Structure and vibrational properties of cobalt clusters (n ≤ 20)

The binding energies and vibration frequencies of free small cobalt clusters containing up to twenty atoms inclusive have been calculated using the interatomic interaction potential obtained in the tight-binding approximation. The minimum frequency of the cluster vibrations has been shown to play the determining role in the evaluation of its dynamic stability. The analysis of the energy parameters and vibrations of clusters has demonstrated that the cobalt clusters in which the number of atoms is n = 4, 6, 13, and 19 are stable.     

Structure,stability and magnetic properties of (NiAl)n(n≤6) clusters

In this paper, density functional theory with generalized gradient approximation (GGA) for the exchange-correlation potential has been used to calculate the energetically global-minimum geometries and electronic states of (NiAl)_n(n≤6) clusters. Full structural optimizations, analysis of energy and frequency calculation are performed. The most stable structures of (NiAl)_n clusters are all three-dimensional structures except NiAl. The average bond lengths of (NiAl)_n clusters are larger than that of Ni_2n, and are smaller than that of Al_2n. The binding energy per atom of Ni_2n and (NiAl)_n has the same change trend, and that are larger than that of Al_2n. Stability analysis shows that Ni₈, (NiAl)₂ and Al₁₀ clusters have higher relative stability than other clusters. Mulliken analysis indicates that charges always transfer from Al atoms to Ni atoms, and the average charges of transfer from Al atoms to Ni atoms have a maximum at (NiAl)₆, implying the strong interaction between Al and Ni atoms in (NiAl)₆. The average atomic magnetic moments of (NiAl)_n are smaller than that of true Ni_2n. The analysis of the static polarizability shows that the electronic structures of (NiAl)_n clusters tend to be compact with the increase of atoms.     

Rydberg excitations in rare gas clusters: structure and electronic spectra of Ar* n (3 ≤ n ≤ 25)

Likely candidates are located for the global potential energy minima of Ar* _n (3 ≤ n ≤ 25) clusters using the diatomics-in-molecules (DIM) approach. The favoured geometries are found to be different from the structures of Ar⁺ _n and correspond to the trimer Ar*₃ bound to the surface of an Ar _n?2 core via a common atom. The Ar _n?2 core is usually only slightly distorted from its own global potential minimum, although in a few cases it corresponds to a nearby local minimum. Therefore, the ‘magic’ sizes of the excimer systems are predicted to differ from those of the ions and correlate instead with the stability of Ar _n?2. The predicted electronic photoabsorption and emission spectra of Ar* _n , and photoexcitation spectra of Ar _n are discussed in terms of experimental data. Global potential energy minima for neutral Ar _n up to n = 55 with the Aziz potential are summarized also; the structure is the same as for the Lennard-Jones potential except at n = 21 where the stabilities of the two lowest Lennard-Jones minima are reversed.     

Density functional study on the bimetallic Ti_mZr_n(n+m ≤ 5) clusters and their interactions with H_2

Equilibrium geometries, stabilities, and electronic properties of small Ti_mZr_n(n + m ≤ 5) clusters were investigated using the density functional method. The ground states were determined, and it was found that the larger clusters and those consisting of more Zr atoms are more stable. The electronic properties of the clusters were discussed based on HOMO-LUMO gaps, vertical ionization potentials(VIP), and vertical electron affinities(VEA). Furthermore, we studied the interactions between those clusters and molecular hydrogen, and found that in all the cases dissociative chemisorptions occurred. According to the chemisorption energies, the pure Zr clusters are relatively more active towards H_2 when compared with the others except Ti_3Zr, which shows the highest activity. The magnetic moments of Ti_mZr_n and Ti_mZr_nH_2 were also compared, and the results show that the hydrogenated clusters have the same or decreased total magnetic moments with respect to the bare clusters except for Ti_3Zr_2.     

Static dipole polarizabilities of Scn （n ≤15） clusters

The static dipole polarizabilities of scandium clusters with up to 15 atoms are determined by using the numerically finite field method in the framework of density functional theory. The electronic effects on the polarizabilities are investigated for the scandium clusters. We examine a large highest occupied molecular orbital --- the lowest occupied molecular orbital (HOMO--LUMO) gap of a scandium cluster usually corresponds to a large dipole moment. The static polarizability per atom decreases slowly and exhibits local minimum with increasing cluster size. The polarizability anisotropy and the ratio of mean static polarizability to the HOMO--LUMO gap can also reflect the cluster stability. The polarizability of the scandium cluster is partially related to the HOMO--LUMO gap and is also dependent on geometrical characteristics. A strong correlation between the polarizability and ionization energy is observed.     

