Models of molecular structures of aluminum–iron clusters AlFe<Subscript>3</Subscript>, Al<Subscript>2</Subscript>Fe<Subscript>3</Subscript>, and Al<Subscript>2</Subscript>Fe<Subscript>4</Subscript> according to quantum-chemical DFT calculations

The geometrical parameters of molecular structures of three types of aluminum–iron clusters containing in total four, five, and six Al and Fe atoms in structural units have been calculated by the OPBE/TZVP density functional theory (DFT) method with the Gaussian09 program package. It has been found that the AlFe₃, Al₂Fe₃, and Al₂Fe₄ clusters can have four, eight, and nine structural modifications, which significantly differ in stability and geometric parameters. Bond lengths and bond and torsion (dihedral) angles are reported for each of these modifications.     

Structures and bonding patterns of nanoannular carbon clusters (C4–C20) through AIM analyses

Structures, binding energies, harmonic frequencies, dipole moments, HOMO–LUMO energy gaps and particularly atoms in molecules (AIM) analyses of some nanoannular carbon clusters (C₄–C₂₀) are investigated at B3LYP/6-31+G(d) level of theory. No correlation is found by plotting the calculated binding energies as a functional number of carbon atoms of carbon clusters. The calculated binding energies sharply increase from C₄ to C₁₀ while slowly from C₁₀ to C₂₀. The binding energies of C_4n+2 clusters including C₆, C₁₀, C₁₄, and C₁₈ have a clear increase when compared with others indicating their aromatic characters which is confirmed by results of HOMO–LUMO energy gaps and geometrical parameters. AIM analyses show that most of our carbon clusters are topologically normal (non-conflict) with stable structures. Nevertheless, the topological networks of small antiaromatic rings, C₄ and C₈, at their equilibrium geometries may change via molecular vibrations. The existence of straight bond paths in 3D molecular graphs of carbon clusters with n > 10 implies that ring strains are decreased as the ring sizes grow. Except for C₄ and C₈, the ellipticity values for the remaining carbon clusters are small indicating that the C–C bond is conserved in these clusters. Dipole moments of even-numbered structures are negligible, whereas odd-numbered ones have μ values of 0.09−0.73 D.     

Gaussian density-functional study for small neutral (Al n ), positive (Al n + ) and negative (Al n − ) aluminium clusters (n=2–5)

The structures and properties of Al _n , Al _n ⁺ , Al _n ^– (n=1,5) clusters have been investigated by using the Linear Combination of Gaussian Type Orbitals (LCGTO) method, considering Local (LSD) and Non Local (NLSD) Spin Density Approximations and employing a Model Core Potential (MCP) that allows the explicit treatment of 3s ² 3p ¹ valence electrons. For each system different geometrical structures and electronic states have been considered. For Al₃, Al ₃ ⁺ , Al ₃ ^– the most stable geometry proved to be the equilateral triangle (D _3h ). Al₄ and Al ₄ ⁺ prefer the rhombus (D _2h ) structure, while the corresponding anion prefers the square (D _4h ) one. The trapezoidal form (C _2v ) is the most stable isomer for Al₅, Al ₅ ⁺ and Al ₅ ^– clusters. The analysis of vibrational frequencies shows that these structures are minima in the potential energy surface. The binding energies (D _e), the adiabatic ionization potentials (IP) and electron affinities (EA), the chemical potentials or absolute hardnesses () and electronegativities () have been computed. Results are in good agreement with the available experimental data and the previous high level theoretical computations.     

Molecular structure of hexatomic heteronuclear (AlFe) metal clusters as determined by the DFT quantum-chemical calculation

Geometric parameters of molecular structures of hexatomic heteronuclear (AlFe) clusters with various number of aluminum atoms (Al₂Fe₄ and Al₃Fe₃) were calculated using the density functional hybrid method in the OPBE/TZVP approximation. It was found that the first of these clusters is able to exist in nine and the second in twenty structural modifications substantially differing from each other in their stability and geometric parameters. The values of bond lengths, planar and dihedral (torsion) angles for some of these modifications are given.     

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.

