原子团簇的稳定结构和幻数

原子团簇介于原子分子和宏观凝聚物质之间 ,一般产生于非平衡条件 ,其结构和性质随所含原子数目而变化。当含有某些特定原子数时 ,团簇特别稳定 ,这就是“幻数”。本文重点讨论几种典型团簇的幻数及其演变规律 ,说明“幻数”是团簇的基本属性之一及其与键合方式的关系     

Diffraction of neutral helium clusters: evidence for "magic numbers"

The size distributions of neutral 4He clusters in cryogenic jet beams, analyzed by diffraction from a 100 nm period transmission grating, reveal magic numbers at N=10-11, 14, 22, 26-27, and 44 atoms. Whereas magic numbers in nuclei and clusters are attributed to enhanced stabilities, this is not expected for quantum fluid He clusters on the basis of numerous calculations. These magic numbers occur at threshold sizes for which the quantized excitations calculated with the diffusion Monte Carlo method are stabilized, thereby providing the first experimental confirmation for the energy levels of 4He clusters.     

Structures of inert atomic clusters and their magic numbers of geometry

The optimal configurations of all atoms in atomic microclusters of an inert element have been obtained from their arbitrary positions and shapes by means of a Lennard-Jones interaction potential between atoms in the clusters, calculating the binding energies of the clusters with the numbers of atoms N ⩽ 14, which have shown the magic numbers of geometry in accordance with the experimental results. The structural pictures of such clusters are also presented.     

Geometric magic numbers of sodium clusters: Interpretation of the melting behaviour

Putative global minima of sodium clusters with up to 380 atoms have been located for two model interatomic potentials in order to identify the structures responsible for the size-dependence of the thermodynamic properties in experiments. Structures based upon the Mackay icosahedra predominate for both potentials, and the magic numbers for the Murrell-Mottram model show excellent agreement with the sizes at which maxima in the latent heat and entropy change at melting have been found in experiment. In particular, the magic numbers at sizes intermediate between the complete Mackay icosahedra are due to unusual twisted icosahedral structures.     

Aln(n=2～7)团簇的结构和能级分布

采用密度泛函B3LYP的方法研究了小原子团簇Al2～7的几何结构和能级分布,分析了随团簇原子数的增加,团簇的几何结构和费米能级的变化情况.研究结果表明:Al2～7的团簇的几何结构在5个原子以前为平面结构,而从六个原子开始为空间立体的稳定结构.电子壳层结构表明,在铝团簇中没有出现非常明显的象碱金属那样的稳定幻数结构.在Al2～Al7团簇中,能级结构呈现明显的分立特征,费米能级随着原子个数的增加而减小,到Al7时又有所增加,且团簇的能量间隙最小.     

Magic numbers of sodium clusters

The cohesive energy E_c of crystalline-like b.c.c. and f.c.c. sodium clusters is calculated as a function of the number of atoms in the cluster using the density functional formalism. The maxima of E_c define the theoretical magic numbers for crystalline clusters. A comparison with theoretical results using the jellium background model and with experimental magic numbers obtained by Knight and co-workers suggests that sodium clusters prepared in those expeiments are in a disordered liquid-like or amorphous state.     

Structure and stability of clusters on metal surfaces

Small clusters of 3d metals Ni/Ni(001), Cu/Cu(001), 4d-Pd/Pd(001), Ag/Ag(001), 5d-Pt/Pt(001), and Au/Au(001) are investigated by semiempirical methods using multiparticle interatomic interaction potentials. It is shown that the same magic numbers (4, 6, and 9) are characteristic for all metals indicated; these numbers are determined by the symmetry characteristics of the clusters, related to the morphology of the fcc (001) substrate. It is shown for Pt/Pt(111) that small clusters of seven, ten, and more atoms are stable for the fcc (111) surface. This confirms that the magic numbers are associated with the symmetry of the clusters. Fiz. Tverd. Tela (St. Petersburg) 41, 1329–1334 (July 1999)     

Magic numbers and erratic level crossings of double-well Bose-Einstein condensates

By developing an approach by which we are able to quickly obtain spectra and eigenstates, we reveal for what is believed to be the first time the two novel phenomena of magic numbers and erratic level crossings in double-well Bose-Einstein condensates of N atoms. For N < or = 27 and values of U/J that are not too small (U is the two-body interaction strength, and J is the hopping parameter), systems with even atoms are shown to be much more stable than those with odd atoms, and hence even integers play a role in such systems as if they were the magic numbers of nuclei. For N > or = 30, erratic level crossings occur as NU > J.     

