硅锗团簇的结构、稳定性及电子性质的理论研究
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摘要
Si,Ge纳米材料具有许多常规半导体无法媲美的奇异特性和非凡的特殊功能,在诸多领域具有空前的应用前景,因此,纳米Si,Ge材料是材料科学领域研究的热点之一,在冶金、电子、化工等领域中有着广泛的潜在用途。团簇的空间尺度是几埃至几百埃,是介于原子、分子与宏观物质之间的物质结构的过渡状态,代表了凝聚态物质的新层次。以半导体材料为基础制作的各种器件在现代信息技术领域中起着重要的作用,因此,半导体元素团簇的结构及其独特的物理化学性质吸引了大量科学工作者浓厚的兴趣。
本文采用了遗传算法(Genetic Algorithm, GA)与密度泛函理论(Density Functional Theory, DFT)相结合的方法对硅锗团簇进行了系统的研究,找到了它们的低能异构体,并确定了其最稳定的几何结构。以此为基础我们对硅锗团簇的相对稳定性,电子性质及解离行为等进行了系统地分析,并得到以下结论:
对2≤n≤33尺度范围内的中性硅团簇的解离行为进行了系统研究,其结果与实验非常吻合。解离能的结果显示Si4,6,7,10是非常稳定的小团簇基元,并且频繁地出现在解离产物中;此外,在11≤n≤20尺度范围内,硅团簇的解离能相对较小,表示在这一尺度范围内,硅团簇较易解离成小团簇。
采用GA搜索和全电子DFT相结合的方法对Ge34– Ge44中性团簇结构及电子性质进行了系统的研究。对Ge34-39团簇的研究结果表明,最稳定锗团簇Ge34-39是扁长的棒状或者呈现Y型的三臂结构。这两种结构均由两到三个稳定的小团簇(Ge6, Ge7, Ge9或Ge10)组成,中间由锗金刚石的体片段(Ge6, Ge8或Ge9)相连接。锗团簇Ge40-44的最稳定几何结构为盘型结构。这类结构的中心有一个Ge4核,周围由四个稳定的小团簇(Ge9或Ge10)组成。这个Ge4核和周围的四个小团簇的部分原子形成了锗金刚石片段。与离子迁移率的实验结果对比表明,这类盘型结构很有可能在实验中存在并被观测到。研究表明,中等尺度的中性锗团簇的结构是由扁长的棒状结构转化为Y型的三臂结构,之后又向盘型结构转化;前者的转折点出现在Ge35或Ge36,而后者的转折点则出现在Ge40。
用B3LYP/6-311G(d)的方法计算并确定了与红外光谱实验相吻合的Si12+团簇的最低能几何结构;用全电子DFT方法对小尺度(2≤n≤15)阳离子锗团簇进行了系统的研究,确定了Ge2+– Ge15+的最稳定几何结构,并且与同尺度的阳离子硅团簇(Si2+– Si15+)的结构进行了对比。比较发现,除了n = 9, 12, 13和14以外,这个尺度范围的阳离子硅锗团簇的最稳定几何结构非常相似。从n = 7开始,两种团簇都包含五角双锥和TTP(三帽三棱柱)结构单元,所不同的是,阳离子硅团簇的五角双锥结构单元出现在Si7+, Si8+, Si9+和Si12+中,而TTP (三帽三棱柱)结构单元则出现在n = 10, 11, 13和15的尺度。对于阳离子锗团簇来说,这两种结构单元分别出现在n = 7– 9和n = 10– 15的尺度范围。
Today, the information technology develops rapidly; semiconductor materials play an important role in manufacturing information storage, information exploration, information transmission, laser and optical device with their particular properties. Among these semiconductor materials, silicon and germanium are applied widely in electronic and optoelectronic devices with their unique physical properties. As the scientific research and production of traditional components mature gradually, the size of microelectronic components can reach to a nano-scale. Recently, cluster research has developed rapidly, and the studies about silicon and germanium clusters have became one of the important research topics.
