Article pubs.acs.org/JPCC
Stuffing Enhances the Stability of Medium-Sized (GaAs)n Clusters Qi Liang Lu,*,† Jun Wei Meng,† Wen Jun Song,† Y. W. Mu,‡ and Jian Guo Wan§ †
School of Physics and Material Science, Anhui University, Hefei 230039, Anhui, P. R. China College of Physics and Electronics Engineering, Shanxi University, Taiyuan 030006, Shanxi, P. R. China § National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, Jiangsu, P. R. China ‡
ABSTRACT: The structure and properties of medium-sized (GaAs)n clusters (n = 18− 36) were investigated using density functional theory with the generalized gradient approximation. In general, stuffed topologies are the lowest energy states. Tubular and other cage-like structures are less energetically preferable. Structural transition from cages to stuffed topologies occurred at an approximate size of n = 20. In addition, the binding energy per unit, the highest occupied molecular orbital and the lowest unoccupied molecular orbital gaps, the density of states, and infrared spectra were investigated.
I. INTRODUCTION In the past few years, researchers have shown increasing interest in the nanostructures of III−V semiconducting materials due to their potential applications in electronic and optoelectronic devices.1,2 A cluster refers to the intermediate state between microscopic atoms and macroscopic condensed matter. In this state, the properties of the particles are very sensitive to size and shape variations due to quantum confinement and therefore very different from those of the bulk phase. Studies on semiconductor clusters can further clarify the growth mechanism of bulk semiconductor materials and develop novel, technologically promising semiconductor nanostructures. To date, numerous studies on (III−V)n clusters, such as (AlN)n,3,4 (BN)n,5−7 (GaN)n,8−10 and (GaP)n,11−13 have been conducted. Among these clusters, GaAs clusters were one of the important subjects of numerous experiments 14−19 and theoretical studies.20−34 Earlier studies showed that small (GaAs)n (n ≤ 16) clusters tend to exhibit cage-like structures.20,33,34 Recent studies indicated that competition exists between hollow cage and core−shell structures in the (GaAs)n (n = 10−15) clusters,32 in which a Ga or an As atom is at the core of the cage. For larger (GaAs)n (n ≤ 17) clusters, Gutsev et al.31 considered a number of fullerene and nonfullerene topologies and found that tubular cages are generally more stable than the other cage isomers. In this paper, we will report on the structural patterns of medium-sized (GaAs)n clusters in the range n = 18−36. The electronic properties of these clusters are discussed in terms of the energy difference between the highest occupied and lowest unoccupied molecular orbitals (HOMO− LUMO gap) and the density of electronic state (DOS).
certain size, a number of structural isomers with different possible combinations of filling atoms and/or outer cages are considered. Afterward, we consider different cages and all possible topologies of the encaged GaAs unit. We also consult structures obtained by a genetic algorithm (GA) code with an empirical Stillinger−Weber potential.35,36 A number of candidate structures were obtained after 4000 steps matting, and cage structures were also searched by basin hopping method. A detailed description of the method is given in our previous works.37 Finally, 12−22 low-energy stuffed (GaAs)n isomers obtained from the handmade construction and the GA search serve as possible candidates for global minima and can be further optimized to compare with hollow cages. In addition, the hollow cages proposed by Gutsev et al.31 are optimized. These structures and their properties are analyzed using the Dmol3 code based on density functional theory (DFT).38 In the Dmol3 electronic structure calculations, all electron treatments and double-numerical polarized (DNP) basis sets are chosen. The density function is treated within a generalized gradient approximation (GGA)39 with the Perdew−Burke− Ernzerhof (PBE) exchange correlation potential.40 Selfconsistent field calculations on the total energy and electron density are performed with a convergence criterion of 10−6 au. We use a convergence criterion of 0.002 hartree/Å on the force, 0.005 Å on the displacement, and 10−6 Hartree on the total energy in the geometry optimization. A fine-quality mesh size for numerical integration is selected. All calculations are spin unrestricted. We perform calculations for spin multiplicities, starting with a spin-singlet configuration for these even-electron systems. The ground state structures are obtained from the
II. COMPUTATIONAL METHODS The coordinates of outer cages are constructed according to the structures of refs 20, 31, and 34. For stuffed (GaAs)n of a
Received: February 8, 2013 Revised: May 23, 2013
© XXXX American Chemical Society
A
dx.doi.org/10.1021/jp401426r | J. Phys. Chem. C XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry C
Article
minimum in the total energy and preferred spin multiplicity. The smearing is set as 0.002 hartree to ensure convergence. Vibrational frequency analyses are performed to simulate the infrared (IR) spectra and check whether the structure is a true minimum without imaginary frequencies. In Dmol3, frequencies are evaluated by finite differences. The calculated Ga−As bond length and cohesive energy of the fully relaxed GaAs solid are 2.496 Å and 6.67 eV per GaAs unit, which is consistent with the experimental value of 2.448 Å and 6.52 eV.41 To further test the functional choice, calculations are also conducted on bulkphase GaAs with other exchange-correlation effects, Wang and Perdew exchange-correlation formula (PW91),42 and Becke exchange plus Lee−Yang−Parr (BLYP) correlation.43 The results of PW91 are 2.496 Å and 6.65 eV per GaAs unit, which is well consistent with that of PBE and experiment. However, BLYP gives results of 3.362 Å and 5.16 eV. Thus, the PBE is a reasonable choice.
