Structure and stability of the defect fullerene clusters of C60: C59, C58, and C57

We have performed density functional calculations for the structures and stabilities of various isomers of the defect fullerene clusters of C(60): C(59), C(58), and C(57). The C(59_)5-8, C(58_)5-5-7, and C(57_)4-5-9 clusters were calculated to be the most stable isomers of the C(59), C(58), and C(57) clusters, respectively. There are obvious relationships between structure and stability of the defect fullerene clusters. First, an unsaturated carbon atom favors being located at a 6-membered ring rather than a 5-membered ring. Second, the most stable isomers prefer to have newly formed 5-membered rings, rather than newly formed 4-membered rings.     

Si_2C_(m-2)(m=4～15)团簇的结构与稳定性

用密度泛函理论(DFT)的B3LYP/6-31G*方法, 对Si2Cm-2(m = 4~15)团簇的几何构型、电子结构、振动频率等性质进行了研究, 讨论了化学键的特征和热力学稳定性, 比较了Si2Cm-2团中环状和线状结构的差异。结果表明, m = 4~13的团簇为线状结构, m=14~15的团簇为环状结构。在线状结构中, 随着m增大, 自旋多重度出现1、3交替变化, 并且Si原子倾向于在C链端部成键;环状结构中, C原子形成环状, 2个Si原子处于椭圆环状构型的两端。m 为奇数的Si2Cm-2团簇比m为偶数的更为稳定。     

Size dependence of the structures and energetic and electronic properties of gold clusters

The structures and stabilities of gold clusters with up to 14 atoms have been determined by density-functional theory. The structure optimizations and frequency analysis are performed with the Perdew-Wang 1991 gradient-corrected functional combined with the effective core potential and corresponding valence basis set (LANL2DZ). The turnover point from two-dimensional to three-dimensional geometry for gold clusters occurs at Au12. The energetic and electronic properties of the small gold clusters are strongly dependent on sizes and structures, which are in good agreement with experiment and other theoretical calculations. The even-odd oscillation in cluster stability and electronic properties predicted that the clusters with even numbers of atoms were more stable than the neighboring clusters with odd numbers of atoms. The stability and electronic structure properties of gold clusters are also characterized by the maximum hardness principle of chemical reactivity and minimum polarizability principle.     

C~nSi(n=28,29)各种可能结构的理论研究

利用量子化学从头计算方法研究了C~nSi(n=28,29)各种可能的结构,研究结果表明:C~2~9Si为硅取代碳笼(Fullerens)中一个碳原子而形成的骨0架硅杂碳笼(Fullerenes),而且C~2~9Si最稳定结构是通过硅取代碳笼(C~3~0)最稳定结构中一个碳原子而得到.C~2~9Si比C~3~0有较低的稳定性和较高的化学活性.C~2~8Si有两种类型结构:(I)外接,(Ⅱ)缺位(hole-defect)型,即硅四连接型.计算结果表明,对C~2~8Si,外接硅型化合物更稳定,即(I)为主要成份.而且C~2~8Si最稳定结构是由C~2~8最稳定结构外接硅而形成.计算结果与实验观测一致。     

Structure of hydrogenated silicon clusters. Medium-sized clusters

The structures of the Si_nH_m clusters containing 10 to 70 silicon atoms and different numbers of hydrogen atoms are calculated in the MINDO/3 approximation using the Monte Carlo technique. The geometry optimization of the clusters showed the existence of several structural varieties that determine the optimal geometry of the clusters differing in size and hydrogen content. Small clusters (n < 20) with various geometrical configurations often have a hollow structure if the number of silicon atoms in the cluster is more than 12. For 20 ≤ n < 60 and the hydrogen content m ≤ n, hollow spheroidal geometry is most favorable. Staring from n ≈ 56−60, diamond structures are more favorable. The ratio c = m/n < 1, at which the spheroidal structure remains optimal, decreases with further increase in n.     

