Geometrical structures,electronic states,and stability of NinAl clusters

Density‐functional with generalized gradient approximation (GGA) for the exchange‐correlation potential has been used to calculate the energetically global‐minimum geometries and electronic states of Ni_nAl (n = 2–8) neutral clusters. Our calculations predict the existence of a number of previously unknown isomers. All structures may be derived from a substitution of a Ni atom at marginal positions by an Al atom in the Ni_n+1 cluster. Aluminum atom remains on the surface of the geometrical configurations. Moreover, these species prefer to adopt three‐dimensional (3D) spacial forms at the smaller number of nickel atoms compared with the pure Ni_n+1 (n ≥ 3) configuration. Atomization energies per atom for Ni_nAl (n = 2–8) have the same trend as the binding energies per atom for Ni_n (n = 3–9). The stabilization energies reveal that Ni₅Al is the relatively most stable in this series. In comparison with the magnetic moment of pure metal nickel (0.6 μ_B), the average magnetic moment of Ni atom increases in Ni Al clusters except the Ni₃Al. Moreover, except the case of Ni₅Al, Ni average magnetic moment decreases when alloyed with Al atoms than that in pure Ni clusters, which originate the effective charge transferring from Al to Ni atoms. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

13-atom Ni-Al alloy clusters: Structures and dynamics

Structural and dynamical properties of model 13-atom Ni_nAl_m alloy clusters derived from a many-body potential are presented and discussed. Characterization of the structures corresponding to a given stoichiometric composition (i.e., chosen number of Ni and Al atoms) is carried out in terms of isomeric (geometric) forms and different distributions of the two types of atoms between the sites of a chosen isomer. We use the term homotops (“the same topography or geometry”) to label the structural forms that differ only by these distributions. The number and the energy spectra of the homotops are sensitive functions of the stoichiometric composition and isomeric form. Similarly to homogeneous clusters, alloy clusters undergo a solid-to-liquidlike transition as their energy is increased. Individual stages in the transition, such as isomerizations involving only surface atoms, isomerizations involving all atoms, surface melting (in a system as small as 13 atoms), and complete melting are identified and characterized. The actual occurrence of some or all of these stages in the meltinglike transition of a given cluster depends on the character of the energy spectra of its homotops, i.e., ultimately, on its stoichiometric composition. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 185–197, 1997     

Adjusting magnetic moments of Sc13 and Y13 clusters by doping different X atom (X = Na,Mg, Al,Si, P)

We have investigated the structural and magnetic properties of the doped XM₁₂ and charged M₁₃ (X = Na, Mg, Al, Si, P; M = Sc, Y) clusters using the density‐functional theory with spin‐polarized generalized gradient approximation. It was found that doped atoms can induce significant change of the magnetic moments of Sc₁₃ and Y₁₃ clusters. The total magnetic moments of the NaM₁₂, MgM₁₂, AlM₁₂, SiM₁₂, and PM₁₂ clusters are regular 5, 6 (12), 7, 8, and 9 μ_b, respectively (but 19 μ_b for Sc₁₃ and Y₁₃, 12 μ_b for Y, 18 μ_b for Sc, Sc, and Y). The doped atom substituting the surface atom of the plausible icosahedral configuration is viewed as the ground‐state structure of the XM₁₂ (X = Na, P; M = Sc, Y) and MgSc₁₂ clusters. While for XM₁₂ (X = Al, Si; M = Sc, Y) and MgY₁₂ clusters, the doped atom occupying the central position of the icosahedral configuration is viewed as the ground‐state structure. The doping and the charging both enhance the stability of the Sc₁₃ and Y₁₃ clusters. These findings should have an important impact on the design of the adjustable magnetic moments systems. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

27Al NMR diffusometry of Al13 Keggin nanoclusters

Although nanometer-sized aluminum hydroxide clusters (i.e., ϵ-Al₁₃, [Al₁₃O₄(OH)₂₄(H₂O)₁₂]⁷⁺) command a central role in aluminum ion speciation and transformations between minerals, measurement of their translational diffusion is often limited to indirect methods. Here, ²⁷Al pulsed field gradient stimulated echo nuclear magnetic resonance (PFGSTE NMR) spectroscopy has been applied to the AlO₄ core of the ϵ-Al₁₃ cluster with complementary theoretical simulations of the diffusion coefficient and corresponding hydrodynamic radii from a boundary element-based calculation. The tetrahedral AlO₄ center of the ϵ-Al₁₃ cluster is symmetric and exhibits only weak quadrupolar coupling, which results in favorable T₁ and T₂ ²⁷Al NMR relaxation coefficients for ²⁷Al PFGSTE NMR studies. Stokes–Einstein relationship was used to relate the ²⁷Al diffusion coefficient of the ϵ-Al₁₃ cluster to the hydrodynamic radius for comparison with theoretical simulations, dynamic light scattering from literature, and previously published ¹H PFGSTE NMR studies of chelated Keggin clusters. This first-of-its-kind observation proves that ²⁷Al PFGSTE NMR diffusometry can probe symmetric Al environments in polynuclear clusters of greater molecular weight than previously considered.     

