A long sought goal in the physical chemistry of macromolecular structure, and one directly relevant to understanding the molecular basis of biological recognition, is predicting the geometry of bimolecular complexes from the geometries of their free monomers. Even when the monomers remain relatively unchanged by complex formation, prediction has been difficult because the free energies of alternative conformations of the complex have been difficult to evaluate quickly and accurately. This has forced the use of incomplete target functions, which typically do no better than to provide tens of possible complexes with no way of choosing between them. Here we present a general framework for empirical free energy evaluation and report calculations, based on a relatively complete and easily executable free energy function, that indicate that the structures of complexes can be predicted accurately from the structures of monomers, including close sequence homologues. The calculations also suggest that the binding free energies themselves may be predicted with reasonable accuracy. The method is compared to an alternative formulation that has also been applied recently to the same data set. Both approaches promise to open new opportunities in macromolecular design and specificity modification.