Effect of Ni and Pd on the geometry, electronic properties, and active sites of copper clusters

The geometry, electronic properties, and active sites of copper clusters doped with Ni or Pd atoms, Cu(n)()(-)(1)M (n = 2-6; M = Ni, Pd) have been investigated using first-principles methods. Planar structures are energetically favorable in Cu(n)()(-)(1)Ni (n = 2-6). However, for Pd-doped clusters, three-dimensional structures are competitive in energy, and for n = 6, the most stable structure is not planar. Several properties of doped copper clusters present odd-even oscillations as the number of copper atoms grow. The different atomic ground-state configuration of Ni and Pd determines the bonding and electronic properties of doped copper clusters. The interaction between impurities and copper atoms can modify the chemical hardness and active sites of doped copper clusters markedly inducing directionality in the reactivity. This effect is relevant to the behavior of catalysts as well as in the growth of metallic films.     

Structural and energetic properties of Ni-Cu bimetallic clusters

The lowest-energy structures for all compositions of Ni n Cu m bimetallic clusters with N = n + m up to 20 atoms, N = 23, and N = 38 atoms have been determined using a genetic algorithm for unbiased structure optimization in combination with an embedded-atom method for the calculation of the total energy for a given structure. Comparing bimetallic clusters with homoatomic clusters of the same size, it is shown that the most stable structures for each cluster size are composed entirely of Ni atoms. Among the bimetallic clusters in the size range N = 2-20, the Ni N-1 Cu 1 clusters possess the highest stability. Further, it has been established that most of the bimetallic cluster structures have geometries similar to those of pure Ni clusters. The size N = 38 presents a special case, as the bimetallic clusters undergo a dramatic structural change with increasing atom fraction of Cu. Moreover, we have identified an icosahedron, a double, and a triple icosahedron with one, two, and three Ni atoms at the centers, respectively, as particularly stable structures. We show that in all global-minimum structures Ni atoms tend to occupy mainly high-coordination inner sites, and we confirm the segregation of Cu on the surface of Ni-Cu bimetallic clusters predicted in previous studies. Finally, it is observed that, in contrast to the bulk, the ground-state structures of the 15-, 16-, and 17-atom bimetallic clusters do not experience a smooth transition between the structures of the pure copper and the pure nickel clusters as a function of the relative number of the two types of atoms. For these sizes, the concentration effect on energy is more important than the geometric one.     

Theoretical studies on carbon and silicon clusters: comparison of the structures and stabilities of neutral and ionic forms

Optimized molecular geometries and electronic structures are determined for neutral, positively charged, and negatively charged carbon and silicon clusters containing up to ten atoms. The effects of polarization functions and electron correlation are included in these claculations. Carbon clusters have linear or monocyclic ground state geometries whereas silicon clusters containing five or more atoms have three-dimensional ground state structures. Neutral C₄, C₆ and C₈ all have linear and monocyclic isomers of comparable stability whereas the ionic forms appear to be generally more stable as linear geometrical arrangements. In the case of neutral and positively charged carbon clusters, the odd-numbered clusters are significantly more stable than the adjacent even-numbered clusters whereas the opposite order of stability occurs for the negative ions. This is due to the large values of the electron affinities of the linear forms of even-numbered clusters such as C₄ and C₆. The relative stabilities of silicon clusters does not change with the charge state of the clusters.     

