Multiple locations of boron atoms in the exohedral and endohedral C60 fullerene

Abstract

We study theoretically the bound states of one and two boron atoms in the exohedral and endohedral ${\mathrm{C}}_{60}$ fullerene. The optimal position of one boron atom is found above the midpoint of the ${\mathrm{C}}_{60}$ double bond in the exohedral complex, and at the center of ${\mathrm{C}}_{60}$ or below a carbon atom in the endohedral complex. However, the optimal position of a boron atom is often altered when the second boron atom is added to the molecular complex. For two boron atoms outside the cage the optimal arrangement is realized when the ${\mathrm{B}}_{2}$ molecule is attached by one boron atom to a double bond midpoint of ${\mathrm{C}}_{60}$ or when two boron atoms are above two double bond midpoints on opposite sides of ${\mathrm{C}}_{60}$. Two endohedral boron atoms can lie on the line joining either two opposite double bond midpoints or two centers of opposite pentagons. The latter case corresponds to the optimal geometry of the ${\mathrm{B}}_{2}$@${\mathrm{C}}_{60}$ complex provided that two boron atoms are close enough to form the ${\mathrm{B}}_{2}$ molecule. In case one boron atom is inside while the other is outside the cage, the optimal locations of atoms are above and below two neighboring carbon atoms belonging to the same hexagon of ${\mathrm{C}}_{60}$. Remarkably, all these optimal arrangements have different spin states: in the exohedral complex ${\mathrm{B}}_{2}{\mathrm{C}}_{60}\phantom{\rule{4pt}{0ex}}S=1$, in the endohedral ${\mathrm{B}}_{2}$@${\mathrm{C}}_{60}\phantom{\rule{4pt}{0ex}}S=2$ (as in the isolated ${\mathrm{B}}_{2}$ molecule), whereas for one boron atom inside and the other outside the cage $S=0$. The effective (Bader) charge of boron in these configurations varies appreciably---from $0.06e$ at the center of ${\mathrm{C}}_{60}$ to $2e$ in the ${\mathrm{B}}_{2}{\mathrm{C}}_{58}$ molecule with two boron atoms substituting for two carbon atoms in ${\mathrm{C}}_{60}$. We also discuss various conformations in the exohedral and endohedral molecular complexes.