The 13-atom encapsulated gold cage clusters

The structure and the magnetic moment of transition metal encapsulated in a Au 12 cage cluster have been studied by using the density functional theory.The results show that all of the transition metal atoms(TMA) can embed into the Au 12 cage and increase the stability of the clusters except Mn.Half of them have the I h or O h symmetry.The curves of binding energy have oscillation characteristics when the extra-nuclear electrons increase;the reason for this may be the interaction between parity changes of extra-nuclear electrons and Au atoms.The curves of highest occupied molecular orbital-lowest unoccupied molecular orbital(HOMO-LUMO) gap also have oscillation characteristics when the extra-nuclear electrons increase.The binding energies of many M@Au 12 clusters are much larger than that of the pure Au 13 cluster,while the gaps of some of them are less than that of Au 13,so maybe Cr@Au 12,Nb@Au 12,and W@Au 12 clusters are most stable in fact.For magnetic calculations,some clusters are quenched totally,but the Au 13 cluster has the largest magnetic moment of 5 μ B.When the number of extra-nuclear electrons of the encapsulated TMA is even,the magnetic moment of relevant M@Au 12 cluster is even,and so are the odd ones.     

Novel metal-encapsulated caged clusters of silicon and germanium

We report the recent findings of metal (M) encapsulated clusters of silicon from computer experiments based on ab initio total energy calculations and a cage shrinkage and atom removal approach. Our results show that using a guest atom, it is possible to wrap silicon in fullerenelike (f) structures, as sp² bonding is not favorable to produce empty cages unlike for carbon. Transition M atoms have a strong bonding with the silicon cage that are responsible for the compact structures. The size and structure of the cage change from 14 to 20 Si atoms depending upon the size and valence of the M atom. Fewer Si atoms lead to relatively open structures. We find cubic, f, Frank-Kasper (FK) polyheral type, decahedral, icosahedral and hexagonal structures for M@Si_n with n = 12-16 and several different M atoms. The magic behavior of 15 and 16 atom Si cages is in agreement with experiments. The FK polyhedral cluster, M@Si₁₆ has an exceptionally large density functional gap of about 2.35 eV calculated within the generalized gradient approximation. It is likely to give rise to visible luminescence in these clusters. The cluster-cluster interaction is weak that makes such clusters attractive for cluster assembled materials. Further studies to stabilize Si₂₀ cage with M = Zr, Ba, Sr, and Pb show that in all cases there is a distortion of the f cage. Similar studies on M encapsulated germanium clusters show FK polyhedral and decahedral isomers to be more favorable. Also perfect icosahedral M@Ge₁₂ and M@Sn₁₂ clusters have been obtained with large gaps by doping with divalent M atoms. Recent results of the H interaction with these clusters, hydrogenated silicon fullerenes as well as assemblies of clusters such as nanowires and nanotubes are briefly presented.     

Experimental and theoretical studies of interactions between Si<Subscript>7</Subscript> clusters

The possibility of using magic Si₇ clusters to form a cluster material was studied experimentally and theoretically. In experiments Si₇ clusters were deposited on carbon surfaces, and the electronic structure and chemical properties of the deposited clusters were measured using X-ray photoelectron spectroscopy (XPS). A non bulk-like electronic structure of Si₇ was found in the Si 2p core level spectra. Si₇ is suggested to form a more stable structure than the non-magic Si₈ cluster and Si atoms upon deposition on carbon surfaces. Theoretically it was possible to study the interaction between the clusters without the effect of a surface. Density functional theory (DFT) calculations of potential curves of two free Si₇ clusters approaching each other in various orientations hint at the formation of cluster materials rather than the fusion of clusters forming bulk-like structures.     

High stability of the goldalloy fullerenes：A density functional theory investigation of M_（12）@Au_（20）（M=Na,Al,Ag,Sc,Y,La,Lu,and Au） clusters

Discovering highly stable metal fullerenes such as the celebrated C 60 is interesting in cluster science as they have potential applications as building blocks in new nanostructures.We here investigated the structural and electronic properties of the fullerenes M 12 @Au 20（M=Na,Al,Ag,Sc,Y,La,Lu,and Au）,using a first-principles investigation with the density functional theory.It is found that these compound clusters possess a similar cage structure to the icosahedral Au 32 fullerene.La 12 @Au 20 is found to be particularly stable among these clusters.The binding energy of La 12 @Au 20 is 3.43 eV per atom,1.05 eV larger than that in Au 32.The highest occupied molecular orbital-lowest unoccupied molecular orbital（HOMO-LUMO） gap of La 12 @Au 20 is only 0.31 eV,suggesting that it should be relatively chemically reactive.     

