Mass spectrometric analysis of fullerenes and dialane cationic clusters: Revealing magic sizes and stability trends.

Correspondence between Magic Numbers and Electron Degeneracy in Alkali Clusters

Electron-bound water clusters [e(-)(H(2)O)(n)] show very strong peaks in mass spectra for n=2, 6, 7, and (11), which are called magic numbers. The origin of the magic numbers has been an enigma for the last two decades. Although the magic numbers have often been conjectured to arise from the intrinsic properties of electron-bound water clusters, we attributed them not to their intrinsic properties but to the particularly weak stability of the corresponding neutral water clusters (H(2)O)(n=2,6,7, and (11)). As the cluster size increases; this nonsmooth characteristic feature in stability of neutral water clusters is contrasted to the smooth increase in stability of e(-)-water clusters. As the magic number clusters have significant positive adiabatic electron affinities, their abundant distributions in atmosphere could play a significant role in atmospheric thermodynamics.

Gas-phase reactions of anionic and cationic rhodium clusters with azidoacetonitrile are studied by Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry under near-thermal conditions. All anionic and large cationic clusters react by adding [C2,N2] in consecutive steps, either by forming interstitial carbides and nitrides or by adding two CN groups to the cluster surface. Small cationic clusters behave differently, with the unimolecular decomposition of the azide determining the reactivity. Saturation is identified via the size-dependent efficiency of consecutive reaction steps. The present results are the first study of organic azides on transition metal clusters. The observed selectivity of the reaction is in contrast to the high exothermicity of any reaction with azide species. The cationic cluster reactivity shows a gradual transition from gas-phase to surface-like behavior with increasing cluster size.

CO adsorption on small cationic, neutral, and anionic Aun (n=1–6) clusters has been investigated using density functional theory in the generalized gradient approximation. Among various possible CO adsorption sites, the on-top (one-fold coordinated) is found to be the most favorable one, irrespective of the charge state of the cluster. In addition, planar structures are preferred by both the bare and the CO-adsorbed clusters. The adsorption energies of CO on the cationic clusters are generally greater than those on the neutral and anionic complexes, and decrease with size. The adsorption energies on the anions, instead, increase with cluster size and reach a local maximum at Au5CO−, in agreement with recent experiment. The differences in adsorption energies for the different charge states decrease with increasing cluster size.

We revisit the reactivity of trapped pure gold (Au(n)+, n < 26) and silver gold alloy cluster cations (Ag(m)Au(n)+, m + n < 7) with carbon monoxide as studied in a Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer. The experimental results are discussed in terms of ab initio computations which provide a comprehensive picture of the chemical binding behaviour (like binding energy, adsorption sites, associated vibrational frequencies) of CO to the noble metal as a function of cluster size and composition. Starting from results for pure gold cluster cations for which an overall decrease of CO binding energy with increasing cluster size was experimentally observed--from about 1.09 +/- 0.1 eV (for n = 6) to below 0.65 +/- 0.1 eV (for n > 26) we demonstrate that metal--CO bond energies correlate with the total electron density and with the energy of the lowest unoccupied molecular orbital (LUMO) on the bare metal cluster cation as obtained by density functional theory (DFT) computations. This is a consequence of the predominantly sigma-donating character of the CO-M bond. Further support for this concept is found by contrasting the predictions of binding energies to the experimental results for small alloy cluster cations (Ag(m)Au(n)+, 4 < m + n < 7) as a function of composition. Here, binding energy drops with increasing silver content, while CO still binds always in a head-on fashion to a gold atom. Finally we show how the CO stretch frequency of Ag(m)Au(n)CO+ may be used to identify possible adsorption sites and pre-screen favorable isomers.