The structures of silicon and germanium clusters were studied in detail using GA (Genetic Algorithm) for unbiased search, combined with the DFT (Density Functional Theory) method. In this work, we analyzed the fragmentation behaviors of silicon clusters; and confirmed the most stable geometries of medium-sized germanium clusters; and found series of low-lying energy isomers; their electronic properties, such as binding energies, second differences in energy, HOMO– LUMO gaps, occupations on the HOMO shells, ionization potentials (IPs) and ion mobility, etc. have been discussed in detail. We also found an unambiguous structure of the Si12+ cluster, whose IR spectrum agrees well with the experiment result. In addition, we identified the lowest-energy structures of Ge2-15+ clusters, and compared with the corresponding Si2-15+ clusters.
The main results could be summarized as the following four aspects:
(1) The binding energies, second differences in energy, HOMO– LUMO gaps and fragmentation behaviors (involving one-step and multi-step fragmentations) of Sin (n =2–33) clusters have been studied at the B3LYP/6-311++G(d) and PW91/6-311++G(d) level. The calculated results indicated that Si4, Si6, Si7 and Si10 are quite stable, and appear frequently in the fragmentation products. For the size range between 11 and 20, the fragmentation energies are obviously small, indicating that Si11?20 can be easily dissociated. We also analyzed the issue about bond broken when cluster dissociate using some examples. In general, in the fragmentation of clusters, the dissociation of a small stable cluster would be favorable. Our calculated results are in good agreement with the experimental observations.
(2) The structures of Gen (n = 34 ? 39) clusters were searched by a genetic algorithm (GA) using a tight-binding (TB)interatomic potential. Density functional theory (DFT) calculations have been performed to further identify the lowest-energy structures. The electronic properties such as binding energies, second differences in energy, ionization potentials (IPs), electron affinities (EAs), HOMO– LUMO gaps and occupations on the HOMO shells have been analyzed. The calculated results show that the Gen (n = 34 ? 39) clusters favor prolate or Y-shaped three-arm structures consisted of two or three small stable clusters (Ge6, Ge7, Ge9 or Ge10) linked by a Ge6 or Ge9 bulk unit. The calculated results suggest that the transition point from prolate to Y-shaped three-arm structures appears at Ge35 or Ge36. In addition, we found some low-lying energy isomers of Ge34– Ge39. We found platelike also is a kind of competitive structure except prolate and Y-shaped structures. There is a competition between the prolate and Y-shaped three-arm structures starting at this size range of n = 34– 39; and at the end of this size range the competition appears between the Y-shaped three-arm and platelike motifs. For example, the energy differences between platelike and Y-shaped structures of Ge39 calculated at PBE/DND is only 0.016eV.
(3) For the Ge40-44 clusters, platelike structures are dominant, which are consisted of four small magic clusters (Ge9 or Ge10), and a Ge4 core. The Ge4 core along with the parts of the four linked small clusters forms a diamond segment. As the cluster size grows from Ge40 to Ge44, the subunit Ge9 will be replaced by Ge10 one by one. Therefore, while Ge40a is a structure with four Ge9s and a Ge4 core, Ge44a consists of four Ge10s and a Ge4 core. We also calculated the ion mobilities of the most stable structures, and the calculated results are in good agreement with the experimental data. Thus we can see, there are some rules about the growth pattern of Gen (n≤44). The clusters Ge2-10 have spherical-like compact geometries. Among them, Ge6,7,9,10 are very stable, which are the important components of larger clusters. From Ge11 to Ge16, it can be seen that the TTP (tri-capped trigonal prism) motif is prevailing; and they are all prolate structures. Ge17– Ge35 are consisted of two stable Ge6,7,9,10, and linked by the Ge6 or Ge9 bulk fragment. From Ge36 and Ge40, the number of Ge6,7,9,10 up to three and four, respectively; and the linkage is also the bulk fragment of Ge diamond. Therefore, we can see clearly, medium-sized germanium clusters consisted of Ge6,7,9,10; and linked with bulk fragment of Ge diamond. Increasing the components Ge6,7,9,10s is dominant about the growth pattern of germanium clusters. There is great significance about this discover for studying the size range of diamond of Ge clusters.
(4) An unambiguous structure of the Si12+ cluster has been determined at the level of B3LYP/6-311G(d), which IR spectrum is quite agreement with the experiment result. The most stable structures of Gen+ (n = 2 ? 15) clusters also have been confirmed using the GA search combined with the DFT method, and compared with the corresponding Sin+. The result shows that most structures between Gen+ and Sin+ clusters are similar except for n = 9, 12, 13 and 14. Furthermore, the motifs of Gen+ (n = 2– 15) clusters differ slightly from the corresponding Sin+ clusters. In Sin+ , the pentagonal bipyramid motif appears in Si7+, Si8+, Si9+ and Si12+; while the TTP (tri-capped trigonal prism) motif exists in the structures with n = 10, 11, 13 and 15. For Gen+, the two types of motifs are contained in the clusters with n = 7– 9 and n = 10– 15, respectively.
