Theory of fragmentation of metal clusters

The theory of shell correction developed for discussing fissing of heavy nuclei is applied to symmetric fragmentation of charged metal clusters. Assuming the effective potential of an anisotropic harmonic oscillator, we calculate the shell correction. We also calculate the energy of deformed charged droplets in the two-dimensional parameter space describing the deformation of droplets such as elongation and neck formation. The symmetric fragmentation of microclusters of alkali and noble metals is discussed.     

铜簇Cun-和羰基铜簇CunCO-(n=2～7)的结构与光谱性质的密度泛函理论研究

应用相对论有效核势密度泛函理论计算方法研究了Cun-和CunCO-簇的平衡几何构型、稳定性、主要碎片化模式、CO吸附能及其团簇的光谱性质.计算结果表明,奇数簇Cun-的电离势比其相邻偶数簇Cun-的电离势大;奇数的Cu5CO-簇有最大的CO解离能.奇数铜簇阴离子相对较高的稳定性与近似浆汁模型的8电子电子闭壳层效应一致.计算得到的Cun-簇碎片化能量表明,较小Cun-的优势解离通道与其包含Cu原子数目的奇偶性有关,偶数的Cun-簇主要解离为Cu原子和Cun-1-,而奇数Cun-簇易以解离成铜的二聚物Cu2和Cun-2-.基于密度泛函理论计算,讨论了这些簇的静态极化率和CO吸附性质与簇大小的关系.     

Metastable decay of Ar n + involving single monomer evaporation and the loss of peculiar numbers of monomers

Production and stability of Ar _n ^+* ions (withn up to 420) formed by electron impact ionization of a supersonic Ar cluster beam were investigated with a double focussing sector field mass spectrometer. The present study confirms previous magic number determinations up to the 4th icosahedral shell. A systematic study of metastable dissociations (monomer evaporation, magic number evaporation) for singly charged cluster ions as a function of cluster size, internal excitation energy and time elapsed since ion formation gives new insight into the ionization process and subsequent reactions of the ions formed. At a well-defined threshold energy ofca. 28 eV, the magic number loss mechanism occurs simultaneously with the well known single monomer evaporation process which proceeds at all energies. The new mechanism is the first known example of cluster ion metastability showing an exponential dependence on time, providing further evidence that the precursor parent cluster ion is produced in a specific energy state.     

Core-shell effects in the ionization of doped helium nanodroplets

Core-shell particles with water clusters as the core and surrounded by an atomic or molecular shell have been synthesized for the first time by adding water and a co-dopant sequentially to helium nanodroplets. The co-dopants chosen for investigation were Ar, O(2), N(2), CO, CO(2), NO and C(6)D(6). These co-dopants have been used to investigate the effect of an outer shell on the ionization of the core material by charge transfer in helium nanodroplets. The specific aim was to determine how the identity of the shell material affects the fragmentation of water cluster ions, i.e. whether it helps to stabilize parent ion ((H(2)O)(n)(+)) formation or increases fragmentation (to form (H(2)O)(n)H(+)). N(2), O(2), CO(2) and C(6)D(6) all show a marked softening effect, which is consistent with the formation of a protective shell around the water cluster core. For CO and NO co-dopants, the response is complicated by secondary reactions which actually favour water cluster ion fragmentation for some water cluster sizes.     

Shell effects on fragmentations of doubly-charged silver clusters

Shell effects are found in the size distributions of fission fragments from doubly-charged silver clusters. The energy differences between parent cluster and sum of a pair of fragmented clusters are calculated for various fission channels using the theory of shell corrections. Oscillative structures observed in the size distribution are shown to be due to shell effects of fragments. It is also found that the cluster deformation due to shell effects produces the even-odd alternation in the size distribution.     

Study of the fragmentation of small sulphur clusters

The fragmentation of sulphur clusters caused by electron impact ionization was studied. For this purpose, a beam ofS _n -clusters withn≦8 was generated in a gas aggregation source and ionized by electrons of variable energy. Special care was taken to maintain constant nucleation conditions so that the neutral cluster composition remained unchanged. It was found that the cluster ion mass spectra drastically depend on the electron energy. Even near threshold fragmentation processes contribute significantly to the dependence of the ion intensities on the electron energy.     

