd6Se6(NH3)6 and from 0.42e to 0.60e in 6823



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Figure 4. Orbital mixing diagrams for the HOMO and LUMO of the Cd6Se6L6 species: Cd6Se6(NH3)6 (a), Cd6Se6(OPH3)6 (b), and Cd6Se6(SCH3)6 (c, open structure). MO energies are given in eV.

their LUMOs, by 0.36 eV for Cd6Se6 and by 0.56 eV for Cd6Te6 (Table 2 and Figure 4c). Thus, the HOMO−LUMO gaps of the capped NPs drop by 1.12 and 0.89 eV for Cd6Se6(SCH3)6 and Cd6Te6(SCH3)6, respectively. Interestingly, in the open structures, the HOMOs are more stable than in the closed structures, but the LUMOs are less stabilized. The calculated HOMO−LUMO gaps of the closed structures are even smaller than those of the open species (see Table 2). SCH3-capping also reduces the vertical IPs of the NPs compared with the bare species (see Table S2, Supporting Information), but by significantly smaller values, 0.65/0.48 eV compared with 2.03/1.73 eV and 2.02/1.97 eV for the NH3and OPH3-capped Cd6Se6/Cd6Te6 species, respectively (see Table S2, Supporting Information). EAv of SCH3-capped NPs increase compared to the NH3- and OPH3-capped Cd6Se6/ Cd6Te6 species by 0.33/0.61 eV, which is attributed to the LUMO stabilization in the SCH3-capped NPs. Comparison of HOMOs and LUMOs of the capped Cd6X6L6 species shows the following drastic differences between the SCH3-capped NPs, on one the one hand, and NH3-/OPH3-capped NPs, on the other hand (Figures 3 and 4): the HOMOs of ammonia/phosphine oxide capped NPs are slightly distorted HOMOs of the parent bare species (see above and also see Figure 4a,b) with some contributions from ligands, and the LUMOs of these species are combinations of the LUMOs of the bare NPs and the ligand LUMOs (Figures 4a,b). In contrast, the HOMOs of the SCH3-capped NPs have either dominating contributions from only sulfur 3p-orbitals of the capping group(s) (for the closed structure) or large contributions from sulfur 3p-orbitals of the capping groups with some minor contributions from NP atoms (for open structure). For closed structures, the HOMOs are responsible for bonding

Table 4. Comparison of the HOMO Energies Calculated for the Capped CdnSen/CdnTen Species (Gas Phase) species

E(HOMO) (A.U.)

Cd6Se6(NH3)6/Cd6Te6(NH3)6 Cd9Se9(NH3)9/Cd9Te9(NH3)9 Cd6Se6(SCH3)6/Cd6Te6(SCH3)6 Cd9Se9(SCH3)9/Cd9Te9(SCH3)9 Cd33Se33(SCH3)21

−0.16767/−0.16627 −0.16748/−0.16274 −0.21032/−0.21421 −0.20567/−0.21331 −0.21899

in Cd6Se6, and from 2.839 to 3.715 Å in Cd6Te6(SCH3)6 vs 2.878/3.043 Å in Cd6Te6 (cf. Figures 1a and 2c,d). Rav(Cd− SCH3) was found to decrease noticeably in open structures compared to closed species, by 0.046/0.042 Å for Cd6Se6(SCH3)6 and Cd6Te6(SCH3)6, respectively. Calculated SCH3 binding energies are very close for both Cd6Se6(SCH3 )6 and Cd6Te6(SCH3)6, −24.2/−24.6 and −25.7/−26.5 kcal/mol for closed/open structures. Interestingly, for the Cd6Se6 NP, the ligand binding energies follow the series OPH3 > SCH3 > NH3, while for Cd6Te6 NP, the sequence is SCH3 > OPH3 > NH3. In sharp contrast with the NH3- and OPH3-capped species, the triplet structures for SCH3-capped NPs were found to be higher than the ground state singlet species by 8.5 and 21.2 kcal/mol for Cd6Se6/Cd6Te6 species, respectively. Mulliken analysis of the capped species shows an increase in positive charges on Cd centers and decrease of negative charge on Se/Te centers (see Figures 1a and 2b−d). Significant negative charge is found on the S atoms ((−0.22 to −0.05)e in Cd6Se6(SCH3)6) and especially on C ((−0.81 to −0.75)e in Cd6Se6(SCH3)6) (see Figure 2b−d). In contrast to NH3 and OPH3 ligands, SCH3 groups cause much smaller HOMO destabilization of capped NPs, by 0.76 eV for Cd6Se6 and by 0.33 eV for Cd6Te6, and the ligands stabilize 6824



