Solving crystal structures of molecular solids without single crystals: a simulated annealing approach

The ab initio determination of relatively complex crystal structures of flexible molecules without the need for single crystals is discussed. A method is described based on simulated annealing in which the powder diffraction patterns of randomly generated trial structures are calculated and compared with the observed powder diffraction pattern in order to identify the model which provides the best fit and therefore the true structure. By employing simulated annealing both downhill (improved fit) and uphill (reduced fit) moves are possible ensuring escape from local minima in order to find the global minimum in the goodness-of-fit, i,e, the true structure. Key to the successful solution of flexible molecules is the introduction of a geometrical description which specifies atomic positions within the unit cell in terms of bond lengths and angles. In this way only those random structures which are chemically plausible are generated., greatly reducing the number of trial structures and rendering tractable the otherwise impossible task of ab initio determination. It is shown that structures with 37 variable parameters can be solved from only a few milligrams of powder. The limits of structural complexity for this method should be similar to those for refinement using powder data, i,e, around 200 variables. The variables may be those of position, or orientation of the molecule(s) in the unit cell as well as bond lengths, bond angles or torsion angles.