We have investigated the structure and stability of alkali- Rare gas ionic and neutral small clusters (LiXe− Li Xe) for n varying from 1 to 35. The potential energy surface is constructed using a simple additive Model, in which the pair interaction potentials for LiXe , Li Xe and are taken from the best available ab initio calculations. Once the potential energy surface is formed, it is explored by the MonteCarlo optimisation method to determine the stable structures, magic numbers and isomers. The energy of these clusters are investigated to explain the stability which can be compared with experimental mass spectra. A three core interaction is also introduced to the potential energy surface to understand its effect on the structure, stability and properties. The relative stability of the LiାXe୬ − Li Xe୬ ionic and neutral clusters is studied by calculating the energy per Xenon atom and the first and second....