Determination and refinement of disordered crystal structures using evolutionary algorithms in combination with Monte Carlo methods

An evolutionary algorithm called 'differential evolution' is combined with Monte Carlo simulation to determine and optimize models of disordered crystal structures. Requirements for successfully finding the parameters describing disorder from diffuse scattering data are discussed and the algorithm is applied to resolving the racemic and associated displacive disorder of the host substructure in a perhydrotriphenylene inclusion compound. Refinement resulted in a very good visual agreement between observed and calculated intensities and in a relatively low value of R-diffuse = 0.148 (3). The computations for determining and refining the structure took 29 d with five to ten workstations running in parallel. Analysis of the progress of the structure determination shows that the essential information can be obtained within a few hours. Limits of the technique and strategies to optimize the procedure are discussed.