Effect of One-Coordinated Atoms on the Electronic and Optical Properties of ZnSe Clusters.

To understand the influence of one-coordinated Zn and Se atoms on the structures, electronic, and optical properties of ZnSe clusters, we investigate the Zn37Se20 clusters employing first-principles theoretical calculations. The Zn37Se20 cluster, constructed from the InP nanocrystal structure, possesses a Zn21Se20 core and 16 one-coordinated surface atoms. The effect of one-coordinated atoms is studied by adding or removing one-coordinated atoms of the Zn37Se20 cluster. The calculations show that the modifications of one-coordinated atoms change slightly the coordination states and bond lengths of the atoms on the cluster surface. The clusters with the same core structure and different amounts of one-coordinated atoms have similar optical spectra, suggesting the importance of the cluster core structure in their optical properties.

Introduction

Colloidal semiconductor quantum dots (QDs) possess unique optical,[1] magnetic,[2] and catalytic[3] properties that are different from bulk materials due to strong quantum confinement of QDs. The properties of QDs can be finely tuned by changing their surface passivation,[4−6] shape,[7] and size.[8,9] The high-quality synthesis of QDs ensures their practical applications in multiple fields, such as biolabeling,[10] solar cells,[11,12] and laser.[13]

Magic-size clusters (MSCs) are a type of nanoparticles with specific numbers of atoms, which usually form along with the nucleation and growth of QDs. The investigations of MSCs are of essential significance to the understanding of the formation mechanism of QDs.[14,15] MSCs have attracted much attention due to their high stability with typical sizes in the range of 1–3 nm.[16,17] Investigation of MSCs, in particular, their atomic structures and optical properties, is crucial for understanding their good performance in nanodevices.[18] Various structures of MSCs, including core–cage (CdSe) (n = 13, 33, and 34),[19] tetrahedral Cd35Se20X30L30,[20] and In37P20(OOCCH2Ph)51 nanoclusters,[21] have been reported. Recently, Robinson and co-workers[22] investigated the CdS MSC with an absorption maximum at about 311 nm (MSC-311), which has been assumed to be of the InP nanocrystal structure.[21] The pair distribution function (PDF) of CdS based on the single crystal of In37P20(OOCCH2Ph)51 coincides with the PDF of CdS MSC-311.[23] These results suggest that the In37P20 structure may be applicable to the II–VI metal chalcogenide cluster systems, such as the ZnSe cluster. We are inspired to investigate whether the ZnSe MSC with the absorption maximum at 299 nm (MSC-299)[24] found previously also has a similar structure to that of InP MSC. The removal and/or substitution of one-coordinated In atoms with three dangling bonds in InP MSCs showed their influence on the structure and optical properties of InP clusters.[25−27] Considering that the one-coordinated atoms are on the cluster surface, an in-depth understanding of the optical and electronic nature of clusters[28] is critical for exploring their formation mechanisms.[29] Hence, it will be interesting to investigate at a molecular level how the atoms in different coordination states influence the optical properties of the ZnSe cluster.

In this work, we choose the Zn37Se20 cluster, which is constructed based on the atomic structure of InP MSC, as a model to investigate the influence of one-coordinated atoms on the property of the cluster. This model has one Zn21Se20 core and 16 one-coordinated Zn atoms. By removing Zn atoms and adding Se atoms, we construct the respective Zn37–Se20 (n = 1–16) and Zn37Se20+ (m = 1–16) clusters and investigate their structures, stabilities, and optical properties.

