Computer-aided molecular design and high-throughput screening of viable host architectures can significantly reduce the efforts in the design of novel ligands for efficient extraction of rare earth elements. This paper presents a computational approach to the deliberate design of bis-phosphine oxide host architectures that are structurally organized for complexation of trivalent lanthanides. Molecule building software, HostDesigner, was interfaced with molecular mechanics software, PCModel, providing a tool for generating and screening millions of potential R-2(O)P-link-P(O)R-2 ligand geometries. The molecular mechanics ranking of ligand structures is consistent with both the solution-phase free energies of complexation obtained with density functional theory and the performance of known bis-phosphine oxide extractants. For the case where the link is -CH2-, evaluation of the ligand geometry provides the first characterization of a steric origin for the,`anomalous aryl strengthening" effect. The design approach has identified a number of novel bis-phosphine oxide ligands that are better organized for lanthanide complexation than previously studied examples.