Theoretical study on the structures and properties of (Br2AlN3) n (n = 1–4) clusters

To look for the single-source precursors, the structures and properties of (Br₂AlN₃) _n (n = 1–4) clusters are studied at the B3LYP/6-311+G* level. The optimized (Br₂AlN₃) _n (n = 2–4) clusters all possess cyclic structures containing Al-N_α-Al linkages. The relationships between the geometrical parameters and the oligomerization degree n are discussed. The gas-phase structures of the trimers prefer to exist in the boat-twisting conformation. As for the tetramer, the most stable isomers have the S ₄ symmetry structure. The IR spectra are obtained and assigned by the vibrational analysis. The thermodynamic properties are linearly related with the oligomerization degree n as well as with the temperature. Meanwhile, the thermodynamic analysis of the gas-phase reaction suggests that the oligomerization be exothermic and favorable under high temperature.     

Theoretical study of silicon–sulfur clusters (SiS2)n (n = 1–6)

 The possible geometrical structures and relative stability of (SiS₂) _n (n=1–6) silicon–sulfur clusters are explored by means of density functional theory quantum chemical calculations. The effects of polarization functions and electron correlation are included in these calculations. The electronic structures and vibrational spectra of the most stable geometrical structures of (SiS₂) _n are analyzed by the same method. As a result, the regularity of the (SiS₂) _n cluster growth is obtained, and the calculation may used for predicting the formation mechanism of the (SiS₂) _n cluster. Received: 17 November 1999 / Accepted: 3 November 2000 / Published online: 3 May 2001     

Computational design and structure-property relationship studies on (I2GaN3) n (n = 1–4) clusters

To look for the single-source precursors, density functional theory calculations were performed to study structures, IR spectra, and stabilities of the possible isomers for the clusters (I₂GaN₃) _n (n = 1–4). It is found that the optimized (I₂GaN₃) _n (n = 2–4) clusters all possess cyclic structure containing Ga-N_α-Ga linkages, and azido group in azides has linear structure. Trends in geometrical parameters with the oligomerization degree n are discussed. The IR spectra are obtained and assigned by vibrational analysis. Thermodynamic properties are linearly correlated with the oligomerization degree n as well as the temperature. Mean-while, the oligomerizations can occur spontaneously at 298.2 K.     

Quantum chemical calculations and the structure of Ni n (C2H2) complexes (n = 1–4)

Complexes of nickel atoms and small clusters with acetylene molecules are studied within the density functional theory. A trend toward the predominant formation of structures with bridge hydrogen atoms is observed in reactions between Ni _n and acetylene with rising n.     

Spatial structure and electronic spectrum of TiSi n − clusters (n = 6–18)

Results from optimizing the spatial structure and calculated electronic spectra of anion clusters TiSi _n ^? (n = 6–18) are presented. Calculations are performed within the density functional theory. Spatial structures of clusters detected experimentally are established by comparing the calculated and experimental data. It is shown that prismatic and fullerene-like structures are the ones most energetically favorable for clusters TiSi _n ^? . It is concluded that these structures are basic when building clusters with close numbers of silicon atoms.     

Density functional theory study of the structures,electronic states and stabilities of Al n Pt (n = 1–15) clusters

The binding energy, dissociation energy, ionization potentials, electron affinities, gap and stability of small Al _n Pt (n = 1–15) clusters, in comparison with pure aluminum clusters have been systematically investigated by means of density functional calculations at the B3LYP level. The growth patten for Al _n Pt clusters is that the Pt atom substituted the surface atom of the Al _{n + 1} clusters for n < 13. Starting from n = 13, the Pt atom completely falls into the center of the Al-frame. The Pt atom substituted the center atom of the Al _{n + 1} clusters to form the Pt-encapsulated Aln geometries for n > 13. We also find that the impurity Pt atom causes local structural distortion due to different atomic radii and different bonding characteristics. The clusters with total atom numbers of 2, 7, and 11 exhibit high stability.     

Structures,stabilities, and electronic properties of Al n Au (n = 1–15) clusters: A density functional study

We present density functional calculations of Al _n Au clusters for n = 1–15. The growth pattern for Al _n Au (n = 1–7, 12, 14, 15) clusters is the Au atom occupying a peripheral position of Al _n clusters, and the growth pattern for Al _n Au (n = 8, 10 and 13) clusters is Au-substituted Al _n+1 clusters. It is found that the Au atom replaces the surface atom of an Al _n+1 cluster and occupies a peripheral position. In addition, the ground state structures of Al _n Au clusters are more stable than pure Aln clusters. It is found that the Al₁₃Au cluster exhibits high stability.     

Heats of formation for Fe(CO)n(n=1–4)

The dissociation energies of Fe(CO)_n (n=2–4) are computed using correlation consistent basis sets and the CCSD(T) approach. The dissociation energies are extrapolated to the CBS limit and are corrected for core–valence (CV), scalar relativistic, spin–orbit, zero-point, and thermal effects. Our iron carbonyl bond strengths agree with experiment within the respective error bars. We use our dissociations energies at 298 K to obtain the heats of formation of Fe(CO)_n (n=1–4).     

