Structural Stability and Electronic Properties of CdS Condensed Clusters

Article pubs.acs.org/JPCC

Structural Stability and Electronic Properties of CdS Condensed Clusters S. Karthikeyan, E. Deepika,† and P. Murugan* CSIR Central Electrochemical Research Institute (CECRI), Karaikudi−630 006, Tamil Nadu, India S Supporting Information *

ABSTRACT: First-principles calculations are carried out to understand the structural stability and electronic properties of 1-D condensed clusters and their fundamental building blocks, CdnSn (n = 1−6) small clusters. By linear stacking of these stable isomers, the condensed clusters, (CdnSn)m, where n = 1−4 and m = 1−9, are modeled. The structural stability of condensed clusters and their building blocks are obtained from the electronic density of states, and it infers that s−p hybridizations play a crucial role in stabilizing these clusters. Electronic properties of all condensed clusters, with m > 4, are interesting in photocatalytic applications as they have a lesser energy gap than that of bulk. Our calculations also show that the (Cd3S3)m clusters are energetically more stable as compared with other-sized condensed clusters, but such clusters can fragment into two smaller clusters by an application of an external temperature, on the order of 450 K.

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biological ligands.13,15 In general, the 1-D assembly of nanostructures, particularly chalcogenide-based compounds, is obtained by condensation of stable clusters or bulk fragments.16−19 Following this, Sangthong et al20 performed firstprinciples calculations on CdS nanorods, obtained from both bulk fragments and condensation of Cd13S13 clusters. They predicted that the nanorod obtained by condensation of stable clusters has more stability, and it transformed to a wurtzite nanorod at a length of 10 nm. Thus, an understanding of stable CdnSn isomers, which act as the building blocks of condensed clusters or 1-D nanoassemblies, is necessary. Various isomers of CdnSn clusters have been studied widely by first-principles calculations.21−26 Interestingly, the geometry of the stable isomer of Cd6S6 was obtained by condensation of two units of Cd3S3, a six-membered planar ring, which is also the stable isomer in this size. Similar large-sized clusters of CdX were also derived from condensation of stable isomers of Cd2X2, Cd3X3, and Cd4X4 (X = S, Se, Te) and were studied by density functional calculations.21,25,27−29 Though such studies have revealed large-sized clusters of CdS being derived from

INTRODUCTION The concept of one-dimensional systems started gaining momentum with the invention of carbon nanotubes (CNTs). Realizing that the potential applications of CNTs were due to their high mechanical strength, ballistic transport, and other novel properties,1 researchers explored such one-dimensional systems of inorganic compounds. Toward this direction, nanotubes and nanowires from Mo−S compounds have been extensively studied and were even suggested2,3 as an alternative to CNTs for certain applications due to their several advantages, viz. synthesis with unique structural and electronic properties and the ability to further tune their properties by adding dopants.4 Recently, 1-D systems of CdS compounds have drawn much attention, leading to the synthesis of their nanowires,5,6 nanotubes,7 and nanorods8−10 with controlled dimensions. This enables their band gaps to be tailored precisely for fabrication of optoelectronic devices.11,12 Similarly, a series of 1D assemblies of various-sized tetrahedral CdS clusters were synthesized13 using bifunctional covalent ligands that link the clusters. In this case, the basic tetrahedral unit was obtained by fragmenting, either the bulk phase of wurtzite or zinc blende. In fact, the clusters of both bulk phases are energetically almost degenerate14 and their stability is increased after adsorption of © 2012 American Chemical Society

Received: May 8, 2011 Revised: January 3, 2012 Published: February 22, 2012 5981

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Figure 1. Construction of (Cd3S3)m condensed clusters. The optimized structures for m = 2 (a), m = 4 (b), m = 6 (c), and m = 9 (d) are shown. Similarly, the structures of the (CdnSn)8 clusters for n = 1 (e), n = 2 (f), and n = 4 (g) are reported.

where E(Cd), E(S), and E(CdnSn) are the total energy of a single Cd atom, a single S atom, and CdnSn clusters, respectively, and n is the number of Cd or S atoms. Similar calculations are extended to condensed clusters. We also carried out the first-principles calculations on infinite CdnSn nanowires with n = 1−4 for the sake of comparison. These are optimized by sampling of BZ, with four k-points along the nanowire axis.

smaller units and Sangthong et al. have compared onedimensional systems obtained by condensation of clusters with those from bulk, the structural stability and electronic properties of various-sized condensed clusters is yet to be understood. Moreover, it is essential to understand the growth condition of these condensed clusters. In the present work, we have studied the atomic structure and electronic properties of condensed clusters and their infinite nanowires by firstprinciples calculations within the framework of density functional theory. The structural stability and bonding nature of these clusters are obtained from electronic density of states. Our study reveals that the Cd3S3 unit prefers to form condensed clusters; however, there is a possibility of condensed clusters to fragment into smaller units, with an application of an external temperature, on the order of 450 K.

