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.     

Size-selected, supported clusters: the interaction of carbon monoxide with nickel clusters

We report on the size-dependent chemical reactivity of nickel clusters with up to 30 atoms. Monodispersed Ni₃₀ clusters show a higher reactivity for CO dissociation than Ni₁₁ and Ni₂₀. Under our experimental conditions the smallest nickel clusters (Ni_x, x<4) produce nickelcarbonyl complexes. These results demonstrate that such small clusters are unique for catalytic reactions not only due to their high surface-to-volume ratio but also essentially because of the distinctive properties of different cluster sizes. In addition thermal desorption spectroscopy of CO shows that on average four molecules are weakly adsorbed per Ni₁₁ at saturation coverage. Using an isotopic mixture of ¹²CO and ¹³CO, infrared spectroscopy reveals the existence of a vibrational coupling interaction between the four COs. A semi-classical model of interacting dipoles is applied to correlate the observed vibrational frequency shifts with the arrangement of the COs on the cluster. This simple analysis favors a three-dimensional structure for the deposited clusters. Received: 23 March 1998/Accepted: 25 August 1998     

Spectroscopy of alkali atoms and molecules attached to liquid He clusters

Large helium clusters, ranging in size from a few hundred to several thousand atoms, are produced in a nozzle expansion. Combining this source with a pick-up scattering cell in which the clusters can be seeded with chromophores allows us to probe the influence of the helium environment on the atoms and molecules attached to the clusters. Using an alkali as chromophore we recorded laser induced fluorescence spectra of Na atoms and molecules attached to helium clusters. Apart from the spectrum of the Na monomer, we have found spectroscopic bands which can unambiguous be assigned to two bound Na atoms. The first of this bands is due to 1^{1 +} (A) 1¹ _g ⁺ (X) excitations of the covalently bound singlet Na₂ molecule while the second is due to 1³ _g ⁺ 1^{3 +} excitations for the van der Waals bound triplet Na₂ dimer. Both bands have been vibrationally resolved. Furthermore we found very large fluorescence intensities in the region 605–635 nm which are likely due to the excitation of a species containing three Na atoms attached to a helium cluster.     

Optical properties of mixed clusters: comparative study of Ni/Ag and Pt/Ag clusters

The optical properties of mixed (Ni_0.5Ag_0.5)_n and Pt/Ag clusters are investigated in the size range 2-5 nm. Low Energy Ion Spectroscopy (LEIS) experiments show that the cluster surface is entirely covered by silver atoms for the two systems. The optical spectra of Ni/Ag clusters exhibit a large Surface Plasmon Resonance (SPR), damped and widened when the cluster size decreases, in agreement with a classical model assuming a core-shell geometry and including the reduction of the conduction electron mean-free path in the silver shell. For Pt/Ag clusters, no SPR emerges in the size range 2-5 nm, although it is predicted within a classical model, a pronounced SPR appearing only for clusters larger than 10 nm in diameter.     

Theory for the ultrafast dynamics of excited clusters: interplay between elementary excitations and atomic structure

We present a theoretical study of the short-time relaxation of clusters in response to ultrafast excitations using femtosecond laser pulses. We analyze the excitation of different types of clusters (Hg_n, Ag_n, Si_n, C₆₀ and Xe_n) and classify the relaxation dynamics in three different regimes, depending on the intensity of the exciting laser pulse. For low-intensity pulses (I<10¹² W/cm²) we determine the time-dependent structural changes of clusters upon ultrashort ionization and photodetachment. We also study the laser-induced non-equilibrium fragmentation and melting of Si_n and C₆₀ clusters, which occurs for moderate laser intensities, as a function of the pulse duration and energy. As an example for the case of high intensities (I>10¹⁵ W/cm²), the explosion of clusters under the action of very intense ultrashort laser fields is described. Received: 26 November 1999 / Published online: 2 August 2000     

Electronic and geometric structure of doped rare-gas clusters: surface, site and size effects studied with luminescence spectroscopy

The electronic and geometric structure of rare gas clusters doped with rare-gas atoms Rg = Xe, Kr or Ar is investigated with fluorescence excitation spectroscopy in the VUV spectral range. Several absorption bands are observed in the region of the first electronic excitations of the impurity atoms, which are related to the lowest spin-orbit split atomic ³P₁ and ¹P₁ states. Due to influence of surrounding atoms of the cluster, the atomic lines are shifted to the blue and broadened (“electronical cage effect”). From the known interaction potentials and the measured spectral shifts the coordination of the impurity atom in Ar_N, Kr_N, Ne_N and He_N could be studied in great detail. In the interior of Kr_N and Ar_N the Xe atoms are located in substitutional sites with 12 nearest neighbours and internuclear distances comparable to that of the host matrix. In Ne_N and He_N the cluster atoms (18 and 22, respectively) arrange themselves around the Xe impurity with a bondlength comparable to that of the heteronuclear dimer. The results confirm that He clusters are liquid while Ne clusters are solid for N≥ 300. Smaller Ne clusters exhibit a liquid like behaviour. When doping is strong, small Rg_m-clusters (Rg = Xe, Kr, Ar, m≤10 ²) are formed in the interior sites of the host cluster made of Ne or He. Specific electronically excited states, assigned to interface excitons are observed. Their absorption bands appear and shift towards lower energy when the cluster size m increases, according to the Frenkel exciton model. The characteristic bulk excitons appear in the spectra, only when the cluster radius exceeds the penetration depth of the interface exciton, which can be considerably larger than that in free Rg_m clusters. This effect is sensitive to electron affinities of the guest and the host cluster.     