Methanol activation catalyzed by Pt7, Pt3Cu4, and Cu7 clusters: A density functional theory investigation

Metal clusters were considered as excellent catalysts for methanol dissociation. In this work, two main decomposition mechanisms of methanol on Pt₇, Pt₃Cu₄, and Cu₇ clusters were investigated by the density functional theory. One was methanol direct dehydrogenation, and the other was non‐CO‐involved oxidation. Stable adsorption configurations, elementary reaction barriers, the potential energy surface (PES), and the charge analysis were elucidated. The results showed that on Pt₇ cluster, methanol was favorable for direct decomposition. On Pt₃Cu₄ and Cu₇ clusters, methanol was inclined to the pathway of non‐CO‐involved oxidation. All the transition‐state energies and the final‐state energies were related in a linear, including those for the clusters. The results may be useful for computational design and catalysts optimization.     

Density functional studies of LiN and LiN+ (N = 2–30) clusters: Structure,binding and charge distribution

Density functional calculations using B3LYP/6‐311G method have been carried out for small to medium‐sized lithium clusters (Li_N, N = 2–30). The optimized geometries of neutral and singly charged clusters, their binding energies, ionization potential, electron affinity, chemical potential, softness, hardness, highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO–LUMO) gap, and static dipole polarizability have been investigated systematically. In addition, we study the distribution of partial charges in detail using natural population analysis (NPA) in small‐sized clusters (Li_N, N = 2–10), both neutral and cationic, and demonstrate the correlation between symmetry and charge. Uniform distribution of charges in cationic clusters confirms them to be energetically more favorable than the neutral counterparts. Whenever possible, results have been compared with available data. An excellent agreement in every case supports new results as reliable predictions. A careful study of optimized geometries shows that Li₉ is derivable from bulk Li structure, i.e., body centered cubic cell, and higher clusters have optimized shapes derived from this. Further, the turnover form two to three dimensional structure occurs at cluster size N = 6. The quantity α^1/3 (α = polarizability) per atom is found to be broadly proportional to softness (per atom) as well as inverse ionization potential (per atom). The present work forms a sound basis for further study of large‐sized clusters as well as other atomic clusters. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Electronic and magnetic properties of small RhnCa (n = 1–9) clusters: A DFT study

The equilibrium geometries, relative stabilities, electronic and magnetic properties of small Rh_nCa (n = 1–9) clusters have been investigated by DFT calculations. The obtained results show that the three‐dimensional geometries are adopted for the lowest‐energy Rh_nCa clusters, and the doped Ca atom prefers locating on the surface of the cluster. Based on the analysis of the second‐order difference of energies, fragmentation energies and the HOMO‐LUMO energy gaps, we identify that the Rh₄Ca, Rh₆Ca, and Rh₈Ca clusters are relatively more stable than their neighboring clusters, and the doping of Ca enhances the chemical reactivity of the pure Rh_n clusters, suggesting that the Rh_nCa clusters can be used as nanocatalysts in many catalytic reactions. The magnetic moment for these clusters is mostly localized on the Rh atoms, and the doping Ca atom has no effect on the total magnetic moment of Rh_nCa clusters. The partial density of states, VIP, VEA, and η of these clusters in their ground‐state structures were also calculated and discussed. © 2015 Wiley Periodicals, Inc.     

Behavior of molecular potential energy curves for large nuclear separations

We prove by elementary geometric methods and within the Born–Oppenheimer approximation that as the nuclei of a molecule are dissociated into spatially separated clusters, the discrete molecular energies approach sums of the energies of isolated subsystems. Our methods also show that the spectral projections associated with the discrete molecular spectrum asymptotically approach direct sums of suitable spectral projections for the isolated subsystems. These results apply to any system of particles interacting by asymptotically vanishing pair potentials. We prove that the 1/R expansion for discrete molecular potential curves is asymptotic as R → ∞, and we discuss the behavior of the coefficients of the 1/R expansion for the ground state of H₂⁺.     

