The Formation of Neutral Copper Clusters from Experimental Binding Energies and Reactivity Descriptors

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.

Magnetic properties of small cobalt-copper clusters

Accurate first-principle calculations on bimetallic cobalt-copper clusters of up to six atoms (Pérez et al 2012 J. Nanopart. Res. 14 933) revealed a close similarity of the ground-state magnetic properties to the ultimate jellium model, provided that a 2D to 3D geometric transition was invoked. We discuss this relationship in terms of partial occupancies of the valence electrons in both cases, with the jellium results described by nonperturbative spherical wavefunctions. Based upon this, we propose a scheme to predict magnetic properties of cobalt-copper clusters of up to twenty atoms using arguments of dimensionality and charge localization, and confirm some of these results with other independent density-functional calculations and experimental available data. The comparison with experiments is carried out for neutral and singly ionized cobalt clusters. Furthermore, a many-body tight-binding pseudopotential is used with Monte Carlo techniques to verify the stability of these new first-principle solutions.

Density functional study of structural and electronic properties of small binary Be(n)Cu(m) (n + m = 2~7) clusters

The geometrical structures, electronic properties and relative stabilities of small bimetallic Be n Cu m (n + m = 2-7) clusters have been systematically investigated by using a density functional method at the B3PW91 level. In the most stable structures of Be n Cu m , the Be atoms tend to gather together and construct similar configurations to those of pure Be n clusters. Meanwhile, there is a tendency for Cu atoms to segregate toward the Be n cluster surface. The successive binding energies, cohesive energies, second difference of energies, the highest occupied-lowest unoccupied molecular orbital energy gaps and chemical hardness of Be n Cu m are also investigated. All of them demonstrate that the clusters with even number of copper atoms present relatively higher stabilities. The natural population analyses on the Be n Cu m clusters reveal that, the charge transfers from Be to Cu when the average coordination numbers (Nc) of Be atom is less than 3, whereas the charge-transferring direction reverses when Nc(Be) increases.

Icosahedral to double-icosahedral shape transition of copper clusters

The lowest-energy isomers of Cu(N) clusters for N = 20-30 are identified using an unbiased search algorithm and density functional theory calculations. The low-energy structures over this size range are dominated by those based on a 13-atom icosahedral (I(h)) core and a 19-atom double icosahedron (DI(h)) core. A transition in the ground-state isomers from I(h)-based to DI(h)-based structures is predicted overt N = 21-23. We discuss this transition in the broader context of the growth pattern for Cu(N) over N = 2-30 that features regions of gradual evolution in which atoms successively add to the cluster surface, separated by sudden changes to a different structural organization and more compact shape. These transitions result from a competition between interatomic bonding energy and surface energy. The implications of this growth pattern for the further evolution of copper from microstructure to bulk are discussed.

Ruling out any electrophilicity equalization principle

Two gas-phase electrophilicity indices, ω(1) and ω(2), introduced by Parr, von Szentpály, and Liu are tested with respect to the recently proposed "principle of electrophilicity equalization." Although electronegativity is equalized in many cases, there is no functioning "hardness equalization principle" nor are the electrophilicity indices principally equalized during molecule formation: they cannot be generally expressed as the mean of the corresponding atomic indices. For large metal clusters and [n]fullerenes, both electrophilicity indices increase proportional to n(1/3) and n(1/2), respectively, as the hardness values converge to zero. Two "principles" are shown to be obsolete: the "geometric mean principle for hardness equalization" and the "principle of electrophilicity equalization", with the latter somewhat relying on the former. An appeal is made to exercise careful judgment before proposing and publishing new structural principles.

Assessment of density functional theory optimized basis sets for gradient corrected functionals to transition metal systems: The case of small Nin (n⩽5) clusters

Density functional calculations have been performed for small nickel clusters, Ni(n), Ni(n) (+), and Ni(n)(-) (n<or=5), using the linear combination of Gaussian-type orbital density functional theory approach. Newly developed nickel all-electron basis sets optimized for generalized gradient approximation (GGA) as well as an all-electron basis set optimized for the local density approximation were employed. For both neutral and charged systems, several isomers and different multiplicities were studied in order to determine the lowest energy structures. A vibrational analysis was performed in order to characterize these isomers. Structural parameters, harmonic frequencies, binding energies, ionization potentials, and electron affinities are reported. This work shows that the employed GGA basis sets for the nickel atom are important for the correct prediction of the ground state structures of small nickel clusters and that the structural assignment of these systems can be performed, with a good resolution, over the ionization potential.

Effect of Ni and Pd on the Geometry, Electronic Properties, and Active Sites of Copper Clusters

The geometry, electronic properties, and active sites of copper clusters doped with Ni or Pd atoms, Cu(n)()(-)(1)M (n = 2-6; M = Ni, Pd) have been investigated using first-principles methods. Planar structures are energetically favorable in Cu(n)()(-)(1)Ni (n = 2-6). However, for Pd-doped clusters, three-dimensional structures are competitive in energy, and for n = 6, the most stable structure is not planar. Several properties of doped copper clusters present odd-even oscillations as the number of copper atoms grow. The different atomic ground-state configuration of Ni and Pd determines the bonding and electronic properties of doped copper clusters. The interaction between impurities and copper atoms can modify the chemical hardness and active sites of doped copper clusters markedly inducing directionality in the reactivity. This effect is relevant to the behavior of catalysts as well as in the growth of metallic films.

Molecular Structure and Bonding of Copper Cluster Monocarbonyls CunCO (n = 1−9)

In this work we analyze CO binding on small neutral copper clusters, Cun (n = 1-9). Molecular structures and reactivity descriptors of copper clusters are computed and discussed. The results show that the condensed Fukui functions and the frontier molecular orbital theory are useful tools to predict the selectivity of CO adsorption on these small clusters. To get further insight into the CO binding to copper clusters, an energy decomposition analysis of the CO binding energy is performed. The Cs symmetry of the formed CunCO clusters (n = 1-8) allows the separation between the orbital interaction terms corresponding to donation and back-donation. It is found that, energetically, the donation is twice as important as back-donation.