We report ab initio molecular orbital calculations on neutral and single-ionized stoichiometric clusters of MgO containing up to 26 atoms. Geometrical parameters of the neutral clusters are optimized at the Hartree–Fock level, whereas for the ionized clusters we have applied the vertical approximation. Correlation corrections in the clusters with 2–12 atoms are included at the equilibrium geometries by means of second order Moller–Plesset calculations. We have found that the structures based on the (MgO)3 subunit are preferred in comparison to cubelike configurations, although the energy difference decreases with the increase in cluster size. The relative stability of neutral and single-ionized clusters has been studied by means of the fragmentation path involving the loss of a neutral MgO molecule. The calculated ‘‘magic numbers’’ for the charged clusters, (MgO)n+, are in complete agreement with the abundance maxima observed in the mass spectra. Finally, we explore the size dependence of structural, energetic, and electronic properties. These properties show a large variation from the monomer to the (three-dimensional) eight atom cluster, followed by a softer approach towards the corresponding bulk limit.

Selenium cluster cations are produced by the combination of laser vaporization and supersonic expansion techniques. Each small cluster cation Sen+ (n=3–8) is mass selected separately and subjected to one-photon laser photodissociation processes. The parent and daughter cluster ions are detected using a reflectron time-of-flight mass spectrometer. The appearance potentials of all the observed cluster fragment ions are estimated from their yield curves as a function of the laser wavelength. The neutral dimer evaporation is found to be the lowest energy photodissociation channel. In general, the odd-numbered cluster cations have much larger dissociation thresholds than those of the even-numbered cluster cations. In addition, the dissociation thresholds of the odd-numbered cations decrease with the increasing cluster size, while those of the even-numbered clusters increase with the increasing cluster size. A sequential neutral dimer evaporation mechanism is demonstrated in the photodissociation of some cluster cations at high photon energies.

The kinetic-energy-dependent cross sections for the reactions of Co(n)+ (n = 2-16) with D2 are measured as a function of kinetic energy over a range of 0-8 eV in a guided ion-beam tandem mass spectrometer. The observed products are Co(n) D+ for all clusters and Co(n)D2+ for n = 4,5,9-16. Reactions for the formation of Co(n)D+ (n = 2-16) and Co9D2+ are observed to exhibit thresholds, whereas cross sections for the formation of Co(n)D2+ (n = 4,5,10-16) exhibit exothermic reaction behavior. The Co(n)+-D bond energies as a function of cluster size are derived from the threshold analysis of the kinetic-energy dependence of the endothermic reactions and are compared to previously determined metal-metal bond energies, D0(Co(n)+-Co). The bond energies of Co(n)+-D generally increase as the cluster size increases, and roughly parallel those for Co(n)+-Co for clusters n > or = 4. These trends are explained in terms of electronic and geometric structures for the Co(n)+ clusters. The bond energies of Co(n)+-D for larger clusters (n > or = 10) are found to be very close to the value for chemisorption of atomic hydrogen on bulk-phase cobalt. The rate constants for D2 chemisorption on the cationic clusters are compared with the results from previous work on cationic and neutral cobalt clusters.

Singly- and doubly-negative carbon clusters in sputtering: Energy spectra, abundance distributions and unimolecular fragmentation

Theoretical study on ammonia cluster ions: nature of thermodynamic magic number

The reactions of gold cluster cations Aun+ (n=1–12) with H2S and H2 have been studied using Fourier-transform ion-cyclotron resonance (FT–ICR) mass spectrometry. The cluster cations were produced by laser ablation of a gold rod in He atmosphere, and their reactions were observed at room temperature and low total pressures of 10−7–10−5 Torr. Initial products of the reactions with H2S were mainly AuSH+ for n=2, AunS+ for n=4–8 and 10, and AunSH2+ for n=9, 11, and 12. No reactions of Au+ and Au3+ with H2S were observed. Even n cluster cations were more reactive than adjacent odd n clusters. The particularly low reactivity at n=1, 3, 9, and 11 is consistent with the low ionization potential of Aun and the weak binding energy of Aun+–Au. Further sulfuration reactions of AunS+ proceeded to give AunSm+ and finally stopped at AunSm+xH2+ when H2 release did not occur. The maximum number of sulfur atoms m+x increased with the cluster size up to n=8, while the sulfuration reaction stopped at early stages for n⩾9. In another series of experiments, no reaction of Aun+ (n=1–12) with H2 gas pulses introduced into the FT–ICR cell was observed. To investigate the stability of gold hydride clusters, laser ablation of gold in a H2/He mixture was performed. The hydride cluster cations AunHm+ were produced for n=1–7, while bare Aun+ clusters were the main products for n⩾8. There is a distinct border between n=7 and 8, as the structure of Aun+ changes from planar for n⩽7 to three-dimensional for n⩾8, suggesting the stability of hydride cluster cations with planar gold frameworks.

