Defective to fully coordinated crossover in complex directionally bonded nanoclusters

Defect-free fully coordinated (FC) structures are well known to be highly stable for a number of materials exhibiting three-coordinated bonding at the nanoscale (e.g., ${\text{C}}_{60}$). For topologically more complex nanosystems with higher bonding connectivities the structures and stabilities of the lowest energy FC structures with respect to low-energy defective isomers are unknown. Herein, we describe a general method to thoroughly search through the low-energy geometries of only those nanoclusters that possess FC atomic connectivities. As a pertinent example of our approach we investigate four-connected ${\text{SiO}}_2$, a fundamentally important network-forming material used in many applications at the nanoscale. Using our method we predict that a structurally complex stability crossover from defective to FC nanoclusters occurs in ${\text{SiO}}_2$ at a size of $\sim 100$ atoms. At variance with previous works, based on constructing FC ${\text{SiO}}_2$ cagelike nanoclusters by hand, we also show that cagelike clusters are only favored for smaller cluster sizes with dense FC topologies becoming energetically favored with increasing system size.

Figure 1

(Color online) Structures, symmetries, and total energies $\left(\text{eV}/{\text{SiO}}_2\right)$ of lowest energy ${\left({\text{SiO}}_2\right)}_{12}$ FC nanoclusters (1–1 to 1–7) relative to the ground state (GS).

Figure 2

(Color online) Structures, symmetries, and total energies $\left(\text{eV}/{\text{SiO}}_2\right)$ of lowest energy ${\left({\text{SiO}}_2\right)}_{18}$ FC nanoclusters (2–1 to 2–7) relative to the ground state (GS).

Figure 3

(Color online) Structures, symmetries, and total energies $\left(\text{eV}/{\text{SiO}}_2\right)$ of lowest energy ${\left({\text{SiO}}_2\right)}_{24}$ FC nanoclusters (3–1 to 3–7) relative to the ground state (GS).

Figure 4

Total energies and average deviation from tetrahedrality of GS and lowest energy FC ${\left({\text{SiO}}_2\right)}_N$ nanoclusters for $N=12,18,24$ (inset: power-law fit to the total energy difference between correspondingly sized GS and lowest energy FC clusters).

Figure 5

(Color online) Comparison of total energy differences $\left(\text{eV}/{\text{SiO}}_2\right)$ between three FC ${\text{Si}}_{30}{\text{O}}_{60}$ (4–1 to 4–3) clusters as calculated by DFT $\left(\text{B}3\text{LYP}/6\text{−}31{\text{G}}^{\ast }\right)$ and the potentials: BKS (Ref. 31), TTAM (Ref. 32), and FB (Ref. 18).