本文采用了遗传算法(Genetic Algorithm, GA)与密度泛函理论(Density Functional Theory, DFT)相结合的方法对硅锗团簇进行了系统的研究,找到了它们的低能异构体,并确定了其最稳定的几何结构。以此为基础我们对硅锗团簇的相对稳定性,电子性质及解离行为等进行了系统地分析,并得到以下结论:
对2≤n≤33尺度范围内的中性硅团簇的解离行为进行了系统研究,其结果与实验非常吻合。解离能的结果显示Si4,6,7,10是非常稳定的小团簇基元,并且频繁地出现在解离产物中;此外,在11≤n≤20尺度范围内,硅团簇的解离能相对较小,表示在这一尺度范围内,硅团簇较易解离成小团簇。
采用GA搜索和全电子DFT相结合的方法对Ge34– Ge44中性团簇结构及电子性质进行了系统的研究。对Ge34-39团簇的研究结果表明,最稳定锗团簇Ge34-39是扁长的棒状或者呈现Y型的三臂结构。这两种结构均由两到三个稳定的小团簇(Ge6, Ge7, Ge9或Ge10)组成,中间由锗金刚石的体片段(Ge6, Ge8或Ge9)相连接。锗团簇Ge40-44的最稳定几何结构为盘型结构。这类结构的中心有一个Ge4核,周围由四个稳定的小团簇(Ge9或Ge10)组成。这个Ge4核和周围的四个小团簇的部分原子形成了锗金刚石片段。与离子迁移率的实验结果对比表明,这类盘型结构很有可能在实验中存在并被观测到。研究表明,中等尺度的中性锗团簇的结构是由扁长的棒状结构转化为Y型的三臂结构,之后又向盘型结构转化;前者的转折点出现在Ge35或Ge36,而后者的转折点则出现在Ge40。
用B3LYP/6-311G(d)的方法计算并确定了与红外光谱实验相吻合的Si12+团簇的最低能几何结构;用全电子DFT方法对小尺度(2≤n≤15)阳离子锗团簇进行了系统的研究,确定了Ge2+– Ge15+的最稳定几何结构,并且与同尺度的阳离子硅团簇(Si2+– Si15+)的结构进行了对比。比较发现,除了n = 9, 12, 13和14以外,这个尺度范围的阳离子硅锗团簇的最稳定几何结构非常相似。从n = 7开始,两种团簇都包含五角双锥和TTP(三帽三棱柱)结构单元,所不同的是,阳离子硅团簇的五角双锥结构单元出现在Si7+, Si8+, Si9+和Si12+中,而TTP (三帽三棱柱)结构单元则出现在n = 10, 11, 13和15的尺度。对于阳离子锗团簇来说,这两种结构单元分别出现在n = 7– 9和n = 10– 15的尺度范围。
Today, the information technology develops rapidly; semiconductor materials play an important role in manufacturing information storage, information exploration, information transmission, laser and optical device with their particular properties. Among these semiconductor materials, silicon and germanium are applied widely in electronic and optoelectronic devices with their unique physical properties. As the scientific research and production of traditional components mature gradually, the size of microelectronic components can reach to a nano-scale. Recently, cluster research has developed rapidly, and the studies about silicon and germanium clusters have became one of the important research topics.
The structures of silicon and germanium clusters were studied in detail using GA (Genetic Algorithm) for unbiased search, combined with the DFT (Density Functional Theory) method. In this work, we analyzed the fragmentation behaviors of silicon clusters; and confirmed the most stable geometries of medium-sized germanium clusters; and found series of low-lying energy isomers; their electronic properties, such as binding energies, second differences in energy, HOMO– LUMO gaps, occupations on the HOMO shells, ionization potentials (IPs) and ion mobility, etc. have been discussed in detail. We also found an unambiguous structure of the Si12+ cluster, whose IR spectrum agrees well with the experiment result. In addition, we identified the lowest-energy structures of Ge2-15+ clusters, and compared with the corresponding Si2-15+ clusters.