Results and Discussion

Structure of Zn37Se20H68

Based on the InP nanocluster structure,[21] the Zn37Se20 model cluster was built by replacing In and P atoms with Zn and Se, respectively. The optimized structure of Zn37Se20 with 68 pseudo hydrogens is shown in Figure , and it can be seen that it largely maintains the structural features of InP MSC. The structure has a pseudo-C2 symmetry, with Se and Zn atoms symmetrically distributed along the C2 axis.[25] The Zn37Se20 structure contains six-membered rings formed by three Se and three Zn atoms (Figure S1) and tetrahedrons by one Se and four neighboring Zn atoms. This is similar to the previously reported zinc blende and wurtzite structures.[30] Specifically, in the absence of pseudo hydrogen atoms, the Zn37Se20 structure has 20 four-coordinated Se atoms, with each atom bonded to four Zn atoms, 7 four-coordinated Zn atoms, with each atom bonded to four Se atoms, 8 three-coordinated Zn atoms, with each atom bonded to three Se atoms, 6 two-coordinated Zn atoms, with each atom bonded to two Se atoms, and 16 one-coordinated Zn atoms, with each atom bonded to one Se atoms (Figures S1 and S2 and Table S1). The three-, two-, and one-coordinated Zn atoms need to be saturated with pseudo hydrogen atoms to result in the Zn37Se20H68 structure prior to calculation. Moreover, it has been reported that the one-coordinated atoms more readily dissociate than those in other coordination states.[6]

Figure 1

Optimized structure of the Zn37Se20 cluster with the dangling bonds saturated with 68 pseudo hydrogens. The different colors in the model represent H (silver), Se (green), and Zn atoms in either one-coordinated state (cyan) or other coordinated states (brown).

The electron density distribution of Zn37Se20H68 is explored via the electron localization function (ELF). As shown in Figure S3, the ELF value of Se atoms is about 0.8, while that of Zn atoms is much lower, suggesting a strong localization of electrons around Se atoms[31] and a relatively low electron density of Zn atoms. These results may suggest a charge transfer from Zn to Se atoms, which is further supported by the charge density difference (CDD) pattern (Figure S4). The charges of pseudo hydrogens are localized at the passivated sites, and no charge transfer is observed between pseudo hydrogens in different sites, consistent with the previous findings.[32] Meanwhile, the Bader charge analysis of the Zn37Se20H68 cluster suggests that each Se atom acquires 0.86 electrons from the surrounding four Zn atoms (Table S1).

Structures of Zn37–Se20 (n = 0–16) and Zn37Se20+ (m = 1–16) Nanoclusters

The one-coordinated atoms are generally chemically active compared to the two-/three-coordinated atoms. To understand the effect of one-coordinated atoms, we modify the Zn37Se20 cluster structure by either removing the one-coordinated Zn atoms or adding Se atoms to the one-coordinated Zn atoms. It is noteworthy that we do not modify the Se atoms of the Zn37Se20 structure as they are all saturated in the four-coordinated state.

The Zn37–Se20 (n = 1–16) (Figures and S5) and Zn37Se20+ (m = 1–16) clusters (Figures and S6) constructed have similar geometries but slightly different coordination states and bond lengths for the surface atoms. It is noted that the coordination states of the surface atoms changed upon removing or adding certain atoms. For example, the Se atom becomes three-coordinated upon removing the corresponding one-coordinated Zn atom, while the one-coordinated Zn atom becomes two-coordinated upon adding one Se atom.

Figure 2

Optimized structures of the Zn37–Se20 (n = 1–8) clusters with the dangling bonds saturated by pseudo hydrogens. The different colors in the model represent H (silver), Se (green), and Zn atoms in either one-coordinated state (cyan) or other coordinated states (brown).

Figure 3

Optimized structures of the Zn37Se20+ (m = 1–8) clusters with the dangling bonds saturated by pseudo hydrogens. The different colors in the model represent H (silver) and Se atoms in four- (green) or one-coordinated state (blue) and Zn atoms in either one-coordinated state (cyan) or other coordinated states (brown).

