Structures and energetics of small lead cluster ions

By a combination of gas phase ion mobility measurements and relativistic density functional theory calculations with inclusion of spin-orbit coupling, we assign structures of lead cluster cations and anions in the range between 4 and 15 atoms. We find a planar rhombus for the tetramer, a trigonal bipyramid for the pentamer, and a pentagonal bipyramid for the heptamer, independent of charge state. For the hexamer, the cation and anion structures differ: we find an octahedron for the anion while the cation consists of fused tetrahedra. For the octamer, we find in both cases structures based on the pentagonal bipyramid motif plus adatom. For the larger clusters investigated we always find different structures for cations and anions. For example, Pb(12)(-) is confirmed to be a hollow icosahedron while Pb(12)(+) is a truncated filled icosahedron. Pb(13)(+) is a filled icosahedron but Pb(13)(-) is a hollow icosahedron with the additional atom capping a face. In order to get experimental information on the relative stabilities, we investigated the collision induced dissociation mass spectra for the different cluster sizes and charge states, and observe a strong correlation with the calculated fragmentation energies. Up to n = 13 the main fragmentation channel is atom loss; for the larger cluster sizes we observe fission into two large fragments. This channel is dominant for larger anions, less pronounced but clearly present for the cations.     

Special stability of cationic MPb12+ clusters and superalkali character of neutral MPb12 clusters (M = B, Al, Ga, In, and Tl)

The electronic structures and stabilities of cationic MPb12+ clusters (M = B, Al, Ga, In, and Tl) with 50 valence electrons are investigated within density functional theory. It is shown that, at the B3LYP/cc-pVDZ(-PP) and BPW91/cc-pVDZ(-PP) levels of theory, the structures of MPb12+ with icosahedra (I(h)) symmetry are energetically favorable, and their high stabilities may arise from the closed-shell nature of the pi subsystems which are subject to the 2(N(pi + 1)2 rule with N(pi = 1). In addition, the possessing of large nucleus-independent chemical shifts of the five kinds of clusters reflects the common aromatic character of these clusters. From the comparison of our studies on the binding energies and the highest occupied molecular orbital and the lowest unoccupied molecular orbital energy gaps, the cluster AlPb12+ has higher stability than the others and this is consistent with the recent mass-spectrometric discovery of Al-doped Pb(n)+ clusters, in which AlPb12+ is highly abundant. The same methods are used to search for the structures of the neutral MPb12 clusters. The calculations reveal that the most stable geometries of the BPb12 and GaPb12 clusters have I(h) symmetry, the AlPb12 and InPb12 clusters have T(h) symmetry, and the TlPb12 cluster has C5v symmetry. Furthermore, the vertical ionization potentials of the neutral MPb12 clusters are smaller than that of some alkali atoms, indicating that the neutral MPb12 clusters possess superalkali character.     

Structure and stability of small boron and boron oxide clusters

To rationally design and explore a potential energy source based on the highly exothermic oxidation of boron, density functional theory (DFT) was used to characterize small boron clusters with 0-3 oxygen atoms and a total of up to ten atoms. The structures, vibrational frequencies, and stabilities were calculated for each of these clusters. A quantum molecular dynamics procedure was used to locate the global minimum for each species, which proved to be crucial given the unintuitive structure of many of the most stable isomers. Additionally, due to the plane-wave, periodic DFT code used in this study a straightforward comparison of these clusters to the bulk boron and B2O3 structures was possible despite the great structural and energetic differences between the two forms. Through evaluation of previous computational and experimental work, the relevant low-energy structures of all but one of the pure boron clusters can be assigned with great certainty. Nearly all of the boron oxide clusters are described here for the first time, but there are strong indications that the DFT procedure chosen is particularly well suited for the task. Insight into the trends in boron and boron oxide cluster stabilities, as well as the ultimate limits of growth for each, are also provided. The work reported herein provides crucial information towards understanding the oxidation of boron at a molecular level.     

