Conventionally, the singly occupied molecular orbital (SOMO) of a radical species is considered to be the highest occupied molecular orbital (HOMO), but this is not the case always. In this study, we considered a number of radicals from smallest diatomic anion radicals such as superoxide anion radical to one-electron oxidized DNA related base radicals that show the SOMO is energetically lower than one or more doubly occupied molecular orbitals (MOs) (SOMO-HOMO level inversion). The electronic configurations are calculated employing the B3LYP/6-31++G** method, with the inclusion of aqueous phase via the integral equation formalism of the polarized continuum model solvation model. From the extensive study of the electronic configurations of radicals produced by one-electron oxidation or reduction of natural-DNA bases, bromine-, sulfur-, selenium-, and aza-substituted DNA bases, as well as 20 diatomic molecules, we highlight the following important findings: (i) SOMO-HOMO level inversion is a common phenomenon in radical species. (ii) The more localized spin density in sigma-orbital on a single atom (carbon, nitrogen, oxygen, sulfur, or selenium), the greater the gap between HOMO and SOMO. (iii) In species with SOMO-HOMO level inversion, one-electron oxidation takes place from HOMO not from the SOMO, which produces a molecule in its triplet ground state. Oxidation of aqueous superoxide anion producing triplet molecular oxygen is one example of many. (iv) These results are for conventional radicals and in contrast with those reported for distonic radical anions in which SOMO-HOMO gaps are smaller for more localized radicals and the orbital inversions vanish in water. Our findings yield new insights into the properties of free radical systems.