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COMPUTATIONAL METHOD All CdS and their condensed clusters reported in this work are optimized by the plane-wave-based first-principles density functional calculations as implemented in VASP.30 Cd and S atoms are described in the limit of the projector augmented wave formalism,31,32 and the exchange-correlation energy is corrected by the generalized gradient approximations.33 Various possible isomers for each CdnSn clusters are modeled, and the stable isomers are identified from their energetics. Condensed (CdnSn)m clusters (n = 1−4 and m = 1−9) are modeled by stacking the stable CdnSn isomers. The cluster is placed in a large supercell, ensuring at least a 10 Å vacuum space around it. Such a large vacuum space is needed to reduce the interaction between the cluster and their periodic images. All atoms in the cluster are relaxed without considering any symmetrical constraints. The process of atomic relaxation is repeated until the force of atoms converges to 10 meV/Å as well as the total energy difference of two consecutive relaxation steps is less than 10−5 eV. The Brillouin zone (BZ) of the supercell is sampled by the Γ point. The binding energy per atom (BE) of a cluster is calculated from BE=

RESULTS AND DISCUSSION

Atomic Structure of CdnSn Clusters. We carried out firstprinciples calculations on the various CdnSn (n = 1−6) clusters, to obtain the stable isomers in each size range, which act as fundamental building blocks of condensed clusters or 1-D nanoassemblies. The optimized structures are shown in Figures S1 and S2 (Supporting Information), and the BE, HOMO− LUMO gap, mean Cd−S bond distance, and bond angle of stable isomers are reported in Table S1 (Supporting Information). The stable isomers of CdnSn clusters from n = 1 to 4 possess linear, rhombic, triangular, and square geometries, respectively, which is quite comparable to earlier reports.21,22,25,26 While all these isomers are planar, the stable isomer for the Cd5S5 cluster is a nonplanar structure. Among the different isomers considered for Cd6S6 clusters, a 3D octahedral isomer that is obtained by the linear condensation of two Cd3S3 triangular isomers (refer to Figure 1a) is stable. Another type of condensed cluster, wherein two Cd3S3 isomers are connected sideways, resembling a steplike arrangement, is found to be less stable by 0.8 eV as compared with the former. Hence, we conclude that the condensed cluster prefers to grow by linear stacking rather than sideways stacking. Condensed Clusters. With a knowledge of stable isomers of CdnSn in each size range, condensed clusters of (CdnSn)m are obtained by linear stacking of m (up to 9) units of stable CdnSn isomers (n = 1−4). We also attempted the condensation of the stable isomer of Cd5S5, but the significant structural distortion was observed due to a larger cavity in the center of the ring. Hence, we did not proceed further. The optimized structures of selected condensed clusters are shown in Figure 1. The (Cd3S3)2 cluster (Figure 1a) is obtained by condensing a planar Cd3S3 isomer at the top and another isomer at the bottom (rotated by 60° along the z axis), thus

nE(Cd) + nE(S) − E(Cd nSn) 2n 5982

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Figure 2. BE (a) and HOMO−LUMO gap (b) of (CdnSn)m are shown. In the inset, BEs of (CdnSn)8 are given for various n. The dotted horizontal line in (b) corresponds to the band gap of bulk CdS (zinc blende), which is obtained from our calculations.