     

Calculated properties of neutral and charged Al<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>Co<Subscript><Emphasis Type="Italic">m</Emphasis></Subscript> clusters by density functional theory

Density functional calculations are performed to study the structures and electronic properties of Al _n Co _m clusters with n = 1–7 and m = 1–2. Frequency analysis is also performed after structural optimization to make sure that the calculated ground states are real minima. The corresponding total and binding energies, adiabatic electron affinities and ionization potentials are presented and discussed to aid the identification of our calculations. The BSSE correction is also considered in our calculation. Among Al _n Co _m , Al _n Co _m ⁻, and Al _n Co _m ⁼ clusters (n = 1–7 and m = 1–2), Al₄Co⁻, Al₆Co⁻, Al₂Co₂, and Al₆Co₂ are predicted to be more stable. Our results are consistent with the available experimental data.     

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.

     

Electronic factors determining the methane bond breaking process on small aluminum clusters

In order to understand the catalytic activity of small metal clusters as a function of their size, we have studied the interaction of CH₄ with Al₄ and Al₅ neutral and charged clusters, as well as neutral thermally expanded clusters in the two lowest lying spin states, using density functional theory. These calculations, via extended search, are used to determine the stable positions of H and CH₃ near the cluster, and the transition state to break the H─CH₃ bond. In order to understand the factors underlying the reactivity of the clusters, we have analyzed the electronic structure at the transition state. By an analysis of the change of the electronic density of states close to the transition state, we identify the orbitals involved in the bond breaking process. In conjunction with our previous studies of Al₂ and Al₃ clusters, we find that the small Al clusters, except for Al₅, lower the CH₃─H dissociation barrier with respect to the gas-phase value, although Al lacks occupied d-orbitals. Still, Al₅ does not catalyze methane bond breaking, which is attributed to the required interaction with low-lying Al sp-states. Furthermore, in all cases where stable methyl-aluminum-hydrides are possible, the recombinative desorption of methane is studied by vibrational analysis and application of transition state theory.     

Study on the Geometric and Electronic Structures of Al<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>Si<Subscript><Emphasis Type="Italic">m</Emphasis></Subscript> (n = 3, 4, 5; m = 1, 2, 3, 4) Clusters

Genetic algorithm combined with the semi-empirical Hamitonian AM1/PM3 is used to search the low energy isomers of Al _n Si _m (n = 3, 5, m ≤ 3 and n = 4, m ≤ 4) and the charged clusters with 20 and 28 valence electrons. The candidate structures were optimized by the density functional theory PBE0 and B3LYP models with the triply split basis sets including polarization functions. The electronic structures show that Al–Si binary clusters behave like metal clusters. The molecular orbitals accord with that predicted by the jellium model, and the electron localization function shows the valence electrons are delocalized over the entire clusters. The clusters having 20 and 28 valence electrons exhibit pronounced stabilities and large energy gaps. The 20 valence electrons of Al₄Si₂ and Al₃Si₃ ⁺, Al₅Si^? form closed shells 1S ²1P ⁶2S ²1D ¹⁰. Al₄Si₄ and Al₅Si₃ ^? have oblate structures and the P, D, F levels spilt considerably in these clusters. The electron density distributions suggest that doping silicon in the aluminum clusters enhances the stability considerably.     

Density-functional calculations of MnC(M = Fe, Co, Ni, Cu, n = 1–6) clusters

The structural, energetic and magnetic properties of M_nC(M = Fe, Co, Ni, Cu, n = 1–6) clusters are systematically investigated by density-functional calculations. We found that the ground-state geometrical structures of M_nC clusters are different from those of pure M_n+1 clusters. Fe₄C, Ni₂C and Cu₄C possess relatively higher stabilities. Doping of a C atom enhances the binding energy of M_n clusters, and the binding energies of Fe_n-C, Co_n-C and Ni_n-C are stronger than that of Cu_n-C.     

Structure and properties of small silicon and aluminum clusters

Small Si_n and Al_n clusters (n = 3–10) were studied with the semiempirical molecular orbital method (MO) method SINDO1. For each n, various structures were optimized to determine the most stable structure. To obtain good qualitative agreement with available ab initio calculations d orbitals had to be omitted from the basis set. Both silicon and aluminum tend to build three-dimensional structures rather than two- or one-dimensional structures, except for n = 3 or 4. The structure growth was studied by approaching various sites of stable structures with one or more atoms. It was found that silicon and aluminum exhibit different structure growth, and consequently, different most-stable structures. Ionization potentials, HOMO -LUMO energy differences, binding energies per atom, and average atomic valencies are presented.     

