Computational investigations of the thermochemical stability and kinetic persistence of binary SxNy compounds, SN2, S2N2, S3N2, S4N2, SN4, S2N4, S3N4, and S4N4, explain why some SxNy stoichiometries exist but not others. There is no direct link between the Huckel 4n + 2 pi-electron count rule and the computed heats of formation (per atom) of the lowest-energy neutral SnN4 (n = 1-4) isomers, but kinetic persistence often is paramount. Thus, the five lowest-energy S2N4 minima at the B3LYP/6-311+G(3df) density functional theory level (A1-A5) all not only have high computed heats of formation [Delta H-f(o) (0 K) > 131 kcal/mol or >22 kcal/mol/atom] but also have low dissociation barriers (less than 21.5 kcal/mol for the most favorable pathways). For comparison, the persistent (but potentially explosive!) cyclic S2N2-c has about the same high heat of formation (per atom) as the least unfavorable S2N4 isomer, but its barrier to ring opening (51 kcal/mol) is much higher. Although aromatic, both SN4 (6 pi electron) and S3N4 (10 pi electron) have low dissociation barriers and, like S2N4, are also absent from the S-N binary family.