The main results could be summarized as the following four aspects:
(1) The binding energies, second differences in energy, HOMO– LUMO gaps and fragmentation behaviors (involving one-step and multi-step fragmentations) of Sin (n =2–33) clusters have been studied at the B3LYP/6-311++G(d) and PW91/6-311++G(d) level. The calculated results indicated that Si4, Si6, Si7 and Si10 are quite stable, and appear frequently in the fragmentation products. For the size range between 11 and 20, the fragmentation energies are obviously small, indicating that Si11?20 can be easily dissociated. We also analyzed the issue about bond broken when cluster dissociate using some examples. In general, in the fragmentation of clusters, the dissociation of a small stable cluster would be favorable. Our calculated results are in good agreement with the experimental observations.
(2) The structures of Gen (n = 34 ? 39) clusters were searched by a genetic algorithm (GA) using a tight-binding (TB)interatomic potential. Density functional theory (DFT) calculations have been performed to further identify the lowest-energy structures. The electronic properties such as binding energies, second differences in energy, ionization potentials (IPs), electron affinities (EAs), HOMO– LUMO gaps and occupations on the HOMO shells have been analyzed. The calculated results show that the Gen (n = 34 ? 39) clusters favor prolate or Y-shaped three-arm structures consisted of two or three small stable clusters (Ge6, Ge7, Ge9 or Ge10) linked by a Ge6 or Ge9 bulk unit. The calculated results suggest that the transition point from prolate to Y-shaped three-arm structures appears at Ge35 or Ge36. In addition, we found some low-lying energy isomers of Ge34– Ge39. We found platelike also is a kind of competitive structure except prolate and Y-shaped structures. There is a competition between the prolate and Y-shaped three-arm structures starting at this size range of n = 34– 39; and at the end of this size range the competition appears between the Y-shaped three-arm and platelike motifs. For example, the energy differences between platelike and Y-shaped structures of Ge39 calculated at PBE/DND is only 0.016eV.
(3) For the Ge40-44 clusters, platelike structures are dominant, which are consisted of four small magic clusters (Ge9 or Ge10), and a Ge4 core. The Ge4 core along with the parts of the four linked small clusters forms a diamond segment. As the cluster size grows from Ge40 to Ge44, the subunit Ge9 will be replaced by Ge10 one by one. Therefore, while Ge40a is a structure with four Ge9s and a Ge4 core, Ge44a consists of four Ge10s and a Ge4 core. We also calculated the ion mobilities of the most stable structures, and the calculated results are in good agreement with the experimental data. Thus we can see, there are some rules about the growth pattern of Gen (n≤44). The clusters Ge2-10 have spherical-like compact geometries. Among them, Ge6,7,9,10 are very stable, which are the important components of larger clusters. From Ge11 to Ge16, it can be seen that the TTP (tri-capped trigonal prism) motif is prevailing; and they are all prolate structures. Ge17– Ge35 are consisted of two stable Ge6,7,9,10, and linked by the Ge6 or Ge9 bulk fragment. From Ge36 and Ge40, the number of Ge6,7,9,10 up to three and four, respectively; and the linkage is also the bulk fragment of Ge diamond. Therefore, we can see clearly, medium-sized germanium clusters consisted of Ge6,7,9,10; and linked with bulk fragment of Ge diamond. Increasing the components Ge6,7,9,10s is dominant about the growth pattern of germanium clusters. There is great significance about this discover for studying the size range of diamond of Ge clusters.
(4) An unambiguous structure of the Si12+ cluster has been determined at the level of B3LYP/6-311G(d), which IR spectrum is quite agreement with the experiment result. The most stable structures of Gen+ (n = 2 ? 15) clusters also have been confirmed using the GA search combined with the DFT method, and compared with the corresponding Sin+. The result shows that most structures between Gen+ and Sin+ clusters are similar except for n = 9, 12, 13 and 14. Furthermore, the motifs of Gen+ (n = 2– 15) clusters differ slightly from the corresponding Sin+ clusters. In Sin+ , the pentagonal bipyramid motif appears in Si7+, Si8+, Si9+ and Si12+; while the TTP (tri-capped trigonal prism) motif exists in the structures with n = 10, 11, 13 and 15. For Gen+, the two types of motifs are contained in the clusters with n = 7– 9 and n = 10– 15, respectively.
