A systematic study of all possible tetraatomic P2N2 structures has been made at the B3LYP/6-311+G(2df) and CASPT2(12e, 12o)/ANO-L levels. A closed-shell butterfly C2, structure (A) is predicted to have the lowest energy on the tetraatomic P2N2 potential energy surface. The energies for dissociation of P2N2 to two PMN or to N-2 and P-2 have been examined. A closed-shell quasi-tetrahedral C-2v structure of P2N2 (B) and a linear open-shell singlet P-Nequivalent to-N-P (E*) have been found to be kinetically stable to fragmentation or rearrangement at the CASPT2/ANO-L level. Several transition states have significant biradical character which reflects the orbital crossings that are found alone, reaction paths of least motion. The fragmentation reaction of P-Nequivalent to N-P to 2P-equivalent toN involves a trans-bent transition state that has a strong similarity to a known transition metal reaction.