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     

Cold Ar 3 + generated by ionization of argon clusters in large helium clusters: Temperature dependence of the photofragmentation

Ionized argon clusters were generated by electron impact ionization of neutral argon clusters embedded in large neutral helium clusters. Photofragmentation spectroscopy of Ar ₃ ⁺ and Ar ₃ ⁺ He produced in this way demonstrates the strong influence of vibrational excitation on the photodissociation dynamics, and indicates the low internal energy of the latter cluster.     

Experimental evidence for molecular ultrafast dissociation in O<Subscript>2</Subscript> clusters

Resonant Auger spectra of O₂ clusters excited at the O1s edge are reported. After excitation to the repulsive 1s^-13σ^* state, the resulting resonant Auger spectrum displays features that remain constant in kinetic energy as the photon energy is detuned. The shift between known atomic fragment features and these features is consistent with that observed for atoms and clusters in singly charged states in direct photoemission. These findings are strong evidence for the existence of molecular ultrafast dissociation processes within the clusters or on their surface.     

EICO measurements of inner-core excited mixed rare-gas clusters

The spectra of deep inner-core excited mixed rare-gas clusters were recorded by using electron ion coincidence (EICO) and multi-hit momentum imaging (MHMI) techniques. The EICO spectra for Ar₉₉Kr₁ clusters reveal that singly charged ions are emitted from the inner-core excited clusters in addition to the multiple charged ions. The dependence of the EICO spectra on photon energy and cluster size suggests that the holes created through vacancy cascade on the krypton atoms are transferred to the surrounding atoms, and that the singly charged ions are the primary product of the krypton photoabsorption. Charge localization is suggested for the inner-core excited mixed rare-gas clusters from the analysis of the EICO peak width. The MHMI measurements give us direct evidence for the strong charge migration from X-ray absorbing atoms to surrounding atoms. The photon energy dependence of the PSD image for fragment ions suggests that the momentum of the fragment ions depends on the number of charges generated by the vacancy cascade.     

Theoretical study on the composition dependence of Ga8−nAsn (n=0-8) clusters

Using full-potential linear-muffin-tin-orbital molecular-dynamics (FP-LMTO-MD) method, we have investigated the dependence of GaAs clusters with eight atoms on composition. It is found that the ground state structures for Ga-rich and As-rich clusters are cube structures. As the ratio between gallium atoms and arsenic atoms is close to one, structural distortion become increasingly severe, or even the clusters adopt other geometrical configurations as their ground state structures. The energy gap E_g between the highest-occupied molecular orbital (HOMO) and the lowest-unoccupied molecular orbital (LUMO), and the vertical electron affinity show a certain degree of even/odd alternation with cluster composition. Among nine Ga_8−nAs_n (n=0-8) clusters, only a few of clusters have different energy orders between the ionic and neutral isomers with large binding energy. Some ionic structures would change into other configurations due to severe structural distortion.     

Femtosecond ionization and fragmentation of free silicon nanoparticles

Femtosecond-laser spectroscopy is used to study the photoionization and photofragmentation of large neutral silicon clusters in a beam. Silicon clusters Si_n with sizes up to n≈6000, corresponding to nanoparticles with diameters up to 6 nm, are generated in a laser vaporization source. Nanosecond- and femtosecond-laser ionization are employed to characterize the free silicon nanoparticles. Excitation with intense femtosecond-laser pulses leads to prompt formation of doubly and triply charged Si_n clusters. Additionally, strong fragmentation of charged clusters occurs by Coulomb explosion, resulting in high released kinetic energies. Multiply charged atoms up to Si⁴⁺ with initial kinetic energies in the range of 500 eV are observed for laser intensities of about 10¹³ W/cm². Pump–probe spectroscopy yields decay times of the intermediate resonances of the nanoparticles. Received: 22 January 2000 / Published online: 7 August 2000     

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     

Electronic structure and magnetism in (CoPt)n(n⩽5) clusters

The geometrical and magnetic properties of bimetallic clusters (CoPt)_n(1?n?5) have been studied by using the generalized gradient correction spin density formalisms. In general, the ground state structures of (CoPt)_n clusters are the three-dimension structures. We found that both the binding energy and magnetism per (CoPt) unit are increasing consistently with the size of the Co–Pt cluster (n). However, as the n increases, the magnetism shows a trace of convergence while the binding energy shows a linearly increasing pattern. Generally, Co average magnetic moment is enhanced when alloyed with Pt atoms than that in pure Co clusters.     

