Ab-initio study of Na n F n and Na n F n−1 clusters: atypical structures

Alkali halide clusters Na _n F _n have most frequently cuboid structures and Na _n F _n?1 clusters are derived from Na _n F _n by removing a F^? centre. An excess electron localises on the site of the removed F^? ion. In this paper, other kind of clusters are studied at the SCF level: i) The non-cubic structures. ii) The cubic Na _n F _n?1 for which the excess electron has no defined site. Due to very large size of these species (at least 27 atoms!) some equivalent fictive linear and planar geometries are studied.     

Evolution of (GaAl) n Clusters and Chemisorptions of H2 on (GaAl) n Clusters

The growth behavior of (GaAl) _n (n = 1–12) and the chemisorptions of hydrogen on the ground state geometries have been studied with the three-parameter hybrid generalized gradient approximation due to Becke-Lee–Yang–Parr (B3LYP). The dissociation energy, the second-order energy differences, and the HOMO–LUMO gaps indicate that the magic numbers of the calculated (GaAl) _n clusters are n = 4 and 6. To my knowledge, this is the first time that a systematic study of chemisorptions of hydrogen on gallium aluminum clusters. The onefold top site of aluminum atom is identified to be the most favorable chemisorptions site for one hydrogen chemisorptions on most (GaAl) _n clusters. In general, dissociative chemisorptions of a hydrogen molecule on a top site of aluminum atom is found common for all sizes clusters considered here except for (GaAl) _n (n = 1–3) clusters. The stability of the (GaAl) _n H _m complexes shows that both large second-order difference and large fragmentation energies for (GaAl)₁₀H₂ and (GaAl)₁₁H₂ make these species behaving like magic clusters.     

The geometric, energetic, and electronic properties of charged phosphorus-doped silicon clusters, PSi n +/PSi n ? (n?=?1�C8)

Charged phosphorus-doped small silicon clusters, PSi _n ⁺/PSi _n ^? (n?=?1?8), have been investigated using the B3LYP/6-311+G* level Kohn?CSham density functional theory (KS-DFT) method. For comparison, the geometries of neutral PSi _n clusters were also optimized at the same level, though most of them have been previously reported. According to our results, cationic PSi _n ⁺ clusters have ground state structures similar to those of pure silicon clusters Si _n+1, with the exception of n?=?5. For anionic PSi _n ^?, most of the lowest-energy structures are in accord with Wade??s 2N+2 rule for closed polyhedra: PSi₄ ^?, PSi₅ ^?, PSi₆ ^?, and PSi₈ ^?, respectively, favor the trigonal bipyramid, tetragonal bipyramid, pentagonal bipyramid, and tricapped trigonal prism (TTP) structures, corresponding to Wade??s 2N+2 rule with N?=?5, 6, 7, and 9. The structures tend to contract when the cationic species is reduced initially to the neutral species and subsequently to the anionic species, implying a strengthening interaction between atoms within the clusters on one and two electron reductions of the cationic species to the neutral and anionic species, respectively. The relative order of stability of the PSi _n ⁺/PSi _n ^? isomers differs from that of the PSi _n isomers. Cluster stability was also analyzed by adiabatic ionization potentials (AIP), adiabatic electron affinities (AEA), binding energies (BE), second-order energy differences (?₂E), and HOMO-LUMO gap values. The results indicate that PSi₄ ^? and PSi₇ ^? clusters are more stable than their neighboring anionic clusters and would be potential species for further mass spectrometric measurements.     

Electron impact ionization of silver clusters Ag n,n≦36

Electron impact ionization of gas phase silver clusters Ag _n ,n≦36 has been achieved in the threshold region. The vertical ionization potentials in this region clearly demonstrate the evidence of shell effects as well as a distinct even-odd oscillation up ton?20. Their general size dependence is somewhat different from that of the alkali metal clusters due to the presence of thed-electrons.     

Stability of isomeric Na n clusters

A method which combines density functional theory and the use of pseudopotentials is applied to obtain ground state and low-lying metastable geometries of Na _n clusters (7≤n≤40). The large variation in the magnitude of energy gaps between isomers suggests that the melting temperature is not a simple monotonous function of size. A detailed study of the differences between electronically stabilized (n=8, 20, 40) and structurally stabilized (n=13) clusters suggests some clues to understand the intriguing behaviour of Na₁₃.     

Electronic structure calculations of small Al n (n=2–8) clusters

The electronic states of small Al _n (n=2–8) clusters have been calculated with a relativistic ab-initio MO-LCAO Dirac-Fock-Slater method using numerical atomic DFS wave-functions. The excitation energies were obtained from a ground state calculation of neutral clusters, and in addition from negative clusters charged by half an electron in order to account for part of the relaxation. These energies are compared with experimental photo-electron spectra.     

