ab initio calculations have been performed using qu antum chemical method to compute optimized geometries, atomic charges, harmonic vibr ational frequencies along with intensities in IR and Raman spectra and depolarization ratios of t he Raman bands for the 1,4-Naphthoquinone (NQ) and 2-Methyl-1,4-Naphthoquinone (MNQ) and thei r corresponding radical anions (NQ - and MNQ - ) species. Most of the vibrational frequencies have nearly the same magnitude for the NQ, MNQ and their radical anions; however, signific ant changes are noticed in their IR intensities, Raman activities and depolarization ra tios of the Raman bands. For the neutral NQ molecule and its radical anions, the magnitude of t he atomic charges at the atoms C 1 and C 4 are almost identical and possess more positive charge d ue to the attachment of O atom at the sites C 1 and C 4 . But in the case of MNQ and its radical anions are found to be not identical due to the electron withdrawing nature of CH 3 group attached at the sites C 2 . The present calculations predict that the thermodynamical stability order ba sed on the total energy E increases in the following orders: NQ - >NQ and MNQ - >MNQ, thus, anionic form is more stable as compared to their neutral form. The magnitude of zero-point vib rational energy (ZPVE) and thermal energy correction (E) decreases slightly in going from NA to NA - (by 4.127/3.609), NQ to NQ - (by 1.396/1.492) and MNQ to MNQ - (by 2.536/1.569) (in Kcal/Mol) respectively.