Production of doubly charged clusters (H2O)n · Ba2+ and (H2O)n · Ca2+ under low temperature fast atom bombardment conditions

Production of doubly charged ions of alkaline earth metals Ba²⁺ and Ca²⁺ and their doubly charged clusters with water molecules (H₂O)_n · Ba²⁺, (H₂O)_n · Ca²⁺ (n = 1, 2, 3) by means of low temperature fast atom bombardment technique is observed in the case of crystalline hydrates of BaCl₂ and CaCl₂ salts, formed during freezing of water-salt solutions. Reasons for a possibility of production of the doubly charged species in the case of the two indicated salts and their absence in the case of chlorides of some other divalent metals (Mg, Mn, Co, Cu, Zn) are discussed. As to singly charged secondary ions Me⁺, MeCl⁺, MeOH⁺, [(H₂O)_n · MeCl]⁺, [(H₂O)_n · MeOH]⁺ (where Me is metal), high efficiency of their production from crystalline hydrates was observed and possible explanation of the phenomenon is suggested.     

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     

Quantum-chemical modeling of gas-phase adsorption of the hydroxyl radical on IB metal clusters Me n (n = 2–8)

The structure of the most stable Me _n clusters and Me _n OH complexes (Me = Cu, Ag, Au; n = 2–8) was calculated using the density functional theory. The enthalpy and Gibbs energy of the interaction of OH^· with metal clusters were calculated. It was shown that the hydroxyl radical is predominantly adsorbed into the bridge position on the metal IB clusters. During the adsorption of the hydroxyl radical, the frequency and intensity of the stretching vibrations of the O-H bond increased relative to the corresponding values for the isolated state; the frequency shift changed in the series Ag < Cu < Au.     

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.     

A Topological Study of the Ferromagnetic “No-Pair Bonding” in Maximum-Spin Lithium clusters: n+1Li n (n=2–6)

The nature of the bonding between lithium atoms, in low-spin and maximum-spin clusters, was investigated using the topological electron localization function (ELF) approach. The maximum-spin clusters are especially intriguing since their bonding is sustained without having even a single electron pair! Hence this type of bonding had been called “no-pair ferromagnetic-bonding” [Danovich, Wu, Shaik J Am Chem Soc 121:3165 (1999); Glokhovtsev, Schleyer Isr J Chem 33: 455 (1993); de Visser, Danovich, Wu, Shaik J Phys Chem A 106:4961 (2002)]. The following conclusions were reached in the study: (a) In the ground state of Li _n , covalent bonding between Li atoms is accounted by the presence of the disynaptic valence basins, which exhibit a significant degree of inter-basin delocalization. (b) Except for the ³Li₂ case, the valence basins of all maximum-spin clusters are populated by unpaired electrons. The valence basins are located off Li–Li axis (or Li–Li–Li plane), so that their spatial distribution minimizes the mutual Pauli repulsion and screens the electrostatic repulsion between the Li cores. The inter-basin delocalization is rather high, thereby indicating that the unpaired electrons are virtually delocalized over all the valence basins. (c) The ELF analysis shows that Li atoms in the low-spin clusters are bonded by “two-center two-electron” and “three-center two-electron” bonds. (d) In the maximum-spin species, bonding is sustained by “two-center one-electron” and “three-center one-electron” bonds. The latter picture is complementary to the valence bond picture [Danovich, Wu, Shaik J Am Chem Soc 121 3165 (1999); de Visser, Danovich, Wu, Shaik J Phys Chem A 106: 4961 (2002)], in which the bicentric ferromagnetic-bonding is delocalized over all the short Li–Li contacts, by the mixing of the ionic structures and other nonredundant structures into the repulsive high-spin covalent structure in which all the electrons populate the 2s atomic orbitals, i.e., the configuration. In such a manner bonding can be sustained from “purely ferromagnetic interactions” without electron pairing.Dedicated to Jean-Paul Malrieu, a friend and a poet-scientist     

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.     

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.     

The Boron conundrum: the case of cationic clusters B n + with n?=?2–20

We investigate the molecular and electronic structure and thermochemical properties of the cationic boron clusters B _n ⁺ with n?=?2–20, using both MO and DFT methods. Several functionals are used along with the MP2, G3, G3B3, G4, and CCSD(T)/CBS methods. The latter is the high accuracy reference. While the TPSS, TPSSh, PW91, PB86, and PBE functionals show results comparable to high-accuracy MO methods, both BLYP and B3LYP functionals are not accurate enough for three-dimensional (3D) structures. A negligible difference is observed between the B3LYP, MP2, and CCSD(T) geometries. A transition between 2D and 3D structures occurs for this series at the B₁₆ ⁺–B₁₉ ⁺ sizes. While smaller clusters B _n ⁺ with n?≤?15 are planar or quasi-planar, a structural competition takes place in the intermediate sizes of B _16–19 ⁺ . The B₂₀ ⁺ cation has a 3D tubular shape. The standard heats of formation are determined and used to evaluate the cluster stability. The average binding energy tends to increase with increasing size toward a limit. All closed-shell species B _n ⁺ has an aromatic character, but an enhanced stability is found for B₅ ⁺ and B₁₃ ⁺ whose aromaticity and electron delocalization are analyzed using the LOL technique.     

