Influence of energy and entropy on the melting of sodium clusters

Energetic and entropic influences on the melting temperatures of size selected sodium clusters are experimentally separated. It is shown that the energetic difference between solid and liquid is the leading influence for the still puzzling features in the size dependence of sodium melting points. Additionally, this energy difference decreases towards smaller cluster sizes and causes steplike melting phase transitions to vanish. The entropy difference between solid and liquid has been found to be strongly correlated with the energy and causes a pronounced damping of the energetic influences.     

Effect of melting on ionization potential of sodium clusters

The effect of melting transition on the ionization potential has been studied for sodium clusters with 40, 55, 142, and 147 atoms, using ab initio and classical molecular dynamics. Classical and ab initio simulations were performed to determine the ionization potential of Na₁₄₂ and Na₁₄₇ for solid, partly melted, and liquid structures. The results reveal no correlation between the vertical ionization potential and the degree of surface disorder, melting, or the total energy of the cluster obtained with the ab initio method. However, in the case of 40 and 55 atom clusters, the ionization potential seems to decrease when the cluster melts. Received 1st November 2002 Published online 24 April 2003 RID="a" ID="a"e-mail: ar@phys.jyu.fi     

Ca掺杂Si团簇的几何结构和电子性质的密度泛函理论研究

采用密度泛函理论(DFT)B3LYP方法在6-311+G(d,p)基组水平,对CaSi_n(n=1~10)的结构进行优化,得出各个尺寸下团簇处于最低能量的结构模型,并对其稳定性等物理化学性质进行理论研究,表明CaSi_2、CaSi_5和CaSi_9为幻数团簇.     

钠原子团簇相变的多极形变特征

运用距离相关紧密结合的分子动力学模型,通过无量纲的形变参数S1对简单金属原子团簇Na4、Na8、Na14和Na20相变时的多极形变特征进行了分析,发现S1可以用作表征团簇形变的灵敏探针.     

Copper clusters: electronic effect dominates over geometric effect

A minimal parameter tight binding molecular dynamics scheme is used to study Cu _n clusters with . We present results for relaxed configurations of different symmetries, binding energies, relative stabilities and HOMO-LUMO gap energies for these clusters. Detailed comparison for small clusters n = 3-9 with ab initio and available experimental results shows very good agreement. Even-odd alternation due to electron pairing and magic behaviour for Cu₂, Cu₈, Cu₁₈ and Cu₂₀ due to electronic shell closing are found. We found electronic effects, electronic shell closing and electron pairing in the HOMO dominates over the geometrical effect to determine the relative stability of copper clusters. The present results indicate that tight-binding molecular dynamics scheme can be relied on to provide a useful semiempirical scheme in modeling interactions in metallic systems.Received: 3 May 2004, Published online: 26 October 2004PACS: 36.40.Cg Electronic and magnetic properties of clusters - 36.40.Mr Spectroscopy and geometrical structure of clusters - 36.40.Qv Stability and fragmentation of clusters     

The geometric structure and electronic properties of Fe3O3 clusters

On the basis of density-functional theory (PW91) and an all-electron numerical basis set, 60 optimized structures of Fe₃O₃⁺ clusters were obtained through optimization calculation and frequency analysis of 216 initial structures. 28 different isomers were ultimately confirmed after analyzing and re-calculating. The binding energies, the energy gaps between the highest occupied molecular orbital and lowest unoccupied molecular orbital, and the total magnetic moments of all stable isomers are reported. Some discussion of the relationship between electronic properties and structures is also presented.     

Structural and energetic properties of sodium clusters

In this work we present results from a theoretical study on the properties of sodium clusters. The structures of the global total-energy minima have been determined using two different methods. With the parameterized density-functional tight-binding method (DFTB) combined with a genetic-algorithm we investigated the properties of Na_N clusters with cluster size up to 20 atoms, and with our own Aufbau/Abbau algorithm together with the embedded-atom method (EAM) up to 60 atoms. The two sets of results from the independent calculations are compared and a stability function is studied as function of the cluster size. Due to the electronic effects included in the DFTB method and the packing effects included in the EAM we have obtained different global-minima structures and different stability functions.     