Structures and its evolution of Ba n ( n =2 ∼ 14) clusters

We have studied the atomic structure and the electronic properties of Ba_n clusters by the ab initio molecular dynamics method. We find that a structural transition to the bulk-like structure begins at Ba₉ cluster, and the structures of the clusters are transferred to be icosahedral-like around n = 13. The relatively high stability for Ba₄, Ba₁₀ and Ba₁₃ clusters are observed. Received 1st December 2000     

Absolute cross sections of electron attachment to molecular clusters: Part I. Formation of (CO2) N −

A procedure of determining absolute cross section σ^? of electron attachment to (CO₂)_N clusters at pair collisions in crossed beams is suggested. The cross section is measured as a function of energy (E = 0.1–50 eV) and of cluster mean size N in a beam $(\bar N = 2 - 4000 molecules)$ . It is found that, even at $\bar N > 200$ and E ≤ 3 eV, σ^? is equal to, or larger than, 7 × 10^?13 cm², i.e., by more than one order of magnitude exceeds the maximal cross section of CO₂ ionization by electron impact. The dependences σ^? $(\bar N,E)$ have two wide continua at E ≤ 5.2 eV and E ≥ 6.9 eV, which correlate well with known functions of CO₂ electron-impact-induced excitation. These continua are attributed largely to formation of (CO₂) _N ^? ions during electron thermalization and solvation in the clusters. At E → 0, the polarization capture of an incident electron by the cluster leads to a sharp increase in cross section σ^?(E). From the dependences σ^? $(\bar N,E)$ measured, the thermalization and sovation probabilities for electrons with E ≤ 0.8 eV and the rate of electron energy loss in the cluster are found.     

Isotope effect of hydrated clusters of hydrogen chloride,HCl(H2O) n and DCl(H2O) n (n = 0–4): application of dynamic extended molecular orbital method

The recently proposed dynamic extended molecular orbital (DEMO) method is applied to the HCl(H₂O) _n and DCl(H₂O) _n (n = 0–4) clusters in order to explore the isotope effect on their structures, wavefunctions, and energies, theoretically. Since the DEMO method determines both electronic and nuclear wavefunctions simultaneously by optimizing all parameters including basis sets and their centres variationally, we can get the different nuclear orbitals for proton and deuteron as well as their electronic wavefunctions. The positions of the centres of nuclear orbitals show that the deuteron has weaker hydrogen bonding than the proton. There are three isomers in the case of n = 3 clusters, and less stable isomers have hydrogen transferred and non-transferred structures. In the conventional MO calculation, both hydrogen transferred and non-transferred isomers are calculated to be energy minima. When we have applied the DEMO method, only the hydrogen transferred structure is obtained for HCl(H₂O)₃, while both structures are optimized for DCl(H₂O)₃. Such strong H/D dependence on the structures of the HCl(H₂O) _n and DCl(H₂O) _n clusters can be expressed directly by using the DEMO method. The present application demonstrates that the DEMO method is a useful tool for analysing the anharmonicity and vibronic effects of a hydrogen bonding system.     

Structures and Electronic Properties ofCuN (N≤ 13) Clusters

A systematic study on the structures and electronic properties of copper clusters has been performed using the density functional theory. In the calculation, there are many isomers near the ground state for small copper clusters. Our results show that the three-dimensional isomers of copper clusters start from Cu₇ cluster and then show a tendency to form more compact structures. The results of the formation energy and the second derivative of binding energy with cluster size show that besides N = 8, N=11is also a magic number. Furthermore, it is the first time to find that the ground state of 11-atom clusters is a biplanar structure as same as the 13-atom cluster. The clear odd-even alternation as cluster size for the formation energy indicates the stability of electronic close shell existed in the range studied.     

Ti_(n-m)Zr_mO_(2n)(n=2-7,0≤m≤n)团簇结构和稳定性研究

应用密度泛函理论中的B3LYP方法对Ti_(n-m)Zr_mO_(2n)(n=2-7,0≤m≤n)团簇的基态几何结构、相对稳定性和电子结构进行了理论研究.结果表明,与桥氧链接的Ti原子被Zr原子取代后形成的混合团簇较为稳定;在团簇尺寸一定的条件下(即n相同),随着Zr原子数m的增加,团簇的结合能基本呈线性增大,团簇的稳定性增强;Ti、Zr、O原子之间发生了电荷转移现象,形成了稳定的Ti-O-Zr键.     

Structures,stabilities and adsorption mechanisms of nitrogen adsorbed on Mon (n = 1–8) clusters

Configurations, stabilities and adsorption mechanisms of ground-state Mo_nN and Mo_nN₂ (n?=?1–8) clusters are calculated by using the density functional method within the PBE level. Evidently, N atoms tend to approach more Mo atoms. Doping with two N impurity prefers to occupy symmetrical position of the host Mo_n (n?=?1–8) cluster except for Mo₂N₂ clusters. Mo₄N, Mo₆N, Mo₂N₂, Mo₄N₂ and Mo₆N₂ clusters have higher structural stabilities than their neighbors by the second derivative of total binding energy. Mo₂N, Mo₄N and Mo₇N, Mo₂N₂, Mo₅N₂ and Mo₇N₂ clusters have higher kinetic reactivity than their neighbors by the HOMO–LUMO gaps. The adsorption capacity of a N atom to Mo₄ cluster is stronger than the other Mo–N clusters.     

