金、铜、钇小团簇的几何结构、势能函数、能级分布和电子特性研究
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摘要
纳米材料和技术是纳米科技领域最富有活力、研究内涵十分丰富的学科分支，纳米材料在整个新材料的研究应用方面占据着核心的位置。原子团簇(cluster)是构成纳米块体、薄膜、多层膜以及纳米结构的基本单元之一，对它的基态结构、能级和电子特性的理论研究是新材料微观结构设计中的重要课题之一，对于“订做”具有特定性能的新材料意义重大。本文采用量子力学中密度泛函(DFT)B3LYP方法和相对论有效原子实模型(RECP)、应用Gaussian98W程序，对金、铜、钇小团簇的分子结构、势能函数进行了计算。在此基础上对Au_n(n=2-9)、Y_n(n=2-8)和Au_nY(n=1-9)团簇的基态结构、能级和电子性质的变化规律进行系统地研究。首次利用团簇的“软球模型”理论解释了Y_n(n=2-8)的基态结构，采用团簇的“壳层模型”和价电子离域均分理论成功地阐明了贵金属掺杂团簇Au_nY(n=1-9)的结构与稳定性的关系。
计算了Au_2、Cu_2、Y_2、AuY、AuCu、Au_3和Au_2Y团簇分子的结构。在原子分子反应静力学基础上，根据分子电子状态构造的群论原理，确定了金、铜、钇小团簇分子的基电子状态，分别为Au_2(X，~1∑_g)，AuY(X ~1∑)，Au_3(~2B_2)和Au_2Y(~2A_1)，以及它们对应的离解极跟。
导出了Au_2、Cu_2、Y_2、AuY和AuCu双原子分子的Murrell-Sorbie势能函数，在此基础上推导出光谱项常数和力常数。利用多体项展式理论方法，首次导出Au_3(~2B_2)和Au_2Y(~2A_1)三原子团簇分子的解析势能函数，并绘出了其等值势能面图。等值势能面图正确地再现了Au_3和Au_2Y平衡稳
四川大学博士学位论文
定构型与能量的关系，分别讨论了AuZ(X忱:)+Au(259)反应和AuZ(x忱g)
十Y(’Dg)反应的势能面静态特征，在这些反应通道上均无鞍点，即无能垒
出现。
采用密度泛函B3u，几ANLZDZ方法对AU、(n=2一9)团簇基态结构的稳定
性、费米能级、电离势和电子亲合能等性质进行系统地研究。结果表明:它
们均存在“奇一偶”振荡和“幻数”效应，n为偶数时团簇稳定性较高、电离
势较大、电子亲合能较小、费米能级较低;n为奇数则相反。本文对Aun(n==2一9)
团簇的电离势计算结果比经验遗传模拟法更接近实验值。小金团簇的基态结
构是平面的，s电子起支配作用，它与碱金属和其它贵金属团簇相似，从2一3
维结构的变化是从An7开始的。基态AuZ一u9团簇的平均原子化能和平均配
位数逐渐增大，团簇的稳定性也逐渐增强。AuZ和A纯特别稳定，具有“幻
数”效应，其价电子为2、8，分别刚好填满认勺od一Saxon球对称势的能级15
(2个电子);15(2个电子)、1试6个电子)。“壳层模型”认为具有封闭电子壳
层结构的团簇是稳定的，计算结果与Au团簇的质谱实验结果吻合。按
KooPmanns定理，最高占据轨道(HoMO)能级的负值代表该团簇的第一电
离能;最低空轨道(LUMO)能级在数值上与分子的电子亲合势相当;
HoMo一LuMo gaPs(HLGs)的大小反应了电子从占据轨道向空轨道发生跃迁
的能力，在一定程度上代表分子参与化学反应的能力。An团簇的HOMO能
级均为负值，团簇不易失去电子;LUMO能级为负，表明An团簇较易得到
电子;Au团簇能隙HLGs较大，化学活性较差。本文首次采用能级图把An
团簇的电子性质直观地表现出来。
首次采用密度泛函B3u印几ANLZDz方法对Yn(n=2一8)，J、团簇基态结构
的稳定性、费米能级、电离势和电子亲合能等性质进行系统地研究。结果表
明:Yn团簇最显著特点之一是上述性质不存在“奇一偶”振荡和“幻数”效
应。这与Y原子的s、p、d轨道的电子参与成键的复杂性有关。Y团簇电离
势的计算结果与Knlckelbein报告的光致电离实验光谱结果很接近，这也意味
着Y团簇的光致电离开始主要是从局域4d轨道进行的而不是55轨道。从
Y。(n=2一8)小团簇基态结构看，Y原子之间形成团簇最稳定的结构是倾向于配
位数最大，即最近邻的原子数目尽可能多。尽管Y3的基态构型是CZ，，但它
很接近于软球模型的D3，结构，除了YS外，其它基态团簇的配位数是其所对
四川大学博士学位论文
应的异构体中最大的，说明Y团簇的稳定性十分类似于惰性元素团簇的“软
球模型”结构，即主要是来源于团簇原子的密堆几何结构效应。姚一Y。的能
隙与AuZ一Aug团簇相比小得多，表明Y团簇比Au团簇的化学活性大。
在Tomasz Dur司石ewicz等人提出Y团簇电离势的计算解析式的基础上，
本文首次提出对公式加以修正，新解析式的计算结果更接近于实验值。
‘首次采用密度泛函B3u?/L ANLZDz方法对A场Y(n=1一9)小团簇基态结
构的稳定性、费米能级、电离势和电子亲合能等性质进行系统地研究。结果
表明:掺杂Y原子的混合团簇AunY与A场团簇一样，随着，n，的变化，其电
子性质出现“奇一偶”振荡和“幻数”现象。.结合实验我们研究了A场Y+(n
二1一9)团簇离子的稳定性。结果表明:(”AuZY+和Au6Y十比其它团簇离子
更稳定，计算结果与质谱实验结果一致，也与本文提出的贵金属及以贵金属
为主体的掺杂团簇适合于“壳层模型”相吻合;(2)价电子离域均分和Au一Y
键数最大效应，即团簇最稳定的异构体(基态)是趋子尽可能地均分离域的、
由组成团簇的所有原子提供的s电子和d电子(Y原子)，Y原子有最大?
