硅锗团簇生长模式和金属/氧气反应机理的理论计算研究
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摘要
纳米半导体材料一直是材料科学领域研究的热点之一,在电子、冶金、化工、等领域有广泛的潜在用途。纳米材料研究的主要目标是合成,设计,和分析具有特殊功能的纳米级的微结构材料。团簇随尺度大小的变化在一定程度上可反应微观向宏观体系转变这个特殊的过程。团簇的结构和其独特的物理化学性质,吸引着许多科学工作者浓厚的兴趣。
本文中,我们使用密度泛函理论(Density Functional Theory, DFT)结合紧束缚(Tight-Binding,TB)势与遗传算法(Genetic Algorithm, GA)搜索的方法对半导体硅锗团簇进行了系统的理论研究,确定了它们的最稳定几何结构,总结了它们的生长模式。在此基础上我们还分析了半导体硅锗团簇的相对稳定性,电子特性,解离通道等,并对具有特殊稳定性的团簇做了深入研究。另一方面,我们对金属原子与氧气的反应势能曲线进行了细致的理论研究,计算分析了碱金属和过渡金属原子与氧气的最佳反应路径,以及体系加入一个负电荷后,相应反应能垒和反应路径所受的影响。
主要结论如下:
对于25≤n≤33尺度范围的中性Sin与Gen团簇我们进行了全局最优结构计算。基于GA/TB搜索与DFT计算组合的方法,获得了Sin与Gen团簇的低能量异构体,比较了这一尺度范围硅锗团簇的生长模式.结果表明硅团簇拥有多种结构特征,低能量异构体包含棒状、类球形、和Y形结构。B3LYP计算结果显示Sin (n = 25 ~ 33)团簇的生长模式在n = 31处经历一个从棒状到笼形结构的转换,而对于PBE计算结果这个转化是发生在n = 26的位置,该结果与实验观测的结构转换范围( 24≤n≤34)相吻合;而在n = 25 ~ 33的尺寸范围,相应的锗团簇却一直保持着棒状的结构模式。Sin与Gen团簇在25≤n≤33的尺度范围,其生长模式具有显著差异。
使用全电子DFT方法对Ge2-Ge33进行了系统研究。详细分析了锗团簇的各种性质:包括结合能,二次差分能,HOMO-LOMO能隙,特别是锗团簇的解离能和解离通道。n≤11尺寸范围的小型锗团簇具有较大的解离能,11 < n≤33尺寸范围的中小型锗团簇有较小的解离能,可以推断11 < n≤33尺度范围的锗团簇很容易分解为稳定的小团簇,这样的连续分解可将产物解离到n≤11的小团簇。在解离产物中,Ge6, Ge7, Ge10显示较大的丰度,表明这类小团簇非常稳定,计算结果和分析与实验光电离质谱测量结果一致。
用第一性原理计算研究了Si70团簇的结构和稳定性。虽然来自DFT-PBE计算结果显示内嵌富勒烯Si16@Si54是Si70的最低能量结构;但DFT-BLYP计算结果表明一个具有硅金刚石体结构片段的结构是最稳定的几何。因为BLYP泛函计算的Si70团簇最稳定结构的电离势更接近实验值,我们认为硅团簇由笼形结构向体结构模式的转变点很有可能在n = 70附近。同时,我们也预测了Si70团簇的多种性质,包括电子态密度,IR振动谱,离子反向迁移率等,为实验提供了重要的理论信息。
用MP2/6-311+G(d)计算方法,分别对过渡金属原子Ti﹑碱金属原子Na与O2的反应势能曲线进行了细致研究。比较了Ti﹑Na垂直O-O键和沿着O-O键逼近O2的不同反应路径的势能曲线的差异,预测了最佳反应方式;同时还比较了Ti/Na+O2和(Ti/Na+O2)–反应势能面的不同,结果显示体系带负电后反能垒降低了280.3 KJ/mol.
Nano- semiconductor materials are an important member of the nanomaterial family. When the size of materials is reduced to a nano-scale, it will show a lot of marvellous physical and chemical properties. The main goals of nanomaterial research are to synthesize, design, and analyze the micro-structural materials with special functions. Clusters, as a transition state from molecular to macroscopic materials, have attracted much attention and interest in both theoretical and experimental studies. The structural and property changes of clusters with cluster size can reflect the micro to macro transformation at some extent. In recent years, the studies of clusters have got rapid development.
In this thesis, we have investigated semiconductor silicon and germanium clusters using the genetic algorithm (GA) with TB (tight-binding) method and density functional theory (DFT) calculations. We try to determine the most stable geometries of Si and Ge clusters, and explore their growth patterns. The energies, HOMO-LUMO gaps, occupations on HOMO shells, densities of states, ionization potentials, IR vibrational spectra, fragmentation behaviors, and mobilities of cluster ions have been studied. On other hand, the reaction mechanisms of Ti, Na with O2 were investigated at the MP2/6-311+G(d) level. We try to understand the optimal reaction pathways of alkali and transitional metal atoms with O2, and the effect of a negative charge on the reaction barriers and pathways.
The main results are listed as follows:
(1) We performed an unbiased search for low-energy structures of medium-sized neutral Sin and Gen clusters (n = 25 ~ 33) using a genetic algorithm (GA) coupled with tight-binding (TB) interatomic potentials. The structural candidates obtained from our GA search were further optimized by first-principles calculations using density functional theory (DFT). Our approach reproduces well the lowest-energy structures of Sin and Gen clusters of n = 25 ~ 29 as compared to previous studies, showing the accuracy and reliability of our approach. In the present study, we pay more attention to determine low-lying isomers of Sin and Gen (n = 29 ~ 33) and their relative stabilities, and study the growth patterns of these clusters. The B3LYP calculations suggest that the growth pattern of Sin (n = 25 ~ 33) clusters undergoes a transition from prolate to cage at n = 31, while this transition appears at n = 26 from the PBE calculated results. In the size range of 25 ~ 33, the corresponding Gen clusters hold the prolate growth pattern. The changes of small cluster structures from the free standing states to the building blocks of large clusters, were also studied.
(2) The lowest-energy structures of Ge2-Ge33 have been optimized using DFT method. The properties of the germanium clusters including binding energies, second differences in energy, HOMO-LOMO gaps, and especially fragmentation energies and fragmentation behaviors have been studied. Our calculation results show that Ge6, Ge7, and Ge10 species display large abundances in the fragmentation products. According to the large fragmentation energies of the small germanium clusters with n≤11 and the small fragmentation energies of the medium-sized clusters with 11 < n≤33, we can conclude that the germanium clusters with 11 < n≤33 can be easily dissociated into small stable germanium clusters. Such dissociations would occur successively until the sizes of fragmentation products are reduced to n≤11. The present calculated results and analyses are consistent with the experimental observations of photo-ionization mass spectra.
(3) We have performed DFT calculations to study the structure and stability of the Si70 cluster. The results from the density functional theory (DFT) calculation with BLYP exchange-correlation functional suggest that a bulk-fragment Si70 isomer is the most stable structure, in contrast to the cage structure of Si60, showing that the transition from cage structure to bulk-like motif for silicon clusters would require only about 70 atoms. In addition, an endohedral fullerene of Si16@Si54 was found to be competitive to bulk-like Si70 if the PBE functional is used. The calculated density of states, IR vibration spectra, ionization potential (IP) and inverse motilities were also calculated and discussed.
(4) The reaction mechanisms of Ti, Na with O2 were investigated at the MP2/6-311+G(d) level. Ti and Na atom were assumed to approach O2 in the manner of horizontally or vertically with respect to the O-O bond, respectively. The binding energy and the charge curves for each reaction pathway have been analyzed in detail, to validate the optimal reaction mode. The vertical pathway is shown to be more favorable than the horizontal one. Both neutral Ti/Na + O2 and anionic (Ti/Na + O2)– systems were considered. The reaction of metal atom (Ti and Na) with O2 is easier for negatively charged system (Ti/Na + O2)– than for the neutral Ti/Na+O2. Meanwhile, the calculated results show that Ti atom prefers to react with the singlet O2 in both neutral and negatively charged systems. Na is easy to react with the singlet O2 in the neutral system, but with triplet O2 in negatively charged system. The potential energy surfaces of Ti with O2 reaction were also calculated at CCSD(T)/6-311++G(3df)//MP2/6-311+G(d) for Ti + O2 and (Ti + O2)– systems.
本文中,我们使用密度泛函理论(Density Functional Theory, DFT)结合紧束缚(Tight-Binding,TB)势与遗传算法(Genetic Algorithm, GA)搜索的方法对半导体硅锗团簇进行了系统的理论研究,确定了它们的最稳定几何结构,总结了它们的生长模式。在此基础上我们还分析了半导体硅锗团簇的相对稳定性,电子特性,解离通道等,并对具有特殊稳定性的团簇做了深入研究。另一方面,我们对金属原子与氧气的反应势能曲线进行了细致的理论研究,计算分析了碱金属和过渡金属原子与氧气的最佳反应路径,以及体系加入一个负电荷后,相应反应能垒和反应路径所受的影响。
主要结论如下:
对于25≤n≤33尺度范围的中性Sin与Gen团簇我们进行了全局最优结构计算。基于GA/TB搜索与DFT计算组合的方法,获得了Sin与Gen团簇的低能量异构体,比较了这一尺度范围硅锗团簇的生长模式.结果表明硅团簇拥有多种结构特征,低能量异构体包含棒状、类球形、和Y形结构。B3LYP计算结果显示Sin (n = 25 ~ 33)团簇的生长模式在n = 31处经历一个从棒状到笼形结构的转换,而对于PBE计算结果这个转化是发生在n = 26的位置,该结果与实验观测的结构转换范围( 24≤n≤34)相吻合;而在n = 25 ~ 33的尺寸范围,相应的锗团簇却一直保持着棒状的结构模式。Sin与Gen团簇在25≤n≤33的尺度范围,其生长模式具有显著差异。
使用全电子DFT方法对Ge2-Ge33进行了系统研究。详细分析了锗团簇的各种性质:包括结合能,二次差分能,HOMO-LOMO能隙,特别是锗团簇的解离能和解离通道。n≤11尺寸范围的小型锗团簇具有较大的解离能,11 < n≤33尺寸范围的中小型锗团簇有较小的解离能,可以推断11 < n≤33尺度范围的锗团簇很容易分解为稳定的小团簇,这样的连续分解可将产物解离到n≤11的小团簇。在解离产物中,Ge6, Ge7, Ge10显示较大的丰度,表明这类小团簇非常稳定,计算结果和分析与实验光电离质谱测量结果一致。
用第一性原理计算研究了Si70团簇的结构和稳定性。虽然来自DFT-PBE计算结果显示内嵌富勒烯Si16@Si54是Si70的最低能量结构;但DFT-BLYP计算结果表明一个具有硅金刚石体结构片段的结构是最稳定的几何。因为BLYP泛函计算的Si70团簇最稳定结构的电离势更接近实验值,我们认为硅团簇由笼形结构向体结构模式的转变点很有可能在n = 70附近。同时,我们也预测了Si70团簇的多种性质,包括电子态密度,IR振动谱,离子反向迁移率等,为实验提供了重要的理论信息。
用MP2/6-311+G(d)计算方法,分别对过渡金属原子Ti﹑碱金属原子Na与O2的反应势能曲线进行了细致研究。比较了Ti﹑Na垂直O-O键和沿着O-O键逼近O2的不同反应路径的势能曲线的差异,预测了最佳反应方式;同时还比较了Ti/Na+O2和(Ti/Na+O2)–反应势能面的不同,结果显示体系带负电后反能垒降低了280.3 KJ/mol.
Nano- semiconductor materials are an important member of the nanomaterial family. When the size of materials is reduced to a nano-scale, it will show a lot of marvellous physical and chemical properties. The main goals of nanomaterial research are to synthesize, design, and analyze the micro-structural materials with special functions. Clusters, as a transition state from molecular to macroscopic materials, have attracted much attention and interest in both theoretical and experimental studies. The structural and property changes of clusters with cluster size can reflect the micro to macro transformation at some extent. In recent years, the studies of clusters have got rapid development.
In this thesis, we have investigated semiconductor silicon and germanium clusters using the genetic algorithm (GA) with TB (tight-binding) method and density functional theory (DFT) calculations. We try to determine the most stable geometries of Si and Ge clusters, and explore their growth patterns. The energies, HOMO-LUMO gaps, occupations on HOMO shells, densities of states, ionization potentials, IR vibrational spectra, fragmentation behaviors, and mobilities of cluster ions have been studied. On other hand, the reaction mechanisms of Ti, Na with O2 were investigated at the MP2/6-311+G(d) level. We try to understand the optimal reaction pathways of alkali and transitional metal atoms with O2, and the effect of a negative charge on the reaction barriers and pathways.
The main results are listed as follows:
(1) We performed an unbiased search for low-energy structures of medium-sized neutral Sin and Gen clusters (n = 25 ~ 33) using a genetic algorithm (GA) coupled with tight-binding (TB) interatomic potentials. The structural candidates obtained from our GA search were further optimized by first-principles calculations using density functional theory (DFT). Our approach reproduces well the lowest-energy structures of Sin and Gen clusters of n = 25 ~ 29 as compared to previous studies, showing the accuracy and reliability of our approach. In the present study, we pay more attention to determine low-lying isomers of Sin and Gen (n = 29 ~ 33) and their relative stabilities, and study the growth patterns of these clusters. The B3LYP calculations suggest that the growth pattern of Sin (n = 25 ~ 33) clusters undergoes a transition from prolate to cage at n = 31, while this transition appears at n = 26 from the PBE calculated results. In the size range of 25 ~ 33, the corresponding Gen clusters hold the prolate growth pattern. The changes of small cluster structures from the free standing states to the building blocks of large clusters, were also studied.