III. RESULTS AND DISCUSSION The lowest energy stuffed geometrical configurations of (GaAs)n, along with the previously proposed hollow cages, are displayed in Figure 1 according to their relative energy. The ground state of them are spin singlet. From this figure, one can clearly see that the states with stuffed structures are more energetically preferable than cage configurations for size n > 18. The ground state geometry of (GaAs)18 is a tubular cage structure consistent with the results of ref 31. The stuffed structure with an endohedral GaAs dimer is slightly unstable by 0.38 eV, which implies that the hollow cage growth pattern is favorable at the present size. Three major types of structures of (GaAs)20 are given in Figure 1. The stuffed structure is found to be the lowest energy state and can be obtained by encaging (GaAs)2 in the (GaAs)18 cage. The most stable state with a fullerene geometry obtained by ref 31 is less competitive and yields 0.09 eV in total energy to the ground state. The rather small energy difference implies competition between the two growth patterns. The structure with the octagonal tubular geometry is less stable in energy by 0.37 eV. For (GaAs)22, the two states with hollow cage topologies are found to be above the stuffed structure by 0.69 and 0.83 eV. The remarkable energy difference means that structural transition from cages to stuffed topologies occurs at about the size of n = 20. In the size region between (GaAs)20 and (GaAs)28, the lowest energy configurations are the patterns filled with two GaAs units. The stuffed structure of (GaAs)32 can be obtained by placing four GaAs units inside a (GaAs)28 cage. Ga−As are not alternating in arrangement in the core unit. A similar wrong bond was found in the most stable structure in the Ga4As4 cluster.20,33,34,44 The arsenic atoms separate into two bonded pairs. The wrong bonds are also found in low-energy isomers of other sized (GaAs)n clusters. However, these structures are less energetically favorable. This phenomenon may be related to antisite defects which were found in bulk GaAs in certain conditions.45 These results demonstrate the need to carefully choose optimal filling atoms and outer cage combinations within the filled fullerene structural pattern. For (GaAs)36, a bulk-like structure was found to be the lowest energy state in ref 31. Our calculation confirms their findings; however, our structure is slightly different from the results of their study. This structure can likewise be viewed as stuffed topologies. There are two innermost GaAs hexagonal rings whose one Ga (As) atom bonds with four As (Ga) atoms.31 The cage topology which
Figure 1. Structures of stuffed, tubular, and cage-like isomers of (GaAs)n clusters are given with respect to the lowest energy state. Interior filling atoms are highlighted, in which the black and green balls are Ga and As atoms, respectively. For (GaAs)36, the bulk-like structure is given.
