Geometric magic numbers of sodium clusters: Interpretation of the melting behaviour

Putative global minima of sodium clusters with up to 380 atoms have been located for two model interatomic potentials in order to identify the structures responsible for the size-dependence of the thermodynamic properties in experiments. Structures based upon the Mackay icosahedra predominate for both potentials, and the magic numbers for the Murrell-Mottram model show excellent agreement with the sizes at which maxima in the latent heat and entropy change at melting have been found in experiment. In particular, the magic numbers at sizes intermediate between the complete Mackay icosahedra are due to unusual twisted icosahedral structures.     

Observation of multiply charged silver-cluster anions

Singly charged silver-cluster anions are produced in a laser vaporization source and transferred into a Penning trap. After size selection the clusters are subjected to an electron bath in the trap, which results in the attachment of further electrons. The relative abundance of dianions or trianions as a function of the clusters' size is analyzed by time-of-flight mass spectrometry. Silver-cluster dianions are observed for sizes n≥ 24 and trianions for n > 100. In addition, a detailed study of the cluster sizes 24 ?n? 60 shows a pronounced resistance to electron attachment for singly charged anions Ag_n ^- with a closed electronic shell, in particular Ag₂₉ ^-, Ag₃₃ ^-, and Ag₃₉ ^-. Both the threshold size for the observation of dianionic silver clusters and the shell effects in the production yield correlate favorably with previous theoretical investigations of the respective electron affinities. Received 24 November 2000     

Chirality, defects, and disorder in gold clusters

Theoretical and experimental information on the shape and morphology of bare and passivated gold clusters is fundamental to predict and understand their electronic, optical, and other physical and chemical properties. An effective theoretical approach to determine the lowest-energy configuration (global minimum) and the structures of low energy isomers (local minima) of clusters is to combine genetic algorithms and many-body potentials (to perform global structural optimizations), and first-principles density functional theory (to confirm the stability and energy ordering of the local minima). The main trend emerging from structural optimizations of bare Au clusters in the size range of 12-212 atoms indicates that many topologically interesting low-symmetry, disordered structures exist with energy near or below the lowest-energy ordered isomer. For example, chiral structures have been obtained as the lowest-energy isomers of bare Au₂₈ and Au₅₅ clusters, whereas in the size-range of 75-212 atoms, defective Marks decahedral structures are nearly degenerate in energy with the ordered symmetrical isomers. For methylthiol-passivated gold nanoclusters [Au₂₈(SCH₃)₁₆ and Au₃₈(SCH₃)₂₄], density functional structural relaxations have shown that the ligands are not only playing the role of passivating molecules, but their effect is strong enough to distort the metal cluster structure. In this work, a theoretical approach to characterize and quantify chirality in clusters, based on the Hausdorff chirality measure, is described. After calculating the index of chirality in bare and passivated gold clusters, it is found that the thiol monolayer induces or increases the degree of chirality of the metallic core. We also report simulated high-resolution transmission electron microscopy (HRTEM) images which show that defects in decahedral gold nanoclusters, with size between 1-2 nm, can be detected using currently available experimental HRTEM techniques.     

Effect of melting on ionization potential of sodium clusters

The effect of melting transition on the ionization potential has been studied for sodium clusters with 40, 55, 142, and 147 atoms, using ab initio and classical molecular dynamics. Classical and ab initio simulations were performed to determine the ionization potential of Na₁₄₂ and Na₁₄₇ for solid, partly melted, and liquid structures. The results reveal no correlation between the vertical ionization potential and the degree of surface disorder, melting, or the total energy of the cluster obtained with the ab initio method. However, in the case of 40 and 55 atom clusters, the ionization potential seems to decrease when the cluster melts. Received 1st November 2002 Published online 24 April 2003 RID="a" ID="a"e-mail: ar@phys.jyu.fi     

Cohesive properties of mercury clusters in the ground and excited states

Optimized structures and cohesive energies of small mercury clusters (Hg_N; N = 3–7, 13, 19) are calculated with the spin-orbit diatomics-in-molecules method. The theory takes into account the effect of s-p mixing which tends to enhance the binding energies in the ground state. It is shown that excimer clusters have significantly short optimum bond lengths and their atomic geometries differ considerably from those in the ground state. Excitation energy gap depends sensitively on both cluster size and nearest-neighbor separation. Numerical results are compared with other theories and experiments.     

