Charged and magnetic fullerenes of silicon by metal encapsulation: Predictions from ab initio calculations

Using ab initio calculations, we show that the encapsulation of Y, La, and Ac metal $\left(M\right)$ atom stabilizes the dodecahedral fullerene anion $M@\mathrm{Si}_{20}{}^{-}$ in the icosahedral symmetry. Similar to ${\mathrm{C}}_{60}$, it is the ideal cage of silicon and the largest that can be stabilized by an $M$ atom. Doping of other rare earths is further shown to stabilize magnetic dodecahedral fullerenes $\mathrm{Pa}@{\mathrm{Si}}_{20}$, $\mathrm{Sm}@{\mathrm{Si}}_{20}$, $\mathrm{Pu}@{\mathrm{Si}}_{20}$, and $\mathrm{Tm}@{\mathrm{Si}}_{20}$ with $1{\mu }_{\mathrm{B}}$, $4{\mu }_{\mathrm{B}}$, $4{\mu }_{\mathrm{B}}$, and $3{\mu }_{\mathrm{B}}$ spin magnetic moments, respectively, in contrast to most previous studies on $M$-encapsulated Si clusters in which the magnetic moment is completely quenched. The highest spin magnetic moment of $7{\mu }_{\mathrm{B}}$ is achieved for $\mathrm{Gd}@\mathrm{Si}_{20}{}^{-}$ with half-filled $4f$ states. The orbital magnetic moment is also calculated and it is $\sim 1{\mu }_{\mathrm{B}}$ in most cases. Neutral $M@{\mathrm{Si}}_{20}$ ($M=\mathrm{Y}$, La, Ac, and Gd) behaves like superhalogen and interaction with a noble or alkali metal atom leads to salt like behavior. These findings could pave way for the realization of silicon fullerenes by doping of several elements.

Figure 1

(Color online) Optimized structures for neutral $M@{\mathrm{Si}}_{20}$, ($M=\mathrm{Y}$, La, Ac, Sm, Gd, and Tm) and icosahedral $M@\mathrm{Si}_{20}{}^{-}$ anions ($M=\mathrm{Y}$, La, and Ac). Fullerenes with $M=\mathrm{Ce}$, ${\mathrm{Pa}}^{+}$, Pa, ${\mathrm{Np}}^{-}$, Pu, and ${\mathrm{Gd}}^{-}$ have $T_h$ symmetry as for Sm and Tm while the neutral fullerenes of Y, La, Ac, and Gd are Jahn-Teller distorted. Blue (magenta) balls show Si $\left(M\right)$ atoms.

Figure 2

(Color online) Electronic energy spectra of $\mathrm{La}@\mathrm{Si}_{20}{}^{-}$, $\mathrm{Sm}@{\mathrm{Si}}_{20}$, $\mathrm{Gd}@\mathrm{Si}_{20}{}^{-}$, and $\mathrm{Tm}@{\mathrm{Si}}_{20}$ fullerenes. Broken lines show unoccupied states. Arrows correspond to the up- and the down-spin spectra. The general features of the spectra are similar except for the $4f$ levels of the $M$ atoms that are marked. These hybridize with the $\mathrm{n}F$ states of the Si cage. For La doped anion, the spectrum has icosahedral symmetry. However, in other cases the symmetry is reduced to $T_h$ due to small changes in the bond lengths which lead to the splitting of the fivefold $\left(H\right)$ and fourfold $\left(G\right)$ symmetry states.

Figure 3

(Color online) (a) Total pseudocharge density isosurface for $\mathrm{Gd}@\mathrm{Si}_{20}{}^{-}$ shows covalent bonding as charge is concentrated in Si-Si bonds. (b) and (c) show the down- and up-spin magnetic polarizations. The magnetic moments are strongly localized around the Gd ion. Small polarization of the same spin is induced around the eight neighboring Si ions as in (b) while a small polarization of opposite spin is induced around the remaining twelve Si ions as in (c). Gd (Si) ion is shown in magenta (blue).

Figure 4

(Color online) (a) Optimized structure of $\mathrm{Cu}\text{−}\mathrm{La}@{\mathrm{Si}}_{20}$ and (b) the isosurface of the total pseudocharge density. Cu is shown by brownish color. The density around Cu is mainly due to $3d$ electrons.