Orientational ordering and binding in alkali doped C60 solids

The binding energy of K3C60, a conductor, is described well by an ionic solid type calculation. This succeeds because there is little overlap between molecular wave functions on neighbouring sites, so that electrons are practically localized on-shell. This leads one to believe that even in K4C60 and K6C60 systems, such calculation may suffice. However, the on shell Coulomb repulsion is large for the C-60 molecule. So, for large charge on the anion, there is a possibility for some electrons to delocalize and go into the s-band. In the calculation of binding energy, we keep these delocalised electrons x, as a parameter and minimize the energy w.r.t. it. We take the intermolecular interaction to be arising out of a C-C potential of 6-exp form (Kitaigorodsky) and a screened Coulomb interaction between the anions and cations and among themselves. The screening is provided by the electrons delocalised from the anion which supposedly go into the s-band of the cations, and are modeled by a free electron fermi gas. The energy of the anion (to be added to the lattice sum) takes into account the onsite Coulomb energy, and is thus a quadratic function of anion charge. The delocalised electrons go into s-band whose position is estimated and corresponding energy added. Model calculations are presented for K1C60, K3C60, K4C60 and K6C60 for which the minimum energy state shows no delocalisation. Cohesive Energy dependence on Lattice constant is used to calculate Bulk Modulus for all systems. We have got a reasonably good resemblance with experimental values. Further, we observe that the cohesive energy shows poor resemblance with experimental values. This can be explained by invoking orientation in these calculations. Further, delocalisation of a fraction of electron at the centre of double bond show considerable increase in cohesive energy.