The photochromic dithionite complex Cp*Rh(μ-CH)(μ-OSSO) (Cp* = η-MeC) is of interest because it undergoes an unusual fully reversible unimolecular photochemical rearrangement to the isodithionite complex Cp*Rh(μ-CH)(μ-OSOSO). In order to obtain more insight into these systems, a comprehensive density functional theory study has been carried out on isomeric CpM(CH)(SO) (M = Rh, Ir) derivatives. The experimentally observed rhodium complexes with coupled sulfur dioxide (SO) units to give dithionite or isodithionite ligands are surprisingly high-energy kinetic isomers in our analysis, reflecting the need for dithionite rather than SO for their synthesis. Many isomeric structures containing two separate SO ligands are found to lie at lower energies than these dithionite and isodithionite complexes. In the lowest-energy CpM(CH)(SO) isomers, the two methylene groups couple to form an ethylene ligand that can be either terminal or bridging. In slightly higher energy structures, a formal hydrogen shift is predicted to occur within the ethylene ligand to give a methylcarbene CHCH ligand. Isomers with a bridging methylcarbene ligand are energetically preferred over isomers with a terminal methylcarbene ligand. Generation of the lower-energy CpRh(CH)(SO) isomers containing separate SO ligands should be achievable through reactions of SO with more highly reduced cyclopentadienylrhodium methylene complexes such as Cp*Rh(μ-CH).