Application of fractals and kinetic equations to cluster formation

The authors present theoretical results describing the adsorption of H2 and H2S molecules on small neutral and cationic gold clusters (Au(n)((0/+1)), n=1-8) using density functional theory with the generalized gradient approximation. Lowest energy structures of the gold clusters along with their isomers are considered in the optimization process for molecular adsorption. The adsorption energies of H2S molecule on the cationic clusters are generally greater than those on the corresponding neutral clusters. These are also greater than the H2 adsorption energies on the corresponding cationic and neutral clusters. The adsorption energies for cationic clusters decrease with increasing cluster size. This fact is reflected in the elongations of the Au-S and Au-H bonds indicating weak adsorption as the cluster grows. In most cases, the geometry of the lowest energy gold cluster remains planar even after the adsorption. In addition, the adsorbed molecule gets adjusted such that its center of mass lies on the plane of the gold cluster. Study of the orbital charge density of the gold adsorbed H2S molecule reveals that conduction is possible through molecular orbitals other than the lowest unoccupied molecular orbital level. The dissociation of the cationic Au(n)SH2+ cluster into Au(n)S+ and H2 is preferred over the dissociation into Au(m)SH2+ and Au(n-m), where n=2-8 and m=1-(n-1). H2S adsorbed clusters with odd number of gold atoms are more stable than neighboring even n clusters.

Bonding in small boron cluster cations (BZTl3+) is examined by measurement of appearance potentials and fragmentation patterns for collision-induced dissociation (CID) with Xe. Cluster stabilities are generally found to increase with increasing cluster size; however, there are large fluctuations from the overall trend. The lowest energy fragmentation channel for all size cluster ions is loss of a single atom. Clusters smaller than six atoms preferentially lose B', while for the larger clusters the charge remains on the BW1+ fragment. The results are used to estimate cluster ionization potentials and geometries. Comparison of measured stabilities with magic numbers in the cluster ion size distribution and with total CID cross sections shows that neither is a reliable indicator of stability. We also report on ab initio calculations for both neutral and ionic BI4. The results include cluster geometries, ionization potentials, charge distributions, dissociation energies, and bonding character. The results for IPS, geometries, and De)s are compared with experiment.

Structure and relative stability of Pdn clusters for n=1–6 were investigated using density functional methods at the B3PW91 level of theory. The structures of the optimized Palladium clusters were investigated and the results are compared with the available experimental values. Stability of the clusters was determined from their relative energy values, binding energies, HOMO-LUMO gap and electronic properties. The binding energy per atom also increases with cluster size. The study revealed that Pd4 and Pd6 are relatively more stable than their neighboring clusters. The most stable isomer for all clusters under investigation is the triplet. The Pd4 and Pd5 showed different Pd-Pd bond lengths due to Jahn-Teller distortion. Stability function and atom addition energy change predict that Pd4, and Pd6 are relatively more stable than their neighboring clusters. Electron affinity (EA), Ionization potential (IP) and electronegativity values suggest that larger clusters have stronger tendency to accept electrons, thereby supporting the relative stability of Pd4 and Pd6. Finally, Collision diameter increases as the cluster size increases.