The Structure of carbodiimide has been studied by using quantum chemical methods. Carbodiimide (HNCNH) has been detected towards Sagittarius B2 (N) in interstellar medium (ISM). Two reaction mechanisms have been proposed to study the formation of interstellar Carbodiimide. The first reaction mechanism is based on molecule-radical and the second one is a radical-radical mechanism, through previously detected interstellar molecules or radicals. Quantum chemical calculations have been performed by using density functional theory (DFT) and Moller-Plesset second order perturbation (MP2) theory, in gas phase as well as in polarizable continuum model (PCM). The proposed reaction paths are exothermic and barrierless which indicates the possibility of carbodiimide formation in ISM. Several basis sets have been used to verify the validity and accuracy of the results. The isotropic and anisotropic polarizabilities of carbodiimide have been calculated from relevant tensor components for both reaction mechanisms with the help of data obtained by DFT/B3LYP and MP2 methods using aug-cc-pVTZ basis sets in gaseous phase as well as in PCM.