Table summarizes the average bond lengths of Se–Zn and those of the three-coordinated Se atoms binding with three neighboring Zn atoms (Se(3)–Zn) and the one-coordinated Se atoms binding with one Zn atom (Se(1)–Zn). The average bond lengths for two- and four-coordinated Se binding with Zn atoms (Se(2)–Zn, Se(4)–Zn) are shown in Table S2. In general, the average Se–Zn bond length changes little at about 2.474 Å upon the modifications. In addition, the Se(1)–Zn bond lengths are the shortest, while those of Se(3)–Zn and Se(4)–Zn are the longest and are similar to each other. It appears that the bonds with the Se atom in a lower coordinated state exhibit shorter lengths, which agrees well with a previous study about the ZnSe nanoclusters.[33]

Table 1

Average Bond Lengths of Se–Zn, Se(3)–Zn, and Se (1)–Zn in Zn37–Se20 (n = 0–16) and Zn37Se20+ (m = 1–16) Clusters

clusters	average bond length of Se–Zn (Å)	average Se (3)–Zn bond length (Å)	clusters	average bond length of Se–Zn (Å)	average Se (1)–Zn bond length (Å)
Zn37Se20H68	2.474
Zn36Se20H66	2.474	2.456	Zn37Se21H70	2.474	2.399
Zn35Se20H64	2.474		Zn37Se22H72	2.473	2.408
Zn34Se20H62	2.474	2.482	Zn37Se23H74	2.473	2.405
Zn33Se20H60	2.474	2.483	Zn37Se24H76	2.472	2.404
Zn32Se20H58	2.474	2.478	Zn37Se25H78	2.472	2.406
Zn31Se20H56	2.474	2.475	Zn37Se26H80	2.471	2.406
Zn30Se20H54	2.474	2.475	Zn37Se27H82	2.471	2.407
Zn29Se20H52	2.474	2.475	Zn37Se28H84	2.470	2.406
Zn28Se20H50	2.474	2.474	Zn37Se29H86	2.470	2.408
Zn27Se20H48	2.474	2.473	Zn37Se30H88	2.469	2.409
Zn26Se20H46	2.474	2.474	Zn37Se31H90	2.469	2.410
Zn25Se20H44	2.474	2.474	Zn37Se32H92	2.469	2.411
Zn24Se20H42	2.474	2.474	Zn37Se33H94	2.469	2.412
Zn23Se20H40	2.475	2.475	Zn37Se34H96	2.469	2.414
Zn22Se20H38	2.475	2.475	Zn37Se35H98	2.468	2.412
Zn21Se20H36	2.475	2.476	Zn37Se36H100	2.468	2.412

Relative Stabilities

We computed the second difference in energy (Δ2E), the binding energy (Eb), and the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy gap (ΔEHL) to evaluate the stability of Zn37–Se20 (n = 0–16) and Zn37Se20+ (m = 0–16) clusters.

The Δ2E reflects the stability of a cluster with respect to its neighbors (Figure a). The calculated Δ2E values of the Zn37–Se20 (n = 0–16) and Zn37Se20+ (m = 0–16) clusters show an oscillation behavior. It is noted that Zn35Se20, Zn32Se20, Zn29Se20, Zn27Se20, and Zn24Se20 clusters exhibit high Δ2E values, suggesting that they are relatively more stable than their neighbors of Zn37–Se20 (n = 0–16) clusters. Similarly, the Zn37Se22, Zn37Se25, Zn37Se29, Zn37Se32, and Zn37Se35 clusters of the Zn37Se20+ (m = 0–16) clusters have relatively high stabilities than their neighbors.

Figure 4

Second-order energy difference Δ2E (a), average binding energies Eb (b), and HOMO–LUMO gap ΔEHL (c) of Zn37–Se20 (n = 0–16) and Zn37Se20+ (m = 0–16) clusters saturated with pseudo hydrogens.

The Eb represents the stability of one species relative to their constituent individual atoms, and Figure b shows that Eb decreases with the decrease of the number of one-coordinated Zn atoms and with the increase of the number of one-coordinated Se atoms.

