Ti-Zr基团簇结构和物理化学性质的理论研究
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摘要
团簇研究是一个多学科交叉领域,在实验和理论上都取得了很大进步,不断有新的光、电、磁、热等物理性质和催化、反应活性等化学性质为人们所发现。过渡金属团簇由于其复杂的d电子结构表现出非常多样的物理化学性质,认识这些性质为新材料的设计、剪裁和修饰提供了良好的基础。
本文利用密度泛函理论(DFT)系统地研究了钛-锆基团簇几何结构和物理化学性质,包括中性Tin、Zrn(n=2-10)团簇及它们的带电Tin+、Tin-、Zrn+和Zrn-团簇、混合团簇TinZrm(n+m≤6)的几何结构、稳定性和电子性质,同时研究了掺杂团簇TinFe、TinMn、 ZrnMn(n=1-8)的几何结构、稳定性和磁性等性质。研究结果表明：
(1)对纯Tin、Zrn(n=2-10)团簇及它们的带电Tin+、Tin-、Zrn+和Zrn-团簇的可能结构进行了全优化,得到了多个低能异构体的稳定结构。Tin和Zrn团簇及它们的带电团簇在尺寸演化过程中都经历了从平面结构到立体结构再到中空笼状结构,笼状结构具有五边形或六边形结构单元。除Ti6以外,中性结构和正负离子团簇结构保持一致。以四角双锥为结构框架的Ti6、Ti8、Ti8+及Ti8-不满足团簇Ti。是由最稳定的Tin-1添加一个Ti原子得到的演化规律。Zrn团簇与其带电团簇的几何构型保持一致,在团簇生长过程中,除了n=8团簇的四角双锥戴两帽特殊结构,其它团簇都是在最稳定的Zrn-1团簇结构上添加Zr原子得到的。当n=6时Tin团簇平均键长变化较大,除Ti4+、Ti6和Ti9-以外,其它带电团簇比中性团簇平均键长稍长。Zrn团簇平均键长的变化充分反映了团簇结构的平面-立体-笼状结构发展规律,其带电团簇Zrn+和Zrn-平均键长与Zrn团簇相比,在平面向立体变化和成为笼状结构时平均键长变化较大。相对稳定性分析表明,Tin和Zrn团簇稳定性幻数规律与实验结果一致,在n=5,7都具有较高的稳定性,而Tin+、Tin-和Zrn+团簇在n=4,7时稳定性相对较高,Zrn-团簇稳定性规律与Zrn团簇稳定性规律一致。能隙、绝热电离势和绝热电子亲和能分析表明,Ti5、Ti7、Ti4+和Ti4-团簇有相对较高的化学稳定性,Ti6团簇的化学活性较强。Zrn和Zrn-团簇化学稳定性变化规律相同,Zr4+团簇化学稳定性较高。
(2)对混合团簇TinZrm(n+m≤6)的稳定结构进行了全面搜索,得到了它们的基态结构。除了n+m=5以外,其它团簇中Zr原子倾向于聚集在一起形成最多的Zr-Zr键,Ti原子倾向于占据在Zr原子周围增加结构的稳定性,这一结果可由形成团簇的原子质量加以解释。混合一个Zr原子的TinZr团簇的结构由Ti组分决定,其它混合团簇结构由Zr组分决定。TinZrm团簇结构受尺寸和组分的双重影响,Ti-Ti、Zr-Zr和Ti-Zr键平均键长的变化非常复杂。相对稳定性分析表明,TinZrm团簇平均结合能随团簇尺寸和组分比例单调增加,能量二阶差分表明TiZr2、Ti3Zr、TiZr3、Ti3Zr2、Ti4Zr和TiZr4有较高的稳定性。受几何结构影响,TinZrm的能隙除了n+m=5时较大以外,随团簇尺寸增加能隙减小,化学稳定性逐渐降低。进一步综合垂直电离势和垂直电子亲和能分析得出Ti3Zr、Ti4Zr和Ti2Zr4团簇的化学稳定性较高。
