VARICELLA: a variable-cell direct space method for structure determination from powder diffraction data

A direct space method for structure determination from powder diffraction data is proposed. Employing a hybrid Monte Carlo algorithm for generating the random conformations of a flexible molecular model, and sampling in a modified multicanonical statistical ensemble, it allows for variable cell parameters during an iterative search process. The acceptance-rejection criterion involves both a disagreement factor between the calculated and the experimental diffraction profiles and a modified crystal energy so that the space of tentative solutions can be widely explored while maintaining some physical meaningfulness of the proposals. Allowing the cell to be variable requires the zero shift to be treated as an optimizing parameter; this, in turn, requiring the disagreement factor to be based on the Fourier transform of the spectrum. The algorithm is presented in both a serial and a parallel version, the latter presenting several advantages, such as the possibility to probe different structures at a time while keeping them far from each other in the space defined by suitable order parameters. The method is built up and carefully tested by using, as a case study, a crystal of 3-ethyl 2,3-exo-disyndiotactic norbornene heptamer recently determined by single crystal x-ray diffraction techniques.