Study on structures and electron affinities of small potassium–silicon clusters Si n K (n = 2–8) and their anions with Gaussian-3 theory

The neutral Si _n K (n = 2–8) clusters and their anions have been systematically studied by means of the higher level of Gaussian-3 schemes. Equilibrium geometries and electron affinities have been calculated and are discussed for each considered size. For neutral Si _n K clusters, the ground state structure is found to be “attaching structure”, in which the K atom is bound to Si _n clusters. The most stable isomer for their anions, however, is found to be “substitutional structures”, which is derived from Si_(n+1) by replacing the Si atom with a K. The dissociation energies of K atom from the lowest energy structures of Si _n K have also been estimated to examine relative stabilities.     

Structure and stability for (AlN) n + and (AlN) n + (n=1–15) clusters

Using density functional theory (DFT) method with 6-31G* basis set, we have carried out the optimizing calculation of geometry, vibrational frequency and thermodynamical stability for (AlN) _n ⁺ and (AlN) _n ⁺ (n=1–15) clusters. Moreover, their ionic potential (IP) and electron affinity (EA) were discussed. The results show that the electrical charge condition of the cluster has a relatively great impact on the structure of the cluster and with the increase of n, this kind of impact is reduced gradually. There are no Al-Al and N-N bonds in the stable structure of (AlN) _n ⁺ or (AlN) _n ^-, and the Al-N bond is the sole bond type. The magic number regularity of (AlN) _n ⁺ and (AlN) _n ^- is consistent with that for (AlN) _n , indicating that the structure with even n such as 2, 4, 6, ... is more stable. In addition, (AlN₁₀ has the maximal ionization power (9.14 eV) and the minimal electron affinity energy (0.19 eV), which manifests that (AlN)₁₀ is more stable than other clusters.     

A REMPI study of solvation of small Hg n clusters by polar molecules

Free Hg _n (DME) _m clusters (where DME=dimethyl-ether,n=1, 2, 3,m=1÷5) formed in a supersonic expansion were studied by the REMPI (Resonance-Enhanced Multi-Photon Ionization) technique. A large decrease of ionization energies due to solvation of Hg _n clusters is observed. Preliminary results are discussed in terms of different equilibrium configurations of the electronic ground, excited and ionic states of clusters.     

Observation of doubly charged mercury cluster ions Hg n 2+, n=1-10 using secondary ion mass spectrometry

Mass spectra of doubly charged mercury clusters (m/z=30-1065) were investigated by secondary ion mass spectrometry. Positively charged ions were generated from an amalgam of mercury and silver by bombardment with a xenon ion beam and mass analysis by a grand-scale sector type mass spectrometer. Hg _n ²⁺, n=1-10 and Hg _n +, n =1- 5 were observed. Some doubly charged mercury clusters, (Hg _n ²⁺) survived at least for 0.1 ms.     

On the localization of electrons and holes in Hg n and rare-gas clusters

We have used a microscopic theory to study the size dependence of the degree of localization of the valence electrons and holes in neutral an ionized rare-gas-and Hg _n clusters. We discuss under which circumstances localization of the electrons and holes is favoured. We have calculated the ionization potential of Xe _n , Kr _n and small Hg _n clusters. Good agreement with experiments is obtained. We have also determined the dependence of the ionization potential on cluster structure.     

Ultraviolet absorption bands of [Cs n+1 I n ]+ (n<14) clusters

Starting from the large photofragmentation cross sections recently reported for mass-selected alkali-halide clusters [1], we have obtained, for the first time, optical absorption spectra forCs _n+1 I _n ⁺ clusters in the ultraviolet charge-transfer bands. In this short report we focus on the spectra ofn=4, 6 and 13 which start to show absorption between the lowest charge-transfer band of the diatomic (ca. 3.8 eV) and that of the bulk (ca. 5.9 eV). The spectral features are analyzed for these sizes and correlated to their structures qualitatively as a preliminary model.     

Unimolecular dissociation of trivalent metal cluster ions (Al n + , Ga n + , In n + ): evidence for a transition from covalent to metallic bonding

Unimolecular dissociation of aluminum, gallium and indium clusters is investigated. Small sizes dissociate into two channels: either the evaporation of a neutral or a charged monomer. Above a given size n _c, only dissociation of a neutral atom subsists. The evaporation of a charged monomer is characteristic of trivalent metal clusters and is consistent with the size evolution of the ionization potential towards the atomic value. The experiments are interpreted in the framework of the statistical R.R.K. model. For smaller sizes (n < n _c), as two evaporation processes are in competition, we have evaluated cluster relative dissociation energies and ionization potentials. The competition between the two evaporation channels is well mirrored by the evolution of the ionization potentials independently measured by near-threshold photoionization experiments. For gallium, our measurements have revealed that the covalent to metal transition occurs for larger sizes (n = 30–50 atoms) than for aluminum clusters.     