Structural,electronic, and magnetoresponsive properties of triangular lanthanide clusters and their free‐standing nitrides

The molecular and electronic structures, stabilities, bonding features, and magnetoresponsive properties of three‐membered [c‐Ln₃]^+/0/? (Ln = La, Ce, Pr, Nd, Gd, Lu) and heterocyclic six‐membered [c‐Ln₃E₃]^q (Ln = La, Ce, Pr, Nd, Gd, Lu; E = C, N; q = 0 or 1) rings have been investigated by means of electronic structure calculation methods at the DFT level. The [c‐Ln₃]^+/0/? clusters are predicted to be bound with respect to dissociation to their constituent atoms, the estimated binding energies ranging from 45.8 to 2056.4 kJ/mol. The [c‐Ln₃] rings capture easily a planar three‐coordinated nitrogen atom at the center or above the center of the ring yielding the lanthanide nitride clusters [c‐Ln₃(μ₃‐N)] adopting a planar geometry, except [c‐La₃(μ₃‐N)] which exhibits pyramidal geometry. The [c‐Ln₃(μ₃‐N)] clusters are predicted to be bound, with respect to dissociation to N (⁴S) atom and [c‐Ln₃] clusters in their ground states, the binding energies ranging from 53.9 to 257.9 kcal/mol. The six‐membered [c‐Ln₃E₃]^q rings are predicted to be bound with respect to dissociation to LnE^q monomers in their ground states with dissociation energies in the range of 173.8 to 318.0 kcal/mol. Calculation of the NICS_zz‐scan curves of the clusters predicted a “hermaphrodic” magnetic response of the [c‐Ln₃]^+/0/? and heterocyclic six‐membered [c‐Ln₃E₃]^q rings, manifested by the coexistence of successive diatropic (aromatic) and paratropic (antiaromatic) zones. The [c‐La₃]^+/0/? and [c‐Lu₃]^? are predicted to be weakly antiaromatic, the [c‐Lu₃]^0/+, [c‐Lu₃C₃]⁺, and [c‐Lu₃N₃] double (σ+π) aromatic, and the [c‐Gd₃C₃] and [c‐Gd₃N₃]⁺ rings (σ+δ)‐aromatic systems. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Structural and electronic properties of stable Aun (n = 2–13) clusters: A density functional study

All-electron scalar relativistic calculations have been performed to investigate the electronic structures of neutral gold clusters (Au_n, n = 2–13) in the gas phase using density functional theory with the generalized gradient approximation. Full geometry optimizations of topologically different clusters and clusters belonging to different symmetry groups have been carried out. Binding energies, ionization potentials, electron affinities, and chemical hardness values are calculated and they are found to be comparable with the available experimental and theoretical results. The most stable structure of each of the cluster has a two-dimensional planar configuration. A three dimensional distorted Y shaped structure (4b) for Au₄, a tri-capped triangle (6b), a chair (6f), and a see-saw structure (6j) for Au₆, an eclipsed sandwich structure (7g) for Au₇, a condensed trigonal bipyramid (9e) and a boat shaped structure (9f) for Au₉, a staggered sandwich (11c) and an eclipsed sandwich structure (11d) for Au₁₁, a ladderane structure (12d) for Au₁₂, and a staggered (13d) and a distorted sandwich structure (13e) for Au₁₃ are characterized for the first time in this work.     

Non-covalent Interactions and Charge Transfer between Propene and Neutral Yttrium-Doped and Pure Gold Clusters

The dopant and size-dependent propene adsorption on neutral gold (Au_n) and yttrium-doped gold (Au_n−1Y) clusters in the n=5–15 size range are investigated, combining mass spectrometry and gas phase reactions in a low-pressure collision cell and density functional theory calculations. The adsorption energies, extracted from the experimental data using an RRKM analysis, show a similar size dependence as the quantum chemical results and are in the range of ≈0.6–1.2 eV. Yttrium doping significantly alters the propene adsorption energies for n=5, 12 and 13. Chemical bonding and energy decomposition analysis showed that there is no covalent bond between the cluster and propene, and that charge transfer and other non-covalent interactions are dominant. The natural charges, Wiberg bond indices, and the importance of charge transfer all support an electron donation/back-donation mechanism for the adsorption. Yttrium plays a significant role not only in the propene binding energy, but also in the chemical bonding in the cluster-propene adduct. Propene preferentially binds to yttrium in small clusters (n<10), and to a gold atom at larger sizes. Besides charge transfer, relaxation also plays an important role, illustrating the non-local effect of the yttrium dopant. It is shown that the frontier molecular orbitals of the clusters determine the chemical bonding, in line with the molecular-like electronic structure of metal clusters.     

