The variety of structures observed for tetraatomic molecules containing 22 valence electrons suggests an energy surface with a number of minima of comparable depths. For S2N2 we have carried out geometry optimized SCF MO RHF/6-31G* calculations and located 9 minima, 7 of which are also minima at the MP2 level. The three lowest energy structures are the linear chain SNNS and the two 4-membered rings SNSN and SNNS. At both RHF and MP2 levels and using basis sets that include additional d-type and even f-type polarization functions as well as diffuse functions, these three structures are real minima on the energy surface. At this level of theory, the three structures are too close in energy to allow us to pick the global minimum. The structure well characterized by experiment is the alternant ring SNSN. Its existence can be rationalized as a result of the method of preparation. A calculated vibrational frequency far the pairwise ring SNNS closely matches that of the vibrational absorption peak that Hassanzadeh and Andrews have attributed to a new isomer of S2N2 which they claim to have produced in matrix isolation experiments. Calculated bond distances in the three low energy isomers can be rationalized by traditional VB and MO models. Qualitative MO arguments are used to evaluate processes by which SN fragments might dimerize to form the SNNS chain and the two rings and to rationalize an activation barrier separating chain and ring.