引文
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[3] HUNTER J M, FYE J L, JARROLD M F, et al. Structural Transitions in Size-Selected Germanium Cluster Ions [J]. Phys. Rev. Lett., 1994, 73: 2063-2066.
[4] SHVARTSBURG A A, HUDGINS R R, DUGOURDB P, et al. Structural information from ion mobility measurements: applications to semiconductor clusters [J]. Chem. Soc. Rev., 2001, 30: 26-35.
[5] JARROLD M F, CONSTANT V A. Silicon cluster ions: Evidence for a structural transition [J]. Phys. Rev. Lett., 1991, 67: 2994-2997.
[6] HAGEN D F. Characterization of isomeric compounds by gas and plasma chromatography [J]. Anal. Chem., 1979, 51: 870-874.
[7] JARROLD M F, BOWER J E. Mobilities of silicon cluster ions: The reactivity of silicon sausages and spheres [J]. J. Chem. Phys., 1992, 96: 9180-9190.
[8] HUDGINS R R, IMAI M, JARROLD M F. High-resolution ion mobility measurements for silicon cluster anions and cations [J]. J. Chem. Phys., 1999, 111: 7865-7870.
[9] SHVARTSBURG A A, LIU B, LU Y, et al. Structures of Germanium Clusters: Where the Growth Patterns of Silicon and Germanium Clusters Diverge [J]. Phys. Rev. Lett., 1999, 83: 2167-2170.
[10] WANG J L, WANG G H, ZHAO J J. Structure and electronic properties of Gen (n = 2– 25) clusters from density-functional theory [J]. Phys. Rev. B, 2001, 64: 205411(1-5).
[11] YOO S, ZENG X C. Search for global-minimum geometries of medium-sized germanium clusters. II. Motif-based low-lying clusters Ge21–Ge29 [J]. J. Chem. Phys., 2006, 124: 184309(1-5).
[12] WANG L, ZHAO J J. Competition between supercluster and stuffed cage structures in medium-sized Gen (n = 30– 39) clusters [J]. J. Chem. Phys., 2008, 128: 024302(1-5).
[13] CHUANG F C, WANG C Z, HO K H. Structure of neutral aluminum clusters Aln (2≤n≤23): Genetic algorithm tight-binding calculations [J]. Phys. Rev. B, 2006, 73: 125431(1-7).
[14] DAVEN D M, TIT N, MORRIS J R, et al. Structural optimization of Lennard-Jones clusters by a genetic algorithm [J]. Chem. Phys. Lett., 1996, 256: 195-200.
[15] MESLEH M F, HUNTER J M, SHVARTSBURG A A, et al. Structural Information from Ion Mobility Measurements: Effects of the Long-Range Potential [J]. J. Chem. Phys., 1996, 100: 16082-16086.
[16] SHVARTSBURG A A, JARROLD M F. An exact hard-spheres scattering model for the mobilities of polyatomic ions [J]. Chem. Phys. Lett., 1996, 261: 86-91.
[17] BUSULU S, YOO S, ZENG X C. Search for global minimum geometries for medium sized germanium clusters: Ge12–Ge20 [J]. J. Chem. Phys., 2005, 122: 164305(1-5).
[18] ??üT S, CHELIKOWSKY J R. Ab initio investigation of point defects in bulk Si and Ge using a cluster method [J]. Phys. Rev. B, 2001, 64: 245206(1-11).
[19] SIECK A, FRAUENHEIM T, JACKSON K A. Shape transition of medium-sized neutral silicon clusters [J]. Phys. stat. sol. (b), 2003, 240: 537-548.
[20] LI S, VAN ZEE R J, WELTNER W, et al. Si3-Si7. Experimental and theoretical infrared spectra [J]. Chem. Phys. Lett., 1995, 243: 275-280.
[21] MELNIKOV D V, CHELIKOWSKY J R. Electron affinities and ionization energies in Si and Ge nanocrystals [J]. Phys. Rev. B, 2004, 69: 113305(1-4).
[22] JACKSON K A, HOROI M H. Unraveling the Shape Transformation in Silicon Clusters [J]. Phys. Rev. Lett., 2004, 93: 013401(1-4).
[23] BERNSTEIN N, AZIZ M J, KAXIRAS E. Atomistic simulations of solid-phase epitaxial growth in silicon [J]. Phys. Rev. B, 2000, 61: 6696-6700.
