Calculation of Crystal Packing: A Novel Approach to the Phase Problem

Abstract

THE structure and relative stability of helical macro-molecules, consisting of repetitions of equivalent monomer units, have been analysed previously^1–5. The conformational potential energy of the helices was computed as a function of the angles of rotation about the skeleton bonds, using semi-empirical potential functions to take into account intramolecular Van der Waals interactions between “non-bonded” atom pairs. The geometry of the most stable helices was deduced from the parameters corresponding to the lowest minima. It was also shown⁶ that the crystal packing of hexamethylbenzene molecules may be predicted by locating the deepest minima of the intermolecular Van der Waals potential energy. By fixing bond lengths and angles arid by knowing lattice parameters and crystal symmetries, the potential energy can be calculated for all the rotational and translational degrees of freedom which define the asymmetric unit position.