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Figure 5. Calculated Cd9X9L9 structures (X = Se (top row), Te (bottom row)) capped by NH3 groups (a), SCH3 groups (b), and OPH3 groups (c). Bond distances (in Å) are shown in black, and Mulliken charges/spins are shown in red. Atoms are represented as follows: Cd by large yellow spheres, X/Se by small red spheres, Te by large light gray spheres, H by small yellow spheres, N by blue balls, S by orange spheres, C by small dark orange spheres, O by purple spheres, and P by small light gray spheres.

between Cd atoms and nonbridging SCH3 ligands, whereas the LUMOs of these NPs have large contributions from both the capping groups and the NP atoms (Figure 3b). As described above, NH3 and OPH3 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 can interact by their unpaired electrons with Cd and Se/Te. Sulfur in the SCH3 ligand has an unpaired electron in its 3p-orbital, and Cd and Se/Te in Cd6X6 (X = Se, Te) have some unpaired electron density due to incomplete electron transfer from Cd to Se/Te (Mulliken analysis shows charges on Cd and X to be 0.42/ 0.28e and −0.42/−0.28e in Cd6Se6/Cd6Te6, respectively. See Figure 1a). It is apparently favorable for the doubly occupied NP HOMO, which has some d-contributions from Cd atoms, to interact with the relatively close-lying (energy gap 2.34 eV, see Figure 4c) singly occupied β−LUMO of the SCH3 ligand, which has strongly pronounced d-character (Figure 4c). This interaction only slightly destabilizes the HOMO of the capped species. The NP LUMO can interact favorably with the α-LUMO of the ligand, apparently with some contributions from the β-LUMO as well, which strongly stabilizes the LUMO of the capped species. c. Capped Cd9X9 (X = Se, Te) Nanoparticles. In this section, we summarize the main differences and similarities found in our study between the capped Cd6X6 and Cd9X9 species. For a detailed description of the Cd9X9L9 results, see the Supporting Information. Calculated Cd9X9L9 structures (X = Se, Te; L = NH3, SCH3, OPH3) are shown in Figure 5, and their frontier orbitals appear in Figure 6. Larger nanoparticles (Cd9X9) undergo significant distortions upon capping, even with NH3 and OPH3 groups. Similar to Cd6X6 species, both intra- and interlayer bond distances change noticeably.

Figure 6. Frontier orbitals of the Cd9X9L9 species (exemplified by Cd9Se9L9) capped by NH3 (a), SCH3 (b), and OPH3 groups (c).

For the SCH3-capped NPs, we found global energy minimum distorted structures with one broken outer hexagonal Cd3X3 layer and with three Cd−S−X bridges formed. This resembles the situation found for Cd6X6(SCH3)6. Interestingly, the OPH3capped NPs were found to undergo the largest distortions of all three species types, in sharp contrast to the OPH3-capped Cd6X6: both the intra- and interlayer Cd−X bonds are extended/ broken, and proton transfers to either X-centers or O-centers of OPH3 groups take place. For the NH3- and OPH3-capped NPs, the triplet structures were found to be 51.5/46.7 and 48.2/48.1 kcal/mol higher in energy than the ground state singlets of Cd9Se9/Cd9Te9, respectively. The SCH3-capped NP doublet species were found to be essentially degenerate with the quadruplets, lower in energy by 0.007/0.01 kcal/mol in the gas 6825



