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.     

Abundance of Na cluster ions ejected from a liquid metal ion source

Sodium cluster ions Na⁺ _n withn ranging up to 25 have been observed from a liquid sodium ion source by using a magnetic mass analyzer. Ion intensity as a function of cluster size showed distinct steps and local maxima atn=3, 5, 11, 13 and 19 (magic numbers), and a pronounced odd-even alternation. The features in the ion abundance curve are attributed to the relative stability of cluster ions. The observed magic numbers are only partially explained by the electronic shell model, indicating need to include a consideration of atomic structure in a cluster.     

Metastable dissociation dynamics of molecular cluster ions

Metastable uni-cluster dissociation for several hydrogen-bonded and van der Waals cluster ions are observed via resonance-enhanced two-photon ionization reflectron time-of-flight (TOF) mass spectrometry. All of the cluster ions studied show evaporation of a single molecule from the respective parent cluster ions as dominant metastable decay processes. Furthermore, the averaged metastable evaporation rate constants (k _evap) of these cluster ions in a fixed time domain of 0.2–50 µs are obtained by analyzing the relative intensity of metastable ion peaks due to evaporation in the acceleration and the field-free drift regions of the TOF mass spectrometer. An intensity anomaly in some of the observed metastable ion peaks, indicative of magic number stability of the cluster ion, is also presented.     

On the structure and stability of Ar n and Ar n + clusters at finite temperature

For Ar_2–29 and Ar _2–29 ⁺ clusters at 20 K in the polarization model presented here the electrodynamical dipole-dipole many-body problem is solved selfconsistently with the Monte-Carlo method (MC) at 20 K, i.e. the instantaneous dipole-dipole interaction is solved to infinite perturbation order and in cluster expansion to the order of the cluster size. The long range many-body dipole-dipole interaction is coupled to exchange interaction by a modified effective dipole polarizability. This model will be compared to the dimer model and classical MC simulation of Ar _n . The resulting different magic numbers in the binding energies are discussed in this connection with different experimental techniques of cluster ionization. By the mean square cluster diameter a shape parameter is introduced and it is found that with this parameter structural form transition in cluster growth can be resolved, and surprisingly do not correlate with the magic numbers.     

Production and stability of neon cluster ions up to Ne+90

Clusters of Ne_n atoms (up to n = 90) formed in a supersonic nozzle expansion have been studied by electron impact ionization mass spectrometery. The Ne cluster mass spectra show the special stability of cluster ions with icosahedral structure (n = 13 and 55) confirming - despite previous discrepancies - the general validity of the sphere-packing principle. Neon cluster ions exhibit other magic numbers, e.g. at n = 21 and 75, not common to all of the other rare gases.     

Unimolecular dissociation of trivalent metal cluster ions (Al n + , Ga n + , In n + ): evidence for a transition from covalent to metallic bonding

Unimolecular dissociation of aluminum, gallium and indium clusters is investigated. Small sizes dissociate into two channels: either the evaporation of a neutral or a charged monomer. Above a given size n _c, only dissociation of a neutral atom subsists. The evaporation of a charged monomer is characteristic of trivalent metal clusters and is consistent with the size evolution of the ionization potential towards the atomic value. The experiments are interpreted in the framework of the statistical R.R.K. model. For smaller sizes (n < n _c), as two evaporation processes are in competition, we have evaluated cluster relative dissociation energies and ionization potentials. The competition between the two evaporation channels is well mirrored by the evolution of the ionization potentials independently measured by near-threshold photoionization experiments. For gallium, our measurements have revealed that the covalent to metal transition occurs for larger sizes (n = 30–50 atoms) than for aluminum clusters.     