Cluster expansion for the energy of the many-electron atom in the nth order of the perturbation theory

A cluster expansion for the nth order correction to the energy of a many-electron atom is derived. A possible application to the calculation of the third order correction to the energy is considered.     

Fragmentation phase transitions in atomic clusters III

We discuss the role and the treatment of polarization effects in many-body systems of charged conducting clusters and apply this to the statistical fragmentation of Naclusters. We see a first order microcanonical phase transition in the fragmentation of Na ₇₀ ^Z+ for Z = 0 to 8. We can distinguish two fragmentation phases, namely evaporation of large particles from a large residue and a complete decay into small fragments only. Charging the cluster shifts the transition to lower excitation energies and forces the transition to disappear for charges higher than Z = 8. At very high charges the fragmentation phase transition no longer occurs because the cluster Coulomb-explodes into small fragments even at excitation energy ε* = 0.     

On a possible mechanism for Ar 4 + fragmentation

The full potential energy surface (PES) for the collinear Ar ₄ ⁺ cluster as a function of the three internuclear distances is computed at the post-Hartree-Fock level using Density Functional Theory (DFT) methods to treat dynamic correlation effects. The behaviour of the overall configuration energy minima as the central Ar ₂ ⁺ bond stretches is analysed as a function of the fragmentation coordinates of the wing atoms. The coupling between the stretching coordinate and the fragmentation coordinates is also analysed over the whole PES. The calculations suggest that large vibrational energy content in the core dimer ion causes localization of the coupling with either wing atoms which could in turn favour energetically the sequential fragmentation, while Ar ₄ ⁺ with a vibrationally cold core markedly lowers any energy barrier to fragment in a concerted fashion. Such suggestions provide further useful information for what has been found in some of the experimental studies on this ionic system (and on larger ionized argon clusters) and underline the possible role which the internal vibrational energy content of the ionic cluster can play in the fragmentation.     

Ion decomposition versus molecular size probed by vacuum ultraviolet photoionization

The molecular size dependence of primary fragmentation is studied for a series of β -naphthyl esters having alkyl chain lengths from C2 to C18. The esters are vaporized at a known ftemperature and ionized by coherent vacuum ultraviolet radiation at 10.5 eV. The photoionization wavelength is energetic enough to cause both metastable and nonmetastable primary fragmentation to m / z 144, but not energetic enough to cause secondary fragmentation to m / z 115 or 116. Under these conditions, the ratio of the nonmetastable-to-metastable daughter ion current, D/m _D ^′ is expected to give a rough indication of the average parent ion dissociation rate. The D / m _D ratio decreases with increasing molecular size, but not as quickly as expected by simple RRK theory. This behavior along with temperature dependence studies suggests that the internal energy required for dissociation is provided in substantial part by both the initial thermal internal energy and the energy imparted by the photoionization step. The role of thermal energy in the dissociation of large ions is discussed.     

A self-consistent reaction field approach to liquid photoionization

A cluster-dielectric model with a self-consistent reaction field interaction is proposed and evaluated for liquid photoionization. The model is numerically applied to solvent binding energy shifts for some cations and anions in aqueous solutions. The role of medium interaction with the ion or with the ion dressed with its first solvation shell cluster is investigated by means of a self-consistent Hatree-Fock method employing a reaction field Fock operator. Total binding energy shifts and orbital energy shifts are obtained as functions of the dielectric constant. It is shown that for the range of values of the dielectric constant corresponding to the most common solvents, variation in the shifts results from structural effects rather than from pure dielectric effects. It is found that the Born approximation, which is poor for the prediction of the BE shift for the pure ion, works well for cations dressed with it first solvation shell cluster. For anions the model with only one solvation shell in addition to the dielectric is not as appropriate as for cations, which can be argued from comparison of present data with experimental and simulation data. The relation between the present method and a previously devised statistical method is established.     

