The design of potential and new electrochemically stable electrolytes for Li-ion batteries is an important task in the field of energy. Room temperature ionic liquids (RTILs) characterized by a wide electrochemical window (EW) are the commonly used electrolytes for Li battery applications. In this work, a novel quantum computational method is proposed to estimate the electrochemical stability of RTILs that accurately predicts the trends in EWs of ammonium based ILs and is computationally faster than the state-of-the-art methods. Subsequently, the EW of ILs with phosphonium and sulfonium cations are computed and compared against the well-established ammonium congeners. Based on the criterion of electrochemical stability defined with respect to Li, the increasing order of stability is found to be: sulfonium < ammonium < phosphonium based ILs. The effect of various substituents like butyl, phenyl and benzyl on the phosphonium and sulfonium based ILs is examined and a greater stability for the phenyl over other substituents is observed. The key factor influencing the reduction potential of the cations is inferred as the thermodynamic stability of the radical formed during decomposition. Based on the results, design guidelines to identify stable IL systems as electrolytes in high voltage Li-ion battery applications are provided.