Charged Metal Clusters Research Articles

The interaction of gold clusters with methanol molecules: Ab initio molecular dynamics of Aun+CH3OH and AunCH3OH

Structural, dynamical, and electronic properties of adducts obtained by adsorbing one methanol molecule onto charged and neutral gold clusters, Aun+–CH3OH and Aun–CH3OH, are investigated using Car–Parrinello ab initio molecular dynamics as a function of the cluster size n. The absorption process occurs by the formation of a Au⋆–O coordination bond to one particular gold atom Au⋆ without altering the structure of the underlying cluster. This chemical bond is much stronger for the charged metal clusters Aun+ than for the neutral analogs Aun. In the charged case, the C–O stretching vibration of the interacting methanol molecule is found to increase discontinuously as the underlying cluster structure changes from two-dimensional to three-dimensional. The weaker C–O bond in the neutral species however has “insufficient strength” to be sensitive to changes in coordination number and cluster structure. This leads to a constant C–O stretching frequency as the size of the cluster increases, including the regime where the Aun cluster changes from planar to three-dimensional.

Phenomenological model for the statistical study of charged metal clusters

We develop a phenomenological model to represent surface charge in microscopic treatments of finite metal systems. This model is simple enough to allow for extensive simulations and global optimization for systems having as much as several hundred atoms. Applications to the Coulombic and thermal stabilities of multiply charged sodium clusters show a good agreement of the appearance sizes with experimental data at high temperatures, as well as systematic deviations to the Rayleigh limit at zero temperature. Statistical investigations also give evidence for a significant charge dependence of both the fragmentation patterns and the solid-liquid phase transition.

Fission of doubly charged binary metal clusters

The coulombic fission of binary metal clusters composed of lithium and calcium atoms has been studied by time-of-flight mass spectrometry following multi-photon ionization. The determined appearance sizes are compatible with predictions of a simple model which assumes a liquid droplet picture for all but the very small clusters involved. Electronic shell effects on the fission process are discussed.

Polarization effects in electron attachment to metallic clusters

New calculations of the low-energy free-electron attachment cross section to neutral and charged metallic clusters are reported. We include all the bound states of the negative ion as well as Rydberg series of neutral cluster targets as possible final states for attachment and calculate the electron attachment cross sections. The influence of the dynamic core polarization on the capture process is studied. Quadrupole contributions are found to play a more important role than in the optical spectra as cluster size increases.

Self-consistent determination of the one-body density matrix and particle-hole excitations

We develop a procedure recently proposed for the treatment of correlations in finite Fermi systems in a more consistent way than the random phase approximation (RPA). The one-body density matrix in the correlated ground state is now no more assumed to be diagonal in the Hartree-Fock basis. An expression is rather provided where this quantity is expressed in terms of the X and Y amplitudes of the particle-hole phonon operators. A set of RPA-like equations depending only on the one-body density matrix is then constructed by means of the method of linearized equations of motion and solved via an iterative procedure. The procedure is employed to calculate spectra and strength distributions of several neutral and charged Na and Li metal clusters within the jellium approximation. Improvements are observed with respect to standard RPA calculations.

Langevin description of fission of hot metallic clusters

A dynamical model of fission of hot charged metallic clusters on the basis of Langevin equations is proposed, where the viscosity is taken from experimental data for the bulk. As an example the process is considered. Decay rates calculated with the full Langevin equations are compared with those of the overdamped limit, which turns out to be a good approximation. Comparison is also made with the Bohr-Wheeler rate, the quasi-stationary Kramers rate, and a rate derived from a mean first passage time approach. A fission delay is predicted which is two orders of magnitude larger than in a calculation without dissipation. This is an order of magnitude larger than the corresponding effect in nuclear fission, where in contrast to the cluster case the fission delay due to friction is well established experimentally. A comparison is also made with the competing decay channels , , and , which are treated as evaporation processes.