Structures and electronic properties of stoichiometric hydrogenated aluminum clusters

The lowest-energy geometries and electronic-structure properties have been obtained for Al_nH_n (n=1-10) clusters within the density-functional theory using the generalized gradient approximation for the exchange correlation potential. The resulting geometries show that the hydrogen atoms tend to occupy outside positions and no hollow positions are found. The subunit Al_n of Al_nH_n (n=1-5) have little distortion, in comparison with corresponding pure Al_n cluster, whereas the subunit Al_n have large distortion from n=6. The stability has been investigated by analyzing the binding energy per atom and the second difference in energy, indicating that Al₈H₈ exhibit higher stability than others. The bonding property has been analyzed by calculating the Mulliken charges and Al–H distances. The calculated energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO-LUMO), the vertical ionization potential, and the vertical electron affinity also confirm that Al₈H₈ is a stable cluster. The density of states (DOS) shows that Al_nH_n exhibit changes from molecular-like (Al₁H₁) to band-like structure (Al₁₀H₁₀) as n increases.     

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.     

Anomalous optical and electronic properties of dense sodium

Based on the density functional theory, we systematically study the optical and electronic properties of the insulating dense sodium phase (Na-hp4) reported recently (Ma et al., 2009). The structure is found optically anisotropic. Through Bader analysis, we conclude that ionicity exists in the structure and becomes stronger with increasing pressure.     

Shape dependence of optical properties of sodium clusters

We develop an analytical approach to calculate the aspect ratios of free alkali metal clusters using measured surface plasmon frequencies. The method is based on the concept of small deviations from a spherical shape and can be applied to clusters with spheroidal, icosahedral and other shapes. Results of experimental data as well as of numerical calculations for the surface plasmon resonance frequencies in small spheroidal sodium clusters containing less than 50 atoms are reproduced accurately through a quite simple formula which links the aspect ratio of the cluster to the observable surface plasmon frequencies. The developed approach allows also to reveal the dependence of the dielectric function of alkali metal on the number of atoms in the cluster.     

Tight-binding study of structural and electronic properties of silver clusters

Tight-binding model is developed to study the structural and electronic properties of silver clusters. The ground state structures of Ag clusters up to 21 atoms are optimized by molecular dynamics-based genetic algorithm. The results on small Ag_n clusters (n = 3-9) are comparable to ab initio calculations. The size dependence of electronic properties such as density of states, s-d band separation, HOMO-LUMO gap, and ionization potentials are discussed. Magic number behavior at Ag₂, Ag₈, Ag₁₄, Ag₁₈, Ag₂₀ is obtained, in agreement with the prediction of electronic ellipsoid shell model. We suggest that both the electronic and geometrical effect play significant role in the coinage metal clusters. Received 7 August 2000     

Structural, electronic and vibrational properties of indium oxide clusters

Geometric, electronic and vibrational properties of the most stable and energetically favourable configurations of indium oxide clusters In_mO_n (1≤m, n≤4) are investigated using density functional theory. The lowest energy geometries prefer the planar arrangement of the constituent atoms with a trend to maximize the number of ionic In-O bonds. Due to the charge transfer from In to O atoms, the electrostatic repulsion occurs between the atoms with the same kind of charge. The minimization of electrostatic repulsion and the maximization of In-O bond number compete between each other and determine the location of the isometric total energy. The most stable linear In-O-In-O structure of In₂O₂ cluster is attributed to the reduced electrostatic repulsive energy at the expense of In-O bond number, while the lowest energy rhombus-like structure of In₂O₃ cluster reflects the maximized number of In-O bonds. Furthermore, the vibrational frequencies of the lowest energy clusters are calculated and compared with the available experimental results. The energy gap and the charge density distribution for clusters with varying oxygen/indium ratio are also discussed.