Multilocal minima on the potential energy surface (PES) of the electronic ground state (X(1)Sigma(+)) of the N2O molecule are predicted by various ab initio methods, The calculations confirm that the global minimum of the molecule possesses an N-N-O linear structure with C-infinity upsilon,, symmetry, as experiment and other theoretical calculations have recognized. The present calculations also predict other local minima on the energy surface: a less stable cyclic isomer with a Ct, symmetry and a least stable linear N-O-N isomer with a D-infinity h,, symmetry. The electronic structures of the local minima indicate that the energy of the system increases if the N-N bond of the molecule becomes weak (the cyclic C-2v case) or breaks (the linear D-infinity h,i, case). The electronic structure and stabilities of the local minima of the N2O molecule are also discussed and analyzed using DFT calculations and wave functions, and a qualitative valence bond representation for the C-infinity v--> C-2v --> D-infinity h isomerization is provided.