New zirconium (Zr) based organometallic catalysts for direct olefin epoxidation using O 2 as oxidant without coreductant were introduced in a previous computational study (T. A. Manz and B. Yang, RSC Adv., 2014, 4, 27755-27774). In this paper, we use density functional theory (DFT) to study three Hf-based catalysts with the same bis(bidentate) ligands as the preceding Zr-based catalysts: (a) the diimine ligand N(Ar)-CH-CH-N(Ar) aka NCCN, (b) the imine-nitrone ligand N(Ar)-CH-CH-N(Ar)-O aka NCCNO, and (c) the dinitrone ligand O-N(Ar)-CH-CH-N(Ar)-O aka ONCCNO [Ar ¼ -C 6 H 3 -2,6-i Pr 2 ]. Complete reaction cycles and energetic spans (i.e., effective activation energies for the entire catalytic cycle) are computed for propene epoxidation. For Hf_NCCNO and Hf_ONCCNO, the reaction cycles are similar to the Zr-basedanalogs and the formation of h 3 -ozone intermediates is still crucial. Hf_ONCCNO has a large enthalpic energetic span (60.4 kcal mol À1 ) due to forming inert octahedral complexes as the catalyst resting state.Our calculations predict an energetic span $40 kcal mol À1 for Hf_NCCN, which indicates it will not be a good catalyst. Computed enthalpic energetic spans of $30 kcal mol À1 are achieved for the Hf_NCCNO and Zr_NCCNO catalysts; however, transfer of allylic hydrogen from the reaction product forms a low energy deactivation product. Therefore, the Hf_NCCNO and Zr_NCCNO catalysts are only suitable for direct epoxidation of alkenes that do not have any allylic hydrogen atoms. As an example of an alkene with no allylic hydrogens, we computed enthalpic energetic spans (kcal mol À1 ) for direct ethylene epoxidation of (a) 25.0 for Hf_NCCNO, (b) 30.2 for Zr_NCCNO, and (c) 52.7 for Zr_NCCN. † Electronic supplementary information (ESI) available: DFT-optimized geometries and energies; imaginary frequency for each transition state; singlet-triplet crossing curves for O 2 addition to Hf_ONCCNO and Hf_NCCN dioxo complexes; constrained optimization curves showing oxo h 3 -ozone and peroxo h 3 -ozone complexes do not exist for the Hf_NCCN system; chemical potential diagrams for Hf_ONCCNO and Hf_NCCN; assigned spin magnetic moments tables; master cycle and table of reaction energies and energetic spans for direct propene epoxidation catalyzed by Hf_ONCCNO; master cycles and tables of reaction energies and energetic spans for direct ethylene epoxidation catalyzed by Zr_NCCN, Hf_NCCNO, and Zr_NCCNO. See