Stability,Infrared Spectra and Electronic Structures of (ZrO2)n(n=3-6)Clusters:DFT Study

The stability, infrared spectra and electronic structures of (ZrO₂)_n (n=3–6) clusters have been investigated by using density‐functional theory (DFT) at B3LYP/6‐31G* level. The lowest‐energy structures have been recognized by considering a number of structural isomers for each cluster size. It is found that the lowest‐energy (ZrO₂)₅ cluster is the most stable among the (ZrO₂)_n (n=3–6) clusters. The vibration spectra of Zr? O stretching motion from terminal oxygen atom locate between 900 and 1000 cm^?1, and the vibrational band of Zr? O? Zr? O four member ring is obtained at 600–700 cm^?1, which are in good agreement with the experimental results. Mulliken populations and NBO charges of (ZrO₂)_n clusters indicate that the charge transfers occur between 4d orbital of Zr atoms and 2p orbital of O atoms. HOMO‐LUMO gaps illustrate that chemical stabilities of the lowest‐energy (ZrO₂)_n (n=3–6) clusters display an even‐odd alternating pattern with increasing cluster size.     

A density functional theory study of the Au7Hn (n = 1–10) clusters

The geometries, electronic, and magnetic properties of the Au₇H_n (n = 1–10) clusters have been systematically investigated by using relativistic all-electron density functional theory with generalized gradient approximation. It is found that the Au₇ on the whole retains its triangle structure after hydrogen atoms adsorption and adsorbing hydrogen atoms can stabilize the Au₇ structure. The Au₇H₇ cluster is much higher stability than the neighboring clusters. The pronounced even–odd alternation of the magnetic moments is observed in the Au₇H_n systems indicating Au₇H_n clusters possess tunable magnetic properties by adding even or odd number of H atoms.     

Density functional theory of the collective electronic excitations in NanKn clusters

The collective electronic response of Na_nK_n clusters has been studied for some model structures. In their low-temperature lowest-energy structure, those clusters have all the K atoms on the surface. The collective oscillation frequencies for clusters with the K atoms segregated to the surface are red-shifted with respect to the corresponding frequencies for isomers with a very similar underlying skeleton but with the Na atoms segregated to the surface. The collective frequency varies smoothly with respect to the degree of relative segregation. These results may be useful in the analysis of the collective response of large alloy clusters and microcrystals. © 1995 John Wiley & Sons, Inc.     

Structures and magnetic properties of Ni<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 36-40) clusters from first-principles calculations

A genetic algorithm (GA) coupled with a tight-binding (TB) interatomic potential is used to search for the low-energy structures of medium-sized Ni _n (n = 36-40) clusters. Structural candidates obtained from our GA search are further optimized with first-principles calculations. The medium-sized nickel clusters ranging from 36 to 40 atoms are found to favor the double-icosahedron-based structures with a Ni₇ core (a pentagonal bipyramidal structure) except Ni₃₈ cluster. The lowest-energy structure of Ni₃₈ can be considered to be a magic cluster, which is a typical face-centered cubic structure with large stability and magnetic moment.     

Geometries and stabilities of Ag n v (v?=?±1, 0; n?=?21–29) clusters

We performed a systematical study on the lowest-energy structures of the medium-sized silver clusters Ag _n (n?=?21?C29) by using a genetic algorithm coupled with a tight-binding method, and the DFT calculations with Perdew?CWang generalized-gradient approximation. The corresponding cluster ions were also searched based on the neutral cluster structures. It is found that the Ag_21?C23 prefer icosahedron or double-icosahedron as core structures. Ag _n (n?=?24?C27) favor a bulk-like fcc stacking motif. Ag₂₈ and Ag₂₉ tend to high symmetrical structures. The relative stabilities, the ionization potentials and electronic affinities of silver clusters analyzed in the paper are consistent with the experimental data. It is interesting to find that the experimental spectra fit reasonable well the optical absorption spectra obtained with the structures calculated by us.     