Fragmentation by electron impact ionization and intracluster reactions of size selected (N2H4) n and (OCS) n clusters

The hydrogen-bonded (N₂H₄) _n clusters and the van der Waals (OCS) _n clusters are size selected in a scattering experiment with a He beam up to the cluster sizen=6. By measuring the angular distributions of the scattered clusters the complete fragmentation pattern of electron impact ionization is obtained. For Hydrazine the two main fragment masses are the protonated species (N₂H₄) _n?1H⁺ and with somewhat weaker intensities also the nominal ion mass (N₂H₄) _n ⁺ . The largest intensity is observed for the monomer ion N₂H ₄ ⁺ to which clusters up ton=5 fragment. For carbonylsulfide, completely different results are obtained. Aside from the fragments of the OCS monomer and the van der Waals cluster fragments (OCS) ₂ ⁺ and (OCS) ₃ ⁺ signals at mass S ₂ ⁺ , S ₃ ⁺ and S₂OCS⁺ are detected. This indicates a fast chemical reaction in the cluster according to: S + OCS → CO + S₂ which occurs for clusters of sizen ≥ 2. Peaks at S ₃ ⁺ and S₂OCS⁺ are seen for the first time forn ≥ 5 according to a further reaction of S₂ in the cluster.     

Molecular-dynamics simulation of the structural stability,energetics, and melting of Cu n(n = 13–135) clusters

Cluster properties of copper have been investigated using the Molecular-Dynamics md technique. The structural stability and energetics of spherical Cu_n (n = 13–135) clusters have been investigated at temperatures T = 1 K and T = 300 K. It has been found that the average interaction energy per atom in the cluster decreases and reaches an asymptotic value as cluster size increases. The melting behaviour of clusters n = 13 and n = 55 have been investigated. It has been found that the melting temperature decreases as cluster size increases, and for clusters with multishell structures melting starts from the outermost shell. In the simulation an emprical potential energy function (PEF) proposed by Erkoç has been used, which contains two-body atomic interactions.     

Phosphido cobalt carbonyl clusters Pn[Co(CO)3]4−n (n = 1, 2, 3)

The P_n[Co(CO)₃]_4?n (n = 1, 2, 3) tetrahedral clusters have been prepared and characterized. The very unstable PCo₃(CO)₉ can be stabilized in the form of (CO)₄FePCo₃(CO)₉     

Magnetic and thermodynamic properties of Heisenberg chains and n-nuclear cyclic clusters: S i = 3/2 (n ≤ 11, n → ∞) and S i = 2 (n ≤ 10, n → ∞) systems

Based on the method considering spin and spatial symmetry, numerical calculations of the spin-level spectra have been performed for n-nuclear cyclic clusters with S _i = 3/2 (n ≤ 11) and S _i = 2 (n ≤ 10). The theoretical curves of the magnetic susceptibility, the magnetic contribution to the heat capacity, the internal energy, and the entropy as a function of temperature have been obtained. The theoretical curves of the magnetic susceptibility and the magnetic contribution to the heat capacity have been extrapolated to n → ∞ with a controlled accuracy.     

Theory for the short-time response of small Hg n clusters after excitation

The short-time behavior of small Hg _n clusters immediately after single or double ionization is studied. We calculate self-consistently the ground state electronic energyE of ionized Hg _n clusters. Upon ionization changes of the potential energy surface (PES) occur, which govern the atomic motion in the cluster. These changes depend on cluster size and charge and are determined by the interplay between the localization of the holes within an ionic core and the polarization energy of the neutral rest of the cluster. In the case of single ionization of the cluster the PES results mainly from hole delocalization. In contrast, in the case of double ionization the PES is governed almost only by strong environment polarization. We use our theory to explain the physical origin of the oscillations in the ionization cross-section of singly and doubly excited Hg _n clusters observed in recent pump-probe experiments.     

Evaporation of tetramers in Sb4n clusters and conditions for the formation of Sb2n+1 clusters

Antimony clusters are produced by the inert gas condensation technique. They are found to be built from Sb₄ units. The fragmentation by evaporation of Sb₄ units is studied as a function of the excess energy in the cluster. By this way the binding energy of the Sb₄ units in the cluster is found to be about 1.5 eV, well below the binding energy of a Sb atom in the bulk and in Sb₄(?3eV). The evolution of ionization potentials of Sb_4n clusters confirms that their structure is probably non metallic. Finally the possible metastable character of this Sb_4n structure is discussed.     

Silver-halogen cluster compounds Ag n X m (n≥2; 0≤m≤n;X=F,Br)

Nonstoichiometric silver-halogen cluster compounds Ag _n X _m (0≤m≤n;X=F, Br) are generated by cocondensation of Ag atoms and AgX species using a slightly modified gas aggregation technique. The AgX molecules are produced by partial decomposition of SF₆ and Br₂ respectively at the surface of the hot silver containing crucible, followed by the reaction of halogen atoms with silver, giving rise to the formation of AgX molecules. In a heterogeneous nucleation between these molecules and evaporated Ag atoms the afore mentioned cluster compounds are formed. The degree of halogenation can either be controlled by the adjustment of the silver evaporation rate, or even more easily by controlling the partial pressure of the halogenating agent. The mass spectra of singly charged halogenated clusters, which are generated by electron impact ionization, reflect the stability of ions. These mass spectra demonstrate that there is an alternation in the intensity pattern up to a relatively high degree of halogenation (m) for each of the investigated compound series Ag _n X _m ,n≤8. This behavior is similar to the well-known odd-even effect for pure metal clusters, allowing us to postulate the existence of a “metallic” core which governs the stability of the cluster ion (at least for not too high degree of halogenation).