(2) The lowest-energy structures of Ge2-Ge33 have been optimized using DFT method. The properties of the germanium clusters including binding energies, second differences in energy, HOMO-LOMO gaps, and especially fragmentation energies and fragmentation behaviors have been studied. Our calculation results show that Ge6, Ge7, and Ge10 species display large abundances in the fragmentation products. According to the large fragmentation energies of the small germanium clusters with n≤11 and the small fragmentation energies of the medium-sized clusters with 11 < n≤33, we can conclude that the germanium clusters with 11 < n≤33 can be easily dissociated into small stable germanium clusters. Such dissociations would occur successively until the sizes of fragmentation products are reduced to n≤11. The present calculated results and analyses are consistent with the experimental observations of photo-ionization mass spectra.
(3) We have performed DFT calculations to study the structure and stability of the Si70 cluster. The results from the density functional theory (DFT) calculation with BLYP exchange-correlation functional suggest that a bulk-fragment Si70 isomer is the most stable structure, in contrast to the cage structure of Si60, showing that the transition from cage structure to bulk-like motif for silicon clusters would require only about 70 atoms. In addition, an endohedral fullerene of Si16@Si54 was found to be competitive to bulk-like Si70 if the PBE functional is used. The calculated density of states, IR vibration spectra, ionization potential (IP) and inverse motilities were also calculated and discussed.
(4) The reaction mechanisms of Ti, Na with O2 were investigated at the MP2/6-311+G(d) level. Ti and Na atom were assumed to approach O2 in the manner of horizontally or vertically with respect to the O-O bond, respectively. The binding energy and the charge curves for each reaction pathway have been analyzed in detail, to validate the optimal reaction mode. The vertical pathway is shown to be more favorable than the horizontal one. Both neutral Ti/Na + O2 and anionic (Ti/Na + O2)– systems were considered. The reaction of metal atom (Ti and Na) with O2 is easier for negatively charged system (Ti/Na + O2)– than for the neutral Ti/Na+O2. Meanwhile, the calculated results show that Ti atom prefers to react with the singlet O2 in both neutral and negatively charged systems. Na is easy to react with the singlet O2 in the neutral system, but with triplet O2 in negatively charged system. The potential energy surfaces of Ti with O2 reaction were also calculated at CCSD(T)/6-311++G(3df)//MP2/6-311+G(d) for Ti + O2 and (Ti + O2)– systems.
引文
[1] COTTON F A. Transition– metal compounds containing clusters of metal atoms, Quarterly Review, Chemistry Society, 1966, 20: 389.
[2]卢嘉锡.原子簇化合物的结构化学,中国化学, 1978年年会学术报告集,北京:科学出版社, 198, 35-60.
[3]徐光宪.原子团簇与有关分子的结构规则(I),高等学校化学学报, 1982, 3(专刊), 114.
[4] KNIGHT W D, CLEMENGER K, HEER W A, et al. Electronic Shell Structure and Abundances of Sodium Clusters [J]. Phys. Rev. Lett., 1984, 52: 2141-2143.
[5] KROTO H W, Health J R, OBrien S C, et al. C60:Buckminster-fullerene [J]. Nature, 1985, 318: 162-163.
[6] KRASCHMER W, LAMB L D, FOSTIROPOULOS K, et al. Solid C60:A New form of Carbon [J]. Nature, 1990, 347: 354-358.
[7] HEBARD A F, ROSSEINSKY M J, HADDON R C, et al. Superconductivity at 18 K in Potassium-doped C60 [J]. Nature, 1991, 350: 600-601.
[8] LIJIMA S. Helical microtubules of graphitic carbon [J]. Nature, 1991, 354: 56-58.
[9] UGARTE D. Curling and closure of graphitic networks under electron beam irradiation [J]. Nature, 1992, 359(6397): 707-709.
[10] JACOBSEN R L, MONTHIOUX M, JACOBSEN R L, et al. Carbon beads with protruding cones [J]. Nature, 1997, 385: 211.
[11] LIU J, DAI H J, HAFNER J H, et al. Fullerene "Crop Circles" [J]. Nature, 1997, 385: 780.
[12]张乾二.林连堂.王南钦.赖善桃.多面体分子轨道的理论方法:III.结构多面体骨架的成键分子轨道.厦门大学学报(自然科学版),1981, 2: 226.
[13] JARROLD M F. Nanosurface Chemistry on Size Selected Silicon Clusters [J]. Science, 1991, 252: 1085-1092.
[14] BROWN W L, FREEMAN R R, RAGHAVACHARI K, et al. Covalent Group IV Atomic Clusters [J]. Science, 1987, 235: 860-865.
[15] GINGERICH K A, SCHMUDE R W, BABA M S, et al. Atomization enthalpies and enthalpies of formation of the germanium clusters, Ge5, Ge6, Ge7, and Ge8 by Knudsen effusion mass spectrometry [J]. J. Chem. Phys., 2000, 112: 7443-7448.
[16] MARTIN T P, SCHABER H. Mass spectra of Si, Ge, and Sn clusters [J]. J. Chem. Phys., 1985, 83: 855-858.
[17] PHILLIPS J C. Pulsed Gen+ microcluster concentration spectra [J]. J. Chem. Phys., 1986, 85: 5246-5250.
[18] SCHULZE W, WINTER B, GOLDENFELD I. Generation of germanium clusters using the gas aggregation technique: Stability of small charged clusters [J]. J. Chem. Phys., 1987, 87: 2402-2403.
[19] YOSHIDA S, FUKE K. Photoionization studies of germanium and tin clusters in the energy region of 5.0–8.8 eV: Ionization potentials for Gen (n = 2–57) and Snn (n = 2–41) [J]. J. Chem. Phys., 1999, 111: 3880-3890.
[20] ZHANG Q L, LIU Y, CURL R F, et al. Photodissociation of semiconductor positive cluster ions [J]. J. Chem. Phys., 1988, 88: 1670-1677.
[21] FUKE K, TSUKAMOTO K, MISAIZU F, et al. Near threshold photoionization of silicon clusters in the 248–146 nm region: Ionization potentials for Sin [J]. J. Chem. Phys., 1993, 99: 7807-7812.
[22] BURTON G R, XU C S, ARNOLD C C, et al. Photoelectron spectroscopy and zero electron kinetic energy spectroscopy of germanium cluster anions [J]. J. Chem. Phys., 1996, 104: 2757-2764.
[23] SCH?FER R, SCHLECHT S, WOENCKHAUS J, et al. Polarizabilities of Isolated Semiconductor Clusters [J]. Phys. Rev. Lett., 1996, 76: 471- 474.
[24] ALFORD J M, LAAKSONEN R T, SMALLEY R E, Ammonia chemisorption studies on silicon cluster ions [J]. J. Chem. Phys., 1991, 94: 2618-2630.
[25] RAY U, JARROLD M F, Reactions of silicon cluster ions, Sin+ (n=10–65), with water [J]. J. Chem. Phys. 1991, 94: 2631-2639.
[26] BERGERON D E, CASTLEMAN JR. A W. Insights into the stability of siliconcluster ions: Reactive etching with O2 [J]. J. Chem. Phys., 2002, 117: 3219-3223.
[27] JARROLD M F, IJIRI Y, RAY U. Interaction of silicon cluster ions with ammonia: Annealing, equilibria, high temperature kinetics, and saturation studies [J]. J. Chem. Phys., 1991, 94: 3607-3618.
[28] SHVARTSBURG A A, LIU B, LU Z 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.
[29] 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).
[30] JARROLD M F, IJIRI Y, CONSTANT V A. Silicon cluster ions: Evidence for a structural transition [J]. Phys. Rev. Lett., 1991, 67: 2994-2997.
[31] 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.
[32] 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.
[33] HUNTER J M, FYE J L, JARROLD M F, et al. Structural Transitions in Size-Selected Germanium Cluster Ions [J]. Phys. Rev. Lett., 1993, 73: 2063-2066.
[34] BAI J, CUI L F, WANG J L, et al. Structural Evolution of Anionic Silicon Clusters SiN (20≤N≤45) [J]. J. Phys. Chem. A, 2006, 110: 908-912.
[35] YOO S, ZENG X C, Structures and relative stability of medium-sized silicon clusters. IV. Motif-based low-lying clusters Si21–Si30 [J]. J. Chem. Phys., 2006, 124: 054304 (1-6).
[36] YOO S, SHAO N, KOEHLER C, et al. Structures and relative stability of medium-sized silicon clusters. V. Low-lying endohedral fullerenelike clusters Si31-Si40 and Si45 [J]. J. Chem. Phys. 2006, 124: 164311(1-6).
[37] ZHOU R L, PAN B C. Low-lying isomers of Sin+ and Sin– (n=31–50) clusters [J]. J. Chem. Phys., 2008, 128: 234302(1-6).
[38] SONG J, ULLOA S E, Drabold D A, Exciton-induced lattice relaxation and the electronic and vibrational spectra of silicon clusters [J]. Phys. Rev. B, 1996, 53: 8042-8051.
[39] LI B X, LIU J H, ZHAN S C. Stability of Si70 cage structures [J]. Eur. Phys. J. D, 2005, 32: 59-62.
[40] SUN Q, WANG Q, JENA P, et al. Stabilization of Si60 Cage Structure [J]. Phys. Rev. Lett., 2003, 90: 135503(1-4).
[41] SUN Q, WANG Q, JENA P, et al. Geometry and energetics of Si60 isomers [J]. Science and Technology of Advanced Materials, 2003, 4: 361-365.
[42] MA S J, WANG G H, Nonorthogonal tight-binding study of Si60 cluster [J]. Journal of Molecular Structure: THEOCHEM, 2005, 757: 47-51.
[43] ONA O, BAZTERRA V E, CAPUTO M C, et al. Modified genetic algorithms to model cluster structures in medium-sized silicon clusters: Si18-Si60 [J]. Phys. Rev. A 2006, 73: 053203(1-11).
[44] ZHAO J J, MA L, WEN B. Lowest-energy endohedral fullerene structure of Si60 from a genetic algorithm and density-functional theory [J]. J. Phys.: Condens. Matter, 2007, 19: 226208(1-6).
[45] YOO S, SHAO N, ZENG X C, Structures and relative stability of medium- and large-sized silicon clusters. VI. Fullerene cage motifs for low-lying clusters Si39, Si40, Si50, Si60, Si70, and Si80 [J]. J. Chem. Phys. 2008, 128: 104316(1-9).
[46] 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).
[47] MA S J, WANG G H. Structures of medium size germanium clusters [J]. Journal of Molecular Structure: THEOCHEM, 2006, 767: 75-79.
[48] LIANG F S, LI B X. Stable structures of Gen (n=21–25) clusters [J]. Phys. Lett. A, 2004, 328: 407-413.
[49] 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).
[50] 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).
[51] BURTON G R, XU C S, ARNOLD C C, et al. Photoelectron spectroscopy and zero electron kinetic energy spectroscopy of germanium cluster anions [J]. J. Chem. Phys., 1996, 104: 2757-2764.
[52] 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.
[53] FUJISHIMA A, HONDA K. Electrochemical photocatalysis of water at a semiconductor electrode [J]. Nature, 1972, 238: 37-38.
[54] OSHIKIRI M, BOERO M, YE J, et al. The electronic structures of the thin films of InVO4 and TiO2 by first principles calculations [J]. Thin Solid Films, 2003, 445: 168-174.
[55] BANDURA A V, SYKES D G, SHAPOVALOV V, et al. Adsorption of Water on the TiO2 (Rutile) (110) Surface: A Comparison of Periodic and Embedded Cluster Calculations [J]. J. Phys. Chem. B, 2004, 108: 7844-7853.
[56] Wei Zhi-Gang(魏志刚), Li Qian-Shu(李前树), Zhang Hong-Xing(张红星) et al.二氧化钛(TiO2)表面上水分解反应的理论研究[J]. Chem. J. Chinese. Universities (高等学校化学学报), 2007, 28(2): 350-351.
[57] TILOCCA A, SELLONI A, Reaction pathway and free energy barrier for defect-induced water dissociation on the (101) surface of TiO2-anatase [J]. J. Chem. Phys., 2003, 119: 7445-7450.
[58] REGO L G C, BATISTA V S. Quantum Dynamics Simulations of Interfacial Electron Transfer in Sensitized TiO2 Semiconductors [J]. J. Am. Chem. Soc. 2003, 125: 7989-7997.
[59] MALLIA1 G, HARRISON N M. Magnetic moment and coupling mechanism of iron-doped rutile TiO2 from first principles [J]. Phys. Rev. B, 2007, 75: 165201(1-11).
[60] GAO G Y, YAO K L, LIU Z L, et al. Magnetism and electronic structure ofCr-doped rutile TiO2 from first-principles calculations [J]. Journal of Magnetism and Magnetic Materials, 2007, 313: 210–213.
[61] DU X S, LI Q X, SU H B, et al. Electronic and magnetic properties of V-doped anatase TiO2 from first principles [J]. Phys. Rev. B, 2006, 74: 233201(1-4).
[62] HAN Y, LIU C J, GE Q F. Interaction of Pt Clusters with the Anatase TiO2 (101) Surface: A First Principles Study [J]. J. Phys. Chem. B, 2006, 110: 7463-7472.
[63] Locatelli A, Pabisiak T, Pavlovska A, et al. One-dimensional Au on TiO2 [J]. J. Phys.: Condens. Matter, 2007, 19: 082202(1-8).