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phase for Cd9Se9/Cd9Te9, respectively (see Table S5, Supporting Information); for simplicity, we consider the doublet species here. This trend is similar to that observed for the capped Cd6X6 species. Similar trends in the stabilization/destabilization of the frontier orbitals and HOMO/LUMO gap changes are observed for both Cd6X6 and Cd9X9 species. NH3 and OPH3 groups destabilize both the Cd9X9 HOMO and LUMO (to a larger extent). This effect drastically increases the HOMO−LUMO gaps of the capped NPs, compared to the bare Cd9X9 species (see Table 3 and Supporting Information). This trend is in agreement with the results of Inerbaev et al.5 for trimethylphosphine oxide capped Cd6Se6 NP and with our results for NH3- and OPH3capped Cd6X6 species. The effect of the OPH3 group is less pronounced. Generally, the HOMO/LUMO destabilization effects of the ligands are smaller for Cd9X9. SCH3 groups generally somewhat destabilize the HOMOs of the Cd9X9 species, but significantly stabilize their LUMOs. The HOMO destabilization and LUMO stabilization leads to a drastic decrease of the HOMO/LUMO gaps (see Table 3 and Supporting Information). These effects are more pronounced than for the SCH3-capped Cd6X6 species (Table 2) and are more significant for the Cd9Se9 species. Calculated Rav(Cd−N) values are slightly increased (by 0.011 Å) on going from Cd9Se9L9 to Cd9Te9L9, Rav(Cd−O) are shortened by 0.028 Å, and Rav(Cd−S) are shortened by 0.004 Å (Figure 5). Generally, bond lengths Rav(Cd−N/O) are shortened when going from Cd6X6 to Cd9X9, but the Rav(Cd−S) distances grow (Table S1, Supporting Information). Calculated ligand-binding energies are again close for both Cd9Se9L9 and Cd9Te9L9 (Table S1, Supporting Information). In contrast, with the capped Cd6X6 species, for both the Cd9Se9 and Cd9Te9 NPs, ligand binding energies follow the order OPH3 > SCH3 > NH3. NH3 and SCH3 binding energies are slightly smaller for larger clusters, in agreement with the results of Nguyen et al.4

The spatial distribution of the HOMOs and LUMOs of the capped Cd9X9 species (Figure 6) are very similar to those found for the capped Cd6X6 NPs (see Figures 3 and 4): frontier MOs of Cd9X9(NH3)9 are mostly derived from the HOMO and LUMO of the parent Cd9X9 species, with some contributions from the ligands. The picture is a bit complicated in the case of Cd9X9(OPH3)9, due to its significant structural distortions. The HOMO and LUMO of Cd9X9(SCH3)9 are very similar to the Cd6X6(SCH3)6 HOMO/LUMO, with dominating contributions from ligands in HOMO and mixture of ligand and nanoparticle contributions in the LUMO. The HOMO energies of the NH3- and SCH3-capped nanoparticles change little with the NP size (Table 4): for NH3-capped CdnSen/CdnTen, the HOMO energies (in A.U.) are −0.16767/−0.16627 → −0.16748/−0.16274 for n = 6 and 9, respectively; for SCH3-capped CdnSen/CdnTen, the HOMO energies follow the order −0.21032/−0.21421 → −0.20567/− 0.21331 → −0.21899 (see Supporting Information) for n = 6, 9, and 33, respectively. For the NH3-capped species, the HOMO destabilization in the series Cd6X6 → Cd9X9 is 0.0052/ 0.096 eV. For the SCH3-capped species, the HOMO energy changes by +0.13/+0.024 eV in the series Cd6X6 → Cd9X9 and by −0.16 → −0.08 eV in the series Cd6Se6 → Cd9Se9 → Cd33Se33. Therefore, partial pinning of the HOMOs is observed for the NH3- and SCH3-capped species. Figure 7 shows the IPv dependence on the NP HOMO energy (in eV). Because of the similarity of these dependencies, we only plot the data for the Cd6Se6L6 and Cd9Se9L9 species. Tables S2 and S3 (Supporting Information) summarize data on vertical ionization potentials (IPv, eV) and vertical electron affinities (EAv, eV) of the bare and capped Cd6Se6/Cd6Te6 and Cd9Se9/Cd9Te9 species, respectively, calculated at the B3LYP/ Lanl2dz level in the gas phase, along with their HOMO/LUMO energies (in A.U. and eV) and HOMO−LUMO gaps (in eV). Analysis of the IPv and EAv values of the capped Cd9X9 species (Table S3, Supporting Information) shows trends similar to those observed for the capped Cd6X6 species (Table S2,

