Definition of a 'guiding function' in global optimization: a hybrid approach combining energy and R-factor in structure solution from powder diffraction data

Two global optimization problems of current interest in solid state science s are crystal structure prediction (optimization of structure with respect to computed energy) and direct-space techniques far crystal structure solut ion from powder diffraction data (optimization of structure with respect to R-factor). As the energy and R-factor hypersurfaces are based on the same parameter space but have differing characteristics, there is a direct oppor tunity to blend these approaches together in the definition of a hybrid hyp ersurface. A strategy for combining R-factor and energy within a direct-spa ce method for structure solution from powder diffraction data is proposed. Normalized energy and normalized R-factor functions are defined, and are co mbined using a sliding weighting function to give a hybrid figure-of-merit G, which behaves as energy when energy is high (thus using energy to guide the calculation towards energetically plausible structures) and gives incre asing importance to R-factor as lower energies are approached, This concept of a 'guiding function' may be widely applicable in other global optimizat ion problems, (C) 2000 Elsevier Science B.V, All rights reserved.