(3)研究了Fe、Mn原子掺杂的TinFe、TinMn和ZrnMn (n=1-8)团簇稳定结构,从团簇基态几何结构我们能够很清楚地总结出掺杂团簇的生长规律：4个原子时掺杂团簇结构向空间立体结构发展,n=3-4时,所形成的立体结构主要以三角锥框架为主；当n≥5时,掺杂团簇的结构主要是四角锥结构框架；当n=8时,掺杂原子Fe、Mn从团簇表面进入团簇内部形成内嵌结构。TinFe团簇中的Ti-Ti平均键长在团簇生长过程中基本保持不变,Ti-Fe、Ti-Mn和Zr-Mn平均键长的变化反映了其几何结构由平面到立体,再到掺杂原子内嵌的变化过程。与纯Ti团簇相比,TinFe团簇结合能变化不大,TinMn和ZrnMn团簇结合能与其纯团簇相比有所降低。TinFe团簇在团簇生长过程中稳定性不断增强,TiFe和Ti6Fe团簇具有较低的化学活性；TinMn和ZrnMn团簇中Ti5Mn、Ti7Mn和Zr5Mn团簇稳定性相对较高,Ti5Mn和Zr5Mn团簇化学稳定性较高。掺杂团簇磁矩分析表明,Ti3Fe、Ti4Fe、Ti8Fe、Ti4Mn、Ti5Mn和Ti6Mn团簇的总磁矩与纯Ti团簇相比增加；掺入Mn原子后ZrnMn团簇磁矩淬灭延迟。电荷布局分析表明,Ti、Zr原子与掺杂的Fe、Mn原子之间发生了电荷转移。Fe、Mn原子内部存在强烈的spd轨道杂化现象,Ti-Fe、Ti-Mn和Zr-Mn原子之间也存在较弱的杂化作用,这是引起掺杂团簇磁矩发生变化主要原因。
In resent years, study of cluster involved is an extensive field of multi-subjects and great progress has been made in the experimental and the theoretical research. Some new physical properties, such as light, electricity, magnetism and heat, have been discovered and chemical reactivity and especially catalytic activity have been known gradually. Transition metal clusters display very peculiar chemical and physical properties because of its complex electronic structures of the d shells. Understanding of these properties provides a good foundation for the design, cutting and modified of new materials.
In this thesis, we investigated systemically geometry structures, physical and chemical properties of Ti-Zr based clusters. First, a particular effort have been done to obtain the structural and electronic properties of neutral small Tin and Zrn (n=2-10) clusters and their charged Tin+, Tin-, Zrn+and Zrn-clusters using density functional theory (DFT) method. Further, geometric structures, stabilities and electronic properties of bimetallic TinZrm(n+m≤6) clusters have been investigated systematically. Meanwhile, we study the structures, electronic properties and magnetism of Fe-doped Tin as well as Mn-doped Tin and Zrn clusters up to n=8by DFT.