Formation,growth mechanism and packing sequences of binary alloy cluster anions from laser ablation of mixtures of lead and transition metals

By using laser ablation of the mixtures of a transition metal (M: Ti, Cr, Mn, Fe, Co, Ni, Cu, Zn, Pd, Ag) plus lead, M/Pb binary cluster anions were observed except for Zn, and the number of transition metal atoms contained in the binary clusters is at most 4. This behavior is different from that reported previously for M/Ge binary clusters. The experiments indicate that it is also very difficult to form Al/Pb clusters. The distribution patterns of M/Pb binary alloy cluster anions are remarkably similar to those of pure Pb clusters, consistent with a formation mechanism in which transition metal atoms are sequentially attached to [M(x-1)Pb(y)](-) clusters and thus form [M(x)Pb(y)](-) clusters by a simple condensation process. As the number of transition metal atoms increases, the intensities of binary clusters gradually decrease. It is proposed that [MPb(4)](-) and [MPb(5)](-) cluster anions might be the unit building blocks of M/Pb binary cluster anions, and the layer packing sequences for magic clusters are predicted on this basis. The [M(x)Pb(y)](-) binary clusters containing 13 atoms (x + y = 13; x not equal 0) are proposed to have an icosahedral structure.     

Structures of medium sized tin cluster anions

The structures of medium sized tin cluster anions Sn(n)(-) (n = 16-29) were determined by a combination of density functional theory, trapped ion electron diffraction and collision induced dissociation (CID). Mostly prolate structures were found with a structural motif based on only three repeatedly appearing subunit clusters, the Sn(7) pentagonal bipyramid, the Sn(9) tricapped trigonal prism and the Sn(10) bicapped tetragonal antiprism. Sn(16)(-) and Sn(17)(-) are composed of two face connected subunits. In Sn(18)(-)-Sn(20)(-) the subunits form cluster dimers. For Sn(21)(-)-Sn(23)(-) additional tin atoms are inserted between the building blocks. Sn(24)(-) and Sn(25)(-) are composed of a Sn(9) or Sn(10) connected to a Sn(15) subunit, which closely resembles the ground state of Sn(15)(-). Finally, in the larger clusters Sn(26)(-)-Sn(29)(-) additional bridging atoms again connect the building blocks. The CID experiments reveal fission as the main fragmentation channel for all investigated cluster sizes. This rather unexpected "pearl-chain" cluster growth mode is rationalized by the extraordinary stability of the building blocks.     

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.     

Finite temperature path integral Monte Carlo simulations of structural and dynamical properties of Ar(N)-CO(2) clusters

We report finite temperature quantum mechanical simulations of structural and dynamical properties of Ar(N)-CO(2) clusters using a path integral Monte Carlo algorithm. The simulations are based on a newly developed analytical Ar-CO(2) interaction potential obtained by fitting ab initio results to an anisotropic two-dimensional Morse∕Long-range function. The calculated distributions of argon atoms around the CO(2) molecule in Ar(N)-CO(2) clusters with different sizes are consistent to the previous studies of the configurations of the clusters. A first-order perturbation theory is used to quantitatively predict the CO(2) vibrational frequency shift in different clusters. The first-solvation shell is completed at N = 17. Interestingly, our simulations for larger Ar(N)-CO(2) clusters showed several different structures of the argon shell around the doped CO(2) molecule. The observed two distinct peaks (2338.8 and 2344.5 cm(-1)) in the υ(3) band of CO(2) may be due to the different arrangements of argon atoms around the dopant molecule.     