The nanometer material and technology is the most alive subject branch, with very abundant research connotation in the nanometer of scientific and technological fields, and nanometer material is occupying central position in research application of the whole new material. The atomic cluster is one of the elementary cell which forms nanometer body, membrane, multilevel membrane and nanometer structure, so the theoretical research for ground-state structures, energy level distribution and electronic properties of its is one of the important subject in the design of micro structure of new material, and has great signification in "custom-made" new material with specific performance. In mis paper, the molecular structure and potential energy function of small cluster of gold, copper and yttrium have been calculated by use of the density function theory (DFT) Becke 3LYP method with relativistic effective core potential (RECP) and Gaussian98W program. On this basis, the ground-state structure, energy level distribution and the electronic properties of cluster of An, ( n=2-9), Yn (n=2-8), and AunY( n=l-9) are researched systematically. It is the first time to use the " soft ball model" theory of duster to explain the structure of Yn ( n=2-8) ,and adopt the "shell model" theory and assigning equally delocalize valence electrons of cluster to elucidate the relativity of structure and stability of doped cluster of noble metal Au,,Y(l -9) successfully.The cluster molecules structures for Au2 Cu2 Y2 AuY AuCu Au and Au Y are calculated At the base of the atomic and molecular reaction statics, according to the group
theory principle of electron state construction of molecule, the electronic state of the small cluster molecule gold, copper and yttrium are determined. Results show that tire ground electronic states for Au2, AuY, Au3 and Au2Y are X , and respectively, and the corresponding reasonable dissociation limits.The Murrell-Sorbie potential energy function curves of diatomic molecule of Au2 Cu2 Y2 AuY and AuCu have been obtained, then the spectral datum and force constants have been derived.. The analytic potential energy functions for ground states of Au (X2 B 2) and Au2 Y (X2A1) molecules are derived by many-boy expansion method, then their equivalence potential energy curves are drawn, which show the stable structure characteristics and energy relation of Au3and Au2 Y, and discuss the static characteristic of potential energy sections of Au2 (X ) +Au and Au2 (X ) +Y (2Dg) , There is no saddle point on these reaction channels, namely no energy threshold appears.It's the first time to use the B3LYP/LANL2DZ method of density function theory to research the stability of the ground state structure of cluster Au,, (n=2-9) Y n (n=2-8) and Aun Y (n=l-9), the Fermi level, ionization potentials and electron affinities and so on, systematically.The research result of cluster An, (n=2-9) indicate that the "odd-even" alternations and "magic numbers" effect exist in all of them, the Aun, cluster demonstrates: higher stability and ionization potentials, lower electron affinities and the Fermi levels while n is even number; or vice versa while n is odd. The