Molecular-dynamics simulation of the structural stability,energetics, and melting of Cu n(n = 13–135) clusters

Cluster properties of copper have been investigated using the Molecular-Dynamics md technique. The structural stability and energetics of spherical Cu_n (n = 13–135) clusters have been investigated at temperatures T = 1 K and T = 300 K. It has been found that the average interaction energy per atom in the cluster decreases and reaches an asymptotic value as cluster size increases. The melting behaviour of clusters n = 13 and n = 55 have been investigated. It has been found that the melting temperature decreases as cluster size increases, and for clusters with multishell structures melting starts from the outermost shell. In the simulation an emprical potential energy function (PEF) proposed by Erkoç has been used, which contains two-body atomic interactions.     

Geometrical and electronic properties of neutral and charged cesium clusters Cs(n) (n=2-10): a theoretical study

We have investigated the structure and electronic properties of cesium clusters following all electron ab initio theoretical methods based on configuration interaction, second-order Moller-Plesset (MP2) perturbation theory, and density-functional theory. Becke's three-parameter nonlocal hybrid exchange-correlation functional (B3LYP) is found to perform best on the present systems with a split valence 3-21G basis function. We have calculated the optimized geometries of neutral and singly charged cesium clusters having up to ten atoms, their binding energy per atom, ionization potentials (IPs), and adiabatic electron affinity (EA). Geometry optimizations for all the clusters are carried out without imposing any symmetry restriction. The neutral clusters having up to six atoms prefer planar structure and three-dimensional structure is preferred only when the number of atoms in a cluster is more than six. There is a good agreement between the present theoretical and reported experimental IP values for the neutral clusters with cluster size n相似文献   

Size dependent melting mechanisms of iron nanoclusters

Molecular dynamics simulations were used to study the change in the mechanism of iron cluster melting with increasing cluster size. Melting of smaller clusters (e.g., Fe₅₅ and Fe₁₀₀) occurs over a large temperature interval where the phase of the cluster repeatedly oscillates between liquid and solid. In contrast, larger clusters (e.g., Fe₃₀₀) have sharper melting points with surface melting preceding bulk melting. The importance of the simulation time, the force field and the definition of cluster melting is also discussed.     

Molecular Dynamics Studies of the Kinetics of Phase Changes in Clusters II: Crystal Nucleation from Molten (RbCl)256 and (RbCl)500 Clusters

Molecular dynamics computer simulations have been carried out to study the effects of cluster size and temperature on the nucleation rate of rubidium chloride clusters in the temperature range of 500-650 K. Clusters with 256 and 500 RbCl molecules have been studied and the results are compared with those obtained from 108 molecule clusters. The melting point (MP) of the clusters was observed to increase with the size of the clusters and can be described by a linear equation MP=997-405 N^−1/3, where N is the number of molecules in the cluster. The nucleation rate is found to decrease with increasing cluster size or increasing nucleation temperature. Both classical nucleation theory and diffuse interface theory are used to interpret our observed results.     

The local electronic and magnetic properties of Fe impurity in Al clusters

The local magnetic property,d electronic structure and the charge transfer effect of Fe impurity in Al clusters have been studied by using a tight-binding model Hamiltonian in the unrestricted Hartree-Fock approximation, which includes intra-atomic and interatomic Coulomb interactions. We have obtained that local magnetic moment of Fe impurity in FeAl _N clusters decreases with increasing cluster size and convergences to zero (that of bulk given by Anderson) withN larger than 12, meanwhile, the local magnetic moment for smaller clusters depends on the clusters size and it is a monotonous descent function of cluster size. We have also found that the spin splitting of the localizedd states decreases as the cluster size increases, which mainly results from the interaction between the localized electrons of Fe atom and the delocalized electrons of Al atoms.     

Magnetic properties of 3d-transition-metal alloy clusters: (Fe x Cr1−x ) n

We present results for the magnetic properties of (Fe _x Cr_1?x ) _n alloy clusters obtained by using a tight-binding Hubbard Hamiltonian in the unrestricted Hartree-Fock approximation. The dependence of the average magnetic moment, local magnetic moments, magnetic order, and cohesive energy on the size and composition of the cluster were determined. In agreement with surface calculations, we find that the average magnetic moment of the alloy is larger than that of the cluster of one element. Forn=15 a transition from ferromagnetic to antiferromagnetic order is obtained forx≈0.4?0.53. We discuss the importance of the overlap interaction in the spin polarized charge distribution of the alloy (e.g., charge transfer, local magnetic moments). The characteristic properties of the mixed clusters are also discussed by comparison with available results for homogeneous clusters.     