possesses the lowest energy structure of (BN)36 with Td symmetry46 is less stable than the bulk-like geometry in energy B
dx.doi.org/10.1021/jp401426r | J. Phys. Chem. C XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry C
Article
minus four GaAs units is not energetically preferable. It implies that there may exist more stable structures in the evolutionary process from general stuffed structure to bulk-like topology. Various possible reasons make the stuffed (GaAs)n clusters favorable. Unlike C, GaAs prefers sp3 hybridization to sp2; therefore, the hollow cages are unstable. Many dangling bonds are found on the surfaces of GaAs cages. To stabilize the cages, some atoms stuffed inside the cage are needed for sp3 hybridization and to saturate the existing dangling bonds on the cage surface. For this to occur, sufficient empty space should be available for the core atoms to bond with atoms in the cage. We believe that the inner space of the cage is large enough for atoms to adhere to (GaAs)n with a cluster size of n = 18. The bulk-like structure of (GaAs)36 supports the assumption of sp3 hybridization. On the other hand, a difference in Pauling electronegativity exists between Ga and As atoms, which is 1.81 for Ga and 2.18 for As. This results in a partially ionic chemical bonding in GaAs clusters. For example, the average on-site charges of Ga atom for stuffed, tubular, and cage-like (GaAs)20 obtained using Mulliken population analysis are 0.47e, 050e, and 0.51e, respectively. Meanwhile, the charges of (GaAs)32 that correspond to the above-mentioned structures are 0.45e, 0.48e, and 0.49e, respectively. Remarkable charge transfers were observed between Ga and As atoms. This condition is different from the semiconductor clusters of single
Figure 2. Binding energy per GaAs unit and HOMO−LUMO gap of stuffed, tubular, and cage-like isomers of (GaAs)n clusters. Dashed line is the calculated value of the bulk forbidden gap.
by 2.94 eV. Results suggest that bulk-type structures are preferable for larger (GaAs)n clusters. The stuffed configuration isomer filled with four GaAs units is less competitive in energy. Nevertheless, it is more stable than other cage-like structures. It should be note that the obtained structure of (GaAs)32 by
Figure 3. Density of states (DOS) of stuffed and cage-like structures of (GaAs)20 and (GaAs)32. Fermi level is set to zero, and Gaussian broadening parameter is taken to be 0.04 eV. C
dx.doi.org/10.1021/jp401426r | J. Phys. Chem. C XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry C
Article
Figure 4. Simulated infrared spectra of stuffed (left column) and the lowest energy cage-like (right column) structures of (GaAs)n clusters.
elements such as C and Si. The compromise between sp3 hybridization and ionic bonding in the (GaAs)n clusters results in energetically preferable stuffed structures. The properties of clusters are very sensitive to structural changes. Figure 2 shows the binding energy per GaAs unit of stuffed, tubular, and cage-like isomer of (GaAs)n clusters. The
binding energy of stuffed structures is about 5.90 eV and slowly increases with cluster size. This value is somewhat close to that of the calculated bulk GaAs solid (6.67 eV). Binding energies of the other two geometry types are slightly smaller than that of stuffed structures with an energy difference of 0.045−0.107 eV/ unit. The calculated bulk forbidden gap value is 1.223 eV, which D
dx.doi.org/10.1021/jp401426r | J. Phys. Chem. C XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry C
Article
structures combined with those of a genetic algorithm search are further optimized within the same level of theory as the structures shown in Figure 1. Only the lowest energy structure of (GaAs)n−1 is considered. The dissociation energy increases rapidly with increasing n until reaching to the maximum value at n = 22. Then it decreases gradually with cluster size. (GaAs)22 has the largest value of 6.13 eV, indicating it is more stable: a larger energy should be required to break the cluster.
IV. CONCLUSIONS The structure and properties of medium-sized (GaAs)n clusters (n = 18−36) were investigated using density functional theory with the generalized gradient approximation (DFT-GGA). Stuffed topologies are the lowest energy states and occur with n = 20. Tubular and other cage-like structures are less energetically preferable. Although our results do not guarantee determination of the most stable structures, elucidating the size-dependent structural evolution of (GaAs)n clusters is important. The properties of clusters are quite sensitive to its geometrical structures. Thus, the properties, such as infrared spectra, of stuffed topologies are different from those of cagelike structures.
Figure 5. Dissociation energy (in eV) for loss of GaAs unit for the lowest energy structure of (GaAs)n clusters.