内嵌金属碳氮化物团簇富勒烯的稳定性与生成机理

Fullerene molecules have nano-scale cavities in which various metal or metal clusters of different sizes can be embedded to form metallofullerenes with unique core-shell structures. The physical and chemical properties of metallofullerenes can be modified through the interaction between the encapsulated metals and the fullerene cages. As such, the investigation of metallofullerenes with novel structures has been a principal research focus in the field of fullerenes. In this study, we investigated the size matching effect between encapsulated clusters and fullerene cages for the endohedral metal carbonitride clusterfullerenes in order to discover new metallofullerenes. The stability and electronic structure of the metallofullerenes formed by encapsulating M₃NC clusters (M = Y, La, Gd) into D₂(186)-C₉₆ and D₂(35)-C₈₈ fullerenes were studied using quantum chemical calculations. It was found that the fullerene cages formed stable structures by accepting six electrons transferred from the encapsulated clusters. The change in configuration of the encapsulated clusters was clarified by a comparison with the corresponding M₃N@C_2n metal nitride clusterfullerenes; the size matching effect between M₃NC cluster and fullerene cage was elucidated on the basis of the calculated results and previous studies on Sc₃NC@I_h(7)-C₈₀. For the D₂(186)-C₉₆ fullerene, the Gd₃NC cluster was found to have smaller changes in the configuration as compared with the La₃NC cluster, proving that Gd₃NC is more suitable than La₃NC for encapsulation in the D₂(186)-C₉₆ fullerene cage. In addition, it was determined that the La₃NC cluster requires a large structural change to maintain its planar configuration. For the D₂(35)-C₈₈ fullerene cage, the Y₃NC cluster is more suitable than Gd₃NC for encapsulation owing to the smaller size of the Y₃NC cluster. The spatial distribution of the highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO) of Gd₃NC@D₂(186)-C₉₆ were found to be similar to those of Gd₃N@D₂(186)-C₉₆. However, a unique endohedral cluster-based occupied molecular orbital was found for Gd₃NC@D₂(186)-C₉₆. This orbital is derived from the interaction between the NC unit and the Gd atoms. The spatial distribution of the HOMO of Y₃NC@D₂(35)-C₈₈ is similar to that of Y₃N@D₂(35)-C₈₈, while the LUMO of Y₃NC@D₂(35)-C₈₈ has a much larger contribution from the endohedral cluster as compared to Y₃N@D₂(35)-C₈₈. Thus, the addition of a carbon atom in the cluster has a remarkable impact on the electronic structure of the metallofullerenes. With respect to structural characteristics, we found that the three fullerene cages, D₂(186)-C₉₆, D₂(35)-C₈₈, and I_h(7)-C₈₀, have a uniform distribution of five-membered carbon atom rings; these fullerenes can be greatly stabilized in the form of C_2n^6- anions. However, the formation mechanism of fullerenes and metallofullerenes, at present, is poorly understood. Based on the structural analysis, we propose a direct mechanism for the formation of fullerenes without the Stone-Wales isomerization, i.e., the rearrangement of five-membered rings through the addition of carbon atoms and the transformation into larger carbon cages while maintaining stable structural units.     

压缩变形对C20富勒烯分子电子传输特性的影响

The geometry,electronic structure and electronic transmission of Au electrode-compressed C20 fullerene Au electrode systems are investigated systemically,and some interesting results are obtained by use of molecular dynamics,Extend Hückel method of the first principle,and Green's function based method. The analytical results show that,due to intervention of Au electrodes,the electronic structure of compressed C20 fullerene is changed significantly,the coalescent between C20 fullerene and Au electrodes is intervenient of covalent bond and electrovalent bond,and the compressed C20 fullerenes are better conductors of electricity than those uncompressed or slightly compressed ones. The methods and the relative conclusions are beneficial to go further deep into electronic transmission of carbon fullerenes.     

Energetic analysis of 24 C20 isomers

Twenty-four individual geometric structures of the 20-carbon system are investigated using hybrid Hartree–Fock/density functional theory (DFT-B3LYP) in combination with the 6-31G and 6-311G* basis sets. These computations are carried out in order to evaluate the relative energies of the various C₂₀ isomers utilizing both geometry optimization and single-point energy calculations. The relative energies of the three most widely studied C₂₀ isomers (ring, bowl, and cage) are compared to the energies of other cyclic, bowl-like, and miscellaneous isomers. Although the ring and the bowl isomers are predicted to be the two most stable species, we have identified three to four additional cyclic structures that are predicted to be energetically competitive with the fullerene structure.     

Geometrical and electronic structure of small copper nanoclusters: XANES and DFT analysis

The geometrical and electronic structure of small copper nanoclusters was studied by density functional theory (DFT) and analysis of X-ray absorption spectra. It was shown that the icosahedral geometry of small copper nanoclusters of 13 atoms was energetically more stable than cuboctahedral geometry. The binding energies in these structures were compared; the theoretical XANES spectra were compared with experiment. The paper gives the results of ab initio calculations of the electronic structure of copper clusters differing in size.     

