双金属团簇磁性与氢化的理论研究
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摘要
随着计算方法和计算机技术的飞速发展,计算物理在物理研究中已经占有越来越重要的地位。基于密度泛函理论的第一性原理方法,由于计算量适中、计算精度较高,成为了凝聚态物理、量子化学和材料科学在当前计算中最常用的研究手段。本文利用第一性原理的计算方法研究了铝原子掺杂钪团簇和过渡金属掺杂铝团簇的几何结构,电子性质和磁性行为,以及氢吸附掺杂团簇的结构特性和电子性质。
第一章主要介绍了团簇科学的一些基本情况。团簇由于其尺寸介于原子和固体之间而具有许多独特的性质,是实验和理论研究的一个重要对象。首先,我们简单介绍了团簇的基本性质;接着,我们从实验和理论两个方面,介绍了团簇研究的基本方法;然后,着重介绍了金属团簇的一些特性。在此基础上,我们对团簇研究的现状做了一个简单的总结和展望。最后,简要介绍了本论文的主要工作。
第二章主要介绍了密度泛函理论的基本框架和发展过程。由于量子化学的发展是密度泛函理论产生的历史基础,我们首先对其进行了简单的回顾。接着,介绍了密度泛函理论的发展过程,从最初的Thomas-Fermi模型,到Hohenberg-Kohn定理,再到成熟的Kohn-Sham方程。此外,简要介绍了两种常用的交换相关泛函。本章最后,简单介绍了本论文所使用的模拟软件。
第三章基于密度泛函理论,在GGA\PW91基组下,利用Dmol3软件包研究了铝原子掺杂钪团簇的基态几何结构,电子性质和磁性行为。我们通过计算结果的理论分析发现:(1)随着ScnAl的尺寸从2增长到14,ScnAl团簇中的掺杂原子Al的位置逐渐从团簇的表面陷入到Sc囚笼之中,其中n=9是转折点。(2)Scn和ScnAl团簇的平均结合能的计算结果表明,Al原子的掺入有利于增强团簇的稳定性。由ScnAl团簇的裂化能和二阶能量差分的计算结果表明,ScnAl团簇在n=3,6,10,12时具有相当高的稳定性。(3)团簇的HOMO-LUMO能隙依赖于团簇的尺寸和几何结构。ScnAl(n>5)团簇的HOMO–LUMO能隙非常小,这表明掺杂以后混合团簇的化学活性较强。所有的HOMO和LUMO轨道都是离域化的。(4)研究其磁性行为可知,Al原子的掺入使主体钪团簇的磁性发生了重大变化。除了Sc9和Sc15团簇,铝原子的掺杂降低了主体钪团簇的磁矩。Sc12Al团簇的磁矩(5μb)远小于纯钪团簇磁矩(15μb),且掺杂团簇在n=5,7,9,11时,磁性发生淬灭。
第四章基于密度泛函理论,在GGA\PW91基组下,利用Dmol3软件包研究了TMAln (TM=Cr,Mn,Fe,Co,Ni, n=1-7, 12)团簇的生长模式、电子性质以及磁性行为。我们通过对计算结果的深入分析发现:(1)对于笼状TMAl12团簇,仅原子半径相对铝原子较小的钴和镍原子陷入到铝囚笼之中,其余均位于二十面体的表面位置。(2)通过对团簇的平均结合能,劈裂能,二阶能量差分和HOMO-LUMO能隙的分析可知,TMAl3团簇有着较高的稳定性。所有的HOMO和LUMO轨道都是离域化的。(3)自然电荷布局分析表明,TMAln团簇电荷的转移主要发生在TM 4s,3d,4p和Al 3s,3p之间。因此,TM原子轨道之间得spd杂化和Al原子轨道之间得sp杂化是共存的,同时在TM和Al原子之间也存在轨道杂化。(4)通过对磁性计算结果的理论分析,我们总结归纳了一些规律:①当团簇的原子数较少,处于平面结构的时候,可以使用价键理论解释它们的磁性行为;②当团簇的几何结构为球形结构时,可以使用凝胶模型解释它们的磁性行为;③当团簇的几何构型基本偏离了球形结构,团簇电子结构以及铝原子与过渡金属原子之间的轨道杂化则对磁性起了决定性的作用。
第五章基于密度泛函理论,在GGA\PBE基组下,利用Dmol3软件包研究了Al12H12和MAl12H12(M=Al,Li,Na,K)团簇的结构特性和电子性质。我们通过计算结果的理论分析发现:(1)Al12H12和MAl12H12(M=Al,Li,Na,K)团簇处于基态结构时,具有二十面体的高对称结构,且12个氢原子均位于顶位。(2)通过对未氢化和氢化后团簇的基态结构的比较可以得出,除了氢化后的Al12H12团簇相对于Al12团簇,体积发生了膨胀,其余团簇的体积相对于未氢化前均缩小了。这种体积的膨胀可能归咎于中心原子的缺失。(3)通过系统和详细地分析团簇的平均结合能,垂直电离势和HOMO-LUMO能隙得出,LiAl12H12比Al12H12具有更高的稳定性,这表明在Al12H12团簇中掺入锂原子可以提高其稳定性,使得利用LiAl12H12储氢更加有力。(4)由团簇体系的HOMO电荷密度分布可以看出,未氢化团簇的电荷总要集中在团簇的表面区域,特别是顶位。这表明这些地方更容易发生氢吸附,这与我们的计算结果也是相一致的。由差分电荷密度分布图可以看出,在氢化之后,电荷明显的集中在氢原子上,这表明氢化之后,电荷由铝原子向氢原子转移了。
Along with the rapid development of computational methods and computer technology, computational physics has become more and more important in modern physics. Due to its moderate computational consume and high precision, density functional theory based first-principles calculation is among the most popular and versatile methods available in condensed-matter physics, quantum chemistry and material science. In this thesis, we investigate the geometric structures, electronic properties and magnetic properties of ScnAl and TMAln clusters, and the electronic properties of hydrogenated Al12 and MAl12 clusters by using density functional theory. The main contents are presented as the followings:
