Comparative study on the structure and properties of small C<Subscript>n</Subscript> and NaC<Subscript>n</Subscript> clusters

The structures, binding energies, and electronic properties of C_n and NaC_n (n=2–12) clusters have been systematically investigated using density functional theory (DFT). A number of previously undiscovered isomers of NaC_n clusters are reported, including fan-like, linear and three-dimensional structures. Moreover, NaC_n clusters with even n are found to be more stable than those with odd n, in contrast with the case of C_n clusters.     

The aluminum arsenides Al<Subscript>m</Subscript>As<Subscript>n</Subscript> (m + n = 2–5) and their anions: Structures,electron affinities and vibrational frequencies

Geometries, electronic states and electron affinities of Al_mAs_n and Al_mAs _n (m+n=2–5) clusters have been examined using four hybrid and pure density functional theory (DFT) methods. Structural optimization and frequency analyses are performed using a 6-311+G(2df) one-particle basis set. The geometries are fully optimized with each DFT method independently. The three types of energy separations reported in this work are the adiabatic electron affinity (EA_ad), the vertical electron affinity (EA_vert), and the vertical detachment energy (VDE). The calculation results show that the singlet structures have higher symmetry than that of doublet structures. The best functional for predicting molecular structures was found to be BLYP, while other functionals generally underestimated bond lengths. The largest adiabatic electron affinity, vertical electron affinity and vertical detachment energy, obtained at the 6-311+G(2df)/BP86 level of theory, are 2.20, 2.04 and 2.27 eV (AlAs), 2.13, 1.94 and 2.38 eV (AlAs₂), 2.44, 2.39 and 2.47 eV (Al₂As), 2.09, 1.80 and 2.53 eV (Al₂As₂), 2.01, 1.57 and 2.36 eV (AlAs₃), 2.32, 2.11 and 2.55 eV (Al₂As₃), 2.40, 1.45 and 3.26 eV (AlAs₄), 1.94, 1.90 and 2.07 eV (Al₄As), respectively. However, the BHLYP method gives the largest values for EA_ad and EA_vert of Al₃As and EA_ad of Al₃As₂, respectively. For the vibrational frequencies of the Al_nAs_m series, the B3LYP method produces good predictions with the average error only about 10 cm^-1 from available experimental and theoretical values. The other three functionals overestimate or underestimate the vibrational frequencies, with the worst predictions given by the BHLYP method.     

Theoretical determination of electron binding energy spectra of anionic magnesium clusters

A recently developed accurate scheme for converting the single-particle eigenenergies of the density functional theory into electron binding energies is used to compute the spectra of electron binding energies in and . The computations are performed for different isomeric forms of the clusters using both pseudopotential and all-electron treatments. The results are compared with the data derived from electron photodetachment experiments, and the role of the different isomers in the interpretation of these data is examined.     

The hydrogenated aluminium trimer: a theoretical examination of the formation and interconversion pathways

Five doublet isomers of the Al₃H₂ cluster lying within a narrow range of 5 kcal/mol, along with the isomerization transition states connecting them, have been located with the coupled-cluster CCSD(T) and DFT methods. The two most stable doublet structures, the C_2v planar including the two Hs bound terminally and C₁ non-planar showing one H in terminal site and the other in threefold site are found to be essentially degenerate. Although the reaction of Al₃ with H₂ to yield Al₃H₂ is found to be significantly exothermic, by 23.5 kcal/mol, this hydrogenation is impeded by a considerable kinetic barrier of 16 kcal/mol. Our result is consistent with the observed lack of reactivity of Al_n towards H₂(D₂) for n=3 under thermal conditions [3]. The quartet Al₃H₂ isomers are predicted to lie 16–21 kcal/mol higher in energy than the doublet analogues. Further dimerization of Al₃H₂ to form Al₆H₄ has also been examined. Electronic supplementary material Supplementary Online Material     

Low-energy surface collision induced dissociation of Ge and Sn cluster ions

Fragmentation of germanium and tin cluster ions in the low-energy collisions with a Si surface has been investigated by means of a tandem time-of-flight mass spectrometer. At low incident energies, smaller clusters fragmented by an atom loss process, whereas larger clusters decayed by fission. The favored fragmentation paths for both cluster ions were similar to those for Si cluster ions. The results support the structural similarities among Si, Ge, and Sn clusters in the present size range. For tin cluster ions, low-energy fragmentation patterns were compared with those obtained from theoretical calculations using generalized gradient approximation (GGA) and the B3PW91 exchange-correlation functional. It has been found that the B3PW91 hybrid functional results are consistent with the experimental observations.     

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.     

