密度泛函方法研究银团簇与原子的相互作用
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摘要
金属团簇和纳米粒子具有优良的催化性能，其催化性能呈现显著的量子尺寸效应。由于电子计算机技术的飞速发展和各种高效率方法的出现，使得第一性原理的理论计算在材料模拟、对实验结果的理解和预测中发挥了日益广泛的作用。由于纳米催化材料的量子尺寸效应是由其电子结构对粒子尺寸的依赖性引起的，因此从理论上研究这一依赖关系，就可以从本质上理解并预测团簇和纳米粒子的量子尺寸效应，从而可以指导实验对催化体系进行性能的修剪和功能的合成，从而为设计高活性，高选择性的催化剂开辟一条新路。
基态银原子具有饱和的内层d电子(4d~(10))和1个价电子(5s~1)的电子构型，与碱金属壳层结构类似，因此被看作“类碱”金属。与大块固体不同，量子尺寸下的银原子簇有着与固体银截然不同的物理和化学性质。有实验表明在催化反应中的Ag活性位可能只包含几个银原子。近年来，原子、小分子与银原子簇的相互作用也引起理论和实验科学家们越来越浓厚的兴趣，O_2、CO、H和卤素原子等在银原子簇上的吸附研究在实验和理论方面都有所报道。本实验室早在1979年就开始研究和应用电解银催化甲醇部分氧化制甲醛的反应，并进行了大量的表面修饰研究以更好地提高反应的活性和选择性，同时采用扫描隧道显微镜[STM]、低能电子衍射谱[LEED]和X-射线光电子能谱[XPS]等现代技术，从而使以上研究不断向分子水平深入。另一方面，本实验室通过量化计算，应用原子簇近似模型模拟研究了银表面碘修饰，氧修饰以及点电荷修饰的三种修饰作用。并采用赝势平面波方法和超元胞模型，围绕表面修饰剂氯和碘的修饰作用机理也进行了理论计算。而本论文则在前人工作的基础上，通过对23种密度泛函方法计算银原子簇体系的结果评估，从中选取一种较为适合该体系的泛函，采用原子簇模型系统研究了银原子簇与原子，小分子相互作用中的量子尺寸效应。
密度泛函方法(DFT)是最近几年兴起的第三类电子结构理论方法。它采用泛函(以密度函数为变量的函数)对薛定谔方程进行求解，由于密度泛函包涵了电子相关，它的计算结果要比HF方法好，计算速度也快，因此在近年来得到迅速发展和广泛的应用。密度泛函方法的可靠性是基于交换-相关能E_(xc)[ρ]的计算。由于构造计算E_(xc)[ρ]的不同，针对特定的体系DFT方法有可能表现出某些优越性或局限性，衡量标准总是将其计算结果与实验值或高精度方法相比较。目前的评估工作主要集中在密度泛函方法对有机小分子的计算上，对含有过渡金属原子体系的评估工作往往只包括3d和4d的过渡金属。对于更重的过渡金属原子，由于计算成本过高，用新的密度泛函方法进行评估的研究十分缺乏。然而在这种含有重金属原子的体系中，采用的现有密度泛函方法能否给出可靠的结构和能量性质是至关重要的。
因此，在对银原子簇这个体系进行计算之前，选取一种合适的密度泛函方法是十分关键的。本文采用了包括GGA方法和杂化方法在内的一共23种密度泛函，用于计算含四个原子之内Ag_n(n≤4)的中性和带电荷的银原子簇。计算包括银原子簇的结构，振动频率，垂直和绝热电离能(VIP and AIP)，VDE(vertical detachment energies)，并与实验值和高精度从头算方法的计算结果做了对比，从而检验不同泛函计算结果的可靠性。
计算结果表明23种DFT方法根据其相关泛函的不同可以被划分为两组。第一组共13种泛函，包括P86，B95，PW91，PBE和TPSS等，它们在相关能计算上均满足均一电子气限定。而另一组共10种泛函，多为B97系列泛函的变种或含有LYP相关泛函。第一组方法在计算Ag_3和Ag_4~-的结构时得到与高精度方法相吻合的结果，能量性质的计算也与实验结果吻合的很好。第二组方法在结构计算上不能给出与高精度方法一致的优化结果，能量性质方面的计算结果实验值差别很大。综合比较第一组中的13种方法，发现PW91PW91在计算能量性质时给出较精确的结果。因此，我们选取PW91PW91方法，进行了以下方面的计算：
1．纯银团簇的结构和性质：研究金属团簇和纳米催化剂中的量子尺寸效应，首先的一点就是要确定这些团簇和纳米粒子的结构。理论计算方面也已经有大量的文献报道了自由Ag原子构成的原子簇和纳米粒子的几何结构，物理性质和电子结构性质。本文优化了含2到7个Ag原子的中性与带正，负电荷的银原子簇的平衡几何构型，用频率分析以确保所得的为稳定结构，得到的最稳定构型与文献报道过的基本一致。计算所得的电离能和电子亲和势与实验值也有较好吻合。
2．银原子簇和卤族原子的相互作用：使用密度泛函中的PW91PW91方法研究卤族原子在中性和带有电荷的银原子簇Ag_n~(0，±1)(n=2-7)上的吸附情况。采用密度泛函理论计算方法研究了气相中的单个的F，Cl，Br，I原子吸附在中性和带正，负电荷的银原子团簇上的平衡几何构型Ag_nX~(0，±1)(X=F，Cl，Br，I)，确定了吸附能，电荷转移量以及碎片化模式。结果表明卤族原子在银原子簇上的吸附得到相似的最稳定几何构型，且具有相似的吸附性质。含奇数个电子的银原子簇的吸附能要大于相邻含偶数个电子的银原子簇。卤族原子在中性银原子簇上吸附时，多倾向于桥位吸附。在负电银簇上吸附时，端位吸附是最稳定的。在正电簇上的吸附可以得到稳定的桥位和面位吸附产物。吸附能和电子转移量的大小顺序为F＞Cl＞Br＞I，与电负性顺序相一致。