Collision induced dissociation of doubly charged stored metal cluster ions

Singly charged noble metal cluster ions from an external laser vaporization source are accumulated in a Penning trap. They are subjected to electron bombardment for further ionization. The doubly charged clusters are size selected and their low energy fragmentation pathways are studied by multiple-collision-induced dissociation. The reaction products are analysed by time-of-flight detection. In general, large clusters tend to evaporate neutral atoms while small clusters fission into two singly charged fragments, one of which is a trimer. The details, however, vary and depend on the specific elements and cluster sizes as exemplified by the fragmentation of doubly charged copper, silver, gold and platinum clusters of size around n = 16. © 1997 John Wiley & Sons, Ltd.

Collision induced dissociation of doubly charged stored metal cluster ions

Collision induced dissociation of doubly charged stored metal cluster ions

Theoretical description of the decay of hot charged alkali metal clusters

Critical (appearance) sizes of multiply charged hot (liquid) alkali metal clusters are calculated by equating the rates for neutral monomer and light charged-particle emission. The rate formulas are based on the Weisskopf model with level densities (with appropriate surface corrections) and Coulomb barriers determined from the measured temperature dependence of the specific heat and the Wigner-Seitz radius of the bulk. The time development of temperature and size of large clusters are also calculated by solving rate equations for multiple emission of cluster atoms.

Excitation and fragmentation of highly charged metal clusters in collisions with ions

We discuss the Coulomb fragmentation of highly charged metal clusters. The analogy with a classical conducting liquid drop is assessed from molecular dynamics calculations. Experimentally, the highly charged metal clusters are formed in collisions with highly charged ions (Xe20+, Ar11+, Ar8+, Ar3+, and O5+) at low velocity. We show new experimental data on the rate of emitted light charged particles that indicate an as yet unobserved fragmentation regime. Collisions of ions with metal clusters also offer a unique method to strongly excite the conducting electron gas within a short time of a few fs opening the possibility to study large amplitude electron dynamics and relaxation in microscopic systems.

Highly charged metal clusters studied by HCI collisions

Highly charged ions provide a unique way to prepare metal clusters in such high charged states that it has opened the possibility to undertake detailed investigations of the dynamics of strong Coulomb instabilities and subsequent fragmentation of charged conducting microclusters. Experimentally, a neutral atomic cluster beam is intersected by a low velocity HCI beam (Xe30+, Xe20+, Ar11+, Ar8+, Ar3+, and O5+) and resulting charged cluster fragments are analysed. We have selected some new experimental data that bear evidence of the efficiency of the method and of the existence of an as yet unobserved fragmentation regime.

Production and investigation of multiply charged metal clusters in a Penning trap

Singly charged gold cluster ions from a laser-vaporization source are transferred into a Penning trap and subjected to electron bombardment. The charged reaction products are analyzed by time-of-flight mass spectrometry after axial ejection from the trap. They include singly charged cluster fragments, multiply charged clusters of the initial size and multiply charged cluster fragments. The multiply charged clusters are selected and further investigated by collision induced dissociation. Two types of reactions can be distinguished: Dissociation into several charged fragments and evaporation of neutrals. Several features of multiply charged clusters relevant for future investigations are reviewed.

Revivals of wave packets: General theory and application to Rydberg clusters.

A universal approach is developed to study revivals of wave packets made of bound states with an arbitrary spectrum ${\mathit{E}}_{\mathit{n}}$ exhibiting hierarchical time scales. An analytic expression in form of a recursion formula is derived, which allows for a given wave packet the prediction of all revival times in any time scale. The theory is applied to metallic Rydberg clusters, i.e., two oppositely charged metallic clusters in a bound state with high angular momentum, taking into account their mutual polarization connected with a complicated n dependence of the spectrum ${\mathit{E}}_{\mathit{n}}$. The theoretical predictions are compared with numerical results using a stroboscopic picture of the autocorrelation function. \textcopyright{} 1996 The American Physical Society.

Formation and Coulomb dissociation of highly charged metal clusters in ion-cluster collisions

Abstract The Coulomb dissociation of higly charged metal clusters is investigated. The analogy with a classical conducting liquid drop is discussed and predictions are given. Coincidence data from recent experiments on the fragmentation of such highly charged metal clusters formed in collisions with multicharged ions are shown. Multi-emission of light charged clusters is well identified.

