In many experimental situations, the interaction potential between the tagged solute and the solvent molecules is often different from that between the two solvent molecules. In such cases, the Stokes-Einstein relation attempts to describe the self-diffusion of the solute in terms of an effective hydrodynamic radius which, along with the hydrodynamic boundary condition (slip or stick), are varied to fit the experimental results. Extensive molecular dynamics (MD) simulations have been carried out to obtain the diffusion coefficient by varying interaction between the solute and the solvent. It is found that when this interaction is more repulsive than that between solvent-solvent, the diffusion can be significantly faster, leading to a complete breakdown of the Stokes-Einstein relation. In the limit of strong attractive interaction, we recover a dynamic version of the solvent-berg picture. The diffusion coefficient of the solute is found to depend strongly and nonlinearly on the magnitude of this specific interaction. The velocity correlation function also shows an interesting dependence on the sign and magnitude of the specific interaction. Another potentially important observation is that the specific solute-solvent interaction can induce a crossover from a sliplike to a stick-like diffusion, if one still uses the hydrodynamic language. Mode coupling theory analysis of the friction shows that the change in it originates largely from the modification of the binary component of the total friction. This is because the cage structure around the solute is modified due to the specific solute-solvent interaction, which directly affects the binary dynamics.