Figure 7. Computed IPv, eV, vs E(HOMO), eV: Cd6Se6L6 (a) and Cd9Se9L9 (b). 6826



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Figure 8. Calculated structures of Cd6X6 NPs (X = Se (a), Te (b)) capped by SCH2CH3 (top row) and SCH2CH2CO2H groups (b). 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, C by small dark orange spheres, and O by purple spheres.

Supporting Information). For the NH3- and OPH3-capped NPs, a noticeable decrease is observed for both the IPv and EAv compared to the bare species. An increase of both EAv and IPv is observed for the SCH3-capped NPs compared to the bare NPs. This is seen in the plots of the IPv values vs E(HOMO), Figure 7. Increasing the number of Cd/X atoms in both bare and capped species generally increases their EAv values, but the effect on IPv is more complex (see Tables S2 and S3, Supporting Information). Increasing the number of atoms in the NPs and changing from Se to Te decreases the IPv due to HOMO energy destabilization. d. Cd6X6 (X = Se, Te) Nanoparticles Capped with S-Containing Ligands with Longer Chains. Calculated structures of Cd 6 X 6 NPs capped by SCH 2 CH 3 and SCH2CH2CO2H groups are presented in Figure 8, and some of their characteristics are provided in Table 5. We were motivated to choose these two capping groups, SCH2CH3 and SCH2CH2CO2H, by the studies of Cui and co-workers7a,8a performed for the CdnSen/CdnTen (n = 3, 4, 6, 9) NPs, where the long-chain capping groups coordination to the NP via the sulfur atom was studied using the Se−Cd−L models (L = thiocontaining ligand). Additional motivation was provided by the study of Neuhauser and co-workers on the Cys-bound H-passivated NPs (CdnSenH2n−Cys and −Cys−Cys systems),10a where the four-membered O−Cd−H−Cd ring structure as well as the Cd−S (or both Cd−S and Cd−OOC) bonds were shown to form when Cys (or Cys−Cys) forms covalent bonds with the hydrogen-passivated CdSe NP. The Cd6X6 capping by

Table 5. Cd6Se6/Cd6Te6 Species Capped by SCH2CH3 and SCH2CH2CO2H Groups Calculated at the B3LYP/Lanl2dz Level of Theory (Gas Phase) species (symmetry state) Cd6Se6(SCH2CH3)6 (C1 1A) Cd6Se6(SCH2CH2CO2H)6 (C1 1A) Cd6Te6(SCH2CH3)6 (C1 1A) Cd6Te6(SCH2CH2CO2H)6 (C1 1A)

E(HOMO/LUMO) (A.U.)

gap (eV)

BEav/L (kcal/mol)

Cd6Se6 −0.20762/−0.12587 −0.20496/−0.10819

2.22 2.63

−24.7 −33.4

Cd6Te6 −0.20744/−0.12801 −0.21996/−0.13968

2.16 2.18

−25.9 −25.7

S-coordinated ligands with longer alkyl chains/carboxyl group produces opening of the nanoparticles due to (i) Cd−X bond breaking (for X both Se and Te), (ii) Cd−S−X bridge formation (only for X = Se), and (iii) coordination of carboxyl oxygens to Cd-centers (only for X = Se), as was observed by Neuhauser and co-workers for Cd6Se6−Cys complexes.10a As can be seen from Figure 8, the Cd6Te6 NP is more stable toward opening caused by long-chain ligand coordination; the absence of Cd−S−X bridge formation and coordination of carboxyl oxygens to Cd could be explained by the smaller charges on Cd and Te (Mulliken analysis shows charges on Cd- and X-centers to be 0.42/0.28e and −0.42/-0.28e in Cd6Se6/Cd6Te6, respectively). SCH2CH3 binding energies are very close for both Cd6Se6 and Cd6Te6, as observed for the SCH3 group (see 6827



