Elastic and reactive collisions of atoms and molecules with neutral alkali clusters

We have measured absolute integral cross sections for low-energy collisions of atoms and molecules with neutral sodium clusters over a wide cluster size range (n=2–40). The cross sections are exceptionally large, reaching values of thousands of square angstroms. Consequently, the scattering involves long-range interactions. The van der Waals force, acting either alone (Na_n+N₂) or in concert with the inelastic charge-transfer “harpooning” channel (Na_n+Cl₂, Na_n+O₂) can describe the measurements. Using interaction parameters taken from spectroscopic studies of alkali clusters, we find very good agreement with the data. This provides a point of contact between beam scattering experiments and studies of cluster electromagnetic response properties.     

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.     

Ab-initio study of optical response properties of nonstoichiometric lithium-hydride and sodium-fluoride clusters with one- and two-excess electrons

Structural and optical response properties of Li _n H _n-m and Na_nF _n-m (n = 2-6, m = 1, 2) clusters containing one- and two-excess electrons are studied using ab-initio methods accounting for electron correlation. The common feature of the optical response obtained for the most stable structures of Na_nF _n-1 (n = 2-6) clusters is the appearance of a dominant intense transition in the infrared regime independently whether the single excess electron is localized at the cuboid corner vacancy (surface F-center) or at the external atom attached to the filled cuboid. In contrast, Li_nH _n-1 (n = 2-6) clusters exhibit substantially different spectroscopic patterns with respect to halides also for the cases with the common structural properties. Optical response features of Li_nH _n-2 (n = 3-6) clusters with two-excess electrons are characterized by dominant transitions in the visible regime reflecting segregation in “metallic” and ionic parts. In contrast, Na_nF _n-2 = 3-6) can be divided according to their optical and structural properties into cuboid “lattice” defect species (Na₄F _n , Na _n F₄) and segregated metallic-ionic systems. For the former, the intense transitions occur in the infrared-visible, and for the latter only in the visible regime. It will be shown that the calculated absorption patterns are excellent fingerprints of structural and bonding properties.     

Monte Carlo bicanonical ensemble simulation for sodium cation hydration free energy in liquid water

A series of bicanonical ensemble Monte Carlo (BC MC) simulations has been performed to calculate Na⁺ hydration Gibbs energy in aqueous solution. The hydration Gibbs energy of Na⁺ ion in aqueous solution is the difference between formation free energies of Na⁺ (H₂O)_n and (H₂O)_n clusters at n → α. The convergence of the hydration free energy to bulk water value is fast, and the results at n = 60 turned out to be in good agreement with experimental ones and those calculated using free energy perturbation method [1]. The ion–water interaction has been described by Aqvist's pair potential [1] and SPC model [2] has been used for water–water interactions. The behaviour of the absolute Gibbs energy, the entropy, the internal energy of the clusters and the development of hydration shells’ structure with the increase of the number of water molecules are discussed.     

Evaporation rates of hot sodium clusters

A scheme based in density functional theory with pseudopotentials is used to obtain the normal modes of vibration of Na _n clusters (4 ≤n ≤ 22). The monomer and dimer evaporation rates from thermally excited clusters are obtained in this harmonic approximation. The time evolution of the abundance spectra from an initial uniform mass distribution of hot clusters is studied and its influence in the experimentally observed spectra is discussed.     

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.     

Melting of gold microclusters

The transition from solid-like to liquid-like behavior in Au _n ,n=6, 7, 13, clusters is studied using molecular dynamics simulations. A Gupta-type potential with all-neighbour interactions is employed to incorporaten-body effects. The melting-like transition is described in terms of short-time averages of the kinetic energy per particle, root-mean-square bond length fluctuations and mean square displacements. A comparison between melting temperatures of Au _n and Ni _n clusters is presented.     

Enrichment and segregation in alkali heteroclusters

A spherical average pseudopotential method (SAPS) is used to investigate some properties of compound alkali clusters. The effect that the substitution of a Sodium atom by a Lithium atom in a Na _n cluster has on the stabilities and geometries is studied forn≤21. We have found that substitution is always energetically possible. On the other hand equiatomic Na _n Cs _n clusters are considered in the size rangen≤16. We find a strong segregation effect of the Cesium atoms towards the cluster surface. This agrees with what happens in liquid Na _x Cs_1?x alloys.     