The internal energy of small ammonia clusters in a supersonic beam and after scattering off LiF(100)

The photoionization efficiency (PIE) of neutral ammonia clusters is studied as a function of photon energy. From these curves the internal energies of clusters in the incident supersonic beam and of clusters surviving after scattering off a LiF(100) surface are derived. A supersonic expansion of ammonia seeded in He produces small clusters of various size but with uniform kinetic energy of about 285 meV per monomer molecule. The mass distribution of clusters in the jet and of the scattered particles is measured in a reflecting time-of-flight mass spectrometer by single photon photoionization using vacuum ultraviolet (VUV) laser radiation tunable between and . In the incident beam the internal energies of clusters up to n = 15 do not vary significantly and amount to an average of about . After scattering off LiF(100) the internal energy of clusters up to n = 4 increases with fragment size and amounts to about half a monomer binding energy. Received 18 October 1999 and Received in final form 10 December 1999     

Hindered Coulomb explosion of embedded Na clusters — stopping,shape dynamics and energy transport

We investigate the dynamical evolution of a Na₈ cluster embedded in Ar matrices of various sizes from N=30 to 1048. The system is excited by an intense short laser pulse leading to high ionization stages.We analyze the subsequent highly non-linear motion of cluster and Ar environment in terms of trajectories, shapes, and energy flow. The most prominent effects are: temporary stabilization of high charge states for several ps, sudden stopping of the Coulomb explosion of the embedded Na₈ clusters associated with an extremely fast energy transfer to the Ar matrix, fast distribution of energy throughout the Ar layers by a sound wave. Other ionic-atomic transfer and relaxation processes proceed at slower scale of few ps. The electron cloud is almost thermally decoupled from ions and thermalizes far beyond the ps scale.     

Structural and energetic properties of sodium clusters

In this work we present results from a theoretical study on the properties of sodium clusters. The structures of the global total-energy minima have been determined using two different methods. With the parameterized density-functional tight-binding method (DFTB) combined with a genetic-algorithm we investigated the properties of Na_N clusters with cluster size up to 20 atoms, and with our own Aufbau/Abbau algorithm together with the embedded-atom method (EAM) up to 60 atoms. The two sets of results from the independent calculations are compared and a stability function is studied as function of the cluster size. Due to the electronic effects included in the DFTB method and the packing effects included in the EAM we have obtained different global-minima structures and different stability functions.     

Charge transfer between alkali cluster ions and atoms in the 1 to 10 keV collisional energy range

The cross-sections for collisional charge transfer between singly charged free clusters M _n ⁺ (M = Li, Na; n=1...50) and atomic targets A (cesium, potassium) have been measured as a function of collisional relative velocity in laboratory energy range 1–10 keV. For each cluster size, the experimental values of the charge transfer cross-section are fitted with an universal parametric curve with two independent parameters and v_m, the maximum cross-section and the corresponding velocity. For small size clusters (), the characteristic parameters show strong variations with the number of atoms in the cluster. Abrupt dips observed for n=10 and n=22 are attributed to electronic properties. Charge transfer patterns observed for various collisional systems present similarities, which appear more sensitive to cluster quantum size effects than to collision energy defects. In their whole, the and v_m parameters show differences in both their size evolution and their absolute values discussed in term of projectile and target electronic structures. Received 13 April 2000 and Received in final form 29 June 2000     

Photodissociation dynamics of Cl in a xenon cluster

The photodissociation of a chlorine molecule in the environment of a xenon cluster has been studied experimentally using the real time pump and probe technique through the formation of an XeCl reaction product. The photodissociating system is probed in such a way that the movement of a single chlorine atom in the xenon environment is detected. Various Xe_nCl₂ cluster sizes have been investigated leading to the distinction between uncapped, half-capped and doubly capped structures for these clusters. These structures have a profound influence on the photodissociation dynamics. Retrapping of one chlorine atomic fragment and stabilization of the XeCl reaction product is only observed for the half and doubly capped clusters. The experimental work is complemented by classical molecular dynamics calculations to get a full picture of the photodissociation. Received: 17 February 1998 / Received in final form and Accepted: 28 July 1998     