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and Se/Te. It is favorable for the doubly occupied NP HOMO (with some d-contributions from Cd atoms) to interact with the relatively close-lying singly occupied β-LUMO of the SCH3 ligand, which has pronounced d-character (Figure 4c). This interaction only slightly destabilizes the HOMO of the capped species. The NP LUMO can interact favorably with the α-LUMO of the ligand, apparently with some contributions from the β-LUMO as well, which strongly stabilizes the LUMO of the capped species. The effects of destabilization of the capped NP HOMOs and stabilization of their LUMOs, taken together, cause a significant decrease in the HOMO−LUMO gap energies of the capped NPs and reduction of vertical IP of the NPs compared with the bare species. The EAv of SCH3capped NPs increase compared to the NH3- and OPH3-capped Cd6Se6/Cd6Te6 species. Larger nanoparticles (Cd9X9) were shown to undergo significant distortions upon capping by all groups studied. The OPH3-capped NPs were found to undergo the largest distortions of all three capped NPs, in sharp contrast with the OPH3-capped Cd6X6 species. Similar trends in stabilization/destabilization of frontier orbitals and HOMO/LUMO gap changes were observed in comparison with capped Cd6X6 species. NP ligand binding energies were found to follow the order OPH3 > SCH3 > NH3. NH3 and SCH3 binding energies are slightly smaller for larger clusters. Also, pinning of the HOMO energies was observed for the NH3- and SCH3-capped species. Finally, the Cd6X6 capping by S-coordinated ligands with longer alkyl chains/carboxyl groups was found to provide opening of the nanoparticles due to (i) Cd−X bond breaking (for X both Se and Te), (ii) Cd−S−X bridge formation (only for X = Se), and (iii) coordination of carboxyl oxygens to Cd-centers (only for X = Se). Cd6Te6 NP was shown to be more stable toward opening caused by the coordination of the ligands with longer chains. SCH2CH3 and SCH2CH2CO2H groups stabilize the HOMOs of both Cd6Se6 and Cd6Te6, even more than the SCH3. However, the stabilizing effect of these ligands on the LUMOs is less pronounced compared with the stabilizing effect of the SCH3 capping groups, which causes some opening of the HOMO−LUMO gaps for the SCH2CH3 and SCH2CH2CO2H capped species compared to the SCH3 capped NPs. Interestingly, our studies of the small CdSe/CdTe NPs capped with relatively short-chain ligands also find staggered type II band alignment, consistent with reports by Waldeck and coworkers of photoinduced electron transfer in aggregates of CdSe/CdTe NPs capped with MPA, trioctylphosphine oxide, N,N,N-trimethyl(11-mercaptoundecyl)ammonium chloride, DEA, N,N,N-trimethyl-1-dodecylammonium chloride, and N,N,N-trimethyl-2-aminoethanechloride chloride.2a In their studies, both the conduction band and the valence band of CdTe NPs (MPA-CdTe) are energetically higher than the corresponding band positions of the CdSe NPs (DEA-CdSe). In our theoretical analysis, the HOMO/LUMOs of CdTe NPs were found to be higher in energy than the corresponding MOs of CdSe NPs for the following NP pairs: Cd6Se 6(NH 3) 6/ Cd6Te6(NH3)6, Cd6Se6(OPH3)6/Cd6Te6(OPH3)6, Cd 6 Se 6 (SCH 3 ) 6/[Cd 6 Te 6(NH 3 ) 6, Cd 6Te 6(OPH 3) 6 ], and Cd 9Se9(SCH 3) 9/[Cd 9Te 9(NH 3) 9,Cd 9Te 9(OPH 3) 9] (see Tables 2 and 3). As such, these combinations of capped NPs may be used as simple initial theoretical models to study electrons between NPs. We also observed partial pinning of the HOMOs of the NH3- and SCH3-capped species in the gas phase. Naaman and co-workers reported Fermi level pinning of the HOMO of CdSe NPs on a dithiol-covered Au electrode.2b In this

