About the hybrid Fourier syntheses: a probabilistic approach.

The difference electron density has recently been revisited via the method of joint probability distribution functions [Burla et al. (2010). Acta Cryst. A 66, 347-361]. New Fourier coefficients were devised which were the basis of a new ab initio method for the solution of the phase problem (i.e. VLD, vive la difference). In this paper we study the joint probability distribution functions P(F, F(p), F(Q)), where F(Q) is the structure factor corresponding to the ideal hybrid Fourier synthesis ρ(Q) = τρ - ωρ(p) and τ and ω are any pair of real numbers. New Fourier coefficients for the calculations of any hybrid synthesis are obtained, and the properties of the corresponding electron-density maps are discussed. The first applications show the correctness of our theoretical approach and suggest possible applications in phasing procedures.