In the first chapter, we give a brief introduction to clusters. With a size beween those of atoms and macroscopical systems, clusters have many unique properties, and attract many experimental and theoretical research attentions. Firstly, we introduce the basic properties of clusters. Secondly, some common methods in experimental and theoretical studies on clusters are discussed. Following, we highlight some of the characteristics of metal clusters. On this basis, we summarize and look forward to the research on clusters. Last but not least, we simply describe the purpose and results of our work on clusters.
In the second chapter, we introduce chiefly the basic concept and progress of density functional theory. First, we briefly reviewed the development of quantum chemistry. Then, we introduce breiefly the development process of density functional theory, and two exchange-correlation functioals. Finally, we pay more attention to the simulation package Dmol3 used in the work.
In the third chapter, we investigate the growth behaviors, stabilities, electronic and magnetic properties of the ScnAl, (n = 1–14) by density functional theory with the generalized gradient approximation. All the calculated results are summarized as follows. (1) In the ground-state structures of ScnAl clusters, the aluminum atom remains on the surface of clusters for n < 9, but is trapped within the cage of Sc host atoms for n≥9. (2) The stability analysis is carried out by calculating the average binding energy and the second-order energy differences. The obtained results show that the doping of the Al atom improves the stability of scandium clusters, and ScnAl clusters at n = 3, 6, 10 and 12 possess relatively higher stability. (3) The HOMO–LUMO gaps of ScnAl clusters are discussed. It is found that the HOMO–LUMO gaps of ScnAl clusters containing more than six atoms are very small, and all the HOMO and LUMO states are nondegenerate and delocalized. (4) This magnetism study reveals that the Al atom is seen to induce significant changes in the magnetic property of the host cluster. The doping of the Al atom reduces the magnetic moment of the host clusters except for Sc9 and Sc15 clusters. Especially, the total magnetic moment of the Sc12Al cluster is only 5μb (but 15μb for Sc13), and the magnetic moment of the ScnAl cluster is quenched for n = 5, 7, 9 and 11. NPA shows that the 3d electrons play a dominant role for the magnetism of the system.