the band gap of the bulk CdS compound. Hence, the photocatalytic activity of these clusters is expected to be higher when compared with that of the bulk. To further understand the structural stability of (Cd3S3)m condensed clusters, we studied the (Cd3S3)9 nanorod modeled from both zinc blende (ZB) and wurtzite (WZ) phases of the CdS compound (Figure S3, Supporting Information). However, the BE of these ZB and WZ nanorods is less than that of condensed clusters by a binding energy difference of 0.057 and 0.151 eV/atom when compared to the (Cd3S3)9 condensed clusters obtained from our work. Moreover, the nanorod from the ZB bulk phase distorts significantly at one of its ends, and it resulted in an energetically less favorable structure when compared to the (Cd3S3)9 condensed cluster. Similarly, the (Cd3S3)9 nanorod obtained from the WZ structure is more stable than the ZB structure with a length of 2.6 nm, but less stable as compared to the condensed cluster. Hence, we conclude that, in this dimension of length, the nanorod from the condensed cluster is energetically more favorable as compared to bulk structures. Also, the structure of the (Cd3S3)m nanorod of this length is deviated from bulk and it is formed from condensed clusters; however, the structure of the nanorod transforms from condensed clusters to the bulk with an increase in its length.20 Electronic Structure. To understand the structural stability of (Cd3S3)m condensed clusters, we obtained the total and partial density of states (DOS) of this cluster with m = 2, 3, and 4, and it is shown in Figure 3. In the DOS, S p states are located in the energy range from −4.0 to −0.0 eV, while Cd s,p states are mainly distributed in the unoccupied region. The structural stability of these clusters can be explained based on molecular orbital theory. The S p states strongly hybridize with Cd s states, to form sp2 or sp3 hybrids (refer to Figure 3), in the lower region of occupied states, and this region can be referred to as bonding states. Closer to the HOMO, the hybridization between S p and Cd s orbitals is quite weaker, and it is often called nonbonding states and antibonding states that lie above the LUMO or unoccupied states. This trend is also found in large-sized condensed clusters (Supporting Information, Figure S4). To support our discussions on s−p hybridization in condensed clusters, we measured the Cd−S−Cd and S−Cd−S bond angles of all CdnSn (n = 1−6) stable isomers as these isomers are their building blocks, and it is reported in Table S1 (Supporting Information). Overall, the Cd−S−Cd angle

increasing the number of Cd−S bonds in the cluster. In a similar way, (Cd3S3)4 and other condensed clusters, (CdnSn)m, are obtained, and optimized structures are shown in Figure 1b− g. Further, other-sized (CdnSn)2 clusters are stacked from their basic unit of CdnSn by rotation of 90° for n = 2, 60° for n = 3, and 45° for n = 4, with respect to another unit. We calculated the BE and HOMO−LUMO gap of all condensed (CdnSn)m clusters, and the results are shown in Figure 2a,b, along with the cohesive energy per atom and band gap of infinite CdnSn nanowires. As expected, the BE of condensed clusters increases exponentially with m and slowly reaches the cohesive energy of the corresponding infinite nanowire, as seen in Figure 2a. In the inset, the BEs of (CdnSn)m condensed clusters with respect to the diameter (in terms of n) are shown. Even though the diameter of the (Cd3S3)m condensed cluster is smaller than that of the (Cd4S4)m cluster, beyond m = 4, the BE of the former is almost equal to that of the latter. For example, the BEs of (Cd3S3)8 and (Cd4S4)8 are 2.362 and 2.361 eV/atom, respectively. Hence, it infers that the (Cd3S3)m condensed clusters are more stable as compared to other-sized condensed clusters and this cluster could preferably extend to nanorod and infinite nanowires. Even our calculations on infinite nanowires supports this conclusion as the cohesive energies of (Cd3S3)2 and (Cd4S4)2 infinite nanowires are almost the same (=2.59 eV/atom). Figure 2b shows the variation of the HUMO−LUMO gaps of the condensed clusters. For the (Cd1S1)m atomic wire, the HOMO−LUMO gap decreases almost exponentially, beyond m = 2. We find that the decrease in the gap is mainly due to variation in the LUMO of atomic wires, which is quite similar to a linear polyene system.34 Similarly, for n = 2, 3, and 4, the HOMO−LUMO gap decreases as the m value increases. It is interesting to observe that, beyond m = 4, the HOMO−LUMO gap for (Cd3S3)m condensed clusters is significantly higher than that of other condensed clusters (including infinite nanowires). This supports our earlier statement that (Cd3S3)m condensed clusters are the most stable among all other clusters. Further, we also noted in Figure 2b that, beyond m = 5, the HOMO− LUMO gap of the (Cd1S1)m atomic wire is less than that of other condensed clusters. It is a consequence of the increase in the number of nonbonding states with the increase in the length of the atomic wire.35 Overall, the HOMO−LUMO gap of all (CdnSn)m condensed clusters, beyond m = 4, is less than 5983

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Figure 4. FE versus m of (Cd3S3)m of various possible two fragments. For better visualization, FE of m = 6−9 is given in the inset.

synthesized below this temperature. It is also worthy to mention that the possibility of fragmenting the condensed clusters into three pieces is also explored. The FE of this fragmentation (3,3,3) for an m = 9 cluster is ∼70 meV/atom, which is higher than that of a two-piece fragmentation (FE = 33 meV/atom). From Figure 4, we observe that the possibility of a (3, m − 3) fragmentation is easier than other fragmentation possibilities. Hence, a (Cd3S3)3 cluster is expected to have more structural stability. We further understand the structural stability of the (Cd3S3)3 cluster from the second derivative of total energy (Δ2E) of condensed clusters, and it is reported in Figure 5. Our

