Li, Yeh, and Taube in 1993 (J. Am. Chem. Sec. 1993, 115, 10384) synthesized a number of complexes which can be formally regarded as protonated Os(II) species. Some of these were paramagnetic, in contrast to the diamagnetism of the closed shell 5d(6) Os(II) ions. This intriguing phenomenon is investigated theoretically using density functional theory. The geometries, stabilities, and electronic structures of a series of six- and seven-coordinate osmium complexes were studied in gas phase and aqueous solution using the B3P86 functional, in conjunction with the isodensity-polarized continuum model of solvation. The general formula for these complexes is [Os(NH3)(4)H(L-1(x))(m)(L-2(y))(n)]((x+y+3)+), where L-1 and L-2 = H2O, NH3, CH3OH, CH3CN, Cl-, and CN-, which could be regarded as protonated Os(II) species or hydrides of Os(IV), although according to this work the osmium-hydrogen interaction is best described as a covalent Os(III)-H bond, in which the hydrogen is near-neutral. The ground states are generally found to be singlets, with low-lying triplet excited states. Solvation tends to favor the singlet states by as much as similar to 18 kcal mol(-1) in the 3+ ions, an effect which is proportional to the corresponding difference in molecular volumes. To have realistic estimates of the importance of spinorbit coupling in these systems, the spin-orbit energy corrections were computed for triplet [Os(NH3)(4)](2+), [Os(NH3)(4)H](3+), and [Os(NH3)(4)H(H2O)](3+), along with gas-phase Os and its ions as well as [Os(H2O)(6)](3+). The seven-coordinate triplet-state complex [Os(NH3)(5)H(CH3OH)(3+), which had been successfully isolated by Li, Yeh, and Taube, is predicted to be a stable six-coordinate complex which strongly binds to a methanol molecule in the second coordination shell. The calculations further suggest that the singlet-triplet splitting would be very small, a few kilocalories per mole at most. The geometries and the electronic structures of the complexes are interpreted and rationalized in terms of Pauling's hybridization model in conjunction with conventional ligand field theory that effectively precludes the existence of true seven-coordinate triplet-state complexes of the above formula.