In the fourth chapter, we investigate the growth behavior, stability, and electronic and magnetic properties of TMAln (TM=Cr,Mn,Fe,Co,Ni, n= 1–7,12) clusters using density functional theory based on generalized gradient approximation. All the calculated results are summarized as follows. (1) TMAln clusters have similar geometries as that of Aln+1 clusters, where the TM atom can be thought of as a substitutional impurity in the Aln+1 clusters with a slight distortion on the whole. For TMAl12 cage-like clusters, substitutional atoms Cr, Mn, and Fe prefer to reside at the cluster surface, while Co and Ni dopant atoms prefer to reside at the cluster center. (2) The stability analysis in relation to the calculation of the average binding energy and second-order energy differences shows that TMAl3 clusters possess relatively higher stability. Besides, the analysis of the HOMO–LUMO gaps of TMAln clusters indicates that TMAl12 clusters have very small HOMO–LUMO gaps, and all the HOMO and LUMO states are non-degenerate and delocalized. (3) The result of NPA shows the charge transfer mainly happens between TM 4s, 3d, and 4p and Al 3s and 3p states. So there exits sd-p hybridization in TM atoms and s-p hybridization in Al atoms, and there also exists strong hybridization between TM 4s, 3d, and 4p and Al 3s and 3p states. (4) This magnetism study reveals that their magnetic behavior of TMAl and TMAl2 clusters, which are the planar structures, can be interpreted in light of the valence-bond theory. Their magnetic behavior of MAl3 (C3v) and MAl4 (C4v) clusters, which are the three-dimensional structures, can be interpreted in light of the spherical jellium model. For TMAln (n > 4) clusters, their geometrical shape basically deviates from spherical structure, and the energy level should also change significantly. At this time, hybridization between the atomic orbitals of the guest atom TM and host atom Al play a decisive role on their magnetic moment.
In the fifth chapter, we investigate structural, energetic, and electronic properties of hydrogenated Al12 and MAl12 (M=Al,Li,Na,K) clusters using density functional theory based on generalized gradient approximation. All the calculated results are summarized as follows. (1) The most stable Al12H12 and MAl12H12 (M=Al,Li,Na,K) clusters possess icosaheral symmetry, with each hydrogen atom bonded to an Al atom in atop position. (2)We compare the ground state structure properties of bare clusters with hydrogenated clusters, and find Al12H12 expands upon hydrogen adsorption on its surface in contrast to the remaining cluster. (3) The stability analysis in relation to the calculation of the average binding energy, vertical ionization potential and HOMO-LUMO gap, shows that hydrogenated clusters enhances the stability of the aluminum clusters, and LiAl12H12 cluster has a relatively high hydrogen storage capacity. (4) The analysis of the charge density of the HOMO show most of the charge of the additional electron is localized at the on-top sites on the surfaces of the bare clusters, thus suggesting their preference toward hydrogen absorption. The analysis of the deformation electron density, show the higher electron density on the H atoms indicates partial electron transfer from the Al atoms towards hydrogen upon adsorption.
第一章主要介绍了团簇科学的一些基本情况。团簇由于其尺寸介于原子和固体之间而具有许多独特的性质,是实验和理论研究的一个重要对象。首先,我们简单介绍了团簇的基本性质;接着,我们从实验和理论两个方面,介绍了团簇研究的基本方法;然后,着重介绍了金属团簇的一些特性。在此基础上,我们对团簇研究的现状做了一个简单的总结和展望。最后,简要介绍了本论文的主要工作。
