Reaction coordinates are computed for the Bergman cyclizations of hex-3-en-1,5-diyne and neutral and protonated 3-azahex-3-en-1,5-diyne at various levels of correlated electronic structure theory, as are singlet-triplet splittings for intermediate arynes. To be effective in low-symmetry situations showing high degrees of biradical character, CCSD(T) calculations benefit from use of Brueckner orbitals. Replacement of a CH fragment by N is predicted to increase the stability of the aryne relative to the iminediyne, and to increase drastically the stability of the isomeric enynenitrile. The barrier for retro-aza-Bergman cyclization of 2,5-pyridyne to pent-3-en-1-ynenitrile is predicted to be only 0.9 kcal/mol, which, combined with a predicted singlet-triplet splitting of -11.6 kcal/mol, suggests that 2,5-pyridynes are poor hydrogen atom abstracting agents. Protonation of nitrogen decreases the singlet-triplet splitting and raises the barrier to retro-aza-Bergman cyclization such that protonated 2,5-pyridynes may be expected to show reactivities similar to all-carbon analogues.