(1)A number of low-lying isomers for Tin, Zrn and their charged Tin+, Tin-,Zrn+and Zrn-clusters have been optimized and the ground-state geometries and typical stable isomers are determined. The results show that the planet geometries of small titanium and zirconium clusters convert to three dimensional structures and further convert to the hollow-caged-like structures with the increasing of the cluster size. The pentagonal and hexagonal arrays (n>8) are very favored energetically. The most stable structures of Tin cluster can be obtained by adding one Ti atom on the most stable structures of Tin-1without Ti6, Ti8, Ti8+and Ti8-. The geometric structures of the charged Zrn+and Zrn-clusters keep consistent with those of neutral Zrn clusters. It is noteworthy that the most stable structures of Zrn, Zrn+and Zrn-clusters can be obtained by adding one Zr atom to the most stable structures of Zrn-1,Zrn-1+and Zrn-1-clusters without n=8. Average bond length of Ti6cluster changes greatly and average bond length of Tin+and Tin-clusters without Ti4+, Ti6-and Ti9-is longer than that of Tin clusters. The change of average bond length fully reflects the growth trend of structures for the small zirconium clusters. For Zrn+and Zrn-clusters, average bond length shows a sharp feature compared with Zrn clusters at n=3,9. From the binding energies and second-order energy differences, we obtained that5-,7-atoms of Tin, Zrn and Zrn-clusters and4-,7-atoms of Tin+, Tin-and Zrn+clusters are the magic numbers. The calculated stability result for neutral clusters is in agreement with the experiment result. On the basis of the most stable structures, various electronic properties are analyzed including the HOMO-LUMO gaps, the adiabatic ionization potential and the adiabatic electron affinity. It is found that Ti5、Ti7、 Ti4+and Ti4-clusters are more stable in the chemical stability while Ti6cluster is stronger in chemical activity. In comparison with Zrn and Zrn-clusters, the change of relative chemical stability follow the same rend. For Zrn+clusters, it is more stable than its neighbours at n=4.
(2) The equilibrium geometries and electronic properties of TinZrm (n+m≤6) clusters have been investigated by the density functional theory. The results indicate that Zr atoms tend to cluster together and form the most Zr-Zr bonds, while Ti atoms inclined to occupy the surface without n+m=5. As a result, aggregation of mixed clusters can be explained according to the atomic mass. When mixed one Zr atom, it is found that and the geometry and shape depends on the Titanium composition in mixed clusters. The structures of other clusters are controlled by the zirconium composition. Change of the average bond length of Ti-Ti, Zr-Zr and Ti-Zr bonds is very complicated because of the influence of cluster size and composition. The average binding energy increases monotonously with the increasing n+m. As for the second-order energy difference, it is found that TiZr2, Ti3Zr, TiZr3, Ti?Zr2, Ti4Zr and TiZr4clusters are more stable than their neighboring clusters. By geometric structures effect, the HOMO-LUMO gaps generally decrease and then the chemical stability decreases with the increasing n+m except that the larger band gaps occurs at n+m=5. Further combined with the vertical ionization potential and vertical electronic affinity, Ti3Zr, Ti4Zr and Ti2Zr4clusters are less reactive.
(3) we have systematically studied the equilibrium geometries, electronic, and magnetic properties of TinFe, TinMn and ZrnMn (n=1-8) clusters using the density functional theory. The growth pattern on the basis of the ground-state structures can be easily summarized. From n=3, the geometric structures trend to form the three dimensional structures. The stable structures are based on triangular pyramidal units for n=3-4and on square pyramidal units for n≥5. The Fe and Mn atoms remain slowly getting trapped beyond n=8. Average bond length of Ti-Ti bonds is almost equal for TinFe clusters. But, the change of average bond length for Ti-Fe, Ti-Mn, Zr-Mn bond correspond with that of geometric structures which are from planet to spatial and then to trapped structures. Compared with pure Ti clusters, the binding energy of TinFe clusters changes little. The binding energy of TinMn and ZrnMn clusters is less than the corresponding pure clusters. The stability of TinFe clusters increases with the increase of the cluster size and TiFe and Ti6Fe clusters are less reactive. For TinMn and ZrnMn clusters, the relative stability of Ti5Mn、Ti7Mn and Zr5Mn clusters are better than their neighbours. It is also found that clusters are more stable in the chemical stability at n=5. The total magnetic moment of Ti3Fe、Ti4Fe、Ti8Fe、Ti4Mn、Ti5Mn and Ti6Mn clusters increases compared with pure Ti clusters. Mixed with Mn atom, the magnetic moment quenching of ZrnMn clusters is delayed. Mulliken charge population analysis indicated that the internal electron transfer in Fe and Mn atoms and charge transfer between Ti. Zr atoms and Fe. Mn atoms occur. The hybridized behavior of the delocalized s-,p-and the unfilled d-electrons is stronger within Fe and Mn atoms, while weaker in the Ti-Fe, Ti-Mn and Zr-Mn atoms, which is the major cause of the magnetic moment change.