First‐principles study of molecular hydrogen dissociation on doped Al12X (X = B,Al, C,Si, P,Mg, and Ca) clusters

Inspired by the concept of superatom via substitutionally doping an Al₁₃ magic cluster, we investigated the H₂ molecule dissociation on the doped icosahedral Al₁₂X (X = B, Al, C, Si, P, Mg, and Ca) clusters by means of density functional theory. The computed reaction energies and activation barriers show that the concept of superatom is still valid for the catalysis behavior of doped metal clusters. The hydrogen dissociation behavior on metal clusters characterized by the activation barrier and reaction energy can be tuned by controllable doping. Thus, doped Al₁₂X clusters might serve as highly efficient and low‐cost catalysts for hydrogen dissociation. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

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.     

Structures and Electronic Properties of Ni–Al Alloy Clusters from First-Principles Calculations

Using the density functional theory calculations with the PBE exchange–correlation energy functional, we have studied the low-energy structures and electronic properties of Ni–Al alloy clusters for adsorbing or doping an aluminum atom to Ni_n (n = 13, 19, 23, 26, 29 and 55) clusters. The most stable structures of Ni_nAl are viewed as adding an Al atom at the hollow triangle and rhombus site of the icosahedron (n = 13, 55) and double-icosahedron (n = 19, 23, 26 and 29) structures, respectively. For Ni_n?1Al, it can be seen that an Al atom gradually moves from surface (n = 13, 19, 23 and 26) to the interior site (n = 29, 55) in the most stable structures. The electronic properties of the Ni–Al alloy clusters including binding energies, magnetic properties, charge transfer and density of states have also been studied.     

Structural evolution of small gold clusters doped by one and two boron atoms

The potential energy surfaces (PES) of a series of gold–boron clusters with formula Au_nB (n = 1–8) and Au_mB₂ (m = 1–7) have been explored using a modified stochastic search algorithm. Despite the complexity of the PES of these clusters, there are well‐defined growth patterns. The bonding of these clusters is analyzed using the adaptive natural density partitioning and the natural bonding orbital analyses. Reactivity is studied in terms of the molecular electrostatic potential. © 2014 Wiley Periodicals, Inc.     

Quantum chemistry of quantum size‐effects in semiconductors: Small clusters electronic structure calculations

Ab initio RHF SCF calculations are used for some small clusters M_xX_y, where M=Cd, Ag; X=S, I; and x, y≤7. Variation of electronic structure with size for some clusters with the bulklike tetrahedral coordination and with the lower symmetry allows one to predict their possible geometries which are compared with experimental data on the existence of the clusters. The chemical‐bonding factor (the chemical nature of bounded atoms, coordination number for metal and nonmetal atoms, hybridization, etc.) is of more importance for properties of the clusters than is the familiar quantum confinement effect of semiconductor clusters. The essential difference in regularities of small cluster formation is analyzed for CdS‐ and AgI‐based structures. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 337–341, 1999     

On the Possibility of Using the Jellium Model as a Guide To Design Bimetallic Superalkali Cations

The potential application of the jellium model as guidance in the rational design of bimetallic superalkali cations is examined under gradient-corrected density functional theory for the first time. By using Li, Mg, and Al as atomic building blocks, a series of bimetallic cationic clusters with 2, 8, 20, and 40 valence electrons are obtained and investigated. As the corresponding neutral clusters tend to lose one valence electron to achieve closed-shell states in the jellium model, these studied cations exhibit much lower vertical electron affinities (EA_vert, 3.42–4.95 eV) than the ionization energies (IEs) of alkali metal atoms, indicating their superalkali identities. The high stability of these cationic clusters is guaranteed by their considerable HOMO–LUMO gaps and binding energies per atom. Moreover, the feasibility of using the designed superalkalis as efficient reductants to activate CO₂ and N₂ molecules and as stable building blocks to assemble ionic superatom compounds is explored. Therefore, this study may provide an effective method for obtaining various metallic superatoms with extensive applications on the basis of the simple jellium rule.     

Structural, Electronic, and Optical Properties of Noble Metal Clusters from First Principles

We examine low-energy isomeric forms, static polarizabilities, and optical absorption spectra of Ag _n , n = 2–8, and Au _n , n = 2–3, clusters using first principles computations within the static and time-dependent versions of the density functional theory. The noticeable decrease in the static polarizabilities of Ag₇ and Ag₈ compared to the values characteristic of Ag _n , n = 2–6, is correlated with the transition from two-dimensional to three-dimensional structures at n = 7. The optical spectra computed within the time-dependent local density approximation for the most stable structures are in good agreement with the available experimental data and the results of earlier theoretical studies. Optical spectra of higher-energy isomers typically present features that are not observed in the experimental spectra. The d electrons affect the spectra of noble metal clusters by quenching the oscillator strengths through screening of the s electrons and by getting directly involved in the excitations. Due to the larger s–d hybridization in Au compared to Ag, these effects are more pronounced in Au _n clusters.     

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.