The effect of volumetric weighting in the interaction of intense laser fields with clusters

Silver clusters embedded in helium nanodroplets are exposed to intense femtosecond laser pulses (10¹³ - 10¹⁶ W/cm²). The signal of highly charged (q≤11) atomic fragments is maximized by delayed plasmon enhanced ionization using stretched laser pulses. Further details with respect to the dynamics of the charging process can be obtained, when the intensity distribution within the laser focus is taken into account. For the first time, the z-scan method is applied to clusters which offers a route to investigate the explicit dependence of the ion signals with respect to the laser intensity. By taking advantage of the volumetric weighting effect ionization thresholds are determined, yielding values well below 10¹⁴ W/cm² for Ag^q+ ions with q≤11.     

Electron detachment and fragmentation in collisions between 1.25 keV/carbon and clusters and

The destruction cross-section for 22.5 and 50 keV C^1- , for 10 and 50 keV C₈ ^1- and for 50 and 75 keV C₆₀ ^1- clusters in collisions with H₂ has been measured by an attenuation method. The destruction of the cluster anions is dominated by electron detachment rather than fragmentation and is of the order of the geometric cross-section. The cross-sections vary little with bombarding energy. Received: 16 September 1998 / Received in final form: 23 February 1999     

Time-resolved photo-electron spectroscopy on mass-selected metal clusters using a regenerative femtosecond amplifier up to 100 Hz

A femtosecond photo-electron experiment is described which provides excellent conditions for measuring time-resolved photo-electron spectra of free, monodispersed cluster anions using repetition rates up to 100 Hz. Cluster anions are synthesized in an electric arc and subsequently cooled in a helium carrier gas. A time-of-flight spectrometer is used for mass separation of the negatively charged clusters. The kinetic energy of the photo-electrons is analyzed by a magnetic-bottle time-of-flight spectrometer, which guarantees a maximum collection efficiency. Femtosecond laser pulses are generated by a seeded regenerative Ti:Sa amplifier, which is externally pumped with the second harmonic of a diode-pumped solid-state Nd:YAG laser. A retroreflector mounted on a computer-controlled translation stage serves as a reproducible time delay of the probe pulse. The high energy output of the laser pulses (∼3 mJ) in combination with the variable repetition rate and the high stability of the amplified pulses provide excellent conditions for recording pump-probe photo-electron spectra of mass-separated cluster anions even at the fairly low ion density of pulsed plasma cluster sources. First results on the electron dynamics of the Pt₃ ^- cluster demonstrate the reliability of the whole system. Further experimental investigations will concentrate on electron-relaxation processes in transition- and noble-metal clusters as well as on the nuclear and transition-state dynamics of chemically reacted adsorbate clusters. Received: 7 January 2000 / Published online: 7 August 2000     

Large-scale molecular dynamics simulations of high energy cluster impact on diamond surface

Large-scale molecular dynamics simulations with high acceleration energy on a diamond surface were performed in order to investigate the surface erosion process. Accelerated argon or CO₂ clusters (∼960 atoms, 100 keV/cluster) impacted on the (111) surface of diamond which consisted of more than 1,000,000 carbon atoms. A typical hemispherical crater appeared about 0.7 ps after the impact, and two or three-layered shockwaves were formed and propagated to certain directions, but the crater was immediately filled up with the fluidized hot carbon material due to the collective elastic recovery before the reflection of the shockwave. The impact energy of the cluster was at first transferred mainly as kinetic energy of the diamond surface in a short time, and the potential energy was activated later. The activated carbon and oxygen atoms from the impact cluster stimulated the evaporation from the diamond surface for the CO₂ cluster impact while the evaporation seemed to be suppressed by the argon atoms themselves for the argon cluster impact. Received 22 November 2000     

Can we rationalize the structure of small silicon-carbon clusters?

A theoretical study of clusters with using density functional theory is presented. Tests of various functionals demonstrate that local spin density approximation (LSDA) is the most adequate functional for the study of these systems. Structures, vibrational frequencies, and IR intensities of the lowest energy isomer of the studied clusters obtained using LSDA are described, and the unusual properties of the Si-C clusters are discussed. A quantitative analysis of the obtained structures was carried out, and relations between the coordinations, interatomic distances, and angles observed in the Si-C clusters were obtained through introduction of the notion of coordination. This analysis also shows that the carbon atoms mainly exhibit sp and sp² hybridizations, and that a majority of silicon atoms do not hybridize. This study is the fi rst step of the implementation of a semi-empirical potential, which would describe the moderately small Si-C clusters. Received: 20 October 1997 / Received in final form: 16 December 1997 / Accepted: 17 December 1997