Electronic properties of aluminum clusters compared with the jellium model

The experimental polarizabilities, ionization potentials and electron affinities of aluminum clusters are compared with jellium predictions. It is found that the clusters have radii and work functions which are close to the jellium model predictions for clusters with more than 13 atoms. The polarizabilities of Al _n correspond with the jellium only forn>40 and the shell structure features in the ionization potentials are anomalous up to 37. We conclude that nonjellium effects are important up ton=40.     

Au_n团簇催化水煤气变换反应机理的密度泛函理论研究

利用密度泛函理论(DFT)研究了Au10、Au13和Au20三类团簇的稳定性和对水煤气变换(WGSR)反应的催化活性,考察了各物质在Aun团簇上的吸附行为和微观反应机理。结果表明,三类Aun团簇的稳定性顺序为Au10Au13Au20,而Aun团簇中电子离域性及吸附能力大小趋势为Au13Au10Au20。在三类Aun团簇上,水煤气变换反应的控速步骤均为H2O的解离,但其反应机理路径有所不同。Au10团簇上为羧基机理,COOH*中间体直接解离;Au13团簇上为氧化还原机理,两个OH*发生歧化反应;Au20团簇上为羧基机理,COOH*和OH*发生歧化反应。通过对三类团簇上的最佳反应路径进行比较发现,Au13团簇在低温下具有较好的催化活性。     

Doubly charged sodium clusters: plasmon response and photoproduction

The optical response of doubly charged sodium clusters Na _n+2 ⁺⁺ was measured for n = 20, 40, and 58 valence electrons, for which the jellium model predicts spherical clusters. A new experimental scheme was developed which allows to separate doubly charged clusters of even mass from the singly charged with half the mass. The optical spectra are dominated by a plasmon-like resonance which is blue shifted and narrower than that of the singly charged clusters. The smallest doubly charged cluster observed was Na ₉ ⁺⁺ . The photo ionization cross section for singly charged clusters was found to be typically 2.6·10^-19cm² per Na atom for photon energies of around 6 eV, which is a factor of 400 smaller than the maximum in the plasmon absorption in the region of hω=2.6 eV.     

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.     

First principles study and database analyses of structural preferences for sodium ion (Na+) solvation and coordination

Extensive computations were performed on aqueous clusters of monovalent sodium cation [Na⁺(H₂O) _n ; (n = 1–20)] using MP2/cc-pVTZ and density functional theory. The structure, energy, and coordination number (CN) preference of a large number of competing conformations of different complexes have been explored. For complexes up to n = 12, the CN 4 is most preferred while 5, 6 CNs are favored in case of larger complexes containing up to 20 water molecules. These results are in very good agreement with experimental observations. The strength of hydrogen bonding among the waters coordinated to the Na⁺ ion is found to play a major role in the stability of the complexes. The varying preferences for CN of Na⁺ ion were explored by screening two important databases: Protein Databank and Cambridge Structural Database. A linear correlation is observed between the M (Metal)–O distance and the charge on metal ion in complex with the increase in CN of metal ion.     

Ground and excited states properties of Na4F m=1−3, Li4H and Li4H2 clusters

Stable ground state structures for neutral and charged Li _n H, Li _n H₂ and Na _n F _m (n?m) have been determined usingab —initio methods accounting for electronic correlation effects. The consequences of replacing alkali-atom by foreign-atom or -atoms have been studied. The similarities and differences with respect to topologies of the most stable Li _n and Na _n clusters will be pointed out. The ionization potentials and spectroscopic patterns are compared with available experimental data. This allows for the geometrical and spectroscopic assignments as well as for a study of the influence of localized versus non localized bonding on the ground and excited state properties of mixed clusters.     

