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 sciences are crystal structure prediction (optimization of structure with respect to computed energy) and direct-space techniques for crystal structure solution 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 opportunity to blend these approaches together in the definition of a hybrid hypersurface. A strategy for combining R-factor and energy within a direct-space method for structure solution from powder diffraction data is proposed. Normalized energy and normalized R-factor functions are defined, and are combined 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 increasing importance to R-factor as lower energies are approached. This concept of a ‘guiding function’ may be widely applicable in other global optimization problems.