3．银原子簇和氢原子的相互作用：使用PW91PW91方法研究了中性和带正，负电荷的Ag_nH~(0，±1)和带负电荷的HAg_nH~-(n=1-7)。我们发现最稳定的Ag_nH~(0，±1)复合物不一定是由氢原子吸附在最稳定的银团簇上得到的。对带正电荷和大多数中性的团簇，在各种可能的吸附构型中，桥位吸附是最稳定的。对带负电的银原子簇Ag_n~-，在n≤4时，端位吸附是最稳定的。当n＞4时，桥位吸附是最稳定的。在负离子上吸附上第二个氢原子后，生成最稳定的HAg_nH~-复合物都是由两个H原子吸附在同一个银原子上的结构。自然键轨道分析表明电子总是由银原子转移至被吸附氢原子上。吸附能曲线存在明显的奇偶振荡性质。
Metal clusters and nanoparticles often have excellent catalytic activities and their catalytic properties are very sensitive to the number of atoms in the clusters. Due to the rapid development of the computational techniques and various high-efficiency methods, the first-principle calculation studies play more and more important role in materials simulation and explanation of experimental phenomenon. The quantum size effects of the clusters are depended on the relations between the electronic structures and cluster sizes, thus the theoretical studies of the relations can help to understand and predict the size effects of clusters and nanoparticles.
The ground state of Ag atom has a closed Ad shell and a single s valence electron, hence it could be seen as 'alkali-like' metals. Small silver clusters usually have very different physical and chemical properties from silver bulk material. There are experiments have proved that the active sites in Ag catalysis are only composed of only few Ag atoms. In recent years, atomic and molecular chemisorption on small silver clusters in the gas phase has been an active field of experimental and theoretical research. Both experimental and theoretical studies on the binding of oxygen, carbon-monoxide and hydrogen on Ag clusters have also appeared. Our groups have done lots of researches on the partial oxidation of methanol to formaldehyde on silver surface, and studied the modification on metal surface by using situ scanning tunneling microscopy (STM), low-energy electron diffraction (LEED) and X-ray photoelectron Spectroscopy (XPS). From the experimental results, the introduction of halogen atoms will enchance the reactivity and the selectivity of the oxidation of methanol. Three kinds of Ag(110) surface modification (chemisorption of halogen atoms, pre-adsorption of oxygen and electrochemical modification) and their effects to adsorption of methanol on the Ag(110) surface have also been investigated by theoretical calculations. So based on the previous work, in this thesis, the bindings of atoms on neutral and charged silver clusters are extensively studied by means of Density Functional Theory (DFT) , with cluster model approximation.