Models of Molecular Structures of Al<Subscript>2</Subscript>Cr<Subscript>3</Subscript> and Al<Subscript>2</Subscript>Mo<Subscript>3</Subscript> Metal Clusters according to Density Functional Theory Calculations

The geometrical parameters of the molecular structures of aluminum–chromium and aluminum–molybdenum clusters Al₂Cr₃ and Al₂Mo₃ have been calculated by the OPBE/TZVP density functional theory (DFT) method with the Gaussian09 programL package. It has been found that each of these metal clusters can exist in twenty structural modifications, which significantly differ in stability and geometric parameters. Bond lengths and bond and torsion (dihedral) angles are reported for each of these modifications.     

Stable High-Energy Density Super-Atom Clusters of Aluminum Hydride

With the concept of super-atom, first principles calculations propose a new type of super stable cage clusters Al_nH_3n that are much more energetic stable than the well established clusters, Al_nH_n+2. In the new clusters, the aluminum core-frame acts as a super-atom with n vertexes and 2n Al-Al edges, which allow to adsorb n hydrogen atoms at the top-site and 2n at the bridge-site. Using Al₁₂H₃₆ as the basic unit, stable chain structures, (Al₁₂H₃₆)m, have been constructed following the same connection mechanism as for (AlH₃)_n linear polymeric structures. Apart from high hydrogen percentage per molecule, calculations have shown that these new clusters possess large heat of formation values and their combustion heat is about 4.8 times of the methane, making them a promising high energy density material.     

硼碳团簇BnC2 (n＝1～6)的理论研究

应用密度泛函理论在B3LYP/6-311＋G(d)水平上研究了硼碳团簇B_nC₂ (n＝1～6)的几何结构、生长机制和相对稳定性. 计算结果表明, 对于n＝2～6的簇, 平面多环状构型为最稳定的结构, 其中C原子分布于环的顶点、有尽可能多的三配位硼原子和尽可能多的B—C键. 碳原子作为杂原子倾向掺杂于团簇的顶点位置, 它的掺杂不改变硼团簇的主体结构. 与平面多环状结构相比, 随着簇尺寸的增大, 三维结构和线性链结构更不稳定. 在低能线性结构中, C原子位于链两侧的第二个位置. 计算的碎片分裂能、递增键能以及HOMO-LUMO能隙表明, B₄C₂为幻数簇.     

Synthesis and structures of new heteronuclear cluster complexes [PPh4][Fe4Rh3Se2(CO)16] and [PPh4]2[Fe3Rh4Te2(CO)15]

The reaction of the K₂[Fe₃Q(CO)₉] clusters (Q = Se or Te) with Rh₂(CO)₄Cl₂ under mild conditions is accompanied by complicated fragmentation of cores of the starting clusters to form large heteronuclear cluster anions. The [PPh₄][Fe₄Rh₃Se₂(CO)₁₆] and [PPh₄]₂[Fe₃Rh₄Te₂(CO)₁₅] compounds were isolated by treatment of the reaction products with tetraphenylphosphonium bromide. The structures of the products were established by X-ray diffraction. In both compounds, the core of the heteronuclear cluster consists of two octahedra fused via a common Rh₃ face. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 775–778, May, 2006.     

Synthesis and X-Ray Crystal Structures of Fe2Ru(CO)12−n (CNBu t ) n and FeRu2(CO)12−n (CNBu t ) n (n=1, 2)

The clusters Fe₂Ru(CO)_12–n (CNBu ^t ) _n (3, n=1; 4, n=2), FeRu₂(CO)_12–n (CNBu ^t ) _n (5, n=1, 6, n=2) and FeRu₂(CO)₁₁(CNCy) (5a) have been prepared by direct substitution from the parent carbonyl precursors Fe₂Ru(CO)₁₂ (1) and FeRu₂(CO)₁₂ (2). All compounds have been characterized spectroscopically and clusters 3, 4, 5, and 6 by single crystal X-ray determinations. In all cases, the isonitrile ligands adopt axial or pseudo-axial positions on a ruthenium atom. The structures of 3–5 are very similar to their parent clusters, but the extent of metal framework disorder is significantly less. Cluster 6 adopts the same C _2v Fe₃(CO)₁₂ type structure as 4, and thus differs markedly from the parent compound 2, which has a D ₃ structure .     