本文利用密度泛函理论(DFT)系统地研究了钛-锆基团簇几何结构和物理化学性质,包括中性Tin、Zrn(n=2-10)团簇及它们的带电Tin+、Tin-、Zrn+和Zrn-团簇、混合团簇TinZrm(n+m≤6)的几何结构、稳定性和电子性质,同时研究了掺杂团簇TinFe、TinMn、 ZrnMn(n=1-8)的几何结构、稳定性和磁性等性质。研究结果表明：
(1)对纯Tin、Zrn(n=2-10)团簇及它们的带电Tin+、Tin-、Zrn+和Zrn-团簇的可能结构进行了全优化,得到了多个低能异构体的稳定结构。Tin和Zrn团簇及它们的带电团簇在尺寸演化过程中都经历了从平面结构到立体结构再到中空笼状结构,笼状结构具有五边形或六边形结构单元。除Ti6以外,中性结构和正负离子团簇结构保持一致。以四角双锥为结构框架的Ti6、Ti8、Ti8+及Ti8-不满足团簇Ti。是由最稳定的Tin-1添加一个Ti原子得到的演化规律。Zrn团簇与其带电团簇的几何构型保持一致,在团簇生长过程中,除了n=8团簇的四角双锥戴两帽特殊结构,其它团簇都是在最稳定的Zrn-1团簇结构上添加Zr原子得到的。当n=6时Tin团簇平均键长变化较大,除Ti4+、Ti6和Ti9-以外,其它带电团簇比中性团簇平均键长稍长。Zrn团簇平均键长的变化充分反映了团簇结构的平面-立体-笼状结构发展规律,其带电团簇Zrn+和Zrn-平均键长与Zrn团簇相比,在平面向立体变化和成为笼状结构时平均键长变化较大。相对稳定性分析表明,Tin和Zrn团簇稳定性幻数规律与实验结果一致,在n=5,7都具有较高的稳定性,而Tin+、Tin-和Zrn+团簇在n=4,7时稳定性相对较高,Zrn-团簇稳定性规律与Zrn团簇稳定性规律一致。能隙、绝热电离势和绝热电子亲和能分析表明,Ti5、Ti7、Ti4+和Ti4-团簇有相对较高的化学稳定性,Ti6团簇的化学活性较强。Zrn和Zrn-团簇化学稳定性变化规律相同,Zr4+团簇化学稳定性较高。
(2)对混合团簇TinZrm(n+m≤6)的稳定结构进行了全面搜索,得到了它们的基态结构。除了n+m=5以外,其它团簇中Zr原子倾向于聚集在一起形成最多的Zr-Zr键,Ti原子倾向于占据在Zr原子周围增加结构的稳定性,这一结果可由形成团簇的原子质量加以解释。混合一个Zr原子的TinZr团簇的结构由Ti组分决定,其它混合团簇结构由Zr组分决定。TinZrm团簇结构受尺寸和组分的双重影响,Ti-Ti、Zr-Zr和Ti-Zr键平均键长的变化非常复杂。相对稳定性分析表明,TinZrm团簇平均结合能随团簇尺寸和组分比例单调增加,能量二阶差分表明TiZr2、Ti3Zr、TiZr3、Ti3Zr2、Ti4Zr和TiZr4有较高的稳定性。受几何结构影响,TinZrm的能隙除了n+m=5时较大以外,随团簇尺寸增加能隙减小,化学稳定性逐渐降低。进一步综合垂直电离势和垂直电子亲和能分析得出Ti3Zr、Ti4Zr和Ti2Zr4团簇的化学稳定性较高。
(3)研究了Fe、Mn原子掺杂的TinFe、TinMn和ZrnMn (n=1-8)团簇稳定结构,从团簇基态几何结构我们能够很清楚地总结出掺杂团簇的生长规律：4个原子时掺杂团簇结构向空间立体结构发展,n=3-4时,所形成的立体结构主要以三角锥框架为主；当n≥5时,掺杂团簇的结构主要是四角锥结构框架；当n=8时,掺杂原子Fe、Mn从团簇表面进入团簇内部形成内嵌结构。TinFe团簇中的Ti-Ti平均键长在团簇生长过程中基本保持不变,Ti-Fe、Ti-Mn和Zr-Mn平均键长的变化反映了其几何结构由平面到立体,再到掺杂原子内嵌的变化过程。与纯Ti团簇相比,TinFe团簇结合能变化不大,TinMn和ZrnMn团簇结合能与其纯团簇相比有所降低。TinFe团簇在团簇生长过程中稳定性不断增强,TiFe和Ti6Fe团簇具有较低的化学活性；TinMn和ZrnMn团簇中Ti5Mn、Ti7Mn和Zr5Mn团簇稳定性相对较高,Ti5Mn和Zr5Mn团簇化学稳定性较高。掺杂团簇磁矩分析表明,Ti3Fe、Ti4Fe、Ti8Fe、Ti4Mn、Ti5Mn和Ti6Mn团簇的总磁矩与纯Ti团簇相比增加；掺入Mn原子后ZrnMn团簇磁矩淬灭延迟。电荷布局分析表明,Ti、Zr原子与掺杂的Fe、Mn原子之间发生了电荷转移。Fe、Mn原子内部存在强烈的spd轨道杂化现象,Ti-Fe、Ti-Mn和Zr-Mn原子之间也存在较弱的杂化作用,这是引起掺杂团簇磁矩发生变化主要原因。
In resent years, study of cluster involved is an extensive field of multi-subjects and great progress has been made in the experimental and the theoretical research. Some new physical properties, such as light, electricity, magnetism and heat, have been discovered and chemical reactivity and especially catalytic activity have been known gradually. Transition metal clusters display very peculiar chemical and physical properties because of its complex electronic structures of the d shells. Understanding of these properties provides a good foundation for the design, cutting and modified of new materials.