[64] CALATAYUD M, MINOT C. Reactivity of the V2O5–TiO2-anatase catalyst: role of the oxygen sites [J]. Topics in Catalysis, 2006, 40: 17-25.
[65] SAMBRANO J R, VASCONCELLOS L A, MARTINS J B L, et al. A theoretical analysis on electronic structure of the (110) surface of TiO2–SnO2 mixed oxide [J]. Journal of Molecular Structure: THEOCHEM, 2003, 629: 307-314.
[1] BORN M, OPPENHEIMER R, Zur Quantentheorie der Molekeln. Annalen der Physik. (Quantum Theory of the Molecules Ann. Phys.), 1927, 84: 457-484.
[2] (a) HEHRE W J, RADOM L, SCHLEYER P V R, et al. Ab Initio Molecular Orbital Theory, John Wiley &Sons, Inc., 1986. (b) MCQUARRIE D A. Quantum Chemistry University, Science Books: Mill Vally. CA. 1983.
[3] (a)唐敖庆.杨忠志.李前树.量子化学,北京,科学出版社, 1982.(b)徐光宪.黎乐民.王德民.量子化学基本原理和从头计算法,北京,科学出版社, 1985.
[4] LOWDIN P O. Correlation Problem in Many-Electron Quantum Mechanics [J]. Adv. Chem. Phys., 1959, 2: 207.
[5] M?LLER C, PLESSET M S. Note on an Approximation Treatment for Many-Electron Systemsp [J]. Phys. Rev., 1934, 46: 618-622.
[6] HEAD-GORDON M, POPLE J A, Frisch M J. A Direct MP2 Gradient Method [J]. Chem. Phys. Lett., 1988, 153: 503-506.
[7] POPLE J A, BINKLEY J S, SEEGER R. Theoretical Models Incorporating Electron Correlation [J]. Int. J. Quant. Chem. Symp., 1976, 10: 1?19.
[8] KRISHNAN R, POPLE J A. Appoximate Forth-Order Perturbation Theory of the Electron Correlation Energy [J]. Int. J. Quant. Chem., 1978, 14: 91?100.
[9] RAGHAVACHARI K, POPLE J A, REPLOGLE E S, et al. Fifth-Order Moller-Plesset Perturbation Theory: Comparison of Existing Correlation Methods and Implementation of New Methods Correct to Fifth-Order [J]. J. Phys. Chem., 1990, 94: 5579-5586.
[10] POPLE J A, SEEGER R, KRISHNAN R. Variational Configuration Interaction Methods and Comparison with Perturbation Theory [J]. Int. J. Quant. Chem. Symp., 1977, 11: 149.
[11] FORESMAN J B, HEAD-GORDON M, POPLE J A, et al. Toward a Systematic Molecular Orbital Theory for Excited States [J]. J. Phys. Chem., 1992, 96: 135-149.
[12] KRISHNAN R, SCHLEGEL H B, POPLE J A. Derivate Studies in Configuration Interaction Theory [J]. J. Chem. Phys., 1980, 72: 4654-4655.
[13] BROOKS B R, LAIDIG W D, SAXE P, et al. Analytic Gradient from Correlated Wave Functions via the Two-Particle Density Matrix and the Unitary Group Approach [J]. J. Chem. Phys., 1980, 72: 4652-4653.
[14] SALTER E A, TRUCKS G W, BARTLETT R J. Analytic Energy Derivatives in Many-Body Methods I. First Derivatives [J]. J. Chem. Phys., 1989, 90 : 1752-1766.
[15] RAGHAVACHARI K, POPLE J A. [J]. Int. J. Quant. Chem., 1981, 20: 167.
[16] POPLE J A, HEAD-GORDON M, RAGHAVACHARI K. Quadratic Configuration Interaction. A General Technique for Determining Electron Correlation Energies [J]. J. Chem. Phys., 1987, 87: 5968-5975.
[17] CIOSLOWSKI J. A New Robust Algorithm for Fully Automated Determination of Attactor Interaction Lines in Moleclues [J]. Chem. Phys. Lett., 1994, 219: 151-154.
[18] SCHLEGEL H B, ROBB M A. MCSCF Gradient Optimization of the H2CO→H2+CO Transition Structure [J]. Chem. Phys. Lett., 1982, 93: 43-46.
[19] EADE R H E, ROBB M A. Direct minimization in mc scf theory. the quasi-newton method [J]. Chem. Phys. Lett., 1981, 83: 362-368.
[20] HEGARTY D, ROBB M A. Application of Unitary Group Methods to Configuration Interaction Calculations [J]. Mol. Phys., 1979, 38: 1795-1812.
[21] POPLE J A, KRISHNAN R, SCHLEGEL H B, et al. Electron correlation theories and their application to the study of simple reaction potential surfaces [J]. Int. J. Quant. Chem., 1978, 14: 545?560.
[22] BARTLETT R J, PURVIS G D. General Application of a Big Molecule Gaussian SCF/CI Program for Calculations of Excited Metastables and of Negative Ion Bound States and Resonances [J]. Int. J. Quant. Chem., 1978, 14: 515-518.
[23] SCUSERIA G E, SCHAEFER H F. Is coupled cluster singles and doubles (CCSD) more computationally intensive than quadratic configuration interaction (QCISD)? [J]. J. Chem. Phys., 1989, 90: 3700-3703.
[24] PURVIS G D, BARTLETT R J. A Full Coupled-Cluster Singles and Doubles Model: The Inclusion of Disconnected Triples [J]. J. Chem. Phys., 1982, 76: 1910-1918.
[25] SCUSERIA G E, JANSSEN C L, SCHAEFER H F. An efficient reformulation of the closed-shell coupled cluster single and double excitation (CCSD) equations [J]. J. Chem. Phys., 1988, 89: 7382-7387.
[26] HOHENBERG P, KOHN W. Inhomogeneous Electron Gas [J]. Phys. Rev., 1964, 136: B864?B871.
[27] KOHN W, SHAM L J. Self-Consistent Equations Including Exchange and Correlation Effects [J]. Phys. Rev., 1965, 140: A1133?A1138.
[28] SLATER J C. Quantum Theory of Molecular and Solids. Vol. 4: The Self-Consistent Field for Molecular and Solids McGraw-Hill: New York, 1974.
[29] SALAHUB D R, ZERNER M C, eds. The Challenge of d and f Electrons ACS: Washington, D.C., 1989.
[30] PARR R G, YANG W. Density-functional theory of atoms and molecules Oxford Univ. Press: Oxford, 1989.
[31] POPLE J A, GILL P M W, JOHNSON B G. Kohn-Sham density-functional theory within a finite basis set [J]. Chem. Phys. Lett., 1992, 199: 557-560.
[32] JOHNSON B G, FRISCH M J. An implementation of analytic second derivatives of the gradient-corrected density functional energy [J]. J. Chem. Phys., 1994, 100: 7429-7442.
[33] LABANOWSKI J K, ANDZELM J W, eds. Density Functional Methods in Chemistry. Springer-Verlag: New York, 1991
[34] POCKETT W E. Pseudopotential methods in condensed matter applications. Comp. Phys. Rep., 1989, 9(3): 115-197.
[35] KRESSE G, HAFNER J. Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements [J]. J. Phys.: Condens. Matter., 1994, 6(40): 8245-8258.
[36] CHELIKOWSKY J R, SAAD Y. Electronic Structure of Clusters and Nanocrystals. Handbook of Theoretical and Computational Nanotechnology [M].American : M. Rieth and W. Schommers. (American Scientific), 2006, 8: 797.
[37] SLATER J C, KOSTER G F. Simplified LCAO Method for the Periodic Potential Problem [J]. Phys. Rev., 1954, 94: 1498-1524.
[38] CHADI D J. Atomic and Electronic Structures of Reconstructed Si (100) Surfaces [J]. Phys. Rev. Lett., 1979, 43: 43-47.
[39] POPLE J A, BEVERIDGE D L. Approximate Molecular Orbital Theory, McGraw-Hill Book Company, 1970.
[40] ELSTNER M, POREZAG D, JUNGNICKEL G, et al. Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties [J]. Phys. Rev. B, 1998, 58: 7260-7268.
[41] DEAVEN D, HO K M. Molecular Geometry Optimization with a Genetic Algorithm [J]. Phys. Rev. Lett., 1995, 75: 288-291.
[42] HO K M, SHVARTSBURG A, PAN B C, et al. Structures of Medium-Sized Silicon Clusters [J]. Nature, 1998, 392: 582-584.
[43] BORN M, OPPENHEIMER R. Zur Quantentheorie der Molekeln Ann. Phsik. (Quantum Theory of the Molecules Ann. Phys.) 1927, 84: 457.
[44]唐敖庆.杨忠志.李前树.量子化学,北京:科学出版社,1982.
[45]徐光宪.黎乐民.王德民.量子化学基本原理和从头计算法,北京:科学出版社,1985.
[46]赵学庄.罗渝然.臧雅茹.万学适.《化学反应动力学原理》下册,高等教育出版社,1990.
[47] FUKUI K. Int. J. Quantum. Chem., 1981, 15 : 633-642.
[48] FUKUI K, TACHIBANA A, YAMASHITA K. Int. J. Quantum. Chem. 1981, 15: 621-632.
[49] BODY R G, MCCLURE D S, CLEMENTI E. SCF Wavefunctions for the NH3 Molecule. Potential-Energy Surface and Vibrational Force Constants [J]. J. Chem. Phys., 1968, 49: 4916-4924.
[50] GARTON D, SUTCHIFFE B T. Theoretical Chemistry, Vol. 1 (Ed. R. N. Dixon), The Chemical Society, London, 1974.
[51] PULAY P. Ab initio Calculation of Force Constants and Equilibrium Geometries.I. Theory [J]. Mol. Phys., 1969, 17: 197-204.
[52] PULAY P. In: Modern Theoretical Chemistry: Applications of Electronic Structure Theory, (H. F. Schaefer, III, Ed.), Plenum Press, New York, 1977, 4: 153-185.
[53] FLETCHER R, POWELL M J D. A Rapidly Convergent Method for Minimization [J]. The Computer Journal, 1963, 6(2): 163-168.
[54] MURTAGH B A, SARGENT R W H. Computational experience with quadratically convergent minimisation methods [J]. The Computer Journal, 1970, 13: 185-194.
[55] MCIVER JR. J W, KOMORNICKI A. Rapid geometry optimization for semi-empirical molecular orbital methods [J]. Chem. Phys. Lett., 1971, 10: 303-306.
[56] POPPINGER D. Geometry optimization in ab initio molecular orbital theory [J]. Chem. Phys. Lett., 1975, 34: 332-336.
[57] PANCUI J. [J]. Collect. Czech. Chem. Commun, 1975, 40: 2726-2732.
[1] GINGERICH K A, SCHMUDE R W, BABA M S, et al. Atomization enthalpies and enthalpies of formation of the germanium clusters, Ge5, Ge6, Ge7, and Ge8 by Knudsen effusion mass spectrometry [J]. J. Chem. Phys., 2000, 112: 7443-7448.
[2] MARTIN T P, SCHABER H. Mass spectra of Si, Ge, and Sn clusters [J]. J. Chem. Phys., 1985, 83: 855-858.
[3] PHILLIPS J C. Pulsed Gen+ microcluster concentration spectra [J]. J. Chem. Phys., 1986, 85: 5246-5250.
[4] SCHULZE W, WINTER B, GOLDENFELD I. Generation of germanium clusters using the gas aggregation technique: Stability of small charged clusters [J]. J. Chem. Phys., 1987, 87: 2402-2403.
[5] HEATH J R, LIU Y, O’BRIEN S C, et al. Semiconductor cluster beams: One and two color ionization studies of Six and Gex [J]. J. Chem. Phys., 1985, 83: 5520-5526.
[6] YOSHIDA S, FUKE K. Photoionization studies of germanium and tin clusters in the energy region of 5.0–8.8 eV: Ionization potentials for Gen (n = 2–57) and Snn (n = 2–41) [J]. J. Chem. Phys., 1999, 111: 3880-3890.
[7] BURTON G R, XU C S, ARNOLD C C, et al. Photoelectron spectroscopy and zero electron kinetic energy spectroscopy of germanium cluster anions [J]. J. Chem. Phys., 1996, 104: 2757-2764.
[8] HUNTER J M, FYE J L, JARROLD M F, et al. Structural Transitions in Size-Selected Germanium Cluster Ions [J]. Phys. Rev. Lett., 1993, 73: 2063-2066.
[9] ALFORD J M, LAAKSONEN R T, SMALLEY R E. Ammonia chemisorption studies on silicon cluster ions [J]. J. Chem. Phys., 1991, 94: 2618-2630.
[10] SHVARTSBURG A A, LIU B, LU Z 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] SHVARTSBURG A A, HUDGINS R R, DUGOURDB P, et al. Structuralinformation from ion mobility measurements: applications to semiconductor clusters [J]. Chem. Soc. Rev., 2001, 30: 26-35.
[12] MARSEN B, LONFAT M, SCHEIER P, et al. Energy gap of silicon clusters studied by scanning tunneling spectroscopy [J]. Phys. Rev. B, 2000, 62: 6892-6895.
[13] RAY U, JARROLD M F. Reactions of silicon cluster ions, Sin+ (n=10–65), with water [J]. J. Chem. Phys., 1991, 94: 2631-2639.
[14] BERGERON D E, CASTLEMAN JR. A W. Insights into the stability of silicon cluster ions: Reactive etching with O2 [J]. J. Chem. Phys., 2002, 117: 3219-3223.
