Binding energies and electronic wavefunctions are found for diatomic and methanelike molecules under the restriction that the electronic configuration contains only j=l-1/2 states. Two models for a diatomic molecule are treated. In the first, the electronic configuration is a p state on one atom and the effect of the other atom is included by a crystal field. In the second model the configuration is an s state on one atom and a p state on the other. The magnitude of the spin-orbit interaction required to make the restriction to j=l-1/2 states a good approximation is found in each case. In the second case, the binding is reduced by a factor of 3 by the restriction. In the methane molecule the restriction to j=l-1/2 states requires the inclusion of d states in the configuration. The binding of the methane can be increased by a distortion and experimental evidence for such a distortion in GeH4 and SiH 4 is pointed out. Application of this approximation to the electronic structure of actinide complexes is briefly discussed.