Size of free neutral CO2 clusters from carbon 1s ionization energies

Free neutral CO(2) clusters were produced by adiabatic expansion and characterized by carbon 1s (C1s) photoelectron spectroscopy using synchrotron radiation. The shift in C1s ionization energy (IE) between the cluster and the monomer, i.e., ΔIE = IE(cluster) - IE(monomer), was found to vary systematically with the experimental conditions. A functional relationship is established between the mean cluster size in the beam, , and ΔIE, in good agreement with theoretical calculations of shifts in ionization energy for model clusters. This makes it possible to use core-level photoelectron spectroscopy to monitor the mean cluster size and also to estimate from expansion conditions.     

Structures, energetics and vibrational spectra of CO2 clusters through molecular tailoring and cluster building algorithm

Clusters of CO(2) are a subject of detailed experimental as well as theoretical investigations due to their interesting applications. In the present article, CO(2) clusters (n = 6 to 13) are studied at the MP2 level of theory. The clusters are grown using a cluster building algorithm developed by our group and the larger ones are optimized at the MP2/aug-cc-pVDZ level by employing a Molecular Tailoring Approach (MTA). Vibrational spectra of these clusters are also calculated at this level of theory within MTA. The computed vibrational frequencies for an asymmetric C-O stretch generally exhibit a blue shift with increasing cluster size. This observation is in agreement with the experimental results. MTA-single point energies for each cluster size at the MP2/aug-cc-pVTZ level are also calculated for estimating the interaction energies at the complete basis set limit.     

Structure, bonding, and magnetism in manganese clusters

We investigate the structures and magnetic properties of small Mn(n) clusters in the size range of 2-13 atoms using first-principles density functional theory. We arrive at the lowest energy structures for clusters in this size range by simultaneously optimizing the cluster geometries, total spins, and relative orientations of individual atomic moments. The results for the net magnetic moments for the optimal clusters are in good agreement with experiment. The magnetic behavior of Mn(n) clusters in the size range studied in this work ranges from ferromagnetic ordering (large net cluster moment) for the smallest (n=2, 3, and 4) clusters to a near degeneracy between ferromagnetic and antiferromagnetic solutions in the vicinity of n=5 and 6 to a clear preference for antiferromagnetic (small net cluster moment) ordering at n=7 and beyond. We study the details of this evolution and present a picture in which bonding in these clusters predominantly occurs due to a transfer of electrons from antibonding 4s levels to minority 3d levels.     

On the localization of electrons and holes in Hg n and rare-gas clusters

We have used a microscopic theory to study the size dependence of the degree of localization of the valence electrons and holes in neutral an ionized rare-gas-and Hg _n clusters. We discuss under which circumstances localization of the electrons and holes is favoured. We have calculated the ionization potential of Xe _n , Kr _n and small Hg _n clusters. Good agreement with experiments is obtained. We have also determined the dependence of the ionization potential on cluster structure.     

Structure and Magnetism of Hybrid Fe and Co Nanoclusters up to N?≤?7 Atoms

The structural and magnetic properties of small gas-phase Fe _m Co _n clusters with m?+?n ranging between 2 and 7 atoms are investigated using spin-polarized density functional theory. For a given cluster size possible compositions are subject to optimization using a variety of initial structures. The geometry, bond lengths, binding energies and magnetization are reported for the lowest energy structures. The results show that a magnetization peak occurs for Fe₄, while for hybrid clusters, switching a cobalt atom with an iron atom increases the cluster’s total magnetization by 1?μ _B . Our structural predictions are generally in agreement with other theoretical results; the origin of the discrepancies arising in some cases is discussed.     