Stabilization of boron clusters with classical fullerene structures by combined doping effect: a quantum chemical study

A combined approach (endohedral doping and exohedral environment) to stabilization of boron clusters with classical fullerene structures has been studied. The boron clusters with classical fullerene structures are stable when heteroatomic part of the complex (endohedral atom and exohedral environment) donates in total 18 electrons to the composite system, stability of which depends on the coordination capabilities and donor ability of the endohedral and surrounding atoms. The most effective stabilization is achieved in the case of the endohedral transition metals atoms, whereas the most effective environment is given by the lithium surrounding.

     

High-stability hydrogenated silicon-carbon clusters: a full study of Si2C2H2 in comparison to Si2C2, C2B2H4, and other similar species

The structural and electronic characteristics of the Si2C2H2 and Si2C2 clusters are studied by ab initio calculations based on coupled cluster and density functional theory using the hybrid B3LYP functional. In addition, similar species, such as SiC2H2 and Si3C2H2, are also studied for comparison. It is illustrated that the lowest energy structures of all three hydrogenated clusters, which have the general form Si(n)(CH)2, n = 1, 2, 3, are fully analogous to the structures of the corresponding organometallic isovalent carboranes. The most stable structure of Si2C2H2 is obtained by attaching two hydrogens onto the carbon atoms of a higher energy (+1.5 eV) planar trapezoidal structure of Si2C2, followed by geometry optimization which leads to puckering of the planar structure. Furthermore, it is demonstrated that Si2C2H2 and the other two "similar" hydrogenated clusters are much more stable than the corresponding bare nonhydrogenated clusters. Comparison of Si2C2H2 and C2B2H4 shows that their structural and bonding similarity includes also nuclear rearrangement similarity. The two species are isomerizable with an energy difference between their lowest energy puckered 1,2- and 1,3-isomers of about +/-0.3 eV. It is suggested that SiC2H2, Si2C2H2, and Si3C2H2 are special cases of a larger class of stable clusters. It is speculated on the basis of the calculated infrared spectrum that Si2C2H2 and perhaps other members of this class of clusters could be found in appreciable abundance in interstellar space.     

The mathematical modelling of cluster geometry

Calculations of minimum energy configurations for aggregates of up to forty atoms, commonly referred to as clusters, are presented. In contrast to previous studies, random initial configurations have been optimised to find the lowest energy structure for a given number of atoms. Three different two-body, bireciprocal potential functions were used in these calculations and in the case of the Lennard-Jones potential, previously calculated results have been confirmed. New structures obtained using softer potentials are also presented. Minimum energy structures of small clusters containing two different types of atoms have also been calculated, and the relationship between the geometry of a cluster and the relative sizes of its constituent atoms examined.     

Studies of iridium nanoparticles using density functional theory calculations

The energetics and the electronic and magnetic properties of iridium nanoparticles in the range of 2-64 atoms were investigated using density functional theory calculations. A variety of different geometric configurations were studied, including planar, three-dimensional, nanowire, and single-walled nanotube. The binding energy per atom increases with size and dimensionality from 2.53 eV/atom for the iridium dimer to 6.09 eV/atom for the 64-atom cluster. The most stable geometry is planar until four atoms are reached and three-dimensional thereafter. The simple cubic structure is the most stable geometric building block until a strikingly large 48-atom cluster, when the most stable geometry transitions to face-centered cubic, as found in the bulk metal. The strong preference for cubic structure among small clusters demonstrates their rigidity. This result indicates that iridium nanoparticles intrinsically do not favor the coalescence process. Nanowires formed from linear atomic chains of up to 4-atom rings were studied, and the wires formed from 4-atom rings were extremely stable. Single-walled nanotubes were also studied. These nanotubes were formed by stacking 5- and 6-atom rings to form a tube. The ring stacking with each atom directly above the previous atom is more stable than if the alternate rings are rotated.     