To date, the Density Functional Theory (DFT) is a practical method to study the metallic systems, which has been rapidly developed recently. The reliability DFT methods is governed by the quality of the approximate exchange-correlation (XC) energy functional E_(xc)[ρ]. In the last decade, a number of new functionals have been suggested, often by forcing the required DFT characteristics to match experimental or high-level ab initio results. Considering the large number of DFT functionals available today, it is quite important that the applicability and accuracy of functionals must be documented, so they can be applied appropriately to electronic structure problems. Compared with the assessment of DFT functionals for organic systems, the assessment of DFT methods on the systems containing transition and coinage metal atoms seems to manifest a more complex picture. Many of these studies involve no more than two atoms of the 3d and Ad transition-metals, comparative studies of new functionals for larger transition metal clusters are still lacking due to the high computational demands. For such systems, reliable predictions of the structures and energies are of paramount importance.
In the present work, as silver clusters are chosen as the model systems, we first tested 23 DFT functionals, including both GGA and hybrid, are adopted in our work on the neutral and ionic Ag_n (n≤4) clusters. The reliability of these functionals is evaluated by comparing predicted DFT equilibrium geometries, vibrational frequencies, vertical and adiabatic ionization potentials (VIP and AIP), and vertical detachment energies (VDE) with available experimental data or high-level ab initio results.
We find that DFT methods incorporating the uniform electron gas limit in the correlation functional part, namely those with Perdew's correlation functionals (PW91, PBE, P86, TPSS), Becke's B95, and the Van Voorhis-Scuseria functional VSXC, generally perform better than the other group of functionals, e.g. those incorporating the LYP correlation functional and variations of the B97 functional. Strikingly, these two groups of functionals can produce qualitatively different results for the Ag_3 and Ag_4 clusters. The energetic properties and vibrational frequencies of Ag_n are also evaluated by the different functionals. The present study shows that the choice of DFT methods for heavy metals may be critical. It is found that the PW91PW91 functional has some advantages for predicting the range of properties. So we chose the PW91PW91 functional to study the following three parts:
1, the structures and the properties of bare silver clusters: a number of DFT investigations of the geometries, physical properties and electronic structures of small neutral and charged silver clusters are already available in the literatures. In this work, for each cluster size and charge state, several initial structures of Ag_n,~(0,±1) (n = 2～7) have been optimized. Our calculated low-energy structures of both the neutral and the charged clusters are in general consistent to the published literatures. The comparison of our calculations (the ionization potential (IP) and electron affinity (EA) for silver clusters) with experiments shows that PW91PW91 functional give satisfactory results.
2, the binding of fluorine, chlorine, bromine, or iodine atom binding to small neutral, anionic, or cationic silver clusters Ag_n,~(0,±1) (n = 2～7) has been studied by using the PW91PW91 density functional method. It was found that the binding of halogen atoms on the lowest-energy bare clusters does not always produce the lowest-energy complexes. In addition, the binding of halogen can greatly change the geometries of the silver clusters in some cases. The most stable structures of complexes, Ag_nX~(0,±1) (X=F, C(?), Br, I) often have similar structures and binding patterns. Among various possible adsorption sites, bridge site is energetically preferred for the neutral Ag_n while top site is energetically more preferred for the anionic Ag_n with n≤6. For cationic clusters, adsorptions on bridge and face sites have similar binding energies, which are much larger than those on top sites. Natural bond orbital analyses show that irrespective of charge state, electrons always transfer from silver atoms to adsorbate and silver acts like alkali metals in the interaction with halogen atom. It was also found that halogen atoms bind more strongly with odd-electron bare clusters than with even-electron bare clusters. These patterns reveal that even-electron clusters are more stable than odd-electron clusters. The binding energy and electron transfer ability are in the order: F>Cl>Br>I, which is consistent to the electronegativity order.
3, small neutral, anionic, and cationic silver cluster hydrides Ag_nH and anionic HAg_nH (n = 1 - 7) have been studied using the PW91PW91 density functional method. It was found that the most stable structure of the Ag_nH complex (neutral or charged) does not always come from that of the lowest-energy bare silver cluster plus an attached H atom. Among various possible adsorption sites, bridge site is energetically preferred for the cationic and most cases of neutral Ag_n. For anionic Ag_n~-, the top site is preferred for smaller Ag_n within n≤4 while bridge site is preferred for bigger clusters. After binding the second H atom, the obtained lowest energy structures HAg_nH~- are those with two H atoms shared with only one Ag atom in anionic clusters. Natural bond orbital analysis shows that irrespective of charge state, electrons always transfer from silver atoms to adsorbate. Significant odd-even alternation patterns that hydrogen atoms bind more strongly with odd-electron bare clusters than that with even-electron bare clusters can be observed.
