The equilibrium geometries, thermochemistry, and vibrational frequencies of the homoleptic metal-carbonyls of the group 4 elements, M(CO)(n) (M = Ti, Zr, Hf; n = 7, 6, 5, 4) were predicted using density functional theory. Analogous M(CO)n Structures were found for all three metals. The global minima for the 18-electron M(CO)(7) molecules are all singlet C-3v capped octahedra. The global minima for the 16-electron M(CO)(6) species are triplet M(CO)(6) structures distorted from O-h symmetry to D-3d symmetry. However, the corresponding singlet M(CO)(6) structures lie within 5 kcal/mol of the triplet global minima. The global minima for M(CO), (n = 5, 4) are triplet structures derived from the D-3d distorted octahedral structures of M(CO)(6) by removal of one or two CO groups, respectively. Quintet D-3h trigonal bipyramidal structures for M(CO)(5) and singlet T-d tetrahedral structures for M(CO)(4) are also found, as well as higher energy structures for M(CO)(6) and M(CO)(7) containing a unique CO group bonded to the metal atom through both M-C and M-O bonds. The dissociation energies M(CO)(7) -> M(CO)(6) + CO are substantial, indicating no fundamental problem in bonding seven CO groups to a single metal atom.