The ΔEHL is closely related to the energy required by the transfer of electrons from HOMO to LUMO.[34,35] The variation of ΔEHL as a function of the number of one-coordinated Zn and Se atoms for Zn37–Se20 (n = 0–16) and Zn37Se20+ (m = 0–16) clusters is presented in Figure c. The ΔEHL values increase slightly first with the decreasing number of one-coordinated Zn atoms of Zn37–Se20 (n = 0–16), reaching the maximum when n = 4. Upon further decreasing the one-coordinated Zn atoms, the corresponding ΔEHL values decrease gradually, which indicates a quite stable nature of the Zn33Se20 cluster. However, the ΔEHL values of the Zn37Se20+ (m = 0–16) clusters have a decreasing trend, which is similar to the previous work on CdSe QDs.[28] It is noteworthy that the differences between the maximum and minimum ΔEHL for Zn37–Se20 (n = 0–16) and Zn37Se20+ (m = 0–16) are 0.03 and 0.08 eV, respectively. Such small variations suggest that one-coordinated atoms only slightly perturb the molecular orbital energy levels of the studied clusters.

Electronic and Optical Properties

To investigate the effect of the one-coordinated Zn and Se atoms on the electronic structures, Figure presents the projected density of states (PDOSs) of three selected clusters, which are Zn37Se20H68, Zn36Se20H66, and Zn37Se21H70 (see Figures S7 to S16 for the PDOS plots of all of the studied clusters).

Figure 5

Projected density of states (PDOSs) of Zn37Se20H68 (a), Zn36Se20H66 (b), and Zn37Se21H70 (c). In the figure, (2–4) = two-, three-, and four-coordinated atoms, (1) = one-coordinated atoms, and (4) = four-coordinated atoms. The Se atoms are all in four-coordinated states except that the added Se atoms are in one-coordinated states in Zn37Se20+ (m = 1–16) clusters. Note that Fermi energy is set to zero.

For Zn37–Se20 (n = 0–16) and Zn37Se20+ (m = 1–16) clusters, their HOMOs mainly arise from Se 4p orbitals and are close in energy with the other occupied orbitals and their LUMOs are predominantly contributed by Zn 4s and Se 4s orbitals. The LUMOs are separated from the higher unoccupied orbitals with differences of up to ∼0.5 eV, comparable with a previously published theoretical work.[36]

The one-coordinated Zn atoms have little contribution to the HOMO and LUMO of those clusters, while the states of one-coordinated Se atoms do not appear near the Fermi level region, merely influencing the optical properties of the studied clusters. The plots also show that the HOMO and LUMO are primarily contributed by the atoms in non-one-coordinated states that are only slightly perturbed by the one-coordinated atoms. That explains why the DOS near the Fermi energy level looks similar for all of the Zn37–Se20 (n = 0–16) and Zn37Se20+ (m = 1–16) clusters.

The calculated optical absorption spectra of Zn37–Se20 (n = 0–16) and Zn37Se20+ (m = 0–16) are shown in Figure . Figure a,b shows that there is the only a minor influence of one-coordinated Zn atoms on the absorption spectra regarding both the peak shape and maxima, and only 3 nm red-shifts are found when the value of n increases from 0 to 16. Similarly, adding Se atoms to Zn37Se20 also does not affect much the optical absorption spectra of the clusters (Figure c,d). A gradual red-shift with a maximum of 7 nm is found when 16 Se atoms are added. The comparison suggests that neither one-coordinated Zn nor one-coordinated Se atoms perturb much the absorption behavior of the clusters, emphasizing the importance of the electron excitations of the cluster core. That is in line with the finding of the PDOS plots in Figure . In addition, it is noted that the calculated absorption spectra of Zn37Se20, Zn37–Se20 (n = 1–16), and Zn37Se20+ (m = 1–16) are all similar to that of ZnSe MSC-299 measured experimentally (see Figures and S17). However, understanding the atomic structure of ZnSe MSC-299 is still not trivial, warranting further efforts.

Figure 6

Calculated absorption spectra of (a) Zn37–Se20 (n = 0–8), (b) Zn37–Se20 (n = 9–16), (c) Zn37Se20+ (m = 0–8), and (d) Zn37Se20+ (m = 9–16) clusters passivated by pseudo hydrogens.