Theoretical study of H2 elimination from [B n H n + 1]− monoanions (n = 6–9, 11)

Transition states of elementary reactions of H₂ molecule elimination from [B _n H _{n + 1}]^? anions (n = 6–9, 11) in which nucleophilic/electrophilic vacancies form at boron atoms have been localized by the density functional theory method (in the B3LYP/6-311++G** approximation). For a series of [B _n H _{n + 1}]^? anions (n = 6–12), the activation barriers to H2 elimination have been compared to consider the possibility of substitution for exopolyhedral hydrogen atoms by the mechanism with the first rate-limiting stage of formation of [B _n H _{n ? 1}]^? (n = 6–12) intermediates with a vacant “bare” vertex of the boron cluster. For the [B _n H _n ]^2?, [B _n H _{n + 1}]^?, and [B _n H _{n ? 1}]^? anions (n = 6–12), the electronic chemical potential μ and Pearson hardness η have been evaluated since these characteristics make it possible to assess the propensity of different reagents to react with each other in terms of the empirical HSAB principle (soft with soft and hard with hard). The application of this principle is exemplified by the interaction of the [B₁₀H₉]^? and [B₁₂H₁₁]^? anions with acetonitrile CH₃CN, furan C₄H₄O, and 18-crown-6.     

Theoretical study of negatively charged Fe(-)-(H2O)(n ≤ 6) clusters

Interactions of a singly negatively charged iron atom with water molecules, Fe(-)-(H(2)O)(n≤6), in the gas phase were studied by means of density functional theory. All-electron calculations were performed using the B3LYP functional and the 6-311++G(2d,2p) basis set for the Fe, O, and H atoms. In the lowest total energy states of Fe(-)-(H(2)O)(n), the metal-hydrogen bonding is stronger than the metal-oxygen one, producing low-symmetry structures because the water molecules are directly attached to the metal by basically one of their hydrogen atoms, whereas the other ones are involved in a network of hydrogen bonds, which together with the Fe(δ-)-H(δ+) bonding accounts for the nascent hydration of the Fe(-) anion. For Fe(-)-(H(2)O)(3≤n), three-, four-, five-, and six-membered rings of water molecules are bonded to the metal, which is located at the surface of the cluster in such a way as to reduce the repulsion with the oxygen atoms. Nevertheless, internal isomers appear also, lying less than 3 or 5 kcal/mol for n = 2-3 or n = 4-6. These results are in contrast with those of classical TM(+)-(H(2)O)(n) complexes, where the direct TM(+)-O bonding usually produces high symmetry structures with the metal defining the center of the complex. They show also that the Fe(-) anions, as the TM(+) ions, have great capability for the adsorption of water molecules, forming Fe(-)-(H(2)O)(n) structures stabilized by Fe(δ-)-H(δ+) and H-bond interactions.     

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.     

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.     

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.     

Characterization of the fluxes of neutral and positively charged clusters (Agn and Agn+; n≤4) produced by argon ion sputtering of silver

The emission of neutral and positively charged silver clusters during sputtering of a polycrystalline silver target by 5 keV Ar⁺ ion bombardment has been studied and the sputter ejected silver flux has been characterized. As a result, the silver flux is found to be strongly dominated byneutral clusters rather than cluster ions. The contribution of neutral clusters in the overall silver flux decreases rapidly and monotonically with increasing cluster size n and decreases, in addition, with decreasing bombarding energy. The well known alternation of the secondary ion intensities of Ag _n ⁺ as a function of cluster size (higher intensities for odd n) is found to be correlated with the effective ionization potentials of the corresponding sputtered neutral clusters.     

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.     