[15] JARROLD M F, IJIRI Y, RAY U. Interaction of silicon cluster ions with ammonia: Annealing, equilibria, high temperature kinetics, and saturation studies [J]. J. Chem. Phys., 1991, 94: 3607-3618.
[16] JARROLD M F, IJIRI Y, CONSTANT V A. Silicon cluster ions: Evidence for a structural transition [J]. Phys. Rev. Lett., 1991, 67: 2994-2997.
[17] SCH?FER R, SCHLECHT S, WOENCKHAUS J, et al. Polarizabilities of Isolated Semiconductor Clusters [J]. Phys. Rev. Lett., 1996, 76: 471- 474.
[18] JARROLD M F, HONEA E C. Dissociation of large silicon clusters: the approach to bulk behavior [J]. J. Phys. Chem., 1991, 95: 9181-9185.
[19] 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.
[20] 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.
[21] ZHANG Q L, LIU Y, CURL R F, et al. Photodissociation of semiconductor positive cluster ions [J]. J. Chem. Phys., 1988, 88: 1670-1677.
[22] FUKE K, TSUKAMOTO K, MISAIZU F, et al. Near threshold photoionization of silicon clusters in the 248–146 nm region: Ionization potentials for Sin [J]. J. Chem. Phys., 1993, 99: 7807-7812.
[23] MITAS L, GROSSMAN J C, STICH I, et al. Silicon Clusters of Intermediate Size: Energetics, Dynamics, and Thermal Effects [J]. Phys. Rev. Lett., 2000, 84:1479-1482.
[24] YOO S, ZENG X C. Motif Transition in Growth Patterns of Small to Medium-Sized Silicon Clusters [J]. Angew. Chem. Int. Ed., 2005, 44: 1491-1494.
[25] GOEDECKER S, HELLMANN W. Global Minimum Determination of the Born-Oppenheimer Surface within Density Functional Theory [J]. Phys. Rev. Lett., 2005, 95: 055501(1-4).
[26] SIECK A, FRAUENHEIM1 T, JACKSON K A. Shape transition of medium-sized neutral silicon clusters [J]. Phys. stat. sol. (b), 2003, 240: 537-548.
[27] JACKSON K A, HOROI M H. Unraveling the Shape Transformation in Silicon Clusters [J]. Phys. Rev. Lett., 2004, 93: 013401(1-4).
[28] YOO S, ZENG X C, ZHU X L, et al. Possible Lowest-Energy Geometry of Silicon Clusters Si21 and Si25 [J]. J. Am. Chem. Soc., 2003, 125: 13318-13319.
[29] YOO S, ZHAO J J, WANG J L, et al. Endohedral Silicon Fullerenes SiN (27≤N≤39) [J]. J. Am. Chem. Soc., 2004, 126: 13845-13849.
[30] BAI J, CUI L F, WANG J L, et al. Structural Evolution of Anionic Silicon Clusters SiN (20≤N≤45) [J]. J. Phys. Chem. A, 2006, 110: 908-912.
[31] YOO S, ZENG X C. Structures and relative stability of medium-sized silicon clusters. IV. Motif-based low-lying clusters Si21–Si30 [J]. J. Chem. Phys., 2006, 124: 054304 (1-6).
[32] YOO S, SHAO N, KOEHLER C, et al. Structures and relative stability of medium-sized silicon clusters. V. Low-lying endohedral fullerenelike clusters Si31-Si40 and Si45 [J]. J. Chem. Phys., 2006, 124: 164311(1-6).
[33] ONA O, BAZTERRA V E, CAPUTO M C, et al. Modified genetic algorithms to model cluster structures in medium-sized silicon clusters: Si18-Si60 [J]. Phys. Rev. A, 2006, 73: 053203(1-11).
[34] 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).
[35] 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).
[36] MA S J, WANG G H. Structures of medium size germanium clusters [J]. Journal of Molecular Structure: THEOCHEM, 2006, 767: 75-79.
[37] LIANG F S, LI B X. Stable structures of Gen (n=21–25) clusters [J]. Phys. Lett. A , 2004, 328: 407-413.
[38] 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).
[39] FRISCH M J, TRUCKS G W, SCHLEGEL H B, et al. Gaussian 03, Revision B. Gaussian, Inc., Pittsburgh, PA, 2003.
[40] (a) DELLEY B. An all-electron numerical method for solving the local density functional for polyatomic molecules [J]. J. Chem. Phys., 1990, 92: 508-517; (b) DELLEY B. Analytic energy derivatives in the numerical local-density-functional approach [J]. J. Chem. Phys., 1991, 94: 7245-7250.
[41] NEGISHI Y, KAWAMATA H, NAKAJIMA A, et al. The infrared HOMO–LUMO gap of germanium clusters [J]. Chem. Phys. Lett., 1998, 294: 370-376.
[1] GINGERICH K A, SCHMUDE R W, BABA M S, et al. Atomization enthalpies and enthalpies of formation of the germanium clusters, Ge5, Ge6, Ge7, and Ge8 by Knudsen effusion mass spectrometry [J]. J. Chem. Phys., 2000, 112: 7443-7448.
[2] MARTIN T P, SCHABER H. Mass spectra of Si, Ge, and Sn clusters [J]. J. Chem. Phys., 1985, 83: 855-858.
[3] PHILLIPS J C. Pulsed Gen+ microcluster concentration spectra [J]. J. Chem. Phys., 1986, 85: 5246-5250.
[4] SCHULZE W, WINTER B, GOLDENFELD I. Generation of germanium clusters using the gas aggregation technique: Stability of small charged clusters [J]. J. Chem. Phys., 1987, 87: 2402-2403.
[5] BURTON G R, XU C S, ARNOLD C C, et al. Photoelectron spectroscopy and zero electron kinetic energy spectroscopy of germanium cluster anions [J]. J. Chem. Phys., 1996, 104: 2757-2764.
[6] ALFORD J M, LAAKSONEN R T, SMALLEY R E. Ammonia chemisorption studies on silicon cluster ions [J]. J. Chem. Phys., 1991, 94: 2618-2630.
[7] MARSEN B, LONFAT M, SCHEIER P, et al. Energy gap of silicon clusters studied by scanning tunneling spectroscopy [J]. Phys. Rev. B, 2000, 62: 6892-6895.
[8] Ray U, Jarrold M F. Reactions of silicon cluster ions, Sin+ (n=10–65), with water [J]. J. Chem. Phys., 1991, 94: 2631-2639.
[9] BERGERON D E, CASTLEMAN JR. A W. Insights into the stability of silicon cluster ions: Reactive etching with O2 [J]. J. Chem. Phys., 2002, 117: 3219-3223.
[10] JARROLD M F, IJIRI Y, RAY U. Interaction of silicon cluster ions with ammonia: Annealing, equilibria, high temperature kinetics, and saturation studies [J]. J. Chem. Phys., 1991, 94: 3607-3618.
[11] SCH?FER R, SCHLECHT S, WOENCKHAUS J, et al. Polarizabilities of Isolated Semiconductor Clusters [J]. Phys. Rev. Lett., 1996, 76: 471- 474.
[12] 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).
[13] 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).
[14] SERDAR OGUT, CHELIKOWSKY J R. Structural changes induced upon charging Ge clusters [J]. Phys. Rev. B, 1997, 55: R4914-R4917.
[15] LI B X, CAO P L. Structures of Gen clusters (n=3–10) and comparisons to Sin clusters [J]. Phys. Rev. B, 2000, 62: 15788-15796.
[16] LU Z Y, WANG C Z, HO K M. Structures and dynamical properties of Cn, Sin, Gen, and Snn clusters with n up to 13 [J]. Phys. Rev. B, 2000, 61: 2329-2334.
[17] HUNTER J M, FYE J L, JARROLD M F, et al. Structural Transitions in Size-Selected Germanium Cluster Ions [J]. Phys. Rev. Lett., 1993, 73: 2063-2066.
[18] JARROLD M F, IJIRI Y, CONSTANT V A. Silicon cluster ions: Evidence for a structural transition [J]. Phys. Rev. Lett., 1991, 67: 2994-2997.
[19] 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.
[20] 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.
[21] MA S J, WANG G H. Structures of medium size germanium clusters [J]. Journal of Molecular Structure: THEOCHEM, 2006, 767: 75-79.
[22] LIANG F S, LI B X. Stable structures of Gen (n=21–25) clusters [J]. Phys. Lett. A , 2004, 328: 407-413.
[23] 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).
[24] YOSHIDA S, FUKE K. Photoionization studies of germanium and tin clusters inthe energy region of 5.0–8.8 eV: Ionization potentials for Gen (n = 2–57) and Snn (n = 2–41) [J]. J. Chem. Phys., 1999, 111: 3880-3890.
[25] ZHANG Q L, LIU Y, CURL R F, et al. Photodissociation of semiconductor positive cluster ions [J]. J. Chem. Phys., 1988, 88: 1670-1677.
[26] HEATH J R, LIU Y, O’BRIEN S C, et al. Semiconductor cluster beams: One and two color ionization studies of Six and Gex [J]. J. Chem. Phys., 1985, 83: 5520-5526.
[1] HEDBERG K, HEDBERG L, BULHL M, et al. Molecular Structure of Free Molecules of the Fullerene C70 from Gas-Phase Electron Diffraction [J]. J. Am. Chem. Soc., 1997, 119: 5314-5320.
[2] COMPAGNON I, ANTONIE R, BROYER M, et al. Electric polarizability of isolated C70 molecules [J]. Phys. Rev. A, 2001, 64: 025201(1-4).
[3] ZOPE R R. The static dipole polarizability of C70 fullerene [J]. J. Phys. B: At. Mol. Opt. Phys., 2007, 40: 3491-3496.
[4] PIMENOVA S M, MELKHANOVA S V, KOLESOV V P. Thermochemical determination of the enthalpies of combustion and formation of fullerene C70 [J]. J. Chem. Thermodynamics, 2003, 35: 189-193.
[5] NAGASE S, KOBAYASHI K, Si60 and Si60X (X=Ne, F? and Na+) [J]. Chem. Phys. Lett., 1991, 187: 291-294.
[6] PIQUERAS M C, CRESPO R, ORTI E, et al. AM1 prediction of the equilibrium geometry of Si60 [J]. Chem. Phys., Lett., 1993, 213: 509-513.
[7] GONG X G, ZHENG Q Q, Electronic structures and stability of Si60 and C60@Si60 clusters [J]. Phys. Rev. B, 1995, 52: 4756-4759.
[8] LESZCZYNSKI J, YANOV I. Possibility of the Existence of Non-Carbon Fullerenes: Ab Initio HF and DFT/B3LYP Studies of the IV Main Group Fullerene-Like Species [J]. J. Phys. Chem. A, 1999, 103: 396-401.
[9] KHAN F S, BROUGHTON J Q. Relaxation of icosahedral-cage silicon clusters via tight-binding molecular dynamics [J]. Phys. Rev. B, 1991, 43: 11754-11761.
[10] MENON M, SUBBASWAMY K R, Structure of Si60. Cage versus network structures [J]. Chem. Phys. Lett., 1994, 219: 219-222.
[11] Li B X, Cao P L, Que D L, Distorted icosahedral cage structure of Si60 clusters [J]. Phys. Rev. B, 2000, 61: 1685-1687.
[12] SONG J, ULLOA S E, DRABOLD D A. Exciton-induced lattice relaxation and t he electronic and vibrational spectra of silicon clusters [J]. Phys. Rev. B, 1996,53: 8042-8051.
[13] LI B X, LIU J H, ZHAN S C, Stability of Si70 cage structures [J]. Eur. Phys. J. D 2005, 32: 59-62.
[14] SUN Q, WANG Q, JENA P, et al. Stabilization of Si60 Cage Structure [J]. Phys. Rev., Lett., 2003, 90: 135503(1-4).
[15] SUN Q, WANG Q, P. JENA P, et al. Geometry and energetics of Si60 isomers [J]. Science and Technology of Advanced Materials, 2003, 4: 361-365.
[16] MA S J, WANG G H, Nonorthogonal tight-binding study of Si60 cluster [J]. Journal of Molecular Structure: THEOCHEM, 2005, 757: 47-51.
[17] ONA O, BAZTERRA V E, CAPUTO M C, et al. Modified genetic algorithms to model cluster structures in medium-sized silicon clusters: Si18-Si60 [J]. Phys. Rev. A, 2006, 73: 053203.
[18] ZHAO J J, MA L, WEN B, Lowest-energy endohedral fullerene structure of Si60 from a genetic algorithm and density-functional theory [J]. J. Phys.: Condens. Matter, 2007, 19: 226208.
[19] YOO S, SHAO N, X. ZENG C, Structures and relative stability of medium- and large-sized silicon clusters. VI. Fullerene cage motifs for low-lying clusters Si39, Si40, Si50, Si60, Si70, and Si80 [J]. J. Chem. Phys., 2008, 128: 104316(1-9).
[20] YOO S, ZHAO J J, Wang J L, et al. Endohedral Silicon Fullerenes SiN (27≤N≤39) [J]. J. Am. Chem. Soc., 2004, 126: 13845-13849.
[21] ZHAO J J, WANG J L, JELLINE J, et al. Stuffed fullerene structures for medium-sized silicon clusters [J]. Eur. Phys. J. D, 2005, 34: 35-37.
[22] WANG J L, ZHOU X L, WANG G H, et al. Optimally stuffed fullerene structures of silicon nanoclusters [J]. Phys. Rev. B, 2005, 71: 113412(1-4).
