Session J40: Theory of Clusters and Nanoscale Systems

Nanomaterials synthesized by electrochemical discharges: qualitative and quantitative performance

During the electrochemical discharges in aqueous solutions, the electronic avalanches induce several reactions of dimerization and recombination of the hydrated electrons and H* and OH* radicals, generated by the radiation of water molecules. With the introduction of metallic ions M$^{z+}$, the successful manufacture of nanoparticles is controlled by the continuous competition of reduction of M$^{z+}$, by the powerful reducing agents e$^{-}_{H}$ and H* to lower levels of valency, and the back reaction of oxidation by OH*. With the assumption that the concentration of metal ions is high enough when compared to those of species e$^{-}_{H}$, H* and OH*, the differential yield G between the formation and consumption of M$^{z+}$ in a given finite volume around the electron-emitting electrode is modeled by homogeneous kinetics. It is found G to be proportional to the concentration of metal ions, the speed and penetration depth of the electrons, and the ratio of rate constants of reactions of nucleation and polymerization, which are supported by previous contributions on the dynamics and stability of the phenomenon.   

Structural Oscillation in Pd$_{13}$ During Oxidation/Reduction

First principles electronic structure calculations within a gradient corrected density functional formalism have been carried out to investigate the electronic structure and magnetic properties of bare and oxidized Pd$_{13}$ clusters. It is shown that the ground state of neutral Pd$_{13}$ is a bilayer structure that can be regarded as a fragment of the bulk, while a compact icosahedron is higher in energy. The addition of an electron, however, reverses the ordering of structures and Pd$_{13}^{-}$ has an icosahedral ground state. Similar reordering of structure occurs as an O$_{2}$ molecule is added to the neutral cluster. The talk will focus on the oscillations between the two structures during catalysis process.   

Computational Studies on the Energy Landscape of Pt-Pd nanoparticles

Bimetallic nanoparticles such as Pt-Pd are currently the subject of intense research mainly due to their important catalytic properties. Clusters structure, composition and degree of mixing or segregation all play important roles in determining their chemical activity. It is presented here an exhaustive study of the structure of Pt-Pd nanoparticles, obtained by a Genetic Algorithm (GA) which incorporates the Gupta potential to mimic interaction for bimetallic atoms. This procedure provided an icosahedral structure as the lowest in energy. The threshold method (TM) is used to analyze the energy landscape of 13-atom Pt@Pd$_{12}$ nanoparticle, as well as the transition probabilities for those structures with pentagonal symmetry found by the TM. Disconnectivity graphs are obtained for both a vast exploration of the potential energy surface (PES) and the exploration around the lowest energy structure. We found low interconversion transition rates for the putative global minimum provided by the GA code, which was confirmed by the TM algorithm.   

Negative ions of transition metal-halogen clusters

A systematic density functional theory based study of the structure and spectroscopic properties of neutral and negatively charged MX$_{n}$ clusters formed by a transition metal atom M (M=Sc, Ti, V) and up to seven halogen atoms X (X=F, Cl, Br) has revealed a number of interesting features: (1) Halogen atoms are bound chemically to Sc, Ti, and V for n $<$ n$_{max}$, where the maximal valence n$_{max}$ equals to 3, 4, and 5 for Sc, Ti, and V, respectively. For n $>$ n$_{max}$, two halogen atoms became dimerized in the neutral species, while dimerization begins at n = 5, 6, and 7 for negatively charged clusters containing Sc, Ti, and V. (2) Magnetic moments of the transition metal atoms depend strongly on the number of halogen atoms in a cluster and the cluster charge. (3) The number of halogen atoms that can be attached to a metal atom exceeds the maximal formal valence of the metal atom. (4) The electron affinities of the neutral clusters abruptly rise at n=n$_{max}$, reaching values as high as 7 eV. The corresponding anions could be used in the synthesis of new salts, once appropriate counterions are identified.   

Crystal Field Splitting and Stabilization of CuMgx- Clusters

The electronic states in clusters group into shells much in the same way as in atoms. Clusters with filled electronic shells exhibit enhanced stability as manifested through observed magic numbers in metal clusters. An important issue is if stable species can be attained at sub-shell fillings. In this work we have carried out first principles electronic structure calculations on CuAl$_{x}^{-}$ and CuMg$_{x}^{-}$ clusters to demonstrate this intriguing effect. It is shown that the ionic cores in the clusters can order to generate internal electric fields that lead to splitting of the supershells, much in the same way as the crystal field splitting of atomic states in crystals. The studies offer a new approach to forming magic species though control of the composition and the arrangement of atoms. The talk will highlight these effects and how they can be seen in experiments.   