Structure and stability of AuXe n Z (n = 1–3, Z = −1, 0, +1) clusters

We have explored the structures and stabilities of AuXe _n ^Z (n = 1–3, Z = ?1, 0, +1) cluster series at CCSD(T) theoretical level. The electron affinities and ionization potentials are correlated to the HOMO–LUMO gaps. The role of the interaction was investigated using the natural bond orbital analysis.     

A density functional theory investigation of CrSin (n=1–6) clusters

Clusters of the form CrSi_n (n=1–6) were investigated computationally using a density functional approach. In particular, geometry optimizations were carried out under the constraint of well-defined point group symmetries at the B3LYP level employing a pseudopotential method in conjunction with double zeta basis sets. In this article, the resulting total energies, Mulliken atomic net populations, overlap populations, fragmentation energies and geometries of CrSi_n (n=1–6) are presented and discussed, together with natural populations and natural electron configurations. In addition, we comment on the charge transfer within the clusters. From this analysis, the 3d orbital of the Cr atom in CrSi_n (n=1–6) cluster absorbs electrons. From this tendency, conclusions are drawn with respect to the electronic populations and the chemical bond between Si and Cr as well as Si and Si.     

Bubble points of hydrogen chloride–water–isopropanol and hydrogen chloride–water–isopropanol–benzene systems and liquid–liquid equilibria of hydrogen chloride–water–benzene and hydrogen chloride–water–isopropanol–benzene systems

Bubble points of the HCl–water–isopropanol and the HCl–water–isopropanol–benzene systems and liquid–liquid equilibria (LLE) of the HCl–water–benzene and the HCl–water– isopropanol–benzene systems were measured at 25–85°C and 30–70°C, respectively. The electrolyte nonrandom two-liquid model proposed by Chen et al. [C.-C. Chen, H.I. Britt, J.F. Boston, L.B. Evans, AIChE J. 28 (1982) 588–596] can satisfactorily correlate bubble points and liquid–liquid equilibria of the present mixed-solvent electrolyte systems over the entire range of temperature and concentrations using only binary adjustable parameters.     

An atom-in-molecules and electron-localization-function study of the interaction between O2 and VxOy+/VxOy (x = 1, 2, y = 1–5) clusters

 The most stable structures of V _x O _y ⁺/V _x O _y (x=1, 2, y=1–5) clusters and their interaction with O₂ are determined by density functional calculations, the B3LYP functional with the 6-31G* basis set. The nature of the bonding of these clusters and the interaction with O₂ have been studied by topological analysis in the framework of both the atoms-in-molecules theory of Bader and the Becke–Edgecombe electron localization function. Bond critical points are localized by means of the analysis of the electron density gradient field, ∇ρ(r), and the electron localization function gradient field, ∇η(r). The values of the electron density properties, i.e., electron density, ρ(r), Laplacian of the electron density, ∇²ρ(r), and electron localization function, η(r), allow the nature of the bonds to be characterized, and linear correlation is found for the results obtained in both gradient fields. Vanadium-oxygen interactions are characterized as unshared-electron interactions, and linear correlation is observed between the electron density properties and the V–O bond length. In contrast, O₂ units involve typical shared-electron interactions, as for the dioxygen molecule. Four different vanadium–oxygen interactions are found and characterized: a molecular O₂ interaction, a peroxo O₂ ²⁻ interaction, a superoxo O₂ ⁻ interaction and a side-on O₂ ⁻ interaction. Received: 15 October 2001 / Accepted: 30 January 2002 / Published online: 24 June 2002     

Superhalogen properties of PdFn (n=1–7) clusters using Quantum chemical method

In this work the interaction of Palladium (Pd) atom with Fluorine (F) has been studied using density functional theory. Up to seven F atoms are bound to a single Pd atom which results in increase of electron affinities of given molecule successively, reaching a peak value of 8.54 eV for PdF₇. By using HOMO–LUMO gap, molecular orbital analysis, binding energy of these clusters, we examined its stability and reactivity. It is found that energy required for dissociation of F₂ molecules are higher than energy required for dissociation of F atoms. The unusual properties brought about by involvement of inner shell 4d-electrons, which not only allow PdF_n clusters to belong to the class of superhalogens but also show that its valence can exceed the nominal value of 1.     

Theoretical predication of third-order optical nonlinearities of [Al4MAl4] n− (n = 0–2, M = Ti, V and Cr) clusters

We investigate the nonlinear third-order polarizabilities of novel sandwichlike clusters [Al₄MAl₄]ⁿ⁻ (n = 0–2, M = Ti, V and Cr). The calculations have been performed by employing time-dependent density functional theory combined with sum-over-states method. The results show that these complexes possess remarkably large third-order static polarizability, and change of a metal centre has a great influence on the third-order nonlinear optical properties. The calculated third-order polarizability follows: [Al₄CrAl₄] > [Al₄VAl₄]⁻ > [Al₄TiAl₄]²⁻. Analysis of the main contributions to the third-order polarizability suggests that charge transfer () along the z-axis direction plays a key role in the nonlinear optical response. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