第二章主要介绍了密度泛函理论的基本框架和发展过程。由于量子化学的发展是密度泛函理论产生的历史基础,我们首先对其进行了简单的回顾。接着,介绍了密度泛函理论的发展过程,从最初的Thomas-Fermi模型,到Hohenberg-Kohn定理,再到成熟的Kohn-Sham方程。此外,简要介绍了两种常用的交换相关泛函。本章最后,简单介绍了本论文所使用的模拟软件。
第三章基于密度泛函理论,在GGA\PW91基组下,利用Dmol3软件包研究了铝原子掺杂钪团簇的基态几何结构,电子性质和磁性行为。我们通过计算结果的理论分析发现:(1)随着ScnAl的尺寸从2增长到14,ScnAl团簇中的掺杂原子Al的位置逐渐从团簇的表面陷入到Sc囚笼之中,其中n=9是转折点。(2)Scn和ScnAl团簇的平均结合能的计算结果表明,Al原子的掺入有利于增强团簇的稳定性。由ScnAl团簇的裂化能和二阶能量差分的计算结果表明,ScnAl团簇在n=3,6,10,12时具有相当高的稳定性。(3)团簇的HOMO-LUMO能隙依赖于团簇的尺寸和几何结构。ScnAl(n>5)团簇的HOMO–LUMO能隙非常小,这表明掺杂以后混合团簇的化学活性较强。所有的HOMO和LUMO轨道都是离域化的。(4)研究其磁性行为可知,Al原子的掺入使主体钪团簇的磁性发生了重大变化。除了Sc9和Sc15团簇,铝原子的掺杂降低了主体钪团簇的磁矩。Sc12Al团簇的磁矩(5μb)远小于纯钪团簇磁矩(15μb),且掺杂团簇在n=5,7,9,11时,磁性发生淬灭。
第四章基于密度泛函理论,在GGA\PW91基组下,利用Dmol3软件包研究了TMAln (TM=Cr,Mn,Fe,Co,Ni, n=1-7, 12)团簇的生长模式、电子性质以及磁性行为。我们通过对计算结果的深入分析发现:(1)对于笼状TMAl12团簇,仅原子半径相对铝原子较小的钴和镍原子陷入到铝囚笼之中,其余均位于二十面体的表面位置。(2)通过对团簇的平均结合能,劈裂能,二阶能量差分和HOMO-LUMO能隙的分析可知,TMAl3团簇有着较高的稳定性。所有的HOMO和LUMO轨道都是离域化的。(3)自然电荷布局分析表明,TMAln团簇电荷的转移主要发生在TM 4s,3d,4p和Al 3s,3p之间。因此,TM原子轨道之间得spd杂化和Al原子轨道之间得sp杂化是共存的,同时在TM和Al原子之间也存在轨道杂化。(4)通过对磁性计算结果的理论分析,我们总结归纳了一些规律:①当团簇的原子数较少,处于平面结构的时候,可以使用价键理论解释它们的磁性行为;②当团簇的几何结构为球形结构时,可以使用凝胶模型解释它们的磁性行为;③当团簇的几何构型基本偏离了球形结构,团簇电子结构以及铝原子与过渡金属原子之间的轨道杂化则对磁性起了决定性的作用。
第五章基于密度泛函理论,在GGA\PBE基组下,利用Dmol3软件包研究了Al12H12和MAl12H12(M=Al,Li,Na,K)团簇的结构特性和电子性质。我们通过计算结果的理论分析发现:(1)Al12H12和MAl12H12(M=Al,Li,Na,K)团簇处于基态结构时,具有二十面体的高对称结构,且12个氢原子均位于顶位。(2)通过对未氢化和氢化后团簇的基态结构的比较可以得出,除了氢化后的Al12H12团簇相对于Al12团簇,体积发生了膨胀,其余团簇的体积相对于未氢化前均缩小了。这种体积的膨胀可能归咎于中心原子的缺失。(3)通过系统和详细地分析团簇的平均结合能,垂直电离势和HOMO-LUMO能隙得出,LiAl12H12比Al12H12具有更高的稳定性,这表明在Al12H12团簇中掺入锂原子可以提高其稳定性,使得利用LiAl12H12储氢更加有力。(4)由团簇体系的HOMO电荷密度分布可以看出,未氢化团簇的电荷总要集中在团簇的表面区域,特别是顶位。这表明这些地方更容易发生氢吸附,这与我们的计算结果也是相一致的。由差分电荷密度分布图可以看出,在氢化之后,电荷明显的集中在氢原子上,这表明氢化之后,电荷由铝原子向氢原子转移了。
Along with the rapid development of computational methods and computer technology, computational physics has become more and more important in modern physics. Due to its moderate computational consume and high precision, density functional theory based first-principles calculation is among the most popular and versatile methods available in condensed-matter physics, quantum chemistry and material science. In this thesis, we investigate the geometric structures, electronic properties and magnetic properties of ScnAl and TMAln clusters, and the electronic properties of hydrogenated Al12 and MAl12 clusters by using density functional theory. The main contents are presented as the followings:
In the first chapter, we give a brief introduction to clusters. With a size beween those of atoms and macroscopical systems, clusters have many unique properties, and attract many experimental and theoretical research attentions. Firstly, we introduce the basic properties of clusters. Secondly, some common methods in experimental and theoretical studies on clusters are discussed. Following, we highlight some of the characteristics of metal clusters. On this basis, we summarize and look forward to the research on clusters. Last but not least, we simply describe the purpose and results of our work on clusters.
In the second chapter, we introduce chiefly the basic concept and progress of density functional theory. First, we briefly reviewed the development of quantum chemistry. Then, we introduce breiefly the development process of density functional theory, and two exchange-correlation functioals. Finally, we pay more attention to the simulation package Dmol3 used in the work.
