Bipolaron Formation in B₁₂ and (B₁₁C)⁺ Icosahedra

Abstract

Boron carbides, B_1-xC_x with 0.085 ≤ × ≤ 0.200, generally contain both B₁₂ and B₁₁C icosahedra. However, the electronic transport with 0.1 ≤ × ≤ 0.2 is believed to occur by means of bipolaron hopping between only B₁₁ C icosahedra [i]. We have calculated the changes in energy, atomic positlions and charge distribution when a pair of electrons is added to the isoelectronic icosahedral clusters B₁₂ and (B₁₁C)⁺. We simulate an icosahedron in a neutral lattice by bonding the icosahedral atoms to hydrogenic atoms which we constrain to be neutral. The computations are performed with a self-consistent molecular-orbital method, PRDDO.

We find a total energy reduction of -3.7 eV for two electrons added to a B₁₂ icosahedron. Of this, -2.7 eV arises from the electrons filling the icosahedron’s bonding orbitals. The remaining -1.0 eV comes from the contraction of the icosahedron’s radius by -0.09 Å. For two electrons added to a (B₁₁C)⁺ icosahedron we find a total energy reduction of -18.2 eV. Of this, -16.5 eV arises from filling the icosahedron’s bonding orbitals. The remainder arises frop a -0.09 Å contraction of the icosahedron’s radius. Thus, we find (B₁₁C) icosahedra to be strongly energetically favored over B₁₂ icosahedra as bipolaron sites.

The positive charge associated with a (B₁₁C)⁺ icosahedron is distributed over the eleven boron atoms. Concomitantly, we find the added two electrons of the bipolaron to be distributed over all twelve sites of the B₁₁C icosahedron. We find the energy difference between an electron pair added to B₁₂ and (B₁₁C)⁺ icosahedra to arise principally from the increased Coulomic attraction provided by the extra positive charge of the (B₁₁C) icosahedron.