Conclusions

In summary, we systematically investigate the effect of one-coordinated atoms on the properties of the ZnSe clusters using first-principles theoretical calculations. The addition or removal of one-coordinated atoms changes the coordination states and the local bond lengths of the remaining surface atoms. However, the plots of PDOS, HOMO, and LUMO show that the modifications only affect slightly the states close to the Fermi level region. The states near the edges of the band gap are mainly attributed to the interior Zn and Se atoms, emphasizing the importance of the cluster core. The calculated absorption spectra of the ZnSe clusters further confirm that the electron excitation of the cluster core is critical for their optical properties. This work provides an in-depth understanding of the structures and optical properties of the ZnSe magic-size clusters.

Computational Methods

The geometric and electronic structures and optical properties are calculated using density functional theory (DFT) with the Kohn–Sham (KS) representation[37] implemented in Vienna Ab initio Simulation Package (VASP).[38] Compared with other first-principles software, such as Amsterdam density functional (ADF)[39] and Gaussian code,[40] VASP has high efficiency in algorithm optimization and good stability. There are dangling bonds on the surface of the ZnSe clusters, which are commonly passivated with chemical ligands after synthesis.[24] Due to the large quantities of atoms in these ligands have, it is difficult to calculate the corresponding structures. Certain ligands with simple structures, such as pseudo hydrogen atoms,[41] may be used to simplify the cluster structure for theoretical studies.[42] Pseudo hydrogen is a type of virtual ligand that exhibits fractional charge, and it has been reported to be able to remove the band gap states introduced by the surface dangling bonds,[41−43] leading to results that match well with the experimental data.[44] Therefore, it may be a good candidate to simplify the structure of ZnSe clusters for calculations. For group II–VI clusters, the surface atom with Z formal valence may be passivated via pseudo hydrogen atoms with fractional charge α = (8-Z)/4.[42,45] Thus, in this work, the Zn and Se atoms with respective formal valences of 2 and 6 are saturated with pseudo hydrogen atoms with charges of 1.5 and 0.5e, respectively.[46] The Zn and Se potentials are simulated by the projector-potential plane wave[47] method from the VASP potential library. The valence electrons of Zn and Se atoms are treated as 3d104s2 and 4s24p4, respectively. The cutoff energy is 370 eV in all calculations. The cell size is set as 30 Å × 30 Å × 30 Å to eliminate the interactions between periodic images of the cluster.[48] We set only one γ point in the calculations.[30,49,50] The convergence of the total energies is set as 10–6 eV for structure optimization. The Heyd–Scuseria–Ernzerhof (HSE06) provides part of the precise exchange functional, and its calculated gap value is close to the one obtained by the experiment.[51,52] HSE06 has previously been shown to be reliable for calculating the properties of molecules and clusters.[31,53] Thus, the electronic structure and optical properties are calculated with HSE06 functional incorporated into the VASP code. The electron localization function (ELF) is employed to analyze the distribution of electrons and the property related to electron localization.[54] The ELF value is between 0 and 1, with the value close to 1 representing a strong localization of electrons.[55] The ELF was calculated using VASP, and its visualization was performed using the VESTA code.[56] In addition, the charge transfer in the clusters was estimated via charge density difference (CDD) and the Bader charge analysis.[57,58]

The CDD is defined as followswhere ρZn, ρZn, ρSe, and ρH are the charge densities of Zn37Se20H68, the noninteracting Zn, Se, and H atoms, respectively.

The second difference in energy is defined aswhere E(Zn37–Se20H) is the total energy of Zn37–Se20H and E(Zn37-(Se20H) and E(Zn37–(Se20H) are the energies of its neighbors.

The average binding energy per atom (Eb) is calculated bywhere E(Zn), E(Se), E(H1.5), and E(H0.5) are the energies of a single Zn, Se, pseudo H (with charge 1.5e), and pseudo H (with charge 0.5e) atoms in ZnSeH.