基态银原子具有饱和的内层d电子(4d~(10))和1个价电子(5s~1)的电子构型，与碱金属壳层结构类似，因此被看作“类碱”金属。与大块固体不同，量子尺寸下的银原子簇有着与固体银截然不同的物理和化学性质。有实验表明在催化反应中的Ag活性位可能只包含几个银原子。近年来，原子、小分子与银原子簇的相互作用也引起理论和实验科学家们越来越浓厚的兴趣，O_2、CO、H和卤素原子等在银原子簇上的吸附研究在实验和理论方面都有所报道。本实验室早在1979年就开始研究和应用电解银催化甲醇部分氧化制甲醛的反应，并进行了大量的表面修饰研究以更好地提高反应的活性和选择性，同时采用扫描隧道显微镜[STM]、低能电子衍射谱[LEED]和X-射线光电子能谱[XPS]等现代技术，从而使以上研究不断向分子水平深入。另一方面，本实验室通过量化计算，应用原子簇近似模型模拟研究了银表面碘修饰，氧修饰以及点电荷修饰的三种修饰作用。并采用赝势平面波方法和超元胞模型，围绕表面修饰剂氯和碘的修饰作用机理也进行了理论计算。而本论文则在前人工作的基础上，通过对23种密度泛函方法计算银原子簇体系的结果评估，从中选取一种较为适合该体系的泛函，采用原子簇模型系统研究了银原子簇与原子，小分子相互作用中的量子尺寸效应。
密度泛函方法(DFT)是最近几年兴起的第三类电子结构理论方法。它采用泛函(以密度函数为变量的函数)对薛定谔方程进行求解，由于密度泛函包涵了电子相关，它的计算结果要比HF方法好，计算速度也快，因此在近年来得到迅速发展和广泛的应用。密度泛函方法的可靠性是基于交换-相关能E_(xc)[ρ]的计算。由于构造计算E_(xc)[ρ]的不同，针对特定的体系DFT方法有可能表现出某些优越性或局限性，衡量标准总是将其计算结果与实验值或高精度方法相比较。目前的评估工作主要集中在密度泛函方法对有机小分子的计算上，对含有过渡金属原子体系的评估工作往往只包括3d和4d的过渡金属。对于更重的过渡金属原子，由于计算成本过高，用新的密度泛函方法进行评估的研究十分缺乏。然而在这种含有重金属原子的体系中，采用的现有密度泛函方法能否给出可靠的结构和能量性质是至关重要的。
因此，在对银原子簇这个体系进行计算之前，选取一种合适的密度泛函方法是十分关键的。本文采用了包括GGA方法和杂化方法在内的一共23种密度泛函，用于计算含四个原子之内Ag_n(n≤4)的中性和带电荷的银原子簇。计算包括银原子簇的结构，振动频率，垂直和绝热电离能(VIP and AIP)，VDE(vertical detachment energies)，并与实验值和高精度从头算方法的计算结果做了对比，从而检验不同泛函计算结果的可靠性。
计算结果表明23种DFT方法根据其相关泛函的不同可以被划分为两组。第一组共13种泛函，包括P86，B95，PW91，PBE和TPSS等，它们在相关能计算上均满足均一电子气限定。而另一组共10种泛函，多为B97系列泛函的变种或含有LYP相关泛函。第一组方法在计算Ag_3和Ag_4~-的结构时得到与高精度方法相吻合的结果，能量性质的计算也与实验结果吻合的很好。第二组方法在结构计算上不能给出与高精度方法一致的优化结果，能量性质方面的计算结果实验值差别很大。综合比较第一组中的13种方法，发现PW91PW91在计算能量性质时给出较精确的结果。因此，我们选取PW91PW91方法，进行了以下方面的计算：
1．纯银团簇的结构和性质：研究金属团簇和纳米催化剂中的量子尺寸效应，首先的一点就是要确定这些团簇和纳米粒子的结构。理论计算方面也已经有大量的文献报道了自由Ag原子构成的原子簇和纳米粒子的几何结构，物理性质和电子结构性质。本文优化了含2到7个Ag原子的中性与带正，负电荷的银原子簇的平衡几何构型，用频率分析以确保所得的为稳定结构，得到的最稳定构型与文献报道过的基本一致。计算所得的电离能和电子亲和势与实验值也有较好吻合。
2．银原子簇和卤族原子的相互作用：使用密度泛函中的PW91PW91方法研究卤族原子在中性和带有电荷的银原子簇Ag_n~(0，±1)(n=2-7)上的吸附情况。采用密度泛函理论计算方法研究了气相中的单个的F，Cl，Br，I原子吸附在中性和带正，负电荷的银原子团簇上的平衡几何构型Ag_nX~(0，±1)(X=F，Cl，Br，I)，确定了吸附能，电荷转移量以及碎片化模式。结果表明卤族原子在银原子簇上的吸附得到相似的最稳定几何构型，且具有相似的吸附性质。含奇数个电子的银原子簇的吸附能要大于相邻含偶数个电子的银原子簇。卤族原子在中性银原子簇上吸附时，多倾向于桥位吸附。在负电银簇上吸附时，端位吸附是最稳定的。在正电簇上的吸附可以得到稳定的桥位和面位吸附产物。吸附能和电子转移量的大小顺序为F＞Cl＞Br＞I，与电负性顺序相一致。
3．银原子簇和氢原子的相互作用：使用PW91PW91方法研究了中性和带正，负电荷的Ag_nH~(0，±1)和带负电荷的HAg_nH~-(n=1-7)。我们发现最稳定的Ag_nH~(0，±1)复合物不一定是由氢原子吸附在最稳定的银团簇上得到的。对带正电荷和大多数中性的团簇，在各种可能的吸附构型中，桥位吸附是最稳定的。对带负电的银原子簇Ag_n~-，在n≤4时，端位吸附是最稳定的。当n＞4时，桥位吸附是最稳定的。在负离子上吸附上第二个氢原子后，生成最稳定的HAg_nH~-复合物都是由两个H原子吸附在同一个银原子上的结构。自然键轨道分析表明电子总是由银原子转移至被吸附氢原子上。吸附能曲线存在明显的奇偶振荡性质。