铜簇Cun-和羰基铜簇CunCO-(n=2～7)的结构与光谱性质的密度泛函理论研究

应用相对论有效核势密度泛函理论计算方法研究了Cun-和CunCO-簇的平衡几何构型、稳定性、主要碎片化模式、CO吸附能及其团簇的光谱性质.计算结果表明,奇数簇Cun-的电离势比其相邻偶数簇Cun-的电离势大;奇数的Cu5CO-簇有最大的CO解离能.奇数铜簇阴离子相对较高的稳定性与近似浆汁模型的8电子电子闭壳层效应一致.计算得到的Cun-簇碎片化能量表明,较小Cun-的优势解离通道与其包含Cu原子数目的奇偶性有关,偶数的Cun-簇主要解离为Cu原子和Cun-1-,而奇数Cun-簇易以解离成铜的二聚物Cu2和Cun-2-.基于密度泛函理论计算,讨论了这些簇的静态极化率和CO吸附性质与簇大小的关系.     

Structure and energetics of small gold nanoclusters and their positive ions

We performed density functional theory calculations at the PW91PW91/LANL2DZ, PW91PW91/Stuttgart 1997, PW91PW91/CRENBL, B3LYP/LANL2DZ, and SVWN5/LANL2DZ levels of theory to attain the minimum-energy structures of neutral and cationic gold clusters of up to nine gold atoms. We locate the 2D-to-3D (two-dimensional to three-dimensional) transition in cationic clusters as occurring between Au(8) (+) and Au(9) (+). We also demonstrate that we can correlate the 2D-to-3D transition in cationic clusters with a linear extrapolation of the energy differences of the lowest-lying 2D and 3D structures of cluster sizes below the transition. We then use the same approach to predict that the 2D-to-3D transition occurs in neutral clusters at Au(11); this is confirmed by locating 3D Au(11) structures that are lower in energy than the best 2D structures reported to date. We examine the effects of choice of basis sets and exchange-correlation functionals on the relative stabilities and other properties of the calculated structures. Finally we find that there is good agreement between calculated and experimental data for clusters with up to six constituent atoms. For clusters with more than seven atoms, there are significant differences observed between the calculated and experimental properties using SVWN5/LANL2DZ, but there is still good agreement for the other levels of theory used.     

多体展开势能函数在碳族元素原子簇研究中的应用III. 锗原子族的结构和相对稳定性

基于从晶体锗确立的多体展开势能函数, 本文通过坐标完全优化, 发现小的锗原子簇分子(Ge~2~Ge~14)倾向于形成密堆积结构, 表面原子分布以蝶形四元环(D~2d)为主; 常见立方晶体“微观晶体碎片”的分层优化结果表明, 在Ge~15~Ge~100范围内, 多数壳层的原子到分子中心的距离均受到压缩, 且以畸变的简单立方、面心立方及体心立方较为稳定; 在这些畸变密堆积结构中, 表面原子向内压缩最为严重, 使整个分子趋于球形化。较为开放的金刚石类层状原子族只有当所含原子数达数百以上时才可能相对更为稳定。     

Structure evolution of gold cluster anions between the planar and cage structures by isoelectronic substitution: Au(n)- (n = 13-15) and MAu(n)- (n = 12-14; M = Ag, Cu)

The structural and electronic effects of isoelectronic substitution by Ag and Cu atoms on gold cluster anions in the size range between 13 and 15 atoms are studied using a combination of photoelectron spectroscopy and first-principles density functional calculations. The most stable structures of the doped clusters are compared with those of the undoped Au clusters in the same size range. The joint experimental and theoretical study reveals a new C(3v) symmetric isomer for Au(13)(-), which is present in the experiment, but has hitherto not been recognized. The global minima of Au(14)(-) and Au(15)(-) are resolved on the basis of comparison between experiment and newly computed photoelectron spectra that include spin-orbit effects. The coexistence of two isomers for Au(15)(-) is firmly established with convincing experimental evidence and theoretical calculations. The overall effect of the isoelectronic substitution is minor on the structures relative to those of the undoped clusters, except that the dopant atoms tend to lower the symmetries of the doped clusters.     

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.     