Fragmentation of doubly charged argon clusters

Fragmentation of doubly charged argon clusters is reported. Neutral argon clusters are excited with monochromatized synchrotron radiation in the energy regime of the argonL ₃/L ₂ absorption edges (240–260 eV) leading predominantly to cluster dication formation. All charged particles are detected in a photoelectron-photoion-photoion-concidence (PEPIPICO) experiment. Symmetric and asymmetric charge separation reactions (Coulomb explosion) are identified for clusters below the critical size of stable dication formation. The peak shapes of the coincidence signals are investigated as a function of neutral cluster size. Characteristic changes in peak shape are observed which are used to derive fragmentation mechanisms involving sequential evaporation of neutrals before and after charge separation. The spectra indicate in accordance with low kinetic energy releases occurring in charge separation of large dissociative cluster dications (Ar _n ²⁺ , withn>50) that due to large charge separation distances the momenta of both singly charged fragments are not any more directed into opposite direction, as it is typical for Coulomb explosion. The results are compared to collision induced fragmentation of mass selected argon cluster dications as well as photon stimulated desorption spectra of condensed argon.     

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.     

On the shell structure and geometry of monovalent metal clusters

The Hückel model is used to study the electronic structure of monovalent metal clusters. In an fcc cluster the Hückel model gives an estimate to the electronic structure of a free electron cluster. It is shown that the surface faceting of the fcc cluster can destroy the electronic shell structure already when the cluster has about 100 electrons. In the Hückel model the icosahedral structure has smaller total energy than the fcc structures, from which the Wulff construction has the smallest energy already when the cluster has 600 atoms.     

Modelization of the fragmentation dynamics of krypton clusters (Kr(n),n=2-11) following electron impact ionization

We present the first prediction for the fragmentation dynamics following electron impact ionization of neutral krypton clusters from 2 to 11 atoms. Fragment proportions and parent ion lifetimes are deduced from a molecular dynamics with quantum transitions study in which the nuclei are treated classically and the transitions between electronic states quantum mechanically. The potential-energy surfaces are derived from a diatomics-in-molecules model to which induced dipole-induced dipole and spin-orbit interactions are added. The results show surprisingly fast and extensive fragmentation for clusters of such a heavy atom, although not as extensive as in the case of neon clusters studied previously [D. Bonhommeau et al., J. Chem. Phys. 123, 54316 (2005)]. The parent ion lifetimes range from 2.8 to 0.7 ps, and the most abundant fragment is Kr(2) (+) for all studied sizes, followed by Kr(+) for sizes smaller than 7 atoms and by Kr(3) (+) for larger sizes. Trimer and larger fragments are found to originate from the lower electronic states of parent ions. The comparison with preliminary results from experiments on size-selected neutral clusters conducted by Steinbach et al. (private communication) reveal a good agreement on the extensive character of the fragmentation. It is checked that the additional internal energy brought by the helium scattering technique used for size selection does not affect the fragment proportions. In addition, the existence of long-lived trajectories is revealed, and they are found to be more and more important for larger cluster sizes and to favor the stabilization of larger fragments. The implications of this work for microsecond-scale dynamics of ionized rare-gas clusters are discussed. In particular, given the extent of fragmentation of the parent clusters and the fast kinetics of the whole process, the small cluster ions that exhibit a monomer loss in the microsecond time window must originate from much larger neutral precursors. The decay rate of the II(12)(u) state of the ionic dimer Kr(2) (+) by spin-orbit coupling is found to be of the order of 3 ps, in contrast to the expected tens of microseconds, but only reasonably faster than the corresponding state of HeNe(+). Finally, the spin-orbit interaction strongly affects both the Kr(+)Kr(2) (+) ratio and some of the characteristic times of the dynamics, especially for smaller sizes, but not the overall dependence of the fragment proportions as a function of cluster size.     