Ternary alloying effect on the melting of metal clusters

Canonical ensemble Monte Carlo simulations are applied to investigate the melting of the icosahedral 55-atom Ag-Cu-Au clusters. The clusters are modeled by the second-moment approximation of the tight-binding (TB-SMA) many-body potentials. Results show that the introduction of the only Cu atom of the third alloying metal in the bimetallic Ag₄₃Au₁₂ cluster, forming the Ag₄₂Cu₁Au₁₂ cluster, can greatly increase the melting point of the cluster by about 100 K. It is also found that the substitution of the only Cu atom of the third alloying metal in the Ag₁Au₅₄ clusters, forming the Ag₁Cu₁Au₅₃ cluster, can result in an increase of 40 K in the melting point. It can be concluded that the melting points of the bimetallic clusters can be tuned by the third metal impurities doping. In addition, the surface segregation of Ag atoms in the Ag-Cu-Au trimetallic clusters occurs even after melting.     

Au和3d过渡金属元素混合团簇结构、电子结构和磁性的研究

采用基于密度泛函理论的第一性原理方法系统研究了Au与3d过渡元素构成的混合小团簇的结构、稳定性、电子结构及磁性,得到了Au与3d过渡元素构成的混合小团簇的稳定结构.计算结果表明,Au与3d元素可形成大量的低能异构体,特别是有些异构体在结构上极相近,这不同于共价或离子键类型的团簇.与纯过渡金属团簇类似,这类团簇也表现出复杂的磁性.过渡金属元素的磁矩相比体材料而言既有增强的、也有减弱的,与轨道的交换劈裂密切相关.对于基态构型,AuCr₂,Au₂Cr_{2关键词： 密度泛函理论 第一性原理方法 团簇 电子结构}     

Behaviour of ‘free-standing’ hollow Au nanocages at finite temperatures: a BOMD study

Finite-temperature behaviour of a hollow golden cage (HGC) plays a crucialrole in its potential applications as a catalyst, drug delivery agent, contrasting agent and so on. This physico-chemical property of HGCs is not well understood so far. In that context, Born–Oppenheimer molecular dynamics (BOMD) simulations are performed on a well-known ‘free-standing’ HGC. The cluster considered in this study is the ground state Au₁₈ cluster (a cage with a diameter of about >5.5 Å). The results thus obtained are compared with the BOMD simulation results reported earlier on Au₃₂ icosahedron cage, a conformation with a diameter of nearly. The sphericity of both the clusters is studied using a shape deformation parameter as a function of time and temperature. These results are supplemented by radial distribution function at various temperatures. The observations and analysis of results indicate that, both the clusters retain an HGC conformation from 300 to 400 K, admitting structural fluxionality by the Au₁₈ cluster. Remarkably, the Au₁₈ cluster is able to maintain its hollowness and sphericity up to a high temperature of 1000 K. Underlying structural and electronic properties influencing the individualistic behaviour of cages are highlighted. Composition of the frontier molecular orbitals and the charge distribution play a crucial role in the finite-temperature behaviour of the Au cages. The conclusions are supplemented by supporting calculations on another degenerate ground state Au₁₈ hollow cage and a well-known pyramidal Au₁₈ cage at 300 and 400 K.     

DFT study on size-dependent geometries, stabilities, and electronic properties of AunM2 (M = Si, P; n = 1–8) clusters

The ab initio method based on density functional theory at the PW91PW91 level has been employed to systematically study the structures, stabilities, electronic, and magnetic properties of gold clusters with or without silicon/phosphorus doping. The optimized geometries show that the most stable isomers for Au _n Si₂ and Au _n P₂ (n = 1–8) clusters prefer a three-dimensional structure when n = 2 and n = 3 upwards, respectively, and they can be viewed as grown from the already observed Au _n−1M₂ (M = Si, P). The relative stabilities of calculated Au _n M₂ (M = Si, P) clusters have been analyzed through the atomic average binding energy, fragmentation energy, second-order difference of energy, and HOMO-LUMO gap. A pronounced odd-even alternative phenomenon indicates that the clusters with even-numbered valence electrons possess a higher stability than their neighboring ones. For both systems, natural population analysis reveals that electronic properties of dopant atoms in the corresponding configuration are mainly related to s and p states. We also investigated magnetic effects of clusters as a function of cluster size, however, their oscillatory magnetic moments were found to vary inversely to the fragmentation energy, second-order difference of energy, and HOMO-LUMO gap.     

