Why are S(n)N4 (n = 1-4) species "missing"? Answers in a broader theoretical context of binary S-N compounds

Computational investigations of the thermochemical stability and kinetic persistence of binary S(x)N(y) compounds, SN(2), S(2)N(2), S(3)N(2), S(4)N(2), SN(4), S(2)N(4), S(3)N(4), and S(4)N(4), explain why some S(x)N(y) stoichiometries exist but not others. There is no direct link between the Hückel 4n + 2 π-electron count rule and the computed heats of formation (per atom) of the lowest-energy neutral S(n)N(4) (n = 1-4) isomers, but kinetic persistence often is paramount. Thus, the five lowest-energy S(2)N(4) minima at the B3LYP/6-311+G(3df) density functional theory level (A1-A5) all not only have high computed heats of formation [Δ(f)H°(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 S(2)N(2)-c has about the same high heat of formation (per atom) as the least unfavorable S(2)N(4) isomer, but its barrier to ring opening (51 kcal/mol) is much higher. Although aromatic, both SN(4) (6π electron) and S(3)N(4) (10π electron) have low dissociation barriers and, like S(2)N(4), are also absent from the S-N binary family.