[23] YOO S, SHAO N, KOEHLER C, et al. Structures and relative stability of medium-sized silicon clusters. V. Low-lying endohedral fullerenelike clusters Si31–Si40 and Si45 [J]. J. Chem. Phys., 2006, 124: 164311(1-6).
[24] Ma L, Zhao J, Wang J, et al. Lowest-energy endohedral fullerene structures of SiN (30≤N≤39) clusters by density functional calculations [J]. Phys. Rev. A, 2006, 73: 063203-063207.
[25] ZHOU R L, PAN B C. Low-lying isomers of Sin+ and Sin– (n=31–50) clusters [J]. J. Chem. Phys., 2008, 128: 234302-234307.
[26] ( a) WANG C Z, PAN B C, HO K M. An environment-dependent tight-binding potential for Si [J]. 1999, 11: 2043-2049; (b) 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] BLOCHL P E, Projector augmented-wave method [J]. Phys. Rev. B, 1994, 50: 17953-17979.
[29] (a) KRESSE G, JOUBERT D, From ultrasoft pseudopotentials to the projector augmented-wave method [J]. Phys. Rev. B, 1999, 59: 1758-1775; (b) KRESSE G, HAFNER J, Ab initio molecular dynamics for open-shell transition metals [J]. Phys. Rev. B, 1993, 48: 13115-13118.
[30] (a) DELLEY B, An all-electron numerical method for solving the local density functional for polyatomic molecules [J]. J. Chem. Phys., 1990, 92: 508-517; (b) DELLEY B. Analytic energy derivatives in the numerical local-density-functional approach [J]. J. Chem. Phys., 1991, 94: 7245-7250.
[31] FUKE K, TSUKAMOTO K, MISAIZU F, et al. Near threshold photoionization of silicon clusters in the 248–146 nm region: Ionization potentials for Sin [J]. J. Chem. Phys., 1993, 99: 7807-7812.
[32] JARROLD M F, CONSTANT V A, Silicon cluster ions: Evidence for a structural transition [J]. Phys. Rev. Lett., 1991, 67: 2994-2997.
[33] HUDGINS R R, IMAI M, JARROLD M F, et al. High-resolution ion mobility measurements for silicon cluster anions and cations [J]. J. Chem. Phys., 1999, 111: 7865-7870.
[34] 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.
[35] (a) MESLEH M F, HUNTER J M, SHVARTSBURG A A, et al. Structural Information from Ion Mobility Measurements: Effects of the Long-RangePotential [J]. J. Phys. Chem., 1996, 100: 16082-16086; (b) 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.
[36] JARROLD M F, HONEA E C, Dissociation of large silicon clusters: the approach to bulk behavior [J]. J. Phys. Chem., 1991, 95: 9181-9185.
[37] BACHELS T, SCHAFER R, Binding energies of neutral silicon clusters [J]. Chem. Phys. Lett., 2000, 324: 365-372.
[38] LENOSKY T J, KRESS J D, KWON I, et al. Highly optimized tight-binding model of silicon [J]. Phys. Rev. B, 1997, 55: 1528-1544.
[1] FUJISHIM A A, HONDA K. Electrochemical photocatalysis of water at a semiconductor electrode [J]. Nature, 1972, 238: 37-38.
[2] UMEBAYASHI T, YAMAKI T S, TANAKA S. et al. Visible light-induced degradation of methylene blue on S-doped TiO2 [J].Chem. Lett., 2003, 32: 330–331.
[3] KHAN S U M, AL-SHAHRY M, INGLER JR. W, et al. Efficient photochemical water splitting by a chemically modified n-TiO2 [J]. Science, 2002, 297: 2243–2245.
[4] LINSEBIGLER A L, LU G Q, YATES J T, et al. Photocatalysis on TiO2. Surfaces: Principles, Mechanism and Selected Results [J]. Chem. Rev. ,1995, 95: 735–758.
[5] YAMASHITA H, HARADA M, MISAKA J, et al. Degradation of propanol diluted in water under visible light irradiation using metal ion-implanted titanium dioxide photocatalysts [J]. J. Photochem Photobiol A: Chem., 2002, 148: 257–261.
[6] ASAHI R, MORIKAWA T, OHWAKI T, et al. Visible-light photocatalysis in nitrogen-doped titanium oxides [J]. Science, 2001, 293: 269–271.
[7] WANG D F, ZOU Z H, YE J H, et al. Photocatalytic H2 evolution over a new visible-light-driven photocatalyst In12NiCr2Ti10O42 [J]. Chem. Phys. Lett., 2005, 411: 285–290.
[8] TERUHISA O, TOSHIKI T, YOUSUKE N, et al. Preparation of S, C cation-codoped SrTiO3 and its photocatalytic activity under visible light [J]. Applied Catalysis A, 2005, 288: 74–79.
[9] FRANK S N, BARD A J. Heterogenerous photocatalytic oxidation of cynide ion in aqueous solutions of titanium dioxide powder [J]. J. Am. Chem. Soc., 1977, 99: 303–305.
[10] ANGELA G R, GESAR P, NEVENKA A, et al. Interaction between E. coli inactivation and DBP-precursors—dihydroxybenzene isomers—in the photocatalytic process of drinking-water disinfection with TiO2 [J]. J. Photochem Photobiol A: Chem., 2001, 139: 233–241.
[11] STEVENSON M, BULLOCK K, LIN W Y, et al. Sonolytic enhancement of thebactericidal activity of irradiated titanium dioxide suspensions in water [J]. Res. Chem. Intermed, 1997, 23: 311–323.
[12] OSHIKIRI M, BOERO M, YE J, et al. The electronic structures of the thin films of InVO4 and TiO2 by first principles calculations [J]. Thin Solid Films, 2003, 445: 168-174.
[13] BANDURA A V, SYKES D G, SHAPOVALOV V, et al. Adsorption of Water on the TiO2 (Rutile) (110) Surface: A Comparison of Periodic and Embedded Cluster Calculations [J]. J. Phys. Chem. B, 2004, 108: 7844-7853.
[14] Wei Zhi-Gang(魏志刚), Li Qian-Shu(李前树), Zhang Hong-Xing(张红星) et al.二氧化钛(TiO2)表面上水分解反应的理论研究[J]. Chem. J. Chinese. Universities (高等学校化学学报), 2007, 28(2): 350-351.
[15] TILOCCA A, SELLONI A. Reaction pathway and free energy barrier for defect-induced water dissociation on the (101) surface of TiO2-anatase [J]. J. Chem. Phys., 2003, 119: 7445-7450.
[16] REGO L G C, BATISTA V S. Quantum Dynamics Simulations of Interfacial Electron Transfer in Sensitized TiO2 Semiconductors [J]. J. Am. Chem. Soc., 2003, 125: 7989-7997.
[17] MALLIA1 G, HARRISON N M. Magnetic moment and coupling mechanism of iron-doped rutile TiO2 from first principles [J]. Phys. Rev. B, 2007, 75: 165201(1-11).
[18] GAO G Y, YAO K L, LIU Z L, et al. Magnetism and electronic structure of Cr-doped rutile TiO2 from first-principles calculations [J]. Journal of Magnetism and Magnetic Materials, 2007, 313: 210–213.
[19] DU X S, LI Q X, SU H B, et al. Electronic and magnetic properties of V-doped anatase TiO2 from first principles [J]. Phys. Rev. B, 2006, 74: 233201(1-4).
[20] HAN Y, LIU C J, GE Q F. Interaction of Pt Clusters with the Anatase TiO2 (101) Surface: A First Principles Study [J]. J. Phys. Chem. B, 2006, 110: 7463-7472.
[21] LOCATELLI A, PABISIAK T, PAVLOVSKA A, et al. One-dimensional Au on TiO2 [J]. J. Phys.: Condens. Matter, 2007, 19: 082202(1-8).
[22] CALATAYUD M, MINOT C. Reactivity of the V2O5–TiO2-anatase catalyst: roleof the oxygen sites [J]. Topics in Catalysis, 2006, 40: 17-25.
[23] SAMBRANO J R, VASCONCELLOS L A, MARTINS J B L, et al. A theoretical analysis on electronic structure of the (110) surface of TiO2–SnO2 mixed oxide [J]. Journal of Molecular Structure: THEOCHEM, 2003, 629: 307-314.
[2]卢嘉锡.原子簇化合物的结构化学,中国化学, 1978年年会学术报告集,北京:科学出版社, 198, 35-60.
[3]徐光宪.原子团簇与有关分子的结构规则(I),高等学校化学学报, 1982, 3(专刊), 114.
[4] KNIGHT W D, CLEMENGER K, HEER W A, et al. Electronic Shell Structure and Abundances of Sodium Clusters [J]. Phys. Rev. Lett., 1984, 52: 2141-2143.
[5] KROTO H W, Health J R, OBrien S C, et al. C60:Buckminster-fullerene [J]. Nature, 1985, 318: 162-163.
[6] KRASCHMER W, LAMB L D, FOSTIROPOULOS K, et al. Solid C60:A New form of Carbon [J]. Nature, 1990, 347: 354-358.
[7] HEBARD A F, ROSSEINSKY M J, HADDON R C, et al. Superconductivity at 18 K in Potassium-doped C60 [J]. Nature, 1991, 350: 600-601.
[8] LIJIMA S. Helical microtubules of graphitic carbon [J]. Nature, 1991, 354: 56-58.
[9] UGARTE D. Curling and closure of graphitic networks under electron beam irradiation [J]. Nature, 1992, 359(6397): 707-709.
[10] JACOBSEN R L, MONTHIOUX M, JACOBSEN R L, et al. Carbon beads with protruding cones [J]. Nature, 1997, 385: 211.
[11] LIU J, DAI H J, HAFNER J H, et al. Fullerene "Crop Circles" [J]. Nature, 1997, 385: 780.
[12]张乾二.林连堂.王南钦.赖善桃.多面体分子轨道的理论方法:III.结构多面体骨架的成键分子轨道.厦门大学学报(自然科学版),1981, 2: 226.
[13] JARROLD M F. Nanosurface Chemistry on Size Selected Silicon Clusters [J]. Science, 1991, 252: 1085-1092.
[14] BROWN W L, FREEMAN R R, RAGHAVACHARI K, et al. Covalent Group IV Atomic Clusters [J]. Science, 1987, 235: 860-865.
[15] GINGERICH K A, SCHMUDE R W, BABA M S, et al. Atomization enthalpies and enthalpies of formation of the germanium clusters, Ge5, Ge6, Ge7, and Ge8 by Knudsen effusion mass spectrometry [J]. J. Chem. Phys., 2000, 112: 7443-7448.
[16] MARTIN T P, SCHABER H. Mass spectra of Si, Ge, and Sn clusters [J]. J. Chem. Phys., 1985, 83: 855-858.
[17] PHILLIPS J C. Pulsed Gen+ microcluster concentration spectra [J]. J. Chem. Phys., 1986, 85: 5246-5250.
[18] SCHULZE W, WINTER B, GOLDENFELD I. Generation of germanium clusters using the gas aggregation technique: Stability of small charged clusters [J]. J. Chem. Phys., 1987, 87: 2402-2403.
[19] YOSHIDA S, FUKE K. Photoionization studies of germanium and tin clusters in the energy region of 5.0–8.8 eV: Ionization potentials for Gen (n = 2–57) and Snn (n = 2–41) [J]. J. Chem. Phys., 1999, 111: 3880-3890.
[20] ZHANG Q L, LIU Y, CURL R F, et al. Photodissociation of semiconductor positive cluster ions [J]. J. Chem. Phys., 1988, 88: 1670-1677.
[21] FUKE K, TSUKAMOTO K, MISAIZU F, et al. Near threshold photoionization of silicon clusters in the 248–146 nm region: Ionization potentials for Sin [J]. J. Chem. Phys., 1993, 99: 7807-7812.
[22] BURTON G R, XU C S, ARNOLD C C, et al. Photoelectron spectroscopy and zero electron kinetic energy spectroscopy of germanium cluster anions [J]. J. Chem. Phys., 1996, 104: 2757-2764.
[23] SCH?FER R, SCHLECHT S, WOENCKHAUS J, et al. Polarizabilities of Isolated Semiconductor Clusters [J]. Phys. Rev. Lett., 1996, 76: 471- 474.
[24] ALFORD J M, LAAKSONEN R T, SMALLEY R E, Ammonia chemisorption studies on silicon cluster ions [J]. J. Chem. Phys., 1991, 94: 2618-2630.
[25] RAY U, JARROLD M F, Reactions of silicon cluster ions, Sin+ (n=10–65), with water [J]. J. Chem. Phys. 1991, 94: 2631-2639.
[26] BERGERON D E, CASTLEMAN JR. A W. Insights into the stability of siliconcluster ions: Reactive etching with O2 [J]. J. Chem. Phys., 2002, 117: 3219-3223.
[27] JARROLD M F, IJIRI Y, RAY U. Interaction of silicon cluster ions with ammonia: Annealing, equilibria, high temperature kinetics, and saturation studies [J]. J. Chem. Phys., 1991, 94: 3607-3618.
[28] SHVARTSBURG A A, LIU B, LU Z 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.
[29] 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).
[30] JARROLD M F, IJIRI Y, CONSTANT V A. Silicon cluster ions: Evidence for a structural transition [J]. Phys. Rev. Lett., 1991, 67: 2994-2997.
[31] 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.
[32] 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.
[33] HUNTER J M, FYE J L, JARROLD M F, et al. Structural Transitions in Size-Selected Germanium Cluster Ions [J]. Phys. Rev. Lett., 1993, 73: 2063-2066.