Table 2), but the average binding energies of SCH2CH2CO2H to Cd6Se6 are noticeably higher than to Cd6Te6, due to coordination of carboxyl oxygens to the Cd. SCH2CH3 and SCH2CH2CO2H groups stabilize the HOMOs of both Cd6Se6 and Cd6Te6 even more compared to the SCH3 group (cf. Tables 2 and 5). However, the stabilizing effect on the LUMOs is less pronounced, which causes some opening of the HOMO−LUMO gaps of the SCH2CH3- and SCH2CH2CO2Hcapped species compared to the SCH3-capped NPs (cf. Tables 2 and 5). The increased gap of the Cd6Se6(SCH2CH2CO2H)6 species could be explained by carboxyl oxygen coordination to Cd atoms and thus destabilization of Cd 5p-orbitals contributing to the LUMO (see above). Further studies of Cd6X6 and Cd9X9 species capped by long-chain ligands coordinated by S, O, or N atoms with various functionalities are in progress.

5. CONCLUSIONS AND OUTLOOK We have performed the first systematic DFT (B3LYP/Lanl2dz) studies of the structural and electronic properties of CdnSen/ CdnTen nanoparticles (n = 6, 9), both bare and capped with amino, thio, or phosphine oxide ligands. We also extended our study to long-chain thio-coordinated ligands with alkyl or carboxyl functionality. Effects of solvents commonly used in experimental studies (water and toluene) on NP structures and properties were investigated as well. For OPH3- and SCH3ligated NPs, changes in both the ligand structure (proton transfer either to NP atoms or to other ligands) and in the NP structure (bridge formation between NP atoms, breakage of Cd−Se/Cd−Te bonds, and opening of nanoparticles) were observed in the energy minimized structures, indicating the strong interplay between surface chemistry and NP structure. Increasing the number of atoms and changing from X = Se to Te in the NPs decreased the computed HOMO−LUMO gaps. The gap for Cd6X6 generally increases slightly in the order gas phase → toluene → water. Cd9X9 does not follow this sequence. This is explained by significant Mulliken charges on the middle layer Cd/X atoms in the Cd9X9 structures (see Figure 1a); the middle layer Cd/X atoms contribute to the Cd9X9 HOMOs/ LUMOs (see Figure 1b), and interaction of the charges on those atoms with polar water molecules can result in the HOMO/ LUMO destabilization, which changes the HOMO/LUMO gaps in a manner different than in the Cd6X6 case. NH3 and OPH3 groups were shown to perturb the Cd6X6 structures, but not very strongly. Both ligands cause noticeable HOMO/LUMO destabilization in capped NPs, more pronounced for the LUMOs than for the HOMOs. This, in turn, was found to drastically reduce both the vertical IP and EA of the NPs compared with the bare species. EAv of both NH3- and OPH3capped NPs were found to be negative. SCH3 groups were shown to form Cd−S−Se/Te bridges, and both SCH3-capped Cd6Se6 and Cd6Te6 NPs were found to form open structures rather than closed structures derived from the original Cd6X6 species. In contrast to NH3 and OPH3 groups, SCH3 binding causes destabilization of capped NP HOMOs and stabilization of their LUMOs. The capped NP HOMOs have either dominating contributions from only sulfur 3p-orbitals of the capping group(s) (for the closed structure) or large contributions from sulfur 3p-orbitals of the capping groups with some minor contributions from NP atoms (for the open structures). The LUMOs of these NPs have large contributions from both the capping groups and from the NP atoms (Figure 3b). The SCH3 ligands apparently can interact with Cd and Se/Te via their lone pairs and also can interact by their unpaired electrons with Cd 6828



