The parity (P) and time reversal (T) violating electric dipole moment of the electron (eEDM) is an important non-accelerator probe of particle physics, and is also relevant to our understanding of the matter-antimatter asymmetry in the universe. This particle physics property can be obtained by measuring a shift in the energy of a molecule in some state due to the eEDM, and combining it with a quantity, the effective electric field, which can only be calculated using relativistic many-body theory. The eEDM has not yet been detected; the best upper bounds have been obtained using ThO, followed by HfF+ and YbF. In light of tremendous advances in experimental techniques as well as many-body theory and high performance computing in recent times, the search for better molecu lar candidates becomes very relevant and useful to search for new physics. In this talk, we shall discuss some of the molecular candidates that we proposed, for future eEDM search experiments.