[34] BAI J, CUI L F, WANG J L, et al. Structural Evolution of Anionic Silicon Clusters SiN (20≤N≤45) [J]. J. Phys. Chem. A, 2006, 110: 908-912.
[35] YOO S, ZENG X C, Structures and relative stability of medium-sized silicon clusters. IV. Motif-based low-lying clusters Si21–Si30 [J]. J. Chem. Phys., 2006, 124: 054304 (1-6).
[36] YOO S, SHAO N, KOEHLER C, et al. Structures and relative stability of medium-sized silicon clusters. V. Low-lying endohedral fullerenelike clusters Si31-Si40 and Si45 [J]. J. Chem. Phys. 2006, 124: 164311(1-6).
[37] ZHOU R L, PAN B C. Low-lying isomers of Sin+ and Sin– (n=31–50) clusters [J]. J. Chem. Phys., 2008, 128: 234302(1-6).
[38] SONG J, ULLOA S E, Drabold D A, Exciton-induced lattice relaxation and the electronic and vibrational spectra of silicon clusters [J]. Phys. Rev. B, 1996, 53: 8042-8051.
[39] LI B X, LIU J H, ZHAN S C. Stability of Si70 cage structures [J]. Eur. Phys. J. D, 2005, 32: 59-62.
[40] SUN Q, WANG Q, JENA P, et al. Stabilization of Si60 Cage Structure [J]. Phys. Rev. Lett., 2003, 90: 135503(1-4).
[41] SUN Q, WANG Q, JENA P, et al. Geometry and energetics of Si60 isomers [J]. Science and Technology of Advanced Materials, 2003, 4: 361-365.
[42] MA S J, WANG G H, Nonorthogonal tight-binding study of Si60 cluster [J]. Journal of Molecular Structure: THEOCHEM, 2005, 757: 47-51.
[43] ONA O, BAZTERRA V E, CAPUTO M C, et al. Modified genetic algorithms to model cluster structures in medium-sized silicon clusters: Si18-Si60 [J]. Phys. Rev. A 2006, 73: 053203(1-11).
[44] ZHAO J J, MA L, WEN B. Lowest-energy endohedral fullerene structure of Si60 from a genetic algorithm and density-functional theory [J]. J. Phys.: Condens. Matter, 2007, 19: 226208(1-6).
[45] YOO S, SHAO N, ZENG X C, Structures and relative stability of medium- and large-sized silicon clusters. VI. Fullerene cage motifs for low-lying clusters Si39, Si40, Si50, Si60, Si70, and Si80 [J]. J. Chem. Phys. 2008, 128: 104316(1-9).
[46] 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).
[47] MA S J, WANG G H. Structures of medium size germanium clusters [J]. Journal of Molecular Structure: THEOCHEM, 2006, 767: 75-79.
[48] LIANG F S, LI B X. Stable structures of Gen (n=21–25) clusters [J]. Phys. Lett. A, 2004, 328: 407-413.
[49] 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).
[50] 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).
[51] BURTON G R, XU C S, ARNOLD C C, et al. Photoelectron spectroscopy and zero electron kinetic energy spectroscopy of germanium cluster anions [J]. J. Chem. Phys., 1996, 104: 2757-2764.
[52] 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.
[53] FUJISHIMA A, HONDA K. Electrochemical photocatalysis of water at a semiconductor electrode [J]. Nature, 1972, 238: 37-38.
[54] OSHIKIRI M, BOERO M, YE J, et al. The electronic structures of the thin films of InVO4 and TiO2 by first principles calculations [J]. Thin Solid Films, 2003, 445: 168-174.
[55] BANDURA A V, SYKES D G, SHAPOVALOV V, et al. Adsorption of Water on the TiO2 (Rutile) (110) Surface: A Comparison of Periodic and Embedded Cluster Calculations [J]. J. Phys. Chem. B, 2004, 108: 7844-7853.
[56] Wei Zhi-Gang(魏志刚), Li Qian-Shu(李前树), Zhang Hong-Xing(张红星) et al.二氧化钛(TiO2)表面上水分解反应的理论研究[J]. Chem. J. Chinese. Universities (高等学校化学学报), 2007, 28(2): 350-351.
[57] TILOCCA A, SELLONI A, Reaction pathway and free energy barrier for defect-induced water dissociation on the (101) surface of TiO2-anatase [J]. J. Chem. Phys., 2003, 119: 7445-7450.
[58] REGO L G C, BATISTA V S. Quantum Dynamics Simulations of Interfacial Electron Transfer in Sensitized TiO2 Semiconductors [J]. J. Am. Chem. Soc. 2003, 125: 7989-7997.
[59] MALLIA1 G, HARRISON N M. Magnetic moment and coupling mechanism of iron-doped rutile TiO2 from first principles [J]. Phys. Rev. B, 2007, 75: 165201(1-11).
[60] GAO G Y, YAO K L, LIU Z L, et al. Magnetism and electronic structure ofCr-doped rutile TiO2 from first-principles calculations [J]. Journal of Magnetism and Magnetic Materials, 2007, 313: 210–213.
[61] DU X S, LI Q X, SU H B, et al. Electronic and magnetic properties of V-doped anatase TiO2 from first principles [J]. Phys. Rev. B, 2006, 74: 233201(1-4).
[62] HAN Y, LIU C J, GE Q F. Interaction of Pt Clusters with the Anatase TiO2 (101) Surface: A First Principles Study [J]. J. Phys. Chem. B, 2006, 110: 7463-7472.
[63] Locatelli A, Pabisiak T, Pavlovska A, et al. One-dimensional Au on TiO2 [J]. J. Phys.: Condens. Matter, 2007, 19: 082202(1-8).
[64] CALATAYUD M, MINOT C. Reactivity of the V2O5–TiO2-anatase catalyst: role of the oxygen sites [J]. Topics in Catalysis, 2006, 40: 17-25.
[65] SAMBRANO J R, VASCONCELLOS L A, MARTINS J B L, et al. A theoretical analysis on electronic structure of the (110) surface of TiO2–SnO2 mixed oxide [J]. Journal of Molecular Structure: THEOCHEM, 2003, 629: 307-314.
[1] BORN M, OPPENHEIMER R, Zur Quantentheorie der Molekeln. Annalen der Physik. (Quantum Theory of the Molecules Ann. Phys.), 1927, 84: 457-484.
[2] (a) HEHRE W J, RADOM L, SCHLEYER P V R, et al. Ab Initio Molecular Orbital Theory, John Wiley &Sons, Inc., 1986. (b) MCQUARRIE D A. Quantum Chemistry University, Science Books: Mill Vally. CA. 1983.
[3] (a)唐敖庆.杨忠志.李前树.量子化学,北京,科学出版社, 1982.(b)徐光宪.黎乐民.王德民.量子化学基本原理和从头计算法,北京,科学出版社, 1985.
[4] LOWDIN P O. Correlation Problem in Many-Electron Quantum Mechanics [J]. Adv. Chem. Phys., 1959, 2: 207.
[5] M?LLER C, PLESSET M S. Note on an Approximation Treatment for Many-Electron Systemsp [J]. Phys. Rev., 1934, 46: 618-622.
[6] HEAD-GORDON M, POPLE J A, Frisch M J. A Direct MP2 Gradient Method [J]. Chem. Phys. Lett., 1988, 153: 503-506.
[7] POPLE J A, BINKLEY J S, SEEGER R. Theoretical Models Incorporating Electron Correlation [J]. Int. J. Quant. Chem. Symp., 1976, 10: 1?19.
[8] KRISHNAN R, POPLE J A. Appoximate Forth-Order Perturbation Theory of the Electron Correlation Energy [J]. Int. J. Quant. Chem., 1978, 14: 91?100.
[9] RAGHAVACHARI K, POPLE J A, REPLOGLE E S, et al. Fifth-Order Moller-Plesset Perturbation Theory: Comparison of Existing Correlation Methods and Implementation of New Methods Correct to Fifth-Order [J]. J. Phys. Chem., 1990, 94: 5579-5586.
[10] POPLE J A, SEEGER R, KRISHNAN R. Variational Configuration Interaction Methods and Comparison with Perturbation Theory [J]. Int. J. Quant. Chem. Symp., 1977, 11: 149.
[11] FORESMAN J B, HEAD-GORDON M, POPLE J A, et al. Toward a Systematic Molecular Orbital Theory for Excited States [J]. J. Phys. Chem., 1992, 96: 135-149.
[12] KRISHNAN R, SCHLEGEL H B, POPLE J A. Derivate Studies in Configuration Interaction Theory [J]. J. Chem. Phys., 1980, 72: 4654-4655.
[13] BROOKS B R, LAIDIG W D, SAXE P, et al. Analytic Gradient from Correlated Wave Functions via the Two-Particle Density Matrix and the Unitary Group Approach [J]. J. Chem. Phys., 1980, 72: 4652-4653.
[14] SALTER E A, TRUCKS G W, BARTLETT R J. Analytic Energy Derivatives in Many-Body Methods I. First Derivatives [J]. J. Chem. Phys., 1989, 90 : 1752-1766.
[15] RAGHAVACHARI K, POPLE J A. [J]. Int. J. Quant. Chem., 1981, 20: 167.
[16] POPLE J A, HEAD-GORDON M, RAGHAVACHARI K. Quadratic Configuration Interaction. A General Technique for Determining Electron Correlation Energies [J]. J. Chem. Phys., 1987, 87: 5968-5975.
[17] CIOSLOWSKI J. A New Robust Algorithm for Fully Automated Determination of Attactor Interaction Lines in Moleclues [J]. Chem. Phys. Lett., 1994, 219: 151-154.
[18] SCHLEGEL H B, ROBB M A. MCSCF Gradient Optimization of the H2CO→H2+CO Transition Structure [J]. Chem. Phys. Lett., 1982, 93: 43-46.
[19] EADE R H E, ROBB M A. Direct minimization in mc scf theory. the quasi-newton method [J]. Chem. Phys. Lett., 1981, 83: 362-368.
[20] HEGARTY D, ROBB M A. Application of Unitary Group Methods to Configuration Interaction Calculations [J]. Mol. Phys., 1979, 38: 1795-1812.
[21] POPLE J A, KRISHNAN R, SCHLEGEL H B, et al. Electron correlation theories and their application to the study of simple reaction potential surfaces [J]. Int. J. Quant. Chem., 1978, 14: 545?560.
[22] BARTLETT R J, PURVIS G D. General Application of a Big Molecule Gaussian SCF/CI Program for Calculations of Excited Metastables and of Negative Ion Bound States and Resonances [J]. Int. J. Quant. Chem., 1978, 14: 515-518.
[23] SCUSERIA G E, SCHAEFER H F. Is coupled cluster singles and doubles (CCSD) more computationally intensive than quadratic configuration interaction (QCISD)? [J]. J. Chem. Phys., 1989, 90: 3700-3703.
[24] PURVIS G D, BARTLETT R J. A Full Coupled-Cluster Singles and Doubles Model: The Inclusion of Disconnected Triples [J]. J. Chem. Phys., 1982, 76: 1910-1918.
[25] SCUSERIA G E, JANSSEN C L, SCHAEFER H F. An efficient reformulation of the closed-shell coupled cluster single and double excitation (CCSD) equations [J]. J. Chem. Phys., 1988, 89: 7382-7387.
[26] HOHENBERG P, KOHN W. Inhomogeneous Electron Gas [J]. Phys. Rev., 1964, 136: B864?B871.
[27] KOHN W, SHAM L J. Self-Consistent Equations Including Exchange and Correlation Effects [J]. Phys. Rev., 1965, 140: A1133?A1138.
[28] SLATER J C. Quantum Theory of Molecular and Solids. Vol. 4: The Self-Consistent Field for Molecular and Solids McGraw-Hill: New York, 1974.
[29] SALAHUB D R, ZERNER M C, eds. The Challenge of d and f Electrons ACS: Washington, D.C., 1989.
[30] PARR R G, YANG W. Density-functional theory of atoms and molecules Oxford Univ. Press: Oxford, 1989.
[31] POPLE J A, GILL P M W, JOHNSON B G. Kohn-Sham density-functional theory within a finite basis set [J]. Chem. Phys. Lett., 1992, 199: 557-560.
[32] JOHNSON B G, FRISCH M J. An implementation of analytic second derivatives of the gradient-corrected density functional energy [J]. J. Chem. Phys., 1994, 100: 7429-7442.
[33] LABANOWSKI J K, ANDZELM J W, eds. Density Functional Methods in Chemistry. Springer-Verlag: New York, 1991
[34] POCKETT W E. Pseudopotential methods in condensed matter applications. Comp. Phys. Rep., 1989, 9(3): 115-197.
[35] KRESSE G, HAFNER J. Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements [J]. J. Phys.: Condens. Matter., 1994, 6(40): 8245-8258.
[36] CHELIKOWSKY J R, SAAD Y. Electronic Structure of Clusters and Nanocrystals. Handbook of Theoretical and Computational Nanotechnology [M].American : M. Rieth and W. Schommers. (American Scientific), 2006, 8: 797.
[37] SLATER J C, KOSTER G F. Simplified LCAO Method for the Periodic Potential Problem [J]. Phys. Rev., 1954, 94: 1498-1524.
[38] CHADI D J. Atomic and Electronic Structures of Reconstructed Si (100) Surfaces [J]. Phys. Rev. Lett., 1979, 43: 43-47.
[39] POPLE J A, BEVERIDGE D L. Approximate Molecular Orbital Theory, McGraw-Hill Book Company, 1970.
[40] ELSTNER M, POREZAG D, JUNGNICKEL G, et al. Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties [J]. Phys. Rev. B, 1998, 58: 7260-7268.
