Developing efficient catalysts for methane functionalization is a longstanding goal in inorganic chemistry. Here, we present theoretical calculations to support efforts to synthesize σmethane complexes that can be studied by NMR spectroscopy. The systems studied are osmium complexes of stoichiometry (C 5 R 5 )Os(diphosphine)(CH 3 )(H) + : when both cyclopentadienyl and diphosphine are relatively strong electron donors, the methyl/ hydride structure is in rapid equilibrium with its σ-methane tautomer at low temperatures, as shown experimentally some years ago. Here, using density functional theory, we examine how changing the steric and electronic properties of the ancillary cyclopentadienyl and diphosphine ligands affects the relative energies of the two tautomers, with the goal of identifying a ligand set for which the σ-methane structure, rather than the methyl/hydride form, is the predominant species in equilibrium. We also examine how varying the ancillary ligands affects the barrier for methane dissociation. The calculations suggest that osmium complexes bearing weakly donating and sterically undemanding ligands stabilize the σ-methane structure both relative to its methyl/hydride tautomer and toward dissociation of the methane ligand. More specifically, osmium σ-methane complexes of fluorinated diphosphines (CF 3 ) 2 PCH 2 P(CF 3 ) 2 and (CF 3 ) 2 PCF 2 P(CF 3 ) 2 are predicted to be stable enough to be observed by variable-temperature NMR spectroscopy.