[24] BERNSTEIN N, MEHL M J, PAPACONSTANTOPOULOS D A, et al. Energetic, vibrational, and electronic properties of silicon using a nonorthogonal tight-binding model [J]. Phys. Rev. B, 2000, 62: 4477-4487.
[25] WANG C Z, PAN B C, HO K M. An environment-dependent tight-binding potential for Si [J]. J. Phys.: Condens. Matter, 1999, 11: 2043-2049.
[26] TANG M S, WANG C Z, CHAN C T, et al. Environment-dependent tight-binding potential model [J]. Phys. Rev. B, 1996, 53: 979-982.
[27] ZHAO L Z, LU W C, QIN W, et al. Comparison of the Growth Patterns of Sin and Gen Clusters (n = 25 ? 33) [J]. J. Phys. Chem. A, 2008, 112: 5815-5823.
[28] QIN W, LU WC, ZHAO LZ, et al. Platelike structures of semiconductor clusters Gen (n = 40– 44) [J]. J. Chem. Phys., 2009, 131: 124507(1-5).
[29] ZHAO L Z, LU W C, QIN W, et al. Fragmentation behavior of Gen clusters (2≤n≤33) [J]. Chem. Phys. Lett., 2008, 455: 225-231.
[1] UGRINOV A, SEVOV S C. [Ge9=Ge9=Ge9]6-: A Linear Trimer of 27 Germanium Atoms [J]. J. Am. Chem. Soc., 2002, 124: 10990-10991.
[2] UGRINOV A, SEVOV S C. [Ge9=Ge9=Ge9=Ge9]8-: A Linear Tetramer of Nine-Atom Germanium Clusters, a Nanorod [J]. Inorg. Chem., 2003, 42: 5789-5791.
[3] HUNTER J M, FYE J L, JARROLD M F, et al. Structural Transitions in Size-Selected Germanium Cluster Ions [J]. Phys. Rev. Lett., 1994, 73: 2063-2066.
[4] SHVARTSBURG A A, HUDGINS R R, DUGOURDB P, et al. Structural information from ion mobility measurements: applications to semiconductor clusters [J]. Chem. Soc. Rev., 2001, 30: 26-35.
[5] JARROLD M F, CONSTANT V A. Silicon cluster ions: Evidence for a structural transition [J]. Phys. Rev. Lett., 1991, 67: 2994-2997.
[6] HAGEN D F. Characterization of isomeric compounds by gas and plasma chromatography [J]. Anal. Chem., 1979, 51: 870-874.
[7] JARROLD M F, BOWER J E. Mobilities of silicon cluster ions: The reactivity of silicon sausages and spheres [J]. J. Chem. Phys., 1992, 96: 9180-9190.
[8] HUDGINS R R, IMAI M, JARROLD M F. High-resolution ion mobility measurements for silicon cluster anions and cations [J]. J. Chem. Phys., 1999, 111: 7865-7870.
[9] SHVARTSBURG A A, LIU B, LU Y, et al. Structures of Germanium Clusters: Where the Growth Patterns of Silicon and Germanium Clusters Diverge [J]. Phys. Rev. Lett., 1999, 83: 2167-2170.
[10] WANG J L, WANG G H, ZHAO J J. Structure and electronic properties of Gen (n = 2– 25) clusters from density-functional theory [J]. Phys. Rev. B, 2001, 64: 205411(1-5).
[11] YOO S, ZENG X C. Search for global-minimum geometries of medium-sized germanium clusters. II. Motif-based low-lying clusters Ge21– Ge29 [J]. J. Chem. Phys., 2006, 124: 184309(1-5).
[12] WANG L, ZHAO J J. Competition between supercluster and stuffed cage structures in medium-sized Gen (n = 30– 39) clusters [J]. J. Chem. Phys., 2008, 128: 024302(1-5).
[13] CHUANG F C, WANG C Z, HO K H. Structure of neutral aluminum clusters Aln (2≤n≤23): Genetic algorithm tight-binding calculations [J]. Phys. Rev. B, 2006, 73: 125431(1-7).
[14] DAVEN D M, TIT N, MORRIS J R, et al. Structural optimization of Lennard-Jones clusters by a genetic algorithm [J]. Chem. Phys. Lett., 1996, 256: 195-200.