Stability and fragmentation processes of highly charged sodium clusters

Highly charged sodium clusters produced in collisions between neutral clusters and multiply charged ions are formed within a large range of temperatures and fissilities, and identified by means of a high-resolution reflectron-type time-of-flight mass spectrometer ( m/m 14000). The limit of stability of these charged clusters is experimentally investigated, and the time-of-flight spectra are compared with theoretical spectra based on Monte-Carlo simulations. The results indicate that the maximum fissility (X) of stable clusters is approaching the Rayleigh limit (X = 1) for larger clusters sizes. It is mainly limited by the initial neutral cluster temperature ( T 100 K) and the energy transfer in the ionizing collision. In addition, the comparison between the measured and simulated spectra suggests for high cluster charges a multi-fragmentation process, in which most of charge is emitted, creating low charged residual cluster ions.     

Predictions of geometrical structures and ionization potentials for small barium clusters Ba

The geometrical structure of ground state Ba_n clusters (n =2-14) has been predicted from various types of calculations including two ab initio approaches used for the smaller sizes namely HF+MP2( n =2-6), DFT (LSDA)( n =2-6, 9) and one model approach HF+pairwise dispersion used for all sizes investigated here. The lowest energy configurations as well as some isomers have been investigated. The sizes n =4, 7 and 13 are predicted to be the relatively more stable ones and they correspond to the three compact structures: the tetrahedron, the pentagonal bipyramid and the icosahedron. The growth behavior from Ba₇ to Ba₁₃ appears to be characterized by the addition of atoms around a pentagonal bipyramid leading to the icosahedral structure of Ba₁₃ which is consistent with the observed size-distribution of barium clusters. Values for vertical ionization potentials calculated for n =2-5 at the CI level are seen to be in quite good agreement with recent measures. Received: 14 May 1997 / Received in final form: 2 February 1998 / Accepted: 27 February 1998     

Dynamics of cluster deposition on Ar surface

Using a combined quantum mechanical/classical method, we study the dynamics of deposition of small Na clusters on Ar(001) surface. We work out basic mechanisms by systematic variation of substrate activity, impact energy, cluster orientations, cluster sizes, and charges. The soft Ar material is found to serve as an extremely efficient shock absorber which provides cluster capture in a broad range of impact energies. Reflection is only observed in combination with destruction of the substrate. The kinetic energy of the impinging cluster is rapidly transfered at first impact. The distribution of the collision energy over the substrate proceeds very fast with velocity of sound. The full thermalization of ionic and atomic energies goes at a much slower pace with times of several ps. Charged clusters are found to have a much stronger interface interaction and thus get in significantly closer contact with the surface.     

Vibrational spectroscopy of large water clusters of known size

The structure of large water clusters of known size distributions 〈n〉 = 20-2000 is investigated by vibrational spectroscopy of the OH stretch mode. The water clusters are predissociated by a pulsed tunable infrared optical parametrical oscillator (OPO) in the frequency range 2800-3800 cm^-1. Their fragments are detected off-axis by electron impact ionization and mass analyzed by a quadrupole mass spectrometer. The largest ion signal stems from the neutral water hexamer fragment. The ion yield is investigated at certain wavelengths while the size of the clusters is varied, and for certain sizes complete absorption spectra of the OH stretch motion are measured. Fingerprints of the different coordination types of the water molecules in the clusters are found and it turns out that our method is especially sensitive to amorphous structures with frequencies shifting in the range of 3300-3400 cm^-1.     

Structure and Spectrum of Binary Classic Systems Confined in a Parabolic Trap

The static and dynamic properties of the two-dimensional classic system of two-species interacting charged particles in a parabolic trap are studied. The ground state energy and configuration for different kinds of binary systems are obtained by Monte Carlo simulation and Newton optimization. The spectrum and normal modes vectors can be gained by diagonalizing the dynamical matrix of the system. It is found that the total particle number, particle number and mass-to-charge ratio of each species are decisive factors for the system structure and spectrum. The three intrinsic normal modes of single species Coulomb clusters are inherent, concluded from our numerical simulations and analytical results.     

