A range of novel octahedral iron(IV)-nitrido complexes with the TMC ligand (TMC = 1,4,8,11-tetramethyl-1,4,8,11-tetraazacyclotetradecane) in the equatorial plane and one axial ligand trans to the nitrido have been designed theoretically, and a systematic comparative study of their geometries, electronic properties, and reactivities in hydrogen atom abstraction reactions regarding the iron(IV)-oxo and -sulfido counterparts has been performed using density-functional theory methods. Further, the relative importance of the axial ligands on the reactivity of the iron(IV)-nitrido systems is probed by sampling the reactions of CH4 with [Fe-IV=N(TMC)(L-ax)](n+), (L-ax = none, CH3CN, CF3CO2-, N-3(-), Cl-, NC-, and SR-). As we find, one hydrogen atom is abstracted from the methane by the iron(IV)-nitrido species, leading to an Fe-III(N)-H moiety together with a carbon radical, similar to the cases by the iron(IV)-oxo and -sulfido compounds. DFT calculations show that, unlike the Well-known iron(IV)-oxo species with the S = 1 ground state where two-state reactivity (TSR) was postulated to involve, the iron(IV)-nitrido and -sulfido complexes stabilize in a high-spin (S = 2) quintet ground state, and they appear to proceed on the single-state reactivity via a dominantly and energetically favorable low-lying quintet spin surface in the H-abstraction reaction that enjoys the exchange-enhanced reactivity. It is further demonstrated that the iron(IV)-nitrido complexes are capable of hydroxylating C-H bond of methane, and potential reactivities as good as the iron(IV)-oxo and -sulfido species have been observed. Additionally, analysis of the axial ligand effect reveals that the reactivity of iron(IV)-nitrido oxidants in the quintet state toward C-H bond activation enhances as the electron-donating ability of the axial ligand weakens.