The structural and electronic properties of C-36 molecules with two most possible geometries (D-2d and D-6h) an studied using the Hartree-Fock (HF), density functional theory (DFT) with the local density approximation (LDA) and generalized gradient approximation (GGA), and hybrid DFT methods. The results show that the ground state of the Dbh isomer strongly depends on the computational methods. The HF and hybrid DFT predict a triplet ground state, whereas the LDA and GGA give a singlet one. The D-2d and D-6h isomers are quasi-isoenergetic at their ground states. Our results indicate that the relative stability of the two isomers can be alternated by gaining or losing: an electron. The D-6h anion is moro stable than the D-2d anion, whereas the D-2d cation is lower in energy than the D-6h cation. These results are used to understand the experimental fact that the C-36 molecule in the solid has D-6h symmetry and to predict the possible D-2d C-36 molecules, ions, and solids. The vibrational frequencies, ionization potentials, electron affinities, energy gaps, and molecular densities of states are obtained for the two isomers. The results are discussed and compared with the available experimental results.