First-principles calculations on the structures,magnetic, and electronic properties of the (Fe2N)m (m = 1–4) and (Fe3N)n (n = 1–3) clusters

The structures, magnetic, and electronic properties of the ground-state (Fe₂N)_m (m?=?1–4) and (Fe₃N)_n (n?=?1–3) clusters have been investigated by using first-principles. The structure of the (Fe₂N)_m and (Fe₃N)_n clusters is a compromise that the N atoms approach more Fe atoms and the N atoms repel each other. The structural stabilities of the (Fe₂N)_m and (Fe₃N)_n clusters increase with the increasing of the N ratio except for the Fe₆N₃ clusters. The (Fe₂N)_m (m?=?1–4) and Fe₉N₃ clusters exhibit more kinetic stabilities than pure iron clusters. The N substitution can decrease the average spin densities of small iron clusters except for the Fe₆N₂ and Fe₈N₄ clusters. The Fe–N bonds exhibit certain covalent bond characteristics.

     

A computational study on CunN0,±1 (n=1–4) clusters by density functional methods

Clusters of the type Cu_nN^0,±1 (n=1–4) are investigated computationally using density functional theory methods. Equilibrium geometries are optimized under the constraint of well-defined point-group symmetries at the B3LYP level employing a pseudo-potential method in conjunction with double-zeta basis sets. In this article, different molecular properties such as total energies, electron affinities, ionization potentials, fragmentation energies and equilibrium geometries of the Cu_nN^0,±1 (n=1–4) clusters are systematically calculated and discussed. In particular, the photoelectron spectra of the anionic Cu_nN⁻¹ (n=2–4) clusters are calculated showing a good agreement with the available experimental results. In addition, Mulliken and natural orbital population analyses, and natural orbital configurations are calculated in order to elucidate the charge distributions in the clusters.     

NMR studies on [VS4–Cun] (n=3, 4, 5, 6) clusters

The complexes containing [VS₄–Cu_n] (n=3, 4, 5, 6) clusters were characterized by NMR spectra. The relationship between the ⁵¹V NMR chemical shift and the number of copper atoms in a cluster was established. ⁵¹V NMR chemical shifts were used to identify possible products of the reactions of Cu(PPh₃)Cl and [VS₄–Cu₃] with various mole ratios in CDCl₃ in order to study their reaction mechanism in solution. The results demonstrate that the reaction of tetranuclear [VS₄–Cu₃] and Cu(PPh₃)Cl in CDCl₃ successively yields penta-, hexa- and hepta-nuclear V–Cu–S heterometallic clusters when the mole ratio of [VS₄–Cu₃] to Cu(PPh₃)Cl is decreased, and the process can be reversed when [VS₄–Cu₃] is added to [VS₄–Cu₆] gradually. Theoretical calculations were also carried out to explain the experimental results.     

Chalcogen-Bonding Interactions in Telluroether Heterocycles [Te(CH2)m]n (n=1–4; m=3–7)

The Te ⋅⋅⋅ Te secondary bonding interactions (SBIs) in solid cyclic telluroethers were explored by preparing and structurally characterizing a series of [Te(CH₂)_m]_n (n=1–4; m=3–7) species. The SBIs in 1,7-Te₂(CH₂)₁₀, 1,8-Te₂(CH₂)₁₂, 1,5,9-Te₃(CH₂)₉, 1,8,15-Te₃(CH₂)₁₈, 1,7,13,19-Te₄(CH₂)₂₀, 1,8,15,22-Te₄(CH₂)₂₄ and 1,9,17,25-Te₄(CH₂)₂₈ lead to tubular packing of the molecules, as has been observed previously for related thio- and selenoether rings. The nature of the intermolecular interactions was explored by solid-state PBE0-D3/pob-TZVP calculations involving periodic boundary conditions. The molecular packing in 1,7,13,19-Te₄(CH₂)₂₀, 1,8,15,22-Te₄(CH₂)₂₄ and 1,9,17,25-Te₄(CH₂)₂₈ forms infinite shafts. The electron densities at bond critical points indicate a narrow range of Te ⋅⋅⋅ Te bond orders of 0.12–0.14. The formation of the shafts can be rationalized by frontier orbital overlap and charge transfer.     

Structures,electronic and magnetic properties of the FemOn@Cx (m = 1–3, n = 1–4, x = 50, 60) clusters

The structures, electronic and magnetic properties of the Fe_mO_n@C_x (m?=?1–3, n?=?1–4, x?=?50, 60) clusters have been investigated by using PBE functional. The C₅₀, C₆₀ can significantly increase the structural stabilities of the Fe_mO_n molecules. Fe₂O₃@C₅₀ and Fe₃O₄@C₅₀ are more chemically stable than the Fe₂O₃@C₆₀ and Fe₃O₄@C₆₀ while FeO@C₆₀ is more chemically stable than the FeO@C₅₀. The spin densities of the Fe_mO_n fragments degenerate to zero. Carbon encapsulation leads to the internal charges of the Fe_mO_n fragments transfer from 4 s to 4p orbital.