Tin-mZrmO2n(n=2-7，0≤m≤n)团簇结构和稳定性研究

应用密度泛函理论中的B3LYP方法对Tin-mZrmO2n (n = 2-7,0≤m≤n) 团簇的基态几何结构、相对稳定性和电子结构进行了理论研究.结果表明,与桥氧链接的Ti原子被Zr原子取代后形成的混合团簇较为稳定;在团簇尺寸一定的条件下（即n相同）,随着Zr原子数m的增加,团簇的结合能基本呈线性增大,团簇的稳定性增强;Ti、Zr、O原子之间发生了电荷转移现象,形成了稳定的Ti-O-Zr键.     

Energy levels of 1s~2n d(n≤9)states for lithium-like ions

The full-core plus correlation method with multi-configuration interaction wave functions is extended to the calculation of the non-relativistic energies of 1s²nd (n ≤ 9) states for the lithium isoelectronic sequence from Z = 11 to 20. Relativistic and mass-polarization effects on the energy are calculated as the first-order perturbation correction. The quantum-electrodynamics correction is also included. The fine structure splittings are determined from the expectation values of spin—orbit and spin—other-orbit interaction operators in the Pauli—Breit approximation. Combining the term energies of lowly excited states obtained with the quantum defects calculated by the single channel quantum defect theory, each of which is a smooth function of energy and approximated by a weakly varying function of energy, the ion potentials of highly excited states (n ≤ 6) are obtained with the semi-empirical iteration method. The results are compared with experimental data in the literature and found to be closely consistent with the regularity.     

单母体遗传算法优化(H2O)n(n≤14)的结构

在传统遗传算法的基础上提出了单母体遗传算法(single-parent genetic algorithm,SPGA),通过对母体团簇实施两种不同的变异操作对结构进行优化,给出了分子团簇结构优化的算法实现.结合TIP3P模型势函数,研究了水分子团簇(H2O)n(n≤14)的稳定结构.优化结构和已有理论及实验结果一致.计算结果表明当n＜8时,平均结合能随n,增加较快;当n≥8时有小的起伏.n=4,8,10,12的团簇结构具有较高对称性,比较稳定.     

Density functional theory study of neutral AlS_n(n=2-9) clusters

This paper investigates the geometrical structures and relative stabilities of neutral AlS n(n = 2-9) using the density functional theory.Structural optimisation and frequency analysis are performed at the B3LYP/6-311G(d) level.The ground state structures of the AlS n show that the sulfur atoms prefer not only to evenly distribute on both sides of the aluminum atom but also to form stable structures in AlS n clusters.The structures of pure S n are fundamentally changed due to the doping of the Al atom.The fragmentation energies and the second-order energy differences are calculated and discussed.Among neutral AlS n(n = 2-9) clusters,AlS 4 and AlS 6 are the most stable.     

The binding of CO molecule with small Wn(n = 2−9) clusters: a DFT investigation

The effect of water conductivity on electrospraying of water was studied in combination with positive DC corona discharge generated in air. We used a point-to-plane geometry of electrodes with a hollow syringe needle anode opposite to the metal mesh cathode. We employed total average current measurements and high-speed camera fast time-resolved imaging. We visualized the formation of a water jet (filament) and investigated corona discharge behavior for various water conductivities. Depending on the conductivity, various jet properties were observed: pointy, prolonged, and fast spreading water filaments for lower conductivity; in contrast to rounder, broader, and shorter quickly disintegrating filaments for higher conductivity. The large acceleration values (4060 m/s² and 520 m/s² for 2 μS/cm and 400 μS/cm, respectively) indicate that the process is mainly governed by the electrostatic force. In addition, with increasing conductivity, the breakdown voltage for corona-to-spark transition was decreasing.     

混合团簇Cu13-nAgn(n≤13)基态结构的遗传算法研究

在混合团簇基态结构优化的遗传算法方案中增加了交换算子,结合Gupta紧束缚模型势研究了Cu13-nAgn团簇的最低能量结构,选择合适的交换和杂交概率,可有效地提高优化效率,优化结果表明,Cu13和Ag13是全对称的二十面体,n=1～10的混合团簇能形成稳定结构,其构型是在二十面体基础上发生畸变,Cu原子趋于处在团簇中心,随着Ag原子数目的增加,原子间的平均距离单调增加,团簇的结合能单调减小,Cu2Ag11和CuAg12只存在亚稳结构.