Quantum chemical calculations have been applied to investigations of the electronic structure of the parent 5-dehydro-m-xylylene (DMX, or 5-dehydro-1,3-quinodimethane, C8H7) triradical containing a six-membered-ring radical coupled with two exocyclic CH2 groups situated in the meta position, each containing an unpaired electron and its 4,6-dinitrogen (DMX-N) and 4,6-diphosphorus (DMX-P) derivatives. The purpose of the study is to determine the identity of their electronic ground states. Our results obtained using state-averaged complete active space self-consistent- field (CASSCF) followed by second-order multistate multiconfiguration perturbation theories MS-CASPT2 and MR-QDPT in conjunction with large ANO-L and the 6-311G(d,p) basis set reveal the following: (i) DMX has a three-open-shell (σ1π1π1) doublet 2B 2 ground state with a 4B2-2B 2 energy gap in the range 1-3 kcal/mol, and (ii) the ground state of both DMX-N and DMX-P triradicals is also the doublet 2B2 being below the 4B2 state by 1 and 2 kcal/mol, respectively. In the triradicals considered, both doublet and quartet states are nearly degenerate but have a slight preference for the low-spin state, apparently violating Hund's rule. Protonation at C5 of DMX giving the MX·+ radical cation modifies the electronic landscape, the one-open-shell doublet 2B1 being the MX·+ ground state. The electron affinities (EAs), ionization energies (IEs), and proton affinities (PAs) are computed for the triradicals. For DMX: EA = 1.1 eV, IE = 7.50 eV, and PA = 401 kcal/mol. For DMX-N: EA = 2.3 eV, IE = 8.20 eV, and PA = 233 kcal/mol. For DMX-P: EA = 4.5 eV, IE = 8.98 eV, and PA = 214 kcal/mol. Comparable data for the anions follows. PA = 401, 367, and 371 kcal/mol for DMX-, DMX-N-, and DMX-P-, respectively.