underestimates the experimental value of 1.424 eV. In Figure 2, the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) gaps of stuffed structures are around the calculated bulk forbidden gap value. The real HOMO−LUMO gap of these clusters is expected to approach the bulk value. The gaps of the other two geometry types are remarkably larger than those of stuffed structures, especially for tubular topologies. The binding energy and HOMO−LUMO gap indicate that the properties of (GaAs)n clusters with stuffed structures are more similar to those of the bulk phase. We chose (GaAs) 20 and (GaAs) 32 as examples in investigating the density of states (DOS) of stuffed and cagelike structures. Calculated spectra are shown in Figure 3 with a Gaussian broadening of 0.04 eV. Remarkable differences can be observed for the spectral shapes of these two kinds of structures. Electronic states of cage-like structures are more localized than those of stuffed topologies at a range of −3.0 eV to the Fermi energy level. Stuffed and cage-like (GaAs)20 possess similar intensities of DOS near the Fermi level. For (GaAs)32, the average density near the Fermi level of the stuffed structure is smaller than that of the cage-like geometry. The presence of fewer states near the Fermi level of a cluster indicate greater stability. Thus, the DOS near the Fermi level reflects the relative stability of these clusters. These species all have real frequencies and are minimum energy structures along the potential energy surfaces. Calculated IR spectra of stuffed and cage-like structures are given in Figure 4. A notable difference between the two structure patterns can be seen. Spectra of cage-like (GaAs)n are much simplee. The dominant IR peaks are located around 290 cm−1. Moreover, spectra of stuffed structures are quite rich. There are many strong IR peaks at the lower frequency region, especially for n ≤ 22. Compared with cage-like (GaAs)n, a red shift of the highest vibrational frequency can be found with the exception of n = 22. The calculated trend in IR spectra may be validated in future experiments. The dissociation energy for the loss of a GaAs unit for the lowest energy structure are plotted in Figure 5. These energies are obtained as the energy difference of the decay processes (GaAs)n → (GaAs)n−1 + GaAs. The initial structures of (GaAs)n−1 are obtained by taking off a GaAs dimer at different sites on the surface of (GaAs)n. These
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS This work was supported by the Natural Science Foundation of Anhui Province (No. 090414186), the Key Research Project of Natural Science Foundation of Anhui Provincial Universities (No. KJ2010A029), and the 211 Project of Anhui University.
■
REFERENCES
(1) Ntakis, I.; Pottier, P.; De La Rue, R. M. Optimization of Transmission Properties of Two-dimensional Photonic Crystal Channel Waveguide Bends Through Local Lattice Deformation. J. Appl. Phys. 2004, 96, 12−18. (2) Liu, Z.; Kumbhar, A.; Xu, D.; Zheng, J.; Sun, Z.; Fang, J. Coreduction Colloidal Synthesis of III−V Nanocrystals: The Case of InP. Angew. Chem., Int. Ed. 2008, 47, 3540−3542. (3) Bai, Q. G.; Song, B.; Hou, J. Y.; He, P. M. First Principles Study of Structural and Electronic Properties of AlnN (n = 1−19) Clusters. Phys. Lett. A 2008, 372, 4545−4552. (4) Zhang, D.; Zhang, R. Q. Geometrical Structures and Electronic Properties of AlN Fullerenes: A Comparative Theoretical Study of AlN Fullerenes with BN and C Fullerenes. J. Mater. Chem. 2005, 15, 3034−3038. (5) Oku, T.; Nishiwaki, A.; Narita, I. Formation and Atomic Structures of BnNn (n = 24−60) Clusters Studied by