[15] MESLEH M F, HUNTER J M, SHVARTSBURG A A, et al. Structural Information from Ion Mobility Measurements: Effects of the Long-Range Potential [J]. J. Chem. Phys., 1996, 100: 16082-16086.
[16] SHVARTSBURG A A, JARROLD M F. An exact hard-spheres scattering model for the mobilities of polyatomic ions [J]. Chem. Phys. Lett., 1996, 261: 86-91.
[17] BUSULU S, YOO S, ZENG X C. Search for global minimum geometries for medium sized germanium clusters: Ge12–Ge20 [J]. J. Chem. Phys., 2005, 122: 164305(1-5).
[18] ??üT S, CHELIKOWSKY J R. Ab initio investigation of point defects in bulk Si and Ge using a cluster method [J]. Phys. Rev. B, 2001, 64 : 245206(1-11).
[19] SIECK A, FRAUENHEIM1 T, JACKSON K A. Shape transition of medium-sized neutral silicon clusters [J]. Phys. stat. sol. (b), 2003, 240: 537-548.
[20] LI S, VAN ZEE R J, WELTNER W, et al. Si3-Si7. Experimental and theoretical infrared spectra [J]. Chem. Phys. Lett., 1995, 243: 275-280.
[21] MELNIKOV D V, CHELIKOWSKY J R. Electron affinities and ionization energies in Si and Ge nanocrystals [J]. Phys. Rev. B, 2004, 69: 113305(1-4).
[22] JACKSON K A, HOROI M H. Unraveling the Shape Transformation in Silicon Clusters [J]. Phys. Rev. Lett., 2004, 93: 013401(1-4).
[23] BERNSTEIN N, AZIZ M J, KAXIRAS E. Atomistic simulations of solid-phase epitaxial growth in silicon [J]. Phys. Rev. B, 2000, 61: 6696-6700.
[24] BERNSTEIN N, MEHL M J, PAPACONSTANTOPOULOS D A, et al. Energetic, vibrational, and electronic properties of silicon using a nonorthogonal tight-binding model [J]. Phys. Rev. B, 2000, 62: 4477-4487.
[25] WANG C Z, PAN B C, HO K M. An environment-dependent tight-binding potential for Si [J]. J. Phys.: Condens. Matter, 1999, 11: 2043-2049.
[26] TANG M S, WANG C Z, CHAN C T, et al. Environment-dependent tight-binding potential model [J]. Phys. Rev. B, 1996, 53: 979-982.
[1] Sha Peng-Yu(沙鹏宇), Liu Yan(刘岩), Xie Lei(谢雷), et al.亲水性有机硅杂化防雾涂料的制备及性能[J]. Chem. J. Chinese. Universities (高等学校化学学报), 2007, 28:2205-2209.
[2] UGRINOV A, SEVOV S C. [Ge9=Ge9=Ge9]6-: A Linear Trimer of 27 Germanium Atoms [J]. J. Am. Chem. Soc., 2002, 124: 10990-10991.
[3] UGRINOV A, SEVOV S C. [Ge9=Ge9=Ge9=Ge9]8-: A Linear Tetramer of Nine-Atom Germanium Clusters, a Nanorod [J]. Inorg. Chem., 2003, 42: 5789-5791.
[4] HUNTER J M, FYE J L, JARROLD M F, et al. Structural Transitions in Size-Selected Germanium Cluster Ions [J]. Phys. Rev. Lett., 1994, 73: 2063-2066.
[5] SHVARTSBURG A A, HUDGINS R R, DUGOURDB P, et al. Structural information from ion mobility measurements: applications to semiconductor clusters [J]. Chem. Soc. Rev., 2001, 30: 26-35.
[6] JARROLD M F, CONSTANT V A. Silicon cluster ions: Evidence for a structural transition [J]. Phys. Rev. Lett., 1991, 67: 2994-2997.
[7] HAGEN D F. Characterization of isomeric compounds by gas and plasma chromatography [J]. Anal. Chem., 1979, 51: 870-874.
[8] JARROLD M F, BOWER J E. Mobilities of silicon cluster ions: The reactivity of silicon sausages and spheres [J]. J. Chem. Phys., 1992, 96: 9180-9190.
[9] HUDGINS R R, IMAI M, JARROLD M F. High-resolution ion mobility measurements for silicon cluster anions and cations [J]. J. Chem. Phys., 1999, 111: 7865-7870.