Hemispheroidal quantum harmonic oscillator

A deformed single-particle shell model is derived for a hemispheroidal potential well. Only the negative parity states of the Z(z) component of the wave function are allowed, so new magic numbers are obtained. The influence of a term proportional to l² in the Hamiltonian is investigated. The maximum degeneracy is reached at a superdeformed hemispheroidal prolate shape whose magic numbers are identical with those obtained at the spherical shape of the spheroidal harmonic oscillator. This remarkable property suggests an increased stability of such a distorted shape of deposited clusters when the planar surface remains opaque.     

Stability and magic numbers of hetero-atomic clusters of simple metals

The main trends in the magic numbers observed for a class of simple-metal hetero-atomic clusters M_xN (M = Na or K; N = monovalent or divalent impurity; X = number of host atoms) is explained using an extension of the jellium model of clusters. The appearance of a “new” magic number, n = 10 (n = number of valence electrons), and the growing importance of n = 20 over n = 18, as Δ₊ increases (Δ₊ is the difference in the density of the jellium backgrounds of the two metals) are explained by an inversion of the order of the energy levels with respect to that of pure clusters.     

Properties of small- to medium-sized mercury clusters from a combined ab initio,density-functional,and simulated-annealing study

Relativistic coupled-cluster and second-order many-body perturbation theories were used to construct two- and three-body potentials for the interaction between mercury atoms. A subsequent combined simulated-annealing downhill simplex and conjugate gradient-optimization procedure gave global minima for mercury clusters with up to 30 atoms. The calculations reveal magic cluster numbers of 6, 13, 19, 23, 26, and 29 atoms. At these cluster sizes, the static dipole polarizability obtained from density-functional theory has a minimum. The calculations also reveal a fast convergence of the polarizability towards the bulk limit in contrast to the singlet-triplet gap or the ionization potential.     

Element- and size-dependent electron delocalization in AuNX+ clusters (X = Sc,Ti, V,Cr, Mn,Fe, Co,Ni)

We investigated the stability of gold clusters doped with open 3d-shell atoms (Sc, Ti, V, Cr, Mn, Fe, Co, Ni). Steps, peaks, and odd-even staggering in mass abundance spectra upon photofragmentation provide evidence for enhanced stability for specific cluster sizes. The observed magic numbers are explained in terms of size- and dopant-dependent modifications of the effective mean-field potential within a phenomenological shell-model approach. Element-dependent 3d electron delocalization and odd-even staggering amplitudes are related to the dopant-atom structure.     

Discrete periodic melting point observations for nanostructure ensembles

We report a study of the thermodynamic properties of indium clusters on a SiN (x) surface during the early stages of thin film growth using a sensitive nanocalorimetry technique. The measurements reveal the presence of abnormal discontinuities in the heat of melting below 100 degrees C. These discontinuities, for which temperature separation corresponds to a spatial periodicity equal to the thickness of an indium monolayer, are found to be related to the atomic "magic numbers," i.e., the number of atoms necessary to form a complete shell of atoms at particle surface.     

Magic numbers in metallo-inorganic clusters: chromium encapsulated in silicon cages

A systematic theoretical study of the equilibrium geometries and total energies of Cr encapsulated in Si clusters reveals that Cr@Si(12) is more stable than its neighbors. The origin of this enhanced stability is consistent with the 18-electron sum rule commonly used in the synthesis of stable chemical complexes, and may provide a criterion for a systematic search of magic numbers in metalloinorganic clusters. The 6 mu(B) magnetic moment of the caged Cr atom, the largest among the 3d transition metal atoms, is completely quenched. This effect of caging on the properties of transition metal atoms may lead to the synthesis of novel cluster based materials.     

