1.5.2 Electronic Structure of o-A₁C₆₀

The degree of one dimensionality of the electronic structure of polymeric o-A₁C₆₀ is not clear at the present time. As mentioned above the NMR and ESR are suggestive of 1d behaviour, but calculations based on the accurate polymer structure[69] suggest that interchain couplings are probably important. This is because electronic motion along the C₆₀ chains is impeded by the nearly sp³ orbitals of the carbon atoms at the C₆₀-C₆₀ bonds. Other band structure calculations of polymeric C₆₀ chains have also been performed[70]. It is clear that the molecular distortion in the polymeric o-A₁ makes the rigid band picture based on the I_h symmetry of the undistorted C₆₀ highly suspect. The distortion lifts the I_h symmetry, and splits the t_1u LUMO. If this splitting is greater than the bandwidth, it may be that the A₁ conduction band is formed from a non-degenerate molecular level and is hence half-full. NMR measurements on Rb₁ under pressure support the three dimensional nature of electronic structure[71]. Moreover, the low temperature magnetic phase is found to be eliminated under pressures exceeding about 6kbar.

Potential magnetic structures for o-A₁ have been considered theoretically[72]. By including a short range repulsive electron-electron interaction together with the band structure of [69], it is found that a complex 3d magnetic state is stable. These authors also note that for certain regions of the antiferromagnetic couplings, the magnetic ordering is geometrically frustrated.

  

Figure 1.1: A truncated icosahedron: The geometric form has 60 vertices, 12 pentagonal faces, and 20 hexagonal faces. The C₆₀ molecule contains a carbon at each vertex, C-C double bonds along the lines separating hexagons, C-C single bonds along the hexagon-pentagon boundaries, and has a diameter of roughly 7.1Å.