Structures and electronic properties of M@Au<Subscript>6</Subscript> (M=Al,Si, P,S, Cl,Ar) clusters: a density functional theory investigation

The geometries and electronic properties of the 3p electrons atoms doped gold cluster: M@Au₆ clusters (M=Al, Si, P, S, Cl, Ar) have been systematically investigated by using relativistic all-electron density functional theory (VPSR) and scalar relativistic effective core potential Stuttgart/Dresden (SDD) basis. Generalized gradient approximation in the Perdue-Burke-Ernzerhof (PBE) functional form is chosen for geometry optimization. A number of new isomers are obtained for neutral M@Au₆ clusters. Both PBE/VPSR and PBE/SDD methods give similar lowest energy structure of each M@Au₆cluster. With the exception of Ar@Au₆, all doped clusters show larger relative binding energies compared with pure Au₇ cluster. It is found that all the ground-state structures of the M@Au₆ clusters prefer the low symmetry structures, which is very different to the 3d transition-metal impurity doped Au₆ clusters. Our results are in excellent agreement with available experiment data.     

Molecular dynamics study of hydrogenated silicon clusters at high temperatures

This paper reports on a study of the stability of silicon clusters of intermediate size at a high temperature. The temperature dependence of the physicochemical properties of 60- and 73-atom silicon nanoparticles are investigated using the molecular dynamics method. The 73-atom particles have a crystal structure, a random atomic packing, and a packing formed by inserting a 13-atom icosahedron into a 60-atom fullerene. They are surrounded by a ‘coat’ from 60 atoms of hydrogen. The nanoassembled particle at the presence of a hydrogen ‘coat’ has the most stable number (close to four) of Si–Si bonds per atom. The structure and kinetic properties of a hollow single-layer fullerene-structured Si₆₀ cluster are considered in the temperature range 10 K ≤ T ≤ 1760 K. Five series of calculations are conducted, with a simulation of several media inside and outside the Si₆₀ cluster, specifically, the vacuum and interior spaces filled with 30 and 60 hydrogen atoms with and without the exterior hydrogen environment of 60 atoms. Fullerene surrounded by a hydrogen ‘coat’ and containing 60 hydrogen atoms in the interior space has a higher stability. Such clusters have smaller self-diffusion coefficients at high temperatures. The fullerene stabilized with hydrogen is stable to the formation of linear atomic chains up to the temperatures 270–280 K.     

Structural,electronic and magnetic properties of Au<Subscript>n</Subscript>Pt (n = 1−12) clusters in comparison with corresponding pure Au<Subscript>n+1</Subscript> (n = 1−12) clusters

An all-electron scalar relativistic calculation on Au _n Pt (n = 1−12) clusters has been performed by using density functional theory with the generalized gradient approximation at PW91 level. Our results reveal that all the lowest energy geometries of Au _n Pt  (n = 1−12) clusters may be generated by substituting Pt atom for one gold atom of the Au _n+1 cluster at the highest coordinated site. Compared with corresponding pure Au _n+1 cluster, the lowest energy geometries of Au _n Pt clusters are distorted slightly and still keep the planar structures due to the strong scalar relativistic effect in small gold cluster. The Au-Pt bonds are stronger and most Au-Au bonds far from Pt atom are weaker than the corresponding Au-Au bonds in pure Au _n+1 cluster. By substituting Pt atom for one gold atom of Au _n+1 cluster at the highest coordinated site, the relatively stable and inactive odd-numbered Au _n+1 cluster becomes the relatively unstable and reactive odd-numbered Au _n Pt cluster, and the relatively unstable and reactive even-numbered Au _n+1 cluster becomes the relatively stable and inactive even-numbered Au _n Pt  cluster chemically and electronically. All the Au _n Pt clusters prefer low spin multiplicity. The even-numbered Au _n Pt clusters are found to exhibit zero magnetic moment and the odd-numbered Au _n Pt clusters are found to possess magnetic moment with the value of 1 μ _B. The odd-even alterations of magnetic moments and electronic configurations for Au _n Pt clusters are very obvious and may be simply understood in terms of the electron pairing effect.     