Collisional process involving atomic cluster ions

Collision of Ar cluster ions, Ar _n ⁺ (n=3–16), with He and Ne atoms was investigated by use of mass spectroscopic techniques. The cross sections for the production of Ar _n ⁺ (nn) were measured as functions of the size of the parent cluster ion and the collision energy (0.1–10 eV in the center-of-mass frame). These results were analyzed in the scheme of hard-sphere spectator collision with RRK theory. It was concluded that the reaction proceeds via collisional excitation of the parent cluster ion and following sequential loss of the constituent Ar atoms.This paper was originally submitted in connection with the 2nd. Int. Conference on Atomic and Nuclear Clusters held in Santorini from 28. June-2. July 1993 and is published here as a regular article after an independent refereeing procedure according to the standards of Z. Phys. D     

Structural,Relative Stable,and Electronic Properties of Pb<Subscript>n</Subscript>Sn<Subscript>n</Subscript> (n = 2–12) Clusters were Investigated Using Density Functional Theory

The structural, relative stable and electronic properties of Pb_nSn_n (n = 2–12) alloy clusters were systematically studied using density functional theory. The isomers of Pb_nSn_n alloy clusters were generated and determined by ab initio molecular dynamics. By comparing the calculated parameters of Pb₂ dimer and Sn₂ dimers with the parameters from experiments, our calculations are reasonable. With the lowest-energy structures for Pb_nSn_n clusters, the average binding energies, fragmentation energies, second- order energy differences, vertical ionization potentials, vertical electron affinities, HOMO–LUMO gaps, and density of states were calculated and analyzed. The results indicate that the Sn atoms have a tendency to bond together, the average binding energies tend to be stable up to n = 8, Pb₈Sn₈ cluster is a good candidate to calculate the molecular interaction energy parameter in Wilson equation, the clusters become less chemical stable and show an insulator-to-metallic transition, 3, 6, 8 and 11 are magic numbers of Pb_nSn_n (n = 2–12) clusters, the charges always transfer from Sn atoms to Pb atoms in Pb_nSn_n clusters except for Pb₁₀Sn₁₀ cluster, and density of states of Pb_nSn_n clusters becoming continuous and shifting toward negative with the increasing size n.     

Growth Pattern, Electronic Structures and Magnetic Moments of Small Lutetium Clusters

The lowest-energy configurations, electronic structures and magnetic moments of small Lu _n (n = 2–20) clusters have been investigated within the framework of density functional theory. The results show that Lu _n (n = 4, 8, 13, and 18) clusters are more stable than their respective neighbors, and structural transformation reveals at n = 16. As the number of atoms increases, the magnetic moments increase in an alternating fashion until they reach a maximum of 4.00 μ_B for Lu₈ clusters, followed by even–odd oscillation between 0.00 and 1.00 μ_B over the range n = 9–20.     

One-Electron Pseudo-Potential Determination of Stable Isomers of the Li*Ar n Excited Clusters: Absorption Spectra

We present pseudo-potential calculations of geometrical structures of stable isomers of LiAr _n clusters with both an electronic ground state and excited states of the lithium atom. The Li atom is perturbed by argon atoms in LiAr _n clusters. Its electronic structure obtained as the eigenfunctions of a single-electron operator describing the electron in the field of a Li⁺Ar _n core, the Li⁺ and Ar atoms are replaced by pseudo-potentials. These pseudo-potentials include core-polarization operators to account for the polarization and correlation of the inert core with the valence Lithium electron [J Chem Phys 116, 1839 1]. The geometry optimization of the ground and excited states of LiAr _n (n = 1–12) clusters is carried out via the Basin-Hopping method of Wales et al. [J Phys Chem 101, 5111 2; J Chem Phys 285, 1368 3]. The geometries of the ground and ionic states of LiAr _n clusters were used to determine the energy of the high excited states of the neutral LiAr _n clusters. The variation of the excited state energies of LiAr _n clusters as a function of the number of argon atoms shows an approximate Rydberg character, corresponding to the picture of an excited electron surrounding an ionic cluster core, is already reached for the 3s state. The result of optical transitions calculations shows that the absorption spectral features are sensitive to isomer structure. It is clearly the case for transitions close to the 2p levels of Li which are distorted by the cluster environment.     

