A density functional study of small copper clusters: Cun (n⩽5)

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.

Size-Specific Reactions of Copper Cluster Ions with a Methanol Molecule

Chemisorption of a methanol molecule onto a size-selected copper cluster ion, Cu(n)+ (n = 2-10), and subsequent reactions were investigated in a gas-beam geometry at a collision energy less than 2 eV in an apparatus based on a tandem-type mass spectrometer. Mass spectra of the product ions show that the following two reactions occur after chemisorption: dominant formation of Cu(n-1)+(H)(OH) (H(OH) formation) in the size range of 4-5 and that of Cu(n)O+ (demethanation) in the size range of 6-8 in addition to only chemisorption in the size range larger than 9. Absolute cross sections for the chemisorption, the H(OH) formation, and the demethanation processes were measured as functions of cluster size and collision energy. Optimized structures of bare copper cluster ions, reaction intermediates, and products were calculated by use of a hybrid method (B3LYP) consisting of the molecular orbital and the density functional methods. The origin of the size-dependent reactivity was explained as the structural change of cluster, two-dimensional to three-dimensional structures.

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.