In this thesis, we investigated systemically geometry structures, physical and chemical properties of Ti-Zr based clusters. First, a particular effort have been done to obtain the structural and electronic properties of neutral small Tin and Zrn (n=2-10) clusters and their charged Tin+, Tin-, Zrn+and Zrn-clusters using density functional theory (DFT) method. Further, geometric structures, stabilities and electronic properties of bimetallic TinZrm(n+m≤6) clusters have been investigated systematically. Meanwhile, we study the structures, electronic properties and magnetism of Fe-doped Tin as well as Mn-doped Tin and Zrn clusters up to n=8by DFT.
(1)A number of low-lying isomers for Tin, Zrn and their charged Tin+, Tin-,Zrn+and Zrn-clusters have been optimized and the ground-state geometries and typical stable isomers are determined. The results show that the planet geometries of small titanium and zirconium clusters convert to three dimensional structures and further convert to the hollow-caged-like structures with the increasing of the cluster size. The pentagonal and hexagonal arrays (n>8) are very favored energetically. The most stable structures of Tin cluster can be obtained by adding one Ti atom on the most stable structures of Tin-1without Ti6, Ti8, Ti8+and Ti8-. The geometric structures of the charged Zrn+and Zrn-clusters keep consistent with those of neutral Zrn clusters. It is noteworthy that the most stable structures of Zrn, Zrn+and Zrn-clusters can be obtained by adding one Zr atom to the most stable structures of Zrn-1,Zrn-1+and Zrn-1-clusters without n=8. Average bond length of Ti6cluster changes greatly and average bond length of Tin+and Tin-clusters without Ti4+, Ti6-and Ti9-is longer than that of Tin clusters. The change of average bond length fully reflects the growth trend of structures for the small zirconium clusters. For Zrn+and Zrn-clusters, average bond length shows a sharp feature compared with Zrn clusters at n=3,9. From the binding energies and second-order energy differences, we obtained that5-,7-atoms of Tin, Zrn and Zrn-clusters and4-,7-atoms of Tin+, Tin-and Zrn+clusters are the magic numbers. The calculated stability result for neutral clusters is in agreement with the experiment result. On the basis of the most stable structures, various electronic properties are analyzed including the HOMO-LUMO gaps, the adiabatic ionization potential and the adiabatic electron affinity. It is found that Ti5、Ti7、 Ti4+and Ti4-clusters are more stable in the chemical stability while Ti6cluster is stronger in chemical activity. In comparison with Zrn and Zrn-clusters, the change of relative chemical stability follow the same rend. For Zrn+clusters, it is more stable than its neighbours at n=4.
