Direct phasing from Patterson syntheses by δ recycling

A new direct-space variant of the direct methods origin-free Patterson (or modulus) sum function is introduced. In the presence of atomicity, its application reduces, for each phase refinement cycle, to a synthesis with E² − 〈E²〉 (or E − 〈E〉) as Fourier coefficients followed by structure-factor calculation from the strongest peaks in the resulting map.

Advances in TALP, a direct-space least-squares strategy for solving molecular crystals from powders

Patterson function and δ recycling: derivation of the phasing equations

The phasing equations of δ recycling direct methods are derived from the minimization of a residual between two differently calculated density functions (one of them including the positivity constraint).