EN
In the present study we investigate the role of van Hove singularity on the optimization of T_c in Rb doped fullerenes C_{60} Rb_3. A first principles self-consistent full potential linear muffin-tin orbital method using density functional theory in local density approximation was employed. The doped Rb atoms are of two types occupying the tetrahedral and interstitial positions in the fcc lattice. The added Rb atoms fill the t_{1u} band of the undoped fullerenes C_{60} up to half which makes C_{60}Rb_3 conducting. Saddle points leading to van Hove singularities are observed in the neighbourhood of the symmetry point L. The shifting of the van Hove singularity with the volume of the lattice is investigated. We observe a saddle point just at the Fermi level for a lattice constant of 14.435Å. The highest value of T_c should thus be observed at the above lattice constant. This result is in excellent agreement with the observed high value of T_c measured in C_{60}Rb_3 for a lattice constant of 14.435Å.