Determination of the molecular packing in diketopiperazine crystal by means of van der Waals and hydrogen-bonding energy calculations

The crystal packing of diketopiperazine may be predicted from the approximate molecular geometry and space group symmetry. The van der Waals and hydrogen bonding energies were computed as a function of three rotational degrees of freedom (space group P2₁/a and Z = 2). The Eulerian angles, relative to the deepest minimum, correspond to a good approximation to the real structure. The calculations were carried out using potential functions tested in some crystals and in the conformational analysis of synthetic and biological macromolecules. A potential function proposed by Stockmayer was chosen to describe the hydrogen bond formation. The rigid-body translations of the molecules in the crystal, known from an analysis of the anisotropic atomic thermal parameters, were qualitatively checked. For this purpose the van der Waals potential energy was computed by moving one chain of molecules and leaving the surrounding chains fixed. The good results obtained again confirm the validity of this method for the solution of the phase problem. It is hoped that this approach may be useful in crystal structure determinations of organic molecules of biological interest.