Evolution of the electronic and structural properties of microclusters

The equilibrium geometries of the ground state of neutral and ionized clusters of Li, Be, Mg, and C atoms have been obtained by minimizing the total energies of these clusters with respect to all independent bond lengths, bond angles, and spin structures. Our method is based on the all-electron self-consistent field–linear combination of atomic orbitals–molecular orbital (SCF-LCAO-MO) method. The exchange interaction is treated at the unrestricted Hartree-Fock level and the correlation contribution is included by using the perturbative Möller-Plesset scheme and configuration interaction. The equilibrium geometries of ${\mathrm{Li}}_{\mathrm{N}}$ clusters for 1<N<6 are planar. ${\mathrm{Be}}_3$ and ${\mathrm{Mg}}_3$ clusters are in the shape of an equilateral triangle whereas ${\mathrm{Be}}_4$ and ${\mathrm{Mg}}_4$ are in the shape of a perfect tetrahedron. ${\mathrm{C}}_{\mathrm{N}}$ clusters for N<3 are linear, but ${\mathrm{C}}_4$ is a rhombus contrary to earlier predictions. It is demonstrated that the ground-state geometries of both neutral and ionized clusters of simple metals, including their preferred spin-multiplet structures, can be understood in terms of a simple bonding-antibonding picture. The ‘‘magic numbers’’ in the mass spectra are discussed in terms of the electronic structure of clusters. It is shown that the magic numbers associated with the initially ‘‘neutral’’ or initially ‘‘ionized’’ clusters can be different and that the fragmentation of clusters during the ionization process can add to the ambiguity in the interpretation of magic numbers. Finally, we elaborate on the relationship between equilibrium geometries and preferred spin-multiplet structures by confining our discussion to ${\mathrm{Li}}_4$ and ${\mathrm{Na}}_4$ clusters.