Coordination Polyhedra RhX6 (X = F,Cl, Br) in Crystal Structures

Voronoi–Dirichlet polyhedra (VDP) and the method of intersecting spheres were used to perform crystal-chemical analyses of compounds containing complexes [Rh _a X _n ] ^z– (X = F, Cl, Br). It was found that, irrespective of oxidation number (+3, +4, or +5), rhodium atoms always exhibit the coordination number 6 with respect to the halogen atoms and have octahedral coordination. The influence of site symmetry and the valence state of Rh on the distortion of RhX₆ octahedra are considered. The electronic configuration of the Rh atoms is shown to influence the symmetry of their valence-force field within the crystal structure.     

Observable Structures of Small Neutral and Anionic Gold Clusters

Since gold clusters have mostly been studied theoretically by using DFT calculations, more accurate studies are of importance. Thus, small neutral and anionic gold clusters (Au_n and Au_n^?, n=4–7) were investigated by means of coupled cluster with singles, doubles, and perturbative triple excitations [CCSD(T)] calculations with large basis sets, and some differences between DFT and CCSD(T) results are discussed. Interesting isomeric structures that have dangling atoms were obtained. Structures having dangling atoms appear to be stable up to n=4 for neutral gold clusters and up to n=7 for anionic clusters. The relative stabilities and electronic properties of some isomers and major structures are discussed on the basis of the CCSD(T) calculations. This accurate structure prediction of small gold clusters corresponding to experimental photoelectron spectral peaks is valuable in the field of atom‐scale materials science including nanocatalysts.     

Ab initio study of electronic structures of Ptn clusters (n = 2–12)

Electronic structures of a series of Pt_n clusters (n = 2–12) have been calculated by ab initio method (SCF/MP2). The result shows that compared to that at the saturated coordination site, Pt at the unsaturated coordination site has lower Pt₆₅ electron occupancies, and the relationship between the electronic structure and the cluster size has been discussed. It is found that when the number of Pt in cluster reaches 7, electronic structures become more like the metallic ones. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62 : 427–436, 1997     

Reaction studies of carbon clusters

Reaction studies of carbon clustersC _n in the rangen=8–37, produced by laser vaporisation in a supersonic nozzle, have been investigated using time-of-flight mass spectrometry. Clear differences in reaction products formed on hydrogenation are detected which show that even and odd clusters behave quite differently and furthermore thatat least two different types of even cluster appear to exist. The reactivity patterns for clusters C _n withn=16, 18 and 22 are in a different class from those withn=20, 24, 26 ..., a behaviour consistent with the existence of closed cage fullerene structures for even clusters with 20 or more carbon atoms (other thann=22).     

The OsX n Coordination Polyhedra (X = O,S, Se,Te) in Crystal Structures

The Voronoi–Dirichlet polyhedra (VDP) and the method of intersecting spheres were used to perform a crystal-chemical analysis of compounds whose structures contain Os atoms surrounded by chalcogen atoms. Depending on the valence state, Os atoms bind four to seven X atoms (X = O, S, Se, Te) forming OsX _n coordination polyhedra which can be tetrahedra (n = 4), trigonal bipyramids or square pyramids (n = 5), octahedra (n = 6), or pentagonal bipyramids (n = 7). In some compounds, pairs of OsO₆ octahedra share edges to form Os–Os bonds. The influence of the Os valence state and the nature of the chalcogen atom on the composition and structure of the [Os _a X _b ] groups is discussed. On the basis of analysis of the crystal-structural data from the standpoint of the 18-electron rule, dependences of the Os–O and Os–Os bond orders on the bond lengths are proposed.     

Theoretical calculations of95Mo-NMR chemical shifts for compounds [MoO4−n S n ]2−

Summary Theoretical calculation of⁹⁵Mo-NMR chemical shifts for [MoO_4–n S _n ]^2– (n=0–4) compounds is reported here for the first time on the basis of Fenske-Hall method and Sum-Over-State (SOS) perturbation theory. A systematic decrease in shielding of⁹⁵Mo nuclei with increase of number of sulfur in [MoO_4–n S _n ]^2–, which is observed experimentally, can be reasonably explained by our calculation. A good linear relationship between chemical shifts of calculation and experiment is obtained. The electronic structure and bonding in these compounds are also discussed.Supported by Nature Science Foundation of China     

Ab initio investigation of water clusters (H2O)n (n = 2–34)