质子化丙酮分子团簇的结构和振动光谱

The stable structures and vibrational spectra of protonated acetone molecule clusters with different sizes （CH3COCH3）nH +（n=1-7）are calculated at the 6-31G（d）level by means of density functional theory （B3LYP）quantum chemical calculations. The corresponding energies are analyzed at the level B3LYP/6-311+G（3df,2p）in order to obtain more accurate results. The proton affinity of neutral cyclic acetone molecule clusters increases with the increasing of cluster size. The calculated results show that the protonated acetone clusters have certain growth regularity with forming a solvation shell at the beginning and then new added acetone molecule attacking different active sites including the middle carbon atoms and the different methyl in solvation shell. The IR spectra of the protonated clusters are more complicate than that of neutral ones. The strongest peaks result from the movement of the proton between the two oxygen atoms in solvant shell apart from the case of n=1. Carbonyl stretching vibraional peaks split into the more and more and in general the corresponding intensities are weakened due to the protonation with the increasing of cluster size.     

Ru_n(n=2~8)金属团簇的结构和能级分布的DFT研究

采用密度泛函理论中的广义梯度近似(DFT/GGA)方法,对Run团簇(n = 2~8)的几何结构与稳定性、束缚能以及能级分布的关系进行了研究,并分析了随着团簇原子数的增加,团簇的几何结构和费米能级的变化,结果表明:Ru簇的几何结构在4个原子以前是平面结构,而从5个原子开始为空间立体的稳定结构,束缚能随金属原子数的增加而增加。能级结构呈明显的分立特征,费米能级随原子个数的增加而增加,但从Ru7开始又有所降低,且团簇的能量间隙逐渐减小,趋近于大块金属的能级特征。     

Electronic properties of Si and Ge atoms doped in clusters: In(n)Si(m) and In(n)Ge(m)

Electronic properties of silicon and germanium atom doped indium clusters, In(n)Si(m) and In(n)Ge(m), were investigated by photoionization spectroscopy of the neutrals and photoelectron spectroscopy of the anions. Size dependence of ionization energy and electron affinity for In(n)Si(1) and In(n)Ge(1) exhibit pronounced even-odd alternation at cluster sizes of n = 10-16, as compared to those for pure In(n) clusters. This result shows that symmetry lowering with the doped atom of Si or Ge results in undegeneration of electronic states in the 1d shell formed by monovalent In atoms.     

Binding energy of large icosahedral and cuboctahedral Lennard-Jones clusters

It is widely believed that the lowest energy configurations for small rare gas clusters have icosahedral symmetry. This contrasts with the bulk crystal structures which have cuboctahedral fcc symmetry. It is of interest to understand the transition between this finite and bulk behavior. To model this transition in rare gas clusters we have undertaken optimization studies within the Lennard-Jones pair potential model. Using a combination of Monte Carlo and Partan Search optimization methods, the lowest energy relaxed structures of Lennard-Jones clusters having icosahedral and cuboctahedral symmetry were found. Studies were performed for complete shell clusters ranging in size from one shell having 13 atoms to 14 shells having 10,179 atoms. It was found that the icosahedral structures are lower in energy than the cuboctahedral structures for cluster sizes having 13 shells or fewer. Additional studies were performed using the more accurate Aziz-Chen [HFD-C] pair potential parameterized for argon. The conclusions appear to be relatively insensitive to the form of the potential.     

Synthesis and characterization of an Al(69)(3-) cluster with 51 naked Al atoms: analogies and differences to the previously characterized Al(77)(2-) cluster

A disproportionation process of a metastable AlCl solution with a simultaneous ligand exchange-Cl is substituted by N(SiMe(3))(2)-leads to a [Al(69)[N(SiMe(3))(2)](18)](3-) cluster compound that can be regarded as an intermediate on the way to bulk metal formation. The cluster was characterized by an X-ray crystal structural analysis. Regarding its structure and the packing within the crystal, this metalloid cluster with 4 times more Al atoms than ligands is compared to the [Al(77)N(SiMe(3))(2)](20)](2-) cluster that has been published four years ago. Although there is a similar packing density of the Al atoms in both clusters as well as in Al metal, the X-ray structural analysis shows significant differences in topology and distance proportions. The differences between these-at a first glance almost identical-Al clusters demonstrate that results of physical measuring, e.g., of nanostructured surfaces which carry supposedly identical cluster species, have to be interpreted with great caution.     

