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 M?ller-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.