In the third chapter, we investigate the growth behaviors, stabilities, electronic and magnetic properties of the ScnAl, (n = 1–14) by density functional theory with the generalized gradient approximation. All the calculated results are summarized as follows. (1) In the ground-state structures of ScnAl clusters, the aluminum atom remains on the surface of clusters for n < 9, but is trapped within the cage of Sc host atoms for n≥9. (2) The stability analysis is carried out by calculating the average binding energy and the second-order energy differences. The obtained results show that the doping of the Al atom improves the stability of scandium clusters, and ScnAl clusters at n = 3, 6, 10 and 12 possess relatively higher stability. (3) The HOMO–LUMO gaps of ScnAl clusters are discussed. It is found that the HOMO–LUMO gaps of ScnAl clusters containing more than six atoms are very small, and all the HOMO and LUMO states are nondegenerate and delocalized. (4) This magnetism study reveals that the Al atom is seen to induce significant changes in the magnetic property of the host cluster. The doping of the Al atom reduces the magnetic moment of the host clusters except for Sc9 and Sc15 clusters. Especially, the total magnetic moment of the Sc12Al cluster is only 5μb (but 15μb for Sc13), and the magnetic moment of the ScnAl cluster is quenched for n = 5, 7, 9 and 11. NPA shows that the 3d electrons play a dominant role for the magnetism of the system.
In the fourth chapter, we investigate the growth behavior, stability, and electronic and magnetic properties of TMAln (TM=Cr,Mn,Fe,Co,Ni, n= 1–7,12) clusters using density functional theory based on generalized gradient approximation. All the calculated results are summarized as follows. (1) TMAln clusters have similar geometries as that of Aln+1 clusters, where the TM atom can be thought of as a substitutional impurity in the Aln+1 clusters with a slight distortion on the whole. For TMAl12 cage-like clusters, substitutional atoms Cr, Mn, and Fe prefer to reside at the cluster surface, while Co and Ni dopant atoms prefer to reside at the cluster center. (2) The stability analysis in relation to the calculation of the average binding energy and second-order energy differences shows that TMAl3 clusters possess relatively higher stability. Besides, the analysis of the HOMO–LUMO gaps of TMAln clusters indicates that TMAl12 clusters have very small HOMO–LUMO gaps, and all the HOMO and LUMO states are non-degenerate and delocalized. (3) The result of NPA shows the charge transfer mainly happens between TM 4s, 3d, and 4p and Al 3s and 3p states. So there exits sd-p hybridization in TM atoms and s-p hybridization in Al atoms, and there also exists strong hybridization between TM 4s, 3d, and 4p and Al 3s and 3p states. (4) This magnetism study reveals that their magnetic behavior of TMAl and TMAl2 clusters, which are the planar structures, can be interpreted in light of the valence-bond theory. Their magnetic behavior of MAl3 (C3v) and MAl4 (C4v) clusters, which are the three-dimensional structures, can be interpreted in light of the spherical jellium model. For TMAln (n > 4) clusters, their geometrical shape basically deviates from spherical structure, and the energy level should also change significantly. At this time, hybridization between the atomic orbitals of the guest atom TM and host atom Al play a decisive role on their magnetic moment.
In the fifth chapter, we investigate structural, energetic, and electronic properties of hydrogenated Al12 and MAl12 (M=Al,Li,Na,K) clusters using density functional theory based on generalized gradient approximation. All the calculated results are summarized as follows. (1) The most stable Al12H12 and MAl12H12 (M=Al,Li,Na,K) clusters possess icosaheral symmetry, with each hydrogen atom bonded to an Al atom in atop position. (2)We compare the ground state structure properties of bare clusters with hydrogenated clusters, and find Al12H12 expands upon hydrogen adsorption on its surface in contrast to the remaining cluster. (3) The stability analysis in relation to the calculation of the average binding energy, vertical ionization potential and HOMO-LUMO gap, shows that hydrogenated clusters enhances the stability of the aluminum clusters, and LiAl12H12 cluster has a relatively high hydrogen storage capacity. (4) The analysis of the charge density of the HOMO show most of the charge of the additional electron is localized at the on-top sites on the surfaces of the bare clusters, thus suggesting their preference toward hydrogen absorption. The analysis of the deformation electron density, show the higher electron density on the H atoms indicates partial electron transfer from the Al atoms towards hydrogen upon adsorption.
引文
[1]王广厚团簇物理学上海科学技术出版社(2003).
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