ZnS bubble clusters with onion-like structures

Following recent studies which showed that the most stable structures for (ZnS)(n) clusters (n= 10-47) are the so-called "bubble clusters", in which all the atoms are three-coordinated, we have used simulated annealing techniques to find the most stable structure for a larger cluster, (ZnS)(60). We find an onion-like structure, with one small cluster enclosed inside a bigger one. The inner cluster has the structure of a sodalite cage. Bonding between the inner and the outer clusters creates a network of four-coordinated atoms.     

Experimental and theoretical studies on carbon-nitrogen clusters C2nN7-

C(2n)N7(-) cluster ions are produced by laser ablating on the K(3)[Fe(CN)6] sample. DFT calculations have been performed for these cluster anions. Various isomeric structures of these clusters are optimized and their energies are compared to find the most stable isomers. The most stable structure for C8N7(-) is similar to that of adenine by theoretical calculation, which is in agreement with the collision-induced dissociation (CID) experimental results. With the increasing even numbers of C atoms from 8 to 16, the N atoms in the double-ring structure are gradually substituted by C atoms from the six-membered ring to the five-membered ring. All these C(2n)N7(-) (n = 3-9) clusters exhibit planar aromatic characters. The energy difference and incremental binding energy analyses show that C(2n)N7(-) (n = 4-8) clusters are more stable than C6N7(-) and C18N7(-), which are consistent with the observed mass spectrum.     

Influence of single impurity atoms on the structure, electronic, and magnetic properties of Ni5 clusters

With a gradient-corrected density functional method, we have studied computationally the influence of single impurity atoms on the structure, electronic, and magnetic properties of Ni5 clusters. The square-pyramidal isomer of bare Ni5 with six unpaired electrons was calculated 23 kJ/mol more stable than the trigonal bipyramid in its lowest-energy electronic configuration with four unpaired electrons. In a previous study on the cluster Ni4, we had obtained only one stable isomer with an O or an H impurity, but we located six minima for ONi5 and five minima for HNi5. In the most stable structures of HNi5, the H atom bridges a Ni-Ni edge at the base or the side of the square pyramid, similarly to the coordination of an H atom at the tetrahedral cluster Ni4. The most stable ONi5 isomers exhibit a trigonal bipyramidal structure of the Ni5 moiety, with the impurity coordinated at a facet, (micro3-O)Ni5, or at an apex edge, (micro-O)Ni5. We located four stable structures for a C impurity at a Ni5 cluster. As for CNi4, the most stable structure of the corresponding Ni5 complex comprises a four-coordinated C atom, (micro4-C)Ni5, and can be considered as insertion of the impurity into a Ni-Ni bond of the bare cluster. All structures with C and five with O impurity have four unpaired electrons, while the number of unpaired electrons in the clusters HNi5 varies between 3 and 7. As a rough trend, the ionization potentials and electron affinities of the clusters with impurity atoms decrease with the coordination number of the impurity. However, the position of the impurity and the shape of the metal moiety also affect the results. Coordination of an impurity atom leads to a partial oxidation of the metal atoms.     

Low energy structures of gold nanoclusters in the size range 3–38 atoms

Using a combination of first principles calculations and empirical potentials we have undertaken a systematic study of the low energy structures of gold nanoclusters containing from 3 to 38 atoms. A Lennard-Jones and many-body potential have been used in the empirical calculations, while the first principles calculations employ an atomic orbital, density functional technique. For the smaller clusters (n=3–5) the potential energy surface has been mapped at the ab initio level and for larger clusters an empirical potential was first used to identify low energy candidates which were then optimised with full ab initio calculations. At the DFT-LDA level, planar structures persist up to six atoms and are considerably more stable than the cage structures by more than 0.1 eV/atom. The difference in ab initio energy between the most stable planar and cage structures for seven atoms is only 0.04 eV/atom. For larger clusters there are generally a number of minima in the potential energy surface lying very close in energy. Furthermore our calculations do not predict ordered structures for the magic numbers n=13 and 38. They do predict the ordered tetrahedral structure for n=20. The results of the calculations show that gold nanoclusters in this size range are mainly disordered and will likely exist in a range of structures at room temperature.