Quantum-chemical calculations with gradient-corrected (B3LYP) density functional theory have been carried out for iron bispentazole and ferrocene. The calculations predict that Fe(η⁵-N₅)₂ is a strongly bonded complex which has D_5d symmetry. The theoretically predicted total bond energy that yields Fe in the ⁵D ground state and two pentazole ligands is D_o= 109.0 kcal mol^-1, which is only 29 kcal mol^-1 less than the calculated bond energy of ferrocene (D_o= 138.0 kcal mol^-1; experimental: 158± 2 kcal mol^-1). The compound Fe(η⁵-N₅)₂ is 260.5 kcal mol^-1 higher in energy than the experimentally known isomer Fe(N₂)₅, but the bond energy of the latter (D_o=33.7 kcal mol^-1) is much less. The energy decomposition analyses of Fe(η⁵-N₅)₂ and ferrocene show that the two compounds have similar bonding situations. The metal-ligand bonds are roughly half ionic and half covalent. The covalent bonding comes mainly from (e_1g) η⁵-N₅ ^- → Fe²⁺ π-donation. The previously suggested MO correlation diagram for ferrocene is nicely recovered by the Kohn-Sham orbitals. The calculated vibrational frequencies and IR intensities are reported.