Kondensierte Al6‐Ringe in den Subiodiden La3Al2I2 und La2Al2I

Condensed Al₆ Rings in the Subiodides La₃Al₂I₂ and La₂Al₂I The subiodides La₃Al₂I₂ and La₂Al₂I are reported. The compounds were prepared from stoichiometric mixtures of lanthanum, aluminium, and LaI₃ under Ar atmosphere in sealed Ta ampoules at 920–950 °C and 980–1000 °C, respectively. La₃Al₂I₂ crystallizes in space group C2/m with a = 19.73(2) Å, b = 4.318(1) Å, c = 12.348(9) Å and β = 121.49(3)°, La₂Al₂I in P6₃/mmc with a = 4.3718(8) Å and c = 17.605(2) Å (isotypic with Gd₂Fe₂I). Both structures are characterized by sheets of trigonal prisms formed by the La atoms centered by aluminium, the latter being arranged in Al₆ rings. These rings are connected to chains in La₃Al₂I₂ (d_{Al(2)–Al(2)} = 2.550(4) Å and 2.615(2) Å, respectively) and layers (d_Al–Al = 2.533(1) Å) in La₂Al₂I. Both compounds are metallic conductors. The electronic structure of both compounds is discussed based on band structure calculations.     

Quantum chemical study of the structure of molybdenum pentafluoride

The geometrical and electronic structure of various configurations of molybdenum pentafluoride are studied in the nonrelativistic approximation of the DV-X_α method. It is shown in a cluster approximation that the presence of the MoF₅ monomer with a distorted trigonal bipyramid (C_2v symmetry) and cyclic trimer [MoF₅]₃(D_3h symmetry) configurations is most probable for the liquid and gaseous phases. High probability of the existence of cyclic tetramers [MoF_{5 4} of lower symmetry (D_2h) is confirmed for the crystalline state. The geometrical parameters calculated for the most stable clusters and the data on their stability agree well with the experimental data.     

Structure and properties of iron oxide clusters: From Fe6 to Fe6O20 and from Fe7 to Fe7O24

Geometrical and electronic structures of the neutral and singly negatively charged Fe₆O_n and Fe₇O_m clusters in the range of 1 ≤ n ≤ 20 and 1 ≤ m ≤ 24, respectively, are computed using density functional theory with the generalized gradient approximation. The largest clusters in the two series, Fe₆O₂₀ and Fe₇O₂₄, can be described as Fe(FeO₄)₅ and Fe(FeO₄)₆ or alternatively as [FeO₅](FeO₃)₅ and [FeO₆](FeO₃)₆, respectively. The Fe₆O₂₀ and Fe₇O₂₄ clusters possess adiabatic electron affinities (EA_ad) of 5.64 eV and 5.80 eV and can be attributed to the class of hyperhalogens since FeO₄ is an unique closed‐shell superhalogen with the EA_ad of 3.9 eV. The spin character of the lowest total energy states in both series changes from ferromagnetic to ferrimagnetic or antiferromagnetic when the first Fe? O? Fe bridge is formed. Oxidation decreases substantially the polarizability per atom of the initial bare clusters; namely, from 5.98 ų of Fe₆ to 2.47 ų of Fe₆O₂₀ and from 5.67 ų of Fe₇ to 2.38 ų of Fe₇O₂₄. The results of our computations pertaining to the binding energies of O, Fe, O₂, and FeO in the Fe₇O_m series provide an explanation for the experimentally observed abundance of the iron oxide nanoparticles with stoichiometric compositions. © 2016 Wiley Periodicals, Inc.     

Comparisons of the theoretical calculation of nitrogen clusters by semiempirical MO method

Various nitrogen clusters, N_x, are selected for the present theoretical study. The number of nitrogen atoms chosen in this work varies from x = 8 to x = 32. PM3, which is known as one of the best semiempirical methods, is selected for the self-consistent molecular orbital calculations. The geometrical optimization, vibrational frequencies, and thermochemical computations are all involved for various types of molecular nitrogen clusters. The results show that all N_x's belong to the category of stable high-energy compounds. Comparison of average bond energy and delocalization energy of all cases reveals that N₂₀(I_h symmetry) is the most stable molecule among all the nitrogen clusters studied. In addition, our results show five-membered rings are the most favored in the structures of nitrogen clusters (N_x). © 1996 John Wiley & Sons, Inc.