Decomposition channels for multiply charged ammonia clusters

Multiply charged ammonia cluster ions are produced by adiabatic nozzle expansion and subsequent ionization by electron impact. They are analyzed in a double focussing sector field mass spectrometer (reversed geometry). Doubly charged clusters are only detected above a critical size of 51 and triply charged clusters above 121. Some of these multiply charged ions decay via metastable dissociation processes in the experimental time window accessible. Doubly charged ammonia clusters with sizes ofn≧51 lose one neutral monomer or, roughly ten times less probable, two neutral monomers. Conversely, triply charged ammonia clusters with sizes 110≦n≦120 show an extremely asymmetric Coulomb dissociation resulting in doubly charged cluster ions of about 90% of the initial mass     

Carbon monoxide clusters: critical size and magic numbers

Fully resolved mass spectra of carbon monoxide clusters have been recorded in the size rangen≦320. Intensity anomalies in these spectra beyondn=135 are strikingly similar to those being observed in krypton and xenon spectra. Particularly pronounced intensity drops occur atn=147 and 309. For the first time, these data provide evidence for icosahedral structure in largemolecular cluster ions. Concerning doubly charged CO clusters, their lower size limit has been measured to ben _c =98.     

Structural,Relative Stable,and Electronic Properties of Pb<Subscript>n</Subscript>Sn<Subscript>n</Subscript> (n = 2–12) Clusters were Investigated Using Density Functional Theory

The structural, relative stable and electronic properties of Pb_nSn_n (n = 2–12) alloy clusters were systematically studied using density functional theory. The isomers of Pb_nSn_n alloy clusters were generated and determined by ab initio molecular dynamics. By comparing the calculated parameters of Pb₂ dimer and Sn₂ dimers with the parameters from experiments, our calculations are reasonable. With the lowest-energy structures for Pb_nSn_n clusters, the average binding energies, fragmentation energies, second- order energy differences, vertical ionization potentials, vertical electron affinities, HOMO–LUMO gaps, and density of states were calculated and analyzed. The results indicate that the Sn atoms have a tendency to bond together, the average binding energies tend to be stable up to n = 8, Pb₈Sn₈ cluster is a good candidate to calculate the molecular interaction energy parameter in Wilson equation, the clusters become less chemical stable and show an insulator-to-metallic transition, 3, 6, 8 and 11 are magic numbers of Pb_nSn_n (n = 2–12) clusters, the charges always transfer from Sn atoms to Pb atoms in Pb_nSn_n clusters except for Pb₁₀Sn₁₀ cluster, and density of states of Pb_nSn_n clusters becoming continuous and shifting toward negative with the increasing size n.     

Magic numbers in sims of Mn similar to those of charged Ar clusters

Manganese cluster ions Mn _k ⁺ (k?60) have been produced by 7 keV Xe ion bombardment and analyzed by a double-focusing mass spectrometer. Discontinuous variations of intensity are found atk=5, 14, 16, 29, 34, 45 and 54. Most of these magic numbers coincide with or differ by only one from those observed in Ar _k ⁺ . The similarity in magic numbers between Mn _k ⁺ and Ar _k ⁺ indicates that the bonding nature in the charged Mn clusters is similar to that in the charged Ar clusters; The polarization force between a positive ion in the center of a cluster and surrounding neutral atoms is dominant binding force.     

On the nature of bulk and surface excitations in Argon clusters

Absorption spectra of Ar clusters containing between 10 and 10⁶ atoms are dominated by strong transitions into bulk and surface states. The intensity variation of bulk and surface excitations is analyzed within a model, which divides the cluster into a surface layer and into an interior part. The thickness of the surface layer is determined by the intensity ratio of bulk and surface excitations. For then=2, 2′ excitons a reasonable value ranging between the radius of then=2 exciton and the nearest neighbour distance is obtained. In case of then=1 excitons the thickness of the surface layer is much smaller than the nearest-neighbour distance indicating that then=1 surface excitons might be interpreted as excitations of atoms on the cluster surface.     

An improved clusterion-photoelectron coincidence technique for the investigation of the ionisation dynamics of clusters

The introduction of photoion-photoelectron coincidence techniques has made it possible to investigate photoionisation properties of heavy clusters, which are not accessible by conventional mass spectrometry. This technique has been further developed in combination with a zero-volt electron energy analyser and greatly improved in performance. The method has been applied to the investigation of different homogeneous and heterogeneous clusters. This type of cluster experiment requires both a very high resolution and a large dynamic range in order to identify also clusters present in low abundance. As an example, a series of coincidence mass spectra of Xe clusters has been recorded at different wavelengths. Below a photon energy of 11.1 eV, the range of observable clusters shifts to higher cluster sizes with decreasing energy. Appearance potentials and the binding energy of different cluster ions were obtained. Intensity fluctuations, already observed in spectra with electron bombardment ionisation (magic numbers), have also been detected in the coincidence spectra and become most pronounced near the ionisation threshold. This indicates that these fluctuations are caused by the size-dependent stability of the ionic and not the neutral cluster. Furthermore, the threshold size does not change linearly with cluster size. The binding energy per particle seems to change drastically aroundn=13 which indicates the existence of a shell structure in the cluster ion.     