Metal clusters and nanoparticles often have excellent catalytic activities and their catalytic properties are very sensitive to the number of atoms in the clusters. Due to the rapid development of the computational techniques and various high-efficiency methods, the first-principle calculation studies play more and more important role in materials simulation and explanation of experimental phenomenon. The quantum size effects of the clusters are depended on the relations between the electronic structures and cluster sizes, thus the theoretical studies of the relations can help to understand and predict the size effects of clusters and nanoparticles.
The ground state of Ag atom has a closed Ad shell and a single s valence electron, hence it could be seen as 'alkali-like' metals. Small silver clusters usually have very different physical and chemical properties from silver bulk material. There are experiments have proved that the active sites in Ag catalysis are only composed of only few Ag atoms. In recent years, atomic and molecular chemisorption on small silver clusters in the gas phase has been an active field of experimental and theoretical research. Both experimental and theoretical studies on the binding of oxygen, carbon-monoxide and hydrogen on Ag clusters have also appeared. Our groups have done lots of researches on the partial oxidation of methanol to formaldehyde on silver surface, and studied the modification on metal surface by using situ scanning tunneling microscopy (STM), low-energy electron diffraction (LEED) and X-ray photoelectron Spectroscopy (XPS). From the experimental results, the introduction of halogen atoms will enchance the reactivity and the selectivity of the oxidation of methanol. Three kinds of Ag(110) surface modification (chemisorption of halogen atoms, pre-adsorption of oxygen and electrochemical modification) and their effects to adsorption of methanol on the Ag(110) surface have also been investigated by theoretical calculations. So based on the previous work, in this thesis, the bindings of atoms on neutral and charged silver clusters are extensively studied by means of Density Functional Theory (DFT) , with cluster model approximation.
