Density functional theory (DFT, PBE0, and range separated DFT, RSH + MP2) and coupled-cluster with single and double and perturbative triple excitations (CCSD-(T)) calculations have been used to probe the structural preference of d(4) MH3Xq (M = Ru, Os, Rh+, Ir+, and Re-; X = H, F, CH3, CF3, SiH3, and SiF3) and of MX4 (M = Ru; X = H, F, CH3, CF3, SiH3, and SiF3). Landis et al have shown that complexes in which the metal is sd(3) hybridized have tetrahedral and non-tetrahedral structures with shapes of an umbrella or a 4-legged piano stool. In this article, the influence of the metal and ligands on the energies of the three isomeric structures of d(4) MH3X and MX4 is established and rationalized. Fluoride and alkyl ligands stabilize the tetrahedral relative to non-tetrahedral structures while hydride and silyl ligands stabilize the non-tetrahedral structures. For given ligands and charge, 4d metal favors more the non-tetrahedral structures than 5d metals. A positive charge increases the preference for the non-tetrahedral structures while a negative charge increases the preference for the tetrahedral structure. The factors that determine these energy patterns are discussed by means of a molecular orbital analysis, based on Extended Huckel (EHT) calculations, and by means of Natural Bond Orbital (NBO) analyses of charges and resonance structures (NRT analysis). These analyses show the presence of through-space interactions in the non-tetrahedral structures that can be sufficiently stabilizing, for specific metals and ligands, to stabilize the non-tetrahedral structures relative to the tetrahedral isomer.