Figure 3. Total and partial DOS of (Cd3S3)m condensed clusters with m = 2 (a), m = 3 (b), and m = 4 (c). The isosurface of partial charge density is drawn for different regions in the DOS of the (Cd3S3)2 cluster, and it is inserted in this figure. Plotted energy ranges in DOS and isosurface charge density values are (1) −3.75 to −3.25 eV, ρ = 0.018 e/Å3; (2) −2.5 to −2.18 eV, ρ = 0.012 e/Å3; (3) −0.4 to 0.2 eV, ρ = 0.037 e/Å3; and (4) 2.65−3.0 eV, ρ = 0.003 e/Å3.

increases with the cluster size and then reaches to that of the bulk, while another angle, the S−Cd−S angle, seems to have no such trend. Thus, the Cd−S−Cd angle plays a significant role in the stability of the CdS cluster. In fact, Cd and S atoms in bulk phases of the CdS compound (both WZ and ZB phases) interact through sp3 hybridization with angles of Cd−S−Cd or S−Cd−S = 110°, as it is well known that the sp3-hybridized angle is around 109.5°. Further, isosurface plots from Figure S5 (Supporting Information) also imply s−p hybrids in stable isomers of CdS clusters. Thus, we conclude that the s−p hybridization plays an important role in the stability of CdS clusters as well as condensed clusters. Fragmentation of Condensed Clusters. We also attempted the possibility of fragmentation of condensed (Cd3S3)m clusters into smaller units to understand their growth stability. For example, the (Cd3S3)4 nanowire can fragment into either two pieces of (Cd3S3)2 clusters or (Cd3S3) and (Cd3S3)3 clusters. The fragmentation energy per atom (FE) is calculated from FE=

Figure 5. Second derivative of energetics of (Cd3S3)m condensed clusters with respect to m is shown. It is calculated using the formula Δ2E = E(m + 1) + E(m − 1) − 2E(m).

calculations show that the Δ2E of (Cd3S3)3 clusters shows the maximum value, which confirms the high structural stability of this cluster. To support this discussion, it is also observed from DOS (Figure 3) that the energy separation between bonding and nonbonding states (near to HOMO) for this cluster is smaller when compared with that of (Cd3S3)2 and (Cd3S3)4 clusters. It allows the delocalization of electrons in both of these states, thus bringing the high structural stability of this cluster. We conclude that the (Cd3S3)3 cluster has higher stability than other clusters and larger-sized clusters can fragment into two smaller units with an application of an external temperature.

E[(Cd3S3)k ] + E[(Cd3S3)m − k ] − E[(Cd3S3)m ] 6m

Each (Cd3S3)m condensed cluster can be split into possible two fragments as follows: (1, m − 1), (2, m − 2), (3, m − 3), and (4, m − 4). FE is calculated and reported in Figure 4. Figure 4 shows that the FE of condensed (Cd3S3)m clusters decreases when the m value increases. It is observed that, for all m > 6, the FE is less than 50 meV/atom. For the (Cd3S3)9 cluster, an FE of 33 meV/atom is required to split into (Cd3S3)6 and (Cd3S3)3 clusters. This infers that this condensed cluster breaks into two smaller units with an application of temperature, on the order of 450 K. However, the condensed clusters as well as the nanorod at this diameter could be

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CONCLUSION We studied the structural stability and electronic properties of (CdnSn)m (n = 1−4, m = 1−9) condensed clusters and their 5984

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building blocks from first-principles calculations. The structural stability of this cluster is explained by the DOS and the Cd−S− Cd bond angle. It infers that the stability arises from the s−p hybridization. Among various-sized condensed clusters, (Cd3S3)m clusters are found to be more stable, but they can fragment into two small pieces, preferably (3, m − 3), by an application of an external temperature. Further, electronic properties of condensed clusters with m > 4 show a lower energy gap as compared with the bulk CdS system, and it would be interesting in photocatalytic applications. Our calculations also reveal that the condensed clusters have more structural stability as compared to 1-D nanorods obtained from the bulk in this dimension.

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ASSOCIATED CONTENT

S Supporting Information *

The optimized geometry of various CdnSn clusters, a table that summarizes the atomic and electronic properties of stable isomers, optimized geometry of various nanorods, DOS of the (Cd3S3)3 cluster along with partial change density diagrams, and charge density diagrams of stable clusters are provided. 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]. Author Contributions †

Contributed during her stay at CECRI.

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ACKNOWLEDGMENTS Calculations were performed at the High Performance Computing Facility at CECRI, Karaikudi. The charge densities were visualized by XCRYSDEN.36 We thank J. Karthikeyan of CECRI for his valuable input.

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REFERENCES

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