Electronic structure of coinage metal clusters

Quantifying electron-correlation effects in small coinage-metal clusters via ab initio calculations

We investigate many-electron correlation effects in neutral and charged coinage-metal clusters Cun, Agn, and Aun (n = 1-4) via ab initio calculations using fixed-node diffusion Monte Carlo (FN-DMC) simulations, density functional theory (DFT), and the Hartree-Fock (HF) method. From very accurate FN-DMC total energies of the clusters and the HF results in the infinity large complete-basis-set limit, we obtain correlation energies in these strongly correlated many-electron clusters involving d orbitals. The obtained bond lengths of the clusters, atomic binding and dissociation energies, ionization potentials, and electron affinities are in satisfactory agreement with the available experiments. In the analysis, the electron correlation effects on these observable physical quantities are quantified by relative correlation contributions determined by the difference between the calculated FN-DMC and HF results. We show that the correlation contribution is not only significant for the quantities related to electronic structures of the coinage-metal clusters, such as electron affinity, but it is also essential for the stability of the atomic structures of these clusters. For example, the electron correlation contribution is responsible for more than 90% of the atomic binding energies of the small neutral copper clusters. We also demonstrate the orbital-occupation dependence of the correlation energy and electron pairing of the valence electrons in these coinage-metal clusters from the electron correlation-energy gain and spin-multiplicity change in the electron addition processes, which are reflected in their ionization potentials and electron affinities.

Relativistic-consistent electron densities of the coinage metal clusters M2, M4, M4(2-), and M4Na2 (M = Cu, Ag, Au): a QTAIM study

We employ second-order Møller-Plesset perturbation theory level in combination with recently developed pseudopotential-based correlation consistent basis sets to obtain accurate relativistic-consistent electron densities for small coinage metal clusters. Using calculated electron densities, we employ Bader's quantum theory of atoms in molecules (QTAIM) to gain insights into the nature of metal-metal bonding in the clusters M(2), M(4), M(4)(2-), and M(4)Na(2) (M = Cu, Ag, Au). For the simplest case of the metal dimer, M(2), we correlate the strength of the metal-metal bond with the value of the electron density at the bond critical point, the total energy density at the bond critical point, the sharing (delocalization) index, and the values of the two principle negative curvatures. We then consider changes to the metal-metal bonding and charge density distribution upon the addition of two metal atoms to form the metal tetramer, M(4), and then followed by the addition of an electron pair to form M(4)(2-) and finally followed by the addition of two alkali metal (sodium) ions to form M(4)Na(2). Using topological properties of the electron density, we present evidence for the existence of σ-aromaticity in Au(4)(2-). We also report the existence of two non-nuclear attractors in the molecular graph of Cu(4)(2-) and large negative charge accumulation in the nonbonded Cu basins of this cluster.

Evidence for d Orbital Aromaticity in Square Planar Coinage Metal Clusters

Quantitative evidence for the existence of aromaticity involving the d orbitals of transition metals is provided for the first time. The doubly bridged square planar (D(4)(h)()) coinage metal clusters (M(4)Li(2), M = Cu (1), Ag (2), and Au (3)) are characterized as aromatic by their substantial nucleus independent chemical shifts (NICS) values in the centers (-14.5, -14.1, and -18.6, respectively). Nevertheless, the participation of p orbitals in the bonding (and cyclic electron delocalization) of 1-3 is negligible. Instead, these clusters benefit strongly from the delocalization of d and to some extent s orbitals. The same conclusion applies to Tsipis and Tsipis' H-bridged D(4)(h)() Cu(4)H(4) ring (4). Canonical MO-NICS analysis of structures 1-3 shows the total diatropic d orbital contributions to the total NICS to be substantial, although the individual contributions of the five sets of filled d orbitals vary. The d orbital aromaticity of Cu(4)Li(2) also is indicated by its atomization energy, 243.2 kcal/mol, which is larger than Boldyrev's doubly (sigma and pi) aromatic Al(4)Li(2) (215.9 kcal/mol).

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.