A Priori Prediction of Crystal Structures

The arrangement of atoms in a crystal is determined by two factors, the bonding preferences of individual atoms (giving rise to short range order), and the translational symmetry operations of the space group (giving rise to long range order). Chemical rules can be used to determine which atoms are bonded, and hence the maximum possible symmetry of the formula unit. Space group theory is then used to find the space groups that are compatible with this symmetry. In favourable cases, using the principle of maximum symmetry, the structure can be completely determined, but in all cases the analysis yields insights into the restrictions that determine what crystal structures might be possible.