To date, the Density Functional Theory (DFT) is a practical method to study the metallic systems, which has been rapidly developed recently. The reliability DFT methods is governed by the quality of the approximate exchange-correlation (XC) energy functional E_(xc)[ρ]. In the last decade, a number of new functionals have been suggested, often by forcing the required DFT characteristics to match experimental or high-level ab initio results. Considering the large number of DFT functionals available today, it is quite important that the applicability and accuracy of functionals must be documented, so they can be applied appropriately to electronic structure problems. Compared with the assessment of DFT functionals for organic systems, the assessment of DFT methods on the systems containing transition and coinage metal atoms seems to manifest a more complex picture. Many of these studies involve no more than two atoms of the 3d and Ad transition-metals, comparative studies of new functionals for larger transition metal clusters are still lacking due to the high computational demands. For such systems, reliable predictions of the structures and energies are of paramount importance.
In the present work, as silver clusters are chosen as the model systems, we first tested 23 DFT functionals, including both GGA and hybrid, are adopted in our work on the neutral and ionic Ag_n (n≤4) clusters. The reliability of these functionals is evaluated by comparing predicted DFT equilibrium geometries, vibrational frequencies, vertical and adiabatic ionization potentials (VIP and AIP), and vertical detachment energies (VDE) with available experimental data or high-level ab initio results.
We find that DFT methods incorporating the uniform electron gas limit in the correlation functional part, namely those with Perdew's correlation functionals (PW91, PBE, P86, TPSS), Becke's B95, and the Van Voorhis-Scuseria functional VSXC, generally perform better than the other group of functionals, e.g. those incorporating the LYP correlation functional and variations of the B97 functional. Strikingly, these two groups of functionals can produce qualitatively different results for the Ag_3 and Ag_4 clusters. The energetic properties and vibrational frequencies of Ag_n are also evaluated by the different functionals. The present study shows that the choice of DFT methods for heavy metals may be critical. It is found that the PW91PW91 functional has some advantages for predicting the range of properties. So we chose the PW91PW91 functional to study the following three parts:
1, the structures and the properties of bare silver clusters: a number of DFT investigations of the geometries, physical properties and electronic structures of small neutral and charged silver clusters are already available in the literatures. In this work, for each cluster size and charge state, several initial structures of Ag_n,~(0,±1) (n = 2～7) have been optimized. Our calculated low-energy structures of both the neutral and the charged clusters are in general consistent to the published literatures. The comparison of our calculations (the ionization potential (IP) and electron affinity (EA) for silver clusters) with experiments shows that PW91PW91 functional give satisfactory results.
2, the binding of fluorine, chlorine, bromine, or iodine atom binding to small neutral, anionic, or cationic silver clusters Ag_n,~(0,±1) (n = 2～7) has been studied by using the PW91PW91 density functional method. It was found that the binding of halogen atoms on the lowest-energy bare clusters does not always produce the lowest-energy complexes. In addition, the binding of halogen can greatly change the geometries of the silver clusters in some cases. The most stable structures of complexes, Ag_nX~(0,±1) (X=F, C(?), Br, I) often have similar structures and binding patterns. Among various possible adsorption sites, bridge site is energetically preferred for the neutral Ag_n while top site is energetically more preferred for the anionic Ag_n with n≤6. For cationic clusters, adsorptions on bridge and face sites have similar binding energies, which are much larger than those on top sites. Natural bond orbital analyses show that irrespective of charge state, electrons always transfer from silver atoms to adsorbate and silver acts like alkali metals in the interaction with halogen atom. It was also found that halogen atoms bind more strongly with odd-electron bare clusters than with even-electron bare clusters. These patterns reveal that even-electron clusters are more stable than odd-electron clusters. The binding energy and electron transfer ability are in the order: F>Cl>Br>I, which is consistent to the electronegativity order.
3, small neutral, anionic, and cationic silver cluster hydrides Ag_nH and anionic HAg_nH (n = 1 - 7) have been studied using the PW91PW91 density functional method. It was found that the most stable structure of the Ag_nH complex (neutral or charged) does not always come from that of the lowest-energy bare silver cluster plus an attached H atom. Among various possible adsorption sites, bridge site is energetically preferred for the cationic and most cases of neutral Ag_n. For anionic Ag_n~-, the top site is preferred for smaller Ag_n within n≤4 while bridge site is preferred for bigger clusters. After binding the second H atom, the obtained lowest energy structures HAg_nH~- are those with two H atoms shared with only one Ag atom in anionic clusters. Natural bond orbital analysis shows that irrespective of charge state, electrons always transfer from silver atoms to adsorbate. Significant odd-even alternation patterns that hydrogen atoms bind more strongly with odd-electron bare clusters than that with even-electron bare clusters can be observed.
引文
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