A theoretical examination of the L-E-E-L class of molecules has been carried out (E = group 14, group 15 element; L = N-heterocyclic carbene, phosphine), for which Si, Ge, P, and As-NHC complexes have recently been synthesized. The focus of this study is to predict whether it is possible to stabilize the elusive E-2 molecule via formation of L-E-E-L beyond the few known examples, and if the ligand set for this class of compounds can be extended from the NHC to the phosphine class of ligands. It is predicted that thermodynamically stable L-E-E-L complexes are possible for all group 14 and 15 elements, with the exception of nitrogen. The unknown ligand-stabilized Sn-2 and Pb-2 complexes may be considered attractive synthetic targets. In all cases the NHC complexes are more stable than the phosphines, however several of the phosphine derivatives may be isolable. The root of the extra stability conferred by the NHC ligands over the phosphines is determined to be a combination of the NHCs greater donating ability, and for the group 15 complexes, superior pi acceptor capability from the E-E core. This later factor is the opposite as to what is normally observed in transition metal chemistry when comparing NHC and phosphine ligands, and may be an important consideration in the ongoing "renaissance" of low-valent main group compounds supported by ligands.