[10] SHVARTSBURG A A, LIU B, LU Y, et al. Structures of Germanium Clusters: Where the Growth Patterns of Silicon and Germanium Clusters Diverge [J]. Phys. Rev. Lett., 1999, 83: 2167-2170.
[11] WANG J L, WANG G H, ZHAO J J. Structure and electronic properties of Gen (n = 2– 25) clusters from density-functional theory [J]. Phys. Rev. B, 2001, 64: 205411(1-5).
[12] YOO S, ZENG X C. Search for global-minimum geometries of medium-sized germanium clusters. II. Motif-based low-lying clusters Ge21– Ge29 [J]. J. Chem. Phys., 2006, 124: 184309(1-5).
[13] WANG L, ZHAO J J. Competition between supercluster and stuffed cage structures in medium-sized Gen (n = 30– 39) clusters [J]. J. Chem. Phys., 2008, 128: 024302(1-5).
[14] CHUANG F C, WANG C Z, HO K H. Structure of neutral aluminum clusters Aln (2≤n≤23): Genetic algorithm tight-binding calculations [J]. Phys. Rev. B, 2006, 73: 125431(1-7).
[15] DAVEN D M, TIT N, MORRIS J R, et al. Structural optimization of Lennard-Jones clusters by a genetic algorithm [J]. Chem. Phys. Lett., 1996, 256: 195-200.
[16] MESLEH M F, HUNTER J M, SHVARTSBURG A A, et al. Structural Information from Ion Mobility Measurements: Effects of the Long-Range Potential [J]. J. Chem. Phys., 1996, 100: 16082-16086.
[17] SHVARTSBURG A A, JARROLD M F. An exact hard-spheres scattering model for the mobilities of polyatomic ions [J]. Chem. Phys. Lett., 1996, 261: 86-91.
[18] BUSULU S, YOO S, ZENG X C. Search for global minimum geometries for medium sized germanium clusters: Ge12– Ge20 [J]. J. Chem. Phys., 2005, 122: 164305(1-5).
[19] ??üT S, CHELIKOWSKY J R. Ab initio investigation of point defects in bulk Si and Ge using a cluster method [J]. Phys. Rev. B, 2001, 64: 245206(1-11).
[20] SIECK A, FRAUENHEIM T, JACKSON K A. Shape transition of medium-sized neutral silicon clusters [J]. Phys. stat. sol. (b), 2003, 240: 537-548.
[21] LI S, VAN ZEE R J, WELTNER W, et al. Si3-Si7. Experimental and theoretical infrared spectra [J]. Chem. Phys. Lett., 1995, 243: 275-280.
[22] MELNIKOV D V, CHELIKOWSKY J R. Electron affinities and ionization energies in Si and Ge nanocrystals [J]. Phys. Rev. B, 2004, 69: 113305(1-4).
[23] JACKSON K A, HOROI M H. Unraveling the Shape Transformation in Silicon Clusters [J]. Phys. Rev. Lett., 2004, 93: 013401(1-4).
[24] BERNSTEIN N, AZIZ M J, KAXIRAS E. Atomistic simulations of solid-phase epitaxial growth in silicon [J]. Phys. Rev. B, 2000, 61: 6696-6700.
[25] BERNSTEIN N, MEHL M J, PAPACONSTANTOPOULOS D A, et al. Energetic, vibrational, and electronic properties of silicon using a nonorthogonal tight-binding model [J]. Phys. Rev. B, 2000, 62: 4477-4487.
[26] WANG C Z, PAN B C, HO K M. An environment-dependent tight-binding potential for Si [J]. J. Phys.: Condens. Matter, 1999, 11: 2043-2049.
[27] TANG M S, WANG C Z, CHAN C T, et al. Environment-dependent tight-binding potential model [J]. Phys. Rev. B, 1996, 53: 979-982.
[28] ZHAO L Z, LU W C, QIN W, et al. Comparison of the Growth Patterns of Sin and Gen Clusters (n = 25?33) [J]. J. Phys. Chem. A, 2008, 112: 5815-5823.
[29] QIN W, LU WC, ZHAO LZ, et al. Platelike structures of semiconductor clusters Gen (n = 40– 44) [J]. J. Chem. Phys., 2009, 131: 124507(1-5).
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