A density functional study for the isomers of anionic sulfur clusters Sn− (n=3–20)

The signals of anionic sulfur clusters are intense in the mass spectrum of sulfur clusters generated in direct laser vaporization. We have acquired numerous isomers of sulfur clusters by means of the B3LYP DFT method. According to total energies, the most stable S_n⁻ (n=3–13) isomers are predicted. The helical S_n (n=14–20) structures are also calculated. Most of the anionic clusters are with chain configurations; the ring clusters with threefold atom(s) are higher in total energy. The most stable forms of isomers, from S₉⁻ to S₁₃⁻, show helical configurations that are completely different from those of the corresponding neutral and cationic clusters.     

Spectroscopy of non-stoichiometric sodium-fluoride clusters Na n F n -1; infrared spectral signature and classification

We report in this paper resonant two-photon spectroscopy from 290nm to 1000nm of Na _n F _n -1 clusters. Spectral signature are shown to be correlated with the structure and allows us to sort these clusters according to a classification which supplements that of Whetten et al.     

Stability and structure of singly-charged xenon-argon clusters [Xe1Arn−1]+,n=3–27

Monte-Carlo calculations have been performed for positively charged xenon-argon clusters in the temperature range between 10K and 40K for cluster sizes up ton=27. The argon-argon interaction potential stems from empirical data, the Xe⁺-Ar potential is determined by ab initio MRD-CI calculations and a semi-empirical treatment of spin-orbit effects. Special stability is found for cluster sizesn=10, 13, 19 and less pronounced forn=23 and 25 fairly independent of the temperature. The geometrical structure of the clusters are given and the construction principle is discussed in light of the interactions among neutral argon atoms and the xenon ion — argon interaction. Comparison with measured mass spectra for mixed rare-gas clusters and [Xe_n]⁺ clusters is made and shows a consistent picture for the building principle.     

Structure, stability and electronic property of the gold-doped germanium clusters: AuGe n (n = 2–13)

The structure, stability and electronic property of the AuGe _n (n = 2–13) clusters with different spin configurations are systematically investigated with density-functional theory approach at UB3LYP/LanL2DZ level. In examining the lowest energy structures, it is found that the growth behaviors for the small-sized AuGe _n (n = 2–9) clusters and relatively large-sized AuGe _n (n = 10–13) clusters are different. As the number of Ge atom increases, the Au atom would gradually move from convex to surface and to interior sites. For the most stable structures of AuGe _n (n = 10–13) clusters, the Au atom would be completely surrounded by the Ge atoms to form Au-encapsulated Ge _n cages. Natural population analysis shows that the charges always transfer from the Au atom to the Ge _n framework except for the AuGe₂ cluster. This indicates that the Au atom acts as electron donor even the 5d orbitals of the Au atom are not significantly involved in chemical bonding. The analyses of the average atomic binding energies as well as the dissociation energies and the second-order differences of total energy show that the AuGe _n clusters with n = 5, 9 and 12 are more stable than their neighboring ones, in which the bicapped pentagonal prism AuGe₁₂ in D _2d symmetry is most stable. The highest occupied molecular orbital–lowest unoccupied molecular orbital gaps are explored to be in the region of semiconductors and the more stable clusters have slightly smaller gaps. It could be expected that the stable clusters might be considered as the novel building blocks in practical applications, e.g., the cluster-assembled semiconductors or optoelectronic material.     

Cluster cations ejected from liquid metal ion source: alkali metals (Li,Na) and group IV elements (Si,Ge, Sn,Pb)

Cluster abundance of Li _n ⁺ (n≤19), Na _n ⁺ (n≤25), Si _n ^z+ (n≤8 forz=1, 3≤n≤7 forz=2), Ge _n ^z+ (n≤11 forz=1, 3≤n≤9 forz=2,n=4 forz=3), Sn _n ^z+ (n≤7 forz=1, 3≤n≤9 forz=2,n=4 forz=3) and Pb _n ^z+ (n≤6 forz=1, 5≤n≤7 forz=2) ejected from a liquid metal ion source has been investigated by mass spectrometry. The abundance spectra of alkali metal clusters showed distinct maxima and steps atn=3, 7, 9, 13 and 19 for Li, and atn=3, 5, 11, 13 and 19 for Na. Mass spectra of Si, Ge and Sn clusters were very similar each other, showing intensity drops aftern=4 and 6 (and alson=10 for Ge) for singly charged clusters. The magic numbers observed are discussed in terms of stability of charged clusters.