Study of water clusters in the n = 2–34 size regime, based on the ABEEM/MM model

Various properties of water clusters in the n = 2–34 size regime with the change of cluster size have been systemically explored based on the newly developed flexible-body and charge-fluctuating ABEEM/MM water potential model. The ABEEM/MM water model is to take ABEEM charges of all atoms, bonds, and lone-pairs of water molecules into the intermolecular electrostatic interaction term in molecular mechanics. The computed correlating properties characterizing water clusters (H₂O) _n (n = 2–34) include optimal structures, structural parameters, ABEEM charge distributions, binding energies, hydrogen bonds, dipole moments, and so on. The study of optimal structures shows that the ABEEM/MM model can correctly predict the following important structural features, such as the transition from two-dimensional (from dimer to pentamer) to three-dimensional (for clusters larger than the hexamer) structures at hexamer region, the transition from cubes to cages at dodecamer (H₂O)₁₂, the transition from all-surface (all water molecules on the surface of the cluster) to one water-centered (one water molecule at the center of the cluster, fully solvated) structures at (H₂O)₁₇, the transition from one to two internal molecules in the cage at (H₂O)₃₃, and so on. The first three structural transitions are in good agreement with those obtained from previous work, while the fourth transition is different from that identified by Hartke. Subsequently, a systematic investigation of structural parameters, ABEEM charges, energetic properties, and dipole moments of water clusters with increasing cluster size can provide important reference for describing the objective trait of hydrogen bonds in water cluster system, and also provide a strong impetus toward understanding how the water clusters approach the bulk limit.     

Melting and glass transition for Ni clusters

The melting of NiN clusters (N = 29, 50-150) has been investigated by using molecular dynamics (MD) simulations with a quantum corrected Sutton-Chen (Q-SC) many-body potential. Surface melting for Ni147, direct melting for Ni79, and the glass transition for Ni29 have been found, and those melting points are equal to 540, 680, and 940 K, respectively. It shows that the melting temperatures are not only size-dependent but also a symmetrical structure effect; in the neighborhood of the clusters, the cluster with higher symmetry has a higher melting point. From the reciprocal slopes of the caloric curves, the specific heats are obtained as 4.1 kB per atom for the liquid and 3.1 kB per atom for the solid; these values are not influenced by the cluster size apart in the transition region. The calculated results also show that latent heat of fusion is the dominant effect on the melting temperatures (Tm), and the relationship between S and L is given.     

Ion calorimetry: Using mass spectrometry to measure melting points

Calorimetry measurements have been used to probe the melting of aluminum cluster cations with 63 to 83 atoms. Heat capacities were determined as a function of temperature (from 150 to 1050 K) for size-selected cluster ions using an approach based on multicollision-induced dissociation. The experimental method is described in detail and the assumptions are critically evaluated. Most of the aluminum clusters in the size range examined here show a distinct peak in their heat capacities that is attributed to a melting transition (the peak is due to the latent heat). The melting temperatures are below the bulk melting point and show enormous fluctuations as a function of cluster size. Some clusters (for example, n = 64, 68, and 69) do not show peaks in their heat capacities. This behavior is probably due to the clusters having a disordered solid-like phase, so that melting occurs without a latent heat.     

中介尺度Au纳米团簇熔化的分子动力学模拟

采用分子动力学模拟技术，研究了原子个数为16～8628的 Au纳米团簇的熔化过程.采用 Johnson的EAM (embedded atom method) 模型,模拟结果表明，金属纳米团簇存在一中介尺度区域.对Au纳米团簇而言，当原子个数N >456时，团簇的热力学性质与团簇尺寸呈线性关系，熔化首先从表面开始，逐步向中心区域推进，且满足Tmb－Tmc(N)＝aN(－1/3)的关系.另外，计算了中介区域的团簇的尺寸、熔化温度、表面能、熵、焓等热力学量以及均方根位移（RMSD）等动力学量，为研究纳米团簇提供定量数据.     

Formation and decomposition of water clusters as observed in a triple quadrupole mass spectrometer

Water clustering up to mass 4000 has been observed using the Finnigan TSQ-700 electrospray mass spectrometer operating in either the normal or discharge modes with the capillary just above room temperature. The mechanism of cluster formation and structure has been studied by changing instrumental parameters including capillary temperature, auxiliary gas flow, and tube lens (skimmer) voltage. As expected, and in agreement with earlier work, enhanced abundances were observed at clusters of n = 21 and 28 molecules of water. Abundances of these same clusters are enhanced after fragmentation of higher mass clusters by MS/MS. Existing models including the clathrate structure are examined and it is suggested that with the exception of the structures at n = 21 and 28, the clusters are based on ice I _c . Also in agreement with previous work, water clusters were found to contain both protons and ammonium ions and the presence of the latter was proved by accurate mass measurement. In one case, these ions also attached to decomposition products formed by the discharge from traces of residual polyethylene glycol.     