[41] DEAVEN D, HO K M. Molecular Geometry Optimization with a Genetic Algorithm [J]. Phys. Rev. Lett., 1995, 75: 288-291.
[42] HO K M, SHVARTSBURG A, PAN B C, et al. Structures of Medium-Sized Silicon Clusters [J]. Nature, 1998, 392: 582-584.
[43] BORN M, OPPENHEIMER R. Zur Quantentheorie der Molekeln Ann. Phsik. (Quantum Theory of the Molecules Ann. Phys.) 1927, 84: 457.
[44]唐敖庆.杨忠志.李前树.量子化学,北京:科学出版社,1982.
[45]徐光宪.黎乐民.王德民.量子化学基本原理和从头计算法,北京:科学出版社,1985.
[46]赵学庄.罗渝然.臧雅茹.万学适.《化学反应动力学原理》下册,高等教育出版社,1990.
[47] FUKUI K. Int. J. Quantum. Chem., 1981, 15 : 633-642.
[48] FUKUI K, TACHIBANA A, YAMASHITA K. Int. J. Quantum. Chem. 1981, 15: 621-632.
[49] BODY R G, MCCLURE D S, CLEMENTI E. SCF Wavefunctions for the NH3 Molecule. Potential-Energy Surface and Vibrational Force Constants [J]. J. Chem. Phys., 1968, 49: 4916-4924.
[50] GARTON D, SUTCHIFFE B T. Theoretical Chemistry, Vol. 1 (Ed. R. N. Dixon), The Chemical Society, London, 1974.
[51] PULAY P. Ab initio Calculation of Force Constants and Equilibrium Geometries.I. Theory [J]. Mol. Phys., 1969, 17: 197-204.
[52] PULAY P. In: Modern Theoretical Chemistry: Applications of Electronic Structure Theory, (H. F. Schaefer, III, Ed.), Plenum Press, New York, 1977, 4: 153-185.
[53] FLETCHER R, POWELL M J D. A Rapidly Convergent Method for Minimization [J]. The Computer Journal, 1963, 6(2): 163-168.
[54] MURTAGH B A, SARGENT R W H. Computational experience with quadratically convergent minimisation methods [J]. The Computer Journal, 1970, 13: 185-194.
[55] MCIVER JR. J W, KOMORNICKI A. Rapid geometry optimization for semi-empirical molecular orbital methods [J]. Chem. Phys. Lett., 1971, 10: 303-306.
[56] POPPINGER D. Geometry optimization in ab initio molecular orbital theory [J]. Chem. Phys. Lett., 1975, 34: 332-336.
[57] PANCUI J. [J]. Collect. Czech. Chem. Commun, 1975, 40: 2726-2732.
[1] GINGERICH K A, SCHMUDE R W, BABA M S, et al. Atomization enthalpies and enthalpies of formation of the germanium clusters, Ge5, Ge6, Ge7, and Ge8 by Knudsen effusion mass spectrometry [J]. J. Chem. Phys., 2000, 112: 7443-7448.
[2] MARTIN T P, SCHABER H. Mass spectra of Si, Ge, and Sn clusters [J]. J. Chem. Phys., 1985, 83: 855-858.
[3] PHILLIPS J C. Pulsed Gen+ microcluster concentration spectra [J]. J. Chem. Phys., 1986, 85: 5246-5250.
[4] SCHULZE W, WINTER B, GOLDENFELD I. Generation of germanium clusters using the gas aggregation technique: Stability of small charged clusters [J]. J. Chem. Phys., 1987, 87: 2402-2403.
[5] HEATH J R, LIU Y, O’BRIEN S C, et al. Semiconductor cluster beams: One and two color ionization studies of Six and Gex [J]. J. Chem. Phys., 1985, 83: 5520-5526.
[6] YOSHIDA S, FUKE K. Photoionization studies of germanium and tin clusters in the energy region of 5.0–8.8 eV: Ionization potentials for Gen (n = 2–57) and Snn (n = 2–41) [J]. J. Chem. Phys., 1999, 111: 3880-3890.
[7] BURTON G R, XU C S, ARNOLD C C, et al. Photoelectron spectroscopy and zero electron kinetic energy spectroscopy of germanium cluster anions [J]. J. Chem. Phys., 1996, 104: 2757-2764.
[8] HUNTER J M, FYE J L, JARROLD M F, et al. Structural Transitions in Size-Selected Germanium Cluster Ions [J]. Phys. Rev. Lett., 1993, 73: 2063-2066.
[9] ALFORD J M, LAAKSONEN R T, SMALLEY R E. Ammonia chemisorption studies on silicon cluster ions [J]. J. Chem. Phys., 1991, 94: 2618-2630.
[10] SHVARTSBURG A A, LIU B, LU Z 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] SHVARTSBURG A A, HUDGINS R R, DUGOURDB P, et al. Structuralinformation from ion mobility measurements: applications to semiconductor clusters [J]. Chem. Soc. Rev., 2001, 30: 26-35.
[12] MARSEN B, LONFAT M, SCHEIER P, et al. Energy gap of silicon clusters studied by scanning tunneling spectroscopy [J]. Phys. Rev. B, 2000, 62: 6892-6895.
[13] RAY U, JARROLD M F. Reactions of silicon cluster ions, Sin+ (n=10–65), with water [J]. J. Chem. Phys., 1991, 94: 2631-2639.
[14] BERGERON D E, CASTLEMAN JR. A W. Insights into the stability of silicon cluster ions: Reactive etching with O2 [J]. J. Chem. Phys., 2002, 117: 3219-3223.
[15] JARROLD M F, IJIRI Y, RAY U. Interaction of silicon cluster ions with ammonia: Annealing, equilibria, high temperature kinetics, and saturation studies [J]. J. Chem. Phys., 1991, 94: 3607-3618.
[16] JARROLD M F, IJIRI Y, CONSTANT V A. Silicon cluster ions: Evidence for a structural transition [J]. Phys. Rev. Lett., 1991, 67: 2994-2997.
[17] SCH?FER R, SCHLECHT S, WOENCKHAUS J, et al. Polarizabilities of Isolated Semiconductor Clusters [J]. Phys. Rev. Lett., 1996, 76: 471- 474.
[18] JARROLD M F, HONEA E C. Dissociation of large silicon clusters: the approach to bulk behavior [J]. J. Phys. Chem., 1991, 95: 9181-9185.
[19] 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.
[20] 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.
[21] ZHANG Q L, LIU Y, CURL R F, et al. Photodissociation of semiconductor positive cluster ions [J]. J. Chem. Phys., 1988, 88: 1670-1677.
[22] FUKE K, TSUKAMOTO K, MISAIZU F, et al. Near threshold photoionization of silicon clusters in the 248–146 nm region: Ionization potentials for Sin [J]. J. Chem. Phys., 1993, 99: 7807-7812.
[23] MITAS L, GROSSMAN J C, STICH I, et al. Silicon Clusters of Intermediate Size: Energetics, Dynamics, and Thermal Effects [J]. Phys. Rev. Lett., 2000, 84:1479-1482.
[24] YOO S, ZENG X C. Motif Transition in Growth Patterns of Small to Medium-Sized Silicon Clusters [J]. Angew. Chem. Int. Ed., 2005, 44: 1491-1494.
[25] GOEDECKER S, HELLMANN W. Global Minimum Determination of the Born-Oppenheimer Surface within Density Functional Theory [J]. Phys. Rev. Lett., 2005, 95: 055501(1-4).
[26] SIECK A, FRAUENHEIM1 T, JACKSON K A. Shape transition of medium-sized neutral silicon clusters [J]. Phys. stat. sol. (b), 2003, 240: 537-548.
[27] JACKSON K A, HOROI M H. Unraveling the Shape Transformation in Silicon Clusters [J]. Phys. Rev. Lett., 2004, 93: 013401(1-4).
[28] YOO S, ZENG X C, ZHU X L, et al. Possible Lowest-Energy Geometry of Silicon Clusters Si21 and Si25 [J]. J. Am. Chem. Soc., 2003, 125: 13318-13319.
[29] YOO S, ZHAO J J, WANG J L, et al. Endohedral Silicon Fullerenes SiN (27≤N≤39) [J]. J. Am. Chem. Soc., 2004, 126: 13845-13849.
[30] BAI J, CUI L F, WANG J L, et al. Structural Evolution of Anionic Silicon Clusters SiN (20≤N≤45) [J]. J. Phys. Chem. A, 2006, 110: 908-912.
[31] YOO S, ZENG X C. Structures and relative stability of medium-sized silicon clusters. IV. Motif-based low-lying clusters Si21–Si30 [J]. J. Chem. Phys., 2006, 124: 054304 (1-6).
[32] YOO S, SHAO N, KOEHLER C, et al. Structures and relative stability of medium-sized silicon clusters. V. Low-lying endohedral fullerenelike clusters Si31-Si40 and Si45 [J]. J. Chem. Phys., 2006, 124: 164311(1-6).
[33] ONA O, BAZTERRA V E, CAPUTO M C, et al. Modified genetic algorithms to model cluster structures in medium-sized silicon clusters: Si18-Si60 [J]. Phys. Rev. A, 2006, 73: 053203(1-11).
[34] 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).
[35] 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).
[36] MA S J, WANG G H. Structures of medium size germanium clusters [J]. Journal of Molecular Structure: THEOCHEM, 2006, 767: 75-79.
[37] LIANG F S, LI B X. Stable structures of Gen (n=21–25) clusters [J]. Phys. Lett. A , 2004, 328: 407-413.
[38] 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).
[39] FRISCH M J, TRUCKS G W, SCHLEGEL H B, et al. Gaussian 03, Revision B. Gaussian, Inc., Pittsburgh, PA, 2003.
[40] (a) DELLEY B. An all-electron numerical method for solving the local density functional for polyatomic molecules [J]. J. Chem. Phys., 1990, 92: 508-517; (b) DELLEY B. Analytic energy derivatives in the numerical local-density-functional approach [J]. J. Chem. Phys., 1991, 94: 7245-7250.
[41] NEGISHI Y, KAWAMATA H, NAKAJIMA A, et al. The infrared HOMO–LUMO gap of germanium clusters [J]. Chem. Phys. Lett., 1998, 294: 370-376.
[1] GINGERICH K A, SCHMUDE R W, BABA M S, et al. Atomization enthalpies and enthalpies of formation of the germanium clusters, Ge5, Ge6, Ge7, and Ge8 by Knudsen effusion mass spectrometry [J]. J. Chem. Phys., 2000, 112: 7443-7448.
[2] MARTIN T P, SCHABER H. Mass spectra of Si, Ge, and Sn clusters [J]. J. Chem. Phys., 1985, 83: 855-858.
[3] PHILLIPS J C. Pulsed Gen+ microcluster concentration spectra [J]. J. Chem. Phys., 1986, 85: 5246-5250.
[4] SCHULZE W, WINTER B, GOLDENFELD I. Generation of germanium clusters using the gas aggregation technique: Stability of small charged clusters [J]. J. Chem. Phys., 1987, 87: 2402-2403.
[5] BURTON G R, XU C S, ARNOLD C C, et al. Photoelectron spectroscopy and zero electron kinetic energy spectroscopy of germanium cluster anions [J]. J. Chem. Phys., 1996, 104: 2757-2764.
[6] ALFORD J M, LAAKSONEN R T, SMALLEY R E. Ammonia chemisorption studies on silicon cluster ions [J]. J. Chem. Phys., 1991, 94: 2618-2630.
[7] MARSEN B, LONFAT M, SCHEIER P, et al. Energy gap of silicon clusters studied by scanning tunneling spectroscopy [J]. Phys. Rev. B, 2000, 62: 6892-6895.
[8] Ray U, Jarrold M F. Reactions of silicon cluster ions, Sin+ (n=10–65), with water [J]. J. Chem. Phys., 1991, 94: 2631-2639.
[9] BERGERON D E, CASTLEMAN JR. A W. Insights into the stability of silicon cluster ions: Reactive etching with O2 [J]. J. Chem. Phys., 2002, 117: 3219-3223.
[10] JARROLD M F, IJIRI Y, RAY U. Interaction of silicon cluster ions with ammonia: Annealing, equilibria, high temperature kinetics, and saturation studies [J]. J. Chem. Phys., 1991, 94: 3607-3618.
[11] SCH?FER R, SCHLECHT S, WOENCKHAUS J, et al. Polarizabilities of Isolated Semiconductor Clusters [J]. Phys. Rev. Lett., 1996, 76: 471- 474.
[12] 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).
[13] 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).
[14] SERDAR OGUT, CHELIKOWSKY J R. Structural changes induced upon charging Ge clusters [J]. Phys. Rev. B, 1997, 55: R4914-R4917.
[15] LI B X, CAO P L. Structures of Gen clusters (n=3–10) and comparisons to Sin clusters [J]. Phys. Rev. B, 2000, 62: 15788-15796.
[16] LU Z Y, WANG C Z, HO K M. Structures and dynamical properties of Cn, Sin, Gen, and Snn clusters with n up to 13 [J]. Phys. Rev. B, 2000, 61: 2329-2334.
[17] HUNTER J M, FYE J L, JARROLD M F, et al. Structural Transitions in Size-Selected Germanium Cluster Ions [J]. Phys. Rev. Lett., 1993, 73: 2063-2066.
[18] JARROLD M F, IJIRI Y, CONSTANT V A. Silicon cluster ions: Evidence for a structural transition [J]. Phys. Rev. Lett., 1991, 67: 2994-2997.
[19] 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.
[20] 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.
