Study of the Structural and Electronic Properties of [Ti@Si₁₆]_n, [Sc@Si₁₆K]_n, and [V@Si₁₆F]_n (n ≤ 9) Aggregates from First Principles

Recent experimental and theoretical work has established that the ground state and low-lying energy isomers of endohedral M@Si 16 clusters (M = Sc −, Ti, or V + ) have a nearly spherical cagelike form, an atomic-like closed shell electronic structure, and a large highest occupied molecular orbital (HOMO)−lowest unoccupied molecular orbital (LUMO) gap of ∼2 eV, which suggests the use of these clusters as basic units (superatoms) in the assembly of optoelectronic materials. As a first step in that direction, in this work are studied, by means of first-principles calculations, the trends in the formation of [Ti@Si 16 ] n, [Sc@Si 16 K] n, and [V@Si 16 F] n aggregates as their sizes increase ( n ≤ 9). We identify especially stable linear, planar, and three-dimensional patterns that can be used to grow low-dimensional periodical systems. When n ≥ 2, the aggregates with greater binding energy result from the bonding of n supermolecular units having D 4 d symmetry for the M@Si 16 cage, instead of the Frank−Kasper symmetry ground state of the basic superatom. Particularly interesting aggregates are (i) [Ti@Si 16 ] n rings when n ≥ 6, which can be grown as wires or nanotubes; (ii) rings and linear forms of [Sc@Si 16 K] n aggregates having a rich variety of nearly degenerate isomers differing in the bonding site of K atoms and strongly varying electric dipole moments; and (iii) [M@Si 16 X] 3 m wires ( m = 1−3) formed by vertically stacking the [M@Si 16 X] 3 starlike trimer with rotation of 60° between consecutive trimer units, which show interesting magnetic configurations for M = V and X = F. The HOMO−LUMO gap for the most favorable structure decreases with size, and the aggregates become nearly metallic when n ≤ 9.