ionization potentials are calculated of cluster Au,, (n=2-9) with this method and the results are more reasonable agreement with the experiment than the experiential genetic simulation method. The ground-state structure of the gold micro-clusters are planar, and electron s plays a controlling role, it is similar to alkali metal and other noble metal cluster, the change of 2-3D structure is from AU7. In the aspect of stability of cluster, the general trend of average atomization energies of ground-states from cluster Au2 to Au9 increases monotonically, so does average coordination number, the stability from cluster Au2 to Au9 strengthens gradually, and Au2 and Au8 are especially steady, all of these can be well explained by the "shell model", the valence electron of Au2 and Au8 are 2,8, just fill-up the levels of the Wood-Saxon spherical symmetrical potential, that is,ls(2elec
计算了Au_2、Cu_2、Y_2、AuY、AuCu、Au_3和Au_2Y团簇分子的结构。在原子分子反应静力学基础上，根据分子电子状态构造的群论原理，确定了金、铜、钇小团簇分子的基电子状态，分别为Au_2(X，~1∑_g)，AuY(X ~1∑)，Au_3(~2B_2)和Au_2Y(~2A_1)，以及它们对应的离解极跟。
导出了Au_2、Cu_2、Y_2、AuY和AuCu双原子分子的Murrell-Sorbie势能函数，在此基础上推导出光谱项常数和力常数。利用多体项展式理论方法，首次导出Au_3(~2B_2)和Au_2Y(~2A_1)三原子团簇分子的解析势能函数，并绘出了其等值势能面图。等值势能面图正确地再现了Au_3和Au_2Y平衡稳
四川大学博士学位论文
定构型与能量的关系，分别讨论了AuZ(X忱:)+Au(259)反应和AuZ(x忱g)
十Y(’Dg)反应的势能面静态特征，在这些反应通道上均无鞍点，即无能垒
出现。
采用密度泛函B3u，几ANLZDZ方法对AU、(n=2一9)团簇基态结构的稳定
性、费米能级、电离势和电子亲合能等性质进行系统地研究。结果表明:它
们均存在“奇一偶”振荡和“幻数”效应，n为偶数时团簇稳定性较高、电离
势较大、电子亲合能较小、费米能级较低;n为奇数则相反。本文对Aun(n==2一9)
团簇的电离势计算结果比经验遗传模拟法更接近实验值。小金团簇的基态结
构是平面的，s电子起支配作用，它与碱金属和其它贵金属团簇相似，从2一3
维结构的变化是从An7开始的。基态AuZ一u9团簇的平均原子化能和平均配
位数逐渐增大，团簇的稳定性也逐渐增强。AuZ和A纯特别稳定，具有“幻
数”效应，其价电子为2、8，分别刚好填满认勺od一Saxon球对称势的能级15
(2个电子);15(2个电子)、1试6个电子)。“壳层模型”认为具有封闭电子壳
层结构的团簇是稳定的，计算结果与Au团簇的质谱实验结果吻合。按
KooPmanns定理，最高占据轨道(HoMO)能级的负值代表该团簇的第一电
离能;最低空轨道(LUMO)能级在数值上与分子的电子亲合势相当;
HoMo一LuMo gaPs(HLGs)的大小反应了电子从占据轨道向空轨道发生跃迁
的能力，在一定程度上代表分子参与化学反应的能力。An团簇的HOMO能
级均为负值，团簇不易失去电子;LUMO能级为负，表明An团簇较易得到
电子;Au团簇能隙HLGs较大，化学活性较差。本文首次采用能级图把An
团簇的电子性质直观地表现出来。
首次采用密度泛函B3u印几ANLZDz方法对Yn(n=2一8)，J、团簇基态结构
的稳定性、费米能级、电离势和电子亲合能等性质进行系统地研究。结果表
明:Yn团簇最显著特点之一是上述性质不存在“奇一偶”振荡和“幻数”效
应。这与Y原子的s、p、d轨道的电子参与成键的复杂性有关。Y团簇电离
势的计算结果与Knlckelbein报告的光致电离实验光谱结果很接近，这也意味
着Y团簇的光致电离开始主要是从局域4d轨道进行的而不是55轨道。从
Y。(n=2一8)小团簇基态结构看，Y原子之间形成团簇最稳定的结构是倾向于配
位数最大，即最近邻的原子数目尽可能多。尽管Y3的基态构型是CZ，，但它
很接近于软球模型的D3，结构，除了YS外，其它基态团簇的配位数是其所对
四川大学博士学位论文
应的异构体中最大的，说明Y团簇的稳定性十分类似于惰性元素团簇的“软
球模型”结构，即主要是来源于团簇原子的密堆几何结构效应。姚一Y。的能
隙与AuZ一Aug团簇相比小得多，表明Y团簇比Au团簇的化学活性大。
在Tomasz Dur司石ewicz等人提出Y团簇电离势的计算解析式的基础上，
本文首次提出对公式加以修正，新解析式的计算结果更接近于实验值。
‘首次采用密度泛函B3u?/L ANLZDz方法对A场Y(n=1一9)小团簇基态结
构的稳定性、费米能级、电离势和电子亲合能等性质进行系统地研究。结果
表明:掺杂Y原子的混合团簇AunY与A场团簇一样，随着，n，的变化，其电
子性质出现“奇一偶”振荡和“幻数”现象。.结合实验我们研究了A场Y+(n
二1一9)团簇离子的稳定性。结果表明:(”AuZY+和Au6Y十比其它团簇离子
更稳定，计算结果与质谱实验结果一致，也与本文提出的贵金属及以贵金属
为主体的掺杂团簇适合于“壳层模型”相吻合;(2)价电子离域均分和Au一Y
键数最大效应，即团簇最稳定的异构体(基态)是趋子尽可能地均分离域的、
由组成团簇的所有原子提供的s电子和d电子(Y原子)，Y原子有最大?