Synthesis, structure, and catalytic properties of polymer-immobilized rhodium clusters

Immobilized Rh₆ clusters (cyclohexene hydrogenation catalysts) were prepared by the polymer-analogous transformations or copolymerization of cluster-containing monomers and characterized. Intermediates formed in the course of a catalytic reaction were studied using IR spectroscopy, XPS, and atomic force microscopy. It was found that the relative intensity of a low-energy line in the Rh3d _5/2 spectrum of the initial polymer-immobilized cluster in the XPS spectrum of Rh₆ increased in the course of hydrogenation. The catalytic activity of the immobilized complex changed symbatically with both the number of Rh atoms bound to the H(CO) group and the number of Rh atoms, the charge on which was greater than that in the parent cluster. Some experimental evidence was obtained in favor of the hypothesis of cluster fragmentation in the course of hydrogenation with the formation of highly active, most likely, nanosized particles, which are true catalysts, in low concentrations. The surface of macrocomplex particles after hydrogenation became more homogeneous and hydrophilic; this fact is also indicative of an increase in the concentration of polar functional groups in surface layers. This was likely due to Rh-Rh bond cleavage in the polymer-immobilized cluster.     

Ion attachment to Van der Waals clusters

Mixed ionized clusters have been produced in a supersonic nozzle beam experiment by attachment of stagnant cations (i.e. NO⁺ and Xe⁺) to neutral van der Waals clusters (i.e.Ar _n ) within a Nier type ion source. This new ionization technique leads to less fragmentation than electron impact ionization and the measured cluster distributions exhibit icosahedral shell and subshell closures which have not been detected in the case of electron impact of Ar _n -clusters ionization so far. Additionally, the obtained appearance energies and metastable fractions give insight into the production mechanism and the stability of the resulting ions.     

Fragmentation channels of large multicharged clusters

We address unifying features of fragmentation channels driven by long-range Coulomb or pseudo-Coulomb forces in clusters, nuclei, droplets, and optical molasses. We studied the energetics, fragmentation patterns, and dynamics of multicharged (A+)n (n=55, 135, 321) clusters. In Morse clusters the variation of the range of the pair-potential induced changes in the cluster surface energy and in the fissibility parameter X=E(Coulomb)2E(surface). X was varied in the range of X=1-8 for short-range interactions and of X=0.1-1.0 for long-range interactions. Metastable cluster configurations were prepared by vertical ionization of the neutral clusters and by subsequent structural equilibration. The energetics of these metastable ionic clusters was described in terms of the liquid drop model, with the coefficients of the volume and surface energies depending linearly on the Morse band dissociation energy. Molecular-dynamics simulations established two distinct fragmentation patterns of multicharged clusters that involve cluster fission into a small number of large, multicharged clusters for X<1 and Coulomb explosion into a large number of individual ions and small ionic fragments for X>1. The Rayleigh instability limit X=1 separates between spatially anisotropic fission and spatially isotropic Coulomb explosion. Distinct features of the fragmentation energetics and dynamics were unveiled. For fission of n=55 clusters, large kinetic and internal energies of the large fragments are exhibited and the characteristic fragmentation time is approximately 700 fs, while for Coulomb explosion the major energy content of the small fragments involves kinetic energy and the characteristic fragmentation time of approximately 300 fs is shorter. The Rayleigh (X=1) limit, leading to isotropic Coulomb explosion, is transcended by a marked enhancement of the Coulomb energy, which is realized for extremely ionized clusters in ultraintense laser fields, or by a dramatic reduction of the surface energy as is the case for the expansion of optical molasses.     

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.     

Time-resolved studies of neutral and ionized Nan clusters with femtosecond light pulses

The real-time dynamics of Na_n (n=3–21) cluster multiphoton ionization and fragmentation has been studied in beam experiments applying femtosecond pump-probe techniques in combination with ion and electron spectroscopy. Three dimensional wave packet motions in the trimer Na₃ ground state X and excited state B have been observed. We report the first study of cluster properties (energy, bandwidth and lifetime of intermediate resonancesNa _n ^* ) with femtosecond laser pulses. The observation of four absorption resonances for the cluster Na₈ with different energy widths and different decay patterns is more difficult to interpret by surface plasmon like resonances than by molecular structure and dynamics. Time-resolved fragmentation of cluster ions Na _n ⁺ indicates that direct photo-induced fragmentation processes are more important at short times than the statistical unimolecular decay.