Theoretical study on adsorption of Au and hydrated Au cations on clean Si(1 1 1) surface

To model the adsorption of Au⁺ cation in aqueous solution on the semiconductor surface, the interactions of Au⁺ and hydrated Au⁺ cations with clean Si(1 1 1) surface were investigated by using hybrid density functional theory (B3LYP) and Møller-Plesset second-order perturbation (MP2) methods. Si(1 1 1) surface was described with Si₇H₁₁, Si₁₁H₁₇ and Si₂₂H₂₁ clusters. The effect of the basis set superposition error (BSSE) was taken into account by applying the counterpoise correction. The calculated results indicated that the binding energies between hydrated Au⁺ cations and clean Si(1 1 1) surface are large, suggesting a strong interaction between hydrated Au⁺ cations and the semiconductor surface. The bonding nature of the chemical adsorption of Au⁺ to Si surface can be classified as partial covalent as well as ionic bonding. As the number of water molecules increases, the water molecules form hydrogen bond network with one another and only one water molecule binds directly to the Au⁺ cation. The Au⁺ cation in aqueous solution will safely attach to the clean Si(1 1 1) surface.     

Au@Sin: Growth behavior, stability and electronic structure

The configurations, stability, and electronic structure of AuSin (n=1-16) clusters have been investigated within the framework of the density functional theory at the B3PW91/LanL2DZ and PW91/DNP levels. The results show that the Au atom begins to occupy the interior site for cages as small as Si₁₁ and for Si₁₂ the Au atom completely falls into the interior site forming Au@Si₁₂ cage. A relatively large embedding energy and small HOMO-LUMO gap are also found for this Au@Si₁₂ structure indicating enhanced chemical activity and good electronic transfer properties. All these make Au@Si₁₂ attractive for cluster-assembled materials.     

Theoretical study on the mono and multiply oxygenated Si60H60 fullerene

We have applied density functional theory (DFT) calculations to study the structures, stabilities, electronic and magnetic properties of mono and multiply oxygenated Si₆₀H₆₀ fullerenes (Si₆₀H_60–2nO_n, n = 1, 3, 6, 9, 10, 12, 18, 20, 21, 27 and 30). DFT results show that rearrangement between the closed [6,6] and [5,6] isomers of Si₆₀H₅₈O follows a two-step pathway involving an intermediate and two transition states. Preserving the C₃ symmetry in the cage structure, extra epoxidation of Si₆₀H₆₀ has been accomplished. Based on our results, formation energies per oxygen atom for the multiple additions of oxygen atoms on Si₆₀H₆₀ cage are positive (endothermic character), and increase with the increasing of the number of oxygen atoms. In general, the oxygenation of Si₆₀H₆₀ cage leads to an increase in the electrophilicity of the Si₆₀H_60–2nO_n oxides. The oxygenation of Si–Si bonds not only introduces a substantial broadening of the NMR pattern but also yield individual peaks, indicating different electrostatic environments of silicon nuclei in the Si₆₀H_60–2nO_n oxides.     

Probing the structural,electronic and magnetic properties of small Au4M (M = Sc–Zn) clusters

Density-functional method PW91 has been selected to investigate the structural, electronic and magnetic properties of Au₄M (M =Sc–Zn) clusters. Geometry optimisations show that the M atoms in the ground-state Au₄M clusters favour the most highly coordinated position. The ground-state Au₄M clusters possess a solid structure for M = Sc and Ti and a planar structure for M = V–Zn. The characteristic frequency of the doped clusters is much greater than that of pure gold cluster. The relative stability and chemical activity are analysed by means of the averaged binding energy and highest occupied molecular orbital and lowest unoccupied molecular orbital energy gap for the lowest energy Au₄M clusters. It is found that the dopant atoms can enhance the thermal stability of the host cluster except for Zn atom. The Au₄Ti, Au₄Mn and Au₄Zn clusters have relatively higher chemical stability. The vertical detachment energy, electron affinity and photoelectron spectrum are calculated and simulated theoretically for all the ground-state structures. The magnetism calculations reveal that the total magnetic moment of Au₄M cluster is mainly localised on the M atom and vary from 0 to 5 μ_B by substituting an Au atom in Au₅ cluster with different transition-metal atoms.     

Structural features of liquid metallic glass former

The structural parameters of Au₇₅Si₂₅ alloy, pure Au, Al₈₈Si₁₂, Cu₈₇Sn₁₃, In₉₈Al₂ and Al₉₃Ni₇ alloys have been measured by X-ray diffractometer. It is found that there are subpeaks in the pair correlation functions in liquid Au₇₅Si₂₅ alloy. The addition of Si in liquid Au results in a decrease in both the correlation radius and the coordination number of the nearest atomic neighbors. The Au₇₅Si₂₅ alloy nearest atomic distance has a more stable dependence on temperature compared to In₉₈Al₂, Al₉₃Ni₇ and Cu₈₇Sn₁₃ alloys. The atomic density change of liquid Au₇₅Si₂₅ alloy is less dependent on temperature than the liquid Au and Al₈₈Si₁₂ alloy. The liquid metallic good glass former Au₇₅Si₂₅ alloy possesses a more stable liquid structure than that of poor glass formers, indicating the essential of the fragility of the superheated melts.     