{\em Ab initio} study of dimer and one-dimensional chain structures of M@Au$_{12}$ (M = W, Mo) clusters

Using density functional theory, we investigate the structural and electronic properties of the dimer and one-dimensional (1D) chain structures composed of metal-encapsulated Au$_{12}$ nanoclusters (M@Au$_{12}$, M = W, Mo) with icosahedral ({\em I} $_{h}$) and cuboctahedral ({\em O}$_{h}$) symmetries. We consider various dimer configurations with different compounds and symmetries to find the most stable dimer structure in each case. We find that during dimerization (either homogeneous or heterogeneous dimer), Au atoms in the one cluster tend to form triangular bonds with counterpart Au atoms in the other. By maximizing the number of Au-Au bonds by dimerization, any cluster is stabilized by about 3 eV. We further find their stable 1D chain structures by considering various 1D chain configurations with different compounds and symmetries. Our results demonstrate that the spin-orbit coupling effects are significant on the electronic and magnetic properties as well as the structural stability due to 5{\em d} electrons in a transition metal atom M of the M@Au$_{12}$ nanocluster. We also present interesting differences in electronic and magnetic properties between {\em I}$_{h}$- and {\em O}$_{h}$-symmetric 1D polymerized M@Au$_{12}$ chain structures.   

Interpretation of Cp(*) - protected Aluminum Clusters as Superatom Complexes

Metal clusters stabilized by a surface ligand shell represent an interesting intermediate state of matter between molecular metal-ligand complexes and bulk metal. Such ``metalloid'' particles are characterized by the balance between metal-metal bonds in the core and metal-ligand bonds at the exterior of the cluster. In previous studies, the electronic stability observed for selected ligand-protected aluminum clusters is not fully understood. By density functional theory calculations, we illustrate here that the electronic stability of various experimentally isolated Cp(*) -- protected aluminum clusters can be explained using the electron shell model for the aluminum core, coupled with an ionic Al-Cp(*) interaction at the surface. Thus, one may classify ligand-protected aluminum clusters as ``superatom complexes'' similar to the ligand-protected gold clusters.   

Probing the existence of energetically degenerate cluster isomers by chemical tagging

Current methods for identifying the ground state geometry of a cluster require synergy between theory and experiment. However, this becomes a difficult problem when the accuracy of the theoretical methods is not sufficient to distinguish between nearly degenerate isomers. Using density functional theory based calculations we show that the near degeneracy between the planar and cage structures can be lifted by tagging these with halogens and superhalogens moieties such as Cl and BO$_{2}$. The energy of the planar Au16- isomer is lowered from 0.15 eV before tagging to 0.51 $\sim $ 0.55 eV after tagging, thus providing a way to probe its coexistence.   

Gold clusters at finite temperature: influence of fluxionality on ligand adsorption

Metal clusters, in particular in relation with their catalytic properties, have been the object of intensive experimental and theoretical studies, in the recent years. A great deal of effort has been devoted by many theoretical groups to understanding the zero kelvin properties of such clusters. Here, by focusing on small gas phase An$_N$ clusters $(3 \leq N \leq 20)$ and their interaction with CO and O$_2$ as a showcase, we illustrate a methodology for the study of small clusters and their interaction with atoms and molecules at finite temperature. We combine all-electron density functional theory, including scf-density dependent van-der-Waals tail corrections, with finite temperature sampling techniques, like Biased MD and Parallel Tempered MD. We find an unusual flexibility of the clusters, at room and lower temperature. At certain sizes, Au$_N$ clusters at room temperature are liquid droplets. This has an important implication, when accounting for the dynamics of ligand adsorption. One has to consider that the energy released by an exothermic ligand adsorption heats up the newly formed complex, and the equilibration with the environment is much longer than the typical timescale for conformational rearrangement. In this respect, the very concept of a preferred adsorption site in the bare cluster might be meaningless.   

Pseudohalogens as Building Blocks of Hyperhalogens: A Case Study with Au(CN)$_{x}$ Complexes

Electron affinity (EA) is one of the major factors that govern reactivity. Halogen atoms possess the highest electron affinities among the elements in the periodic table since it takes only one electron to close their shell. Pseudohalogens also require one electron to close their shell and thus mimic the properties of halogens. A typical example is the CN moiety whose electron affinity (3.8 eV) is slightly larger than that of Cl. Using calculations based on density functional theory we show that when a Au atom is surrounded by CN moieties, the electron affinity of Au(CN)$_{x}$ complexes rise above that of CN for x$\ge $2 and reach a value as high as 8.4 eV, thus forming hyperhalogens. Electron affinities also show odd even alternation with the clusters with even x having higher EA values. Equilibrium geometries, electronic structure and spectroscopic properties of these complexes will be presented and results will be compared with available experimental data.   