Homogeneous and heterogeneous clustering in the accretion regime

Condensation of nano-droplets in a supersaturating vapor decomposes in two steps: the formation of a nucleation center, also called critical nuclei or nucleation seed, and the growth sequence, by accretion of further atoms on the nucleation center. These two steps have been investigated separately through the clustering of homogeneous particles Na_n and heterogeneous particles Na_nX in a helium buffer gas (X = (Na₂O)₂ or (NaOH)₂). The growth sequence is analyzed with preformed molecules X injected in a supersaturating sodium vapor and driving production of Na_nX clusters. Cluster distribution mean sizes are controlled by sodium concentration and by the condensation cell effective length. The signal intensities observed for homogeneous and heterogeneous clusters are proportional to the homogeneous and heterogeneous nucleation center numbers respectively. We can measure the efficiency for the homogeneous nucleation center production versus sodium concentration. This process is the onset of the condensation phase transition.     

Plasmon response in K, Na and Li clusters: systematics using the separable random-phase-approximation with pseudo-Hamiltonians

The systematics of the plasmon response in spherical K, Na and Li clusters in a wide size region is studied. Two simplifying approximations whose validity has been established previously are considered: (a) a separable approach to the random-phase-approximation, involving an expansion of the residual interaction into a sum of separable terms, (b) the electron-ion interaction is modeled within the pseudo-Hamiltonian jellium model (PHJM) including nonlocal effects by means of realistic atomic pseudoHamiltonians. In cases where nonlocal effects turn out to be negligible, the Structure Averaged Jellium Model (SAJM) has been used. The leading role of Landau damping in forming the plasmon width in medium and large clusters is demonstrated. Good agreement with available experimental data is achieved for K, Na (using the SAJM) and small Li clusters (invoking the PHJM). The trends for peak position and width are generally well reproduced, even up to details of the Landau fragmentation in several clusters. Less good agreement, however, is found for large Li clusters. The possible reasons of the discrepancy are discussed. Received: 22 April 1998 / Accepted: 24 July 1998     

Stacking faults in close-packed clusters

Ground state geometries of small hard sphere clusters were studied using two different type of contact interaction, a pair-potential and a many-atom interaction. Monte Carlo method in an FCC lattice with all possible (111) stacking faults was used to obtain the minimum energy geometries for clusters up to 59 atoms. Due to the surface energy, FCC packing is generally favoured as opposite to the HCP structure. However, in most cluster sizes the ground state obtained with the many-atom interaction has one or more stacking faults. The most symmetric geometry is usually not the ground state. Clusters with 59 and 100 atoms were studied due the possibility of a high symmetry cluster with stacking faults in all four directions. The size dependence of the total energy has similarities with that of the average moment of inertia. Received 6 February 2002 / Received in final form 11 April 2002 Published online 19 July 2002     

Fragmentation and reliable size distributions of large ammonia and water clusters

The interaction of large ammonia and water clusters in the size range from <n> = 10 to 3 400 with electrons is investigated in a reflectron time-of-flight mass spectrometer. The clusters are generated in adiabatic expansions through conical nozzles and are nearly fragmentation free detected by single photon ionization after they have been doped by one sodium atom. For ammonia also the (1+1) resonance enhanced two photon ionization through the state with v = 6 operates similarly. In this way reliable size distributions of the neutral clusters are obtained which are analyzed in terms of a modified scaling law of the Hagena type [Surf. Sci. 106, 101 (1981)]. In contrast, using electron impact ionization, the clusters are strongly fragmented when varying the electron energy between 150 and 1 500 eV. The number of evaporated molecules depends on the cluster size and the energy dependence follows that of the stopping power of the solid material. Therefore we attribute the operating mechanism to that which is also responsible for the electronic sputtering of solid matter. The yields, however, are orders of magnitude larger for clusters than for the solid. This result is a consequence of the finite dimensions of the clusters which cannot accommodate the released energy. Received 21 November 2001