Combined experimental and theoretical study of small aluminum oxygen clusters

We report a combined experimental and computational investigation of small Al_nO_m species (n ≤20, m ≤ 12), produced in a laser vaporization cluster source. The oxygen content in the clusters was tuned by varying the oxygen concentration in the carrier gas. Ionization energies are bracketed using different ionizing photon energies in the energy range between 5.37 and 7.89 eV. Among the singly doped Al_nO species, Al₃O and Al₁₅O are found to have relatively low ionization energies, which can be related to the magic character of the corresponding cations. Peculiarly low ionization energies also are observed for specific oxygen rich species (m > 1), suggesting the formation of ionically bound subunits. The structures and ionization energies of singly doped Al_nO^0,+ (n = 1 - 7) clusters were determined using density functional theory (B3LYP/6-311+G(d)). Electronic supplementary material Supplementary Online Material     

Dissociation channels of silver bromide cluster Ag<Subscript>2</Subscript>Br,silver cluster Ag<Subscript>3</Subscript> and their ions studied by using alkali metal target

Various dissociation channels of silver bromide cluster ion Ag₂Br⁺ and silver cluster ion Ag₃ ⁺ were observed in high-energy collisionally-activated dissociation (CAD) using a Cs target. The fragment patterns of the high-energy CAD were compared with those of the metastable dissociation and low-energy CAD. The difference in the fragment patterns between the high-energy CAD and the other dissociation methods was explained in terms of the internal energy distributions. The dissociation mechanisms of neutral silver bromide cluster Ag₂Br and silver cluster Ag₃ were also investigated by charge inversion mass spectrometry using the Cs target. While the fragment ions AgBr^- and Ag₂ ^- were dominantly observed in the charge inversion spectrum of Ag₂Br⁺, the undissociated ion Ag₃ ^- was observed as a predominant peak in the case of Ag₃ ⁺. The dissociation behavior of Ag₂Br^* can be explained on the basis of the calculated thermochemical data. Contrary to this, the predominant existence of the undissociated Ag₃ ^- cannot be explained by the reported thermochemical data. The existence of undissociated Ag₃ ^- suggests that the dissociation barrier is higher than the internal energy of Ag₃ ^* (theoretical: 1.03 eV, experimental: 2.31 eV) estimated from the ionization potentials of Ag₃ and Cs.     

Spherical averaged jellium model with norm-conserving pseudopotentials

The effect of non-local norm-conserving pseudo-potentials on the static and dynamic properties of Na_n and Li_n cluster with n=6,8 is investigated in the frame of self-consistent LDA calculations with spherically averaged ionic density (SAPS model). A comparison with previous calculations which use local pseudo-potentials as well with uniform averaged non-local pseudo-jellium calculation has been carried out. A better quantitative agreement with experiments has been found in the calculation of the photoresponse cross-section with respect to either simple jellium or pseudo-jellium model, even in very small clusters, where deviations from sphericity are not negligible. Received: 3 March 1998 / Received in final form and Accepted: 2 June 1998     

Dynamical aspects of thermionic emission of C 60 studied by 3D imaging

We present the first experimental results of the time-dependent photoelectron spectrum observed in thermionic emission of hot C₆₀ excited by multiphoton absorption. Time resolved velocity-map imaging is used to record photoelectron spectra. As opposed to the evolution of the total photoelectron current that follows a power law as a function of the delay after excitation, it is shown that the photoelectron spectrum bears precise information on the degree of excitation of the ensemble of clusters. The effective temperature deduced from the experimental spectrum is found to be directly related to the average internal energy in the initial step of the decay, while after typically 1 s the photoelectron spectrum is almost independent on the initial excitation process. The subsequent evolution of the spectrum as a function of the time-delay after excitation is found to be very slow.     

Static electric dipole polarizabilities of Na clusters

The static electric dipole polarizability of Na _N clusters with even N has been calculated in a collective, axially averaged and a three-dimensional, finite-field approach for , including the ionic structure of the clusters. The validity of a collective model for the static response of small systems is demonstrated. Our density functional calculations verify the trends and fine structure seen in a recent experiment. A pseudopotential that reproduces the experimental bulk bond length and atomic energy levels leads to a substantial increase in the calculated polarizabilities, in better agreement with experiment. We relate remaining differences in the magnitude of the theoretical and experimental polarizabilities to the finite temperature present in the experiments. Received 8 November 1999     

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     

Threshold laws in delayed emission: an experimental approach

Delayed emission is a common decay process for very excited complex systems where the excitation energy is, to a large extent, statistically distributed over all accessible degrees of freedom. A rich variety of delayed decay processes is found in complex molecules and clusters such as thermionic emission, evaporation of heavy fragments or blackbody radiation. In this article, we present the general threshold laws that govern the kinetic energy spectrum of matter particles (electrons or fragments) ejected from spherically symmetric species in such processes, and we illustrate these laws by experimental results obtained in photoelectron and photoion spectroscopy. Deviations from simple laws for non spherical species are also evidenced.     

