Energy Landscape of Fullerene Materials: A Comparison of Boron to Boron Nitride and Carbon

Using the minima hopping global geometry optimization method on the density functional potential energy surface we show that the energy landscape of boron clusters is glasslike. Larger boron clusters have many structures which are lower in energy than the cages. This is in contrast to carbon and boron nitride systems which can be clearly identified as structure seekers. The differences in the potential energy landscape explain why carbon and boron nitride systems are found in nature whereas pure boron fullerenes have not been found. We thus present a methodology which can make predictions on the feasibility of the synthesis of new nanostructures.

Figure 1

The configurational energy spectrum of ${\mathrm{B}}_{16}{\mathrm{N}}_{16}$. Boron atoms are shown in blue (dark gray) and nitrogen atoms in red (medium gray). The higher energy cage structures can be described as a “basket” with a “handle” made out of a chain of 4 atoms (two of each type).

Figure 2

Global minima of ${\mathrm{B}}_{32}$, ${\mathrm{B}}_{33}$, and ${\mathrm{B}}_{34}$.

Figure 3

The configurational energy spectrum of ${\mathrm{B}}_{80}$. The energy of the Szwacki fullerene is taken to be zero. The energy levels of the icosahedron-dome structures are centered whereas the levels shifted to the left are fullerenelike structures. The levels on the right correspond to centered icosahedron structures. The atoms of the icosahedra are shown in yellow (light gray). The structure at an energy of $-2.7\mathrm{eV}$ is the putative global minimum from Ref 8. The energy per atom of our lowest energy ${\mathrm{B}}_{80}$ structure is about 0.13 eV per atom higher in energy than the sheet structure of Tang and Ismail-Beigi [17].

Figure 4

Two high energy ${\mathrm{C}}_{60}$ cage structures. The structure on the left has only threefold coordinated atoms even though it contains two seven-member rings. It is 20.5 eV above the ground state. Structures that are even higher in energy can possess some chains with twofold coordination and anchor atoms for these chains with fourfold coordination. The structure on the right is an example of such a cage and is 25 eV higher than the ground state.

Figure 5

The isosurfaces of the valence charge density in our lowest ${\mathrm{B}}_{80}$ cluster and the ${\mathrm{C}}_{60}$ fullerene. They are evaluated at 70% of the maximum value (0.12 a.u. respectively 0.24 a.u.). Whereas in ${\mathrm{C}}_{60}$ we see only two center bonds, both 2 and 3 center bonds are visible in ${\mathrm{B}}_{80}$.