In this work, the geometries, harmonic vibrational frequencies, and high-energy density material (HEDM) properties of a novel species and its six derivatives with the general formula C14N12-R-6 (R = H, OH, F, CN, N-3, NH2, and NO2) have been investigated at the restricted and unrestricted B3LYP/cc-pVDZ levels of theory. Natural bond orbital (NBO), natural orbital (NO), and atoms in molecules (AIM) analyses are applied to examine their electronic topologies. It is found that for the four species of R = H, CN, N3, and NO2, (1) there exist high LUMO occupation numbers, (2) there is considerable spin density congregated on the two central carbon atoms, (3) there exists through space interaction (or intramolecular interaction, which is one of the stabilizing factors of a diradicaloid) between the two central carbon atoms, (4) the distance (about 3 A) between the two central carbon atoms (as the apexes of two trigonal pyramids with their bases facing each other) is suitable and favorable for diradical formation. All the results support that these four species are diradicals or diradicaloids. Furthermore, the appreciable singlet-triplet energy gaps indicate that these four diradicals tend to have a singlet ground state. There is a moderate HOMO-LUMO gap (on the order of 1.5 to 2.1 eV) for these four species. These four singlet diradicals may be novel organic semiconductor materials or nonlinear optical materials. On the other hand, the remaining three species, with R = OH, F, and NH2, are not diradicaloids.