Attempts to predict molecular structure often try to minimize some potential function over a set of structures. Much effort has gone into creating potential functions and into creating algorithms for minimizing these potential functions. This paper develops a formalism that addresses a complementary question : What are the accuracy requirements for a potential function that predicts molecular structure? The formalism is applied to a simple model of a protein structure potential. The results of this calculation suggest that high accuracy predictions (approximately 1 angstrom rms deviation in alpha-carbon positions) of protein structures require monomer-monomer interaction energies accurate to within 5% to 15%. The paper closes with a discussion of the implications of these results for practical structure prediction.