Chirality in Metallic Clusters

In this work, we present a theoretical study on the structural, vibrational, electronic, and optical properties of chiral bare gold clusters. We consider the case of the Au$_{34}^{-}$ cluster for which extensive experimental studies on its structural and electronic behavior had been published recently. Our results show that the lowest-energy isomers of the Au$_{34}^{-}$ cluster correspond to two chiral structures with C$_{1}$ and C$_{3}$ point symmetry groups, being the C$_{1}$ isomer slightly more stable than the C$_{3}$ one. The calculated structure factors, which have been measured using trapped ion electron diffraction, indicate that these isomers are almost indistinguishable. On the other hand, their electronic DOS show different features around the HOMO-LUMO energy gap, which may be detected through optical spectroscopies. In fact, our calculated absorption and circular dichroism spectra show clear differences in the optical behavior of these chiral clusters. Another important property that distinguishes the C$_{1}$ and C$_{3}$ isomers is the different spatial distribution of the atomic coordination on the cluster surface, which would generate distinct enantiospecific adsorption patterns with chiral molecules. These results confirm the existence of intrinsically chiral bare gold clusters.   

Free gold clusters in CO and O$_2$ atmosphere: an ab initio study

The marked catalytic activity of gold nanoparticles has inspired a large number of scientific contributions~ from different fields. However, many questions still lack a satisfying answer, for example what are the structures and stoichiometries of the gold particles in the presence of the reactive gases, and how do their catalytic properties depend on the particle size [1]. We answer these questions for neutral gold clusters modeled in a gas phase atmosphere containing CO and O$_2$ in variable compositions, and in a temperature range between 100 and 600 K. To this aim, DFT (PBE)--based \textit{ab initio atomistic thermodynamics} technique [2] is applied, including full account of the vibrational contribution to the free energy. As a result, the preferred cluster+adsorbate structures for different environmental conditions are obtained and interpreted as candidate intermediates in the catalytic CO oxidation reaction.\\[4pt] ~[1] R. Meyer, C. Lemire, S. K. Shaikhutdinov and H. J. Freund, \textit{Gold Bull}. \textbf{2004}, \textit{37}, 72--124.\\[0pt] [2] K. Reuter and M. Scheffler, \textit{Phys. Rev. B} \textbf{2001}, \textit{65}, 035406; C. M. Weinert and M. Scheffler, \textit{Mat. Sci. Forum} \textbf{1986}, \textbf{10--12}, 25--30; M. Scheffler and J. Dabrowski, \textit{Phil. Mag. A} \textbf{1988}, \textit{58}, 107--121.   

Structure-specific spectroscopy of plasmon-supporting nanoparticles

Recent advances in the development of sensitive ultrashort laser-based spectroscopic probes to investigate dynamics of high surface-to-volume metal and alloy nanostructures will be discussed. Electronic relaxation and interparticle electromagnetic coupling processes in hollow gold nanospheres (HGNs) and HGN aggregates were studied using femtosecond pump-surface plasmon probe and second harmonic generation spectroscopies, including single-particle measurements. In the case of HGNs, an unexpected, but systematic, blue shift of the spectral position of the surface plasmon resonance was observed upon nanoparticle aggregation. Femtosecond time-resolved measurements, high-resolution TEM, and Finite-Difference Time-Domain calculations demonstrate that this blue shift results from interparticle cavity coupling, an effect not possible for solid nanospheres. The efficiency of this coupling was tailored by controlling HGN aspect ratio over a vast range of sizes (20 nm to 80 nm outer diameters). This effect may be applied to developing more efficient optical and electronic devices, including photovoltaics.   

Rare Earth Doped Magnetic Clusters of Gold for Medical Application

In recent years gold clusters have been studied extensively due to their unusual properties and applications in cancer treatment and catalysis. Small gold clusters having up to 15 atoms are planar as shown in figure 1. Thereafter a transition occurs to 3D structures but the atomic structures continue to have high dispersion. Doping of these clusters could transform them in to new structures and affect the properties. Gold clusters with cage structures such as W@Au12 can be prepared with large highest occupied-lowest unoccupied molecular orbital (HOMO-LUMO) gap by doping with a transition metal atom such as W. By changing the transition metal atom, cage structures of different sizes as well as different HOMO-LUMO gaps can be formed which could be useful in different optical applications. In these structures gold clusters are generally non-magnetic. However, it is also possible to form magnetic clusters of gold such as Gold clusters have been found to be good for cancer treatment. We have performed ab initio calculations on doping of rare earths in small gold clusters to obtain magnetic clusters using projector augmented wave pseudopotential method within generalized gradient approximation for the exchange-correlation energy. Elemental gold clusters having up to 15 atoms are planar and thereafter 3D structures become favorable. We have explored the changes in the growth behavior when a rare earth atom is doped and studied the variation in the magnetic behavior as a function of size. Our results suggest that gold clusters may have twin advantage of treating cancer as well as be helful in magnetic imaging such as by MRI.