Comparison of static polarizabilities of Cun, Nan, and Lin (n⩽9) clusters

Polarizability of neutral copper clusters

Neutral copper clusters are characterized through their molecular structures, binding energy and electric dipole polarizability. It is shown that the mean and anisotropy of polarizability tensor are useful properties in the characterization and rationalization of reactivity and growth patterns in copper clusters. We also found a relationship between softness per atom and cubic root polarizability per atom which can be useful to get global softness in copper clusters.

Self-assembly of oxide-supported metal clusters into ring-like structures

Self-assembly is a phenomenon that continuously occurs at the nanoscale, as atoms form predetermined building blocks such as molecules and clusters, which then themselves gather into structures of a larger scale. The interplay of competing forces is a decisive factor in the emergence of these organized systems, but the precise mechanism by which this self-assembly progresses is seldom known. Using a combination of physical cluster deposition and atomic force microscopy, we have investigated the spontaneous formation of μm-sized rings of SiO(x)-supported metal nanoclusters. With the help of molecular dynamics simulations, we show that the competition between short-range van der Waals attractions and long-range repulsive dipolar forces, induced by the ionic surface, plays a key role in the self-assembly of these structures.

Correlations of the stability, static dipole polarizabilities, and electronic properties of yttrium clusters

Static dipole polarizabilities for the ground-state geometries of yttrium clusters (Yn, n < or = 15) are investigated by using the numerically finite field method in the framework of density functional theory. The structural size dependence of electronic properties, such as the highest occupied molecular orbital-lowest occupied molecular orbital (HOMO-LUMO) gap, ionization energy, electron affinity, chemical hardness and softness, etc., has been determined for yttrium clusters. The energetic analysis, minimum polarizability principle, and principle of maximum hardness are used to characterize the stability of yttrium clusters. The correlations of stability, static dipole polarizabilities, and electronic properties are analyzed especially. The results show that static polarizability and electronic structure can reflect obviously the stability of yttrium clusters. The static polarizability per atom decreases slowly with an increase in the cluster size and exhibits a local minimum at the magic number cluster. The ratio of the mean static polarizability to the HOMO-LUMO gap has a much lower value for the most stable clusters. The static dipole polarizabilities of yttrium clusters are highly dependent on their electronic properties and are also partly related to their geometrical characteristics. A large HOMO-LUMO gap of an yttrium cluster usually corresponds to a large dipole moment. Strong correlative relationships of the ionization potential, softness, and static dipole polarizability are observed for yttrium clusters.

Polarizability evolution on natural and artificial low dimensional binary semiconductor systems: A case study of stoichiometric aluminum phosphide semiconductor clusters

The dependences of the static dipole polarizabilities per atom (PPAs) on the bonding and shape of selected stoichiometric aluminum phosphide clusters (ground states and higher lying species) of small and medium sizes have been comprehensively studied at Hartree-Fock and the second order Moller-Plesset perturbation levels of theory. It is shown that the nonmonotonic size variations in the mean PPAs of AlP species which maintain closed cagelike structures, frequently observed in clusters, are directly related to covalent homoatomic bonds inside each cluster's framework. Accordingly, the PPAs of clusters which are characterized by one or more bonds between the Al and P atoms are larger than the PPAs of clusters with the uniform alternating Al-P bond matrix. This is caused by the electron transfer increase from the electropositive Al to the electronegative P atom with the cluster growth. This transfer is larger for the clusters characterized by alternating Al-P bonding. The later effect explains the decrease in the PPA of AlP species which maintain closed cage-like structures, with the cluster growth. However, this picture drastically changes for artificial metastable prolate species built up by the ground states of smaller clusters. It is demonstrated that for prolate binary AlP clusters of medium size, the shape dominates against any other structural or bonding factor, forcing the PPA to increase with the cluster size. Nonetheless, as the cluster size grows, it is predicted that the PPAs of the studied prolate clusters will saturate eventually with the cluster size. Also, it is verified that the theoretical predicted polarizabilities of AlP semiconductor clusters are larger than the bulk polarizability in accord with other theoretical predictions for similar systems. Lastly, it is pointed out that major bonding or structural changes should take place in order the convergence with the bulk polarizability to be accomplished since it is revealed that the size increase is a necessary but not a sufficient factor for the cluster to bulk transition.

First-principles study of intermediate size silver clusters: Shape evolution and its impact on cluster properties

Low-energy isomers of Ag(N) clusters are studied within gradient-corrected density functional theory over the size range of N = 9-20. The candidate conformations are drawn from an extensive structural database created in a recent exploration of Cu(N) clusters [M. Yang et al., J. Chem. Phys. 124, 24308 (2006)]. Layered configurations dominate the list of the lowest-energy isomers of Ag(N) for N < 16. The most stable structures for N > 16 are compact with quasispherical shapes. The size-driven shape evolution is similar to that found earlier for Na(N) and Cu(N). The shape change has a pronounced effect on the cluster cohesive energies, ionization potentials, and polarizabilities. The properties computed for the most stable isomers of Ag(N) are in good agreement with the available experimental data.