Ion-pair evaporation from ionic liquid clusters

A differential mobility analyzer (DMA) is used in atmospheric pressure N₂ to select a narrow range of electrical mobilities from a complex mix of cluster ions of composition (CA)_n(C⁺)_z. The clusters are introduced into the N₂ gas by electrospraying concentrated (～20 mM) acetonitrile solutions of ionic liquids (molten salts) of composition CA (C⁺ = cation, A^? = anion). Mass analysis of these mobility-selected ions reveals the occurrence of individual neutral ion-pair evaporation events from the smallest singly charged clusters: (CA)_nC⁺→(CA)_{n? 1}C⁺+CA. Although bulk ionic liquids are effectively involatile at room temperature, up to six sequential evaporation events are observed. Because this requires far more internal energy than available in the original clusters, substantial heating (～10 eV) must take place in the ion guides leading to the mass analyzer. The observed increase in IL evaporation rate with decreasing size is drastic, in qualitative agreement with the exponential vapor pressure dependence predicted by Kelvin’s formula. A single evaporation event is barely detectable at n = 13, while two or more are prominent for n ≤ 9. Magic number clusters (CA)₄C⁺ with singularly low volatilities are found in three of the four ionic liquids studied. Like their recently reported liquid phase prenucleation cluster analogs, these magic number clusters could play a key role as gas-phase nucleation seeds. All the singularly involatile clusters seen are cations, which may help understand commonly observed sign effects in ion-induced nucleation. No other charge-sign asymmetry is seen on cluster evaporation.     

A new proposal for the reason of magic numbers in alkali cation microhydration clusters

Alkali cation microhydration clusters M⁺(H₂O)_n, n≤24, M = Na, K, Cs, have been globally optimised, using a specialised version of genetic algorithms and the common TIP4P/OPLS model potential. The results constitute a first unbiased and systematic overview on structures of alkali cation microhydration clusters. Simple reasons for differing structural trends could be provided. Dodecahedral cages occur, but do not play as prominent a role as frequently believed. In particular, they do not seem to determine the occurrence of magic numbers. A structural pattern all magic number cluster structures do have in common is that only three and/or four-coordinated water molecules can be observed. Molecular dynamics simulations were run in the canonical ensemble, and free energy differences of dissociating clusters were obtained, with dodecahedral cages again showing no special feature. Structures containing only three and/or four-coordinated water molecules, however, are more stable than others thus arriving at a possible explanation for magic numbers.     

Benzene clusters in a supersonic beam

A supersonic beam is employed to produce benzene clusters (C₆H₆) _n up ton=40. Mass analysis is achieved after two-photon ionization in a reflectron mass spectrometer. Photon energy is chosen so that the internal energy of the cluster ions is less than 700 meV and a slow decay on the µs time scale is observed. By an energy analysis with the reflecting field it is found that the elimination of one neutral benzene monomer is the favoured dissociation process of the cluster ions. Information about the dissociation pathways of the cluster ions is essential if one is to obtain neutral cluster abundances from the ion mass spectrum. Furthermore an experimental method is presented to obtain pure intermediate state (S ₁←S₀) spectra of selected clusters without interferences from the other clusters present in the molecular beam. This method is based on the observation of the metastable decay of the corresponding cluster ion. When the metastable signal is recorded as a function of photon energy it reflects theS ₁←S ₀ intermediate state spectrum. Spectra are presented for the benzene dimer, trimer, tetramer and pentamer.     