[21] MA S J, WANG G H. Structures of medium size germanium clusters [J]. Journal of Molecular Structure: THEOCHEM, 2006, 767: 75-79.
[22] LIANG F S, LI B X. Stable structures of Gen (n=21–25) clusters [J]. Phys. Lett. A , 2004, 328: 407-413.
[23] 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).
[24] YOSHIDA S, FUKE K. Photoionization studies of germanium and tin clusters inthe energy region of 5.0–8.8 eV: Ionization potentials for Gen (n = 2–57) and Snn (n = 2–41) [J]. J. Chem. Phys., 1999, 111: 3880-3890.
[25] ZHANG Q L, LIU Y, CURL R F, et al. Photodissociation of semiconductor positive cluster ions [J]. J. Chem. Phys., 1988, 88: 1670-1677.
[26] HEATH J R, LIU Y, O’BRIEN S C, et al. Semiconductor cluster beams: One and two color ionization studies of Six and Gex [J]. J. Chem. Phys., 1985, 83: 5520-5526.
[1] HEDBERG K, HEDBERG L, BULHL M, et al. Molecular Structure of Free Molecules of the Fullerene C70 from Gas-Phase Electron Diffraction [J]. J. Am. Chem. Soc., 1997, 119: 5314-5320.
[2] COMPAGNON I, ANTONIE R, BROYER M, et al. Electric polarizability of isolated C70 molecules [J]. Phys. Rev. A, 2001, 64: 025201(1-4).
[3] ZOPE R R. The static dipole polarizability of C70 fullerene [J]. J. Phys. B: At. Mol. Opt. Phys., 2007, 40: 3491-3496.
[4] PIMENOVA S M, MELKHANOVA S V, KOLESOV V P. Thermochemical determination of the enthalpies of combustion and formation of fullerene C70 [J]. J. Chem. Thermodynamics, 2003, 35: 189-193.
[5] NAGASE S, KOBAYASHI K, Si60 and Si60X (X=Ne, F? and Na+) [J]. Chem. Phys. Lett., 1991, 187: 291-294.
[6] PIQUERAS M C, CRESPO R, ORTI E, et al. AM1 prediction of the equilibrium geometry of Si60 [J]. Chem. Phys., Lett., 1993, 213: 509-513.
[7] GONG X G, ZHENG Q Q, Electronic structures and stability of Si60 and C60@Si60 clusters [J]. Phys. Rev. B, 1995, 52: 4756-4759.
[8] LESZCZYNSKI J, YANOV I. Possibility of the Existence of Non-Carbon Fullerenes: Ab Initio HF and DFT/B3LYP Studies of the IV Main Group Fullerene-Like Species [J]. J. Phys. Chem. A, 1999, 103: 396-401.
[9] KHAN F S, BROUGHTON J Q. Relaxation of icosahedral-cage silicon clusters via tight-binding molecular dynamics [J]. Phys. Rev. B, 1991, 43: 11754-11761.
[10] MENON M, SUBBASWAMY K R, Structure of Si60. Cage versus network structures [J]. Chem. Phys. Lett., 1994, 219: 219-222.
[11] Li B X, Cao P L, Que D L, Distorted icosahedral cage structure of Si60 clusters [J]. Phys. Rev. B, 2000, 61: 1685-1687.
[12] SONG J, ULLOA S E, DRABOLD D A. Exciton-induced lattice relaxation and t he electronic and vibrational spectra of silicon clusters [J]. Phys. Rev. B, 1996,53: 8042-8051.
[13] LI B X, LIU J H, ZHAN S C, Stability of Si70 cage structures [J]. Eur. Phys. J. D 2005, 32: 59-62.
[14] SUN Q, WANG Q, JENA P, et al. Stabilization of Si60 Cage Structure [J]. Phys. Rev., Lett., 2003, 90: 135503(1-4).
[15] SUN Q, WANG Q, P. JENA P, et al. Geometry and energetics of Si60 isomers [J]. Science and Technology of Advanced Materials, 2003, 4: 361-365.
[16] MA S J, WANG G H, Nonorthogonal tight-binding study of Si60 cluster [J]. Journal of Molecular Structure: THEOCHEM, 2005, 757: 47-51.
[17] ONA O, BAZTERRA V E, CAPUTO M C, et al. Modified genetic algorithms to model cluster structures in medium-sized silicon clusters: Si18-Si60 [J]. Phys. Rev. A, 2006, 73: 053203.
[18] ZHAO J J, MA L, WEN B, Lowest-energy endohedral fullerene structure of Si60 from a genetic algorithm and density-functional theory [J]. J. Phys.: Condens. Matter, 2007, 19: 226208.
[19] YOO S, SHAO N, X. ZENG C, Structures and relative stability of medium- and large-sized silicon clusters. VI. Fullerene cage motifs for low-lying clusters Si39, Si40, Si50, Si60, Si70, and Si80 [J]. J. Chem. Phys., 2008, 128: 104316(1-9).
[20] YOO S, ZHAO J J, Wang J L, et al. Endohedral Silicon Fullerenes SiN (27≤N≤39) [J]. J. Am. Chem. Soc., 2004, 126: 13845-13849.
[21] ZHAO J J, WANG J L, JELLINE J, et al. Stuffed fullerene structures for medium-sized silicon clusters [J]. Eur. Phys. J. D, 2005, 34: 35-37.
[22] WANG J L, ZHOU X L, WANG G H, et al. Optimally stuffed fullerene structures of silicon nanoclusters [J]. Phys. Rev. B, 2005, 71: 113412(1-4).
[23] YOO S, SHAO N, KOEHLER C, et al. Structures and relative stability of medium-sized silicon clusters. V. Low-lying endohedral fullerenelike clusters Si31–Si40 and Si45 [J]. J. Chem. Phys., 2006, 124: 164311(1-6).
[24] Ma L, Zhao J, Wang J, et al. Lowest-energy endohedral fullerene structures of SiN (30≤N≤39) clusters by density functional calculations [J]. Phys. Rev. A, 2006, 73: 063203-063207.
[25] ZHOU R L, PAN B C. Low-lying isomers of Sin+ and Sin– (n=31–50) clusters [J]. J. Chem. Phys., 2008, 128: 234302-234307.
[26] ( a) WANG C Z, PAN B C, HO K M. An environment-dependent tight-binding potential for Si [J]. 1999, 11: 2043-2049; (b) 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] BLOCHL P E, Projector augmented-wave method [J]. Phys. Rev. B, 1994, 50: 17953-17979.
[29] (a) KRESSE G, JOUBERT D, From ultrasoft pseudopotentials to the projector augmented-wave method [J]. Phys. Rev. B, 1999, 59: 1758-1775; (b) KRESSE G, HAFNER J, Ab initio molecular dynamics for open-shell transition metals [J]. Phys. Rev. B, 1993, 48: 13115-13118.
[30] (a) DELLEY B, An all-electron numerical method for solving the local density functional for polyatomic molecules [J]. J. Chem. Phys., 1990, 92: 508-517; (b) DELLEY B. Analytic energy derivatives in the numerical local-density-functional approach [J]. J. Chem. Phys., 1991, 94: 7245-7250.
[31] FUKE K, TSUKAMOTO K, MISAIZU F, et al. Near threshold photoionization of silicon clusters in the 248–146 nm region: Ionization potentials for Sin [J]. J. Chem. Phys., 1993, 99: 7807-7812.
[32] JARROLD M F, CONSTANT V A, Silicon cluster ions: Evidence for a structural transition [J]. Phys. Rev. Lett., 1991, 67: 2994-2997.
[33] HUDGINS R R, IMAI M, JARROLD M F, et al. High-resolution ion mobility measurements for silicon cluster anions and cations [J]. J. Chem. Phys., 1999, 111: 7865-7870.
[34] 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.
[35] (a) MESLEH M F, HUNTER J M, SHVARTSBURG A A, et al. Structural Information from Ion Mobility Measurements: Effects of the Long-RangePotential [J]. J. Phys. Chem., 1996, 100: 16082-16086; (b) 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.
[36] JARROLD M F, HONEA E C, Dissociation of large silicon clusters: the approach to bulk behavior [J]. J. Phys. Chem., 1991, 95: 9181-9185.
[37] BACHELS T, SCHAFER R, Binding energies of neutral silicon clusters [J]. Chem. Phys. Lett., 2000, 324: 365-372.
[38] LENOSKY T J, KRESS J D, KWON I, et al. Highly optimized tight-binding model of silicon [J]. Phys. Rev. B, 1997, 55: 1528-1544.
[1] FUJISHIM A A, HONDA K. Electrochemical photocatalysis of water at a semiconductor electrode [J]. Nature, 1972, 238: 37-38.
[2] UMEBAYASHI T, YAMAKI T S, TANAKA S. et al. Visible light-induced degradation of methylene blue on S-doped TiO2 [J].Chem. Lett., 2003, 32: 330–331.
[3] KHAN S U M, AL-SHAHRY M, INGLER JR. W, et al. Efficient photochemical water splitting by a chemically modified n-TiO2 [J]. Science, 2002, 297: 2243–2245.
[4] LINSEBIGLER A L, LU G Q, YATES J T, et al. Photocatalysis on TiO2. Surfaces: Principles, Mechanism and Selected Results [J]. Chem. Rev. ,1995, 95: 735–758.
[5] YAMASHITA H, HARADA M, MISAKA J, et al. Degradation of propanol diluted in water under visible light irradiation using metal ion-implanted titanium dioxide photocatalysts [J]. J. Photochem Photobiol A: Chem., 2002, 148: 257–261.
[6] ASAHI R, MORIKAWA T, OHWAKI T, et al. Visible-light photocatalysis in nitrogen-doped titanium oxides [J]. Science, 2001, 293: 269–271.
[7] WANG D F, ZOU Z H, YE J H, et al. Photocatalytic H2 evolution over a new visible-light-driven photocatalyst In12NiCr2Ti10O42 [J]. Chem. Phys. Lett., 2005, 411: 285–290.
[8] TERUHISA O, TOSHIKI T, YOUSUKE N, et al. Preparation of S, C cation-codoped SrTiO3 and its photocatalytic activity under visible light [J]. Applied Catalysis A, 2005, 288: 74–79.
[9] FRANK S N, BARD A J. Heterogenerous photocatalytic oxidation of cynide ion in aqueous solutions of titanium dioxide powder [J]. J. Am. Chem. Soc., 1977, 99: 303–305.
[10] ANGELA G R, GESAR P, NEVENKA A, et al. Interaction between E. coli inactivation and DBP-precursors—dihydroxybenzene isomers—in the photocatalytic process of drinking-water disinfection with TiO2 [J]. J. Photochem Photobiol A: Chem., 2001, 139: 233–241.
[11] STEVENSON M, BULLOCK K, LIN W Y, et al. Sonolytic enhancement of thebactericidal activity of irradiated titanium dioxide suspensions in water [J]. Res. Chem. Intermed, 1997, 23: 311–323.
[12] OSHIKIRI M, BOERO M, YE J, et al. The electronic structures of the thin films of InVO4 and TiO2 by first principles calculations [J]. Thin Solid Films, 2003, 445: 168-174.
[13] BANDURA A V, SYKES D G, SHAPOVALOV V, et al. Adsorption of Water on the TiO2 (Rutile) (110) Surface: A Comparison of Periodic and Embedded Cluster Calculations [J]. J. Phys. Chem. B, 2004, 108: 7844-7853.
[14] Wei Zhi-Gang(魏志刚), Li Qian-Shu(李前树), Zhang Hong-Xing(张红星) et al.二氧化钛(TiO2)表面上水分解反应的理论研究[J]. Chem. J. Chinese. Universities (高等学校化学学报), 2007, 28(2): 350-351.
[15] TILOCCA A, SELLONI A. Reaction pathway and free energy barrier for defect-induced water dissociation on the (101) surface of TiO2-anatase [J]. J. Chem. Phys., 2003, 119: 7445-7450.
[16] REGO L G C, BATISTA V S. Quantum Dynamics Simulations of Interfacial Electron Transfer in Sensitized TiO2 Semiconductors [J]. J. Am. Chem. Soc., 2003, 125: 7989-7997.
[17] MALLIA1 G, HARRISON N M. Magnetic moment and coupling mechanism of iron-doped rutile TiO2 from first principles [J]. Phys. Rev. B, 2007, 75: 165201(1-11).
[18] GAO G Y, YAO K L, LIU Z L, et al. Magnetism and electronic structure of Cr-doped rutile TiO2 from first-principles calculations [J]. Journal of Magnetism and Magnetic Materials, 2007, 313: 210–213.
[19] DU X S, LI Q X, SU H B, et al. Electronic and magnetic properties of V-doped anatase TiO2 from first principles [J]. Phys. Rev. B, 2006, 74: 233201(1-4).
[20] HAN Y, LIU C J, GE Q F. Interaction of Pt Clusters with the Anatase TiO2 (101) Surface: A First Principles Study [J]. J. Phys. Chem. B, 2006, 110: 7463-7472.
[21] LOCATELLI A, PABISIAK T, PAVLOVSKA A, et al. One-dimensional Au on TiO2 [J]. J. Phys.: Condens. Matter, 2007, 19: 082202(1-8).
[22] CALATAYUD M, MINOT C. Reactivity of the V2O5–TiO2-anatase catalyst: roleof the oxygen sites [J]. Topics in Catalysis, 2006, 40: 17-25.
[23] SAMBRANO J R, VASCONCELLOS L A, MARTINS J B L, et al. A theoretical analysis on electronic structure of the (110) surface of TiO2–SnO2 mixed oxide [J]. Journal of Molecular Structure: THEOCHEM, 2003, 629: 307-314.