Structure and shape variations in intermediate-size copper clusters

Using extensive, unbiased searches based on density-functional theory, we explore the structural evolution of Cu(n) clusters over the size range n=8-20. For n=8-16, the optimal structures are plateletlike, consisting of two layers, with the atoms in each layer forming a trigonal bonding network similar to that found in smaller, planar clusters (n<or=6). For n=17 and beyond, there is a transition to compact structures containing an icosahedral 13-atom core. The calculated ground-state structures are significantly different from those predicted earlier in studies based on empirical and semiempirical potentials. The evolution of the structure and shape of the preferred configuration of Cu(n), n<or=20, is shown to be nearly identical to that found for Na clusters, indicating a shell-model-type behavior in this size range.

Theoretical Study of the Interaction of Molecular Oxygen with Copper Clusters

A new method based on frontier orbital theory has been used to investigate the binding site of molecular oxygen to neutral and anion copper clusters. It has been shown that one can make useful predictions of the binding sites based on the knowledge of the donor local reactivity of the cluster using the condensed Fukui function, f(-)(Ff). In this way, it was found that Cu(3), Cu(5), and Cu(5)(-) have the highest reactivity toward molecular oxygen.

Homonuclear transition-metal trimers

Density-functional theory has been used to determine the ground-state geometries and electronic states for homonuclear transition-metal trimers constrained to equilateral triangle geometries. This represents the first application of consistent theoretical methods to all of the ten 3d block transition-metal trimers, from scandium to zinc. A search of the potential surfaces yields the following electronic ground states and bond lengths: Sc3(2A1',2.83 A), Ti3(7E',2.32 A), V3(2E",2.06 A), Cr3(17E',2.92 A), Mn3(16A2',2.73 A), Fe3(11E",2.24 A), Co3(6E",2.18 A), Ni3(3A2",2.23 A), Cu3(2E',2.37 A), and Zn3(1A1',2.93 A). Vibrational frequencies, several low-lying electronic states, and trends in bond lengths and atomization energies are discussed. The predicted dissociation energies DeltaE(M3-->M2+M) are 49.4 kcal mol(-1)(Sc3), 64.3 kcal mol(-1)(Ti3), 60.7 kcal mol(-1)(V3), 11.5 kcal mol(-1)(Cr3), 32.4 kcal mol(-1)(Mn3), 61.5 kcal mol(-1)(Fe3), 78.0 kcal mol(-1)(Co3), 86.1 kcal mol(-1)(Ni3), 26.8 kcal mol(-1)(Cu3), and 4.5 kcal mol(-1)(Zn3).

First-principles investigations of the polarizability of small-sized and intermediate-sized copper clusters

Density functional theory calculations are used to compute the dipole polarizabilities of copper clusters. Structures for the clusters are taken from the literature for n = 2-32 and several isomers are used for each cluster size for n < or = 10. The calculated polarizabilities are in good agreement with the prediction of a simple jellium model, but much smaller than experimental observations for n = 9-32 [M. B. Knickelbein, J. Chem. Phys., 120, 10450 (2004)]. To investigate this difference, the calculated polarizabilities are tested for the effects of basis set, electron correlation, and equilibrium geometry for small-size clusters (n = 2-10). These effects are too small to account for the theory-experiment gap. Temperature effects are also studied. Thermal expansion of the clusters leads to very small changes in polarizability. On the other hand, the presence of permanent dipoles in the clusters could account for the experimental observations if the rotational temperature of the clusters were sufficiently low. The potential importance of the cluster dipole moments implies that reliable ground-state structures and experimental temperatures are needed to find quantitative agreement between calculated and observed polarizabilities.

Electric dipole polarizabilities of copper clusters

The static electric dipole polarizabilities of Cu(9)-Cu(61) have been measured via a molecular beam deflection method. The clusters display per-atom polarizabilities that decrease monotonically with size, from approximately 16 A(3) per atom Cu(9-10) to approximately 5 A(3) (Cu(45-61)). Absent are any discernible discontinuities or odd-even alternations due to electronic shell filling or electron pairing effects. For the smallest clusters, the experimental polarizabilities are approximately 3 times larger than those predicted classically for conducting ellipsoids, and approach the classical values only for clusters containing more than approximately 45 atoms.

Mechanism for large first hyperpolarizabilities of phosphonic acid stilbene derivatives

This paper presents calculations of dipole moments (mu), static polarizabilities (alpha), and first hyperpolarizabilities (beta) of phosphonic acid stilbene derivatives calculated in the framework of density functional theory. These calculations were performed using a finite field approach implemented in the density functional program ALLCHEM and were of an all-electron type using local exchange-correlation functional and specially designed basis sets. The molecular structures have been fully optimized using the semiempirical program MSINDO. Some of the investigated stilbenes have been synthesized very recently while others are described for the first time. Donor and acceptor groups of these analogues have been modified and the influence of these changes on the first hyperpolarizabilities has been investigated. This work demonstrates that the nonlinear optical response beta of these compounds increases dramatically when the acceptor moiety is displaced by analogues containing alkali metal groups. A general mechanism for the design of novel nonlinear optical materials with large first hyperpolarizabilities is described.