Observations of magic numbers in gas phase hydrates of alkylammonium ions

Hydration of alkylammonium ions under nonanalytical electrospray ionization conditions has been found to yield cluster ions with more than 20 water molecules associated with the central ion. These cluster ion species are taken to be an approximation of the conditions in liquid water. Many of the alkylammonium cation mass spectra exhibit water cluster numbers that appear to be particularly favorable, i.e., “magic number clusters” (MNC). We have found MNC in hydrates of mono- and tetra-alkyl ammonium ions, NH₃(C _m H_2m+1)⁺(H₂O) _n , m=1–8 and N(C _m H_2m+1) ₄ ⁺ (H₂O) _n , m=2–8. In contrast, NH₂(CH₃) ₂ ⁺ (H₂O) _n , NH(CH₃) ₃ ⁺ (H₂O) _n1 and N(CH₃) ₄ ⁺ (H₂O) _n do not exhibit any MNC. We conjecture that the structures of these magic number clusters correspond to exohedral structures in which the ion is situated on the surface of the water cage in contrast to the widely accepted caged ion structures of H₃O⁺(H₂O) _n and NH ₄ ⁺ (H₂O) _n .     

Electron-impact ionization of helium clusters close to the threshold: appearance energies

We have investigated the ionization threshold behavior of small helium cluster ions (cluster size n=2-10) formed via electron-impact ionization of neutral helium droplets and derive appearance energies for mass-selected cluster ions using a nonlinear least-square-fitting procedure. Moreover, we report magic numbers in the mass spectrum observed at the electron energy of 70 eV. The apparatus used for the present measurements is a hemispherical electron monochromator combined with a quadrupole mass spectrometer. Our experiment demonstrates that helium clusters are not only exclusively formed via direct ionization above the atomic ionization potential but also indirectly via autoionizing Rydberg states. The present results are compared with previous electron-impact and photoionization results.     

Molecular dynamics calculation of half-lives for thermal decay of Lennard-Jones clusters

Molecular dynamics has been used with a Lennard-Jones (6–12) potential in order to study the decay behavior of neutral Argon clusters containing between 12 and 14 atoms. The clusters were heated to temperatures well above their melting points and then tracked in time via molecular dynamics until evaporation of one or more atoms was observed. In each simulation, the mode of evaporation, energy released during evaporation, and cluster lifetime were recorded. Results from roughly 2000 simulation histories were combined in order to compute statistically significant values of cluster half-lives and decay energies. It was found that cluster half-life decreases with increasing energy and that for a given value of excess energy (defined asE=(E _tot ?E _gnd)/n), the 13 atom cluster is more stable against decay than clusters containing either 12 or 14 atoms. The dominant decay mechanism for all clusters was determined to be single atom emission.     

Theoretical study of the stability of small triply charged carbon clusters Cn3+ (n = 3–12)

Using density functional theory, coupled cluster and multireference methods, dissociation energies and 3rd ionization potentials for, respectively, triply charged and neutral carbon clusters have been evaluated. The results show that the smaller C_n³⁺ clusters are metastable, i.e., they present a fragmentation channel with negative dissociation energy. The lowest dissociation channel always corresponds to evaporation of a singly charged carbon atom. Good agreement with available experimental data is found for most two-fragment channels. The third ionization potential of the corresponding neutral species decreases with cluster size.     

Evolution of (GaAl) n Clusters and Chemisorptions of H2 on (GaAl) n Clusters

The growth behavior of (GaAl) _n (n = 1–12) and the chemisorptions of hydrogen on the ground state geometries have been studied with the three-parameter hybrid generalized gradient approximation due to Becke-Lee–Yang–Parr (B3LYP). The dissociation energy, the second-order energy differences, and the HOMO–LUMO gaps indicate that the magic numbers of the calculated (GaAl) _n clusters are n = 4 and 6. To my knowledge, this is the first time that a systematic study of chemisorptions of hydrogen on gallium aluminum clusters. The onefold top site of aluminum atom is identified to be the most favorable chemisorptions site for one hydrogen chemisorptions on most (GaAl) _n clusters. In general, dissociative chemisorptions of a hydrogen molecule on a top site of aluminum atom is found common for all sizes clusters considered here except for (GaAl) _n (n = 1–3) clusters. The stability of the (GaAl) _n H _m complexes shows that both large second-order difference and large fragmentation energies for (GaAl)₁₀H₂ and (GaAl)₁₁H₂ make these species behaving like magic clusters.