Mass Spectrometry, High-resolution Electron Microscopy and Molecular Orbital Calculations. Physica B 2004, 351, 184−190. (6) Strout, D. L. Structure and Stability of Boron Nitrides: The Crossover between Rings and Cages. J. Phys. Chem. A 2001, 105, 261− 263. (7) Matxain, J. M.; Ugalde, J. M.; Towler, M. D.; Needs, R. J. Stability and Aromaticity of BiNi Rings and Fullerenes. J. Phys. Chem. A 2003, 107, 10004−10010. (8) Zhao, J. J.; Wang, B. L.; Zhou, X. L.; Chen, X. S.; Lu, W. Structure and Electronic Properties of Medium-sized GanNn Clusters (n = 4− 12). Chem. Phys. Lett. 2006, 422, 170−173. E
dx.doi.org/10.1021/jp401426r | J. Phys. Chem. C XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry C
Article
(31) Gutsev, G. L.; Mochena1, M. D.; Saha1, B. C.; Weatherford, C. A.; Derosa, P. A. Structure and Properties of (GaAs)n Clusters. J. Comput. Theor. Nanosci. 2010, 7, 254−263. (32) Lu, B.; Guo, Z.; Wang, L.; Zhao, J. Competition Between CoreShell and Hollow Cage Structures in the GanAsn (n = 10−15) Clusters. J. Comput. Theor. Nanosci. 2011, 8, 2488−2491. (33) Gutsev, G. L.; Johnson, E.; Mochena, M. D.; Bauschlicher, C. W., Jr. The Structure and Energetics of (GaAs)n, (GaAs)n−, and (GaAs)n+ (n = 2−15). J. Chem. Phys. 2008, 128, 144707. (34) Gutsev, G. L.; O’Neal, R. H., Jr.; Saha, B. C.; Mochena, M. D.; Johnson, E.; Bauschlicher, C. W., Jr. Optical Properties of (GaAs)n Clusters (n = 2−16). J. Phys. Chem. A 2008, 112, 10728−10735. (35) Stillinger, F. H.; Weber, T. A. Computer Simulation of Local Order in Condensed Phases of Silicon. Phys. Rev. B 1985, 31, 5262− 5271. (36) Wang, Z. Q.; Stroud, D. Monte Carlo Study of Liquid GaAs: Bulk and Surface Properties. Phys. Rev. B 1990, 42, 5353−5356. (37) Mu, Y. W.; Li, J. R.; Wan, J. G.; Song, F. Q.; Wang, G. H. Structures and Polarizabilities of Medium-sized GanAsm Clusters. Chem. Phys. Lett. 2011, 511, 97−100. (38) Dmol3 is a density functional theory (DFT) package distributed by MSI Delley, B. An All-Electron Numerical Method for Solving the Local Density Functional for Polyatomic Molecules. J. Chem. Phys. 1990, 92, 508−517. (39) Perdew, J. P.; Wang, Y. Accurate and Simple Analytic Representation of the Electron-gas Correlation Energy. Phys. Rev. B 1992, 45, 13244−13249. (40) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (41) Rohrer, G. S. Structure and Bonding in Crystalline Materials; Cambridge University Press: Cambridge, England, 2001. (42) Wang, Y.; Perdew, J. P. Spin Scaling of the Electron-gas Correlation Energy in the High-density Limit. Phys. Rev. B 1991, 43, 8911−8916. (43) Becke, A. D. A Multicenter Numerical Integration Scheme for Polyatomic Molecules. J. Chem. Phys. 1988, 88, 2547−2553. Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlationenergy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785−789. (44) Kikuchi, E.; Iwata, S.; Ishii, S.; Ohno, K. First-principles GW Calculations of GaAs Clusters and Crystal Using an All-electron Mixed Basis Approach. Phys. Rev. B 2007, 76, 075325. (45) Komsa, H. P.; Pasquarello, A. Comparison of Vacancy and Antisite Defects in GaAs and InGaAs Through Hybrid Functionals. J. Phys.: Condens. Matter 2012, 24, 045801. (46) Wu, H. S.; Xu, X. H.; Strout, D. L.; Jiao, H. The Structure and Stability of B36N36 Cages: A Computational Study. J. Mol. Model. 2005, 12, 1−8.