Magic rule for Al(n)H(m) magic clusters

Using the electronic shell closure criteria, we propose a new electron counting rule that enables us to predict the size, composition, and structure of many hitherto unknown magic clusters consisting of hydrogen and aluminum atoms. This rule, whose validity is established through a synergy between first-principles calculations and anion-photoelectron spectroscopy experiments, provides a powerful basis for searching magic clusters consisting of hydrogen and simple metal atoms.     

Experimental study of the spatial distributions of relativistic electron beams reflected and refracted by a thin foil

The ratio of the cross section for inelastic scattering to the total cross section for scattering of a fast electron by a cluster, depending on the number of atoms in the cluster, is shown to be not a monotonic function. This nonmonotonicity is not related to the well-known nonmonotonic dependences determined, for example, by the magic numbers in the shell model of clusters but is of purely quantum origin: the coherence of elastic electron scattering and the incoherence of inelastic one by a multipartice target.     

密度泛函理论研究H2与Rhn（n=1—8）团簇的相互作用

采用密度泛函理论对H₂与Rh_n（n=1—8）团簇的相互作用进行了系统研究.结果表明, Rh_nH₂体系的最低能量结构是在Rh_n团簇最低能量结构的基础上吸附H原子生长而成.吸附H原子没有改变Rh_n团簇的结构, 键长是影响Rh_n和Rh_nH₂磁矩的主要因素.从优化后的几何结构可以看出吸附后的H₂发生断键,表明H₂分子发生了解离性吸附.当n≤5,H原子的吸附以桥位为主,当n≥6时,H原子开始出现空位吸附.H原子的吸附提高了Rh_n的稳定性和化学活性,较小的吸附能表明H原子易从Rh_nH₂中解离出来.二阶能量差分表明4是Rh_nH₂和Rh_n团簇的幻数. 关键词： nH₂和Rh_n团簇')" href="#">Rh_nH₂和Rh_n团簇 平衡结构 电子性质     

Density functional theory study of MgnNi2 （n=1-6） clusters

The geometries of Mg n Ni 2(n = 1-6) clusters are studied by using the hybrid density functional theory(B3LYP) with LANL2DZ basis sets.For the ground-state structures of Mg n Ni 2 clusters,the stabilities and the electronic properties are investigated.The results show that the groundstate structures and symmetries of Mg clusters change greatly due to the Ni atoms.The average binding energies have a growing tendency while the energy gaps have a declining tendency.In addition,the ionization energies exhibit an odd-even oscillation feature.We also conclude that n = 3,5 are the magic numbers of the Mg n Ni 2 clusters.The Mg 3 Ni 2 and Mg 5 Ni 2 clusters are more stable than neighbouring clusters,and the Mg 4 Ni 2 cluster exhibits a higher chemical activity.     

Doping of magic nanoclusters in the submonolayer In/Si(100) system

Si(100)4 x 3-In reconstruction is essentially a superlattice of magic (identical-size) Si7In6 nanoclusters. Using scanning tunneling microscopy (STM) observations, we have found that under appropriate growth conditions up to 35% of these clusters can be modified; namely, two Si atoms in the cluster can be replaced by two In atoms, thus forming a Si5In8 cluster. This modification can be considered as a doping of the magic cluster, as it changes the electronic properties of the cluster from semiconducting towards metallic. The doped cluster is less rigid than the ordinary one and swings in the electrical field of the STM tip. The atomic structure and stability of the doped magic cluster have been examined using first-principles total-energy calculations.     

Structure and thermodynamic characteristics of small inert gas clusters

The relaxation dynamics of small groups of identical atoms interacting according to the Lennard-Jones law was studied experimentally. It is shown that for a fixed number of atoms, the probabilities of the formation of clusters with different structures depend on the random initial distribution of atoms in space, i.e., on the initial total energy and geometry of the particle distribution. Probabilities of the emergence of different structures of clusters vary greatly and do not contradict classical statistics. Except in extraordinary cases (e.g., N = 13), distances between the nearest atoms in clusters are different and change with the addition of each subsequent atom. The thermodynamics is constructed from the canonical ensembles of clusters with different numbers of particles. The resulting dependence of the cluster energy on the number of particles proves to be a smooth function, since only pair interactions were taken into account.