小尺寸金属团簇熔化过程的分子动力学模拟

运用分子动力学方法模拟了小尺寸金属团簇的熔化过程, 原子之间的作用采用嵌入原子法(EAM)模型, 计算了均方根键长涨落δ随温度的变化, 以及升温过程中团簇热容的变化. 包含55、56个原子的面心立方(FCC)结构Au团簇的熔化过程是基本相同的. 而同样结构和数目Cu团簇的熔化过程却呈现出不同的趋势. Cu55、Cu56在模拟过程中都出现了FCC结构到二十面体结构的转变. 但由于表面多出了一个原子, Cu56的热容曲线比Cu55多了一个峰, 体系出现了预熔化现象. 这表明小尺寸团簇的固液转变的过程与团簇的原子类型、几何结构和原子数目密切相关.     

Connection between the virial equation of state and physical clusters in a low density vapor

We carry out Monte Carlo simulations of physical Lennard-Jones and water clusters and show that the number of physical clusters in vapor is directly related to the virial equation of state. This relation holds at temperatures clearly below the critical temperatures, in other words, as long as the cluster-cluster interactions can be neglected--a typical assumption used in theories of nucleation. Above a certain threshold cluster size depending on temperature and interaction potential, the change in cluster work of formation can be calculated analytically with the recently proposed scaling law. The breakdown of the scaling law below the threshold sizes is accurately modeled with the low order virial coefficients. Our results indicate that high order virial coefficients can be analytically calculated from the lower order coefficients when the scaling law for cluster work of formation is valid. The scaling law also allows the calculation of the surface tension and equilibrium vapor density with computationally efficient simulations of physical clusters. Our calculated values are in good agreement with those obtained with other methods. We also present our results for the curvature dependent surface tension of water clusters.     

Competing thermal activation mechanisms in the meltinglike transition of Na(N) (N = 135-147) clusters

The meltinglike transition in unsupported icosahedral Na(N)() clusters, with N = 135-147, has been studied by isokinetic molecular dynamics simulations based on an orbital-free version of density functional theory. A maximum in the melting temperature, T(m), is obtained for Na141, while the latent heat, deltaE, and entropy of melting, deltaS, are maximal for Na147. These observations are in close agreement with calorimetric experiments on N clusters. The size evolution of deltaS is rationalized by the emergence of important premelting effects associated with the diffusive motion of atomic vacancies at the cluster surface. The precise location of the maximum in T(m) is explained in terms of two different thermally activated structural instability mechanisms which trigger the meltinglike transition in the size ranges N = 135-141 and N = 141-147, respectively.     

The structure of deposited metal clusters generated by laser evaporation

Metal clusters have been produced using a laser evaporation source. A Nd-YAG laser beam focused onto a solid silver rod was used to evaporate the material, which was then cooled to form clusters with the help of a pulsed high pressure He beam. TOF mass spectra of these clusters reveal a strong occurrence of small and medium sized clusters (n<100). Clusters were also deposited onto grid supported thin layers of carbon-films which were investigated by transmission electron microscopy. Very high resolution pictures of these grids were used to analyze the size distribution and the structure of the deposited clusters. The diffraction pattern caused by crystalline structure of the clusters reveals 3-and 5-fold symmetries as well asfcc bulk structure. This can be explained in terms of icosahedron and cuboctahedron type clusters deposited on the surface of the carbon layer. There is strong evidence that part of these cluster geometries had already been formed before the depostion process. The non-linear dependence of the cluster size and the cluster density on the generating conditions is discussed. Therefore the samples were observed in HREM in the stable DEEKO 100 microscope of the Fritz-Haber-Institut operating at 100 KV with the spherical aberrationc _S =0.5 mm. The quality of the pictures was improved by using the conditions of minimum phase contrast hollow cone illumination. This procedure led to a minimum of phase contrast artefacts. Among the well-crystallized particles were a great amount of five- and three-fold symmetries, icosahedra and cuboctahedra respectively. The largest clusters with five- and three-fold symmetries have been found with diameters of 7 nm; the smallest particles displaying the same undistorted symmetries were of about 2 mm. Even smaller ones with strong distortions could be observed although their classification is difficult. The quality of the images was improved by applying Fourier filtering techniques.