(2) The equilibrium geometries and electronic properties of TinZrm (n+m≤6) clusters have been investigated by the density functional theory. The results indicate that Zr atoms tend to cluster together and form the most Zr-Zr bonds, while Ti atoms inclined to occupy the surface without n+m=5. As a result, aggregation of mixed clusters can be explained according to the atomic mass. When mixed one Zr atom, it is found that and the geometry and shape depends on the Titanium composition in mixed clusters. The structures of other clusters are controlled by the zirconium composition. Change of the average bond length of Ti-Ti, Zr-Zr and Ti-Zr bonds is very complicated because of the influence of cluster size and composition. The average binding energy increases monotonously with the increasing n+m. As for the second-order energy difference, it is found that TiZr2, Ti3Zr, TiZr3, Ti?Zr2, Ti4Zr and TiZr4clusters are more stable than their neighboring clusters. By geometric structures effect, the HOMO-LUMO gaps generally decrease and then the chemical stability decreases with the increasing n+m except that the larger band gaps occurs at n+m=5. Further combined with the vertical ionization potential and vertical electronic affinity, Ti3Zr, Ti4Zr and Ti2Zr4clusters are less reactive.
(3) we have systematically studied the equilibrium geometries, electronic, and magnetic properties of TinFe, TinMn and ZrnMn (n=1-8) clusters using the density functional theory. The growth pattern on the basis of the ground-state structures can be easily summarized. From n=3, the geometric structures trend to form the three dimensional structures. The stable structures are based on triangular pyramidal units for n=3-4and on square pyramidal units for n≥5. The Fe and Mn atoms remain slowly getting trapped beyond n=8. Average bond length of Ti-Ti bonds is almost equal for TinFe clusters. But, the change of average bond length for Ti-Fe, Ti-Mn, Zr-Mn bond correspond with that of geometric structures which are from planet to spatial and then to trapped structures. Compared with pure Ti clusters, the binding energy of TinFe clusters changes little. The binding energy of TinMn and ZrnMn clusters is less than the corresponding pure clusters. The stability of TinFe clusters increases with the increase of the cluster size and TiFe and Ti6Fe clusters are less reactive. For TinMn and ZrnMn clusters, the relative stability of Ti5Mn、Ti7Mn and Zr5Mn clusters are better than their neighbours. It is also found that clusters are more stable in the chemical stability at n=5. The total magnetic moment of Ti3Fe、Ti4Fe、Ti8Fe、Ti4Mn、Ti5Mn and Ti6Mn clusters increases compared with pure Ti clusters. Mixed with Mn atom, the magnetic moment quenching of ZrnMn clusters is delayed. Mulliken charge population analysis indicated that the internal electron transfer in Fe and Mn atoms and charge transfer between Ti. Zr atoms and Fe. Mn atoms occur. The hybridized behavior of the delocalized s-,p-and the unfilled d-electrons is stronger within Fe and Mn atoms, while weaker in the Ti-Fe, Ti-Mn and Zr-Mn atoms, which is the major cause of the magnetic moment change.
引文
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