Lowest-energy endohedral fullerene structures of ${\mathrm{Si}}_{\mathrm{N}}$ $(30⩽\mathrm{N}⩽39)$ clusters by density functional calculations

The endohedral fullerene structures of medium-sized ${\mathrm{Si}}_{\mathrm{N}}$ $(30⩽\mathrm{N}⩽39)$ clusters have been studied using the density functional theory (DFT) with gradient correction. For each cluster size, fullerene cages with different topologies and those filled by a different number of atoms were constructed. These cage isomers were then optimized by DFT-based molecular dynamic relaxations followed by numerical optimization. Compared with recent theoretical calculations [S. Yoo, J. J. Zhao, J. L. Wang, and X. C. Zeng, J. Am. Chem. Soc. 126, 13845 (2004)], the energies of the lowest-energy fullerene cage structures obtained here are lower for most clusters. In particular, the optimal filling and/or cage combination ratios for ${\mathrm{Si}}_{37}$ and ${\mathrm{Si}}_{38}$ were found to be ${\mathrm{Si}}_5@{\mathrm{Si}}_{32}$ and ${\mathrm{Si}}_6@{\mathrm{Si}}_{32}$, different from the previously proposed ones (${\mathrm{Si}}_3@{\mathrm{Si}}_{34}$ and ${\mathrm{Si}}_4@{\mathrm{Si}}_{34}$).

Figure 1

(Color online) The lowest-energy endohedral fullerene structures from this work [denoted as (a)] and obtained in Ref. 20 [denoted as $\left(R\right)$] for medium-sized ${\mathrm{Si}}_{\mathrm{N}}$ $(30⩽\mathrm{N}⩽39)$ clusters. The interior filling atoms are highlighted.

Figure 2

Binding energy per atom $\left(E_{\mathrm{b}}\right)$ of medium-sized ${\mathrm{Si}}_{\mathrm{N}}$ $(30⩽\mathrm{N}⩽39)$ clusters as a function of the inverse of the cluster radius ${\mathrm{N}}^{–1∕3}$. The theoretical results (black squares) obtained for the lowest-energy structures are compared to experimental data given by Eq. (2). We used the bulk binding energy $E_{\mathrm{b}}\left(\infty \right)=4.58\mathrm{eV}$ from GGA calculations with a shift of $-0.023\mathrm{eV}$ for a better coincidence.