The nanometer material and technology is the most alive subject branch, with very abundant research connotation in the nanometer of scientific and technological fields, and nanometer material is occupying central position in research application of the whole new material. The atomic cluster is one of the elementary cell which forms nanometer body, membrane, multilevel membrane and nanometer structure, so the theoretical research for ground-state structures, energy level distribution and electronic properties of its is one of the important subject in the design of micro structure of new material, and has great signification in "custom-made" new material with specific performance. In mis paper, the molecular structure and potential energy function of small cluster of gold, copper and yttrium have been calculated by use of the density function theory (DFT) Becke 3LYP method with relativistic effective core potential (RECP) and Gaussian98W program. On this basis, the ground-state structure, energy level distribution and the electronic properties of cluster of An, ( n=2-9), Yn (n=2-8), and AunY( n=l-9) are researched systematically. It is the first time to use the " soft ball model" theory of duster to explain the structure of Yn ( n=2-8) ,and adopt the "shell model" theory and assigning equally delocalize valence electrons of cluster to elucidate the relativity of structure and stability of doped cluster of noble metal Au,,Y(l -9) successfully.The cluster molecules structures for Au2 Cu2 Y2 AuY AuCu Au and Au Y are calculated At the base of the atomic and molecular reaction statics, according to the group
theory principle of electron state construction of molecule, the electronic state of the small cluster molecule gold, copper and yttrium are determined. Results show that tire ground electronic states for Au2, AuY, Au3 and Au2Y are X , and respectively, and the corresponding reasonable dissociation limits.The Murrell-Sorbie potential energy function curves of diatomic molecule of Au2 Cu2 Y2 AuY and AuCu have been obtained, then the spectral datum and force constants have been derived.. The analytic potential energy functions for ground states of Au (X2 B 2) and Au2 Y (X2A1) molecules are derived by many-boy expansion method, then their equivalence potential energy curves are drawn, which show the stable structure characteristics and energy relation of Au3and Au2 Y, and discuss the static characteristic of potential energy sections of Au2 (X ) +Au and Au2 (X ) +Y (2Dg) , There is no saddle point on these reaction channels, namely no energy threshold appears.It's the first time to use the B3LYP/LANL2DZ method of density function theory to research the stability of the ground state structure of cluster Au,, (n=2-9) Y n (n=2-8) and Aun Y (n=l-9), the Fermi level, ionization potentials and electron affinities and so on, systematically.The research result of cluster An, (n=2-9) indicate that the "odd-even" alternations and "magic numbers" effect exist in all of them, the Aun, cluster demonstrates: higher stability and ionization potentials, lower electron affinities and the Fermi levels while n is even number; or vice versa while n is odd. The ionization potentials are calculated of cluster Au,, (n=2-9) with this method and the results are more reasonable agreement with the experiment than the experiential genetic simulation method. The ground-state structure of the gold micro-clusters are planar, and electron s plays a controlling role, it is similar to alkali metal and other noble metal cluster, the change of 2-3D structure is from AU7. In the aspect of stability of cluster, the general trend of average atomization energies of ground-states from cluster Au2 to Au9 increases monotonically, so does average coordination number, the stability from cluster Au2 to Au9 strengthens gradually, and Au2 and Au8 are especially steady, all of these can be well explained by the "shell model", the valence electron of Au2 and Au8 are 2,8, just fill-up the levels of the Wood-Saxon spherical symmetrical potential, that is,ls(2elec
引文
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