Density functional theory study of AunMn(n=1-8) clusters

Equilibrium geometries, relative stabilities, and magnetic properties of small Au_nMn (n=1-8) clusters have been investigated using density functional theory at the PW91P86 level. It is found that Mn atoms in the ground state Au_nMn isomers tend to occupy the most highly coordinated position and the lowest energy structure of Au_nMn clusters with even n is similar to that of pure Au_n+1 clusters, except for n=2. The substitution of Au atom in Au_n+1 cluster by a Mn atom improves the stability of the host clusters. Maximum peaks are observed for Au_nMn clusters at n=2, 4 on the size dependence of second-order energy differences and fragmentation energies, implying that the two clusters possess relatively higher stability. The HOMO-LUMO energy gaps of the ground state Au_nMn clusters show a pronounced odd-even oscillation with the number of Au atoms, and the energy gap of Au₂Mn cluster is the biggest among all the clusters. The magnetism calculations indicate that the total magnetic moment of Au_nMn cluster, which has a very large magnetic moment in comparison to the pure Au_n+1 cluster, is mainly localized on Mn atom.     

Electronic properties of assembled islands of hydrogen-saturated silicon clusters on Si(111)-(7 x 7) surfaces studied by scanning tunneling spectroscopy

We present results of scanning tunneling spectroscopy (STS) measurements of hydrogen-saturated silicon clusters islands formed on Si(111)-( 7×7) surfaces. Nanometer-size islands of Si₆H₁₂ with a height of 0.2-4 nm were assembled with a scanning tunneling microscope (STM) using a tip-to-sample voltage larger than 3 V. STS spectra of Si₆H₁₂ cluster islands show characteristic peaks originating in resonance tunneling through discrete states of the clusters. The peak positions change little with island height, while the peak width shows a tendency of narrowing for the tall islands. The peak narrowing is interpreted as increase of lifetime of electron trapped at the cluster states. The lifetime was as short as 10^-13 s resulting from interaction with the dangling bonds of surface atoms, which prevents charge accumulation at the cluster islands. Received 30 November 2000     

Stability of gold cages (Au<Subscript>16</Subscript> and Au<Subscript>17</Subscript>) at finite temperature

We have employed ab initio molecular dynamics to investigate the stability of the smallest gold cages, namely Au₁₆ and Au₁₇, at finite temperatures. First, we obtain the ground state structure along with at least 50 distinct isomers for both the clusters. This is followed by the finite temperature simulations of these clusters. Each cluster is maintained at 12 different temperatures for a time period of at least 150 ps. Thus, the total simulation time is of the order of 2.4 ns for each cluster. We observe that the cages are stable at least up to 850 K. Although both clusters melt around the same temperature, i.e. around 900 K, Au₁₇ shows a peak in the heat capacity curve in contrast to the broad peak seen for Au₁₆.      

Geometrical, electronic, and magnetic properties of small AunSc (n=1-8) clusters

Geometrical, electronic, and magnetic properties of the Sc-doped gold clusters, Au_nSc (n=1-8), have been studied using the density-functional theory within the generalized gradient approximation. An extensive structural search shows that the Sc atom in low-energy Au_nSc isomers tends to occupy the most highly coordinated position. The substitution of a Sc atom for an Au atom in the Au_n+1 cluster markedly changes the structure of the host cluster. Moreover, we confirm that the ground-state Au₆Sc cluster has a distortion to a lower D_2h symmetry. The relative stabilities and electronic properties of the lowest-energy Au_nSc clusters are analyzed based on the averaged binding energies, second-order energy differences, fragmentation energies, chemical hardnesses, and HOMO-LUMO gaps. It is found that the magic Au₃Sc cluster can be perceived as a superatom with high chemical stability and its HOMO-LUMO gap is larger than that of the closed-shell Zr@Au₁₄ cluster. The high symmetry and spin multiplicity of the Au₃Sc and Au₆Sc clusters are responsible for their large vertical ionization potential and electron affinity. The magnetism calculations indicate that the magnetic moment of the Sc atom in the ground-state Au_nSc (n=2-8) clusters gradually decreases for even n and is completely quenched for odd n.