Recent experimental work shows that the 18-electron molybdenum complexes (1,2,4-CHtBu)Mo(PMe)H (CpMoH) and (CHiPr)Mo(PMe)H (CpMoH) undergo oxidatively induced reductive elimination of dihydrogen (H), slowly forming the 15-electron monohydride species in tetrahydrofuran and acetonitrile. The 17-electron [CpMoH] derivative was stable enough to be characterized by X-ray diffraction, while [CpMoH] was not. Density functional theory calculations of the H elimination pathways for both complexes in the gas phase and in a continuum solvent model indicate that H elimination from [CpMoH] has a lower barrier than that from [CpMoH]. Further, a specific solvent association, which is stronger for [CpMoH] than for [CpMoH], contributes to the stability of the former. In agreement with the experimental observations, the calculations predict that [CpMoH] would be in a quartet state at room temperature and a doublet state at 4.2 K, while [CpMoH] is in a doublet state even at room temperature.