Liquid Drop Model for Charged Spherical Metal Clusters

The average ground-state energy of a charged spherical metal cluster withNatoms andzexcessive valence electrons, i.e., with net chargeQ=−ezand radiusR=rsN1/3, is presented in the liquid drop model (LDM) expansionE(N, z)=avN+asN2/3+acN1/3+a0(z)+a−1(z) N−1/3+O(N−2/3). We derive analytical expressions for the leading LDM coefficientsav,as,ac, and, in particular, for the charge dependence of the further LDM coefficientsa0anda−1, using the jellium model and density functional theory in the local density approximation. We obtain for the ionization energyI(R)=W+α(e2/R)+O(R−2), with the bulk work functionW=[Φ(+∞)−Φ(0)]−eb, given first by Mahan and Schaich in terms of the electrostatic potentialΦand the bulk energy per electroneb, and a new analytical expression for the dimensionless coefficientα. We demonstrate that within classical theoryα=12 but, in agreement with experimental information,αtends to ∼0.4 if quantum-mechanical contributions are included. In order to test and confirm our analytical expressions, we discuss the numerical results of semiclassical density variational calculations in the extended Thomas-Fermi model.

STATIC POLARIZABILITIES OF CHARGED SILVER METAL CLUSTERS EXTRACTED FROM THE OPTICAL SPECTRA

The use of sum rules appears to be a powerful tool for obtaining experimental data on static properties of charged metal clusters which are currently not available. For this purpose the optical spectra of the clusters must be known. The measured absorption profiles of sputtered, i.e. hot, [Formula: see text] and [Formula: see text] which have been measured in our group give information about the desired properties. The extracted static polarizabilities show a distinct shell structure which reflects the overall electronic shape of the cluster. A comparison is made with AgN and positive alkali metal clusters. The polarizabilities of closed-shell [Formula: see text] and [Formula: see text] are in reasonable agreement with SIC-LDA corrected RPA polarizabilities.

Ionic structure and global deformation of axially symmetric simple metal clusters

The ground-state structure and shape parameters of neutral and singly charged simple metal clusters with up to 40 valence electrons have been calculated within the cylindrically averaged pesudopotential scheme (CAPS). Na and Ba have been chosen as typical monovalent and divalent metals. The obtained structures agree very well with the results of more elaborate methods. A simple growth pattern for the most stable ionic geometries is deduced. The ionic and electronic multipole moments from CAPS are very similar to those of the structure averaged jellium model (SAJM) and of the plasma model. The surface energies derived from the CAPS results agree with experimental values.

Semi-empirical model for the fission of multiply charged metal clusters

A semi-empirical model is proposed to calculate the fission barrier height for large highly-charged simplemetal clusters. The fusion barrier is obtained making use of a bonding potential, and the classical metallic drop model is employed for calculating the heats of fission and evaporation. We have found a good agreement between calculated critical sizes and experimental results for the appearance of charged clusters in mass spectra. Within the same model, we predict the critical numbers for spontaneous fission.

Barriers and Deformation in Fission of Charged Metal Clusters

The influence of electronic shell effects on the barriers and channels pertaining to metal-cluster fission is studied using a shell correction method in connection with an asymmetric two-center-oscillator model potential. This approach has the advantage that the ensuing shape parametrization allows for an independent variation of the deformations of parent and daughter clusters. Results for both symmetric and asymmetric channels associated with the parent clusters Na{sub 10}{sup 2+} and Na{sub 18}{sup +} are presented. We find that barriers, which separate the parent configuration from molecular-type configurations associated with preformation of the fragments, are most important and must be considered, together with the subsequent separation process, for proper elucidation of metal-cluster fission phenomena. 23 refs., 3 figs.

On the decay of hot charged alkali metal clusters

Abstract On the basis of the liquid drop model, the decay of charged hot alkali metal clusters is investigated theoretically. Above a critical cluster size n c z the decay is dominated by neutral monomer cluster atom evaporation, whereas below this critical size evaporation of singly charged cluster atoms is dominant, which might be considered as highly asymmetric fission. We apply the Weisskopf evaporation theory, developed in nuclear physics, to calculate the decay rates, and thus the time scales, for neutral and charged cluster fragment emission. The critical cluster sizes are determined by equating the rates for neutral and charged cluster atom emission.