(9) Goldberger, J.; He, R.; Zhang, Y.; Lee, S.; Yan, H.; Choi, H. J.; Yang, P. Single-crystal Gallium Nitride Nanotubes. Nature 2003, 422, 599−602. (10) Kandalam, A. K.; Blanco, M. A.; Pandy, R. Theoretical Study of Neutral and Anionic Group III Nitride Clusters: MnNn (M = Al, Ga, and In; n = 4−6). J. Phys. Chem. B 2003, 107, 4508−4514. (11) Zhao, J. J.; Wang, L.; Jia, J. M.; Chen, X. S.; Zhou, X. L.; Lu, W. Lowest-energy Structures of AlnPn (n = 1−9) Clusters From Density Functional Theory. Chem. Phys. Lett. 2007, 443, 29−33. (12) Gómez, H.; Taylor, T. R.; Neumark, D. M. Anion Photoelectron Spectroscopy of Aluminum Phosphide Clusters. J. Phys. Chem. A 2001, 105, 6886−6893. (13) Gómez, H.; Taylor, T. R.; Zhao, Y.; Neumark, D. M. Spectroscopy of the Low-lying States of the Group III−V Diatomics, AlP, GaP, InP, and GaAs via Anion Photodetachment Spectroscopy. J. Chem. Phys. 2002, 117, 8644−8656. (14) Schäfer, R.; Schlecht, S.; Woenckhaus, J.; Becker, J. A. Polarizabilities of Isolated Semiconductor Clusters. Phys. Rev. Lett. 1996, 76, 471−474. (15) Taylor, T. R.; Gómez, H.; Asmis, K. R.; Neumark, D. M. Photoelectron Spectroscopy of GaX2−, Ga2X−, Ga2X2−, and Ga2X3− (X = P, As). J. Chem. Phys. 2001, 115, 4620−4631. (16) Schäfer, R.; Becker, J. A. Photoabsorption Spectroscopy on Isolated GaNAsM Clusters. Phys. Rev. B 1996, 54, 10296−10299. (17) Jin, C.; Taylor, K. J.; Conceicao, J.; Smalley, R. E. Ultraviolet Photoelectron Spectra of Gallium Arsenide Clusters. Chem. Phys. Lett. 1990, 175, 17−22. (18) O’Brien, S. C.; Liu, Y.; Zhang, Q.; Heath, J. R.; Tittel, F. K.; Curl, R. F.; Smalley, R. E. Supersonic Cluster Beams of III−V Semiconductors: GaxAsy. J. Chem. Phys. 1986, 84, 4074−4079. (19) Zhang, Q. L.; Liu, Y.; Curl, R. F.; Tittel, F. K.; Smalley, R. E. Photodissociation of Semiconductor Positive Cluster Ions. J. Chem. Phys. 1988, 88, 1670−1677. (20) Zhao, J. J.; Xie, R. H.; Zhou, X. L.; Chen, X. S.; Lu, W. Formation of Stable Fullerenelike GanAsn Clusters (6 ≤ n ≤ 9): Gradient-corrected Density-functional Theory and a Genetic Global Optimization Approach. Phys. Rev. B 2006, 74, 035319. (21) Sun, Y.; Chen, X.; Sun, L.; Guo, X.; Lu, W. Nanoring Structure and Optical Properties of Ga8As8. Chem. Phys. Lett. 2003, 381, 397− 403. (22) Zhao, W.; Cao, P. L.; Duan, W. Study of Structure Characteristics of the Ga8As8 Cluster. Phys. Lett. A 2006, 349, 224− 229. (23) Karamanis, P.; Begué, D.; Pouchan, C. Structure and Polarizability of Small (GaAs)n Clusters (n = 2, 3, 4, 5, 6, and 8). Comp. Lett. 2006, 2, 255−258. (24) Lan, Y. Z.; Cheng, W. D.; Wu, D. S.; Shen, J.; Huang, S. P.; Zhang, H.; Gong, Y. J.; Li, F. F. A Theoretical Investigation of Hyperpolarizability for Small GanAsm (n + m = 4−10) Clusters. J. Chem. Phys. 2006, 124, 094302. (25) Feng, Y. P.; Boo, T. B.; Kwong, H. H.; Ong, C. K.; Kumar, V.; Kawazoe, Y. Composition Dependence of Structural and Electronic Properties of GamAsn Clusters From First Principles. Phys. Rev. B 2007, 76, 045336. (26) Gutsev, G. L.; Mochena, M. D.; Bauschlicher, C. W., Jr. Structure and Magnetic Properties of (GaAs)nMnm and (GaAs)nFem Clusters. Chem. Phys. Lett. 2007, 439, 95−101. (27) Maroulis, G.; Karamanis, P.; Pouchan, C. Hyperpolarizability of GaAs Dimer is Not Negative. J. Chem. Phys. 2007, 126, 154316. (28) Karamanis, P.; Pouchan, C.; Maroulis, G. Structure, Stability, Dipole Polarizability and Differential Polarizability in Small Gallium Arsenide Clusters From All-electron ab initio and Density-functionaltheory Calculations. Phys. Rev. A 2008, 77, 013201. (29) Karamanis, P.; Carbonnière, P.; Pouchan, C. Structures and Composition Dependent Polarizabilities of Open- and Closed-shell GanAsm Semiconductor Clusters. Phys. Rev. A 2009, 80, 053201. (30) Karamanis, P.; Pouchan, C.; Weatherford, C. A.; Gutsev, G. L. Evolution of Properties in Prolate (GaAs)n Clusters. J. Phys. Chem. C 2011, 115, 97−107. F
dx.doi.org/10.1021/jp401426r | J. Phys. Chem. C XXXX, XXX, XXX−XXX
