About difference electron densities and their properties

Difference electron densities do not play a central role in modern phase refinement approaches, essentially because of the explosive success of the EDM (electron-density modification) techniques, mainly based on observed electron-density syntheses. Difference densities however have been recently rediscovered in connection with the VLD (Vive la Difference) approach, because they are a strong support for strengthening EDM approaches and for ab initio crystal structure solution. In this paper the properties of the most documented difference electron densities, here denoted as F - F-p, mF - F-p and mF - DFp syntheses, are studied. In addition, a fourth new difference synthesis, here denoted as (F) over bar (q) synthesis, is proposed. It comes from the study of the same joint probability distribution function from which the VLD approach arose. The properties of the (F) over bar (q) syntheses are studied and compared with those of the other three syntheses. The results suggest that the (F) over bar (q) difference may be a useful tool for making modern phase refinement procedures more efficient.