Various properties of typical structures of water clusters in the n = 2–34 size regime with the change of cluster size have been systematically explored. Full optimizations are carried out for the structures presented in this article at the Hartree–Fock (HF) level using the 6‐31G(d) basis set by taking into account the positions of all atoms within the cluster. The influence of the HF level on the results has been reflected by the comparison between the binding energies of (H₂O)_n (n = 2–6, 8, 11, 13, 20) calculated at the HF level and those obtained from high‐level ab initio calculations at the second‐order Møller–Plesset (MP2) perturbation theory and the coupled cluster method including singles and doubles with perturbative triples (CCSD(T)) levels. HF is inaccurate when compared with MP2 and CCSD(T), but it is more practical and allows us to study larger systems. The computed properties characterizing water clusters (H₂O)_n (n = 2–34) include optimal structures, structural parameters, binding energies, hydrogen bonds, charge distributions, dipole moments, and so on. When the cluster size increases, trends of the above various properties have been presented to provide important reference for understanding and describing the nature of the hydrogen bond. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Calculation of the properties of small boron and aluminum clusters

CNDO calculations were carried out for B _n and Al _n clusters, n=2–7, 12, and 13. The energetically most stable cluster structures were determined for each n. The results show that the stability of the more compact structures increases in going from boron to aluminum. We conclude that the CNDO model used is suitable for discerning the difference in the structure formation of boron and aluminum, which is manifest, in particular, in the formation of crystalline modifications by boron based on an icosahedral structural element, while crystalline aluminum has an FCC lattice.Institute of Theoretical and Applied Mechanics, Siberian Branch, Academy of Sciences of the USSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 30, No. 5, pp. 48–54, September–October, 1989.     

An ab Initio Study on the Chemical Bond and Reactivity of Molybdenum–Sulfur Clusters with a Mo2O n S4−n (n=1–3) Core

Using the ab initio method and natural bond analysis, the reactivity and chemical bond of dinuclear molybdenum sulfur clusters with Mo₂O _n S_4–n (n=1–3) core were studied. The results show that the Mo--Mo bonds in these clusters are significantly affected by the delocalization effects of the multicenter d--p and Mo--X ₁ bonds, besides the direct interactions between Mo atoms. The substitution reactions of the cluster core are also discussed, and it is indicated that sulfur atoms have a preference for the bridging sites and the oxygen atoms tend to attach to the terminal sites.     

Evolution of the geometrical and electronic structures of Gan(n=2-26) clusters: a density-functional theory study

Density-functional theory with generalized gradient approximation for the exchange-correlation potential has been used to calculate the lowest-energy geometries and electronic structure of neutral gallium clusters containing up to 26 atoms. Harmonic vibrational frequency analysis is undertaken to assure that the lowest-energy geometries are real local minima. With increasing cluster size, we find that the gallium clusters tend to adopt compact structures. The structures comprise triangular units that connect each other with different dihedral angles. The lowest-energy structure can be obtained by capping an atom on the structure of smaller one. The capping site occurs at a site where interactions with more atoms are available. The binding energy evolves monotonically with size, but Ga(8), Ga(14), and Ga(20) exhibit particularly higher stability. Except Ga(2) and Ga(4), all even-numbered gallium clusters we studied are closed-shell singlet states with a substantial highest occupied and lowest unoccupied molecular orbitals gap. The odd-numbered clusters are open shell with a small gap. The size dependence of cluster's ionization potentials and electron affinities is discussed and compared with available experiment.     

Nature of the Chemical Bond and the Mutual Influence of Ligands in Co(III) Dioximinates

The results of MWG calculations of the electronic structures of real Co(III) complexes [Co(HD)₂L¹L²] ⁿ were used to analyze the electron density distribution and to determine the charges on atoms and configurations, where nis the charge of the complex and HD is the acid residue of dimethylglyoxime (H₂D); L¹= NH₃at L²= NH₃, Cl^–, Br^–, or I^–and L¹= L²= Cl^–; and L¹= H₂O or NO^– ₂at L²= NO^– ₂, with self-consistency over all atoms of the system and over d, s, and pconfigurations of cobalt. The mutual influence of the ligands (trans- and cis-) was shown to be determined by the atomic charges and bond orders on the axial coordinate and in the equatorial plane of the complex. The following order of the trans-effect was proposed: I^–> Br^–> Cl^–> NO^– ₂> NH₃> H₂O. The effects of the electronic factors on distorsion and conformational processes in the complexes were discussed.