Is the uniform electron gas limit important for small Ag clusters? Assessment of different density functionals for Ag(n) (n < or = 4)

Twenty-three density functional theory (DFT) methods, including the second- and the third-generation functionals, are tested in conjunction with two basis sets (LANL2DZ and SDD) for studying the properties of neutral and ionic silver clusters. We find that DFT methods incorporating the uniform electron gas limit in the correlation functional, namely, those with Perdew's correlation functionals (PW91, PBE, P86, and TPSS), Becke's B95, and the Van Voorhis-Scuseria functional VSXC, generally perform better than the other group of functionals, e.g., those incorporating the LYP correlation functional and variations of the B97 functional. Strikingly, these two groups of functionals can produce qualitatively different results for the Ag3 and Ag4 clusters. The energetic properties and vibrational frequencies of Ag(n) are also evaluated by the different functionals. The present study shows that the choice of DFT methods for heavy metals may be critical. It is found that the exact-exchange-incorporated PBE functional (PBE1PBE) is among the best for predicting the range of properties.     

Theoretical study of the stability of small triply charged carbon clusters Cn3+ (n = 3–12)

Using density functional theory, coupled cluster and multireference methods, dissociation energies and 3rd ionization potentials for, respectively, triply charged and neutral carbon clusters have been evaluated. The results show that the smaller C_n³⁺ clusters are metastable, i.e., they present a fragmentation channel with negative dissociation energy. The lowest dissociation channel always corresponds to evaporation of a singly charged carbon atom. Good agreement with available experimental data is found for most two-fragment channels. The third ionization potential of the corresponding neutral species decreases with cluster size.     

A first principle study of hydrogen storage in titanium-doped small carbon clusters (C2nTin,n = 2–6)

Structural Chemistry - Hydrogen storage in Ti-doped small carbon clusters, C2nTin (n = 2–6), has been studied using density functional theory. Using the principle of maximum hardness (η)...     

Density functional study of the charge on Aun clusters (n=1-7) supported on a partially reduced rutile TiO2(110): are all clusters negatively charged?

It is widely believed that small gold clusters supported on an oxide surface and adsorbed at the site of an oxygen vacancy are negatively charged. It has been suggested that this negative charge helps a gold cluster adsorb oxygen and weakens the O-O bond to make oxidation reactions more efficient. Given the fact that an oxygen vacancy is electron rich and that Au is a very electronegative element, the assumption that the Au cluster will take electron density from the vacancy is plausible. However, the density functional calculations presented here show that the situation is more complicated. The authors have used the Bader method to examine the charge redistribution when a Aun cluster (n=1-7) binds next to or at an oxygen vacancy on rutile TiO2(110). For the lowest energy isomers they find that Au1 and Au3 are negatively charged, Au5 and Au7 are positively charged, and Au2, Au4, and Au6 exchange practically no charge. The behavior of the Aun isomers having the second-lowest energy is also unexpected. Au2, Au3, Au5, and Au7 are negatively charged upon adsorption and very little charge is transferred when Au4 and Au6 are adsorbed. These observations can be explained in terms of the overlap between the frontier molecular orbitals of the gold cluster and the eigenstates of the support. Aun with even n becomes negatively charged when the lowest unoccupied molecular orbital has a lobe pointing in the direction of the oxygen vacancy or towards a fivefold coordinated Ti (5c-Ti) located in the surface layer; otherwise it stays neutral. Aun with odd n becomes negatively charged when the singly occupied molecular orbital has a lobe pointing in the direction of a 5c-Ti located at the vacancy site or in the surface layer, otherwise it donates electron density into the conduction band of rutile TiO2(110) becoming positively charged.     

Growth pattern of Ag(n) (n = 1-8) clusters on the α-Al2O3(0001) surface: a first principles study

We report an extensive first-principles study of the structure and electronic properties of Ag(n) (n = 1-8) clusters isolated in gas phase and deposited on the α-Al(2)O(3) surface. We have used the plane wave based pseudopotential method within the framework of density functional theory. The electron ion interaction has been described using projector augmented wave (PAW), and the spin-polarized GGA scheme was used for the exchange correlation energy. The results reveal that, albeit interacting with support alumina, the Ag atoms prefers to remain bonded together suggesting an island growth motif is preferred over wetting the surface. When compared the equilibrium structures of Ag clusters between free and on alumina substrate, a significant difference was observed starting from n = 7 onward. While Ag(7) forms a three-dimensional (3D) pentagonal bipyramid in the isolated gas phase, on alumina support it forms a planar hexagonal structure parallel to the surface plane. Moreover, the spin moment of the Ag(7) cluster was found to be fully quenched. This has been attributed to higher delocalization of electron density as the size of the cluster increases. Furthermore, a comparison of chemical bonding analysis through electronic density of state (EDOS) shows that the EDOS of the deposited Ag(n) cluster is significantly broader, which has been ascribed to the enhanced spd hybridization. On the basis of the energetics, it is found that the adsorption energy of Ag clusters on the α-Al(2)O(3) surface decreases with cluster size.