Ab initio study of small acetonitrile cluster anions

Ab initio electronic structure calculations have been performed for (CH(3)CN)(2) (-) and (CH(3)CN)(3) (-) cluster anions using a diffuse basis set. We found both the dipole-bound structures and internal structures, where in the former structure an excess electron is mainly distributed on the surface of the cluster while an excess electron is internally trapped in the latter configuration. The optimized structures found for cluster anions were compared to those for neutral clusters. Potential-energy surfaces were also plotted as a function of appropriate internal coordinates in order to understand the interconversions of the optimized structures of clusters. The relative stabilities of the optimized confirmers have been discussed on the basis of the characteristics of these potential surfaces, relative energies, and electron vertical detachment energies.     

Nitric oxide decomposition on small rhodium clusters, Rh(n)+/-

The decomposition of nitric oxide on small charged rhodium clusters Rh(n)(+/-) (6 < n < 30) has been investigated by Fourier transform ion cyclotron resonance mass spectrometry. For both cationic and anionic naked clusters, the rates of reaction with NO increase smoothly with cluster size in the range studied without the dramatic size-dependent fluctuations often associated with the reactions of transition-metal clusters. The cationic clusters react significantly faster than the anions and both exhibit rate constants exceeding collision rates calculated by average dipole orientation theory. Both the approximate magnitude and the trends in reactivity are modeled well by the surface charge capture model recently proposed by Kummerl?we and Beyer. All clusters studied here exhibit pseudo-first-order kinetics with no sign of biexponential kinetics often interpreted as evidence for multiple isomeric structures. Experiments involving prolonged exposure to NO have revealed interesting size-dependent trends in the mechanism and efficiency of NO decomposition: For most small clusters (n < 17), once two NO molecules are coadsorbed on a cluster, N(2) is evolved, generating the corresponding dioxide cluster. By analogy with experiments on extended surfaces, this observation is interpreted in terms of the dissociative adsorption of NO in the early stages of reaction, generating N atoms that are mobile on the surface of the cluster. For clusters where n < 13, this chemistry, which occurs independently of the cluster charge, repeats until a size-dependent, limiting oxygen coverage is achieved. Following this, NO is observed to adsorb on the oxide cluster without further N(2) evolution. For n = 14-16 no single end-point is observed and reaction products are based on a small range of oxide structures. By contrast, no evidence for N(2) production is observed for clusters n = 13 and n > 16, for which simple sequential NO adsorption dominates the chemistry. Interestingly, there is no evidence for the production of N(2)O or NO(2) on any of the clusters studied. A simple general mechanism is proposed that accounts for all observations. The detailed decomposition mechanisms for each cluster exhibit size (and, by implication, structure) dependent features with Rh(13)(+/-) particularly anomalous by comparison with neighboring clusters.     

InAs管状团簇及单壁InAs纳米管的结构、稳定性和电子性质

采用密度泛函理论研究了InnAsn (n≤90)管状团簇以及单壁InAs纳米管的几何结构、稳定性和电子性质. 小团簇InnAsn (n=1-3)基态结构和电子性质的计算结果与已有报道相一致. 当n≥4时优化得到了一族稳定的管状团簇, 其结构基元(In原子与As原子交替排列的四元环和六元环结构)满足共同的衍化通式. 团簇的平均结合能表明横截面为八个原子的管状团簇稳定性最好. 管状团簇前线轨道随尺寸的变化规律有效地解释了一维稳定管状团簇的生长原因, 同时也说明了实验上之所以能合成InAs纳米管的微观机理. 此外, 研究结果表明通过管状团簇的有效组装可得到宽带隙的InAs半导体单壁纳米管.