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experimental work, a relatively weak size dependence of the HOMO energy was measured for NPs larger than 2.8 nm. The HOMO energy pinning was explained by interactions between the NP HOMO and the states of the substrate (Au electrode) coated with dithiol (thiol:Au states or interfacial states). Very recently Naaman and co-workers observed near pinning of the CdSe NP LUMO relative to the conduction band of a TiO2 electrode. This phenomenon was explained by strong NP−electrode interactions.2k The mechanisms of HOMO energy pinning are different in the theoretical and experimental studies, and it will be of significant interest to extend our studies of both HOMO/LUMO energy alignment and HOMO pinning to Cd6X6 and Cd9X9, and to larger species capped by long-chain ligands coordinated to the NPs by S, O, and N atoms. From the results for Cd9X9 and for Cd6X6 species capped with long-chain S-coordinated ligands, we suggest that larger NPs, which are of great experimental interest, may also undergo Cd−S−X bridge formation, breaking some Cd−X bonds, formation of hydrogen bonds between protons of the ligands and X atoms of the NPs, and proton transfer among ligands and X-centers of the NPs. These processes could cause various and (potentially) useful changes of structure, electronic, and optical properties of capped NPs and charge transfer activity. Thorough exploration of these structural effects on NP electronic properties and charge transfer dynamics is an enticing goal.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Detailed review of theoretical studies of small bare and capped CdnSen/CdnTen NPs; complete reference 15; detailed description of the results for the capped Cd9X9 (X = Se, Te) NPs; data for the Cd6Se6/Cd6Te6 species calculated at the B3LYP/ Lanl2dz [HF/Lanl2dz] level of theory (gas phase; H2O; C6H5CH3); data for the Cd9Se9/Cd9Te9 species calculated at the B3LYP/Lanl2dz [HF/Lanl2dz] level of theory (gas phase; H2O; C6H5CH3); data for the Cd6Se6/Cd6Te6 species capped by SCH2CH3 and SCH2CH3CH3 groups calculated at the B3LYP/Lanl2dz [HF/Lanl2dz] level of theory (gas phase; H2O; C6H5CH3); results of the studies of the large capped nanoparticles. 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]. Present Address ∥

Department of Physics, University of Houston, Houston, TX, 77204, United States. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This material is based in part upon work supported as part of the UNC EFRC: Solar Fuels, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001011 (to D.N.B. and S.S.S. in supervision of this research, and to A.K. and D.B. for preliminary studies). This work was also supported by DOE grant ER 46430 (for the quantum chemical studies by A.K.). Additional support by DOE ASCR under SciDAC-e award DE-FC02-06ER25764 is gratefully acknowledged. 6829



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(21) Varetto, U. Molekel 5.4.0.8; Swiss National Supercomputing Centre: Manno, Switzerland. (22) Schaftenaar, G.; Noordik, J. H. J. Comput.-Aided Mol. Des. 2000, 14, 123−134. (23) Bhattacharya, S. K.; Kshirsagar, A. Phys. Rev. B 2007, 75, 035402. (24) Jose, R.; Zhanpeisov, N. U.; Fukumura, H.; Baba, Y.; Ishikawa, M. J. Am. Chem. Soc. 2006, 128, 629−636. (25) Talapin, D. V.; Lee, J.-S.; Kovalenko, M. V.; Shevchenko, E. V. Chem. Rev. 2010, 110, 389−459 and references therein. (26) Nanoparticles: From Theory to Applications; Schmid, G., Ed.; Wiley-VCH: Weinheim, Germany, 2010. (27) Haram, S. K.; Kshirsagar, A.; Gujarathi, Y. D.; Ingole, P. P.; Nene, O. A.; Markad, G. B.; Nanavati, S. P. J. Phys. Chem. C 2011, 115, 6243−6249. (28) (a) Dagtepe, P.; Chikan, V.; Jasinski, J.; Leppert, V. J. J. Phys. Chem. C 2007, 111, 14977−14983. (b) Rogach, A. L.; Franzl, T.; Klar, T. A.; Feldmann, J.; Gaponik, N.; Lesnyak, V.; Shavel, A.; Eychmuller, A.; Rakovich, Y. P.; Donegan, J. F. J. Phys. Chem. C 2007, 111, 14628− 14637. (c) Yu, W. W.; Qu, L.; Guo, W.; Peng, X. Chem. Mater. 2003, 15, 2854−2860. (29) Kilina, S.; Ivanov, S.; Tretiak, S. J. Am. Chem. Soc. 2009, 131, 7717−7726.

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