CRYSTAL-STRUCTURE REFINEMENT USING ANALYTICAL DERIVATIVES OF THE ENERGY FUNCTION - APPLICATION TO 1,2-DILAUROYL-DL-PHOSPHATIDYLETHANOLAMINE

Methods are presented for refining crystal structures of organic molecules by minimization of the energy. The crystal energy is expressed as a sum of intramolecular and intermolecular terms and includes nonbonded, hydrogen-bonded, electrostatic, and torsional contributions. Equations are given for computing the first derivatives of the crystal energy with respect to intramolecular bond rotations, rigid-body motions, and the lattice constants. These methods were used to carry out an energy refinement of the crystal structure of 1,2-dilauroyl-DL-phosphatidylethanolamine:acetic acid (DLPE:HAc). Minimization was simultaneously performed with respect to all intramolecular bond rotations (34 in DLPE and 2 in the cocrystallized molecule of acetic acid) and all rigid-body parameters (6 each for DLPE and acetic acid). The crystal energy changed from -129.7 to-142.5 kcal/mol and the derivatives decreased to values close to zero as a result of minimization. Prior to energy refinement of the structure, minimization with respect to the lattice constants caused an increase of 57 A3 in the unit cell volume, but after refinement the energy-minimized lattice constants were within the error limits of the experimental values. An analysis of the total crystal energy is given in terms of the monolayer, intrabilayer, and interbilayer contributions to the total energy. © 1990 American Chemical Society.