Deposition of Ni<Subscript> 13</Subscript> and Cu<Subscript> 13</Subscript> clusters on Ni(111) and Cu(111) surfaces

The soft deposition of Ni₁₃ and Cu₁₃ clusters on Ni(111) and Cu(111) surfaces is studied by means of constant-energy molecular-dynamics simulations. The atomic interactions are described by the Embedded Atom Method. It is shown that the shape of the nickel clusters deposited on Cu(111) surfaces remains rather intact, while the copper clusters impacting on Ni(111) surfaces collapse forming double and triple layered products. Furthermore, it is found that for an impact energy of 0.5 eV/atom the structures of all investigated clusters show the lowest similarity to the original structures, except for the case of nickel clusters deposited on a Cu(111) surface. Finally, it is demonstrated that when cluster and substrate are of different materials, it is possible to control whether the deposition results in largely intact clusters on the substrate or in a spreading of the clusters. This separation into hard and soft clusters can be related to the relative cohesive energy of the crystalline materials.     

Exact scattering length for a potential of Lennard-Jones type

For a modified Lennard-Jones interaction potential of the form ∼[(r₀/r)^2n-2-(r₀/r)ⁿ], an exact and simple expression for the s-wave scattering length is presented, and discussed in some detail. For heavy alkali atoms, which nowadays are routinely being employed to produce Bose-Einstein condensates, this potential is well compatible with known experimental data when n = 6.     

Improved endohedral fullerenelike structures of silicon clusters Si31–Si39 by density functional calculations

We extensively search for the endohedral silicon-fullerene structures of Si₃₁–Si₃₉ using the combination of a tight-binding potential with the density functional theory. The resulting structures of our best candidates characterize more compact features comparing to previous isomers [J. Am. Chem. Soc. 126, 13845 (2004); J. Chem. Phys. 124, 164311 (2006)]. Most of our best candidates belong to new families featuring different core/cage combinations or different original carbon fullerene cages with respect to those of previous isomers. Energy calculations reveal that our best candidates are more stable than the previous best ones at the PW91 level, except for n = 34 and 38. The predicted relative stabilities of these isomers remain even at finite temperatures. In addition, the densities of dangling-bond atoms in the surfaces of our Si₃₃ and Si₃₉ isomers are significantly lower than the previous best candidates, as well as lower than those of their neighbors. This finding together with the densities of the active sites in the surfaces of the previous best candidates of Si₃₄ and Si₃₈ is roughly consistent with the observed relative reactivities of the silicon clusters in the size range of n = 31-39.     

Photoionization of argon, krypton and xenon clusters in the inner valence shell region

Photoionization of rare gas clusters in the innervalence shell region has been investigated using threshold photoelectron and photoion spectrometers and synchrotron radiation. Two classes of states are found to play an important role: (A) valence states, correlated to dissociation limits involving an ion with a hole in its innervalence ns shell, (B) Rydberg states correlated to dissociation limits involving an ion with a hole in its outervalence np shell plus an excited neutral atom. In dimers, class A states are “bright”, that is, accessible by photoionization, and serve as an entrance step to form the class B “dark” states; this character fades as the size of the cluster increases. In the dimer, the “Mulliken” valence state is found to present a shallow potential well housing a few vibrational levels; it is predissociated by the class B Rydberg states. During the predissociation a remarkable energy transfer process is observed from the excited ion that loses its innershell electron to its neutral partner. Received: 10 February 1998 / Revised: 17 July 1998 / Accepted: 31 July 1998     

Dynamical study of the Cs<Superscript>+</Superscript>(<Superscript>1</Superscript>S<Subscript>0</Subscript>)+Mg(3 <Superscript>1</Superscript>S<Subscript>0</Subscript>) non adiabatic collision system in the few keV energy range

The dynamics of collisional processes between Mg atoms and caesium ions is studied using the hemiquantal (HQ) approach with special attention to the collisional channels leading to Mg(3 ¹P) and Cs(6 ²P) states, for which the corresponding emission excitation functions have been previously measured in our laboratory. The radial and angular non-adiabatic couplings between the manifold of quasimolecular states have been determined using an ab initio configuration interaction calculation. The cross-sections for the different channels, as a function of the laboratory collisional energy, are compared with experimental values. The dynamical calculations indicate that, for the inelastic processes considered, the range of relevant impact parameters is small, active collisions being of the head-on type. .     

Catalyst poisoning in the conversion of CO and N 2O to CO 2 and N 2 on Pt 4 - in the gas phase

Pt₄ ^- catalyses the conversion of CO and N₂O to CO₂ and N₂ in the gas phase, as observed by Fourier transform ion cyclotron (FT-ICR) mass spectrometry. The partial pressures of CO and N₂O determine the extent of poisoning and the turnover numbers that can be achieved. The catalytic conversion terminates as soon as two CO are adsorbed on the cluster. With N₂O, the reactivity of Pt₄O₂ ^- and Pt₄O₃ ^- is reduced to 41% and 34% compared to Pt₄O^-, respectively, and with Pt₄O₄ ^- this value is reduced to 1%. In contrast, Pt₄ ⁺ shows no apparent catalytic activity. Density functional theory calculations of Pt₄ ^+/- with CO and N₂O adsorbates reveal significantly different stabilities of the reaction intermediates for the different charge states.     

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.